FINANCE
ESSENTIALS
KIDWELL | BRIMBLE | MAZZOLA | MORKEL-KINGSBURY | JAMES
Finance essentials
FIRST EDITION
David S. Kidwell
Mark Brimble
Paul Mazzola
Nigel Morkel-Kingsbury
Jenny James
First edition published 2018 by
John Wiley & Sons Australia, Ltd
42 McDougall Street, Milton Qld 4064
Australian edition © John Wiley & Sons Australia, Ltd 2018
Typeset in 10/12pt Times LT Std
The moral rights of the authors have been asserted.
National Library of Australia
Cataloguing-in-Publication data
Author:
Title:
ISBN:
Subjects:
Kidwell, David. S., author
Finance essentials / David S. Kidwell, Mark Brimble, Paul Mazzola,
Nigel Morkel-Kingsbury, Jenny James
9780730344599 (ebook)
Corporations — Finance.
Financial institutions — Australia.
Money market — Australia.
Business enterprises — Australia.
Other Authors/
Contributors:
Brimble, Mark, author.
Mazzola, Paul, author.
Morkel-Kingsbury, Nigel, author.
James, Jennifer, author.
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10 9 8 7 6 5 4 3 2 1
CONTENTS
MODULE 1
Finance in business
1
Module preview 2
1.1 Understanding finance, money and markets 2
Finance in society 4
Finance in business 5
1.2 Business structures and finance 6
Sole traders 6
Partnerships 7
Companies 7
1.3 The financial goals of a business 8
What should management maximise? 8
Why not maximise profits? 8
Maximise the value of the company’s shares 9
Can management decisions affect share
prices? 10
1.4 The financial manager 11
The financial manager 11
Three fundamental decisions in financial
management 13
1.5 Managing the financial function 15
Organisation structure 15
Positions reporting to the CFO 16
External auditors 17
The audit committee 17
1.6 Ethics in business 17
Are business ethics different from everyday
ethics? 17
Types of ethical conflicts in business 18
The importance of an ethical business culture 20
Summary 21
Key terms 22
Endnotes 23
Acknowledgements 23
MODULE 2
The financial system
24
Module preview 25
2.1 The financial system 26
The financial system at work 26
How funds flow through the financial system
Direct financing 28
A direct financing transaction (without using
the market) 28
Direct financing (using the market) 29
27
2.2 Financial markets 30
Types of financial markets 31
Primary and secondary markets 31
Exchanges and over‐the‐counter
markets 32
Money and capital markets 32
Public and private markets 33
Futures and options markets 33
Foreign exchange markets 33
2.3 Financial institutions 34
Indirect market transactions 34
Financial institutions and their services 35
Risks faced by financial institutions 37
Companies and the financial system 39
2.4 International financial markets 40
Internationalisation of financial markets 41
International organisations 41
International assets of Australian
institutions 42
2.5 Capital market efficiency 42
Efficient market hypotheses 43
Summary 45
Key terms 46
Endnotes 47
Acknowledgements 47
MODULE 3
Financial markets
48
Module preview 49
3.1 Money markets 50
The cash market 51
One‐name paper 52
Bank‐accepted bills 54
3.2 Capital markets 55
Functions of capital markets 56
Capital market participants 56
Major capital market instruments 56
3.3 Bond markets 59
Size of the bond markets 59
Turnover in the bond markets 60
Commonwealth Government Securities 60
State government bonds 61
Corporate bonds 61
Investors in corporate bonds 62
The primary market for corporate bonds 62
The secondary market for corporate bonds 63
3.4 Equity markets 64
Primary equity markets 64
Secondary equity markets 65
Characteristics of markets 66
Equity trading 66
3.5 Derivative markets 67
Differences between futures and forward
markets 68
Uses of the financial futures markets 69
Options markets 69
3.6 Foreign exchange markets 70
The difficulties of international trade 71
The operations of foreign exchange markets 72
Balance of payments 74
The globalisation of financial markets 75
Summary 78
Key terms 78
Endnotes 82
Acknowledgements 82
MODULE 4
The Reserve Bank of Australia
and interest rates 83
Module preview 84
4.1 Money supply 85
Measures of money supply 85
Money supply changes 86
4.2 Cash rate 88
Market equilibrium interest rate 88
Importance of cash rate 90
Managing risk: RBA’s impact on share and
bond markets 91
4.3 Monetary policy 91
Price stability 91
Full employment 93
Economic growth 94
Other goals 95
Possible conflicts among goals 95
4.4 Economic activity 96
Consumer spending 97
Business investment 97
Net exports 99
4.5 Determinants of interest rates 99
What are interest rates? 99
Determinants of real rate of interest 100
Loan contracts and inflation 102
Fisher equation and inflation 102
Restatement of Fisher equation 103
iv CONTENTS
Cyclical and long‐term trends in interest
rates 105
Forecasting interest rates 107
Summary 109
Summary of key equations 109
Key terms 110
Endnotes 110
Acknowledgements 111
MODULE 5
Time value of money
112
Module preview 113
5.1 The time value of money 113
Consuming today or tomorrow? 114
Using time lines as aids to
problem‐solving 114
Financial calculator 115
5.2 Future value decisions 116
Single‐period investment 116
Two‐period investment 117
Future value equation 118
The future value factor 120
Calculator tips for future value problems 127
5.3 Present value decisions 129
Future and present value equations are the
same 130
Applying the present value formula 130
Relationship between time, discount rate and
present value 132
Calculator tips for present value problems 134
Future value versus present value 134
5.4 Additional concepts and applications 135
Finding the interest rate 135
Finding how many periods it takes an investment
to grow to a certain amount 138
Solving time value problems 139
Summary 140
Summary of key equations 140
Key terms 141
Acknowledgements 141
MODULE 6
Discounted cash flows and
valuation 142
Module preview 143
6.1 Multiple cash flows 144
Future value of multiple cash flows 144
Present value of multiple cash flows 145
6.2 Annuities 148
Present value of an ordinary annuity 148
Future value of an ordinary annuity 151
Annuities due 153
6.3 Perpetuities 157
6.4 Additional concepts and applications 159
Finding the value of periodic payments 159
Finding the number of payments 161
Preparing a loan amortisation schedule 165
6.5 Comparing interest rates 168
Why the confusion? 168
Calculating the effective annual interest rate 169
Comparing interest rates 170
Consumer protection acts and interest rate
disclosure 172
Appropriate interest rate factor 172
Summary 174
Summary of key equations 175
Key terms 175
Acknowledgements 175
MODULE 7
Risk and return
176
Module preview 177
7.1 Risk and return relationship 178
More risk means a higher expected return 178
7.2 Measures of return 178
Holding period returns 178
7.3 Expected returns 180
7.4 Variance and standard deviation 183
Calculating the variance and standard
deviation 183
Interpreting the variance and standard
deviation 186
Historical market performance 188
7.5 Risk and diversification 191
Single‐asset portfolios 192
Portfolios with more than one asset 194
The limits of diversification 200
7.6 Systematic risk 201
Why systematic risk is all that matters 201
Measuring systematic risk 202
Compensation for bearing systematic risk 205
7.7 Capital Asset Pricing Model 207
Security Market Line 207
Capital Asset Pricing Model and portfolio
returns 208
Summary 212
Summary of key equations 213
Key terms 213
Acknowledgements
214
MODULE 8
Bond valuation
215
Module preview 216
8.1 Government securities 216
Treasury bonds 217
Treasury indexed bonds 218
Investors in Commonwealth Government
Securities 218
State government bonds 219
8.2 Corporate bonds 220
Types of corporate bonds 222
8.3 Bond valuation 223
The bond valuation formula 224
Par, premium and discount bonds 226
Semiannual compounding 228
Zero coupon bonds 230
8.4 Bond yields 232
Yield to maturity 232
Effective annual yield 233
Realised yield 235
8.5 Interest rate risk 236
Bond theorems 237
Bond theorem applications 238
8.6 The structure of interest rates 239
Marketability 240
Call provision 240
Default risk 240
Default risk premium 241
8.7 The term structure of interest rates 242
Summary 245
Summary of key equations 246
Key terms 247
Endnotes 248
Acknowledgements 248
MODULE 9
Share valuation
249
Module preview 250
9.1 The market for shares 250
Secondary markets 251
Secondary markets and their efficiency 251
Reading the share market listings 253
9.2 Ordinary and preference shares 254
Preference shares: debt or equity? 255
Ordinary share valuation 255
CONTENTS
v
9.3 General dividend valuation
model 258
Growth share pricing paradox 259
9.4 Share valuation: some simplifying
assumptions 260
Zero growth dividend model 260
Constant growth dividend model 261
Calculating future share prices 264
Relationship between R and g 266
Mixed (supernormal) growth dividend
model 266
9.5 Valuing preference shares 270
Preference shares with a fixed maturity 270
Perpetuity preference shares 272
Summary 273
Summary of key equations 274
Key terms 274
Endnotes 274
Acknowledgements 275
MODULE 10
Capital budgeting and cash
flows 276
Module preview 277
10.1 Introduction to capital budgeting 277
Importance of capital budgeting 278
Capital budgeting process 278
Sources of information 279
Classification of investment projects 279
Basic capital budgeting terms 280
10.2 Capital budgeting methods 280
Net present value 281
Payback period 285
Accounting rate of return 288
Internal rate of return 289
When IRR and NPV methods agree —
independent projects and conventional cash
flows 291
When IRR and NPV methods disagree — mutually
exclusive projects and unconventional cash
flows 292
IRR versus NPV: a final comment 295
Capital budgeting in practice 295
10.3 Project cash flows 296
Capital budgeting is forward looking 297
Incremental after‐tax free cash flows 297
FCF calculation 298
Cash flows from operations 299
Cash flows associated with investments 300
FCF calculation: an example 300
vi CONTENTS
10.4 Estimating cash flows in practice 304
Five general rules for incremental after‐tax
FCF calculations 304
Tax rates and depreciation 307
Calculating the terminal‐year FCF 309
Summary 312
Summary of key equations 313
Key terms 313
Acknowledgements 314
MODULE 11
Cost of capital and working
capital management 315
Module preview 316
11.1 Overall cost of capital 316
Estimating the cost of capital 317
Debt financing 318
Estimating the cost of debt 319
Tax and the cost of debt 321
Estimating the average cost of debt 321
Cost of equity 322
11.2 Using the weighted average cost of
capital 328
Calculating WACC: an example 329
Limitations of using WACC as a discount
rate 331
11.3 Working capital basics 333
Working capital terms and concepts 334
Working capital accounts and
trade-offs 334
Operating and cash conversion cycles 335
Operating cycle 337
11.4 Financing working capital 340
Strategies for financing working
capital 340
Sources of short-term financing 342
Summary 344
Summary of key equations 344
Key terms 345
Endnotes 345
Acknowledgements 346
MODULE 12
Capital structure and dividend
policy 347
Module preview 348
12.1 Choosing a capital structure
Capital structure theories 349
The empirical evidence 351
348
12.2 Benefits and costs of using
debt 352
Benefits of debt 352
Costs of debt 357
12.3 Dividends 360
Dividends reduce shareholders’ investment
in a company 362
Dividends and taxation 362
Dividend payment process 363
Benefits and costs of dividends 366
Share price reactions to dividend
announcements 369
12.4 Other types of distributions to
shareholders 370
Share buy‐backs 370
Bonus share issues 370
Share splits 371
12.5 Setting a dividend policy 372
What managers tell us 372
Practical considerations 373
Summary 374
Summary of key equations 375
Key terms 375
Endnotes 376
Acknowledgements 376
Appendix 377
CONTENTS
vii
MODULE 1
Finance in business
LEA RNIN G OBJE CTIVE S
After studying this module, you should be able to:
1.1 understand the importance of finance, money and markets
1.2 identify the basic forms of business structures
1.3 discuss the financial goals of a business
1.4 identify the key financial decisions facing the financial manager
1.5 describe the typical organisation of the financial function in a large company
1.6 discuss the relevance of ethics in business.
Module preview
This text provides an introduction to finance. In it we focus on the responsibilities of the financial
manager, who oversees the accounting and treasury functions, and sets the overall financial strategy
for the company. We pay special attention to the financial manager’s role as a decision‐maker. To that
end, we emphasise the mastery of fundamental finance concepts and the use of a set of financial tools
which will result in sound financial decisions that create value for shareholders. These financial concepts
and tools apply not only to business organisations but also to other organisations, such as government
entities, not‐for‐profit groups and sometimes even your own personal finances. We also examine the
financial markets in terms of their roles, the types of markets and the financial instruments that are
traded on them. Finally, the regulatory architecture is reviewed and the importance of having an efficient
and effective financial system discussed.
We open this module by discussing the importance of understanding finance and the role that finance
plays in society and in business. Next, we describe common forms of business structures. We then dis­
cuss the major responsibilities of the financial manager including the three major types of decisions
that a financial manager makes: capital budgeting decisions, financing decisions and working capital
management decisions. After next discussing how the financial function is managed in a large company,
we explain why maximising the price of the company’s shares is an appropriate goal of the business.
Finally, we discuss the importance of ethical conduct in business, describing the conflicts of interest that
can arise between shareholders and financial managers, and the mechanisms that help align the interests
of these two groups.
1.1 Understanding finance, money and markets
LEARNING OBJECTIVE 1.1 Understand the importance of finance, money and markets.
Whether we like it or not, money is an important element of modern society. On one hand, money is
required for transactions that allow us to conduct our daily affairs — to purchase food, pay the rent, buy
the morning coffee or take the family out to the local fun park. On the other hand, accumulating money
allows us to build savings and wealth for that next big purchase or activity, to prepare for retirement or
to provide a degree of security and comfort that, if financial resources are needed, they are available.
2 Finance essentials
Money is thus simply a means of exchanging value between parties; just imagine what it would be like
with no money (neither hard currency nor electronic currency). We would be forced to barter in order
to transact, which might work well for some transactions, but for everyday activity would be inefficient.
It is therefore not surprising that transacting has moved with technology and now happens not just
through our wallets, but through our phones, watches and the internet. Indeed, financial technology is
one of the fastest growing industries in the world. The efficient, timely and reliable transfer of money
between parties underpins economic activity and heavily influences how we conduct our daily activities.
The importance of this becomes clear when we consider how many transactions occur on a daily basis
across the nation. Even a small economy like Australia has over 975 000 points of access (e.g. ATMs,
bank branches, EFTPOS terminals) to the financial system, through which more than 430 million debit
card transactions worth more than $23 billion are transacted every month.1 Indeed, there are more than
16.6 million credit card accounts in Australia, through which a further 220 million transactions worth
$27.6 billion take place.2 Without money to operationalise these transactions, there would need to be a
lot of bartering going on!
In order for this trade to occur, markets are required to facilitate buyers and sellers interacting,
agreeing on the terms of a transaction and executing that transaction. This could be a physical market,
such as a shopping centre, where buyers and sellers come together in person to exchange money for
goods and services. Alternatively, there are online or virtual markets, where this interaction occurs elec­
tronically and thus buyers and sellers do not physically meet. Either way, markets are a key component
of facilitating trade. There are a range of markets in the financial system, including the market for cash,
the share market, the bond market and the foreign exchange market, where different financial products
are bought and sold. Each has its own purpose, rules of trade and mechanisms for allowing that trade
to occur. We look at the detail of these (and other) markets later to illustrate the diversity in market
characteristics.
The term finance is a broad term that is widely used in society. It refers to both the study of how
money is managed and the process of acquiring money. This text deals with both of these com­
ponents by examining the elements of the financial system that facilitate individuals, businesses and
governments managing and transacting their money. We also examine how these parties finance these
activities, for example by borrowing money in the form of loans, accumulating internal resources
(savings) or utilising the financial markets to raise funds by issuing shares, bonds or other financial
instruments. The financial system offers a range of ways to finance our activities. The job of the
finance manager at home, in business and in government is to work out the best way to structure our
finances and thus make effective financial decisions. This is easy to say, but in practice is much more
difficult!
A key task of the financial system is to ensure finance, money and markets operate efficiently to
allow the economy to work and individuals to make effective decisions. In many respects we often take
these systems for granted. Many consumers live in blissful ignorance of the financial system archi­
tecture that allows us to transact in the modern economy — we simply put the card in the wall and
wait for the cash to come out! To some extent this ignorance is a good thing, as it means the system is
working and we have confidence in it. But all we have to do is recall the last time the EFTPOS machine
was down and we had no cash in our wallet, and we realise how dependent we are on the financial
system. This, of course, does not happen by itself. Rather, it is the result of the efficient operation of
the components of the financial system — money, markets, financial institutions, financial regulation
and market participants.
In Australia, we are lucky that we have not had any major financial system failures in recent decades.
While we have had our issues (the failure of HIH Insurance in the early 2000s, securities trader Opes
Prime Stockbroking Limited’s failure in 2008 and Storm Financial Limited’s collapse in 2009), we
have not had the large bank failures and the widespread lack of confidence in the system that much of
the northern hemisphere has recently endured. As you progress through this text, you will encounter
many of the reasons for this. You would be well advised to learn as much as you can about finance,
MODULE 1 Finance in business 3
money and markets for both your own personal financial decision‐making and your career — because
the financial system will influence both!
Finance in society
The importance of finance in society is driven by the economic principle of scarcity. There is only so
much money available in the economy and thus individuals, businesses and governments need to use
what they have wisely and make decisions carefully in relation to the future acquisition and use of it.
At the level of the economy, a key task of the financial system is to ensure this scarce resource is used
effectively and thus allocated to purposes that will build wealth over time for the economy, maintaining
and improving our living standards. The complexity of the financial system means this may not happen
for every transaction, but over the longer term the system is designed to achieve this.
It should also be noted that the financial system evolves over time as the economy develops, regu­
lation changes, technology advances and other factors, such as consumer trends and environmental
change, shift. Examples of such changes that have affected the operation of the financial system include
the complexity of products and services, technological advances, the ageing population and financial
illiteracy.
In terms of the complexity of the financial system, we just have to read a product disclosure statement
(PDS) for an everyday financial product or service to understand this (look up a PDS for your bank and
have a read!). They are typically long documents, written in legalese, that try to explain the terms and
conditions of the product/service of relevance. While increased disclosure is generally a good thing,
the complexity and length of these documents make them difficult for many consumers to use. This is
exacerbated by the sheer range of financial products available, the heavy use of jargon and acronyms,
and the general low knowledge base and lack of confidence that many consumers bring to financial
decision‐making. Thus, the financial system has evolved to (for example) increase disclosure, place
more obligation on product providers to explain their services to consumers, encourage consumers to
obtain independent advice, and p­ rovide cooling‐off periods. At the same time, increased regulation and
oversight of the finance sector have been put in place, all with a view to protecting consumers and
building their confidence in the system.
Technological advancement is occurring at a somewhat frightening pace: from branch banking to
ATMs, online banking, micro/app‐based investing, paying with our mobile phones and robo advice in
only a few decades. While these advances may have improved the efficiency of and access to the system,
it is important that they maintain consumer confidence and protection at the same time. Thus, it is
interesting to note that the regulatory environment is struggling to keep up with the pace of change in
some jurisdictions and more innovative and more collaborative regulatory design approaches are being
used (e.g. look up the Australian Securities and Investments Commission’s (ASIC) regulatory sandbox
approach to financial technology).
A compounding issue is the ageing population. As the baby boomer population bubble moves into
retirement, the mix of retirees and workers is changing (more retirees and fewer workers). Further­
more, life expectancy is increasing and those in retirement are living more active lives. This places more
emphasis on industries such as health services, aged care and the superannuation sector, while govern­
ments will simply not be able to afford to provide a pension system to meet the needs of the population
as a result. Thus the move over time from a state‐funded retirement system to a self‐funded system is
in motion. For individuals, this places significant emphasis on accumulating wealth to fund retirement,
which in turn is a critical issue for society in relation to our overall living standards and the ability of
the government to provide services. Hence, making long‐term financial decisions that allow individuals/
households to accumulate wealth is a societal imperative. The multi‐million‐dollar question for everyone
to ask themselves is: How much will I need to save? (Look up a retirement calculator online to see your
expected number!)
A final issue is financial illiteracy. This has received a lot of attention from governments and
other agencies around the world in recent years. Financial literacy is essentially the combination of
4 Finance essentials
knowledge and behaviour that underpins effective financial decision‐making. Unfortunately, too many
people are not sufficiently equipped in one or both of these areas, increasing the risk of insufficient
wealth accumulation over time, greater susceptibility to schemes and scams, and higher levels of finan­
cial stress. Thus, improving financial literacy, protecting consumers through financial system design
and encouraging consumers to seek financial advice are important economic and social elements of
the financial system.
In summary, finances are of great economic and social importance. At the macro level, they drive the
operation and performance of the economy. For governments, they influence the fiscal position of the
nation and the ability of the government to provide services, and thus influence our living standards. For
business, finance heavily influences profitability and the long‐term sustainability of the enterprise, while
for consumers our ability to make effective financial decisions and accumulate wealth over the long term
is influenced. All in all, knowing more about the financial system is important for everyone. We hope
this text will help you in this regard!
Finance in business
Finance is a key factor in the success or otherwise of any business and, accordingly, a sound under­
standing of finance concepts and techniques is essential for any manager. Businesses need finance to:
•• start up — this involves expenditures such as paying rent in advance on premises and purchasing the
equipment and materials required to produce the business’s products or services
•• operate — it is important that a business has sufficient cash on hand to pay staff wages and suppliers
as these expenses fall due
•• expand — this might necessitate the purchase of new machinery to increase production capacity,
research and development costs for new products, or marketing costs associated with identifying and
entering new markets.
A major concern for all businesses is the way they are financed. It is important for managers to
select appropriate funding, as all entities need funding, no matter how small or large their turnover
or asset base. Australian businesses tend to look to the financial institutions, in the first instance, as
suppliers of intermediated finance. While larger entities with standing in the community are able to
access the financial markets and financial institutions for funds, smaller entities typically approach one
or several financial institutions for long‐term funding.
Entities wanting to raise debt finance from the Australian market have corporate bonds, notes and
debentures to choose from as methods of finance. To a great extent, these securities are similar methods
of financing; the differences mainly lie in their historical roles. Essentially, borrowing entities issue
bonds, notes or debentures as proof that debts exist. After that, if these securities are traded, the security
itself (the physical piece of paper) or the proof of registration with issues which is electronically
recorded, merely acts as proof of current ownership. Naturally, the owner of a bond at maturity is the
entity that receives the repayment of face value from the issuer.
Owners may at times wish to expand their entities or liquidate some or all of their ownership rights.
They achieve this by selling ownership rights to other investors; that is, raising equity finance. The
media by which ownership rights are packaged, sold (and bought) and transferred are ordinary shares
and preference shares. Ordinary shares are by far the more common of the two. All companies issue
ordinary shares; some, but not all, companies issue preference shares.
The size of a business and the nature of its ownership often determine the finance options available
to it. Businesses can be owned by sole operators, partnerships of two to twenty people or perhaps some
hundreds, or thousands of individual shareholders and large investment institutions in the case of listed
public corporations.
This text discusses the financial decisions faced by all these businesses, no matter how small or large
and no matter how they are owned. In practice, however, it is likely that small businesses will take a
less rigorous approach to decision‐making and financial analyses than is advocated here because these
MODULE 1 Finance in business 5
businesses tend not to employ people trained in finance. Additionally, the managements of many small
businesses judge that the benefits of employing a financial manager or a financial consultant do not
exceed the costs.
Every business has reasons for being. Because of their different sizes and ownership structures, it is to
be expected that there are a range of goals among businesses. For example, a family partnership which
owns a small auto‐electrical business might want to earn enough to live comfortably, put away some
funds to educate the children, not work on Saturdays or Sundays, and develop a reputation for doing
good work on time and at reasonable cost. Eventually, the family might want to sell the business to fund
a comfortable retirement. In contrast, the ownership of a large corporation is much more removed from
the operations of the company. The owners are you and me — through our direct shareholdings and
indirectly through our superannuation funds and managed funds. Because the owners are not closely
connected with the everyday operations of the business, it is likely that their goals are simplified and
focused largely on financial metrics, such as profit maximisation and shareholder returns.
This text presents the financial concepts and techniques that assist businesses to achieve their financial
goals, whatever these may be.
BEFORE YOU GO ON
1.
2.
3.
4.
Explain the role of money in an economy.
Discuss the key functions of financial markets.
Why is it important for everyone to have at least a basic understanding of the financial system?
Explain why finances are important to society and business.
1.2 Business structures and finance
LEARNING OBJECTIVE 1.2 Identify the basic forms of business structures.
In this section, we look at the ways companies organise in order to conduct their business activities. The
owners of a business usually choose the structure that will help management to maximise the value of
the business entity. Important considerations are the size of the business, the manner in which income
from the business is taxed, the legal liability of the owners and their ability to raise cash to finance
the business.
Most start‐ups and small businesses operate as either sole traders or partnerships, because of their
small operating scale and capital requirements. Large businesses in Australia, such as Woolworths
­Limited, are most often organised as companies. As a business grows larger, the benefits to organising as
a company become greater and are more likely to outweigh any disadvantages.
Sole traders
A sole trader is a business owned by one person, typically consisting of the trader and a handful of
employees. Becoming a sole trader offers several advantages. It is the simplest type of business to start
and it is the least regulated. In addition, sole traders keep all the profits from the business and do not
have to share decision‐making authority. From the taxation point of view, business losses can be written
off against the sole trader’s tax from other employment under certain circumstances.
On the downside, a sole trader has unlimited liability for all the business’s debts and other obli­
gations. This means that creditors can look beyond the assets of the business to the trader’s personal
wealth for payment. Another disadvantage is that the amount of equity capital that can be invested in
the business is limited to the owner’s personal wealth, which may restrict the possibilities for growth.
Finally, it is difficult to transfer ownership of a sole trader because there are no shares or other such
interests to sell.
6 Finance essentials
Partnerships
A partnership consists of two or more owners who have
joined together legally in order to manage a business.
Partnerships are typically larger than sole trader busi­
nesses. In forming a partnership, it is recommended that a
formal partnership agreement is drawn up on the roles and
authority of each partner, how much capital each partner
will contribute, how key management decisions will be
made, how the profits will be divided, who has limited lia­
bility, how the partnership will be closed down and assets
distributed, and how disputes will be dealt with.
The key advantages of partnerships are similar to
those of sole traders. In addition, partnerships have
access to more capital, and the pooling of knowledge,
experience and skills. The key drawbacks of partnerships
are possible disputes among the partners over profit‐
sharing, administration and business development. Also,
each partner is personally responsible for business debts
and liabilities incurred by the other partners.
The problem of unlimited liability can be avoided
in a limited partnership, which consists of general and
limited partners. Here, one or more general partners
have unlimited liability and actively manage the busi­
ness, while the limited partners are liable for business
obligations only up to the amount of capital they have contributed to the partnership. In other words, the
limited partners have limited liability. To qualify for limited‐partner status, a partner cannot be actively
engaged in managing the business.
Companies
Most large businesses are companies. A company is an independent legal entity able to do business
in its own right. In a legal sense, it is a ‘person’ distinct from its owners. Companies can sue and be
sued, enter into contracts, issue debt, borrow money and own assets. The owners of a company are its
shareholders.
Starting a company is more costly than starting a business as a sole trader or partnership. Those
starting the company, for example, must set out a memorandum that details its powers and articles
of association to describe who can use these powers. All companies are registered with and regulated
by ASIC.
A major advantage of the company form of business structure is that shareholders have limited
liability for the debts and other obligations of the company. However, directors and employees are
personally liable under the Corporations Act 2001 if found to be committing fraudulent, negligent
or reckless acts. The major disadvantages of the company form are the cost of establishment and
registration, and the higher compliance costs and stricter record‐keeping requirements as compared to
other business structures.
A company can also list on a stock exchange, such as the Australian Securities Exchange (ASX), as
a public company in order to attract investors. In contrast, private companies are typically owned by
a small number of key managers and shareholders. Over time, as the company grows in size and needs
larger amounts of capital, management may decide that the company should ‘go public’ in order to gain
access to the public markets.
MODULE 1 Finance in business 7
BEFORE YOU GO ON
1. Why are many businesses operated as sole traders?
2. What are some advantages and disadvantages of operating as a partnership?
3. What are some advantages and disadvantages of operating as a company?
1.3 The financial goals of a business
LEARNING OBJECTIVE 1.3 Discuss the financial goals of a business.
For business owners, it is important to determine the appropriate goal for financial management decisions.
Should the goal be to keep costs as low as possible? Or to maximise sales or market share? Or to achieve
steady growth and earnings? Let’s look at this fundamental question more closely.
What should management maximise?
Suppose you own and manage a pizza restaurant. Depending on your preferences and tolerance for risk,
you can set any goal for the business that you want. For example, you might have a fear of insolvency
and losing money. To minimise the risk of insolvency, you could focus on keeping your costs as low as
possible, by paying low wages, avoiding borrowing, advertising minimally and remaining cautious about
expanding the business. In short, you avoid any action that increases your business’s risk. You will sleep
well at night, but you may eat poorly because of meagre profits.
Conversely, you could focus on maximising market share and becoming the largest pizza place in
town. Your strategy might include cutting prices to increase sales, borrowing heavily to open new pizza
outlets, spending lavishly on advertising and developing menu items using exotic toppings. In the short
term, your high‐risk, high‐growth strategy will have you both eating poorly and sleeping poorly as you
push the business to the edge. In the long term, you will either become very rich or become insolvent!
There must be a better operational goal than either of these extremes.
Why not maximise profits?
One goal for financial decision‐making that seems reasonable is profit maximisation. After all, don’t
shareholders and business owners want their companies to be profitable? However, although profit
maximisation may seem a logical goal for a business, it has some serious drawbacks.
One problem with profit maximisation is that it is hard to pin down what is meant by ‘profit’. To
the average businessperson, profits are just revenues minus expenses. To an accountant, however, a
decision that increases profit under one set of accounting rules can reduce it under another. This is
the origin of the term creative accounting. A second problem is that accounting profits are not n­ ecessarily
the same as cash flows. For example, many companies recognise revenues at the time a sale is made,
which is typically before the cash payment for the sale is received. Ultimately the owners of a business
want cash because only cash can be used to make investments or to buy goods and services.
Yet another problem with profit maximisation as a goal is that it does not distinguish between
­getting a dollar today and getting a dollar sometime in the future. In finance, the timing of cash flows
is extremely important. For example, the longer we go without paying our credit card balance, the
more interest we must pay the bank for the use of the money. The interest accrues because of the
time value of money; the longer we have access to money, the more we have to pay for it. The time
value of money is one of the most important concepts in finance and is the focus of two modules in
this text.
Finally, profit maximisation ignores the uncertainty (or risk) associated with cash flows. A basic
principle of finance is that there is a trade‐off between expected return and risk. When given a choice
8 Finance essentials
between two investments that have the same expected returns but different risks, most people choose the
less risky one. This makes sense because people do not like bearing risk and, as a result, must be com­
pensated for taking it. The profit maximisation goal ignores differences in value caused by differences in
risk. We return to the important topics of risk, its measurement and the trade‐off between risk and return
in a later module. What is important here is that you understand that investors do not like risk and must
be compensated for bearing it.
The timing of cash flows affects their value
A dollar today is worth more than a dollar in the future because, if you have a dollar today, you can
invest it and earn interest. For businesses, cash flows can involve large sums of money and receiving
money just one day late can cost a great deal. For example, if a bank has $100 billion of consumer loans
outstanding and the average annual interest payment is 5 per cent, it would cost the bank $13.7 million
if every consumer decided to make an interest payment one day later.
The riskiness of cash flows affects their value
A risky dollar is worth less than a safe dollar. The reason is because investors do not like risk and so must
be compensated for bearing it. For example, if two investments have the same return — say 5 per cent —
most people will choose the investment with the lower risk. Thus, the more risky an investment’s cash
flows, the less it is worth.
In summary, it appears that profit maximisation is not an appropriate goal for a company because
the concept is difficult to define and does not directly account for the company’s cash flows. What we
need is a goal that looks at a company’s cash flows and considers both their timing and their riskiness.
­Fortunately, we have just such a measure: the market value of the company’s shares.
Maximise the value of the company’s shares
The underlying value of any asset is determined by the future cash flows generated by that asset. This prin­
ciple holds whether we are buying a bank certificate of deposit, a corporate bond or an office building.
Furthermore, as we will discuss in the module on share valuation, when security analysts and investors
determine the value of a company’s shares, they consider: (1) the size of the expected cash flows; (2) the
timing of the cash flows; and (3) the riskiness of the cash flows. Note that the mechanism for determining
share values overcomes all the cash flow objections we raised with regard to profit maximisation as a goal.
Thus, an appropriate goal for financial management is to maximise the current value of the company’s
shares. By maximising the current share price, the financial manager is maximising the value of the
shareholders’ shares. Note that maximising share value is an unambiguous objective and it is easy to
measure. We simply look at the market value of the shares in the news on a given day to determine the
value of the shareholders’ shares and whether it has gone up or down. Publicly traded securities are
ideally suited for this task because public markets are wholesale markets with large numbers of buyers
and sellers where securities trade near their true value.
What about companies whose equity is not publicly traded, such as private companies and partner­
ships? The total value of the shares in such a company is equal to the value of the shareholders’ equity.
Thus, our goal can be restated for these companies as: maximise the current value of equity. The only
other restriction is that the entities must be for‐profit businesses.
The financial manager’s goal is to maximise the value of the
company’s shares
The goal for financial managers is to make decisions that maximise the company’s share price. By
maximising share price, management will help to maximise shareholders’ wealth. To do this, managers
must make investment and financing decisions so that the total value of cash inflows exceeds the total
value of cash outflows by the greatest possible amount (benefits > costs). Note that the focus is on
maximising the value of cash flows, not profits.
MODULE 1 Finance in business 9
Can management decisions affect share prices?
An important question is whether management decisions actually affect the company’s share price.
­Fortunately, the answer is yes. As noted earlier, a basic principle in finance is that the value of an asset
is determined by the future cash flows it is expected to generate. As shown in figure 1.1, a company’s
management makes many decisions that affect its cash flows. For example, management decides what
type of products or services to produce and what productive assets to purchase. The company’s share
price is affected by a number of factors and management can control only some of them. Managers
exercise little control over external conditions (blue boxes) such as the general economy, although they
can closely observe these conditions and make appropriate changes in strategy. Managers make many
other decisions that do directly affect the company’s expected cash flows (red boxes) — and hence the
price of the company’s shares.
Managers also make decisions concerning the mix of debt to equity, debt collection policies and
policies for paying suppliers, to mention a few. In addition, cash flows are affected by how efficient
management is in making products, the quality of the products, management’s sales and marketing skills,
and the company’s investment in research and development of new products. Some of these decisions
affect cash flows over the long term, such as a decision to build a new plant, while other decisions have
a short‐term impact on cash flows, such as launching an advertising campaign.
Of course, the company also must deal with a number of external factors over which it has little or
no control, such as economic conditions (recession or expansion), war or peace and new government
regulations. External factors are constantly changing and management must weigh the impact of these
changes and adjust its strategy and decisions accordingly.
FIGURE 1.1
Major factors that affect share prices
Economic shocks
1. Wars
2. Natural disasters
Business environment
1. Corporate laws
2. Environmental regulations
3. Procedural and safety
regulations
4. Tax
The economy
1. Level of economic
activity
2. Level of interest rates
3. Consumer sentiment
Current
share
market
conditions
The company
1. Line of business
2. Financial management
decisions
a. Capital budgeting
b. Financing the company
c. Working capital
management
3. Product quality and cost
4. Marketing and sales
5. Research and development
Expected cash flows
1. Magnitude
2. Timing
3. Risk
Share
price
The important point here is that, over time, management makes a series of decisions when execu­
ting the company’s strategy that affect the company’s cash flows and, hence, the price of the com­
pany’s shares. Companies that have a better business strategy are more nimble, make better business
10 Finance essentials
decisions and can execute their plans well will have a higher share price than similar companies that
just can’t get these right.
When taking into consideration a long‐term horizon, the only corporate objective that maximises the
economic interests of all stakeholders over time is for management to make decisions that maximise
the wealth of shareholders. For example, in April 2012 Telstra issued a press release announcing that
it expected to generate $2–3 billion in excess free cash flows over the next three years. The company
also confirmed that its capital management strategy priorities were to maximise returns for shareholders
(through both dividends and capital growth), maintain financial strength and retain financial flexibility.
If these priorities are executed well, this will enable Telstra to serve its existing customers better, grow
customer numbers, maintain its A credit rating and build new growth businesses. As you can see from
this example, even though Telstra’s main priority is to maximise the wealth of its shareholders, other
stakeholders such as customers, employees and lenders will also benefit from the implementation of its
capital management strategies.3
1.4 The financial manager
LEARNING OBJECTIVE 1.4 Identify the key financial decisions facing the financial manager.
While the term corporate finance implies that these topics are only relevant to corporations, this is not
the case. The topics covered in this section are basic financial principles that apply to all forms of busi­
ness structure. However, the corporate structure is used because it is easier to explain these topics when
the parties involved are distinctly separate from each other, which is usually not the case in small busi­
ness entities. Now we look at the role of the financial manager and three fundamental decisions they
make when running a business. These decisions will be covered throughout the text. We then discuss
how the financial function is managed in large corporations. The ultimate goal of the business is then
justified.
The financial manager
The financial manager is responsible for making decisions that are in the best interests of the business’s
owners, whether it is a start‐up business with a single owner or a billion‐dollar company owned by
thousands of shareholders. The decisions made by the financial manager and owners should be one and
the same. In most situations this means the financial manager should make decisions that maximise the
value of the owners’ shares. This helps maximise the owners’ wealth. Our underlying assumption in this
text is that most people who invest in businesses do so because they want to increase their wealth. In the
following discussion, we describe the responsibilities of the financial manager in a new business in order
to illustrate the types of decisions that such a manager makes.
Stakeholders
Before we discuss the new business, you may want to look at figure 1.2, which shows the cash flows
between a company and its owners (in a company, the shareholders) and various stakeholders. A
­stakeholder is someone other than an owner who has a claim on the cash flows of the company: managers, who want to be paid salaries and performance bonuses; creditors, who want to be paid interest
and principal; employees, who want to be paid wages; suppliers, who want to be paid for goods or
services; and the government, which wants the company to pay tax. Stakeholders may have interests
that differ from those of the owners. When this is the case, they may exert pressure on management to
make decisions that benefit them. We will return to these types of conflict of interest later. For now, we
are primarily concerned with the overall flow of cash between the company and its shareholders and
stakeholders.
MODULE 1 Finance in business 11
FIGURE 1.2
Cash flows between the company and its stakeholders and owners
Stakeholders and
shareholders
The company
A
Cash flows are generated
by productive assets
through the sale of
goods and services.
Company’s
management
invests in assets
Current assets
• Cash
• Inventory
• Accounts
receivable
Productive assets
• Plant
• Equipment
• Buildings
• Technology
• Patents
Cash paid as
wages and salaries
Managers
and other
employees
Cash paid to
suppliers
Suppliers
Cash paid
as tax
Government
Cash paid as
interest and principal
Creditors
Shareholders
B
Residual cash flow
Cash flow reinvested
in business
Dividends paid to
shareholders
It’s all about cash flows
To produce its goods or services, a new company needs to acquire a variety of assets. Most will be long‐
term assets or productive assets. Productive assets can be tangible assets, such as equipment, machinery
or a manufacturing facility, or intangible assets, such as patents, trademarks, technical expertise or other
types of intellectual capital. Regardless of the type of asset, the company tries to select assets that will
generate the greatest profits. The decision‐making process through which the company purchases long‐
term productive assets is called capital budgeting and it is one of the most important decision processes
in a company.
Making business decisions is all about cash flows, because only cash can be used to pay bills and to
buy new assets. Cash initially flows into the company as a result of the sale of goods or services. The
company uses these cash inflows in a number of ways: to invest in assets, to pay wages and salaries, to
buy supplies, to pay taxes and to repay creditors. Any cash that is left over (residual cash flows) can be
reinvested in the business or paid as dividends to shareholders.
Once the company has selected its productive assets, it must raise money to pay for them. Financing
decisions are concerned with the ways that companies obtain and manage long‐term financing to
acquire and support their productive assets. There are two basic sources of funds: debt and equity.
Every company has some equity, because equity represents ownership in the company. It consists
of capital contributions by the owners plus earnings that have been reinvested in the company. In
addition, most companies borrow from a bank or issue some type of long‐term debt to finance
productive assets.
After the productive assets have been purchased and the business is operating, the company tries
to produce products at the lowest possible cost while maintaining quality. This means buying raw
12 Finance essentials
materials at the lowest possible cost, holding production and labour costs down, keeping manage­
ment and administrative costs to a minimum, and seeing that shipping and delivery costs are com­
petitive. In addition, the company must manage its day‐to‐day finances so that it has sufficient cash
on hand to pay salaries, purchase supplies, maintain inventories, pay tax and cover the myriad other
expenses necessary to run a business. The management of current assets, such as money owed by
customers who purchase on credit, and inventory, and current liabilities, such as money owed to
suppliers, is called working capital management. From accounting, current assets are assets that
will be converted into cash within 1 year and current liabilities are liabilities that must be paid
within 1 year.
A company generates cash flows by selling the goods and services it produces. A company is suc­
cessful when these cash inflows exceed the cash outflows needed to pay operating expenses, creditors
and tax. After meeting these obligations, the company can pay the remaining cash, called residual cash
flows, to the owners as a cash dividend or it can reinvest the cash in the business. The reinvestment of
residual cash flows back into the business to buy more productive assets is a very important concept.
If these funds are invested wisely, they provide the foundation for the company to grow and provide
larger residual cash flows in the future for the owners. The reinvestment of cash flows (earnings) is the
most fundamental way that businesses grow in size. Figure 1.2 illustrates how the revenue generated by
productive assets ultimately becomes residual cash flow.
A company is unprofitable when it fails to generate sufficient cash inflows to pay operating expenses,
creditors and tax. Companies that are unprofitable over time will be forced into insolvency by their
creditors if the owners do not shut them down first. In insolvency, the company will be reorganised or
its assets will be liquidated, whichever is more valuable. If the company is liquidated, creditors are paid
in a priority order according to the structure of the company’s financial contracts and prevailing insol­
vency law. If anything is left after all creditor and tax claims have been satisfied, which usually does not
happen, the remaining cash, or residual value, is distributed to the owners.
Cash flows matter most to investors
Cash is what investors ultimately care about when making an investment. The value of any asset —
shares, bonds or a business — is determined by the future cash flows it will generate. To understand this
concept, consider how much you would pay for an asset from which you could never expect to obtain
any cash flows. Buying such an asset would be like giving your money away. It would have a value of
exactly zero. Conversely, as the expected cash flows from an investment increase, you would be willing
to pay more and more for it.
Three fundamental decisions in financial management
Based on our discussion so far, we can see that financial managers are concerned with three fundamental
decisions when running a business:
1. capital budgeting decisions — identifying the productive assets the company should buy
2. financing decisions — determining how the company should finance or pay for assets
3. working capital management decisions — determining how day‐to‐day financial matters should be
managed so the company can pay its bills, and how surplus cash should be invested.
Figure 1.3 shows the impact of each decision on the company’s balance sheet. (Note that the bal­
ance sheet can also be called the statement of financial position but the term balance sheet will be used
throughout this text.) We briefly introduce each decision here and discuss them in greater detail in later
modules.
MODULE 1 Finance in business 13
FIGURE 1.3
How the financial manager’s decisions affect the balance sheet
Balance sheet
Assets
Current assets
(including cash,
inventory and
accounts receivable)
Long-term
assets (including
productive assets;
may be tangible
or intangible)
Liabilities and equity
Working capital
management decisions
deal with day-to-day financial
matters and affect current
assets, current liabilities and
net working capital.
Net working capital — the
difference between current
assets and current liabilities
Capital budgeting
decisions
determine what long-term
productive assets the
company will purchase.
Financing decisions
determine the company’s
capital structure — the
combination of long-term
debt and equity that will
be used to finance the
company’s long-term
productive assets.
Current liabilities
(including
short-term debt and
accounts payable)
Long-term debt
(debt with a
maturity of over
1 year)
Shareholders’
equity
Capital budgeting decisions
A company’s capital budget is simply a list of the productive (capital) assets that management wants to
purchase over a budget cycle, typically 1 year. The capital budgeting decision process addresses which
productive assets the company should purchase and how much money it can afford to spend. As shown
in figure 1.3, capital budgeting decisions affect the asset side of the balance sheet and are concerned with
a company’s long‐term investments.
Capital budgeting decisions, as we mentioned earlier, are among management’s most important
decisions. Over the long run, they have a large impact on the company’s success or failure. The reason is
twofold. First, capital assets generate most of the cash flows for the company. Second, capital assets are
long term in nature. Once they are purchased, the company owns them for a long time and they may be
hard to sell without taking a financial loss.
The fundamental question in capital budgeting is this: Which productive assets should the company
purchase? A capital budgeting decision may be as simple as a movie theatre’s decision to buy a pop­
corn machine or as complicated as Airbus’s decision to invest more than $10 billion into designing and
building the A380 passenger jet. Capital investments may also involve the purchase of an entire busi­
ness, such as Woolworths Limited’s acquisition of hardware distributor Danks to compete with home‐
improvement giant Bunnings.
Regardless of the project, a good capital budgeting decision is one in which the benefits are worth
more to the company than the cost of the asset. Not all investment decisions are successful. Just open
the business news on any day and you will find stories of bad decisions. For example, the 2011 film The
Green Lantern turned out to be a flop despite the popularity of superhero movies, losing US$90 million
14 Finance essentials
for the production company. After failing at the box office, it is unlikely that the movie’s overall cash flow
(from box office takings, DVD sales, merchandise and so on) was worth more than its US$200 million
cost. When, as in this case, the cost exceeds the value of the future cash flows, the project will decrease
the value of the company by that amount.
Sound investments are those where the value of the benefits exceeds their costs
Financial managers should invest in a capital project only if the value of its future cash flows exceeds
the cost of the project (benefits > cost). Such investments increase the value of the company and thus
increase shareholders’ (owners’) wealth. This rule holds whether you are making the decision to purchase
new machinery, build a new plant or buy an entire business.
Financing decisions
Financing decisions concern how companies raise cash to pay for their investments, as shown in
figure 1.3. Productive assets, which are long term in nature, are financed by long‐term borrowing, equity
investment or both. Financing decisions involve trade‐offs between advantages and disadvantages to the
company.
A major advantage of debt financing is that debt payments are tax deductible for many companies.
However, debt financing increases a company’s risk, because it creates a contractual obligation to make
periodic interest payments and, at maturity, to repay the amount that is borrowed. Contractual obli­
gations must be paid regardless of the company’s operating cash flow, even if it suffers a financial loss.
If the company fails to make payments as promised, it defaults on its debt obligation and could be forced
into insolvency.
In contrast, equity has no maturity and there are no guaranteed payments to equity investors. In a
company, the board of directors has the right to decide whether dividends should be paid to share­
holders. This means that if the board decides to omit or reduce a dividend payment, the company will
not be in default. Unlike interest payments, however, dividend payments to shareholders are not tax
deductible.
The mix of debt and equity on the balance sheet is known as a company’s capital structure. The term
capital structure is used because long‐term funds are considered capital and these funds are raised in
capital markets — financial markets where equity and debt instruments with maturities of greater than
1 year are traded.
Financing decisions affect the value of the company
How a company is financed with debt and equity affects its value. The reason is that the mix between
debt and equity affects the amount of tax the company pays and the probability that the company will
become insolvent. The financial manager’s goal is to determine the exact combination of debt and equity
that minimises the cost of financing the company.
Working capital management decisions
Management must also decide how to manage the company’s current assets, such as cash, inven­
tory and accounts receivable, and its current liabilities, such as trade credit and accounts payable.
The dollar difference between current assets and current liabilities is called net working capital, as
shown in figure 1.3. As we mentioned earlier, working capital management is the day‐to‐day manage­
ment of the company’s short‐term assets and liabilities. The goals of managing working capital are to
ensure that the company has enough money to pay its bills and to profitably invest any spare cash to
earn interest.
The mismanagement of working capital can cause a company to default on its debt and become
insolvent even though, over the long term, the company may be profitable. For example, a company
that makes sales to customers on credit but is not diligent about collecting the accounts receivable can
quickly find itself without enough cash to pay its bills. If this condition becomes chronic, trade creditors
can force the company into insolvency if it cannot obtain alternative financing.
MODULE 1 Finance in business 15
A company’s profitability can also be affected by its inventory level. If the company has more
inventory than it needs to meet customer demands, it has too much money tied up in non‐earning
assets. Conversely, if the company holds too little inventory, it can lose sales because it does not
have products to sell when customers want them. The company must therefore determine the optimal
inventory level.
1.5 Managing the financial function
LEARNING OBJECTIVE 1.5 Describe the typical organisation of the financial function in a large company.
As we discussed earlier in the module, financial managers are concerned with a company’s investment,
financing and working capital management decisions. The senior financial manager holds one of the
top executive positions in the company. In a large company, the senior financial manager usually has
the rank of deputy chief executive or senior executive and goes by the title of chief financial officer
(CFO). In smaller companies, the job tends to focus more on the accounting function and the top finan­
cial officer may be called the controller or chief accountant. In this section, we focus on the financial
function in a large company.
Organisation structure
Figure 1.4 shows a typical organisational structure for a large company, with special attention to the
financial function. As shown, the top management position in the company is the chief executive officer
(CEO), who has the final decision‐making authority among all the company’s executives. The CEO’s
most important responsibilities are to set the strategic direction of the company and to see that the man­
agement team executes the strategic plan. The CEO reports directly to the board of directors, which is
accountable to the company’s shareholders. The board’s responsibility is to see that the top management
makes decisions that are in the best interest of the shareholders.
The CFO reports directly to the CEO and focuses on managing all aspects of the company’s financial
side, as well as working closely with the CEO on strategic issues. A number of positions report directly
to the CFO. In addition, the CFO often interacts with people in other functional areas on a regular basis,
because all senior executives are involved in financial decisions that affect the company and their areas
of responsibility.
Positions reporting to the CFO
Figure 1.4 also shows the positions that typically report to the CFO in a large company and the activities
managed in each area.
•• The treasurer looks after the collection and disbursement of cash, investing excess cash so that it
earns interest, raises new capital, handles foreign exchange transactions and oversees the company’s
superannuation arrangements. The treasurer also assists the CFO in handling important financial
relationships, such as those with investment bankers and credit rating agencies.
•• The risk manager monitors and manages the company’s risk exposure in financial and commodity
markets, and the company’s relationships with insurance providers.
•• The controller is really the company’s chief accounting officer. The controller’s staff prepares the
financial statements, maintains the company’s financial and cost accounting systems, prepares the tax
returns and works closely with the company’s external auditors.
•• The internal auditor is responsible for identifying and assessing the major risks facing the company
and performing audits in areas where the company might incur substantial losses. The internal auditor
reports to the board of directors as well as the CFO.
16 Finance essentials
FIGURE 1.4
Simplified company organisation chart
Shareholders
Shareholders control
Board controls
Board of directors
Audit committee
Chief executive
officer (CEO)
External auditor
CEO controls
CFO controls
Chief information officer (CIO)
Chief financial officer (CFO)
Chief operating officer (COO)
Treasurer
Risk manager
Controller
Internal auditor
• Cash payments/
collections
• Foreign exchange
• Superannuation
• Derivatives hedging
• Marketable
securities portfolio
• Monitor company’s
risk exposure in
financial and
commodities
markets
• Design strategies
for limiting risk
• Manage insurance
portfolio
• Financial accounting
• Cost accounting
• Taxes
• Accounting
information system
• Prepare financial
statements
• Audit high-risk
areas
• Prepare working
papers for
external auditor
• Internal consulting
for cost savings
• Internal fraud
monitoring and
investigation
External auditors
Nearly every large business entity hires a licenced public accounting business to provide an indepen­
dent annual audit of the company’s financial statements. Through this audit, the accountant comes to
a conclusion as to whether the company’s financial statements present fairly, in all material respects,
its financial position and the results of its activities; in other words, whether the financial numbers
are reasonably accurate, accounting principles have been consistently applied from year to year and
do not significantly distort the company’s performance, and the accounting principles used conform
to those generally accepted by the accounting profession. Creditors and investors require independent
audits and ASIC requires large private companies and all public companies to supply audited finan­
cial statements.
The audit committee
The audit committee, a powerful subcommittee of the board of directors, has the responsibility of over­
seeing the accounting function and the preparation of the company’s financial statements. In addition,
the audit committee oversees or, if necessary, conducts investigations of significant fraud, theft or mal­
feasance in the company, especially if it is suspected that senior managers in the company may be
involved.
External auditors report directly to the audit committee to help ensure their independence from man­
agement. On a day‐to‐day basis, however, they work closely with the CFO staff. The internal auditor
also reports to the audit committee so that the position is more independent from management, and the
internal auditor’s ultimate responsibility is to the audit committee. On a day‐to‐day basis, however, the
internal auditor, like the external auditors, works closely with the CFO staff.
MODULE 1 Finance in business 17
1.6 Ethics in business
LEARNING OBJECTIVE 1.6 Discuss the relevance of ethics in business.
The term ethics describes a society’s ideas about what actions are right and wrong. Ethical values are not
moral absolutes and they can and do vary across societies. Regardless of cultural differences, however,
if we think about it, we would all probably prefer to live in a world where people behave ethically —
where people try to do what is right.
In our society, ethical rules include considering the impact of our actions on others, being willing to
sometimes put the interests of others ahead of our own interests, and realising that we must follow the
same rules we expect others to follow. The golden rule — ‘Do unto others as you would have them do
unto you’ — is an example of a widely accepted ethical norm. A less noble version occasionally heard
in business is ‘The one who has the gold makes the rules’.
Are business ethics different from everyday ethics?
Perhaps business is a dog‐eat‐dog world where ethics do not matter. People who take this point of view
link business ethics to the ‘ethics of the poker game’ and not to the ethics of everyday morality. Poker
players, they suggest, must practise cunning deception and must conceal their strengths and their inten­
tions. After all, they are playing the game to win. How far should we go to win?
Normally, investors only learn the hard way about companies that have been behaving unethically.
As noted previously, in 2008 Storm Financial Limited, a Queensland‐based financial advisory company
with 13 000 clients around Australia, collapsed. Storm Financial Limited often advised clients to mort­
gage their homes in order to secure margin loans to invest in indexed share funds. Many of its clients,
mostly elderly investors, lost their life savings and some lost their homes when the share market plum­
meted. Following investigations of Storm Financial Limited’s investment schemes, ASIC decided to sue
the Commonwealth Bank, Macquarie Group and Bank of Queensland for their involvement in these
unregistered schemes. ASIC is taking legal action against the three banks for approximately $1 billion as
compensation for the investors, who lost more than $3 billion.4
Several months before the demise of Storm Financial Limited, Opes Prime Stockbroking Limited, a
Victorian financial advisory company servicing 1200 investors, collapsed owing more than $1 billion.5
The collapse of Storm Financial Limited and Opes Prime Stockbroking Limited prompted investi­
gation into practices in the financial advisory industry and the role of commissions in creating conflicts
of interest. A parliamentary inquiry resulted in eleven recommendations being made to parliament in
November 2009. Many of these recommendations related to alterations to ASIC’s powers under the
­Corporations Act to help protect consumers.6
We believe those who argue that ethics do not matter in business are mistaken. Indeed, most academic
studies on the topic suggest that traditions of morality are very relevant to business and to financial
markets in particular. The reasons are practical as well as ethical. Corruption in business creates inef­
ficiencies in an economy, inhibits the growth of capital markets and slows a country’s rate of economic
growth.
For example, as Russia made the transition to a market economy, it had a difficult time establishing
a share market and attracting foreign investment. The reason was a simple one: corruption was ram­
pant in local government and in business. Contractual agreements were not enforceable and there was
no reliable financial information about Russian companies. Not until the mid 1990s did some Russian
companies begin to display enough honesty and financial transparency to attract investment capital. In
economics, transparency refers to openness and access to information.
Types of ethical conflicts in business
We turn next to a consideration of the ethical problems that arise in business dealings. Most such prob­
lems involve three related areas: agency obligations, conflicts of interest and information asymmetry.
18 Finance essentials
Financial managers have agency obligations to
act honestly and to see that their subordinates act
honestly with respect to financial transactions.
Of all the company officers, financial managers,
when they are guilty of misconduct, present the
most serious dangers to shareholder wealth. A
product recall or environmental offence may cause
temporary declines in share prices. However, revel­
ations of dishonesty, deception and fraud in finan­
cial matters have a huge impact on the share price.
If the dishonesty is flagrant, the company may
become insolvent, as we saw with the insolvency
of Storm Financial Limited and Opes Prime
Stockbroking Limited.
Conflicts of interest often arise in business
relationships. For example, suppose you’re inter­
ested in buying a house and a local real estate agent
is helping you find the home of your dreams. As it
turns out, your agent is also the listing agent for the dream house. Your agent has a conflict of interest
because their professional obligation to help you find the right house at a fair price conflicts with their
professional obligation to get the highest price possible for the client whose house they have listed.
Organisations can be parties to conflicts of interest. In the past, for example, many large accounting
practices provided both consulting services and audits for the same companies. This dual function might
compromise the independence and objectivity of the audit opinion, even though the work is done by
different parts of the accounting practice. For example, if consulting fees from an audit client become a
large source of income, is the auditing arm of the practice less likely to render an adverse audit opinion
and thereby risk losing the consulting business?
Conflicts of interest are typically resolved in one of two ways. Sometimes complete disclosure is suf­
ficient. Thus, in real estate transactions it is not unusual for the same lawyer or realtor to represent both
the buyer and the seller. This practice is not considered unethical as long as both sides are aware of the
fact and give their consent. Alternatively, the conflicted party can withdraw from serving the interests
of one of the parties. Sometimes the law mandates this solution. For example, Australian legislation
requires that public accounting practices not provide certain consulting services to their audit clients,
because safeguards cannot reduce threats to independence to an acceptable level.7
The existence of information asymmetry in business relationships is commonplace. Information
asymmetry occurs when one party in a business transaction has information that is unavailable to the
other parties in the transaction. For example, suppose you decide to sell your 10‐year‐old car. You know
much more about the real condition of the car than does a prospective buyer. The moral issue is this:
how much should you tell the prospective buyer? In other words, to what extent is the party with the
information advantage obligated to reduce the amount of information asymmetry?
Decisions in this area often centre on issues of fairness. Consider the insider trading of shares based
on confidential information not available to the public. Using insider information is considered morally
wrong and, as a result, has been made illegal. The rationale for the notion is ethical fairness. The central
idea is that investment decisions should be made on a ‘level playing field’.
What counts as fair and unfair is somewhat controversial, but there are a few ways to determine
fairness. One relates to the golden rule and the notion of impartiality that underlies it. You treat
another fairly when you ‘do unto others as you would have them do unto you’. Another test of fair­
ness is whether you are willing to publicly advocate the principle behind your decision. Actions
based on p­ rinciples that do not pass the golden rule test or that cannot be publicly advocated are not
likely to be fair.
MODULE 1 Finance in business 19
The importance of an ethical business culture
Some economists have noted that the legal system and market forces impose substantial costs on indi­
viduals and institutions that engage in unethical behaviour. As a result, these forces provide important
incentives that foster ethical behaviour in the business community. These incentives include financial
losses, legal fines, jail time and destruction of companies (insolvency). Ethicists argue, however, that
laws and market forces are not enough. For example, the financial sector is one of the most heavily
regulated areas of the Australian economy. Yet, despite heavy regulation, the sector has a long and rich
history of financial scandals.
In addition to laws and market forces, then, it is important to create an ethical culture in the company.
Why is this important? An ethical business culture means that people have a set of principles — a moral
compass, so to speak — that helps them identify moral issues and make ethical judgements without
being told what to do. The business culture has a powerful influence on the way people behave and the
way they make decisions.
An unethical business culture can lead to adverse consequences — not only to the management and
investors, but also to the general public. For example, the consequences of the global financial crisis
of 2007–08 continue to be felt in many ways, including by financial services business that have been
investigated as a result. For example, in mid‐September 2016 it was announced that the US Department
of Justice has asked Deutsche Bank (one of Germany’s key banks) to pay US$14 billion to settle an
investigation into its dealings during the GFC. This is on top of the US$1.9 billion the bank had already
agreed to pay to settle an earlier claim in 2013. The bank’s stock price fell 8 per cent as a result. It is
also not alone. Citigroup paid a US$7 billion fine in 2014 and early in 2016 Goldman Sachs Group
paid more than US$5 billion to settle the claims of investors who claimed to have been misled by them
during mortgage bond purchases. Other institutions also continue to be investigated. This highlights the
financial damage such behaviour can do, and suggests the equally significant reputational damage for the
business and for confidence in the financial system as a whole.
Clearly, business ethics is a topic of high interest and increasing importance in the business commu­
nity, and it is a topic that will be discussed throughout the text. More than likely, you will be confronted
with ethical issues during your professional career. Knowing how to identify and deal with ethical issues
is thus an important part of your professional ‘survival kit’.
BEFORE YOU GO ON
1. What is a conflict of interests in a business setting?
2. How would you define an ethical business culture?
20 Finance essentials
SUMMARY
1.1 Understand the importance of finance, money and markets.
We all use finance, money and markets on an almost daily basis. Many consumers have a low level
of understanding of how the system operates, but benefit greatly from the efficiency and effective­
ness of the modern financial system. This confidence is based on an efficient and reliable system
that allows them to transfer value between themselves and other parties using money, and to engage
with other buyers and sellers in either physical or virtual markets to settle transactions in order to
conduct their daily affairs and finance their long‐term activities. The sheer volume of transactions
that occur on a daily basis underpins our reliance on the financial system.
Finance impacts heavily on our lives. The ability to raise and use funds efficiently affects short‐
term and long‐term economic and social outcomes for households, businesses and governments.
This is complicated by the complexity of financial products and services, the ageing population, the
move from state‐funded to self‐funded retirement, high levels of financial illiteracy and our desire
to maintain high living standards. Be it the government agency funding services for the community,
the business finance manager generating returns for shareholders or the individual investing for a
better financial future, the outcomes will be significantly influenced by the ability to make effective
financial decisions.
Finance is a key factor in the success or otherwise of any business and, accordingly, a sound
understanding of finance concepts and techniques is essential for any manager. Businesses need
finance to start up, operate and expand. A major concern for all businesses is the way they are
financed. It is important for managers to select appropriate funding, as all business entities need
funding, no matter how small or large their turnover or asset base.
1.2 Identify the basic forms of business structures.
A business can organise in three basic ways: as a sole trader, a partnership or a company (public
or private). The owners of a business select the form of organisation that they believe will best
allow management to maximise the value of the business. Most large businesses elect to organise as
public companies because of the ease of raising money; the major disadvantage is high regulation
compliance costs. Smaller businesses tend to organise as sole traders or partnerships. The advan­
tages of these forms of organisation include ease of formation and taxation at the personal income
tax rate; their major disadvantage is the owners’ unlimited personal liability.
1.3 Discuss the financial goals of a business.
A business is no different to any other economic entity when it comes to the importance of plan­
ning and working towards outcomes. Traditionally business has focused on maximising returns
to shareholders and, while this is still critical, the means of measuring this are varied and not
just simply based on looking at bottom‐line profit. Factors such as the risk accepted in order to
generate a given return, long‐term value versus short‐term profit and the overall sustainability of
the business are also key considerations. Furthermore, the standing of the business in the eyes of
the community (the so‐called social licence) is another key consideration for business and finance
managers to consider.
1.4 Identify the key financial decisions facing the financial manager.
In running a business, the financial manager faces three basic types of decisions: (1) which pro­
ductive assets the company should buy (capital budgeting); (2) how the company should finance
the productive assets purchased (financing decisions); and (3) how the company should manage its
day‐to‐day financial activities (working capital decisions). The financial manager should make these
decisions in a way that maximises the current value of the company’s shares.
MODULE 1 Finance in business 21
1.5 Describe the typical organisation of the financial function in a large company.
In a large company, the financial manager generally goes by the title of chief financial officer.
The CFO reports directly to the company’s CEO. Positions reporting directly to the CFO generally
include the treasurer, the risk manager, the controller and the internal auditor. The audit committee
of the board of directors is also important in relation to the financial function. The committee hires
the external auditor for the company, and the internal auditor, external auditor and compliance
officer all report to the audit committee.
1.6 Discuss the relevance of ethics in business.
If we lived in a world without ethical norms, we would soon discover that it was difficult to do
business. As a practical matter, the law and market forces provide important incentives that foster
ethical behaviour in the business community, but they are not enough to ensure ethical behav­
iour. An ethical culture is also needed, in which people have a set of moral principles — a moral
compass — that help them identify ethical issues and make ethical judgements without being told
what to do.
KEY TERMS
capital markets financial markets where equity and debt instruments with maturities of greater than
1 year are traded
capital structure the mix of debt and equity that is used to finance a company
chief financial officer (CFO) the most senior financial manager in a company
company an independent legal entity able to do business in its own right; in a legal sense, it is a
‘person’ distinct from its owners
finance both the study of money management and the process of acquiring needed financial
resources
information asymmetry situation in which one party in a business transaction has information that is
unavailable to the other parties in the transaction
insolvency the inability to pay debts when they are due
limited liability the legal liability of a limited partner or shareholder in a business, which extends only
to the capital contributed or the amount invested
markets a medium that allows buyers and sellers of a specific service or good to transact
money a medium of exchange of value between parties
net working capital the dollar difference between current assets and current liabilities
partnership two or more owners who have joined together legally to manage a business and share in its
profits
productive assets the tangible and intangible assets a company uses to generate cash flows
public company a company that lists on a stock exchange, such as the ASX, in which large amounts
of debt and equity are publicly traded
residual cash flows the cash remaining after a company has paid operating expenses and what it
owes creditors and in taxes; can be paid to the owners as a cash dividend or reinvested in the
business
sole trader a business owned by a single individual
stakeholder anyone other than an owner (shareholder) with a claim on the cash flows of a company,
including employees, suppliers, creditors and the government
wealth the economic value of the assets someone possesses
22 Finance essentials
ENDNOTES
1. Reserve Bank of Australia, 2016, www.rba.gov.au/statistics/tables.
2. ibid.
3. Coleman, D 2012, ‘Telstra announces its capital management strategy, expected excess free cash of $2 to 3 billion over the next
three years and its NBN plans’, media release, Telstra Limited, Melbourne, 19 April, www.telstra.com.au.
4. ABC News 2012, ‘Hope for Storm investors’ payout to top $1b’, 15 August, www.abc.net.au.
5. Butler, B 2011, ‘ASIC reveals case on Opes Prime collapse’, The Age, 1 March, www.theage.com.au.
6. Australian Securities & Investments Commission (ASIC) 2009, ‘Parliamentary inquiry into financial products and services in
Australia’, 18 August, https://storm.asic.gov.au/storm/storm.nsf/byheadline/parliamentaryInquiry?opendocument.
7. Joint Accounting Bodies 2008, ‘Independence guide: Interpretations in a co‐regulatory environment’, version 3, June,
www.charteredaccountants.com.au.
ACKNOWLEDGEMENTS
Photo: © John Lamb / Getty Images
Photo: © wavebreakmedia / Shutterstock.com
Photo: © marekuliasz / Shutterstock.com
MODULE 1 Finance in business 23
MODULE 2
The financial system
LEA RN IN G OBJE CTIVE S
After studying this module, you should be able to:
2.1 discuss the primary role of the financial system in the economy, and how fund transfers take place
2.2 describe the primary, secondary and money markets, and explain why these markets are so important
to businesses
2.3 explain how financial institutions serve consumers and small businesses that are unable to participate
in the direct financial markets, and describe how companies use the financial system
2.4 discuss the internationalisation of financial markets and the role played by the BIS in ensuring the
global financial markets remain stable
2.5 explain what an efficient capital market is and why market efficiency is important to financial managers.
Module preview
Previously we identified three kinds of decisions that financial managers make: capital budgeting
decisions, which concern the purchase of capital (non‐current) assets; financing decisions, which concern how these assets will be paid for; and working capital management decisions, which concern day‐
to‐day financial matters such as having enough cash for payment of bills and invoices. Making sound
decisions in any of these areas requires knowledge of financial markets and the services offered by
institutions involved in these markets.
In making capital budgeting decisions, financial managers should select projects whose cash flows
increase the value of the company. The financial models used to evaluate these projects require
an understanding of and inputs from financial markets and interest rates. In making financing
decisions, financial managers naturally want to obtain capital at the lowest possible cost, which means
that they need to know how financial markets work and what financing alternatives are available.
Finally, working capital management is concerned with making sure that a company has enough
money to pay its bills when they are due and how it invests its spare cash, if any, to earn a return
(e.g. interest).
Clearly, then, financial managers need to have a good knowledge of financial markets and financial
institutions. This module provides a quick overview of the financial sector and the services it provides
to businesses. The financial system works properly when consumers receive the highest possible interest
rates for their deposits and when only loans with favourable rates of return and good credit standing are
financed. The more efficient and competitive the financial system, the more likely this is to happen. We
will revisit many of the topics covered here in later modules.
We begin the module by looking at how the financial system facilitates the transfer of money from
those who have it to those who need it. Then we describe direct financing, through which large companies
finance themselves by issuing debt and equity, and the important role that investment banks play in the
process. Next we explain why smaller companies and consumers must finance themselves indirectly by
borrowing from financial institutions such as commercial banks. We then examine other types of services
that financial institutions provide to large and small businesses, and the internationalisation of financial
markets. Finally, we discuss the concept of efficient capital markets and explain why market efficiency is
important to financial managers.
MODULE 2 The financial system
25
2.1 The financial system
LEARNING OBJECTIVE 2.1 Discuss the primary role of the financial system in the economy, and how
fund transfers take place.
The financial system consists of financial markets and financial institutions. These markets and institutions provide the structure to the financial system. Financial market is a general term that includes a
number of different types of markets (e.g. money market, capital market) for the creation and exchange
of financial assets, such as loans, bonds and shares. Financial institutions are companies such as commercial banks, credit unions, insurance companies, superannuation funds and finance companies that provide
financial services to the economy. The distinguishing feature of financial institutions is that they invest
their funds in financial assets, such as business loans, shares and bonds, rather than real assets, such as
property, plant and equipment.
The critical role of the financial system in the economy is to gather money from people and businesses
with surplus funds and channel the gathered money to those who need it. Businesses need money for day‐to‐
day expenses or to invest in new productive assets to expand their operations. Consumers too, need money,
which they use to purchase things such as houses, cars and boats — or to pay university fees. Some of the
players in the financial system are household names, such as the Commonwealth Bank of Australia (a commercial bank), Macquarie Bank Limited (a merchant bank), QBE Insurance Group Limited (an insurance
company), AMP Limited (a wealth management/advice business) and the Australian Securities Exchange
(ASX) (a capital market). Others are less well‐known but important companies such as the superannuation
company AustralianSuper.
A well‐developed financial system is critical for the operation of a complex economy such as that of
Australia. An economy cannot function efficiently without a competitive and sound financial system that
gathers money and channels it into the best investment opportunities. Let’s look at a simple example to
illustrate how the financial system channels money to businesses.
The financial system at work
Suppose you are a university student. Assume at the beginning of the university year, you receive $10 000
from your parents to help pay your expenses for the year, but you need only $5000 for the first semester.
You wisely decide to invest the remaining $5000 for a short time to earn some interest income. After
shopping at several banks near your campus, you decide that the best deal is a $5000 term deposit that
matures in 3 months and pays 5 per cent interest.
The bank pools your money with funds from other term deposits and uses this money to make business and consumer loans. In this case, assume that the bank makes a loan to the pizza restaurant near
campus: $30 000 for 5 years at a 9 per cent interest rate. The bank decides to make the loan because of
the pizza restaurant’s sound credit rating and because it expects the pizza restaurant to generate enough
cash flows to repay the loan. The pizza restaurant owner wants the money to invest in additional assets
to earn greater returns (net cash inflows) and thereby increase the value of the business. During the same
week, the bank makes loans to other businesses and also rejects a number of loan requests because the
potential borrowers have poor credit ratings or the proposed projects have low rates of return.
From this example, we can draw some important inferences about financial systems.
•• If the financial system is competitive, the interest rate the bank pays on term deposits will be at or near
the highest rate that you can earn on a term deposit of similar maturity and risk. At the same time,
the pizza restaurant and other businesses will have borrowed at or near the lowest possible interest
cost, given their risk profiles (i.e. given how risky their businesses are). Competition among banks for
deposits will drive term‐deposit interest rates up and loan interest rates down.
•• The bank gathers money from you and other consumers in small dollar amounts, aggregates it and
then makes loans in much larger dollar amounts. Saving by consumers in small dollar amounts is the
origin of much of the money that funds large business loans in the economy.
26 Finance essentials
•• An important function of the financial system is to direct money to the best investment opportunities
in the economy. If the financial system works properly, only business projects with high rates of
return and good credit standing are financed. Those with low rates of return or poor credit standing
will be rejected. Thus, financial systems contribute to higher production and efficiency in the overall
economy.
•• A key role of the financial system is allowing for financial risk to be managed and/or transferred to
other parties. This provides various mechanisms to financial system participants: systems to manage
the risks they are exposed to, including insurance products, securitisation (packaging like assets and
selling them on to a third party) and derivative products (discussed later in this module).
•• Finally, note that the bank has earned a profit from the deal. The bank has borrowed money at
5 per cent by selling term deposits to consumers and has lent money to the pizza restaurant and other
businesses at 9 per cent. Thus, the bank’s gross profit is 4 per cent (9 − 5), which is the difference
between the bank’s lending and borrowing (deposit) rates. Banks earn much of their profits from the
spread between the lending and borrowing rates.
How funds flow through the financial system
We have seen how banks, an example of an institution in the financial system, play a critical role in
the economy. The system moves money from lender‐savers (whose income exceeds their spending)
to borrower‐spenders (whose spending exceeds their income), as shown schematically in figure 2.1.
Lender‐savers are also called surplus spending units (SSU) and borrower‐spenders are also called deficit
spending units (DSU). The largest lender‐savers in the economy are households, but some businesses
and many state and local governments at times have excess funds to lend to those who need money. The
largest borrower‐spenders in the economy are generally businesses, followed by the Commonwealth
Government.
FIGURE 2.1
The flow of funds through the financial system
Direct financing
Financial markets
Lender-savers
• Consumers
• Businesses
• Government
Wholesale markets for the creation
and sale of financial securities, such as shares,
bonds and money market instruments. Large
corporations use the financial markets to sell
securities directly to lenders.
Funds
Borrower-spenders
Funds
Funds
• Consumers
• Businesses
• Government
Financial institutions
Funds
Institutions, such as commercial
banks, that invest in financial assets and
provide financial services. Financial
institutions collect money from lender-savers
in small amounts, aggregate the funds, and
make loans in larger amounts to consumers,
businesses and government.
Funds
Indirect financing
MODULE 2 The financial system
27
The arrows in figure 2.1 show that there are two basic mechanisms by which funds flow through the
financial system: (1) funds can flow directly through financial markets (the route at the top of the diagram), wherein lender‐savers invest directly in financial securities; and (2) funds can flow indirectly
through financial institutions (the route at the bottom of the diagram), wherein the financial institutions
mediate between lender‐savers and borrower‐spenders. In the following sections, we look more closely
at the direct flow of funds and at the financial markets. After that, we discuss financial institutions and
the indirect flow of funds.
Direct financing
In direct transactions, the lender‐savers and the borrower‐spenders deal ‘directly’ with one another:
borrower‐spenders sell securities, such as shares and bonds, to lender‐savers in exchange for money.
These securities represent claims on the borrowers’ future income or assets. A number of interchangeable
terms are used to refer to securities, including financial instruments and financial claims.
The financial markets where direct transactions take place deal with large sums, with a typical
minimum transaction size of $1 million. For most companies, these markets provide funds at the lowest
possible cost. The major buyers and sellers of securities in the direct financial markets are: commercial
banks; other financial institutions, such as insurance companies and finance companies; large business
companies; the Commonwealth Government; hedge funds; and some wealthy individuals. Even not‐so‐
wealthy people buy and sell shares in the share market. It is important to note that financial institutions
are major buyers of securities in the direct financial markets. For example, superannuation funds buy
large quantities of corporate bonds and shares for their investment portfolios. In figure 2.1 the arrow
leading from financial institutions to financial markets depicts this flow.
Although individuals participate in direct financial markets, they can also gain access to many of the
financial products produced in these markets through retail channels at investment banks or financial
institutions such as commercial banks (the lower route in figure 2.1). For example, individuals can buy
or sell shares and bonds in small dollar amounts at Macquarie Bank Limited or from the Commonwealth
Bank’s retail brokerage business, Commonwealth Securities Limited (CommSec). We discuss indirect
financing through financial institutions later in this module.
A direct financing transaction (without using the market)
Let’s look at a typical direct market transaction. When managers decide to engage in a direct market
transaction, they often have a specific capital project in mind that needs financing, such as building
a new shopping centre. Suppose that the Westfield Group needs $200 million to build a new centre
and decides to fund it by selling long‐term bonds with a 15‐year maturity. Say that Westfield contacts
a superannuation fund, which expresses an interest in buying Westfield’s bonds. The superannuation
fund will buy Westfield’s bonds only after determining that the bonds are priced fairly for their level
of risk and the interest rate they carry. Westfield will sell its bonds to the superannuation fund only
after studying the current bond market to be sure the price offered by the superannuation fund is
competitive.
If Westfield and the superannuation fund strike a deal, the flow of funds between them will be as
shown below:
$200 million
Superannuation fund
Westfield group
$200 million debt
28 Finance essentials
Assume that Westfield sells its bonds to the superannuation fund for $200 million and gets the use of the
money for 15 years. For Westfield, the bonds are a liability, and it pays the bondholders interest for use
of the money and pays back the $200 million principal on maturity (in 15 years). For the superannuation
fund, the bonds are an asset, which earns interest. The superannuation fund also owns a financial claim
for the $200 million principal.
Direct financing (using the market)
To raise finance, companies can issue their own securities (e.g. bonds and shares) in the financial market,
particularly in the capital market. For example, to raise $200 million Westfield could issue bonds or shares
in the capital market (i.e. through the ASX). To issue securities to the market, a company needs to follow
a rigorous process, including issuing a public document called a prospectus. Typically companies need
help from experts to organise, issue and sell securities in the market.
Investment banks and direct financing
An important player in delivering critical services to companies that sell securities in the direct financial markets is an investment bank. Investment banks specialise in helping companies sell new debt or
equity, although they also provide other services, such as the broker and dealer services discussed later.
When investment bankers help companies bring new debt or equity securities to market, they perform
two important tasks: origination and underwriting.
Origination
Origination is the process of preparing a security issue for sale. During the origination phase, the investment banker may help the client company determine the feasibility of the project being funded and the
amount of capital that needs to be raised. Once this is done, the investment banker helps secure a credit
rating if needed, determines the sale date, obtains legal clearances to sell the securities and gets the
securities printed or created. If securities are to be sold in the public markets, the issuer must also lodge
a prospectus with the Australian Securities and Investments Commission (ASIC). Securities sold in
private are not required by ASIC to lodge a prospectus.
Underwriting
Underwriting is the process by which the investment banker, the underwriter, guarantees that the company will raise the funds it expects from its new security issue. In the most common type of underwriting
arrangement, called stand‐by underwriting, the investment banker guarantees to the company that the
total funds that the company plans to raise by issuing new securities will be raised. The guarantee of
the total amount of funding is important to the issuing company. It is likely that the company needs a
specific amount of money to pay for a particular project or to fund operations, and receiving anything
less than this amount will pose a serious problem. As you would expect, financial managers almost
always prefer to have their new security issues underwritten on a stand‐by basis. Stand‐by underwriting
is known as ‘firm commitment underwriting’ in the rest of the world.
Under a stand‐by underwriting arrangement, the investment banker will purchase any securities that
are not sold from the issue at the offer price. Later, it will resell these shares in the market at the prevailing market price. The underwriter bears the risk that the resale price might be lower than the price
the underwriter paid to the issuing company — this is called price risk. The resale price can be lower if
the investment banker overestimates the value of the shares when determining the initial offer price of
the issue. If this happens, the investment bank suffers a financial loss.
The investment banker’s compensation for underwriting is called the underwriting spread. This
is the difference between the price the investment banker pays for the security and the initial sale
price.
MODULE 2 The financial system
29
DEMONSTRATION PROBLEM 2.1
Underwriter’s compensation
Problem:
Assume Harvey Norman needs to raise $500 million for
an expansion and decides to issue long‐term bonds.
The financial manager hires an investment bank to help
design the bond issue and to underwrite it. The issue
consists of 500 000 bonds with a face value of $1000
each and the investment banker agrees to underwrite
the entire issue on a stand‐by basis, effectively
guaranteeing Harvey Norman a price of $1000 per bond.
The issue raises a total of $520 million at an initial sale
price of $1040 per bond. What is the underwriter’s total
compensation and per‐bond compensation?
Approach:
The underwriter’s total compensation is the total underwriting spread, which is the difference between
the total amount raised by selling the bonds in the market and the total amount guaranteed to the
company by the underwriter. The underwriting spread per bond is then calculated by dividing the total
underwriting spread by the number of bonds that are issued.
Solution:
Step 1: Calculate the total underwriting spread:
$520 000 000 − $500 000 000 = $20 000 000
Step 2: Calculate the underwriting spread per bond:
$20 000 000/500 000 = $40
Note that, because of the guarantee, the issuer gets a cheque from the underwriter for $500 million
regardless of the price at which the bonds are sold.
BEFORE YOU GO ON
1. What essential role does the financial system play in the economy?
2. What are the two basic ways in which funds flow through the financial system from lender‐savers
to borrower‐spenders?
2.2 Financial markets
LEARNING OBJECTIVE 2.2 Describe the primary, secondary and money markets, and explain why these
markets are so important to businesses.
Financial markets are just like any kind of market you have seen before: people buy and sell, haggle
and argue, win and lose, and, yes, some may become rich playing the financial markets while others
may lose it all. Markets can be informal, like a flea market in your community, or highly organised and
structured, like the gold markets in London or Zurich. The only difference is that in financial markets,
people buy and sell financial instruments, such as stocks, bonds, futures contracts or mortgage‐backed
securities. In this section, we turn our attention to several types of financial markets.
30 Finance essentials
Types of financial markets
We have seen that direct and indirect flows of funds occur in financial markets. However, as already
mentioned, financial market is a very general term; in fact, it is a broad concept that covers all forms of
markets that deal with short‐term and long‐term funds. When the focus is on short‐term funds, such a
market is called a money market. In contrast, when the focus is on the long‐term funds, such a market
is called a capital market. The same institution may be involved in both the money market and the
capital market. A complex industrial economy such as ours includes many different types of financial
markets and institutions involved in direct and indirect financing. Next, we examine some widely used
classifications of financial markets. Note that these classifications overlap to a large extent.
Primary and secondary markets
A primary market is any market where companies initially sell new security issues (debt or equity).
Suppose Wesfarmers Limited needs to raise $100 million for a business expansion and decides to raise
the money through the sale of ordinary shares. The company will sell the new equity issue (ordinary
shares) in the primary market for corporate shares — probably with the help of an underwriter, as discussed in the previous section. When such issues are open to the public, they are called initial public
offerings (IPOs). The primary market may be a wholesale market where the sales take place outside the
public view.
A secondary market is any market where owners of securities (i.e. those who have already bought the
securities) can sell them to other investors. Securities already issued (i.e. outstanding securities) are bought
and sold in the secondary market. When securities are bought and sold in the secondary market, the original issuers (i.e. the companies that issued these securities in the primary market) do not receive any money.
Conceptually, secondary markets are like used‐car markets in that they allow the current owners of the cars
to sell second‐hand cars. Car manufacturing companies do not receive any money from transactions in the
used‐car market. Secondary markets for securities are important because they enable investors to buy and sell
securities (e.g. shares, bonds) as frequently as they want. As you might expect, investors are willing to pay
higher prices for securities that have active secondary markets, compared to similar securities which do not
have active secondary markets. Secondary markets are important to companies as well, because investors are
willing to pay higher prices for securities in primary markets if the securities have active secondary markets.
Thus, companies whose securities have active secondary markets enjoy lower funding costs (i.e. they raise
funds at a lower cost) than similar companies whose securities do not have active secondary markets.
An important characteristic of a security to investors is its marketability. Marketability is the ease with
which a security can be sold and converted into cash. A security’s marketability depends on whether buyers
for the security are readily available, and also on the costs of trading and searching for information, so‐called
transaction costs. The lower the transaction costs, the greater a security’s marketability. Because secondary
markets make it easier to trade securities, their existence increases a security’s marketability.
A concept closely related to marketability is liquidity. Liquidity is the ability to convert an asset into
cash quickly without loss of value. In common use, the terms marketability and liquidity are often used
interchangeably, but they are different. Liquidity implies that when the security is sold, its value will be
preserved; marketability does not carry this implication.
Two types of market specialists facilitate transactions in secondary markets. Brokers are market
specialists who bring buyers and sellers together for a sale to take place. They execute the transaction
for their clients (the buyers and the sellers) and charge a fee from both buyers and sellers for their services. They bear no risk of ownership of the securities during the transactions; their only service is that
of ‘matchmaker’. In Australia, CommSec is a well‐known broker.
Dealers, in contrast, ‘make markets’ for securities and do bear risk. They make a market for a security
by buying and selling from an inventory of securities they own. Dealers make their profit, just as retail
merchants do, by selling securities at a price above what they paid for them. The risk that dealers bear is
price risk, which is the risk that they will sell a security for less than they paid for it.
MODULE 2 The financial system
31
Exchanges and over‐the‐counter markets
Financial markets can be classified as either organised markets (more commonly called exchanges) or
over‐the‐counter (OTC) markets. Traditional exchanges, such as the ASX, provide a platform and facilities for members to buy and sell securities or other assets (such as commodities) under a specific set
of rules and regulations. All members of the ASX are brokers. Only members can use the exchange to
facilitate their clients’ transactions (buying and selling of securities).
Securities not listed on an exchange are bought and sold in OTC markets. These differ from organised exchanges in that the ‘market’ has no central trading location. Instead, investors can execute OTC
transactions by visiting or telephoning an OTC dealer or by using a computer‐based electronic trading
system linked to the OTC dealer. Traditionally, shares traded over the counter have been those of small
and relatively unknown companies, most of which would not qualify to be listed on a major exchange.
Money and capital markets
Money markets are where short‐term debt instruments, those which have maturities of less than 1 year,
are sold. Money markets are wholesale markets in which the minimum transaction is $1 million and
transactions of $100 million are not uncommon. Money market instruments are lower in risk than other
securities because of their high liquidity and low default risk. In fact, the term ‘money’ market is used
because these instruments are close substitutes for cash. The most important and largest money markets
are in New York, London and Tokyo. Figure 2.2 lists the most common money market instruments and
the dollar amounts outstanding.
Large companies use money markets to adjust their liquidity positions. Liquidity, as mentioned, is the
ability to convert an asset into cash quickly without loss of value. Liquidity problems arise because cash
receipts and expenditures of companies are rarely perfectly synchronised. For example, expenditures
may have to be paid before a company can collect money from its customers. To manage a temporary
cash shortfall, a company can raise cash overnight by selling money market instruments from its portfolio. In contrast, if a company has a temporary cash surplus, it can invest such money in short‐term
money market instruments without keeping the surplus money idle.
Recall from module 1 that capital markets are markets where intermediate‐term and long‐term debt
and corporate shares are traded. In these markets, companies raise funds to finance capital assets, such as
property, plant and equipment. The ASX as well as the New York, London and Tokyo stock exchanges
are capital markets. Figure 2.2 lists the major Australian capital market instruments and the dollar
amounts outstanding. Compared with money market instruments, capital market instruments carry more
default risk and have longer maturities.
FIGURE 2.2
Selected money market and capital market instruments, June 2016 ($billions)1
Money market instruments
Treasury notes
Bank certificates of deposit, bank bills and commercial paper
$  23.8
263.5
Capital market instruments
Treasury bonds
State government bonds
Corporate bonds
Corporate bonds issued offshore
Corporate equity (at market value)
Eurobonds
Residential mortgage securities
$ 641.0
8.0
512.1
553.8
1619.7
50.8
114.1
he figure shows the size of the Australian market for some of the most important money and capital market instruments.
T
Compared with money market instruments, capital market instruments have longer maturities and higher default risk.
32 Finance essentials
Public and private markets
Public markets are organised financial markets where members of the general public buy and sell
securities through their stockbrokers. The ASX, for example, is a public market. ASIC regulates public
securities markets in Australia. This body is responsible for overseeing the securities industry and regulating all primary and secondary markets in which securities are traded. Most companies want access
to the public markets, because they can sell their securities at competitive prices and raise funds at
the lowest possible cost. The downside for companies selling in the public markets is that they have
to comply with the various ASIC regulations. The cost of such compliance can be significant.
In contrast to public markets, the private market involves direct transactions between two parties.
Transactions in a private market are often called private placements. In a private market, a company
contacts investors directly and negotiates a deal to sell them all or part of a security issue. Larger companies may be equipped to handle these transactions themselves. Smaller companies are more likely
to use the services of an investment bank, which will help locate investors, help negotiate the deal and
handle the legal aspects of the transaction. Major advantages of a private placement are the speed at
which funds can be raised and low transaction costs. Downsides are that privately placed equity dilutes
the value of shares owned by existing shareholders because private placements are normally placed at a
discount to the current market price of the security; further, the dollar amounts that can be raised from
private placements tend to be smaller.
Futures and options markets
Markets also exist for trading in futures and options. Perhaps the best‐known futures markets
are the New York Board of Trade and the Chicago Board of Trade. In Australia, the ASX conducts the
markets for futures and options, following the merger with the Sydney Futures Exchange in 2008. These
securities are listed on the ASX 24 market and traded on ASX Trade24,2 the ASX’s proprietary trading
platform.
Futures and options are often called derivative securities because they derive their value from some
underlying asset. Futures contracts are contracts for the future delivery of such assets as securities,
foreign currencies, interest cash flows or commodities. Companies use these contracts to reduce (hedge)
risk exposure caused by fluctuations in things such as foreign exchange rates or commodity prices. We
discuss this use of futures contracts further in the module on financial markets.
Options contracts call for one party (the option writer) to perform a specific act if called upon to do
so by the option buyer or owner. Options contracts, like futures contracts, can be used to hedge risk in
situations where a company faces risk from price fluctuations. Options are also discussed in more detail
in the module on financial markets.
Foreign exchange markets
Foreign currencies are bought and sold in the foreign exchange markets. Foreign currencies such
as the US dollar, the UK pound, the yen and the euro are traded against the Australian dollar or
against other foreign currencies. They are traded either for spot or forward delivery over the counter
at large commercial banks or investment banking firms. Futures contracts for foreign currencies
are traded on organised exchanges such as the ASX, New Zealand Futures and Options Exchange
(NZFOX) and Hong Kong Stock Exchange (HKE). There are three important reasons for the
development of foreign exchange (FX) markets. First, they provide a mechanism for transferring
purchasing power from one currency to another. Second, FX markets provide a means for passing
the risk associated with changes in exchange rates to professional risk‐takers. Third, FX markets
facilitate the provision of credit internationally. FX markets are discussed further in the module on
financial markets.
MODULE 2 The financial system
33
BEFORE YOU GO ON
1. What is the difference between primary and secondary markets?
2. How and why do large companies use money markets?
3. What are capital markets and why are they important to companies?
2.3 Financial institutions
LEARNING OBJECTIVE 2.3 Explain how financial institutions serve consumers and small businesses
that are unable to participate in the direct financial markets, and describe how companies use the
financial system.
As mentioned earlier, many companies are too small to sell their debt or equity directly to investors.
They have neither the expert knowledge nor the reputation and money to transact in wholesale markets.
When these companies need funds for capital investments or liquidity adjustments, their only choice
may be to borrow in the indirect market from financial institutions. These financial institutions act as
intermediaries, converting financial instruments with one set of characteristics into instruments with
another set of characteristics. This process is called financial intermediation. The hallmark of indirect
financing is that a financial institution — an intermediary — stands between the lender‐saver and the
borrower‐spender. This route is shown at the bottom of figure 2.1.
Indirect market transactions
We worked through an example of indirect financing at the beginning of the module. In that scenario, a
university student had $5000 to invest for 3 months. A bank sold the student a 3‐month term deposit for
$5000, pooled this $5000 with the proceeds from other term deposits and used the money to make small‐
business loans, one of which was a $30 000 loan to our pizza restaurant owner. Following is a schematic
diagram of that transaction:
Pizza restaurant’s
loan
Pizza restaurant
$30 000
Commercial
bank
(intermediary)
Sells term deposits
Cash
Investors and
depositors
The banks raise money by selling financial instruments, such as cheque accounts, savings accounts,
term deposits and various securities, and then use the money to make loans to businesses or consumers.
On a smaller scale, both superannuation funds and insurance companies provide a significant portion
of the long‐term financing in the Australian economy through the indirect finance market. Superannuation funds collect individuals’ contributions and then invest into the money market and the long‐term
equity and bond market. Insurance companies also invest into debt and equity securities using the funds
that they receive when they sell insurance policies to individuals and businesses. The schematic diagram
for intermediation by an insurance company is as follows:
Issues debt or equity
Company
Cash
Insurance
company
(intermediary)
Sells policies
Cash
Investors and
policyholders
Note an important difference between the indirect and direct financial markets. In the direct market,
as securities flow between lender‐savers and borrower‐spenders, the form of the securities remains
34 Finance essentials
unchanged. In the indirect market, however, as securities flow between lender‐savers and borrower‐
spenders, they are repackaged and their form is changed. In the example above, money from the sale
of insurance policies becomes investments in debt or equity. By repackaging securities, financial intermediaries tailor‐make a wide range of financial products and services that meet the needs of consumers,
small businesses and large companies. Their products and services are particularly important for smaller
businesses that do not have access to direct financial markets. The benefits of financial intermediation
include:
•• denomination divisibility: financial intermediaries are able to produce a wide range of denominations
from $1 to many millions by pooling the funds of many individuals and investing them in direct
securities of varying sizes
•• currency transformation: financial intermediaries help finance the global expansion of Australian
companies by buying financial claims denominated in one currency and selling financial claims
denominated in other currencies
•• maturity flexibility: financial intermediaries are able to create securities with a wide range of maturities
from 1 day to more than 30 years
•• credit risk diversification: by purchasing a wide variety of securities, financial intermediaries are able
to spread risk
•• liquidity: most commodities produced by intermediaries are highly liquid, so they are able to be
converted into money quickly with minimal transaction cost.
Somewhat surprisingly, the indirect markets are a much larger and more important source of financing
to businesses than the more newsworthy direct financial markets, such as share markets. This is true not
only in Australia, but in all countries.
Financial institutions and their services
We have briefly discussed the role of financial institutions as intermediaries in the indirect financial
market. Next, we look at various types of financial institutions and the services they provide to small
businesses as well as large companies. We discuss only financial institutions that provide a significant
amount of services to businesses.
Commercial banks
Commercial banks are the most prominent and largest financial intermediaries in the economy, and offer
the widest range of financial services to businesses. Nearly every business, small or large, has a significant
relationship with a commercial bank — usually a cheque or transaction account and also some type of credit
or loan arrangement. For businesses, the most common type of bank loan is a line of credit (often called an
overdraft), which works much like a credit card. A line of credit is a commitment by a bank to lend a company an amount up to a predetermined limit, which can be used as needed. Banks also make term loans,
which are fixed‐rate loans with a typical maturity of 1 year to 10 years. In addition, banks do a significant
amount of equipment lease financing. A lease is a contract that gives a business the right to use an asset, such
as a truck or a photocopier, for a period of time in exchange for payments.
Life and general insurance companies
Two types of insurance companies are important in the financial markets: (1) life insurance companies;
and (2) general insurance companies, which sell protection against loss of property from fire, theft,
accidents and other predictable causes. The cash flows for both types of companies are fairly predictable. As a result, they are able to provide funding to companies through the purchase of shares and
bonds in the direct finance markets, as well as funding for private companies through private placement
financing. Businesses of all sizes often purchase life insurance programs as part of their employee benefit packages, and purchase general insurance policies to protect physical assets such as cars, truck fleets,
equipment and entire plants.
MODULE 2 The financial system
35
Superannuation funds
Superannuation is Australia’s retirement savings scheme whereby employers are required to contribute
9.5 per cent of an employee’s salary to a complying superannuation fund. Superannuation funds then
invest these contributions in financial market securities on behalf of the employees. Superannuation
funds receive contributions during an employee’s working years and then provide a lump sum payment
and/or monthly cash payments (a pension or an annuity) to the employee on retirement. Because of the
predictability of these cash flows, superannuation fund managers invest in money market securities and
capital market securities (bonds and shares) and also participate in the private placement market.
Investment funds
Investment funds, such as retail funds, sell shares to investors and use the funds to purchase a wide variety of direct and indirect financial instruments. As a result, they are an important source of business
funding. For example, retail funds may focus on purchasing: (1) equity or debt securities; (2) securities
of small or medium‐sized companies; (3) securities of companies in a particular industry, such as energy,
computer or information technology; or (4) foreign investments.
Finance companies
Finance companies, such as Esanda Limited, obtain the majority of their funds by selling short‐term
debt, called commercial paper, to investors in direct credit markets. These funds are used to make
a variety of short‐term and intermediate‐term loans and leases to individuals and to small and large
businesses. The loans are often secured by accounts receivable or inventory. Finance companies are
typically more willing than commercial banks to make loans and leases to companies with higher levels
of default risk.
Financial planning practices
Financial planning practices,3 such as AMP Limited, are run by qualified investment professionals who
assist individuals and corporations to meet their long‐term financial goals by analysing each client’s
36 Finance essentials
financial status and setting a program to achieve their goals. Financial planners specialise in wealth
management, tax planning, asset allocation, risk management, retirement and estate planning services.
Risks faced by financial institutions
Financial institutions, in providing financial intermediation services to consumers and businesses, must
transact in the financial markets. They intermediate between savers, or surplus spending units (SSUs),
and borrowers, or deficit spending units (DSUs), in the hope of earning a profit by acquiring funds at
interest rates that are lower than those they charge when they sell their financial products. But there is
no free lunch here. The differences in the characteristics of the financial claims that financial institutions
buy and sell expose them to a variety of risks in the financial markets. The global financial crisis (GFC)
in 2007–09 testifies to the importance of successfully managing these risks: the plethora of institutions
that either failed or survived only due to significant government bailouts demonstrate this. Managing
the risks does not mean eliminating them: there is a trade‐off between risk and higher profits. Managers
who take too few risks sleep well at night, but eat poorly. Their slumber reaps a reward of declining
earnings and stock prices that their shareholders will not tolerate for long. On the other hand, excessive
risk‐taking — betting the bank and losing — is also bad news. It will place you in the ranks of the
unemployed with an armada of expensive lawyers defending you.
In their search for higher long‐term earnings and stock values, financial institutions must manage and
balance five basic risks: credit, interest rate, liquidity, foreign exchange and political risk. Each of these
risks is related to the characteristics of the financial claim (e.g. term to maturity) or to the issuer (e.g. default
risk). Each must be managed carefully to balance the trade‐off between future profitability and potential
failure. For now, this section summarises nine risks and briefly discusses how they affect the management
of financial institutions in order to provide a frame of reference for other topics in the modules.
Credit risk
When a financial institution makes a loan or invests in a bond or other debt security, the institution bears
credit risk (or default risk) because it is accepting the possibility that the borrower will fail to make
either interest or principal payments in the amount and at the time promised. To manage the credit risk
of loans or investments in debt securities, financial institutions should diversify their portfolios, conduct
careful credit analysis of potential borrowers to measure default risk exposure, and monitor borrowers
over the life of the loan or investment to detect any critical changes in financial health, which is just
another way of expressing the borrowers’ ability to repay the loans.
Interest rate risk
Interest rate risk is the risk of fluctuations in a security’s price or reinvestment income caused by
changes in market interest rates. In other words, a change in interest rates will alter forecast cash flows
and affect the value of interest rate–sensitive assets and liabilities. For example, if a bank issues fixed‐
rate loans and then interest rates go up, the value of the loans will decline because the bank could have
been receiving higher returns from other loans and the cost of replacing the issued funds will be higher.
The concept of interest rate risk is applicable not only to loans but also to a financial institution’s balance
sheet. Financial institutions are exposed to interest rate risk whenever they plan to borrow or lend at a
variable rate. Interest rate risk may affect a significant proportion of a financial institution’s assets and
liabilities, making it a serious issue.
Liquidity risk
Liquidity risk is the risk that a financial institution will be unable to generate sufficient cash inflow
to meet required cash outflows. Liquidity is critical to financial institutions: banks and other authorised deposit‐taking institutions (ADIs) need liquidity to meet deposit withdrawals and to pay off other
liabilities as they come due; superannuation funds need liquidity to meet contractual superannuation
payments; and life insurance companies need liquidity to pay death benefits. Liquidity also means that
MODULE 2 The financial system
37
an institution need not pass up a profitable loan or investment opportunity because of a lack of cash. If a
financial institution is unable to meet its short‐term obligations because of inadequate liquidity, the firm
will fail even though over the long run it is profitable.
Foreign exchange risk
Foreign exchange risk is the fluctuation in the earnings or value of a financial institution that arises
from changes in exchange rates. Many financial institutions deal in foreign currencies either on their own
account or for their customers. Also, financial institutions invest in the direct credit markets of other countries and sell indirect financial claims overseas. Because of changing international economic conditions
and the relative supply and demand of local and foreign currencies, the rates at which foreign currencies
are converted into Australian dollars change. These changes can cause gains or losses in the currency
positions of financial institutions and the Australian‐dollar values of non‐Australian financial investments.
Political risk
Political risk is the risk of fluctuation in the value of a financial institution resulting from the actions
of Australian or foreign governments. Domestically, if the government changes the regulations faced by
financial institutions, their earnings or values are affected. Internationally, the concerns are much more
dramatic, especially when institutions consider lending in developing countries without stable governments or well‐developed legal systems. Governments can repudiate (i.e. cancel) foreign debt obligations.
Repudiations are rare, but less rare are debt reschedulings, in which foreign governments declare a moratorium on debt payments and then attempt to renegotiate more favourable terms with the foreign lenders.
In either case, the lending institution is left ‘holding the bag’. To grow and be successful in the international arena, managers of financial institutions must understand how to measure and manage these risks.
Reputational risk
Reputational risk is defined as the potential for negative publicity regarding an institution’s business practices to cause a decline in the customer base, costly litigation or revenue reduction. This is
irrespective of whether the publicity is accurate or not.4 It is no secret that financial institutions, banks in
particular, are not the classroom favourite when it comes to public reputation. This has been exacerbated
as their profits have grown, fees have increased and perceptions of customer service have declined. To
top it off, the huge bonuses and corporate salaries paid by many of these institutions are regarded as
excessive by many. The GFC, which the populist view suggests was caused by greed within the sector,
is another thorn in the sector’s side in this regard.
Environmental risk
Environmental risk issues, such as climate change and environmental litigation, are increasingly being
recognised as key risk factors for financial institutions and their clients. Climate change is seen as one
of the most significant challenges to face business, government and the community in the foreseeable
future.5 While the financial sector is a comparatively low emissions sector, it is accepted that the financial sector will be critical to climate change response due to its role as a provider of capital. In addition,
the effects of climate change (extreme weather patterns, sea level rises and atmospheric changes) on
asset values, business performance and risk will have a material impact on the performance of credit,
investment and insurance portfolios. This will also lead to significant regulatory risk as governments
move to respond to climate change and other environmental concerns.
Operational risk
Financial institutions are often large and complex businesses with billions of dollars in assets and liabilities. They are usually highly geared (i.e. they have a lot of debt in comparison to their assets) and
have investments in risky assets (loans) funded predominantly by short‐term liabilities (deposits). This
complexity and scale create a risk of loss due to the failure or inadequacy of internal systems, people
and processes that should ensure the effective and efficient operation of a financial institution. This
38 Finance essentials
is referred to as operational risk, which is therefore significant in these businesses and needs to be
actively managed and monitored. Indeed, these risks have become increasingly of interest to regulators
in recent decades, and the international capital accords require management of these risks.
Contagion risk
Failure of a financial institution can have significant economic and social consequences. These consequences can reach far beyond the failed institution, given the interdependence between institutions and
the impact that a failure can have on market confidence. The risk of financial difficulties in one organisation spreading to others due to the complex interrelationships between institutions and the nature of
the exchange settlement systems is referred to as contagion risk. Contagion can destabilise the entire
sector, as was seen in the GFC when the US$600 billion‐plus collapse of US investment bank Lehman
Brothers triggered a collapse in an already nervous market. A month later the market closed at a six‐year
low and financial institutions around the globe were in chaos, with government bailout and guarantee
packages stepping in to keep the global system alive, albeit only just. Indeed, the competitive landscape
changed in financial services as a result of the GFC.
Companies and the financial system
We began this module by saying that financial managers need to understand the financial system in order to
make sound decisions. We now follow up on that statement by briefly describing how companies operate
within the financial system. The interaction between the financial system and a large public company is
shown in figure 2.3. The arrows show the major cash flows for a company over a typical operating cycle.
These cash flows relate to some of the key decisions that the financial manager must make. As you know,
these decisions involve three major areas: capital budgeting, financing and working capital management.
FIGURE 2.3
Cash flows between a company and the financial system
Transactions
The financial
system
B
Private
placement of debt
Debt
markets
C
Sale of
commercial paper
Money
markets
D
Bank loans and
lines of credit
E
Sale of shares
The company
Lease
manufacturing
A facility and
equipment
Management
invests in assets:
• Current assets
• Productive assets
Plant
Equipment
Buildings
Technology
Patents
Financial
intermediaries
Equity
markets
G
Cash
inflows
from
operations
H
Cash reinvested
in business
F
Cash
dividend
MODULE 2 The financial system
39
Let’s work through an example using figure 2.3 to illustrate how businesses use the financial system.
Suppose you are the chief financial officer (CFO) of a new high‐tech company with business ties to
Telstra. The new venture has a well‐thought‐out business plan, owns some valuable technology and has
one manufacturing facility. The company is large enough to have access to public markets. The company
plans to use its core technology to develop and sell a number of new products that the marketing
department believes will generate a strong market demand.
To start the new company, management’s first task is to sell equity and debt to finance the expansion of the company. Assume 70 per cent of the long‐term funds will come from an initial public
offering (IPO) of ordinary shares. An IPO is a company’s first offering of its shares to the public. For
example, management hires Macquarie Bank Limited as its investment bank to underwrite the new
securities. After the deal is underwritten, the new venture receives the proceeds from the share sale,
less Macquarie’s fees (see arrow E in figure 2.3). The financial markets module contains a discussion
of the IPO process.
In addition to the equity financing, 30 per cent of the company’s long‐term funds will come
from the sale of long‐term debt through a private placement deal with a large superannuation fund
(see arrow B). Management has decided to use a private placement because the lender is willing to
commit to lending the company additional money in the future if the company meets certain performance goals. Since management has ambitious growth plans, locking in a future source of funds is
important.
Once the long‐term funds from the debt and equity sales are in hand, they are deposited in the com­pany’s
cheque account at a commercial bank. Management then decides to lease an existing manufacturing
facility and equipment to manufacture the new high‐technology products; the cash outflow is represented
by arrow A.
To begin manufacturing, the company needs to raise short‐term funds for the working capital and does
this by: (1) selling commercial paper in the money markets (arrow C); and (2) obtaining a line of credit
from a bank (arrow D). As the company becomes operational, it generates cash inflows from its earning
assets (arrow G). Some of this cash inflow is reinvested in the company (arrow H) and the remainder is
used to pay a cash dividend to shareholders (arrow F).
BEFORE YOU GO ON
1. What is financial intermediation and why is it important?
2. What are some services that commercial banks provide to businesses?
3. What are some of the risks faced by the financial system and the institutions that comprise it?
2.4 International financial markets
LEARNING OBJECTIVE 2.4 Discuss the internationalisation of financial markets and the role played by
the BIS in ensuring the global financial markets remain stable.
Financial markets can be classified as either domestic or international. The most important international
financial markets for Australian firms are the short‐term US market and eurocurrency market, and the
long‐term eurobond market. In these markets, domestic and overseas firms can borrow or lend large
amounts of Australian dollars that have been deposited in overseas banks. These markets are closely
linked to the Australian money and capital markets. Large financial institutions, business firms and institutional investors, both in Australia and overseas, conduct daily transactions between the Australian
domestic markets and the international markets.
40 Finance essentials
Internationalisation of financial markets
It is generally accepted that a strong financial system is a key ingredient of economic prosperity.
Domestic financial markets are, however, part of a global financial system, intermediating borrowing
and lending between the local nation and the rest of the world. This has been necessitated by expanding
international trade and production, and the development of multinational corporations. The rapid development of technology and communication systems has made this growth possible. This places emphasis
on multilateral cooperation between nations and their central banks to ensure that the global financial
system and domestic systems are stable. The Bank for International Settlements (BIS) has become
pivotal in encouraging this cooperation.
International organisations
In addition to the domestic financial institutions discussed, important international organisations play a
significant role in the global financial markets. Examples of these are as follows.
•• The Bank for International Settlements (BIS): the BIS has a mandate to encourage international
monetary and financial cooperation. It also operates as a banker for the central banks of countries
around the world. Furthermore, the BIS plays an important role in helping to maintain the stability of
the global financial system.
•• The World Bank: the World Bank6 is not a bank per se, but an agency of the United Nations that
aims to reduce poverty and improve living standards in developing nations. It has 189 member
nations (including Australia and New Zealand), which jointly finance and allocate its resources. The
‘Bank’ side of the World Bank commonly refers to the International Bank for Reconstruction and
Development and the International Development Association, which are divisions of the World Bank
Group. They provide low‐interest and no‐interest credit and grants to developing countries. With
lending averaging almost US$57 billion per year over the 2012–16 period, the World Bank plays a
major role in the global community.
•• The International Monetary Fund (IMF): the IMF was also established under the United Nations and
has 188 member nations. The role of the IMF is contained in its articles of agreement:7
To promote international monetary cooperation through a permanent institution which provides the
machinery for consultation and collaboration on international monetary problems.
To facilitate the expansion and balanced growth of international trade, and to contribute thereby to the
promotion and maintenance of high levels of employment and real income and to the development of the
productive resources of all members as primary objectives of economic policy.
To promote exchange stability, to maintain orderly exchange arrangements among members, and to
avoid competitive exchange depreciation.
To assist in the establishment of a multilateral system of payments in respect of current transactions
between members and in the elimination of foreign exchange restrictions which hamper the growth of
world trade.
To give confidence to members by making the general resources of the Fund temporarily available to
them under adequate safeguards, thus providing them with opportunity to correct maladjustments in their
balance of payments without resorting to measures destructive of national or international prosperity.
In accordance with the above, to shorten the duration and lessen the degree of disequilibrium in the
international balances of payments of members.
•• The Asian Development Bank (ADB): this is a multilateral development bank that aims to reduce poverty
and improve living conditions and quality of life in the Asia–Pacific region. The ADB has 48 regional
members and 19 non‐regional members. Australia has been a member of the ADB since 1966 and has
contributed 5.80 per cent of the contributed capital.8
MODULE 2 The financial system
41
International assets of Australian institutions
In the Australian financial system, Australian banks have accumulated significant offshore assets and liabilities. As of June 2016, Australian banks had international assets of US$295 billion and international
liabilities of US$615.1 billion, the majority of which are denominated in US$.9 In comparison with
those for other countries that report to the BIS, these figures are not large as a percentage of GDP,
and Australia’s reliance on international funding is more apparent when the net liability position of
Australian banks is considered. Therefore, it is necessary in any study of financial markets and institutions to consider aspects of the international financial system and the importance of globalisation.
BEFORE YOU GO ON
1. What are two of the most important international financial markets for Australian firms?
2. Which international organisations play a significant role in ensuring the stability of the global
financial markets?
2.5 Capital market efficiency
LEARNING OBJECTIVE 2.5 Explain what an efficient capital market is and why market efficiency is
important to financial managers.
Security markets, such as the bond and share markets, help bring buyers and sellers of securities together.
They reduce the cost of buying and selling securities by providing a physical location or computer
trading system where investors can trade securities. The supply and demand for securities are better
reflected in organised markets because much of the total supply and demand for securities flows through
these centralised locations or trading systems. Any price that balances the overall supply and demand for
a security is a market equilibrium price.
42 Finance essentials
Ideally, economists would like financial markets to price securities at their true (intrinsic) value. A
security’s true value is the present value of the cash flows that an investor who owns that security can
expect to receive in the future. This present value, in turn, reflects all available information about the
size, timing and riskiness of the cash flows at the time the price was set. As new information becomes
available, investors adjust their cash flow estimates through buying and selling, and the price of a security
adjusts to reflect this information.
Markets such as those just described are called efficient capital markets. More formally, in an efficient
capital market security prices fully reflect the knowledge and expectations of all investors at a particular point in time. If markets are efficient, investors and financial managers have no reason to believe
securities are not priced at or near their true value. The more efficient a security market, the more likely
securities are to be priced at or near their true value.
The overall efficiency of a capital market depends on its operational efficiency and its informational
efficiency. Market operational efficiency focuses on bringing buyers and sellers together at the lowest
possible cost. The costs of bringing buyers and sellers together are called transaction costs and include
such things as broker commissions and other fees and expenses. The lower these costs, the more operationally efficient markets are. Why is operational efficiency important? If transaction costs are high,
market prices will be more volatile, fewer financial transactions will take place and prices will not reflect
the knowledge and expectations of investors as accurately.
Markets exhibit market informational efficiency if market prices reflect all relevant information
about securities at a particular point in time. As suggested above, informational efficiency is influenced
by operational efficiency, but it also depends on the availability of information, and the ability of investors to buy and sell securities based on that information. In an informationally efficient market, prices
adjust quickly to new information as it becomes available. Prices adjust quickly because many security
analysts and investors are gathering and trading on information about securities in a quest to make a
profit. Note that competition among investors is an important driver of informational efficiency.
Efficient market hypotheses
Public financial markets are efficient in part because regulators such as ASIC require issuers of
publicly traded securities to disclose a great deal of information about those securities to investors.
Investors are constantly evaluating the prospects for these securities and acting on the conclusions
from their analyses by trading them. If the price of a security is out of line with what investors
think it should be, then they will buy or sell that security, so causing its price to adjust to reflect
their assessment of its value. The ability of investors to easily observe transaction prices and trade
volumes, and to inexpensively trade securities in public markets contributes to the efficiency of this
process. This buying and selling by investors is the mechanism through which prices adjust to reflect
the market’s consensus. The theory about how well this mechanism works is known as the efficient
market hypothesis.
Strong‐form efficiency
The market for a security is perfectly informationally efficient if the security’s price always reflects all
available information. The idea that all information about a security is reflected in its price is known as
the strong form of the efficient market hypothesis. Few people really believe that the market prices of
public securities reflect all available information, however. It is widely accepted that insiders have information that is not reflected in the security prices. Thus, the concept of strong‐form market efficiency
represents the ideal case, rather than the real world.
If a security market were strong‐form efficient, then it would not be possible to earn abnormally high
returns (returns greater than those justified by the risks) by trading on private information — information unavailable to other investors — because there would be no such information. In addition, since
all available information would already be reflected in security prices, the price of a share of a particular
security would change only when new information about its prospects became available.
MODULE 2 The financial system
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Semistrong‐form efficiency
A weaker form of the efficient market hypothesis, known as the semistrong form, holds only that all
public information — information available to all investors — is reflected in security prices. Investors
who have private information are able to profit by trading on this information before it becomes public.
As a result of this trading, prices adjust to reflect the private information. For example, suppose that
conversations with the customers of a company indicate to an investor that the company’s sales, and
therefore its cash flows, are increasing more rapidly than other investors expect. To profit from this information, the investor buys some of the company’s shares. By buying the shares, the investor helps drive
up the price to the point where it accurately reflects the higher level of cash flows.
The concept of semistrong‐form efficiency is a reasonable representation of the public share markets
in developed countries, such as Australia. In a market characterised by this sort of efficiency, as soon as
information becomes public it is quickly reflected in share prices through trading activity. Studies of the
speed at which new information is reflected in share prices indicate that, by the time you read a hot tip in
the Australian Financial Review or a business magazine, it is too late to benefit by trading on it.
Weak‐form efficiency
The weakest form of the efficient market hypothesis is known, aptly enough, as the weak form. This
hypothesis holds that all information contained in past prices of a security is reflected in current prices,
but there is both public and private information that is not. In a weak‐form efficient market, it would not
be possible to earn abnormally high returns by looking for patterns in security prices, but it would be
possible to do so by trading on public or private information.
An important conclusion from efficient market theory is that, at any point in time, all securities of the
same risk class should be priced to offer the same expected return. The more efficient the market, the
more likely this is to happen. Since both the bond and share markets are relatively efficient, this means
that securities of similar risk will offer the same expected return. This conclusion is important because
it provides the basis for identifying the proper discount rate to use in applying the bond and share
valuation models developed in this module and the module on share valuation.
BEFORE YOU GO ON
1. How is information about a company’s prospects reflected in its share price?
2. What is strong‐form market efficiency? Semistrong‐form market efficiency? Weak‐form market
efficiency?
44 Finance essentials
SUMMARY
2.1 Discuss the primary role of the financial system in the economy, and how fund transfers take place.
The primary role of the financial system is to gather money from people and businesses with surplus funds (lender‐savers) and channel the money to businesses and consumers who need to borrow
money (borrower‐spenders). If the financial system works properly, only creditworthy investment
projects with high rates of return (higher than the cost of capital) are financed and all other projects
are rejected. Money flows through the financial system in two basic ways: (1) directly, through
financial markets; and (2) indirectly, through financial institutions.
2.2 Describe the primary, secondary and money markets, and explain why these markets are so
important to businesses.
Primary markets are markets in which new securities are sold for the first time. Secondary markets
provide the aftermarket for securities previously issued. Not all securities have secondary markets.
Secondary markets are important because they enable investors to convert securities easily to cash.
Companies whose securities are traded in secondary markets are able to issue new securities at
a lower cost than they otherwise could because investors are willing to pay a premium price for
securities that have secondary markets.
Large companies use money markets to adjust their liquidity because cash inflows and outflows
are rarely perfectly synchronised. Thus, on the one hand, if cash expenditures exceed cash receipts,
a company can borrow short term in the money markets or, if the company holds a portfolio of
money market instruments, it can sell some of these securities for cash. On the other hand, if cash
receipts exceed expenditures, the company can temporarily invest the funds in short‐term money
market instruments. Businesses are willing to invest large amounts of idle cash in money market
instruments because of their high liquidity and their low default risk.
2.3 Explain how financial institutions serve consumers and small businesses that are unable to
participate in the direct financial markets, and describe how companies use the financial system.
One problem with direct financing is that it takes place in a wholesale market. Most small businesses and consumers do not have the expert skills or the money to transact in this market. In contrast, a large portion of the indirect market focuses on providing financial services to consumers and
small businesses. For example, commercial banks collect money from consumers in small dollar
amounts by selling them cheque accounts, savings accounts and term deposits. They then aggregate
the funds and make loans in larger amounts to consumers and businesses. The financial services
bought and sold by financial institutions are tailor‐made to fit the needs of the market they serve.
Figure 2.3 illustrates how companies use the financial system.
2.4 Discuss the internationalisation of financial markets and the role played by the BIS in ensuring
the global financial markets remain stable.
Domestic financial markets are part of a global financial system, intermediating borrowing and lending
between the local nation and the rest of the world. This has been necessitated by expanding international
trade and production, and the development of multinational corporations. The rapid development of
technology and communication systems has made this growth possible. This places emphasis on multilateral cooperation between nations and their central banks to ensure that the global financial system and
domestic systems are stable. The BIS has become pivotal in encouraging this cooperation.
2.5 Explain what an efficient capital market is and why market efficiency is important to
financial managers.
An efficient capital market is a market where security prices reflect the knowledge and expectations
of all investors. Public markets, for example, are more efficient than private markets because issuers
of public securities are required to disclose a great deal of information about these securities to
investors, while investors are constantly evaluating the prospects for these securities and acting on
the conclusions from their analyses by trading them. Market efficiency is important to investors
because it assures them that the securities they buy are priced close to their true value.
MODULE 2 The financial system
45
KEY TERMS
brokers market specialists who bring buyers and sellers together, usually for a commission
contagion risk risk of the effects of financial difficulties in one organisation spreading to others
because of the complex interrelationships between institutions and the nature of the exchange
settlement systems
credit risk risk that the borrower will fail to make either interest or principal payments in the amount
and at the time promised
dealers market specialists who ‘make markets’ for securities by buying and selling from their own
inventories of securities
efficient capital market market where prices reflect the knowledge and expectations of all investors
efficient market hypothesis theory concerning the extent to which information is reflected in security
prices and how information is incorporated into security prices
environmental risk actual or potential threat of adverse impacts on value from changes in the
environment and/or organisational effects on the environment
eurocurrency market market for short‐term borrowing or lending of large amounts of any currency
held in a time deposit account outside its country of origin
financial intermediation conversion of financial instruments with one set of characteristics into
financial instruments with another set of characteristics
foreign exchange markets markets in which foreign currencies are bought and sold
foreign exchange risk fluctuation in the earnings or value of a financial institution that arises from
changes in exchange rates
initial public offering (IPO) primary offering of a company that has never before offered a particular
type of security to the public, meaning the security is not currently trading in the secondary market;
an unseasoned offering
interest rate risk risk that changes in interest rates will cause an asset’s price and realised yield to
differ from the purchase price and initially expected yield
investment banks companies that underwrite new security issues and provide broker‐dealer services
liquidity the ability to convert an asset into cash quickly without loss of value
liquidity risk risk that a financial institution will be unable to generate sufficient cash inflow to meet
required cash outflows
market informational efficiency degree to which current market prices reflect relevant information
and, therefore, the true value of the security
market operational efficiency degree to which the transaction costs of bringing buyers and sellers
together are minimised
marketability the ease with which a security can be sold and converted into cash
money markets markets where short‐term financial instruments are traded
operational risk risk of loss from the execution of a company’s business, in particular inadequate or
failed internal processes, people and systems, or from external events
political risk country or sovereign risk that can result in financial claims of foreigners being repudiated or
becoming unenforceable because of a change of government or in government policy in a country
primary market a financial market in which new security issues are sold by companies directly to
initial investors
private information information that is not available to all investors
private placements sales of securities directly to an investor, such as an insurance company
public information information that is available to all investors
public markets financial markets where securities listed on an exchange are sold
reputational risk potential that negative publicity will cause a decline in the customer base, costly
litigation or revenue reduction
46 Finance essentials
secondary market a financial market in which the owners of outstanding (already existing) securities
sell them to other investors
semistrong form (of the efficient market hypothesis) theory that security prices reflect all public
information but not all private information
stand‐by underwriting an underwriting agreement in which the underwriter guarantees the full
amount of funds to be raised through a securities issue
strong form (of the efficient market hypothesis) theory that security prices reflect all available
information
true (intrinsic) value for a security, value of the cash flows that an investor who owns that security
can expect to receive in the future
weak form (of the efficient market hypothesis) theory that security prices reflect all information in
past prices, but do not reflect all private or all public information
ENDNOTES
1.
2.
3.
4.
5.
6.
7.
8.
9.
Reserve Bank of Australia (RBA) 2016, Tables F7, D4.
www.asx.com.au/services/trading-services.htm.
Source: www.investopedia.com/terms/f/financialplanner.asp.
Federal Reserve of Chicago n.d., www.chicagofed.org/banking_information/legal_reputational_risk.cfm, accessed
1 September 2009.
IPCC 2007, ‘Climate change 2007: The physical science basis’. Contribution of Working Group 1 to the Fourth Assessment
Report of the Intergovernmental Panel on Climate Change [Solomon, S, Qin, D & Manning, M (eds)].
www.worldbank.org/en/about/annual-report/wbg-summary-results.
International Monetary Fund n.d., ‘Articles of agreement of the International Monetary Fund’, Article I — Purposes.
www.adb.org.
Bank of International Settlements (BIS) 2016, Locational banking statistics for Australia, table A5, www.bis.org/statistics/
bankstats.htm?m=6%7C31%7C69.
ACKNOWLEDGEMENTS
Photo: © Bianda Ahmad Hisham / Shutterstock.com
Photo: © TK Kurikawa / Shutterstock.com
Photo: © Jean-Philippe Menard / Shutterstock.com
Photo: © hywards / Shutterstock.com
MODULE 2 The financial system
47
MODULE 3
Financial markets
LEA RN IN G OBJE CTIVE S
After studying this module, you should be able to:
3.1 explain the characteristics of money market instruments
3.2 explain the role and function of capital markets, and how their role differs from that of the money markets
3.3 differentiate treasury bonds, semis and corporate bonds
3.4 explain how equity securities are traded in the secondary markets and discuss how the markets are operated
3.5 describe the most common types of derivative contracts
3.6 explain how the foreign exchange markets operate and facilitate international trade.
Module preview
The purpose of this module is to explain how money, capital, derivative and foreign exchange markets
work and to describe how businesses, government units and individuals use and participate in these
important markets.
The first section of this module discusses money markets, which are a collection of markets, each
trading a distinctly different financial instrument. There is no central exchange for money markets,
because they are over‐the‐counter (OTC) markets. Money markets are distinct from other financial
markets in that they are wholesale markets because of the large transactions involved. The most impor­
tant economic function of the money market is to provide an efficient means for economic units to adjust
their liquidity positions. Liquidity problems occur because the timing of cash receipts and expenditures
is rarely perfectly synchronised. Money market instruments allow economic units to bridge the gap
between them, solving their liquidity problems.
The next section of this module begins with a discussion of the function of capital markets and their major
participants. Next it discusses capital market instruments, whose terms, conditions and risks vary substan­
tially. Capital market instruments are defined as long‐term financial instruments with an original maturity of
greater than 1 year. As the name implies, the proceeds from the sale of capital market instruments are usually
invested in permanent assets, such as industrial plants, equipment, buildings and inventory.
The module then turns to bond markets: the markets for long‐term Commonwealth and state govern­
ment securities, corporate bonds and hybrids. It discusses the size of the bond market, its turnover, types
of bond securities and investors. Next it describes the primary and secondary markets for bonds. Bonds
are capital market instruments whose terms, conditions and risks vary substantially. Corporate bonds are
unsecured debt and investors’ greatest fear is that the issuer will default. On the other hand, government
securities are often referred to as risk‐free securities. However, in July 2016, one‐third of all government
debt in developed countries was trading at negative interest rates, whereas in the euro zone more than
50 per cent of bond issues have negative yields.1 This means that the price of these bonds is more than
the amount investors will receive in return!
MODULE 3 Financial markets 49
The following section discusses how equity securities are traded in primary and secondary markets. It
then describes the characteristics of the equity market and the major venues for trading equities in Australia.
Every day in newspapers and on television, reporters eagerly describe the ups and downs of the share market
because many in society view its performance as an important indicator of the economy’s health. The term
equity implies an ownership claim and holders of equity securities have a right to share in a corporation’s
profits. People dream of reaping riches from investing in the share market and, whether we realise it or not,
most of us own equity securities indirectly through superannuation funds or managed investments.
Because many people are concerned with interest rates, exchange rates and share market risks, financial
futures markets have grown explosively in recent years. Financial engineers have developed a wide variety
of financial instruments so that individuals and institutions can alter both their risk exposure and return poss­
ibilities. The new financial derivative securities derive their value from changes in the value of other assets
(such as shares or bonds), values (such as interest rates) or events (such as credit defaults, catastrophes or
even temperature changes in certain localities). The next section of this module describes the nature of the
most important markets for financial derivatives. It starts with forward and futures markets, then discusses
options markets. It discusses how markets work and the financial instruments traded in each.
English is the international language for airlines. If there was not one single language, imagine the
difficulty pilots would have, with so many languages spoken in the world. There is no equivalent uni­
versal currency that businesses can use to conduct business transactions. Few people around the world
are willing to use a foreign currency to conduct their domestic transactions. Consequently, the world’s
citizens and businesses use many different currencies. When conducting business internationally,
Australian citizens need to concern themselves with the Australian‐dollar value of export sales denomi­
nated in foreign currencies, the Australian‐dollar value of assets they own abroad or the Australian‐dollar
cost of imported materials. The use of many different currencies makes accounting and planning more
difficult for all Australians who invest or do business internationally.
The final section examines the major economic and political forces that influence foreign exchange
(FX) markets. FX markets developed to reduce currency risk, so that people can convert their cash into
different currencies as they conduct business or personal affairs. Furthermore, because payments across
borders can be difficult to enforce and creditworthiness can be hard to assess, elaborate credit procedures
have developed to facilitate international loans and financing. Commercial banks play a major role in
financing and arranging FX transactions because of their expertise in financing business, checking credit
and transferring money. In addition, investment banks and FX dealers play important roles in the foreign
currency markets.
3.1 Money markets
LEARNING OBJECTIVE 3.1 Explain the characteristics of money market instruments.
The money markets are where depository institutions and other businesses adjust their liquidity positions
by borrowing or investing for short periods. In addition, the Reserve Bank of Australia (RBA) conducts
monetary policy in the money markets and the Australian Office of Financial Management (AOFM) can
finance the day‐to‐day operations of the federal government there, although at present it rarely does so.
The instruments traded in the money markets typically have short‐term maturities, low default risk and
active secondary markets. These markets are called ‘money’ markets because their instruments have charac­
teristics very similar to those of money. The close substitutability of market instruments links these markets.
Given the economic role of money markets — to provide liquidity adjustments — it is not difficult
to determine the characteristics of ‘ideal’ money market instruments and the types of organisations that
could issue them. Specifically, those who invest in money market instruments want to take as little
risk as possible. Therefore, these instruments have low default risk, have low price risk (short terms to
maturity), are highly marketable (i.e. they can be bought or sold quickly) and are sold in large denomi­
nations, so the per‐dollar cost for executing transactions is very low. Why do money market instruments
have these characteristics?
50 Finance essentials
If you have money to invest temporarily, you first want to purchase financial claims only of firms with
the highest credit standing to minimise any loss of principal caused by default. Therefore money market
instruments are issued by economic units of the highest credit standing (i.e. the lowest default risk).
Second, you do not want to hold long‐term securities, because they have greater price fluctuations
(interest rate risk) than short‐term securities if interest rates change. Furthermore, if interest rates do
change significantly, for short‐term securities maturity is not far away, when they can be redeemed for
their face value.
Third, temporary investments need to be highly marketable in case the funds are unexpectedly needed
before maturity. Therefore most money market instruments have active secondary markets. To be highly
marketable, they must have standardised features (no surprises). Furthermore, the issuers must be well
known in the market and have good reputations. Finally, the transaction costs need to be low. Therefore
money market instruments are generally sold in large wholesale denominations — usually in units of
$1 million or more. It costs a fixed fee of $3 to trade one line of securities in the Australian Securities
Exchange (ASX) Austraclear system (which can be worth anything from $100 000 to $100 billion — if
you have it!).
The individual money market instruments and the characteristics of their markets are now discussed.
The cash market
The cash market is the market for cash held in exchange settlement funds (ESAs) at the RBA. It is
one of the most important financial markets in Australia and can be thought of as the ‘official’ short‐term
money market. It provides the means by which commercial banks and a few other financial institutions
can immediately trade large amounts of liquid funds with one another over short periods, a day or even
less. The cash rate, the overnight or one‐day interest rate, is of particular interest because: it measures
the return on the most liquid of all financial assets; it is closely related to the conduct of monetary
policy; and it influences commercial banks’ decisions concerning interest rates on loans to businesses,
consumers and other borrowers. The role of the cash market in monetary policy implementation is
discussed further in the module on the RBA and interest rates.
In the cash market, commercial banks borrow and lend excess ESA balances held at the RBA. The
name ‘cash’ market is misleading: the RBA does not physically transfer large volumes of notes and
coins (in cash) from one account to another. Rather, the system is electronic: when a transaction is made
between two commercial banks, one ESA is debited while the other is credited, leaving the system with
the same total amount of liquidity.
Interbank borrowing and lending make up most cash market transactions. These can be either secured
or unsecured transactions. The typical unit of trade is $1 million or more. Indeed, many participants are
unwilling to enter into trades for anything less than $20 million. This may seem like a lot at first. But
considering that most lending and borrowing of funds in the cash market are only for very short periods,
the interest accrued on funds lent must be enough to satisfy lenders that they are making a worthwhile
return after paying transaction fees on clearing and settlement systems such as the SWIFT payment
delivery system (for cash transfers) and Austraclear (for debt securities), which link to the Reserve Bank
Information and Transfer System (RITS). To give you some idea of the size of the cash market, intraday
repos (lending cash against some form of collateral — usually a bond) for less than 1 day averaged
$4.2 billion worth of transactions per day in June 2016,2 which is a lot, but only a small proportion of
the $167 billion settled each day of that financial year through ESAs.3
The interbank borrowing and lending market holds an extremely important place within the
­financial markets. Any hint of malfunctioning of the interbank market can send tremors through the rest
of the credit market. This was very much evident during the recent global financial crisis (GFC), when
banks virtually stopped lending to each other and the interbank market in many countries including
Australia almost came to a standstill, with interest rates soaring to record highs. The higher rates in
the interbank market also had serious implications for the nonbank borrowers, as their loan rates are
MODULE 3 Financial markets 51
tied to interbank funding costs. It took interventions from governments around the world, often at
­unprecedented scales, to thaw the frozen liquidity and restore the flow of credit within the financial
system.
One‐name paper
One‐name paper refers to short‐term debt where the liability is with a single issuer and it does not
rely on the credit enhancement provided by acceptance. Examples are Treasury notes (issued by
the ­Commonwealth Government), short‐term negotiable bank certificates of deposit, and short‐term
asset‐backed securities and short‐term debt issued by major corporations. The amount of one‐name
paper outstanding in Australia varies, depending on economic and market conditions. Generally, less
corporate paper is issued during high‐interest periods and more when money is more readily available.
Since 2010, global concerns have grown over the European sovereign debt situation. Although the
Australian economy has remained resilient, many sectors of the economy, such as manufacturing,
tourism and retail, are experiencing sluggish conditions. Consumers have become more cautious by
paying down debt and increasing savings. In this environment, the need for short‐term borrowing by
banks and corporations has declined. As a result, the number of outstanding tradable papers has reduced
significantly. At the time of writing, the debt crisis in Europe had worsened and Italy was also in turmoil.
This situation makes the liquidity and funding requirements of Australian banks, the largest players in
the one‐name paper market, somewhat uncertain in the near future.
In the following sections, we describe the major types of one‐name paper: Treasury notes, commercial
paper, negotiable certificates of deposit and asset‐backed commercial paper.
Treasury notes
To finance the operations of the Commonwealth Government, the AOFM issues various types of debt. Trad­
itionally, Treasury notes (T‐notes) have been the most important. They are issued by the Commonwealth
Government to cover current deficits (i.e. expenses that exceed revenues) and to refinance maturing
Government debt. Subject to need, T‐notes are sold through an auction process (described later) and
before July 2000 had original maturities of 5 weeks, 13 weeks or 26 weeks. Since July 2000, T‐notes
have been issued at any maturity under 1 year. They are typically issued in tranches of $200 million,
$300 million, $400 million, $500 million and $1 billion. Bids at auction must be for a minimum amount
of $100 000 and in increments of $5000 thereafter. In the secondary markets, subsequent transactions
can be in multiples of $5000. The relatively small denomination of $5000 is a political concession by the
federal government to individual investors, so that they can purchase small‐denomination T‐notes from
dealers in the secondary markets. Overall, however, the market for Treasury securities is wholesale: they
are usually traded in multiples of $1 million.
Notably, the AOFM did not auction any new T‐notes between October 2003 and February 2009. The
reason is that the Australian Government had been running budget surpluses and the excess revenue
was placed in term deposits at the RBA. However, changed economic conditions in the aftermath of the
GFC resulted in the prospect of the government running budgetary deficits for the next several years. In
view of this, issuance of T‐notes recommenced from March 2009 to meet the government’s short‐term
financing requirements. As of 28 October 2016, T‐notes on issue amounted to $4000 million.4 As shown
in figure 3.1, T‐notes on issue represent only a small portion of Australian government securities on issue.
Treasury bonds are discussed later in this module.
T‐notes are considered to have virtually no default risk because they are backed by the Commonwealth
Government. The yield on them is often referred to as the risk‐free rate. Of course, in reality there is no
risk‐free rate, but T‐note yields are the best available proxy. They also have little price risk because of
their short maturities, and they can be readily converted into cash at very low transaction costs because
of their large and active secondary market. Because of these factors, T‐notes are considered the ideal
money market instrument.
52 Finance essentials
FIGURE 3.1
Australian Government Securities on issue
Treasury bonds
Treasury indexed
bonds
400
Treasury notes
Other securities
$ billions
300
200
100
0
Treasury bonds,
Australian
government
securities on
issue*, 417 541
Treasury indexed
bonds, Australian
government
securities on
issue*, 31 029
Treasury notes,
Australian
government
securities on
issue*, 4000
Other securities,
Australian
government
securities on
issue*, 21
* Face value of amount on issue as at 28 October 2016.
Commercial paper
Commercial paper, or corporate paper as it is sometimes called, is a name for short‐term, unsecured
promissory notes, typically issued by large corporations to finance short‐term working capital needs.
Some firms also use commercial paper as a source of interim financing for major construction projects.
The basic reason that firms issue commercial paper is to achieve interest rate savings as an alternative
to bank borrowing. Because commercial paper is an unsecured promissory note, the issuer pledges no
assets to protect the investor in the event of default. As a result, only large, well‐known firms of the
highest credit standing (lowest default risk) can issue commercial paper.
The commercial paper market is part of the money market, making up almost one‐third of all trans­
actions in short‐term instruments (excluding repos). Most commercial paper is sold in denominations of
$100 000, $250 000, $500 000 and $1 million, with maturities that are often up to 180 days but are most
commonly less than 45 days.
Negotiable certificates of deposit
A negotiable certificate of deposit (NCD) acts simply as a bank term deposit that is negotiable.
Because the receipt is negotiable, it can be traded any number of times in the secondary market before
its maturity. The denominations of certificates of deposit (CDs) range from $100 000 to $10 million.
However, few NCDs have denominations of less than $500 000 because smaller denominations, although
technically negotiable, are not as marketable.
NCDs typically have maturities between 30 and 180 days. There is a market for longer‐maturity CDs
but, beyond six months, the volume is small and the secondary market is not as liquid. Australian banks
had about $235 billion in NCDs outstanding at the end of June 2013.5
MODULE 3 Financial markets 53
Asset‐backed commercial paper
Asset‐backed commercial papers (ABCP) are issued in order to finance the purchase of financial
assets such as mortgages, receivables and long‐term securities, including residential mortgage–backed
securities (RMBS). These papers generally have a term to maturity of less than 1 year. Since ABCPs
are essentially short‐term papers issued to fund investments in longer term assets, this type of funding
strategy relies on the ability to ‘roll over’ the paper when it matures (i.e. new ABCPs are issued to repay
maturing ABCPs).
ABCPs are commonly issued by so‐called conduits in Australia. Conduits are usually set up, or ‘spon­
sored’, by a bank, although they are a legally separate entity. For a fee, the sponsor provides adminis­
trative services and often provides liquidity facilities and/or credit enhancement. Credit enhancement
and liquidity facilities can also be provided by third parties. Conduits are ongoing entities that have a
revolving structure, with assets going in and out of the pool of collateral that backs the ABCP.
Bank‐accepted bills
A bank‐accepted bill (BAB) is a time draft drawn on and accepted by a commercial bank. Time drafts
are orders to pay a specified amount of money to the bearer on a given date. When drafts are accepted,
a bank unconditionally promises to pay to the holder the face value of the draft at maturity, even if
the bank encounters difficulty in collecting from its customers. It is the act of the bank in substituting
its creditworthiness for that of the issuer that makes bankers’ acceptances marketable instruments.
Bank‐accepted bills are the most important instrument in the money markets. They are also called
two‐name papers because they have both the name of the original borrower and that of the bank on them.
Since there are three parties in a BAB contract — the drawer, the acceptor (the bank) and the holder —
some also refer to it as a three‐name paper. Note that a time draft does not become a BAB until it
is stamped ‘accepted’ by a bank. This acceptance means the draft is now a liability of the accepting
bank when it comes due.
Often, BABs arise in international transactions between exporters and importers of different countries.
In these transactions, the accepting bank can be either an Australian or a foreign bank, and the trans­
action can be denominated in any currency. However, the Australian secondary market consists primarily
of dollar acceptance financing, in which the accepter is an Australian bank and the draft is denominated
in Australian dollars.
Creating a bank‐accepted bill
The following example illustrates how BABs are created. The sequence of events for the transaction can
be followed in figure 3.2 (there are many ways to create acceptances and to do so requires a great deal of
specialised knowledge on the part of the accepting bank). Assume that an Australian importer wishes to
finance the importation of Colombian coffee. Furthermore, the Australian importer wishes to pay for the
coffee in 90 days. To obtain financing, the importer has an Australian bank write an irrevocable letter of
credit for the amount of the sale, which is sent to the Colombian exporter. The letter of credit specifies
the details of the shipment and authorises the Colombian exporter to draw a time draft for the sale
price on the importer’s bank. When the coffee is shipped, the exporter draws the draft on the Australian
bank and then transfers the draft at a discount to its local bank, receiving immediate cash payment for
the coffee. The exporter’s bank then sends the time draft, along with the proper shipping documents,
to the Australian bank. The Australian bank accepts the draft. The bank either returns the time draft
(acceptance) to the exporter’s bank or immediately pays the exporter’s bank for it at a discounted price
reflecting the time value of money during the waiting period. If the Australian bank pays the exporter’s
bank for the acceptance, it can then either hold the accepted draft as an investment or sell it in the open
market as a source of funds. When the draft matures, the Australian importer is responsible for paying
the accepting bank. If for some reason the importer fails to pay, the accepting bank has legal recourse to
collect from the Colombian exporter.
54 Finance essentials
The sequence of a bank‐accepted bill transaction
au
tho
ris
ati
on
f
nd
it a
red
fc
4
ro
3
tte
Le
7
1
Money
or
a
dr
aft
2
Colombian
exporter
of coffee
Money
Request for letter of credit
Australian
buyer
of coffee
Authorised draft on Australian bank
FIGURE 3.2
Australian
bank
5
Draft and shipping
documents
Money
6
Colombian
bank
The advantages of BABs in international trade are apparent from this simplified example. First, the
exporter receives their money promptly and avoids delays that could arise in international shipping.
Second, the exporter is shielded from FX risk because a local bank pays in domestic funds. Third, the
exporter does not need to examine the creditworthiness of the Australian firm because a large, well‐
known bank has guaranteed payment for the merchandise. Therefore, it is not surprising that BABs are
often used for international transactions.
BEFORE YOU GO ON
1. Explain the characteristics of money markets.
2. Briefly describe four major types of one‐name papers.
3. Define a bank‐accepted bill and explain why it is also known as a two‐name paper.
3.2 Capital markets
LEARNING OBJECTIVE 3.2 Explain the role and function of capital markets, and how their role differs
from that of the money markets.
Capital market transactions match savings to the requirements of individuals, businesses and govern­
ments for investments that are longer term than those offered in money markets. Individuals own
real assets to produce income and wealth. The owner of a machine hopes to profit from the sale of
products from the machine shop and the owner of a factory hopes to earn a return from the goods
produced there. Similarly, owners of apartments, office buildings, warehouses and other tangible assets
hope to earn a stream of future income by using their resources to provide services directly to con­
sumers or to other businesses. These assets are called capital goods; they are the stock of assets used
in production. In capital markets, capital goods are financed with stock or long‐term debt instruments.
MODULE 3 Financial markets 55
Compared with money market instruments, capital market instruments are less marketable, default
risk levels vary widely between issuers and maturities range from 5 to 30 years. Financial institutions
are the connecting link between the short‐term money markets and the longer term capital markets.
These institutions, especially those that accept deposits, typically borrow short term and then invest
in longer term capital projects, either indirectly through business loans or directly into capital market
instruments.
Functions of capital markets
The motive of firms for issuing or buying securities in capital markets is very different from those for
acting in money markets. As seen in the previous section, in money markets, firms are either:
•• making short‐term investments of surplus funds to earn interest rather than leaving them idle; or
•• borrowing to cover short‐term shortfalls of funds that arise because of the time needed to collect cash
that is owed.
Firms buy capital goods such as plant and equipment in order to make products to earn a profit.
Most of these investments are central to firms’ core business activities. Capital goods normally have a
long economic life, ranging from a few years to 10, 20 or 30 years or more. Capital assets are usually
not highly marketable. As a result, firms like to finance capital goods with long‐term debt or equity to
lock in their borrowing cost for the life of the project and to eliminate the problems associated with
periodically refinancing assets.
For example, say a firm buys a plant with an expected economic life of 15 years. Because short‐term
rates are typically lower than long‐term rates, at first glance short‐term financing may look like a great
deal. However, if interest rates rise dramatically, as they did at times during the 1980s and early 1990s,
the firm may find its borrowing cost skyrocketing because it has to refinance its short‐term debt. In
the worst case, the firm may find it does not have adequate cash flows to support the debt and may be
forced into bankruptcy. Similarly, if market conditions become uncertain, issuers may find themselves
unable to refinance their short‐term debt; if no other lenders are found, bankruptcy could again be the
end result.
On the other hand, if long‐term securities such as bonds are used, the cost of funds is known for the
life of the asset and there should be fewer refinancing problems. It is no surprise, then, that when issuing
debt for capital expenditures, firms often try to match the expected asset life with the maturity of the
debt. However, there is a cost in reducing interest rate and reinvestment risk, in that long‐term interest
rates tend to be higher than short‐term rates because of risk premiums.
Capital market participants
Capital markets bring together borrowers and suppliers of long‐term funds. The market also allows
those holding previously issued securities to trade those securities for cash in the secondary capital
markets.
The largest purchasers of capital market securities are individuals and households and, from time to
time, foreign investors. Financial institutions are also important participants in capital markets, although
their net position (assets minus liabilities) is not large because of their role as financial intermediaries.
That is, they purchase funds from individuals and others, and then issue their own securities in exchange.
Consequently, individuals and households may invest directly in the capital markets but, more likely,
they purchase stocks and bonds through financial institutions such as commercial banks, insurance
companies, mutual funds and superannuation funds.
Major capital market instruments
A financial instrument is classified as a capital market instrument if it has an original term to maturity of
1 year or more. The major capital market instruments are now briefly described.
56 Finance essentials
Bonds
Bonds are contractual obligations of a borrower to make periodic cash payments to a lender over a
given number of years. Bonds constitute debt; so there is a borrower and a lender. In market jargon, the
borrower is referred to as the bond issuer. The lender is referred to as the investor or the bondholder.
A bond consists of two types of contractual cash flows. First, upon maturity the lender is paid the
original sum borrowed, which is called the principal, face value or par value of the bond. Note that
these three terms are interchangeable. Secondly, the borrower or issuer must make periodic interest pay­
ments to the bondholder. These interest payments are called the coupon payments. The magnitude of
the coupon payments is determined by the coupon rate, which is the annual coupon payment of a bond
divided by the bond’s face value.
To determine the timing of the cash flows, it is necessary to know the term to maturity (or maturity)
of a bond, which is the number of years over which the bond contract extends. Note that for most bonds,
it is assumed that the coupon and principal payments are received at the end of the year. In addition,
many bonds pay coupon interest semiannually (or every six months) instead of once per year at the end
of the year.
It is important to keep in mind that for most bonds, the coupon rate, the par value and the term to
maturity are fixed over the life of the bond contract. Most bonds are first issued in $1000 or $5000
denominations. Coupon rates are typically set at or near the market rate of interest or yield on similar
bonds available in the market. A similar bond is one that is a close substitute, nearly identical in maturity
and risk.
Also, note that the coupon rate and the market rate of interest may differ. The coupon rate is fixed
throughout the life of a bond. The yield on a bond varies with changes in the supply and demand for
credit or with changes in the issuer’s risk. How to calculate a bond’s yield and the pricing of bonds are
discussed in the module on bond valuation.
Government bonds
Government bonds are the long‐term debt obligations of governments. They are used to finance capital
expenditure for things such as schools, highways and airports. This is usually done in the context of
the federal or state annual budget, which forecasts income and expenditures. If the budget is in surplus,
the government may use the additional resources to reduce its debt, but if the budget is in deficit, then
the government will need to borrow funds to cover the forecast expenditure.
In Australia, the AOFM issues T‐notes (short‐term securities discussed earlier) and Treasury bonds
for the Commonwealth Government. Treasury bonds are long‐term securities (with maturities of up to
10 years) and can be issued at a discount or a premium depending on the yield of the security relative to
the tender price (see the module on bond valuation for a detailed discussion of bond pricing).
Corporate bonds
When large corporations need money for capital expenditure, they may issue bonds. Corporate bonds
are, therefore, long‐term IOUs that represent a claim against the firm’s assets. Unlike equity holders’
returns, bondholders’ returns are fixed: they receive only the amount of interest that is promised plus the
repayment of the principal at the end of the loan contract. Even if the corporation turns in unexpected
above‐market performance, the bondholders will only receive the fixed amount of interest agreed to at the
bonds’ issue. Corporate bonds typically have maturities from 5 to 30 years and their secondary market
is not as active as that for equity securities. It is also important to note that there are different forms of
corporate bonds and other corporate debt instruments. These are discussed in detail later in the module.
Mortgages
Mortgages are long‐term loans secured by real estate. They are the largest segment in the capital markets
in terms of the amount outstanding. More than half of the mortgage funds go into financing family homes,
with the remainder financing business property, apartments, other buildings and farm construction. Mort­
gages by themselves do not have good secondary markets. However, many mortgages can be pooled to
form new securities called mortgage‐backed securities, which have an active secondary market.
MODULE 3 Financial markets 57
Shares
Shares take several forms. Ordinary shares are equity shares that represent the basic ownership claim
in a corporation. O
­ rdinary shareholders directly share in the firm’s profits and losses. However, the dis­
tinguishing feature of ordinary shares is that holders are entitled only to a residual claim against the
firm’s cash flows or assets. If a firm is liquidated, ordinary shareholders cannot be paid until the claims
of employees, the government, short‐term creditors, bondholders and preference shareholders are first
satisfied. After these prior claims are paid, the shareholders are entitled to what is left over, the residual.
In most company collapses, the residual is zero. Indeed, very often the prior claimants receive only part
payment of their entitlements. The residual nature of ordinary shares means that they are more risky than
a firm’s bonds or preference shares.
Legally, ordinary shareholders enjoy limited liability, which means that their losses are limited to the
original amount of their investment. It also implies that the personal assets of a shareholder cannot be
obtained to satisfy the obligations of the corporation. In contrast, a sole proprietor is personally liable for
their firm’s obligations. Given limited liability, it is not surprising that most large firms in the developed
world are organised as corporations.
As do ordinary shares, preference shares represent an ownership interest in the corporation but, as the
name implies, holders receive preferential treatment over ordinary shareholders with respect to dividend
payments and the claim against the firm’s assets in the event of bankruptcy or liquidation. In liqui­
dation, preference shareholders are entitled to the issue price of their preference shares plus accumulated
dividends after other creditors have been paid and before ordinary shareholders are paid.
Preference shares are usually designated by the percentage amount of their dividend, which is a fixed
obligation of the firm, similar to the interest payments on corporate bonds. Most preference shares are
both nonparticipating and cumulative. Nonparticipating means that the preference dividend remains
constant regardless of any increase in the firm’s earnings. Although a firm can decide not to pay the
dividends on preference shares without being declared in default, the cumulative feature of preference
shares means that the firm cannot pay a dividend on its ordinary shares until it has paid the prefer­
ence shareholders the dividends in arrears. Some preference shares are issued with adjustable rates.
Adjustable‐rate preference shares became popular in the early 1980s when interest rates were rapidly
changing. The dividends of adjustable‐rate preference shares are adjusted periodically in response to
changing market interest rates.
Preference shares may also be redeemable in that the company has the right to buy them back from
their holders. Preference shares with a fixed redemption date are very similar to debt securities, although
they still have some of the characteristics of equity. The decision to request or offer buy‐back lies with
either the holder or the company, but will normally be specified in the issue documentation. The only
other major characteristic of shares is whether they are partly paid or contributing shares. Preference
shares are for all practical purposes never issued as contributing shares, because the issuers are normally
in need of all the funding represented by the shares.
Generally preference shareholders do not vote at company meetings. Exceptions to this general rule
can occur when matters affecting the preference shareholders are under decision.
Convertible preference shares can be converted into ordinary shares at a predetermined ratio (such
as one ordinary share for each preference share). By buying these shares, an investor can obtain a good
dividend return plus have the possibility that, should the ordinary shares rise in price, the investment
would rise in value.
Modern convertible preference shares tend to behave much like debt. Although each issue has individual
characteristics, typically they are issued at $100 each and have a set dividend rate for a 5‐year reset period.
At the end of the reset period, the holders may take the new reset terms, redeem at face value or convert the
shares, normally at a discount to the current ordinary share price; for example, 5 per cent. Because the con­
version is made in terms of the dollar value of the shares — for example, $10 000 worth of the preference
shares convert to $10 000 worth of ordinary shares — the price of these hybrids does not react to the move­
ment in the ordinary share price and they therefore behave in a similar way to fixed interest securities.
58 Finance essentials
Convertible notes are securities that can be exchanged at maturity for ordinary shares. However, until
conversion they are corporate debt, so their interest and principal payments are contractual obligations
of the firm and must be made lest the corporation default. Most convertible bonds are subordinated debt.
Consequently, their holders have lower ranking claims than do most other debt holders, although their
claims rank ahead of those of shareholders.
Because convertible notes both increase in value with rising share prices and provide the fixed income
and security of bonds, they are popular with investors, who are usually willing to pay more to acquire
convertible debt than they would be for conventional debt issued by the same corporation. From the
corporation’s perspective, convertible notes provide a means for the corporation to issue debt and later
convert it to equity at a price per share that exceeds the shares’ present market value. This feature is
attractive because it allows the corporation to issue shares at a higher future price.
BEFORE YOU GO ON
1. Explain the differences between money markets and capital markets.
2. Identify the most important capital market securities.
3. Describe the major differences between ordinary shares and preference shares.
3.3 Bond markets
LEARNING OBJECTIVE 3.3 Differentiate treasury bonds, semis and corporate bonds.
The major issuers of capital market securities are the Commonwealth Government, state governments
and corporations. Commonwealth Government Securities (CGSs) are notes and bonds issued by the
Commonwealth Government to finance its operations or to refinance existing debt that is about to
mature. Similarly, state governments issue debt to finance their operations. Issuance is restrained
only by taxpayers’ willingness to support government deficits. Government units cannot issue stock
because they are not allowed to sell ownership in themselves. Corporations can issue both bonds and
stock. The decision to issue debt (and of which type) is complex and depends upon management’s
philosophy towards capital structure, its willingness to bear risk and the receptivity of lenders to the
securities offered.
Size of the bond markets
The long‐term debt or bond markets are massive in scope, exceeding $1765.7 billion. The long‐term
government bond market (Commonwealth and semi‐government) is the largest segment of the market
as of June 2016, totalling around $649 billion. However, its relative importance in the bond market
has declined since 1996. During the past decade the bonds issued by non‐resident (i.e. foreign)
companies have grown exponentially, reaching $553.8 billion at the end of June 2016. At $512.1 billion,
the corporate bond market, which includes both financial and nonfinancial corporations, comes next.
The asset‐backed securities market, which witnessed phenomenal growth until 2007, contracted after the
GFC. At 30 June 2016, there were $114.1 billion of asset‐backed securities outstanding.6
The structure of the Australian bond market has changed greatly since 1992. The Commonwealth
Government has played an important role in this. Like businesses, the government manages the timing
of long‐term and short‐term cash flows, and funds any shortfall in its long‐term capital requirements,
which occurs when it runs a deficit, largely by issuing Commonwealth Government Bonds. The federal
government decided to keep the market active, as Commonwealth Government Bonds are very impor­
tant low‐risk securities and the role they play is unique in the capital markets. Without them, the costs of
managing interest rate risk across the economy would be substantially higher.
MODULE 3 Financial markets 59
In the last five years, the CGS market has once again become very active. To mitigate the impact of
the global economic downturn on the Australian economy, the government pumped billions of dollars
into the economy through its fiscal stimulus package. This government spending resulted in the budget
being dragged into a deficit once again. To finance the deficit, the Commonwealth Government relied on
the issue of long‐term debt securities. State governments which ran budgetary deficits during this time
also raised money by issuing bonds.
Turnover in the bond markets
The secondary market for bonds is the market in which bonds are sold from one investor to another. In
the secondary market for government bonds, only a few transactions are undertaken through brokers on
the ASX, although it is possible to do so. These are known as on‐exchange transactions. Off‐exchange
transactions are conducted directly between two parties or arranged through a broker, who acts as an
intermediary between two parties.
There are many reasons prompting market participants to undertake transactions in the secondary
market. Often, banks are required by law to hold a portion of their assets in certain safe, liquid securities,
in what is known as a reserve requirement. Usually, this requirement requires some of the securities
purchased to be government bonds. That means an increase in deposits will prompt banks to purchase
securities. In 1986, the RBA created a prime assets requirement (PAR) for banks in Australia. Initially,
this meant that an amount equivalent to 12 per cent of a bank’s liabilities had to be held in CGS, notes
and coins, or in accounts at the RBA. This requirement was lessened over time, until in 1997–98 the
PAR rate was reduced to 3 per cent and the set of acceptable assets was widened to include state govern­
ment securities. From April 1998, banks have not been required to hold a specified level of assets but the
RBA has stated that it expects banks to maintain a minimum level of liquid assets. Today, banks are still
required to manage their liquidity prudently to the satisfaction of the regulator, the Australian Prudential
Regulation Authority (APRA).
Institutions also hold securities in case they have a liquidity shortfall and require cash quickly, because
government bonds can be sold immediately to meet this need. Interest rate expectations also prompt
market participants to buy or sell securities. Bond prices are inversely related to interest rates (i.e. they
increase when interest rates fall and decrease when interest rates rise). If a bank believes interest rates
are likely to fall, it may purchase securities to reap the benefit of increasing prices. Alternatively, it might
sell bonds to avoid price falls if it believes a rise in interest rates is likely.
Some institutions like to maintain a certain maturity profile for their bond portfolios. For example,
superannuation funds generally prefer to hold long‐term bonds, while cash management trusts prefer
short‐term bonds. As the bonds held by a market participant approach maturity, it is likely to sell them
and purchase longer dated bonds. Financial institutions are also active in the market because of their
clients’ loan funding requirements. Banks and others will hold securities so that if a client requires a
loan, the security can be quickly sold and the cash lent.
Commonwealth Government Securities
CGSs are Treasury bonds and Treasury notes (T‐notes) issued by the AOFM and are backed by the
full faith and credit of the Commonwealth Government. They are considered to be free of default risk.
Treasury bonds differ from T‐notes in that they are coupon instruments (paying interest semiannually).
In addition to the fixed‐principal bonds discussed, the Commonwealth Government also issues bonds
that adjust for inflation. These securities are referred to as Treasury indexed bonds (TIBs). Just like the
fixed‐coupon Treasury bonds, issues are sold through the tender process, taking the lowest yield bids
first. Unlike the fixed‐principal securities, interest is paid quarterly and the principal amount upon which
the coupon payments are based changes with the inflation rate. TIBs are designed to provide investors
with a way to protect their investment against inflation. As shown in figure 3.1, as at 28 October 2016
60 Finance essentials
Treasury bonds valued at $417 541 million and Treasury indexed bonds valued at $31 029 million were
on issue.
State government bonds
The states and territories of Australia have responsibility for government‐administered services such as
hospitals, schools, policing, roads, electricity and water. In case of funding shortfalls, state and terri­
tory borrowing authorities issue bonds called semis (semi‐government bonds) backed by their respective
governments for the same reasons as the Commonwealth Government. Some examples of state borrowing
authorities include: Queensland Treasury Corporation (QTC), New South Wales Treasury Corporation
(NSW T‐corp) and Treasury Corporation of Victoria (TCV).
Semis differ from CGSs in important ways. The price they trade at is lower than that for an other­
wise identical CGS. In other words, semis trade at a higher yield. This occurs because, although states
can be rated AAA (the same rating as for the Commonwealth Government), their debt is not considered
risk free. In the Australian capital markets, only Commonwealth debt receives this endorsement. Semis
are also not as highly traded as CGSs and, therefore, trade with a liquidity premium in their yields.
This lower liquidity also means that the spreads between bid and ask prices quoted for semis by market
dealers are larger than those for CGSs. Trading occurs through Austraclear.
Unlike CGSs, semis are not issued through a tender system but are instead issued to dealer panels.
This is a small set of bond dealers of up to 12 members. They agree to buy semis from state governments
in either closed auctions (in which stock is assigned to the best bids) or through agreeing to buy a given
amount at a given price. State borrowing authorities use dealer panels to sell semis because they increase
the stocks’ liquidity by finding other dealers to sell bonds to and making a market for them by quoting
bid and ask prices on the stock to other dealers.
New Zealand has recently formed the Local Government Funding Agency (LGFA) to act as a cen­
tral borrowing vehicle for all city councils and municipalities to consolidate the local government issuer
market. Like Australian semi‐government bonds, these bonds would not be explicitly guaranteed by the
New Zealand Government. However, the rating agencies usually consider an implied government guarantee
when assigning their rating. There is a joint guarantee built into the legal framework of the LGFA, which
means the councils have joint liability if an individual borrowing entity is unable to meet its obligations.
Corporate bonds
Corporate bonds are debt contracts requiring borrowers to make periodic payments of interest and
to repay principal at the maturity date. Corporate bonds can be unsecured notes or debentures. An
unsecured note is a bond that has no specified security attached as collateral in the case of default.
Debentures come in two forms, fixed and floating. Fixed‐charge debenture holders have the right to
the proceeds of sale of the assets specified in the debenture should the bond default. Floating‐charge
debenture holders have the right to the proceeds of sale of the assets specified in the debenture that are
not already pledged against a fixed charge in any other debenture in the case of default as well. This
usually ends up being capital assets and produced goods. It should also be noted that a floating charge
ranks behind a fixed charge in the case of default; that is, the holders of fixed charges have first right
to the specified assets, with floating‐charge holders having access to what remains once fixed‐charge
holders’ debts have been satisfied. Unsecured note and debenture holders have equal ranking claims to
the proceeds of company assets that are not specified in a debenture in the case of default.
Examples of assets that can be pledged in a debenture include: land and buildings; specific indus­
trial equipment or ‘rolling stock’ such as railroad cars, trucks or aeroplanes; and even stocks and bonds
issued by other corporations or government units. Bond contracts that pledge assets in the event of
default have lower yields than similar bonds that are unsecured.
Corporate bonds are usually issued in denominations of $1000 and pay coupon interest semiannually.
Corporate debt can be sold in the domestic bond market or in the Australian‐dollar eurobond market,
MODULE 3 Financial markets 61
which is a market for the debt of Australian companies denominated in Australian dollars but traded
overseas. Bonds can also be classified as either senior debt, giving the bondholders first priority to the
firm’s assets (after secured claims are satisfied) in the event of default, or subordinated (junior) debt,
in which bondholders’ claims to the company’s assets rank behind senior debt.
Corporate bonds are secured with a trust deed or unsecured note deed that formalises the company’s
obligations to investors. The trust deed is the legal contract that states covenants and undertakings made
by the bond issuer which are designed to ensure the issuer can meet its obligations to bond investors, and
protects the security of the debenture investors in terms of the seniority of their claims on the proceeds
of asset sales in case of default. Provisions may entail limitations on the total liabilities or other lia­
bilities a company may take on, and may include terms related to the rights of bond investors to convert
their bond holdings under certain circumstances.
Hybrid securities are financial products issued in Australia that have characteristics of both debt
and equity. Traditionally, they have a set coupon or ‘dividend’ rate and set conversion dates when they
can be exchanged for ordinary equity. But the nature and characteristics of hybrids that are issued have
been evolving very rapidly over the past five years and no two hybrid securities are exactly the same. A
feature often found in hybrid securities is a reset date. On this date, the hybrid issuer can elect to change
the terms of the security (by changing either the next reset date or the coupon rate). Hybrid investors
can choose to convert their securities into shares or accept the new terms at the reset date. Hybrids can
also have cumulative or non‐cumulative interest payments. This means that if a coupon is not paid as
expected, a cumulative hybrid will pay it at the next coupon date, while a non‐cumulative hybrid holder
loses that coupon. Redeemable hybrids have the feature that they can be sold back to the issuer at the
original price they were bought for.
Another class of hybrid securities, which are a lot like ordinary equity, are called redeemable preference shares. These are preference shares that the company states it will buy back on a specified maturity
date. Because they are preference shares, they rank ahead of ordinary shares in a claim on assets of the
company, but rank behind debentures and other purer forms of debt. As such, they have the most equity‐
like characteristics of the hybrid securities. Because hybrids have these unusual features, their prices are
often correlated with the share price and they are sometimes classified as debt and sometimes as equity
by the Australian Taxation Office.
Investors in corporate bonds
Life insurance companies and superannuation funds are the dominant purchasers of corporate bonds.
Households and foreign investors also own large quantities of them. Corporate bonds are attractive to
insurance companies and superannuation funds because of the stability of their cash flows and the long‐
term nature of their liabilities. That is, by investing in long‐term corporate bonds, these firms are able to
lock in high market yields with maturities that closely match the maturity structure of their liabilities,
reducing their interest rate risk. In addition, most fund managers in Australia follow mandates that state
they can only invest in the leading Australian index, the UBS Australia Composite Bond Index. Until
2005, this index comprised only bonds rated A– and higher by Standard & Poor’s (S&P). The index
has since been expanded to cover bonds rated as low as BBB–. Also helping to drive the expansion of
the corporate bond market in Australia is the exemption from interest withholding tax (IWT) for most
issues. A bond is exempt from IWT if it meets the public offer test in the legislation. The intention of
this is to ensure that lenders in the capital markets are made aware of the new issue and that the bond is
made widely available to investors.
The primary market for corporate bonds
New corporate bond issues may be brought to market by two methods: public sale or private placement.
A public sale means the bond issue is offered publicly in the open market to all interested buyers; a
private placement means the bonds are sold privately to a few investors.
62 Finance essentials
Public offerings
Public offerings of bonds are usually made through an investment banking firm, which underwrites
them by purchasing the bonds from the issuer at a fixed price and then reselling them to individuals and
institutions. The investment banker can purchase the bonds either by competitive sale or through nego­
tiation with the issuer. A competitive sale is, in effect, a public auction. The issuer advertises publicly
for bids from underwriters and the bond issue is sold to the investment banker submitting the bid that
results in the lowest borrowing cost to the issuer. In contrast, a negotiated sale represents a contrac­
tual arrangement between the underwriter and the issuer in which the investment banker obtains the
exclusive right to originate, underwrite and distribute the new bond issue. The major difference between
these two methods of sale is that in a negotiated sale, the investment banker provides the origination and
advising services to the issuer as part of the negotiated package. In a competitive sale, the issuer or an
outside financial adviser performs origination services. It is generally believed that issuers will receive
the lowest possible interest cost through competitive, rather than negotiated, sales.
Private placement
Private placements occur occasionally in the Australian market, but they are generally only used
by ­Australian companies issuing offshore bonds in the United States of America. In contrast to
Australia, where no large private placement market has emerged, the US private placement market
grew because of the registration requirements of the Securities and Exchange Commission (SEC) on
publicly issued securities in the USA. The registration requirements were intended to protect individual
investors by forcing the issuing firms to disclose a modicum of information about their securities.
Unregistered securities (i.e. private placements) could be sold only to large, financially sophisticated
investors (in practice, usually large insurance companies or perhaps other institutional investors) as long
as fewer than 35 investors were involved and as long as the securities did not change hands quickly.
The rationale for exempting private placements from registration and disclosure requirements was
that large institutional investors possessed both the resources and sophistication to analyse the risks
of securities.
The secondary market for corporate bonds
Most secondary trading of corporate bonds occurs through dealers, although a few are traded on the
ASX. The secondary market for corporate bonds is thin compared with the markets for money market
securities or corporate stock. This means secondary market trades of corporate bonds are relatively infre­
quent. As a result, the bid–ask spread quoted by dealers of corporate bonds is quite high compared
with those of other, more marketable, securities. The higher bid–ask spread compensates the dealer for
holding relatively risky and illiquid securities in inventory.
Corporate bonds are less marketable than money market instruments and corporate equities for at least
two reasons. First, corporate bonds have special features, such as call provisions or sinking funds, that
make them difficult to value. Second, corporate bonds are long term; in general, longer term securities
are riskier and less marketable. To buy or sell a corporate bond in the secondary market, you must
contact a broker, who in turn contacts a dealer (or the ASX for exchange‐listed bonds), who provides
bid–ask quotes.
BEFORE YOU GO ON
1. Outline the major issuers of capital market securities.
2. What are hybrid securities? Outline their features.
3. Briefly discuss two methods used to issue corporate bonds in the primary market.
MODULE 3 Financial markets 63
3.4 Equity markets
LEARNING OBJECTIVE 3.4 Explain how equity securities are traded in the secondary markets and
discuss how the markets are operated.
Equity securities, also known as shares and stocks, represent part ownership of a corporation. Today in
Australia and New Zealand, most equity securities are no longer (paper) certificates but ownership rights
held on electronic databases. Equities are the most visible securities in most modern economies. As at
the end of October 2016, when the S&P/ASX 200 index stood at about 5318, the market capitalisation
of Australian‐listed domestic equities was $1664 billion.7
Australia has a high proportion of share ownership among its population; indeed, one of the highest
in the world according to the 2014 Australian Share Ownership Study released by the ASX.8 This
popularity of shares as a form of financial investment stems essentially from government policy: past
privatisations of publicly owned corporations, taxation policy and retirement incomes policy. In
late 2014, 6.48 million people, or 36 per cent of the adult Australian population, participated in the
Australian share market either directly (via shares or other listed investments) or indirectly (via unlisted
managed funds). This is a decline from 38 per cent two years previously in 2012.
From these data, it is obvious that share ownership is not just a feature of the financial affairs of the
wealthy. People from most income and wealth levels and most levels of education own and trade shares.
Proportionately more men (38 per cent) than women (27 per cent) own shares directly.9
Primary equity markets
New issues of securities are called primary offerings because they are sold in the primary market.
The company can use the funds raised by the sale of equity securities to expand production, enter new
markets, further research and the like. If the company has never before offered shares to the public and
so is essentially a privately held company looking to sell shares more widely, the primary offering is
called an initial public offering (IPO). All securities undergo a single primary offering, in which the
64 Finance essentials
issuer (seller) receives the proceeds of the offering and the investors receive the securities. Thereafter,
whenever the securities are bought or sold, the transaction occurs in the secondary market.
New issues of equity securities may be sold directly to investors by the issuing corporation through
dividend reinvestment schemes, rights issues and private placements. A dividend reinvestment program
(DPO) allows shareholders to increase their shareholdings gradually by automatically reinvesting their
dividends in extra shares as each dividend is ‘paid’. The issued shares are normally issued at either the
market price averaged over several days’ trading (often just after the record date for the dividend is
declared) or at a slight discount to this price. These dividends, although not received in cash, are still
taxable and still have franking credits attached in the same way as do cash dividends.
Companies may raise extra funds and place equity securities directly with their existing shareholders
through a rights issue, where a company’s shareholders are given the right to purchase additional shares
at a slightly below‐market price in proportion to their current ownership in the company. Therefore, a
two‐for‐five rights offer at a subscription price of $4 per share allows a shareholder with 5000 shares
to subscribe to another 2000 shares at $4 each. Rights are either renounceable or non‐renounceable.
Renounceable rights may be sold on the market if shareholders do not want to subscribe to the issue
and so increase their shareholdings. Non‐renounceable rights cannot be sold on the market; share­
holders have the option to subscribe or let the offer lapse. Renounceable rights have a positive value
when the subscription price for the rights‐issue shares is less than the current market price for the shares.
(Once issued, the rights‐issue shares are no different from the other shares of the same class available
on the market.)
Companies undertaking IPOs and indeed major rights issues normally engage the services of a mer­
chant or investment bank. Its task includes advising on the type of offering to make, the range of prices
that might be successfully charged and whether the offering will be fixed price or market sensitive. A
modern market‐sensitive method is the book build, a system in which larger institutions submit bids for
blocks of stock and, from these bids, the firm and its advisers decide what price or prices to charge the
public and the institutions.
Some equity securities are distributed through private placements in which the company or a merchant
bank acting as the company’s agent (and receives a commission or fee) negotiates directly with normally
large or institutional investors to set the terms and conditions of the issue. Private placements are
normally cheaper than public issues.
Many issues of equity by companies are underwritten, which assures the issuing firm that the total
amount of the sought funds will be raised.
Other capital transactions are share splits and share amalgamations or reverse splits. These trans­
actions do not raise more capital or change the existing book value of capital of the firm. Share splits
encompass the division of the entity’s shares into units of smaller value. For example, CSL Limited split
its shares in a 3:1 ratio (three new shares for each old share). Why would a firm go to the expense of
doing this? At the time, the shares were selling for about $90. The directors thought the shares would
become more attractive to retail investors and more highly traded if they were made more affordable.
Share amalgamations, the revaluation and elimination of some of the firm’s issued shares, encompass
the reduction of issued shares accompanied by a rise in value. A 3:1 amalgamation, for example, would
reduce the number of shares issued by a firm by two‐thirds. This is often done if the share value has
fallen so low that they look ‘too cheap’. Theoretically, a 10‐cent share in a firm amalgamating at the
rate of 3:1 would initially be traded at 30 cents in the market. (Other forces would probably very shortly
change the traded price.)
Secondary equity markets
Any trade of a security after its primary offering is said to be a secondary‐market transaction. When
an investor buys 1000 shares of ANZ Bank on the ASX, the proceeds of the sale do not go to ANZ
but rather to the investor who sold the shares. The investor who buys the shares is said to now be long
on ANZ, meaning that they have bought and are holding the shares in their portfolio. The contrasting
MODULE 3 Financial markets 65
position holds when a speculator thinks they might profit from a fall in the market, sells a security before
buying it, waits for the market to fall and then buys the security to make the delivery required from their
initial sale. This is called a short sale. Various exchanges around the world allow this type of trading,
but strictly regulate these operations to retain market confidence.
In Australia, almost all secondary‐market equity trading is done on the ASX. In October 2016, the
market capitalisation (market value) of 2190 ASX‐listed firms’ securities was $1.664 trillion.10 There
are, however, two other licenced stock exchanges, the National Stock Exchange of Australia (NSX),
which had 76 listed companies with a market capitalisation of $2.2 billion as at June 2016,11 and Chi‐X
Australia, which launched its exchange in October 2011 and now offers trading on the full suite of
ASX‐listed companies. By 2016 it was regularly recording over $1 billion of daily trading activity with
approximately 20 per cent of the market share.12
In New Zealand there is only one stock exchange, the New Zealand Exchange (NZX). The
NZX is much smaller than the ASX, with only 170 listed companies, many of which are large
Australian firms with significant businesses in the New Zealand and South Pacific areas. In
September 2016, market capitalisation was about NZ$122.2 billion and daily average value traded was
about NZ$175 million.13
Characteristics of markets
From an investor’s perspective, the function of secondary markets is to provide liquidity at fair prices.
Liquidity is the ease with which an asset may be converted to cash without a loss in value. It is achieved
if investors can trade large amounts of securities without affecting the prices. Prices are fair if they
reflect the underlying value of the security correctly.
There are several liquidity‐related characteristics of a secondary market that investors find desirable.
First, a secondary market is said to have market depth if orders exist both above and below the price at
which a security is currently trading. When a security trades in a deep market, temporary (split‐second!)
imbalances of purchase or sales orders at a given price, which would otherwise create substantial price
changes, encounter offsetting, thus stabilising sale or purchase orders.
Second, a secondary market is said to have market breadth if the orders that give the market depth
exist in significant volume. The broader the market, the greater the potential for stabilisation of tem­
porary price changes that may arise from order imbalances. Third, a market exhibits market resilience
if new orders pour in promptly in response to price changes resulting from temporary order imbalances.
For a market to be resilient, investors must be able to quickly learn of price changes. However, what
investors are most concerned with is having complete information concerning a security’s current price
and where that price can be obtained. The advent of the internet has greatly increased resilience because
all traders, no matter how large or small, can monitor market movements in real time. Additionally, the
introduction of internet trading has probably contributed somewhat to the significant increases in daily
trading volumes on the ASX in recent years.
Equity trading
As noted, there are three licenced stock exchanges in Australia: the ASX, the NSX and Chi‐X Australia.
All transactions conducted under the auspices of the ASX are done electronically. So although news
outlets love to show markets with physical trading floors, brokers’ employees gesticulating and shouting
bids and offers to each other, to illustrate stories about share market issues, these video clips are not of
the ASX at work. The ASX moved to the more efficient electronic model some years ago and, indeed, has
been at the forefront of world markets in developing software and systems to facilitate electronic trading.
Types of orders
Investors can ordinarily place two types of orders with their brokers, either directly electronically through
internet brokers or indirectly by email or telephone. A market order is an order to buy or sell at the
66 Finance essentials
best price available at the time the order reaches the market. So, for example, an Acrux Limited order to
buy 5000 shares at market when the quote was ‘Buy $3.21; sell $3.22’ would be executed immediately
at $3.22.
A limit order is an order to buy or sell at a designated price (the limit price stated on the order) or
any better price. Therefore, a limit order is actually a bid for, or offering of, securities. To continue the
example, a limit order to buy 5000 Acrux Limited shares at $3.22 when the quote was ‘Buy $3.21;
sell $3.22’ would be executed immediately at $3.22 if 5000 shares were on offer at that price. If only
3000 shares were available, these would be bought at $3.22 and the order would remain partly filled
until more shares were offered at $3.22. Sometimes the market will move away from the target price
and an order remains unfilled for some time. Suppose the market moves up to $3.23, $3.24, $3.25, then
moves back down gradually to $3.22. This order would be completed only when the market moved back
to $3.22 and 2000 more shares were available at that price.
When a limit order carries a price that is not close to current market prices, the order joins the market
depth list — the list of all buy and sell bids at prices far from the current market price — but is unlikely
to be executed quickly. For example, a bid or purchase order at $2.80 for Acrux Limited might not be
satisfied for days or weeks, and might never be satisfied.
Another possibility with a limit order is that, while it may be ‘Buy 5000 at $3.22’, the market has
moved downwards while the order is being submitted and processed. Suppose the market moves to
$3.19 and 10 000 shares are available for sale at that price. The limit order for 5000 shares at $3.22 will
be processed at $3.19.
BEFORE YOU GO ON
1. Describe three types of equity securities.
2. Explain how equity securities are traded in the primary market.
3. Explain how equity securities are traded in the secondary market.
3.5 Derivative markets
LEARNING OBJECTIVE 3.5 Describe the most common types of derivative contracts.
The securities discussed in previous sections have diverse payoff characteristics, and most financial insti­
tutions and other investors pursue their investment objectives by picking and choosing among those
securities. At any given point in time, however, these investors may be exposed to more or less risk than
they desire in one or more securities or markets. This is where derivative securities come in.
Derivative securities generate substantial fee income for the financial institutions that invent and
market them. On top of the individual benefits in the form of fee income derived by financial insti­
tutions marketing derivatives, the derivatives markets provide significant benefits to national financial
markets. First, derivatives trading allows risk to be shared among market participants. Some participants
will take on risk in return for earning fees, while others will be pleased to shed risk for a known and
realised cost. Second, derivatives can increase liquidity in any given market by increasing turnover and
trading depth. Third, an important function of derivatives markets is the transmission of information. If
the price of the six‐month forward SPI 200 Equity Index contract rises, what does this tell you about
the market’s expectations of the future movement generally of Australian share prices? The answer is
that investors generally believe the market will rise. Therefore, derivatives have an important role in
information transmission and sharing.
A derivative security is a financial instrument whose value depends on, or is derived from, some
underlying security. For example, the value of a futures contract to buy grain or gold at some future
point in time is derived from the value of grain and gold; similarly, the value of a futures contract to buy
Treasury bonds is derived from the value of those bonds.
MODULE 3 Financial markets 67
The most common types of derivative contracts are a forward contract, a futures contract and
an option contract. Virtually all derivative securities are some combination of these three basic
contracts.
Derivatives are an integral part of a successful risk management program because they offer an inex­
pensive means of changing a firm’s risk profile. This profile describes how the firm’s value or cash flows
will change in response to changes in some risk factor. Common risk factors are interest rates, commodity
prices, share market indices and FX rates. By taking a position in a derivative security that offsets the
firm’s risk profile, the firm can limit how much its value is affected by changes in the risk factor. Similarly,
investors can use derivative securities to speculate on these risk factors.
Given the effectiveness of derivative securities in managing a firm’s risk exposures, it is not surprising
that the markets for derivative securities have seen tremendous growth in the past 25 years. In fact,
according to a recent survey by the International Swaps and Derivatives Association (ISDA), 94 per cent
of the world’s largest companies use derivatives to manage their risks.14 Differences between the first
two of these basic derivative securities, forwards and futures, are now discussed.
Differences between futures and forward markets
Futures contracts differ from forward contracts in several ways. Many of the differences can be attributed
to futures contracts being traded on an organised exchange, such as the ASX, while forward contracts
are traded in the informal OTC market.
One of the most important differences between futures and forwards is that the former are stan­
dardised in quantities, delivery periods and grades of deliverable items, whereas the latter are not.
Most futures contracts call for the delivery of specific commodities, securities or currencies either on
specific future dates or over limited periods. For example, bank‐bill futures have a contract size of one
A$1 million face‐value 90‐day BAB or electronic equivalent. Delivery months are limited to March,
June, September and December up to 20 quarter‐months (5 years) ahead. This standardisation results in
a relatively large volume of transactions for a given contract. This makes trading in the contract easy
and inexpensive.
In addition, although there must be a buyer and seller when any new contract is initiated, both parties
in a futures‐market transaction hold formal contracts with the futures exchange, not with each other.
This device decreases the risk involved in futures trading. This is technically called novation because
another (new) party is involved in each contract. Every major futures exchange operates a clearinghouse
that acts as the counterparty to all buyers and all sellers. Although individual traders interact with each
other either electronically, as with the ASX, or face to face in a trading ‘pit’, the actual contract drawn
up to formalise the trade breaks this direct link between buyer and seller and instead inserts the clear­
inghouse as the counterparty. This means traders need not worry about the creditworthiness of the party
they trade with (as forward market traders must) but only about the wisdom of the transaction itself.
Forward contracts are riskier because one party may default if prices change dramatically before the
delivery date.
The futures exchange is protected from default risk by requiring daily cash settlement of all contracts,
called marking to market. By its very nature, a futures contract is a zero‐sum game in that, whenever
the market price of a commodity changes, the underlying value of a long (purchase) or short (sale) pos­
ition also changes — and one party’s gain is the other party’s loss. By requiring each contract’s loser to
pay the exchange (on behalf of the winner) the net amount of this change each day, futures exchanges
eliminate the possibility that large unrealised losses will build up over time. Market participants post
margin money (if necessary) to take account of gains or losses accruing from daily price fluctuations.
In a forward contract, on the other hand, there are no cash flows between origination and termination of
the contract.
Because the futures exchange acts as the counterparty in all futures contracts and all contracts are
marked to market daily, either party in a futures contract can liquidate its future obligation to buy
(or deliver) goods by offsetting it with a sale (or purchase) of an identical futures contract before the
68 Finance essentials
scheduled delivery date. In the forward exchange markets, contracts are ordinarily satisfied by actual
delivery of specified items on the specified date. In the futures market, almost all contracts are offset
before delivery.
Uses of the financial futures markets
Financial futures markets have grown rapidly because they provide a way for financial market partici­
pants to insulate themselves against changes in interest rates and asset prices. Financial futures can be
used to reduce the systematic risk of share portfolios or to guarantee future returns or costs. In general,
financial futures prices move inversely with interest rates and directly with financial asset prices, so the
sale of futures can offset asset price risk. Systematic risk will be covered in more detail in the module
on risk and return.
Options markets
One drawback of so‐called hedging with futures is that the hedging process can completely insulate a
firm against price changes. While this reduces the firm’s losses if prices move adversely, it also elim­
inates potential gains if prices move favourably. Because hedging with futures eliminates gains as
well as losses, some people prefer to use options rather than futures contracts to insure themselves
against interest rate risk. Options have been available on shares for many years and have been traded on
organised exchanges globally since 1973. In 1980, the Sydney Futures Exchange (SFE) introduced the
world’s first exchange‐traded options on financial futures with options on bank bills and US dollars. US
exchanges offered their first futures options in 1982.
The nature of options
An option gives the holder the right, but not the obligation, to buy or sell an asset. An option need not
be exercised if it is not to the buyer’s advantage to do so. Therefore options allow holders to enter into
contracts to buy or sell shares, commodities or other securities at a predetermined price, called the strike
or exercise price, until some future time. Unlike futures contracts, in which both the buyer and the seller
have obligations, an option buyer has a right but not an obligation, while the option seller or writer has
an obligation if the other party exercises the option.
Clearly option writers will not agree to such arrangements unless they are compensated. The price
that an option buyer pays an option seller is called the option premium. In addition, an option is good
for only a limited time. With an American option, the option can be exercised at any time before
and including the expiry date. With a European option, the option can be exercised only on the expiry
date. Generally options are traded in Australia under the anytime American model, but the ASX Index
option is European in style.
The buyer of the option pays the seller (writer) a premium. The writer keeps the premium regardless.
An option provides the buyer with a choice. If price movements are advantageous, the option buyer exer­
cises the option and realises a gain. If price movements are adverse, the buyer can limit potential losses
by letting the option expire unexercised. The option premium is the price of this insurance.
Option premiums are influenced by the difference between the strike prices offered, and the current
and expected market prices for the underlying shares. Additionally, the premiums in any one trading day
will rise or fall according to the interaction of supply and demand, the normal forces affecting the price
of any good or service.
Options versus futures
The gains and losses to buyers and sellers of futures contracts are quite different from those for buyers
and sellers of option contracts (see figure 3.3). For futures, both gains and losses can vary virtually
without limit. Therefore some buyers (and sellers) prefer options to futures contracts. For instance, sup­
pose a portfolio manager thinks interest rates will decline but is not sure. To take advantage of the rate
decline, the manager might want to buy many long‐term bonds that would increase in value as rates fell.
MODULE 3 Financial markets 69
However, if rates rose the bonds would lose value and the manager might lose their job. If the manager
hedged in the futures market by selling bond futures, they would be safe if rates rose, because the loss
on the bonds in the portfolio would be offset by the gain on the short sale of the bond futures. However,
if rates fell, the loss on the bond futures would eliminate the gain in value of the bonds in the portfolio.
Consequently, the portfolio manager might prefer to buy a bond put option (a contract that gives the
owner the right, but not the obligation, to sell a specified volume of a security at a specific price within
a specific time frame). If bond prices fell, the put option would rise in value and offset the loss on the
bond portfolio. However, if rates fell as expected, the market value of the bonds would rise and the man­
ager could let the bond put expire unused, losing only the premium. Similar measures could be used by
financial institution managers who want to buy protection against unexpected rises in interest rates that
could lower the value of their mortgage portfolios.
FIGURE 3.3
Gain
+5
0
−5
Loss
Gains and losses on options and futures contracts if options are exercised at expiry
Buyer of call at 40
with premium of $5
40 45
Writer of call at 40
for premium of $5
Price of security
(a)
Gain
+5
0
−5
Loss
Buyer of put at 40
with premium of $5
35 40
Writer of put at 40
for premium of $5
Price of security
(b)
Gain
+5
0
−5
Loss
Buyer of future at 40
40
Seller of future at 40
Price of security
(c)
Options, then, give a price protection as well as upside potential that is not available from futures.
However, the premiums on options may be high and options experience time decay. The potential buyer
of the protection must decide whether the insurance value provided by the option is worth its price.
BEFORE YOU GO ON
1. What role does the exchange play in futures market transactions?
2. What does the seller of a put option hope will happen?
3. Explain the nature of an option contract.
3.6 Foreign exchange markets
LEARNING OBJECTIVE 3.6 Explain how the foreign exchange markets operate and facilitate
international trade.
If you have travelled internationally, you will have used an amount of your domestic currency to buy
an amount of another currency or foreign exchange (FX) to use overseas. You will have noticed that
exchange rates move over time, even over a period of days. For example, the cost of holidaying in
Europe was lower in September 2012 than in September 2016 because of the lower cost of the euro (as
purchased with Australian dollars).15 Australian firms that conduct business in foreign countries with
different currencies face two additional risks: currency and country risks. Currency risk stems from
the values of currencies fluctuating relative to each other. Country risk comes from the possibility of
financial claims and other business contracts being repudiated or becoming unenforceable because of a
change in government policy or government.
70 Finance essentials
The difficulties of international trade
When Australian manufacturers need to buy raw materials, they want to get the best possible deal. So
they investigate several potential suppliers to determine the availability and quality of materials from
each, how long it takes to receive an order and the total delivered price. When all potential suppliers are
located in Australia, comparison of the alternatives is relatively easy. Both suppliers and customers keep
their books, price their goods and services, and pay their employees in the same currency: the Australian
dollar. Furthermore, since the federal government regulates commerce, it is unlikely that there will be
any problems in shipping between states. If a dispute arises, the buyer and the seller are governed by the
same legal traditions and have access to the court system.
When potential suppliers are not located in Australia, comparisons are more difficult because the
evaluation process is complicated by at least four factors. The first problem is that the Australian buyer
prefers to pay for the purchase with Australian dollars, but the foreign supplier must pay employees and
other local expenses with its domestic currency. Therefore, one of the two parties to the transaction will
be forced to deal in a foreign currency. The second difficulty is that no single country has total authority
over all aspects of these transactions. Nations may erect barriers to control international product and
capital flows, such as high tariffs and controls on FX. Third, countries may have distinctly different legal
traditions, such as the English common law used in Australia and the French codified civil law which
is encountered in many other nations. Finally, banks and other lending agencies often find it difficult
to obtain reliable information on which to base credit decisions in many countries.
To facilitate these international transactions, there are two distinct kinds of international markets: the
international money and capital markets, which provide the market for credit (international lending and
borrowing); and the FX markets, which deal in the media of exchange or the means of payment. Both
markets influence each other in a variety of ways. In particular, it is impossible to transfer funds across
international borders without using the FX market.
Exchange rates
The complicating factor in comparing suppliers that price their goods in currency units other than the
Australian dollar is the easiest to overcome. To make these comparisons, the Australian buyer can
check the appropriate exchange‐rate quotation in the FX market. An exchange rate is the price of one
monetary unit, such as the US dollar, stated in terms of another currency unit, such as the Australian
dollar. The FX market has a well‐defined set of conventions governing the quotations of currencies.
Participants in these markets must be aware of these conventions when asking for the price of foreign
currency. Further, the order in which currencies are expressed, for example, USD/AUD or AUD/USD,
has a specific meaning in the FX market. The first currency in the quote is the base currency or the unit
of the quotation, since it is the price of one unit of that currency being traded or quoted. The second‐
named currency in the FX quote is the terms currency, or the currency in which the price is expressed.
In many FX markets, exchange rates are quoted as the domestic currency per unit of foreign currency,
with most currencies quoted against the USD. Such exchange rates are known as direct quotes. When
direct quotes are used, the foreign currency is the base currency and the domestic currency is the terms
currency.
An exchange quotation given in the form ‘USD/AUD — 1.3333’ means that the price of one US dollar
is A$1.3333. We are not accustomed to hearing or seeing the AUD quoted in direct terms but, given
that exchange rate, we can easily find the value of one AUD by inverting the rate. Thus: AUD/USD =
1/1.3333 = 0.7500
An exchange rate quotation given in the form ‘AUD/USD — 0.7500’ means that the value of one
Australian dollar is 75 US cents. Again, given that exchange rate quotation, we can easily find the value
of one USD by inverting the rate. Thus: USD/AUD = 1/0.7500 = 1.3333
However, exchange rates are not constant. Today, most exchange rates are free to move up and down
in response to changes in the underlying economic environment. The demand for a country’s products
MODULE 3 Financial markets 71
will be higher when the country’s currency declines against other currencies. A change in the exchange
rate for the dollar is likely to lead to a reversal of purchase decisions even though the price of the
product remains unchanged.
A global currency war has been intensifying since 2010. Central banks are competing to lower their
exchange rates and boost their economies. The currency war involves central banks — most prominently
the Bank of Japan (yen/JPY), People’s Bank of China (renminbi/RMB), Central Bank of Brazil (real/
BRL) and Swiss National Bank (Swiss franc/SFr). These central banks are battling it out to increase
exports and/or lower exchange rates to perceived fundamental value. Very large monetary stimulus in
countries that face weak domestic demand, such as in Europe, Japan and the USA, has led to global
trade tensions emerging and becoming a prominent concern for policymakers.16
The operations of foreign exchange markets
Before discussing the modern operations of floating‐rate FX markets, this section firstly looks briefly
at some history, government intervention in FX markets and general considerations about exchange
rates.
Each country or monetary union around the world is responsible for the determination of its exchange
rate regime; that is, the method by which the exchange rate of the currency is calculated. Over the ages,
currencies have been defined in terms of gold and other items of value. After World War II, most nations
adopted a fixed exchange rate system where each country was required to fix the value or exchange
rate of its currency in terms of the USD, with only the USD being convertible to gold. Today, major
currencies, such as the US dollar (USD), the UK pound sterling (GBP), the Japanese yen (JPY), the
European Monetary Union euro (EUR) and the Australian dollar (AUD) all adopt a floating exchange
rate regime or a free float. FX regimes change over time and a number of other countries utilise a managed float, where the currency is allowed to move within a defined range or band relative to another
major currency such as the USD. Other regimes include a crawling peg and pegged exchange rate.
China applies a crawling peg FX regime that allows its currency to appreciate gradually over time within
72 Finance essentials
a limited range determined by its government. Hong Kong uses a pegged FX regime where it directly
links its currency to the USD.
Inflation and exchange rates
One of the most important mechanisms by which governments may influence foreign currency values is
through their monetary policies, insofar as those policies affect domestic inflation. A country with high
inflation will tend to have higher nominal interest rates, often coupled with lower real interest rates and a
deteriorating balance of merchandise trade. As interest rates and trade flows are tied closely to exchange
rates, it should not be surprising that exchange rates are materially affected by changes in a country’s
rate of inflation.
Given that inflation causes prices to rise in Australia relative to other countries, Australian buyers
are likely to switch from domestic goods to imported foreign goods. Similarly, foreigners are likely to
switch from Australian products to those from other countries. Thus the demand for Australian goods
will tend to fall at the same time that Australians supply more dollars in exchange for foreign currencies
so that they can buy foreign goods. Consequently, these inflation‐generated supply and demand shifts
will cause the dollar’s exchange rate to fall relative to other currencies. Conversely, as the Australian
inflation rate falls relative to another country, the exchange value of the dollar should rise relative to that
country’s currency and vice versa.
Foreign exchange markets
Many references have been made in this module to FX markets. In these markets, individuals, corpor­
ations, banks and governments interact with each other to convert one currency into another. These
markets are efficient and competitive. In July 2016, FX transactions amounted to $171.5 billion per day
by Australian dealers.17
The primary rationale for FX markets is that they provide a mechanism for transferring purchasing
power from those who normally deal in one currency to those who generally do business in another.
Import and export of goods and services are facilitated by this conversion service, because the parties to
the transactions can deal in terms of mediums of exchange instead of having to rely on bartering. The
currencies of some countries, such as those of centrally planned socialist countries, are not convertible
into other currencies. If a corporation chartered in another country wants to do business in a country
whose currency is non‐convertible, the corporation may be required to accept locally produced merchan­
dise in lieu of money as payment for goods and services. This practice is known as countertrade and
occurs periodically between Australia and China.
A second reason that efficient FX markets have developed is that they provide a means for passing
the risk associated with changes in exchange rates to professional risk takers. This hedging function is
particularly important to corporations in the present era of floating exchange rates.
The third important reason for the continuing prosperity of FX markets is the provision of credit.
The time span between shipment of goods by an exporter and their receipt by an importer can be con­
siderable. While the goods are in transit, they must be financed. FX markets are one device by which
financing and related currency conversions can be accomplished efficiently and at low cost.
Market structure
There is no single or dominant formal Australian FX market equivalent to the ASX, which exists for the
sale of shares. The FX market is an OTC market similar to the one for money market instruments. More
specifically, the FX market is composed of a group of informal markets closely interlinked through inter­
national branch banking and correspondent bank relationships. The participants are linked electronically.
The market has no fixed trading hours and, since 1982 when a forward market opened in Singapore, FX
trading can take place at any time on every day of the year. There are also no written rules governing
the operation of the FX markets. However, transactions are conducted according to principles and a
code of ethics that have evolved over time. How much a country’s currency is traded in the worldwide
MODULE 3 Financial markets 73
market depends, in some measure, on local regulations that vary from country to country. Virtually every
country has some type of active FX market.
Major participants
The major participants in FX markets are the large multinational commercial banks, although many
investment banking houses have established FX trading operations in recent years. In Australia, the
market is dominated by the major banks. These operate in the FX market on two levels. First, on the
retail level banks deal with individuals and corporations. Second, on the wholesale level banks operate
in the interbank market. Major banks usually transact directly with the foreign institutions involved.
However, many transactions are mediated by FX brokers. These brokers preserve the anonymity of the
parties until the transaction is concluded.
The other major participants in FX markets are the central banks of various countries. Central banks
typically intervene in FX markets to smooth out fluctuations in currency exchange rates. Additional
participants in FX markets are individuals and nonfinancial businesses, which enter the market through
banks for various commercial reasons.
Trading foreign exchange
In commercial banks, FX trading is usually done by only a few people. As in the money markets, the
pace of transactions is rapid and traders must be able to make on‐the‐spot judgements about whether
to buy or sell a particular currency. They have a dual responsibility in that, on the one hand, they must
maintain the bank’s position (inventory) to meet customer needs; however, on the other hand, they must
not take large losses if the value of a currency falls. The task is difficult because currency values tend to
fluctuate rapidly and often widely, especially given that currencies are always subject to possible deval­
uations by their governments. However, if a currency is expected to fall in value, banks may want to sell
it to reduce their FX losses.
Transfer process
The international funds‐transfer process is facilitated by interbank clearing systems. The large multi­
national banks of each country are linked through international correspondent relationships, as well as
through their worldwide branching systems. Within each country, regional banks are linked to international
banks’ main offices, through either nationwide branching systems or domestic correspondent networks.
Balance of payments
At the heart of the movement of FX rates is the change in a country’s balance of payments. The balance
of payments is a convenient way to summarise a country’s international balance of trade (its exports
less its imports) and the payments to and receipts from foreigners. Although more complicated, the
accounting is similar to how an individual or family would keep records of all their expenditures and
receipts. For example, a deficit in the family budget means that family members spent more money than
was collected. A deficit in the Australian balance of payments means that collectively we are paying out
more money abroad for imports and foreign services than we are collecting from foreigners who buy our
exported goods and services.
International trade and exchange rates
According to the classical theory of international trade, nations produce the goods and services for
which they enjoy a comparative advantage, and then they trade with foreigners to obtain other goods and
services. Anything that affects the demand for a country’s exports or imports has the potential to cause
shifts in the supply and demand curves for foreign currency and, consequently, to alter the price of its
currency in the FX market. Five factors that influence long‐run supply and demand conditions are:
•• relative prices: the relative costs of the factors of production can give one country an advantage
over another
74 Finance essentials
•• barriers to trade: such as tariffs, quotas, other trade restrictions and taxes
•• resource endowment: for example, Asian nations tend to have an abundant supply of inexpensive labour
•• tastes: relative tastes for Australian goods versus foreign goods affect the supply and demand for
traded goods
•• productivity: a country’s productivity relative to other countries.
A theory that explains international trade flows is purchasing power parity (PPP). This means that
exchange rates tend to move to levels at which the cost of goods in any country is the same in the same
currency. For instance, if a Big Mac hamburger costs $3 in Australia and ¥330 in Japan, PPP would
exist when the A$/¥ exchange rate was ¥110, because then a Big Mac would cost the same in the same
currency in both countries.
Because of transportation costs and trade restrictions, PPP is only an abstract concept. Factors such
as relative prices, productivity and tastes are at the heart of what affects the flow of goods and services
between countries, and have an effect on exchange rates. Although exchange rates tend to adjust so that
similar products cost a similar amount in the same currency in different countries, the adjustment may
not be complete for all products and may take years to happen. Therefore, some additional factors that
drive the volatility of FX rates must be sought.
Capital flows and exchange rates
As discussed, Australia has run a deficit in its current account for many years. The current account
deficit means that foreign citizens will be increasing their holdings of Australian dollars and other claims
on Australian assets. If foreigners sell their extra AUD to obtain their domestic currency, the value of the
AUD will fall. Therefore many people think that when Australia runs a deficit on its balance of payments
current account, the AUD should fall in value relative to other currencies. However, this is not always
the case, as foreigners can buy Australian capital assets as well as Australian goods and services. If
interest rates in Australia are high and Australian inflation is expected to be low, foreigners can expect to
earn high real returns if they invest in Australia. Therefore, net foreign demand for both short‐term and
long‐term investments may be great enough to support a higher price for the AUD even if Australia runs
a balance of payments current account deficit. The change in the dollar value cannot be predicted unless
these desired intracountry investment (capital) flows are also taken into account.
At least three types of international capital flows can affect a currency’s exchange rate and explain the
volatility of exchange rates:
•• investment capital flows: either short‐term money market flows motivated by differences in interest
rates or long‐term capital investments in a nation’s real or financial assets
•• political capital flows: international capital flows that respond to changed political conditions in
a country
•• central banks’ FX market operations: FX market operations undertaken to damp down wild swings in
their currencies’ exchange rates.
The globalisation of financial markets
In the past 30 years, the globalisation of business and the exponential growth of international finan­
cial markets have been strongly in evidence. Financial instruments and even entire markets that did not
exist in the early 1970s have developed and grown to maturity. A complex interaction of historical, pol­
itical and economic factors drives the globalisation of financial markets. Historical and political factors
include the demise of the Bretton Woods system of fixed exchange rates, economic disruption caused by
fluctuating oil prices, large trade deficits experienced by the USA, Japan’s rise to financial pre‐eminence
during the 1980s and its weakness in the 1990s and early 2000s, the global economic expansion that
began in late 1982, the Asian economic crisis in the late 1990s, the fall of the Soviet Union and adoption
of the euro in 1999.
Long‐term economic and technological factors that have promoted the internationalisation of financial
markets include the global trend towards financial deregulation, standardisation of business practices
MODULE 3 Financial markets 75
and processes, ongoing integration of international product and service markets, and breakthroughs in
telecommunications and computer technology.
The discussion now turns to factors that have led to the globalisation of financial markets.
Emergence of floating exchange rates
Australia floated its currency in late 1983. Despite the movement to floating exchange rates that swept
the developed world in the 1970s, Australia was rather late to adopt this reform. However, the RBA was
forced to ‘go with the flow’ because it had become virtually impossible to implement monetary policy
under the fixed‐rate regime. This was because, under the fixed exchange rate system, the central bank
was forced to buy or sell all Australian dollars offered or requested. The 1980s were a time of very high
interest rates (the overnight rate hit 15 per cent in 1984) and Australia enjoyed large foreign capital
inflows. The RBA was forced to purchase these foreign currencies and sell Australian dollars. Therefore
the money supply in Australia could not be controlled and inflation could not be effectively managed.
Annual inflation during this period regularly exceeded 10 per cent. Having a floating rate that was set
by supply and demand in the market allowed the RBA to regain control over economic activity through
using expansionary or contractionary monetary policy as deemed necessary.
Rise of multinational companies
As the economies of the world have become increasingly interdependent in recent years, large, multi­
national companies have grown ever more powerful. For these companies, their capital is almost
completely mobile, and their approach to financial management is global in scope and sophisticated
in technique. Many large, multinational firms have integrated sales and production operations in
100 or more countries, which also requires state‐of‐the‐art systems for currency trading, cash manage­
ment, capital budgeting and risk management. The financial needs of these companies have been met
by the major international banks, which have followed their customers as they expanded around
the world.
Technology
Breakthroughs in telecommunications and computer technology have transformed international finance
at least as much as they have transformed our own lives and careers. Daily international capital move­
ments larger than the gross national products of most countries have now become routine as a result of
the speed, reliability and pervasiveness of information‐processing technology. Computers now direct
multibillion‐dollar program trading systems in equity, futures and options markets around the world,
and a telecommunications ‘global village’ has become a reality for currency traders operating 24 hours
a day, 365 days a year from outposts on every continent. The future will certainly bring even more rapid
innovation.
The US dollar as the ‘new gold standard’
One of the problems that currencies encounter is that governments develop reputations for the way
they conduct monetary policy. For example, say a country conducts monetary policy in an irresponsible
manner by issuing too much currency, which leads to high rates of domestic inflation and possible
devaluation of the currency. People soon become reluctant to hold that currency.
Because of the devaluation risk, people who lend money in that currency demand higher interest rates
as compensation for risk bearing. Because people wish to trade with stable currencies that are widely
accepted, the US dollar has benefited. For instance, it is estimated that roughly two‐thirds of all US cur­
rency outstanding is held outside the USA. The reason, in part, is because the US dollar is highly valued
for trade and as a store of value because the USA has low inflation relative to most countries. This works
out as a good deal for the USA. That is, by printing pieces of paper that are used as currency in many
countries around the world, the USA and its citizens are able to obtain valuable goods in exchange.
76 Finance essentials
The development of the euro
The euro currency is another example of the development of a multicountry standard of value. The
euro was introduced in two stages: initially in January 1999, when people could write cheques or get loans
in euros but could not make cash transactions; then cash transactions were introduced three years later.
Now the euro circulates as the EU’s single currency and most national currencies have been phased out.
Twenty‐seven European countries are EU members. Once a country becomes a member of the EU, it
can elect to join the Economic and Monetary Union (EMU), which operates the EU’s central bank, the
European Central Bank (ECB). However, to be admitted into the single currency community, a prospec­
tive EU member must meet strict fiscal and monetary qualifications. Not all of the member nations have
adopted the euro as their national currency: among others, Denmark, the United Kingdom and Sweden
have not. In these three nations, there is strong public anxiety that dropping their national currencies would
involve giving up too much independence, in particular, their national currency, central bank and monetary
policy independence. This has recently manifested itself with the UK voting in a public referendum to exit
(the so‐called Brexit) the European Union, heightening anxiety among other member nations.
The EU motivation for adopting a common currency is to make member countries more competitive
in global markets by better integrating their national economies and reducing the economic inefficiency
caused by large fluctuations in FX rates. In addition, the ECB was established to set a single monetary
policy and interest rates for the adopting nations. The establishment of the EU is widely regarded as a
major step towards European political unification.
BEFORE YOU GO ON
1. Explain how the exchange rate is quoted.
2. Briefly describe five factors that influence long‐run supply and demand conditions for international
trade.
3. Outline the factors that led to the globalisation of financial markets.
MODULE 3 Financial markets 77
SUMMARY
3.1 Explain the characteristics of money market instruments.
Investors in money market instruments want to take as little risk as possible given the temporary
nature of their cash surplus. Issuers of money market instruments are trying to deal with temporary
cash deficits. Money market instruments have low default risk, have low price risk because of their
short terms to maturity, are highly marketable because they can be bought or sold quickly and are sold
in large denominations, typically $1 million or more, so that the cost of executing transactions is low.
3.2 Explain the role and function of capital markets, and how their role differs from that of the
money markets.
The capital markets are where businesses finance assets that produce core business products for
them. They produce these products in order to earn a profit. Capital assets normally have a long
economic life, so capital market instruments have long maturities, typically 5 years or longer, and
involve more risk than money market securities.
3.3 Differentiate treasury bonds, semis and corporate bonds.
Treasury bonds are Commonwealth Government Securities issued by the AOFM and backed by the
Commonwealth Government. They are sold through auctions, pay fixed coupons semiannually and
carry the lowest default risk (being classed as risk free). Semis are state government bonds sold through
dealer panels. Semis trade at a higher yield than treasury bonds as they are not considered risk free. Cor­
porate bonds are typically made through public offerings within Australia, while private placements are
made mainly in offshore markets. Corporate bonds can be unsecured notes or debentures.
3.4 Explain how equity securities are traded in the secondary markets and discuss how the
markets are operated.
Any trade of a previously issued security takes place in the secondary market. Secondary markets
provide liquidity by allowing equity holders to convert their shares into cash with relative ease and
without loss of value. Secondary markets may have depth (many purchase and sale orders above and
below the current trading price), breadth (a significant volume of transactions that provide depth)
and resilience (the generation of new orders to correct temporary order imbalances).
3.5 Describe the most common types of derivative contracts.
The three most common types of derivative contracts are forward, futures and options contracts. A
forward contract is a contract that guarantees delivery of a certain amount of goods, such as foreign
currency, for exchange into a specific amount of another currency, such as dollars, on a specific day in
the future. A futures contract is a contract to buy (or sell) a particular type of security or commodity
from (or to) the futures exchange during a predetermined future time period. An options contract
allows the holder to buy (or sell) a specified asset at a predetermined price before its expiration date.
3.6 Explain how the foreign exchange markets operate and facilitate international trade.
FX markets exist because they provide a mechanism for transferring purchasing power from indi­
viduals who normally deal in one currency to people who generally transact business using a different
monetary unit. The FX market is an OTC market similar to the one for money market instruments. It is
composed of a group of informal markets linked electronically. The market has no fixed trading hours
and trading can take place at any time on every day of the year. FX markets facilitate international trade
by allowing firms to compare the cost of foreign goods in the home currency and to effect payments.
KEY TERMS
adjustable‐rate preference shares preferred shares issued with adjustable rates; the dividends are
adjusted periodically in response to changing market interest rates
American option option that can be exercised at any time until the option expires
asset‐backed commercial papers (ABCP) short‐term securities backed by financial assets including
mortgages, receivables and long‐term securities
78 Finance essentials
balance of payments set of accounts that summarises a country’s international balance of trade, and
the payments to and receipts from foreigners
bank‐accepted bill (BAB) a draft drawn on a bank by a corporation to pay for merchandise, the draft
promising payment of a certain sum of money to its holder at some future date; in effect, the bank
substitutes its credit standing for that of the issuing corporation
base currency first‐named currency in the FX quote: one unit expressed in terms of another currency
being traded
bondholder the lender in a bond contract
bond issuer the borrower in a bond contract
bonds debt‐based contractual obligations where corporate or government borrowers issue a security
that has fixed characteristics, such as term interest (coupon) payments and principal (which is repaid
at maturity)
book build system in which larger institutions submit bids for blocks of stock in an IPO and,
from these bids, the firm and its advisers decide what price or prices to charge the public and the
institutions
capital markets financial markets where equity and debt instruments with maturities of greater than
1 year are traded
cash market another name for the spot market, which involves the exchange of securities or other
financial claims for immediate payment
cash rate the overnight (or one‐day) interest rate for unsecured loans between banks
clearinghouse back office that records, clears and settles contracts and acts as a counterparty in
futures trading
commercial paper an unsecured, short‐term promissory note issued by a large, creditworthy business
or financial institution
contributing shares shares issued when partly paid for, so that there is an obligation on the holder to
contribute the balance
convertible preference shares preference shares that can be converted into ordinary shares at a
predetermined ratio
corporate bonds long‐term IOUs that represent a claim against a firm’s assets
countertrade in international trade transactions, the practice of accepting locally produced
merchandise in lieu of money as payment for goods and services
country risk risk tied to political developments in a country that affect the return on loans or
investments
coupon payments the periodic interest payments in a bond contract
coupon rate the annual coupon payment of a bond divided by the bond’s face value
crawling peg a managed float where an exchange rate is allowed to appreciate in controlled steps over
time
cumulative a feature of preference shares that means the firm cannot pay a dividend on its ordinary
shares until it has paid the preference shareholders the dividends in arrears
currency risk risk resulting from changes in FX values that affect the return on loans or investments
denominated in other currencies
dealer panel a small set of bond dealers, mostly comprising banks, that agree to buy semis from state
governments in either closed auctions (where stock is assigned to the best bids) or through agreeing
to buy a given amount at a given price
debentures debt instruments usually issued by corporate borrowers; they may be unsecured
and hence rely on the creditworthiness of the issuer, or secured by charges over the corporate
borrower’s assets
direct quotes from the perspective of the Australian FX market, a quotation that provides the cost of
obtaining one unit of foreign currency in exchange for domestic currency
MODULE 3 Financial markets 79
dividend reinvestment program (DRP) program in which a company sells new shares, free of
commission, to dividend recipients who elect to automatically reinvest their dividends in the
company’s shares
European option option that can be exercised only at expiry
exchange rate rate at which one nation’s currency can be exchanged for another’s at the present time
exchange settlement funds funds held in accounts of the RBA to facilitate settlement between
clearing banks
fixed exchange rate a constant rate of exchange between currencies; governments try to fix their
exchange rates by buying or selling their currency whenever its exchange value starts to vary
floating exchange rate regime an exchange rate determined by the supply and demand factors in
FX markets
forward contract contract that guarantees delivery of a certain amount of goods, such as foreign
currency, for exchange into a specific amount of another currency, such as dollars, on a specific day
in the future
futures contract contract to buy (or sell) a particular type of security or commodity from (or to) the
futures exchange during a predetermined future time period
futures exchange place in which buyers and sellers can exchange futures contracts; the exchange
keeps the books for buyers and sellers when contracts are initiated or liquidated
government bonds long‐term debt obligations of governments used to finance capital expenditure for
things such as schools, highways and airports
hybrid securities financial products with characteristics of both debt and equity
initial public offering (IPO) primary offering of a company that has never before offered a particular
type of security to the public, meaning the security is not currently trading in the secondary market;
an unseasoned offering
letter of credit financial instrument issued by an importer’s bank that obligates the bank to pay the exporter
(or other designated beneficiary) a specified amount of money once certain conditions are fulfilled
limit order order to buy or sell at a designated price or any better price
limited liability the legal liability of a limited partner or shareholder in a business, which extends only
to the capital contributed or the amount invested
liquidity the ability to convert an asset into cash quickly without loss of value
long buying and holding shares in a portfolio
managed float an exchange rate that is allowed to float or move within a defined range or set band
relative to another currency
margin in futures markets, money posted to guarantee that contracts will be honoured and to take
account of gains or losses accruing from daily price movements
market breadth feature of a secondary market if the orders that give the market depth exist in
significant volume
market depth a feature of a secondary market if orders exist both above and below the price at which
a security is currently trading
market order order to buy or sell at the best price available at the time the order reaches the exchange
market resilience feature of a market if new orders pour in promptly in response to price changes
resulting from temporary order imbalances
marking to market in futures markets, a requirement that gains or losses on futures positions be taken
into account in determining the value of all contracts each day
mortgages long‐term loans secured by real estate
negotiable certificate of deposit (NCD) unsecured liability of banks that can be resold before
maturity in a dealer‐operated secondary market
non‐renounceable rights rights that cannot be sold on the market; shareholders have the option to
subscribe to the rights issue or let the offer lapse
80 Finance essentials
nonparticipating a feature of preference shares that means the preference dividend remains constant
regardless of any increase in the firm’s earnings
novation process of setting up a contract with a new party, such as when clearinghouses insert
themselves between the buyer and seller of a futures contract
one‐name paper short‐term debt where liability is with the issuer alone
option contract contract that allows the holder to buy (or sell) a specified asset at a predetermined
price before its expiration date
option premium price of an option
ordinary shares equity shares that represent the basic ownership claim in a company
pegged exchange rate where the value of the pegged currency is tied to the value of another currency
or a basket of currencies
preference shares shares that confer preference over ordinary shares in terms of dividend payments
and the claim against the firm’s assets in the event of bankruptcy or liquidation
primary offerings offerings of new issues of shares or bonds
prime assets requirement former regulatory requirement that banks in Australia hold 3 per cent of
their liabilities in specific acceptable assets
principal, face value, par value the stated value of a bond; for debt instruments, the par value is
usually the final principal payment
purchasing power parity (PPP) economic concept that says the purchasing power of a currency
should be equal in every country if goods, services, labour, capital and other resources can flow
freely between countries; however, because there are impediments to free trade, PPP often do not
hold, so then goods often cost more in one country than in another
record date date by which an investor must be a shareholder of record in order to receive the declared
dividend; date on which a company ceases to effect transfers of its shares
redeemable the right of the issuer to buy back shares from the holders
renounceable rights rights that may be sold on the market if shareholders do not want to subscribe to
a rights issue and increase their shareholdings
residual claim a feature of common stock that is a claim against a firm’s cash flow or assets: if the
firm is liquidated, those with prior claims are paid first and the common stockholders are entitled to
what is left over, the residual
rights issue the issue of new shares to existing shareholders
senior debt debt that has priority in the event of default
share amalgamations revaluation and elimination of some of the firm’s issued shares, resulting in
a smaller number of shares of a higher value, the overall market capitalisation of the company
remaining unchanged
share splits division of the entity’s shares into a greater number of units of smaller value, maintaining
the overall market capitalisation of the company
short sale process of selling a security before buying it, waiting for the market to fall and then buying
the security to make the delivery required from the initial sale
strike (exercise) price price at which an option can be exercised
subordinated (junior) debt debt that ranks behind senior debt in the event of default
subscription price the amount that must be paid per share to buy a new issue
systematic risk risk that tends to affect the entire market similarly, also known as market risk or non‐
diversifiable risk
term to maturity the length of time until the final payment of a debt security
terms currency second‐named currency in the FX quote: used to express the value or price of the base
currency
thin description of relatively infrequent secondary market trades of corporate bonds
unsecured note a bond for which there is no underlying specified security as collateral in the case of default
writer seller of an option
MODULE 3 Financial markets 81
ENDNOTES
1. Karaian, J 2016, ‘A third of global government debt now has negative interest rates’, 7 July 2016, http://qz.com/725005/athird-of-all-government-bonds-are-guaranteed-money-losers, accessed 1 November 2016.
2. Source: www.economagic.com/em-cgi/data.exe/rba/crtgsvidr.
3. Reserve Bank of Australia (RBA) 2016, Annual Report, www.rba.gov.au/publications/annual-reports/rba/2016/banking-andpayment-services.html, accessed 3 November 2016.
4. Australian Office of Financial Management (AOFM) 2016, Market Statistics, http://aofm.gov.au.
5. Australian Securities Exchange (ASX) 2016, ‘The negotiable securities market’, www.asx.com.au/products/interest-ratederivatives/short-term-interest-rate-derivatives.htm.
6. Reserve Bank of Australia (RBA) 2016, Tables F7, D4.
7. Australian Securities Exchange (ASX) 2016, Historical Market Statistics, October.
8. Australian Securities Exchange (ASX) 2015, 2014 Australian Share Ownership Study, ASX, Sydney.
9. ibid.
10. Australian Securities Exchange (ASX) 2016, Market Statistics, www.asx.com.au/about/market-statistics.htm.
11. National Stock Exchange (NSX) 2016, Annual Report, www.nsxa.com.au.
12. Source: Chi‐x 2016, http://cmsau.chi-x.com/ABOUT.aspx.
13. New Zealand Exchange (NZX) 2016, ‘Monthly shareholder metrics’, September 2016, www.nzx.com, accessed 3 November
2016.
14. International Swaps and Derivatives Association (ISDA) 2009, ‘ISDA derivatives usage survey’, No. 2.
15. Source: www.xe.com/currencycharts/?from=EUR&to=AUD&view=10Y.
16. Euromoney 2016, ‘Currency wars: Special focus’, Euromoney, 19 October 2016, www.euromoney.com.
17. Reserve Bank of Australia (RBA) 2016, ‘Statistical tables: Foreign exchange dealers transactions — Foreign exchange
turnover against all currencies, Table F10’, www.rba.gov.au/statistics/by-subject.html.
ACKNOWLEDGEMENTS
Photo: © Rawpixel.com / Shutterstock.com
Photo: © Tupungato / Shutterstock.com
Photo: © Artur Marciniec / Getty Images
Photo: © bopav / Shutterstock.com
82 Finance essentials
MODULE 4
The Reserve Bank
of Australia and
interest rates
LEA RNIN G OBJE CTIVE S
After studying this module, you should be able to:
4.1 explain how the Reserve Bank of Australia (RBA) measures the money supply
4.2 explain how the RBA influences the level of interest rates in the economy
4.3 discuss the objectives of the RBA in conducting monetary policy
4.4 explain how the RBA’s policies are transmitted through the economy and affect economic activity
4.5 explain how interest rates are determined and calculate the nominal and real rates of interest.
Module preview
In the lead‐up to the monthly board meetings of the Reserve Bank of Australia (RBA), there is often
intense conjecture about interest rate changes by the news media and economic commentators. The
RBA uses its powers to change the interest rate target in an effort to implement its response to economic
conditions. This action is known as monetary policy. In response to the global financial crisis (GFC),
which resulted in a severe decrease in economic growth, the RBA dramatically dropped interest rates
and implemented the most expansionary monetary policy seen in nearly half a century.
During 2016, the media was questioning whether the RBA would continue to cut interest rates. Financial concerns that continued to emanate out of Europe and slower economic growth in China fuelled
speculation that the RBA would continue to cut interest rates as a means of boosting the economy. In a
speech in October 2016, the RBA governor, Philip Lowe, stated that ‘there remain reasonable prospects
that inflation will return to around average levels over the next couple of years’. This comment largely
justified the RBA Board’s decision to maintain the interest rate target at 1.5 per cent over the four‐month
period up to October 2016. The media constantly tries to predict the RBA’s decisions regarding cash rate
movements. During 2016, the central bank continued to maintain a cautious approach towards any significant change in interest rates. The stabilisation of interest rates followed a period of reductions since
November 2010, when the cash rate stood at 4.75 per cent.
Although the RBA uses the cash rate target as a monetary policy tool, it does not determine the cash
rate in a direct regulatory sense. The cash rate is a market‐determined rate negotiated between borrowers
and lenders in the overnight bank market, in which banks lend overnight funds to one another. The
reason the media closely follows statements made by the RBA is that, through open‐market operations,
it is able to expand or contract the total reserves in the banking system, which, in the short term, has an
impact on the cash rate and other interest rates in the economy. However, on any given day many factors
affect interest rates. Additionally, the media simplifies the comments contained in public releases by the
RBA after board meetings to try to capture the public’s attention.
This module helps you to appreciate the nuances contained in statements like this. It explains how
the RBA conducts monetary policy, which affects the money supply, the level of interest rates, the rate
84 Finance essentials
of inflation and the level of economic activity. Additionally, to help you better understand why the RBA
makes some of its monetary policy decisions, the module discusses policy goals which the RBA, as the
nation’s central bank, is responsible for achieving. Finally, we discuss the factors that determine the
general level of interest rates in the economy and explain why interest rates vary over the business cycle.
4.1 Money supply
LEARNING OBJECTIVE 4.1 Explain how the Reserve Bank of Australia (RBA) measures the money supply.
One of the most important powers of the RBA is its ability to control liquidity in the financial system.
Control of liquidity is exerted through management of exchange settlement funds (ESFs) held by
financial institutions at the RBA in exchange settlement accounts (ESA). ESFs are the funds used to
settle obligations among the financial institutions and between the institutions and the RBA. All of the
billions of dollars of daily spending in the economy by individuals and businesses are reduced for settlement purposes to real‐time gross settlement (RTGS) obligations between the banks and the RBA. By
controlling the ESFs, the RBA is able to control the money supply. Thus, the RBA uses its power over
these funds to control the amount of money circulating in the country.
Measures of money supply
Money has many different definitions and each measure reflects a role in monetary policy. Some of the
definitions of money are based on theoretical arguments: is money primarily transactional or primarily
a safe haven to store purchasing power? Putting theory aside, inside the RBA things are more practical;
that is, what the RBA really wants to know is what definition of money has the greatest impact on
interest rates, unemployment and inflation when it increases or decreases the money supply.
The following are the most widely used definitions of money. M1 is the definition that focuses on
money as a ‘medium of exchange’. M1 consists of financial assets that people hold to buy things with:
transaction balances. Therefore, the definition of M1 includes financial assets such as currency and
current accounts at depository institutions.
M3 is M1 plus all other bank deposits of the private nonbank sector (including savings deposits,
money‐market deposit accounts, overnight repurchase agreements, money‐market managed funds and
term deposits). Broad money is M3 plus borrowings from the private sector by nonbank financial institutions (NBFIs) less currency and bank deposits of NBFIs. M3 and broad money are the concepts of
money that emphasise the role that money plays as a ‘store of value’.
A further term you should know is money base. This is the value of currency held by the private
sector plus the value of deposits made by banks with the RBA and any other liabilities to the private
sector held by the RBA. It is not strictly a total money supply descriptor, but is an important value for
monetary authorities in determining the cash interest rate, as the RBA’s ability to successfully pursue
a target for the cash rate stems from its control over the supply of funds (ESFs) that banks use to
settle transactions among themselves in their ESAs. Another way of looking at the money base is that
its size is affected by the Commonwealth Government’s budgetary stance (surplus or deficit), official
government foreign exchange (FX) transactions, and sales or purchases of Commonwealth Government
Securities (CGS) to the Australian public.
How large are these pools of money? Table 4.1 displays the data (at 30 June over several years) and shows
how the money supply has been allowed to grow as Australia has managed its economic recovery since the
GFC. Between the height of the GFC, in 2007, and 2009 the money base grew in excess of 22 per cent, more
than double the growth experienced in preceding years. In the period 2010 to 2012, the ‘emergency’ stance
on monetary policy adopted during the GFC was removed, resulting in the growth in money supply returning
to a level commensurate with the long‐term historical average growth rate. However, as signs of European,
US and Chinese economic difficulties surfaced in 2013, the loose monetary policy stance previously adopted
by the RBA returned, with the money base increasing by an average annual rate of over 17 per cent.
MODULE 4 The Reserve Bank of Australia and interest rates 85
TABLE 4.1
Monetary aggregates, Australia, 30 June 2007–16 ($ billion)
Year
Currency
M1
2007
37.9
226.0
2008
39.8
234.2
2009
45.1
256.2
2010
46.3
242.0
2011
47.6
2012
2013
M3
Broad money
Money base
869.5
964.0
43.7
1035.6
1121.1
46.5
1178.3
1246.4
53.4
1230.3
1271.9
53.6
267.2
1340.7
1365.0
54.6
51.0
279.2
1464.5
1479.7
58.1
54.4
258.8
1559.2
1569.6
61.4
2014
57.6
280.8
1667.7
1673.5
85.6
2015
62.8
308.1
1780.0
1786.6
91.7
2016
67.6
332.0
1887.1
1893.5
98.3
Source: Reserve Bank of Australia Dataset, October 2016.
Money supply changes
How does money supply change? If there was no government sector and economic activity took place
only in the private sector, the level of money supply would not change. The same amount of money (no
matter which aggregate was being considered) would swirl around in the economy. People would earn
money, spend money, save money and invest money, but the total would remain the same.
When the government enters the scene, there are taxes to pay for the provision of government services
and to help even up the inequalities that exist in an unmanaged economy. Taxes represent leakages
of money from the economy. So when taxes are paid by the private sector to the Commonwealth
Government, money supply falls. The government, however, does not keep the total value of taxes
collected, but spends some on goods and services, employment of people and subsidy of activities that
it considers to be ‘social goods’ and wants to encourage. Examples of these social goods are education
and health. The government also wishes to encourage export development and restitution of the natural
environment. These expenditures increase the money supply. In addition, the government makes transfer
payments in the form of social security payments such as the age pension and unemployment, sickness
and child support benefits. These payments also increase the money supply.
Apart from these payments made to the government and by it to Australians, the Commonwealth
Government also changes money supply through CGS and FX transactions made with domestic businesses (and individuals, if any are in a position to make deals of the required magnitude). When the
government issues securities to the Australian public, the public receives the debt (an electronic record)
and the government receives the funds. Money supply decreases. Conversely, when the government
repays debt or buys back issued CGS, the investors receive the funds and money supply increases.
Nowadays, the RBA makes great use of repurchase agreements (repos), in which CGS are bought or
sold together with contracts to resell or rebuy at a stated later time. On average, repurchase contracts
are exercised in about 14 days. Repos are an effective tool for manipulating the money supply over the
short term.
Deregulation of the FX market occurred in 1983 and resulted in the ‘floating’ of the Australian dollar
(AUD), subjecting its value to the forces of international supply and demand for the currency. Previous to
1983, the AUD traded at a fixed price established by the Australian government. Under a floating currency,
traders are allowed to hold and trade FX, and to hold and trade gold. Importers wanting a foreign currency
to pay for imported goods merely approach a financial institution dealing in that currency. Exporters with
FX to sell similarly approach a dealer or a financial institution dealing in that currency to sell their FX in
return for AUD. The government is not involved in these trades. However, the government still chooses
to make some FX transactions. These trades are made to augment the CGS trading that takes place to
86 Finance essentials
manage the money supply. (This is explained in greater detail later in the module.) Volumes of the RBA’s
FX trading, including its share of total market volume from 1989, are shown below.
Figure 4.1 shows that the RBA was responsible for only a very small proportion of trading in the
market, never exceeding a 1.5 per cent share since 1989. Before deregulation the RBA was involved in
all trading, but post‐regulation the majority of trading in FX markets is transactions between financial
institutions. Occasionally the RBA trades in the FX market with the intention of directly influencing or
supporting the value of the AUD. These FX interventions do have an impact on the money supply and
the cash interest rate. For example, if the RBA believes the AUD value is too high, it may sell AUD
(and purchase foreign currency) in the FX market, increasing the amount of AUD in circulation. This
increases the money supply and causes a fall in the cash interest rate. If the RBA considers the AUD
value is too low, it buys AUD (sells foreign currency) in the FX market, reducing the money supply, with
a subsequent increase in the cash interest rate. This strategy is considered an unsterilised FX intervention by the RBA. If the RBA wishes to influence the value of the AUD without these liquidity effects on
the money supply and interest rates, then it must undertake sterilised intervention, which is achieved by
offsetting sales or purchases of CGS. When the RBA is selling (or buying) AUD it will sell (or buy) CGS
and reduce (or increase) liquidity and the money supply, thereby sterilising or neutralising its actions in
the FX market and the impact on the money supply and interest rates.
FIGURE 4.1
RBA foreign exchange transactions 1989–2016
%
US$
1
1.0
Average daily intervention as a
share of turnover*
(LHS)
0
0.8
−1
0.6
US$ per A$
(RHS)
−2
0.4
1991
1996
2001
2006
2011
2016
Year
Note: Data up to 30 June 2015; a positive value indicates a purchase of foreign exchange, while a negative value indicates
a sale of foreign exchange.
Sources: Bloomberg; RBA; Thomson Reuters.
BEFORE YOU GO ON
1. Briefly describe three definitions of money.
2. Define the money base.
3. How does the money supply change? Discuss.
MODULE 4 The Reserve Bank of Australia and interest rates 87
4.2 Cash rate
LEARNING OBJECTIVE 4.2 Explain how the RBA influences the level of interest rates in the economy.
The RBA influences the whole interest rate structure in the economy by having control over the
cash rate, which is the interest rate that underpins all the many interest rates charged for loans of various
types. The cash rate is the most closely watched interest rate in the economy. In simple terms, the cash
rate is the unsecured overnight interbank lending rate and represents the primary cost of short‐term loanable funds. The cash rate is of particular interest because: (a) it measures the return on the most liquid
of all financial assets (bank reserves); (b) it is integral to monetary policy; and (c) it directly reflects
the available reserves in the banking system, which in turn influences commercial banks’ decisions on
making loans to consumers, businesses and other borrowers. A graph of historical cash rate changes is
given in figure 4.2 below.
Market equilibrium interest rate
The Board of the RBA is responsible for the direction and management of monetary policy in Australia.
Accordingly, it meets monthly and decides whether the current cash rate is appropriate, or if it would be
wise to shift the rate up to stem expected inflationary forces or down to encourage and increase demand
and economic activity. The Board considers a wide range of economic data to come to its decision. Have
a look at the quarterly reports ‘Statements on monetary policy’, which are available on the RBA website
(www.rba.gov.au) to appreciate the wide range of data considered in managing monetary policy. Once a
decision is made, it is normally announced at 2.30 pm on the same day.
FIGURE 4.2
Daily cash rates 1993–2016
%
%
7
7
6
6
5
5
4
4
3
2
3
Actual cash rate (IBOC)
Cash rate target
2
1
1
1996
2001
2006
2011
2016
Year
Source: Reserve Bank of Australia.
It should be appreciated that the cash rate is not held in place by government decree. It is the result of
market forces — supply and demand — in the short‐term money market, but the supply side is manipulated by the RBA to ensure the market‐clearing equilibrium price is the announced or targeted cash rate.
How does this happen? The short‐term money market encompasses the supply and demand for ESA
funds, the funds held by banks and a few other financial institutions at the RBA for debt‐settlement
88 Finance essentials
purposes. Changes in the money supply are transmitted through the ESAs. Expenditure by the
government on goods and services, transfer payments, and purchases of CGS and FX all increase
the balances in the ESAs; conversely, the payment of taxes to and purchases of CGS and FX from the
government by the private sector all decrease the balances in the ESAs. In addition, the purchase of
currency notes by the banks from the RBA to increase their holdings of currency decreases the ESA
balances.
The aggregate value of all these types of transactions each day can be large. There are obviously cash
flows in both directions and some are netted off by equal flows in the other direction. However, the net
flow values can still be quite high each day. The RBA manipulates the supply‐side forces. The government spends on goods and services through the operations of government departments, and transfer
payments are fixed in the sense that pension and allowance rates are determined and announced usually
twice a year. The RBA has no control over any of these types of expenditures. It does, however, have
control over the raising of government funds through the sale of CGS and the supply of other ESA funds
through open‐market operations.
Open‐market operations
Open‐market operations encompass repos and the outright purchase or sale of securities by the RBA
in the money markets to maintain the cash interest rate consistent with its stance on monetary policy.
Nowadays, most transactions involve repos in which the first leg of the agreement is a purchase of
securities (increasing ESA balances and money supply), followed by a subsequent resale to the same
parties (decreasing ESA balances and money supply).
ESA holders are free to hold any sized balances they like in their accounts, so long as these account
balances do not fall into the negative (overdraft). However, because ESA balances earn interest rates
0.25 percentage points lower than the cash rate, profit‐making account holders manage their balances
carefully and do not keep excess funds in these accounts. A graph showing aggregate ESA balances
since 2000 is shown in figure 4.3 below.
FIGURE 4.3
‘Surplus’ exchange settlement balances 2000–16
$b
$b
15
15
12
12
9
9
6
6
3
3
0
0
2000
2004
2008
2012
2016
Year
Note: Net of account holders’ ‘late’ direct entry receipts and open positions in RBA Repos contracted at the cash rate target.
Source: Reserve Bank of Australia.
MODULE 4 The Reserve Bank of Australia and interest rates 89
The figure shows that ESA balances are generally stable and hovering under $2 billion, although in
periods of financial market instability (such as during the height of the GFC) ESA balances increase as
the RBA seeks to reduce the cash rate target.
Open‐market operations are undertaken on most business days. This is because ESA balances change
virtually by the minute, as transactions are made and settled in real time. The RBA must manage the
supply of ESA funds at all times so that supply and demand are in equilibrium at the price (interest rate)
target of the RBA Board. When the Board at its monthly meeting determines that no change in the cash
rate is necessary, the supply of ESA funds must be manipulated daily to generate an equilibrium price
for the target cash rate.
The RBA has been particularly effective in its management of the cash rate. The deviation of the
actual cash rate in the market from the target rate over the last decade or so has been very small.
Open‐market operations are managed in this way. Each day, RBA staff estimate the likely net settlement
obligations between the ESA holders and the RBA for that day. The RBA then decides whether supply
needs to be changed to maintain the desired cash rate. It then announces at 9.30 am whether it intends
to buy or sell for the day, and its preferred deals. Market dealers then have 15 minutes to communicate
electronically with the RBA their bids for, or offers of, securities or repos. These bids/offers are then
ranked in order of acceptability and suit­ability, and the best deals are accepted down to the last needed to
just supply the required ESA funds, or soak up the excess ESA funds. The successful dealers are notified
by phone and the results of the bidding operation are made public electronically by about 10.30 am.
Settlement then takes place.
Discount rates and reserve requirements
Discount window rates refer to the practice of some central banks to offer funds facilities to banks so
that they can increase their liquidity or loans business with the general public. Normally the funding
comes from discounting securities held by the banks. For example, a bank holding 6 per cent bonds or
notes might sell these back to the central bank at a penalty rate of return. Although the bank gains extra
liquidity, it does so at a higher cost of funds than it would otherwise have. Therefore, the discounting
practice ensures liquidity, but the penalty cost helps to dissuade profit‐maximising banks from relying on
this source of funds. The RBA offers such an extensive range of repos and intraday liquidity arrangements
that it no longer formally refers to this service as a monetary policy tool.
Importance of cash rate
The financial markets pay so much attention to changes in the cash rate mainly because changes in it
reflect changes in monetary policy. The main reason that the RBA tries to change the monetary base
and, in the short run, interest rates is to affect the level of economic activity in the economy. Monetarist
economists believe that when people have more money relative to their needs, they will spend more
freely and thus will stimulate the economy directly. Conversely, if people have less money than they
need, given their income and expenditure levels, they will spend less so they can accumulate more cash.
So for monetarists, the key variable that drives changes in activity in the economy is the money supply
as measured by the monetary base. The cash rate and other short‐term interest rates serve primarily as a
signal of how monetary policy is proceeding.
Keynesian economists, who follow theories first developed during the Great Depression (1929–33) by
John Maynard Keynes, tend to disregard the direct effects of changes in the money supply on purchases
of goods and services. Instead, they focus on the impact that changes in the level of interest rates have on
spending in the economy. They note that when people and banks have more money, they will tend to buy
more securities and make more loans, driving down interest rates and increasing credit availability. So
in the Keynesian view, expansive monetary policy usually stimulates the economy by reducing interest
rates and increasing credit availability so people and businesses can borrow more inexpensively and thus
spend more freely.
90 Finance essentials
For a view that monetary policy may have only a limited impact on economic activity in a low interest
rate environment, refer to the following link: http://ro.uow.edu.au/buspapers/449
Managing risk: RBA’s impact on share and bond markets
When there is an increase in market interest rates, the value of fixed‐income securities (e.g. bonds, notes
and bills), which promise to pay predetermined fixed amounts, declines. Conversely, if market interest
rates decline, the value of all fixed‐income securities rises. There is a similar, albeit weaker and less
precise, inverse relationship between interest rates and share prices. This weak relationship can be somewhat explained by a substitution effect. Investors sell their fixed‐interest investments when rates fall and
buy shares, and conversely they buy bonds or notes when rates rise and sell shares. Most participants in
financial markets constantly monitor RBA policy actions to remain as fully informed as possible so that
they can manage their risk.
BEFORE YOU GO ON
1. How is an increase in the cash rate likely to affect mortgage interest rates?
2. How is an increase in the cash rate likely to affect imports?
3. How is an increase in the cash rate likely to affect the exchange rate?
4.3 Monetary policy
LEARNING OBJECTIVE 4.3 Discuss the objectives of the RBA in conducting monetary policy.
In Western democracies, governments are charged with the responsibility to achieve certain social, political and economic goals. Politically and socially, these goals centre on preserving individual rights,
freedom of choice, equality of opportunity, equitable distribution of wealth, individual health and welfare, and the safety of individuals and society as a whole. Economically, the goals typically centre on
obtaining the highest overall level of material wealth for society as a whole and for each of its members.
In Australia, the responsibility of the RBA in relation to monetary policy is set out in s. 10(2) of the
Reserve Bank Act 1959. The charter of the RBA states that:
It is the duty of the Reserve Bank Board, within the limits of its powers, to ensure that the monetary and
banking policy of the Bank is directed to the greatest advantage of the people of Australia and that the
powers of the Bank . . . are exercised in such a manner as, in the opinion of the Reserve Bank Board, will
best contribute to:
(a) the stability of the currency of Australia;
(b) the maintenance of full employment in Australia; and
(c) the economic prosperity and welfare of the people of Australia.
Price stability
Price stability refers to stability in the average price of all goods and services in the economy. Price stability and currency stability are virtually synonymous. Price stability does not refer to the price of individual goods. In a market economy such as Australia’s, consumers have a free choice to buy or not buy
whatever goods and services they want. Price movements — up or down — signal to producers what
consumers want by reflecting changes in demand. If the price of a product rises in the absence of cost
increases, the product is more profitable and producers increase production to gain the additional profits.
Price stability, then, means that for some large market basket of goods, the average price change of all
the products is near zero. Within the market basket, however, the prices of individual products can rise
or fall, depending on supply and demand conditions.
MODULE 4 The Reserve Bank of Australia and interest rates 91
Inflation is defined as a continuous rise in the average price level. Because the value of money is
its purchasing power, inflation affects a person’s economic welfare. That is, when we have an
inflationary economy, over time we have less and less purchasing power: our money buys less than
it did before.
Therefore, the value of money is determined by the prices of a broad range of goods and services that
it will buy in the economy. Changes in prices of goods and services that money can buy are measured
by price indices such as the Consumer Price Index (CPI), which is based on a market basket of goods
and services purchased by consumers, or the many producer price indicators that measure changes in
specialist production goods. There is an inverse relationship between price levels and the purchasing
power of money. If prices rise, fewer goods can be purchased with the same amount of money;
thus the purchasing power of money has declined. Conversely, if the prices of goods fall, we can buy
more commodities with the same amount of money, so the purchasing power of money rises when
prices fall.
DECISION‐MAKING EX AMPLE 4.1
Inflation and purchasing power
Situation:
Assume that you have a rich grandmother who has promised to give you a new car two years from now
when you graduate. You immediately go shopping and find that the car of your dreams is a BMW coupe
which happens to cost $70 000. Grandma agrees to give you that amount. However, you will not get the
money until you graduate.
If you graduate in two years and inflation has been non‐existent, the car should still cost $70 000.
However, if during the two years all prices in the economy rise by 10 per cent per year, could you still
buy the car?
Decision:
Of course, the answer is no.
In such an inflationary environment, the car would now cost:
$70 000 × (1.1) × (1.1) = $84 700.
Therefore, with only $70 000 in hand, you would have to buy a less desirable car on graduation.
The major problem with inflation is that it causes unintended transfers of purchasing power between
parties of financial contracts if the inflation is unexpected or the parties are unable to adjust to expected
inflation. For instance, people on fixed incomes may expect inflation but cannot alter their income streams
if prices rise. Retired people on pensions are particularly likely to experience this kind of difficulty. On
the other hand, if inflation is expected and the appropriate adjustments are made, no unintended transfer
of purchasing power occurs and inflation has no economic effect. Unfortunately, in the real world this is
rarely the case.
Figure 4.4 shows consumer price inflation for the period 1993–2016. Prior to 2006, it seldom exceeded
3 per cent a year. From 2006 onwards, the volatility in the inflation rate concerned the RBA. Breaching
the RBA’s target band of 2 to 3 per cent, the inflation rate reached 4 per cent in 2006, followed by a
sudden decline to less than 2 per cent in 2007. It rebounded to peak at 5 per cent in September 2008,
before high domestic interest rates, the GFC and a worldwide recession caused inflation to fall sharply
in 2009. The inflation rate has been following a declining trend since then amid continuing uncertainty
in international financial markets.
92 Finance essentials
FIGURE 4.4
Consumer price inflation 1993–2016
%
%
5
5
Year-ended
4
4
3
3
2
2
1
1
0
−1
0
Quarterly
(seasonally adjusted)
1996
2001
2006
Year
2011
2016
−1
Note: Excluding interest charges prior to the September quarter 1998 and adjusted for the tax changes of 1999–2000.
Sources: Australian Bureau of Statistics; Reserve Bank of Australia.
Since 1993, monetary policy has been focused on constraining consumer price inflation to 2 to 3 per cent
per annum. Monetary policy aims to achieve this over the medium term and also, subject to this important constraint, to encourage strong and sustainable growth in the economy. Controlling inflation is
important to the goal of preserving the value of money and preventing the skewing of economic signals
that dictate economic behaviour. Rampant inflation changes how people spend, save and invest. In the
longer run, the principal way that monetary policy can help to form a sound basis for long‐term growth
in the economy is the constraint of inflation.
Full employment
Full employment implies that every person of working age who wishes to work can find employment.
Although most would agree that full employment is a desirable goal, in practice it is difficult to achieve.
For example, a certain amount of unemployment in the economy is frictional unemployment, which
means that a portion of those who are unemployed are in transition between jobs. Another reason for
people not working is structural unemployment, meaning that there is a mismatch between a person’s
skill levels and available jobs, or there are jobs in one region of the country but few in another region.
Therefore, a policy issue is whether workers should be required to move across the country for jobs or
stay where their family/and friends are. As a result, government policymakers are willing to tolerate
a certain level of unemployment — the natural rate of unemployment — a sort of ‘full employment
unemployment rate’. But even this rate is subject to debate and change. For example, in the 1980s full
employment was considered to be 5 per cent unemployment, but the comparable actual unemployment
rate by 2008 was less than 5 per cent.
The acceptable rate of unemployment depends largely on the actual unemployment rate. The actual
unemployment rate in the early 1990s was at times more than 10 per cent. Therefore, the politically
acceptable rate of unemployment was also high. Today, the acceptable rate of unemployment is about
6 per cent. The graph in figure 4.5 below shows the declining trend of unemployment since 1995 with a
subsequent deterioration since the GFC.
MODULE 4 The Reserve Bank of Australia and interest rates 93
FIGURE 4.5
Unemployment rate 1995–2016
%
%
8
8
7
7
6
6
5
5
4
4
3
1996
2000
2004
Year
2008
2012
2016
3
Source: Australian Bureau of Statistics.
The following graph in figure 4.6 shows the participation rate, which measures the proportion of the
population willing to work. The rate steadily increased in the early 2000s, peaking at 67 per cent in
2008, and has subsequently declined to around 65 per cent in 2016.
FIGURE 4.6
Employment and participation rates 1995–2016
%
%
Participation rate
64
64
61
61
58
58
Employment to working-age population
55
1996
2000
2004
Year
2008
2012
2016
55
Source: Australian Bureau of Statistics.
Economic growth
Economic growth is expansion and development in an economy. Economic growth is made possible
through increased productivity of labour and capital. Typically, labour becomes more productive through
94 Finance essentials
education and training, and capital through the application of better technologies. Increases in economic
growth normally mean a better standard of living for people living in an economy, but not all people may
receive the same share in the benefits. The third duty of the RBA, quoted above, is to manage the monetary
and banking policy in Australia so that it contributes to the economic prosperity and welfare of the people.
Although Australia followed the rest of the world into a sharp economic decline following the GFC, it
avoided a technical recession, recording 0.6 per cent growth in 2009. Figure 4.7 reflects RBA’s relative success
in its monetary policy, achieving a GDP rate which has mostly remained within its target band of 2 to 3 per cent.
Other goals
Apart from these three goals of monetary policy, the RBA has other responsibilities. Through the Payments System Board, it has responsibility for the stability of the financial system. Disruptions in the
financial system can inhibit the ability of financial markets to channel funds efficiently between surplus
spending units and deficit spending units. Any reduction in the flow of funds reduces consumer spending
and business investment, which will lead to slower economic growth. Also, individuals may find it more
difficult or expensive to borrow, so they may have to postpone certain purchases such as buying a new car.
In addition, the Payment Systems Board must promote efficiency and competition in the payment
services markets. Responsibility for these goals is shared with the Australian Prudential Regulation
Authority (APRA) and the Australian Competition and Consumer Commission (ACCC). The work of
the RBA in the areas of efficiency and competition has been most recently seen in the reforms to credit
card interchange fees and consumer charges.
FIGURE 4.7
GDP growth rates, Australia, quarterly, 1994–2016
%
%
Year-ended
4
4
2
2
0
0
Quarterly
−2
1996
2000
2004
Year
2008
2012
2016
−2
Source: Australian Bureau of Statistics.
Possible conflicts among goals
Fortunately, most of the goals of the RBA are relatively consistent with one another. The goals that have
often been perceived to be in conflict are full employment and stable prices, at least in the short run. This
is not the only conflict, but it is the one that has historically gained the most attention from academic
journals, policymakers and the popular financial press.
The conflict revolves around the perception that, as unemployment decreases, inflation usually
increases. The argument goes like this. At high levels of unemployment, there is substantial unused
MODULE 4 The Reserve Bank of Australia and interest rates 95
industrial capacity, and we would tend to believe that the most productive workers and most efficient
manufacturing facilities are being used. As the economy begins to expand, unemployment starts to
decline as workers are called back to work. Additional capacity is used as more goods and services are
produced. As the expansion continues, less‐efficient workers are called back to work and wages begin to
rise as labour becomes scarce; additionally, less‐efficient manufacturing facilities are brought online and
raw materials supplies become scarce, leading to an increase in the rate of inflation for the consumer.
Another explanation of the link between inflation and lower unemployment concerns the demand
side rather than the cost side of the markets. As unemployment decreases, there is higher demand in
the economy because more people have more money. If production, for one reason or another, cannot
expand fast enough, more money is chasing relatively fewer goods, so prices are bid up. Inflation ensues.
BEFORE YOU GO ON
1. What are the objectives of the RBA in conducting monetary policy?
2. During an economic contraction, the RBA increases money supply by purchasing securities on the
open market. What impact does this have on the economy?
3. During an economic expansion, when there is upward pressure on inflation, what does the RBA do
to increase interest rates so that investment and expenditure are discouraged and increases in the
average price level are constrained?
4.4 Economic activity
LEARNING OBJECTIVE 4.4 Explain how the RBA’s policies are transmitted through the economy and
affect economic activity.
Monetary policy is thought to affect the economy through three basic expenditure channels: business
investment, consumer spending and net exports. Businesses spend on investment in plant, equipment,
96 Finance essentials
new buildings and inventory accumulation. Consumer spending is typically divided into two cate­gories:
first, durable goods such as automobiles, boats, appliances and electronic equipment; and second,
housing, which tends to be very sensitive to interest rates. Net exports are the difference between goods
and services exported into the country and those imported. Clearly, exports and imports are sensitive to
the exchanges rate between the AUD and the currencies of foreign countries.
To understand better how monetary policy affects interest rates and the various sectors of the economy,
the transmission process for monetary policy needs to be examined. By examining the transmission process, you will be able to trace changes in the money supply and see how these changes affect interest
rates in financial markets and at financial institutions, the impact of money on spending in the four
sectors of the economy, and ultimately its impact on the GDP and inflation.
Assume that the economy has begun to slow down and the RBA Board has met and decided that
now is an appropriate time to stimulate the economy by easing monetary policy. Therefore, the Board’s
decision is to increase the rate of activity in the economy by decreasing the cash rate and increasing the
money supply through purchasing appropriate securities in open‐market operations.
Figure 4.8 shows how the process starts with the open‐market purchase of securities or repos, which
inject additional ESA cash into the banking system and so increase money supply. This happens because
banks enjoy increased deposits. An increase in the money supply also means an increase in the quantity of funds available to lend. If all else remains the same, an increase in the supply of loanable funds
causes a decline in interest rates in financial markets, as well as a decline in lending rates at financial
institutions.
Consumer spending
A decline in interest rates in financial markets increases the market value of fixed‐income securities such
as corporate bonds, mortgages and mortgage‐backed securities. This increase in the value of investment
securities adds to the wealth of investors. At the same time, the reduced lending rates at financial institutions encourage borrowing by consumers. Consequently, consumer spending will tend to increase in
response to an increase in the money supply. There are several channels through which an increase in
the money supply can cause an increase in consumption expenditures. First, greater (or lesser) holdings of money can cause the public to spend more (or less) freely. Second, when credit becomes more
readily available and interest rates decline, consumers may borrow more to buy cars and other durable
goods. Third, when consumers perceive that their current purchasing power has increased (or decreased)
because of changes in their wealth holdings or in the market value of their stocks or other securities, they
may spend more (or less) on durable goods.
Housing investment is particularly sensitive to interest rate changes because of the large size and long
maturity of mortgage debt obligations. A relatively small change in interest rates can substantially alter
monthly payments and amounts due on mortgage loans. So if interest rates decline, many people will
find it easier to finance a new home mortgage. This in turn increases the demand for housing and the rate
of housing investment. The reverse occurs when rates increase.
Business investment
Similarly, business spending also tends to increase in response to lower interest rates and increased
security values. Investors in new plant and equipment always consider the potential return on an investment and its financing costs. If costs decline or credit becomes more readily available (a particularly
important consideration for small firms), these investors are more likely to undertake investment projects. When monetary policy becomes tighter on the other hand, credit availability also tightens and
interest rates increase, so fewer investment projects will be undertaken. Therefore, investment spending
on plant and equipment is sensitive to changes in financial market conditions brought on by changes in
monetary policy. Business investment in inventory is also sensitive to the cost and availability of credit.
When interest rates are low, firms and retailers are more likely to acquire additional inventory.
MODULE 4 The Reserve Bank of Australia and interest rates 97
FIGURE 4.8
How monetary policy affects economic variables
RBA directive to
buy securities
OMO department
buys securities
Real sector of economy
Financial sector of economy
Money supply
increases
Interest rates
decline in financial
markets
Exchange
rates
decline
Lending rates
decline at financial
institutions
Market value of
securities increases
Business
spending
increases
98 Finance essentials
Exports
increase,
imports decrease
Residential
construction
increases
Consumer
spending
increases
Nominal GDP
increases
How close to full
employment
How close to full
use
Increase real GDP
Increase inflation
Net exports
A decline in interest rates combined with the expectations of increased inflation that typically coincide
with an increase in the money supply will tend to make the AUD less desirable than foreign currencies.
Therefore, an increase in the money supply will also tend to cause a decline in the value of the AUD
against foreign currencies. As the relative value of the AUD declines, the cost of imported goods increases
for Australian consumers and the demand for imports declines. Conversely, the cost of Australian goods
declines for foreign consumers and the demand for exports increases. As exports increase relative to
imports, the Australian economy will be stimulated and domestic production, as measured by GDP, and
income will rise. If the rising production level causes inflation to increase, however, Australian goods
will no longer be cheaper relative to foreign goods. If inflation in Australia is sufficiently great, the flow
of exports and imports may reverse their direction unless the AUD’s exchange rate continues to fall.
As business spending increases, exports increase, imports decrease, consumer spending increases
and residential construction increases, and we observe an increase in nominal GDP. Whether real GDP
increases or inflation increases depends largely on how close the economy is to full use of production
capacity and how close employment levels are to full employment. GDP equals the quantity of goods
and services produced times the price of goods and services produced. It can increase if the quantity
of goods and services increases or if their price increases. Real GDP growth occurs when the quantity of goods and services increases. If monetary policy is overly expansive and the economy nears full
employment and full use of capacity, inflation may increase to the point that it dominates the nominal
increase in GDP. In other words, the price level has increased faster than the quantity of goods and services. An extreme example of this effect is if the quantity of goods and services decreased while prices
were increasing rapidly. It would then be possible to observe an increase in nominal GDP from the
price level increase, even though the quantity of goods and services went down. An overly restrictive
monetary policy, on the other hand, can limit both real and nominal GDP growth.
BEFORE YOU GO ON
1. The monetary policy is thought to affect the economy through three basic expenditure channels.
Name these three basic expenditure channels.
2. What impact will a decline in interest rates in the financial markets have on the market value of
fixed‐income securities such as corporate bonds, mortgages and mortgage‐backed securities?
3. What impact will an increase in the money supply have on the value of the Australian dollar against
foreign currencies? Discuss.
4.5 Determinants of interest rates
LEARNING OBJECTIVE 4.5 Explain how interest rates are determined and calculate the nominal and real
rates of interest.
We conclude this module by examining the factors that determine the general level of interest rates in the
economy and describing how interest rates vary over the business cycle. Understanding interest rates is
important because the financial instruments and most of the financial services discussed in this module
are priced in terms of interest rates.
What are interest rates?
For thousands of years people have been lending goods to other people, and on occasion they have asked
for some compensation for this service. This compensation is called rent: the price of borrowing another
person’s property. Similarly, money is often lent, or rented, for its purchasing power. The rental price
MODULE 4 The Reserve Bank of Australia and interest rates 99
of money is called the interest rate and is usually expressed as an annual percentage of the nominal
amount of money borrowed. Therefore, an interest rate is the price of borrowing money for the use of
its purchasing power.
To a person borrowing money, interest is the penalty paid for consuming income before it is earned.
To a lender, interest is the reward for postponing current consumption until the maturity of the loan.
During the life of a loan contract, borrowers typically make periodic interest payments to the lender.
On maturity of the loan, the borrower repays the same amount of money borrowed (the principal) to
the lender.
As do other prices, interest rates serve an allocative function in the economy. The allocative function
of interest rates allocates funds between surplus spending units (SSUs), which are commonly known as
savers, and deficit spending units (DSUs), which are commonly known as borrowers, among financial
markets. For SSUs, the higher the rate of interest, the greater the reward for postponing current consumption and the greater the amount of saving in the economy. Some large DSUs such as governments,
institutions and corporations issue debt securities to raise funds. For DSUs, the higher the yield paid on
a particular security, the greater the demand for that security (by SSUs). However, the higher yield will
make it more expensive for DSUs to raise funds and they will naturally be less willing to supply the
security. Therefore, SSUs want to buy financial claims with the highest returns, whereas DSUs want to
sell financial claims at the lowest possible interest rate.
Determinants of real rate of interest
The fundamental determinant of interest rates is the interaction of the production opportunities facing
society and the individual’s time preference for consumption. Let’s examine how producers (investors
in capital projects) and savers interact to determine the market rate of interest. Businesspeople and other
producers have the opportunity to invest in capital projects that are productive in the sense that they yield
additional real output in the future. Real output means more cars, housing, smart TV sets and so on. The
extra output generated constitutes the return on investment. The higher the return on investment, the
more likely producers are to undertake a particular investment project.
For a capital project to be accepted, its return on investment must exceed the company’s cost of funds
(cost of debt and equity); otherwise, the project will be rejected. Intuitively, this decision rule makes
sense because if an investment earns a return greater than the company’s cost of funding, it should be
profitable and thus should increase the value of the company. For example, if a company’s average
cost of funding — often called the cost of capital — is 15 per cent, a 1‐year capital project with an
18 per cent return on investment would be accepted (18 per cent > 15 per cent). If the capital project
was expected to earn only 13 per cent, the project would be rejected (13 per cent < 15 per cent). The
company’s cost of capital is the minimum acceptable rate of return on capital projects.
Individuals have different preferences for consumption over time. All other things being equal, most
people prefer to consume goods today rather than tomorrow. This is called a positive time preference
for consumption. For example, most people prefer to go on a vacation or purchase a phone or new car
sooner rather than later. People consume today, however, realising that their future consumption may be
less because they have forgone the opportunity to save and earn interest on their savings.
Given most people’s positive time preference, the interest rate offered to savers will determine how
thrifty those persons are. At low interest rates, most people will postpone very little consumption for
the sake of saving. To coax people to postpone additional current consumption and save more, higher
interest rates, or rewards, must be offered. However, as the interest rate rises, fewer business projects can
earn an expected return high enough to cover the added interest expense related to financing the project.
As a result, at higher interest rates, fewer investment projects are undertaken.
Therefore, the interest rate paid on savings basically depends on the rate of return producers
can expect to earn on investment capital and on savers’ time preference for current over future
consumption. The expected return on investment projects sets an upper limit on the interest rate producers can pay to savers, whereas consumer time preference for consumption establishes how much
100 Finance essentials
consumption consumers are willing to forgo (save) at the different levels of interest rates offered by
producers.
Figure 4.9 shows the determination of the market equilibrium interest rate for the economy in a
supply‐and‐demand framework. Aggregate savings for the economy represent the desired amount of
savings by consumers at various rates of interest. Similarly, the aggregate investment schedule represents
the amount of desired investment by producers at various interest rates. The two curves show that consumers will save more if producers offer higher interest rates on savings, and producers will borrow
more if consumers will accept a lower return on their savings. The figure shows that the equilibrium rate
of interest (r) is the point where the desired level of lending (L) by lender‐savers equals the desired level
of borrowing (B) by people and businesses to finance capital projects and/or consumption. At this point,
funds are allocated over time in a manner that fits people’s preferences for current and future consumption. Note that the model presented here is based on the loanable funds theory of market equilibrium;
saving (or giving up current consumption) is the source of loanable funds, and business spending (or
investment) is the use of funds.
Determinants of the equilibrium rate of interest
FIGURE 4.9
The amount lendersavers want to lend (L)
goes up as interest rates
go up and lending
becomes more profitable.
Interest rate (%)
B
Equilibrium
rate of interest
L=B
r
L
Equilibrium
quantity of
lending/
borrowing
The equilibrium rate of
interest (r ) is the rate at
which the desired level of
lending (L) equals the
desired level of
borrowing (B).
The amount borrowerspenders want to borrow
(B) goes down as interest
rates go up and borrowing
becomes more expensive.
Quantity of lending/borrowing in the economy ($)
The equilibrium rate of interest is called the real rate of interest. This is the fundamental long‐run
interest rate in the economy. It is called the ‘real’ rate of interest because it is determined by the real
output of the economy.
Inflation is the amount by which aggregate price levels rise over time. The real rate of interest
measures the inflation‐adjusted (i.e. inflation‐deducted) return earned by lender‐savers and represents
the inflation‐adjusted (i.e. inflation‐deducted) cost incurred by borrower‐spenders when they borrow to
finance capital goods. We focus on capital investments because they are the productive assets that create
economic wealth in the economy.
The real rate of interest is rarely observable, because most industrial economies operate with some
degree of inflation and periods of zero inflation are not common. The rate that actually exists at any
point in time and that we actually observe in the marketplace is called the nominal rate of interest. The
factors that determine the real rate of interest, however, are the underlying determinants of all the interest
rates we observe in the marketplace. For this reason, an understanding of the real rate is important.
MODULE 4 The Reserve Bank of Australia and interest rates 101
Fluctuations in real rate
In the supply‐and‐demand framework discussed, any economic factor that causes a shift in desired
lending or desired borrowing will cause a change in the equilibrium rate of interest. For example, a
major breakthrough in technology should cause a shift to the right in the desired level of borrowing
(i.e. the demand curve), thus increasing the real rate of interest. This makes intuitive sense because the
new technology should spawn an increase in investment opportunities, increasing the desired level of
borrowing. Similarly, a reduction in the company tax rate should encourage businesses to invest more.
This will increase the desired level of borrowing and cause the real rate of interest to increase.
One factor that would shift the desired level of lending to the right, and hence lead to a decrease in
the real rate of interest, would be a decrease in the income tax rates for individuals (when the income tax
rate is reduced, the tax to be paid on interest income will become lower). Another would be monetary
policy action by the RBA to increase the money supply in the economy.
Other forces that could affect the real rate of interest include growth in population, demographic variables such as the age of the population and cultural differences. In sum, the real rate of interest reflects a
complex set of forces that control the desired level of lending and borrowing in the economy.
Loan contracts and inflation
The real rate of interest ignores inflation, but in the real world price‐level changes are a fact of life and
these changes affect the value of a loan contract or, for that matter, any financial contract. For example,
if prices rise (inflation) during the life of a loan contract, the purchasing power of the dollars received
back by the lender decreases because the borrower repays the loan with inflated dollars — dollars with
less buying power. Recall from economics two important relationships: (1) the value of money is its purchasing power — what you can buy with it; and (2) there is a negative relationship between changes in
price level and the value of money: as the price level increases (inflation) the value of money decreases,
and as the price level decreases (deflation) the value of money increases. This makes sense because
when we have rising prices (inflation), our dollars buy less.
To see the impact of inflation on a loan, let’s look at an example. Suppose that you lend a friend
$1000 for 1 year at a 4 per cent interest rate. Furthermore, you plan to buy a new surfboard for $1040
in 1 year when you graduate from university. With the $40 of interest you will earn ($1000 × 0.04), you
will have just enough money to buy the surfboard. At the end of the year, you graduate and your friend
pays off the loan, giving you $1040. Unfortunately, the rate of inflation during the year was an unexpected 10 per cent and your surfboard now costs 10 per cent more, or $1144 ($1040 × 1.10). You have
experienced a 10 per cent decrease in your purchasing power due to the unanticipated inflation. The loss
of purchasing power is $104 ($1144 − $1040).
Fisher equation and inflation
The preceding example suggests that protection against price‐level changes is achieved when the nominal rate of interest is divided into two parts: the real rate of interest, which is the rate of interest that
exists in the absence of price level changes; and the expected percentage change in price levels over the
life of the loan contract. This can be written as an equation as follows:
i = r + ∆Pe (4.1)
where:
i = observed nominal rate of interest (contract rate)
r = real rate of interest
∆Pe = expected annual percentage change in the average price
Equation 4.1 is commonly referred to as the Fisher equation. It is named after Irving Fisher, who
was one of the world’s best‐known economists and is credited with first developing the concept. Fisher
102 Finance essentials
is most acclaimed for his theory of the real rate of interest (presented here) and his analysis of the quantity theory of money. Regarding interest rates, Fisher stated that two basic forces determine the real
rate of interest in a market economy: (1) subjective forces reflecting the preference of individuals for
present consumption over future consumption; and (2) objective forces depending on available investment opportunities and the productivity of capital. Fisher also recognised the distinction between the
nominal and the real rate of interest: the nominal rate of interest being composed of a real component
and an inflation premium that compensates lenders for losses in purchasing power caused by inflation.
Fisher’s classic treatise on interest The Theory of Interest Rates was first published in the 1930s and is
still in print today. His views on interest are the foundation for contemporary interest rate theory.
A couple of important points should be noted about the Fisher equation. First, note that the equation
uses the expected percentage price‐level changes, ∆Pe, not the observed or reported rate of inflation (or
deflation). This way, the lender is compensated for expected inflation (deflation) during the loan contract.
Therefore, to determine nominal interest rates properly it is necessary to predict price‐level changes over
the life of the contract. Most economies experience some rate of inflation most of the time. Deflation is
not common and usually only occurs during a deep or prolonged recession. Second, note that the nominal rate of interest is defined as the rate of interest actually observed in financial markets: the market
rate of interest. For real and nominal rates to be equal, the expected rate of price‐level changes (inflation
or deflation) must be zero (∆Pe = 0). Finally, as with all expectations or predictions, the actual rate
of inflation, which can only be determined at the end of the loan contract, may be different from the
expected rate of inflation, which is estimated by the market at its beginning.
Restatement of Fisher equation
The ‘derivation’ of the Fisher equation given above is an intuitive approach, leading to an approximation. How do we write a loan contract that provides protection against loss of purchasing power due to
inflation? We have no crystal ball to tell us what the actual rate of inflation will be. However, market
participants collectively (often called the market) have expectations about how prices will change during
the contract period.
To incorporate these inflation expectations into a loan contract, we need to adjust the real rate of
interest by the amount of inflation that is expected during the contract period. The mathematical equation
used to adjust the real rate of interest for the expected rate of inflation is as follows:
1 + i = (1 + r ) × (1 + ∆Pe ) (4.2)
Solving the Fisher equation for i, the following equation is obtained:
i = r + ∆Pe + r ∆Pe (4.3)
where:
i = nominal (or market) rate of interest
r = real rate of interest
ΔPe = expected annualised price‐level change
rΔPe = adjustment of interest rate payment for loss of purchasing power due to inflation
If either r or ΔPe is small, rΔPe is very small, approximately zero. Applying equation 4.3 to our
earlier example, we can find what the nominal rate of interest should be if the expected inflation rate is
4 per cent and the real rate of interest is 3 per cent:
i = r + ∆Pe + r ∆Pe
= 0.03 + 0.04 + ( 0.03 × 0.04 )
= 0.0712, or 7.12%
MODULE 4 The Reserve Bank of Australia and interest rates 103
So by using our restated Fisher equation, for the 1‐year loan of $1000 in our example above the contract interest rate is 7.12 per cent. If we had used equation 4.1 and simply added the expected inflation
rate of 4 per cent and the real rate of interest of 3 per cent, our answer would be 7 per cent. The difference in the contract loan rate between the two variations of the Fisher equation (equations 4.1 and
4.3) is 0.12 per cent (7.12 − 7.00): less than a 2 per cent error (0.12/7.12 = 1.69%). So dropping r∆Pe
makes the insights from the first Fisher equation easier to understand without creating a significant
computational error.
DEMONSTRATION PROBLEM 4.1
Calculating a new inflation premium
Problem:
Say the current 1‐year Treasury bond rate is 5.5 per cent. In the news, several economists at leading
investment and commercial banks predict that the annual inflation rate is going to be 0.25 per cent
higher than originally expected. The higher inflation forecast reflects unexpectedly strong employment
figures released by the Australian Bureau of Statistics that day. What is the current inflation premium?
When the market opens tomorrow, what should happen to the Treasury bond rate? (Assume the real
rate of interest is 4.0 per cent.)
Approach:
You must first estimate the current inflation premium using equation 4.1. Then adjust this premium to
reflect the economists’ revised belief. Finally, this revised inflation premium can be used in the Fisher
equation to estimate what the Treasury bond rate will be tomorrow morning.
Solution:
Current inflation premium:
i = r + ∆Pe
∆Pe = i – r
= 5.5% – 4.0%
= 1.5%
New inflation premium:
∆Pe = 1.5% + 0.25% = 1.75%
The opening Treasury bond rate in the morning will be:
i = r + ∆Pe = 4.0% + 1.75% = 5.75%
DEMONSTRATION PROBLEM 4.2
International consulting experience
Problem:
You are the financial manager at a manufacturing company that is going to make a 1‐year loan to a key
supplier in another country. The loan will be made in the supplier’s local currency. The supplier’s government controls the banking system and there is no reliable market data available. For this reason, you
have spoken with five economists who have some knowledge about the economy. Their predictions for
inflation next year are 6, 8, 9, 10 and 12 per cent.
What rate should your company charge for the 1‐year business loan if you are not concerned about
the possibility that your supplier will default? The real rate of interest is, on average, 4 per cent.
104 Finance essentials
Approach:
Although the sample of economists is small, it should provide a reasonable estimate of the expected
rate of inflation (ΔPe). This value can be used in equation 4.1 to calculate the nominal rate of interest.
Solution:
∆Pe = (6% + 8% + 9% + 10% + 12%) / 5
= 45% / 5
= 9%
Nominal rate of interest:
i = r + ∆Pe
= 4% + 9%
= 13%
This number is a reasonable estimate, given that you have no market data.
Cyclical and long‐term trends in interest rates
Now let’s look at some market data to see how interest rates have actually fluctuated over the past four
decades in Australia. Figure 4.10 plots the interest rate yield on 10‐year government bonds since 1870
to represent interest rate movements. In addition, the figure plots the annual rate of inflation, represented by the annual percentage change in the CPI, a price index that measures the change in prices of
a market basket of goods and services that a typical consumer purchases. Finally, the figure indicates
periods of recession. Recession occurs when real output from the economy decreases and unemployment
increases. The recessionary periods indicated in the figure begin at the peak of the business cycle and
end at the bottom (or trough) of the recession. From our discussion of interest rates and an examination
of figure 4.10, we can draw two general conclusions.
1. The level of interest rates tends to rise and fall with changes in the actual rate of inflation. The
positive relationship between the rate of inflation and the level of interest rates is what we should
expect given equation 4.1. You may have noted there is a positive relationship, but there is no
‘perfectly’ positive relationship (i.e. a one‐to‐one relationship or exact correlation) between annual
inflation and the interest rate (in this case, the 10‐year government bond yield). However, we
feel comfortable concluding that inflationary expectations have a major impact on interest rates.
Our findings also explain in part why interest rates can vary substantially between countries. For
example, in July 2007 the rate of inflation in Australia was 2.1 per cent; during the same period
the rate of inflation in Russia was 8.5 per cent. If the real rate of interest is 4.0 per cent, the short‐
term interest rate in Australia should have been around 6.1 per cent (2.1 + 4.0) and the Russian
interest rate should have been around 12.5 per cent (assuming the real interest rate in Russia was also
4 per cent). In fact, during that period the Australian short‐term interest rate was 6.25 per cent and
the Russian rate was 10.0 per cent. Although hardly scientific, this analysis illustrates the point that
countries with higher rates of inflation or expected rates of inflation will have higher interest rates
than countries with lower inflation rates.
2. The level of interest rates tends to rise during periods of economic expansion and decline during
periods of economic contraction. It makes sense that interest rates should increase during years of
economic expansion. The reasoning is that, as the economy expands, businesses begin to borrow
money to build up inventories and invest in more production capacity in anticipation of increased
sales. As unemployment begins to decrease, the economic future looks bright and consumers begin
to buy more homes, cars and other durable items on credit. As a result, the demand for funds by both
businesses and consumers increases, driving interest rates up. Also, near the end of expansion the
MODULE 4 The Reserve Bank of Australia and interest rates 105
rate of inflation begins to accelerate, which puts upward pressure on interest rates. At some point the
RBA becomes concerned over the increasing inflation in the economy and begins to increase interest
rates, slowing the economy down. The higher interest rates discourage spending by both businesses
and consumers.
FIGURE 4.10
Relationship between annual inflation rate and long-term interest rate, 1870–2015
Aust 10-year gov’t bond yields
CPI inflation rate
Bond
yields
15%
Long bond yields at 3% in
the latter years of 1890s
depression, but inflation
was severely negative
10%
5%
Bond yields
Long bond yields at 3% in
the latter years of 1930s
depression, but inflation
was severely negative
1931 gov’t bond
defaults/restructure
by Australia + NSW
Yields and inflation
peak in late 1970s
–early 1980s
Bonds yield below 3%
in 2012 and 2014–15
but inflation positive
War-time price
controls
1974–75
recession
post-WW I
recession
0%
1890s
depression
post-Korean
war recession
1930s
depression
Inflation rate
1990–01
recession
Sub-prime +
Euro crises
Inflation rate
1890s
depression
WW I
1930s
depression
Inflation
rate
+20%
+0%
WW II
−20%
1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020
Year
Philo capital
Source: https://cuffelinks.com.au.
Based on this graph, we can draw two important conclusions about interest rate movements. First,
the level of interest rates tends to rise and fall with the actual rate of inflation — a conclusion also supported by the Fisher equation, which suggests that interest rates rise and fall with the expected rate of
inflation. Second, the level of interest rates tends to rise during periods of economic expansion and to
decline during periods of economic contraction. During a recession, businesses and consumers rein in
their spending and their use of credit, putting downward pressure on interest rates. To stimulate demand
for goods and services, the RBA will typically begin to lower interest rates (e.g. the cash rate) and hence
encourage business and consumer spending. As an example, at the beginning of the GFC in late 2008 the
RBA, fearing a deep recession, reduced interest rates to levels not seen in Australia for over 40 years. At
the time of writing (October 2016) the cash rate is 1.5 per cent.1 The cash rate in the USA is 0.5 per cent
and in the UK is 0.25 per cent.2 The opposite takes place when there is economic expansion.
Also note in figure 4.10 that periods of business expansion tend to be much longer than periods
of contraction (recessions). Since the end of the Great Depression (1929–33), the average period of
economic expansion has lasted three to four years, and the average period of contraction about nine
months. Keep in mind that these numbers are averages and that actual periods of economic expansion
and contraction can vary widely from averages. For example, the current period of business expansion
in Australia has lasted more than 25 years (1991–2016)3 and the last recession lasted 12 months (June
1990 to June 1991).
It is important for a financial manager to understand what factors determine the level of interest rates
and what factors cause interest rates to vary over the business cycle. The financial manager’s goal is
106 Finance essentials
to obtain funds at the lowest possible cost so that the company’s management can achieve its strategic
objectives. The lower the company’s overall cost of funds, the greater the value of the company.
Forecasting interest rates
There has always been considerable interest in forecasting interest rate movements. The reason, of
course, is that changes in the level of interest rates affect the present value of streams of future payments; that is, they affect the prices of financial assets: our economic wealth! Moreover, beginning in
the 1980s interest rate movements became more volatile than in the past and, therefore, firms and individual investors faced substantial exposure to interest rate risk. In general, economists use a variety
of approaches to forecast interest rates. These range from naïve forecasting models based on subjective adjustments to extremely complicated financial models of the economy. An examination follows of
two of the popular forecasting methods used by economists: statistical models of the economy and the
flow‐of‐funds approach.
How good are the forecasters?
Clearly, a great deal of analysis, judgement and luck are necessary for a good forecast. Studies over
the years have assessed the accuracy of interest rate forecasts. Most of these studies conclude that
interest rate forecasters perform poorly. McNees reports that forecasts by professional forecasters of the
three‐month Treasury rate six months into the future were within 2 percentage points of the actual rate
67 per cent of the time.4 Therefore, if the three‐month Treasury rate was forecast to be 6 per cent in July,
there was a 67 per cent chance in January that the actual rate would fall somewhere between 4 per cent
and 8 per cent. Other studies show that, as the forecast period is lengthened, the forecast errors are
larger.5 Another study looked at how professional forecasters did in predicting the direction of interest
rate movements.6 That is, if interest rates were forecast to increase, did they increase? For the period
MODULE 4 The Reserve Bank of Australia and interest rates 107
1982–86, nine professional forecasters correctly predicted the direction of change of the three‐month
Treasury rate six months into the future 42 per cent of the time. If interest rate movements were random,
a 50 per cent record would be expected. Sadly, only one of the nine forecasters predicted the direction of
change more than 50 per cent of the time, predicting correctly on six of the ten forecasting opportunities.
The worst prediction record was two correct predictions in ten chances.
The overall conclusion, then, is that forecasters are not consistently accurate with their forecasts and
in some cases they are way off the mark. Forecasting, therefore, is a very difficult profession; however,
forecasts are the basis on which highly important monetary policy decisions are based.
BEFORE YOU GO ON
1. Explain how the real rate of interest is determined.
2. How are inflationary expectations accounted for in the nominal rate of interest?
3. Explain why interest rates follow the business cycle.
108 Finance essentials
SUMMARY
4.1 Explain how the Reserve Bank of Australia (RBA) measures the money supply.
The RBA has different measures of money supply, which reflect the continuum between a transactional view of money and the view that money is primarily a store of value. These measures are:
•• M1, which includes financial assets such as currency and current accounts at depository institutions
•• M3, which is M1 plus all other bank deposits of the private nonbank sector (including savings
deposits, money‐market deposit accounts, overnight repurchase agreements, money‐market
managed funds and time deposits)
•• broad money, which is M3 plus borrowings from the private sector by nonbank financial
institutions (NBFIs) less currency and bank deposits of NBFIs
•• the money base, which is the value of currency held by the private sector plus the value of the
deposits made by banks with the RBA (ESAs) and any other liabilities to the private sector held
by the RBA.
4.2 Explain how the RBA influences the level of interest rates in the economy.
The RBA influences the level of interest rates in the economy by changing the target cash rate, which
is the interest rate on overnight loans of reserves among banks. Through its open‐market operations,
the RBA manages closely the amount of reserves in the banking system so that supply equals demand
just at the target price (interest rate). When the RBA purchases securities on the open market, reserves
tend to increase. A greater supply of reserves puts downward pressure on the cash rate. When the
RBA sells securities, cash is drained from the system and upward pressure is applied to the cash rate.
4.3 Discuss the objectives of the RBA in conducting monetary policy.
The RBA’s objectives are:
•• the stability of Australia’s currency
•• the maintenance of full employment in Australia
•• the economic prosperity and welfare of Australia’s people
•• the stability of the financial system.
4.4 Explain how the RBA’s policies are transmitted through the economy and affect economic activity.
When the RBA increases the money supply by purchasing securities on the open market, there is
downward pressure on interest rates. Lower interest rates make it more attractive for businesses to
spend money on long‐term investments and for consumers to spend on durable goods and housing.
Increases in business and consumer spending lead to increases in GDP. How close the economy is
to full use of capacity and full employment determines whether a portion of the increase in nominal
GDP owes to increases in the average price level (or inflation).
4.5 Explain how interest rates are determined and calculate the nominal and real rate of interest.
The real rate of interest is the interest rate in the economy in the absence of inflation. It is determined
by the interaction of: (1) the rate of return that businesses can expect to earn on capital goods; and
(2) individuals’ time preference for consumption. The interest rate we observe in the marketplace
is called the nominal rate of interest. The nominal rate of interest is composed of two parts: (1) the
real rate of interest; and (2) the expected rate of inflation. Equations 4.1 and 4.3 are used to calculate the nominal (real) rate of interest when you have the real (nominal) rate and the inflation rate.
SUMMARY OF KEY EQUATIONS
Equation
Description
Formula
4.1
Fisher equation approximation
i = r + ∆ Pe
4.2
Fisher equation
1+ i = (1+ r ) × (1+ ∆ Pe )
4.3
Fisher equation simplified
i = r + ∆ Pe + r ∆ Pe
MODULE 4 The Reserve Bank of Australia and interest rates 109
KEY TERMS
allocative function of interest rates the function of interest rates in the economy to allocate funds
between SSUs and DSUs in financial markets
broad money M3 plus borrowings from the private sector by NBFIs less currency and bank deposits
of NBFIs
cash rate the overnight (or one‐day) interest rate for unsecured loans between banks
exchange settlement funds (ESFs) funds held in accounts at the RBA to facilitate settlement between
clearing banks
Fisher equation i = r + ∆ Pe where i = observed nominal rate of interest (contract rate), r = real
rate of interest and ∆Pe = expected annual percentage change in average price level in the economy
(expected inflation)
frictional unemployment unemployment caused by being in transition between jobs
full employment the case in which every person of working age who wishes to work can find
employment
inflation a continuous rise in the average price level
interest rate the rental price of money, usually expressed as an annual percentage of the nominal
amount of money borrowed; the price of borrowing money for the use of its purchasing power
M1 the definition of money that focuses on money as a ‘medium of exchange’; M1 consists of
financial assets that people hold to buy things with (such as currency and current accounts at
depository institutions)
M3 M1 plus all other bank deposits of the private nonbank sector (including savings deposits,
money‐market deposit accounts, overnight repurchase agreements, money‐market managed funds
and term deposits)
money base the value of currency held by the private sector plus the value of deposits made by banks
with the RBA (ESAs) and any other liabilities to the private sector held by the RBA
nominal rate of interest the rate of interest unadjusted for inflation
open‐market operations trading operations undertaken in the financial markets to effect changes in
the banks’ ESAs
positive time preference the preference of people to consume goods today rather than tomorrow
price stability the stability of the average price of all goods and services in the economy
real rate of interest the interest rate that would exist in the absence of inflation
return on investment the future additional real output generated by investment in productive capital
projects
structural unemployment the case in which some of those who are unemployed are unemployed
because there is a mismatch between their skill levels and available jobs, or there are jobs in one
region of the country but few in another
ENDNOTES
1.
2.
3.
4.
Source: www.global-rates.com/interest-rates/central-banks/central-bank-australia/rba-interest-rate.aspx.
Data Global Rates 2016.
Source: www.tradingeconomics.com/australia/gdp-growth.
McNees, SK 1986, ‘Forecasting accuracy of alternative techniques: a comparison of US macroeconomic forecasts’, Journal of
Business and Economic Statistics, vol. 4, no. 1, January, pp. 5–15.
5. Zarnowitz, V 1985, ‘Rational expectations and macroeconomic forecasts’, Journal of Business and Economic Statistics, vol. 3,
no. 4, October, pp. 73–108.
6. Belongia, MT 1987, ‘Predicting interest rates: a comparison of professional and market‐based forecasts’, Economic Review,
Federal Reserve Bank of St Louis, March, pp. 9–15.
110 Finance essentials
ACKNOWLEDGEMENTS
Photo: © ChameleonsEye / Shutterstock.com
Photo: © xiao yu / Shutterstock.com
Photo: © g0d4ather / Shutterstock.com
Figure 4.1: © Reserve Bank of Australia
Figure 4.2: © Reserve Bank of Australia
Figure 4.3: © Reserve Bank of Australia
Figure 4.4: © Reserve Bank of Australia
Figure 4.5: © Reserve Bank of Australia
Figure 4.6: © Reserve Bank of Australia
Figure 4.7: © Reserve Bank of Australia
Table 4.1: © Reserve Bank of Australia
Extract: © Reserve Bank of Australia
MODULE 4 The Reserve Bank of Australia and interest rates 111
MODULE 5
Time value of money
LEA RN IN G OBJE CTIVE S
After studying this module, you should be able to:
5.1 explain what the time value of money is and why it is so important in the field of finance
5.2 explain the concept of future value, including the meaning of the terms principal, simple interest and
compound interest, and use the future value formula to make business decisions
5.3 explain the concept of present value and how it relates to future value, and use the present value
formula to make business decisions
5.4 discuss how the future value formula can be used to make business decisions when the interest rate or
number of periods is unknown.
Module preview
Businesses routinely make decisions to invest in productive assets in order to earn income. Some assets
such as property, plant and equipment are tangible, while other assets such as patents and trademarks are
intangible. Regardless of the type of investment, a company pays out money now in the hope that the
value of the future benefits (cash inflows) will exceed the cost of the asset. This process is what value
creation is all about — buying productive assets that are worth more than they cost.
The valuation models presented in this text will require you to calculate the present and future values
of cash flows. This module and the next one provide the fundamental tools for making these calculations.
This module explains how to value a single cash flow in different time periods and module 6 covers
valuation of multiple cash flows. These two modules are critical for your understanding of ­corporate
finance.
We begin this module with a discussion of the time value of money. We then look at future value,
which tells us how funds will grow if they are invested at a particular interest rate. Next we discuss
present value, which answers the question ‘What is the value today of cash payments received in the
future?’ We conclude with a discussion of several additional topics related to time value calculations.
5.1 The time value of money
LEARNING OBJECTIVE 5.1 Explain what the time value of money is and why it is so important in the
field of finance.
In financial decision‐making, one basic problem managers face is determining the value of (or price to
pay for) cash flows expected in the future. Why is this a problem? Consider, for example, if the Lott
changed the way it paid out the Division 1 prize for Oz Lotto, which is played throughout Australia. Cur­
rently, the jackpot builds up until some lucky person’s ticket matches seven numbers for that particular
draw and the winner is paid the jackpot amount in full, as a lump sum. The payout for a Division 1
prize has in the past reached $111.97 million.
MODULE 5 Time value of money 113
Now, if the Lott gave the winner the option of taking the winning amount as either a series of 21 pay­
ments over 20 years or a lesser amount (equal to 65 per cent of the winning total) as a lump sum
today, which would you choose? If you won $111.97 million, does this mean your winning ticket was
worth $111.97 million under this scenario? The answer is no. If you won $111.97 million and chose
to receive the series of payments, the 21 payments would total $111.97 million. If you chose the lump
sum option, the Lott would pay you $72.78 million now, which is less than the stated value of $111.97
million. Thus the value, or price, of the $111.97 million ticket would really be $72.78 million because of
the time value of money and the timing of the 21 cash payments. An appropriate question to ask now is:
‘What is the time value of money?’
Consuming today or tomorrow?
The time value of money is based on the idea that people prefer to consume goods today rather than
waiting to consume similar goods in the future. Most people would prefer to have that new smart TV
today rather than in a year from now, for example. Money has a time value because a dollar in hand
today is worth more than a dollar to be received in the future. This makes sense because, if you had the
dollar today, you could buy something with it — or instead you could invest it and earn interest. For
example, if you had $100 000, you could put it in a bank term deposit paying 5 per cent interest and earn
$5000 interest for the year. At the end of the year, you would have $105 000 ($100 000 + $5000). So
$100 000 today is worth $105 000 a year from today. If the interest rate was higher, you would have even
more money at the end of the year.
Based on this example, we can make several generalisations. First, the value of a dollar invested at
a positive interest rate grows over time. Thus, the further in the future you receive a dollar, the less it
is worth today. Second, the trade‐off between money today and money at some future date depends in
part on the rate of interest you can earn by investing. The higher the rate of interest, the more likely you
will elect to invest your funds and forgo current consumption. Why? At the higher interest rate, your
­investment will earn more money.
The value of money changes with time
The term time value of money reflects the notion that people prefer to consume things today rather than
at some time in the future. For this reason, people require compensation for deferring consumption. The
effect of this is to make a dollar in the future worth less than a dollar today.
In the remainder of this module, we look at two views of time value — future value and present
value. First, however, we describe the use of time lines, which are graphical aids to help solve future
and present value problems, and the use of financial calculators to solve time value of money problems.
Using time lines as aids to problem‐solving
Time lines are an important tool for analysing problems that involve cash flows over time. They provide
an easy way to visualise the cash flows associated with investment decisions. A time line is a horizontal
line that starts at time zero and shows cash flows as they occur over time. The term time zero is used to
refer to the beginning of a transaction in time value of money problems. Time zero is often the current
point in time (today).
Figure 5.1 shows the time line for a 5‐year investment opportunity and its cash flows. Here, as
in most finance problems, cash flows are assumed to occur at the end of the period. The project involves
a $10 000 initial investment (cash outflow), such as the purchase of a new machine, that is expected to
generate cash inflows over a 5‐year period: $5000 at the end of year 1, $4000 at the end of year 2, $3000
at the end of year 3, $2000 at the end of year 4 and $1000 at the end of year 5. Because of the time value
of money, it is critical to identify not only the size of the cash flows, but also their timing.
114 Finance essentials
FIGURE 5.1
0
−$10 000
5%
Five-year time line for a $10 000 investment
1
$5000
2
3
4
5
$4000
$3000
$2000
$1000
Year
Cash flows at the end of each year
If it is appropriate, the time line will also show the relevant interest rate for the problem. In figure 5.1
this is shown as 5 per cent. Also note in figure 5.1 that the initial cash flow of $10 000 is represented
by a negative number. It is convention that cash outflows from the company, such as for the purchase
of a new machine, are treated as negative values on a time line and cash inflows to the company,
such as revenues earned, are treated as positive values. The −$10 000 therefore means that there is a
cash outflow of $10 000 at time zero. As you will see, it makes no difference how you label cash
inflows and outflows as long as you are consistent. That is, if all cash outflows are given a negative
value, then all cash inflows must have a positive value. If the signs get ‘mixed up’ — if some cash
inflows are negative and some positive — you will get the wrong answer to any problem you are
trying to solve.
Financial calculator
We recommend that all students purchase a financial calculator for this course. A financial calculator will
provide the calculation tools to solve most problems in the text. A financial calculator is just an ordinary
calculator that has preprogrammed future value and present value algorithms. Thus, all the variables you
need to make financial calculations exist on the calculator keys. To solve problems, all you have to do is
press the proper keys. The instructions in this text are generally meant for Sharp calculators such as the
EL‐738. If you are using another type such as an HP or Texas Instruments financial ­calculator, consult
the appropriate user manual.
It may sound as if the financial calculator will solve problems for you. It won’t. To get the correct
answer to textbook or real‐world problems, you must first analyse the problem correctly and then
identify the cash flows (as to size and timing), placing them correctly on a time line. Only then will
you be able to enter the correct inputs into your financial calculator. The calculator will, however,
eliminate calculation errors. But it is important that you understand the calculations that the calculator
is performing. For this reason we recommend that, when you first start using a financial calculator,
you solve problems by hand first and then use the calculator’s financial functions to check your
answers.
To help you master your financial calculator, throughout this module we provide helpful hints on how
to best use the calculator. We also recognise that some lecturers or students may want to solve prob­
lems using one of the popular spreadsheet programs. In this module and a number of others, we provide
solutions to several problems that lend themselves to spreadsheet analysis. In solving these problems,
we have used Microsoft Excel. The analysis and basic commands are similar for other spreadsheet
programs.
BEFORE YOU GO ON
1. Why is a dollar today worth more than a dollar 1 year from now?
2. What is a time line and why is it important in financial analysis?
MODULE 5 Time value of money 115
5.2 Future value decisions
LEARNING OBJECTIVE 5.2 Explain the concept of future value, including the meaning of the terms
principal, simple interest and compound interest, and use the future value formula to make business decisions.
The future value (FV) of an investment is what the investment will be worth after earning interest for
one or more time periods. The process of converting the initial amount into future value is called compounding. We will define this term more precisely later. First, we illustrate the concepts of future value
and compounding with a simple example.
Single‐period investment
Suppose you place $100 in a bank savings account that pays interest at 10 per cent a year. How much
money will you have in 1 year? Go ahead and make the calculation. Most people can intuitively arrive
at the correct answer, $110, without the aid of a formula. Your calculation could have looked something
like this:
Future value at the end of year 1 = principal + interest earned
= $100 + ($100 × 0.10)
= $100 × (1 + 0.10)
= $100 × (1.10)
= $110
This approach calculates the amount of interest earned ($100 × 0.10) and then adds it to the initial, or
principal, amount ($100). Notice that when we solve the equation, we factor out the $100.
116 Finance essentials
By doing this in our future value calculation, we arrive at the term (1 + 0.10). This term can be stated
more generally as (1 + i), where i is the interest rate. As you will see, this is a pivotal term in all time
value of money calculations.
Let’s use our intuitive calculation to generate a more general formula. First, we need to define the
variables used to calculate the answer. In our example, $100 is the principal amount (P0), which is the
amount of money deposited (invested) at the beginning of the transaction (time zero); the 10 per cent is
the simple interest rate (i); and the $110 is the future value (FV1) of the investment after 1 year. We can
write the formula for a single‐period investment as follows:
FV1 = P0 + (P0 × i)
= P0 × (1 + i)
Looking at the formula, we more easily see mathematically what is happening in our intuitive calcu­
lation. P0 is the principal amount invested at time zero. If you invest for one period at an interest rate of
i, your investment, or principal, will grow by (1 + i) per dollar invested. The term (1 + i) is the future
value interest factor — often called simply the future value factor — for a single period, such as 1 year.
To test the equation, we plug in our values:
FV1 = $100 × (1 + 0.10)
= $100 × 1.10
= $110
Good, it works!
Two‐period investment
We have determined that at the end of 1 year (one period), your $100 investment has grown to $110.
Now let’s say you decide to leave this new principal amount (FV1) of $110 in the bank for another
year earning 10 per cent interest. How much money would you have at the end of the second year
(FV2)? To arrive at the value for FV2, we multiply the new principal amount by the future value factor
(1 + i). That is, FV2 = FV1 × (1 + i). We then substitute the value of FV1 (the single‐period invest­
ment value) into the equation and algebraically rearrange the terms, which yields FV2 = P0 × (1 + i)2.
The mathematical steps to arrive at the equation for FV2 are shown in the following; recall that
FV1 = P0 × (1 + i):
FV2 = FV1 × (1 + i)
= [P0 × (1 + i)] × (1 + i)
= P0 × (1 + i)2
So the future value of your $110 at the end of the second year (FV2) is as follows:
FV2 = P0 × (1 + i)2
= $100 × (1 + 0.10)2
= 100 × (1.10)2
= $100 × 1.21
= $121
MODULE 5 Time value of money 117
Another way of thinking about a two‐period investment is that it is two single‐period investments back
to back. From that perspective, based on the preceding equations, we can represent the future value of
the deposit held in the bank for 2 years as follows:
FV2 = P0 × (1 + i)2
Turning to figure 5.2, we can see what is happening to your $100 investment over the 2 years we have
already discussed and beyond. The future value of $121 at the end of year 2 consists of three parts. First
is the initial principal of $100 (column 2). Second is the $20 ($10 + $10) of simple interest earned at
10 per cent for the first and second years (column 3). Third is the $1 interest earned during the second
year (column 4) on the $10 of interest from the first year ($10 × 0.10 = $1.00). This is called interest on
interest. The total amount of interest earned is $21 ($10 + $11), which is called compound interest and
is shown in column 5.
FIGURE 5.2
Future value of $100 at 10 per cent
(1)
(2)
(3)
(4)
Interest earned
(5)
(6)
Year
Value at
beginning
of year
Simple
interest
Total
(compound)
interest
Value at
end of year
1
$100.00
$10.00
+
$ 0.00
2
110.00
10.00
+
1.00
=
$10.00
$110.00
=
11.00
3
121.00
10.00
+
121.00
2.10
=
12.10
4
133.10
10.00
+
133.10
3.31
=
13.31
146.41
Interest on
interest
5
146.41
10.00
+
4.64
=
14.64
161.05
5‐year total
$100.00
$50.00
+
$11.05
=
$61.05
$161.05
With compounding, interest earned on an investment is reinvested so that in future periods, interest is
earned on interest as well as on the principal amount. Here, interest on interest begins accruing in year 2.
We are now in a position to formally define some important terms already mentioned in our discussion.
The principal is the amount of money on which interest is paid. In our example, the principal amount
is $100. Simple interest is the amount of interest paid on the original principal amount. With simple
interest, the interest earned each period is paid only on the original principal. In our example, the simple
interest is $10 per year or $20 for the two years. Interest on interest is the interest earned on the rein­
vestment of previous interest payments. In our example, the interest on interest is $1. Compounding is
the process by which interest earned on an investment is reinvested so that, in future periods, interest is
earned on the interest previously earned as well as the principal. In other words, with compounding you
are able to earn compound interest, which consists of both simple interest and interest on interest. In
our example, the compound interest is $21.
Future value equation
Let’s continue our bank example. Suppose you decide to leave your money in the bank for 3 years.
Looking back at the equations for single‐period and two‐period investments, you can probably guess that
the equation for the future value of money invested for 3 years is:
FV3 = P0 × (1 + i)3
118 Finance essentials
With this pattern clearly established, we can see that the general equation to find the future value after
any number of periods is as follows:
FVn = PV × (1 + i)n where:
(5.1)
FVn = future value of investment at the end of period n
PV = original principal (P); often called the present value
i = rate of interest per period
n = n umber of periods; a period can be a year, a quarter, a month, a day or some other
unit of time
(1 + i)n = future value factor
Let’s test our general equation. Say you leave your $100 invested in the bank savings account at
10 per cent interest for 5 years. How much would you have at the end of 5 years? Applying equation 5.1
yields the following:
FVn = PV × (1 + i)n
FV5 = $100 × (1 + 0.10)5
= $100 × (1.10)5
= $100 × 1.6105
= $161.05
Figure 5.2 shows how the interest is earned on a year‐by‐year basis. Note that the total compound
interest earned over the 5‐year period is $61.05 (column 5) and is made up of two parts: (1) $50.00 of
simple interest (column 3); and (2) $11.05 of interest on interest (column 4). Thus, the total interest can
be expressed as follows:
Total compound interest = total simple interest + total interest on interest
= $50.00 + $11.05
= $61.05
The simple interest earned is ($100 × 0.10) = $10.00 per year, and thus the total simple interest for
the 5‐year period is $50.00 (5 years × $10.00). The remaining balance of $11.05 ($61.05 – $50.00)
comes from earning interest on interest.
A helpful equation for calculating simple interest can be derived by using the equation for a single‐
period investment and solving for the term FV1 – P0, which is equal to the simple interest. The equation
for the simple interest earned (SI) is:
SI = P0 × i
where:
i = the simple interest rate for the period, usually 1 year
P0 = the initial or beginning principal amount
Thus, the calculation for simple interest is:
SI = P0 × i = $100 × 0.10 = $10.00
MODULE 5 Time value of money 119
Figure 5.3 shows graphically how the compound interest in figure 5.2 grows. Note that the simple
interest earned each year remains constant at $10, but the amount of interest on interest increases every
year. The reason, of course, is that interest on interest increases with the cumulative interest that has
been earned. As more and more interest builds, the compounding of interest accelerates the growth of
the interest on interest and therefore the total interest earned.
How compound interest grows on $100 at 10 per cent
FIGURE 5.3
$180
Principal
$160
$140
Future value of $100
$161.05
Simple interest
$146.41
Interest on interest
$121.00
$120
$100
$10
10
10
$10
10
10
10
$10
10
10
10
10
3
4
5
$133.10
$110.00
$10
$10
10
1
2
Compound interest
earned = $61.05
$80
$60
$40
$20
$0
0
Year
An interesting observation about equation 5.1 is that the higher the interest rate, the faster the invest­
ment will grow. This fact is illustrated in figure 5.4, which shows the growth in the future value of $1
at different interest rates and for different time periods into the future. First, note that the growth in the
future value over time is not linear, but exponential. The dollar value of the invested funds does not
increase by the same amount from year to year — it increases by a greater amount each year. In other
words, the growth of the invested funds is accelerated by the compounding of interest. Second, the
higher the interest rate, the more money accumulated in any time period. Looking at the right‐hand side
of the figure, you can see the difference in total dollars accumulated if you invest $1 for 10 years: at
5 per cent, you will have $1.63; at 10 per cent, you will have $2.59; at 15 per cent, you will have $4.05;
and at 20 per cent, you will have $6.19. Finally, as you should expect, if you invest a dollar at 0 per cent
for 10 years, you will only have $1 at the end of the period.
The future value factor
To solve a future value problem, we need to know the future value factor, (1 + i)n. Fortunately, almost
any calculator suitable for university‐level work has a power key (the yx key) that we can use to make
this calculation. For example, to calculate (1.08)10 we enter 1.08, press the yx key and enter 10, then
press the ‘=’ key. The number 2.159 should emerge. Give it a try with your calculator. For the Sharp
EL‐738 we enter 1.08, press the 2nd F key, then the yx key, then 10 and ‘=’. An alternative way to
perform this calculation is to multiply 1.08 by itself 10 times; however, we do not recommend this
procedure.
120 Finance essentials
FIGURE 5.4
Future value of $1 for different periods and interest rates
$7.00
Future value of $1
$6.00
Interest
rate
Value of $1
after 10 years
(FV10)
20%
$6.19
15%
$4.05
10%
$2.59
5%
$1.63
0%
$1.00
$5.00
$4.00
$3.00
$2.00
$1.00
$0.00
0
1
2
3
4
5
6
Time (years)
7
8
9
10
DEMONSTRATION PROBLEM 5.1
The power of compounding
Problem:
Your wealthy uncle has passed away and one of the assets he has left to you is a savings account
that your great‐grandfather set up 100 years ago. The account had a single deposit of $1000 and paid
10 per cent interest a year. How much money have you inherited, what is the total compound interest
and how much of the interest earned came from interest on interest?
Approach:
We first need to determine the value of the inheritance, which is the future value of $1000 retained in a
savings account for 100 years at 10 per cent interest. Our time line for the problem is:
0
10%
1
2
3
99
100 Year
FV100 = ?
$1000
To calculate FV100 we begin by calculating the future value factor. We then plug this number into the
future value formula (equation 5.1) and solve for the total inheritance. Finally, we calculate the total compound interest and the total simple interest, and find the difference between these two numbers, which
gives us the interest earned on interest.
Solution:
First, we find the future value factor:
(1+ i )n = (1+ 0.10)100 = (1.10)100 = 13 780.612
Then we find the future value:
FVn = PV × (1+ i )n
FV100 = $1000 × (1.10)100
= $1000 × 13 780.612
= $13 780 612.34
MODULE 5 Time value of money 121
Your total inheritance is $13 780 612.34. The total compound interest earned is this amount less the
original $1000 investment, or $13 779 612:
$13 780 612.34 − $1000 = $13 779 612.34
The total simple interest earned is calculated as follows:
P × i = $1000 × 0.10 = $100 per year
$100 × 100 years = $10 000
The interest earned on interest is the difference between the total compound interest earned and the
simple interest:
13 779 612.34 − $10 000 = $13 769 612.34
That’s quite a difference!
As demonstration problem 5.1 indicates, the relative importance of interest is especially significant for
long‐term investments. As you might expect, interest earned on interest has a great impact on how much
money people ultimately have for their retirement. For example, consider someone who inherits and
invests $10 000 on their 27th birthday and earns 8 per cent a year for the next 40 years. By the investor’s
67th birthday, this investment will grow to:
$10 000 × (1 + 0.08)40 = $217 245.22
In contrast, if the same individual waited until their 37th birthday to invest the $10 000, when they
turned 67 they would have only:
$10 000 × (1 + 0.08)30 = $100 626.57
Of the $116 618.65 difference in these two amounts, the difference in simple interest accounts for only
$8000 (10 years × $10 000 × 0.08 = $8000). The main difference is attributable to the difference in
interest earned on interest. This example illustrates both the importance of compounding for investment
returns and the importance of getting started early on saving for your retirement. The sooner you start
saving, the better off you will be when you retire.
Compounding drives most of the earnings on long‐term investments
The earnings from compounding drive most of the return earned on a long‐term investment. The
reason is that the longer the investment period, the greater the proportion of total earnings from
interest earned on interest. Interest earned on interest grows exponentially as the investment period
increases.
Compounding more frequently than once a year
Interest can, of course, be compounded more frequently than once a year. In equation 5.1, the term n
represents the number of periods and it can describe annual, semiannual, quarterly, monthly or daily
payments. The more frequently interest payments are compounded, the larger the future value of $1
122 Finance essentials
for a given time period. Equation 5.1 can be rewritten to explicitly recognise different compounding
periods:
FVn = PV × (1 + i / m)m × n
where m is the number of times per year that interest is compounded and n is the number of periods,
specified in years.
Let’s say you invest $100 in a bank account that pays a 5 per cent interest rate semiannually (2.5 per cent
twice a year) for 2 years. In other words, the annual rate quoted by the bank is 5 per cent, but the bank
calculates the interest based on a semiannual rate of 2.5 per cent. In this example there are four semiannual
periods, and the amount of principal and interest you will have at the end of these four periods will be:
FV2 = $100 × (1 + 0.05 / 2)2 × 2
= $100 × (1 + 0.025)4
= $100 × 1.1038
= $110.38
It is not necessary to ‘memorise’ the above equation; using equation 5.1 will do fine. All you have
to do is determine the interest paid per compounding period (i/m) and calculate the total number of
compounding periods (m × n) as the exponent for the future value factor. For example, if the bank
compounds interest quarterly, then both the interest rate and compounding periods must be expressed in
quarterly terms: (i/4) and (4 × n).
If the bank in the above example paid interest annually instead of semiannually, at the end of the 2‐year
period you would have:
FV2 = $100 × (1 + 0.05)2 = $110.25
The difference between this amount and the $110.38 above is due to the additional interest earned
on interest when the compounding period is shorter and the interest payments are compounded more
frequently.
You can see the difference between quarterly and daily compounding in demonstration problem 5.2.
DEMONSTRATION PROBLEM 5.2
Changing the compounding period
Problem:
Your grandmother has $10 000 that she wants to put into a bank savings account for 5 years. The bank
she is considering is within walking distance, pays 5 per cent annual interest compounded quarterly
(5 per cent per year/4 quarters per year = 1.25 per cent each quarter), and provides free coffee and cake
in the morning. Another bank in town pays 5 per cent interest compounded daily. Getting to this bank
requires a bus trip, but your grandmother can travel free as a senior citizen. More importantly, though,
this bank does not serve coffee and cake. Which bank should your grandmother select?
Approach:
We need to calculate the difference between the two banks’ interest payments. Bank A, which compounds quarterly, will pay ¼ of the annual interest per quarter, (0.05/4) = 0.0125, and there will be
20 compounding periods over the 5‐year investment horizon (5 years × 4 quarters per year). The time
line for quarterly compounding is as follows:
0
5%/4
$10 000
1
2
3
19
20
Quarter
FV20 = ?
MODULE 5 Time value of money 123
Bank B, which compounds daily, has 365 compounding periods per year. Thus, the daily interest rate is
0.000 137 (0.05/365 = 0.000 137) and there are 1825 (5 years × 365 = 1825 days) compounding periods.
The time line for daily compounding is:
0
5%/365
1
2
3
1824
1825
Day
FV1825 = ?
$10 000
We use equation 5.1 to solve for the future values the investment would generate at each bank. We then
compare the two.
Solution:
Bank A:
FVn = PV(1+ i )n
FVqtrly = $10 000 × (1+ 0.05 / 4)4×5
= $10 000 × (1+ 0.0125)20
= $10 000 × 1.012520
= $10 000 × 1.282037
= $12 820.37
Bank B:
FVn = PV(1+ i )n
FVdaily = $10 000 × (1+ 0.05 / 365)365×5
= $10 000 × (1+ 0.000 137)1825
= $10 000 × 1.000 1371825
= $10 000 × 1.284 003
= $12 840.03
With daily compounding, the extra interest earned by your grandmother is $19.66:
$12 840.03 − $12 820.37 = $19.66
Given that the interest gained over 5 years by daily compounding is less than $20, your grandmother
should probably select her local bank and enjoy the daily coffee and cake. (If she is on a diet, of course,
she should take the higher interest payment and walk to the other bank.)
It is worth noting that the longer the investment period, the greater the additional interest earned
from daily compounding versus quarterly compounding. For example, if the $10 000 was invested for
40 years instead of 5 years, the additional interest earned would increase to $900.23. (You should confirm this by doing the calculation.)
Continuous compounding
We can continue to divide the compounding interval into smaller and smaller time periods such as minutes
and seconds until, at the extreme, we would compound continuously. In this case, m would approach infinity
(∞). The formula to calculate the future value for continuous compounding (FV∞) is stated as follows:
FV∞ = PV × ei × n (5.2)
where e is the exponential function, which has a known mathematical value of about 2.71828, n is the
number of periods specified in years, and i is the annual interest rate. Although the formula may look a
little intimidating, it is really quite easy to apply. Look for a key on your calculator labelled ex. If you
don’t have this exponent key, you still can work the problem.
Let’s go back to the example in demonstration problem 5.1, where your grandmother wants to put
$10 000 in a savings account at a bank. How much money would she have at the end of 5 years if the
124 Finance essentials
bank paid 5 per cent annual interest compounded continuously? To find out, we enter these values into
equation 5.2:
FV∞ = PV × ei × n
= $10 000 × e 0.05 × 5
= $10 000 × e 0.25
= $10 000 × 2.718280.25
= $10 000 × 1.284025
= $12 840.25
If your calculator has an exponent key, all you have to do to calculate e0.25 is enter the number 0.25, then
hit the ex key and the number 1.284 025 should appear (depending on your calculator, you may have
to press the [=] key for the answer to appear). Then multiply 1.284025 by $10 000 and you’re done!
If your calculator does not have an exponent key, then you can calculate e0.25 by inputting the value of
e (2.71828) and raising it to the 0.25 power using the yx key, as described earlier in the module.
Let’s look at your grandmother’s $10 000 bank balance at the end of 5 years with several different
compounding periods: yearly, quarterly, daily and continuous. The future value calculation for annual
compounding is: FVyearly = $10 000 × (1.05)5 = $12 762.82.
(1)
Compounding
period
(2)
Total
earnings
(3)
Compound
interest
(4)
Additional
interest
Yearly
$12 762.82
$2 762.82
—
Quarterly
$12 820.37
$2 820.37
$57.55 more than yearly compounding
Daily
$12 840.03
$2 840.03
$19.66 more than quarterly compounding
Continuous
$12 840.25
$2 840.25
$0.22 more than daily compounding
Note that your grandmother’s total earnings grow as the frequency of compounding increases, as
shown in column 2, but the earnings increase at a decreasing rate, as shown in column 4. The largest
gain comes when the compounding period goes from an annual interest payment to quarterly interest
payments. The gain from daily compounding to continuous compounding is small on a modest savings
balance such as your grandmother’s. Twenty‐two cents over 5 years will not buy her a cup of coffee,
let alone a cake. However, for businesses and governments with mega‐dollar balances held at financial
­institutions, the difference in compounding periods can be substantial.
DECISION‐MAKING EX AMPLE 5.1
Which bank offers depositors the best deal?
Situation:
You have just received a bonus of $10 000 and are looking to deposit the money in a bank account for
5 years. You investigate the annual deposit rates of several banks and collect the following information:
Bank
Compounding
frequency
Annual rate
A
Annually
7.00%
B
Quarterly
7.00%
C
Monthly
6.80%
D
Daily
6.85%
MODULE 5 Time value of money 125
You understand that the more frequently interest is earned in each year, the more you will have at the
end of your investment horizon. To determine which bank you should deposit your money in, you calculate how much money you will earn at the end of 5 years at each bank. You apply equation 5.2 and
come up with these results. Which bank should you choose?
Bank
Investment
amount
Compounding
frequency
Rate
Value after
5 years
A
$10 000
Annually
7.00%
$14 025.52
B
$10 000
Quarterly
7.00%
$14 147.78
C
$10 000
Monthly
6.80%
$14 036.00
D
$10 000
Daily
6.85%
$14 084.19
Decision:
Even though you might expect Bank D’s daily compounding to result in the highest value, the calculations reveal that Bank B provides the highest value at the end of 5 years. Thus, you should deposit the
amount in Bank B because its higher rate offsets the more frequent compounding at Banks C and D.
USING EXCEL
Time value of money
Spreadsheet calculator programs are a popular method for setting up and solving finance and
accounting problems. Throughout this text, we will show you how to structure and calculate some problems using Microsoft Excel, a widely used spreadsheet program. Spreadsheet programs are like your
financial calculator but are especially efficient at doing repetitive calculations. For example, once the
spreadsheet program is set up, it will allow you to make calculations using preprogrammed formulas.
Thus, you can simply change any of the input cells and the preset formula will automatically recalculate
the answer based on the new input values. For this reason, we recommend that you use formulas whenever possible.
We begin our spreadsheet applications with time value of money calculations. As with the financial
calculator approach, there are five variables used in these calculations, and knowing any four of them
will let you calculate the fifth one.
Excel has preset formulas for you to use. These are as follows:
Solving for
Formula
PV
= PV (rate, nper, pmt, fv)
FV
= FV (rate, nper, pmt, pv)
Discount Rate
= RATE (nper, pmt, pv, fv)
Payment
= PMT (rate, nper, pv, fv)
Number of Periods
= NPER (rate, pmt, pv, fv)
To enter a formula, all you have to do is type in the equal sign, the abbreviated name of the variable
you want to calculate and an open parenthesis, and Excel will automatically prompt you to enter the rest
of the variables. Here is an example of what you would type to calculate the future value:
1. =
2. FV
3. (
There are three important things to note when entering the formulas: (1) be consistent with signs for
cash inflows and outflows; (2) enter the rate of return as a decimal number, not a percentage; and
(3) enter the amount of an unknown payment as zero.
126 Finance essentials
To see how a problem is set up and how the calculations are made using a spreadsheet, return to
demonstration problem 5.2.
Calculator tips for future value problems
As we have mentioned, all types of future value calculations can be done easily on a financial calculator.
Here we discuss how to solve these problems and identify some potential problem areas to avoid.
A financial calculator includes the following five basic keys for solving future value and present value
problems:
N
I/Y PV PMT FV
The keys represent the following inputs.
•• N is the number of periods, which can be days, months, quarters or years.
•• I/Y is the interest rate per period, expressed as a percentage.
•• PV is the present value or the original principal (P0).
•• PMT is the amount of any recurring payment.
•• FV is the future value.
Given any four of these inputs, the financial calculator will solve for the fifth. Note that the interest rate
key I/Y differs with different calculator brands: Sharp EL‐738 and Texas Instruments calculators use the
I/Y key, whereas Hewlett‐Packard uses an i, %i or I/Y key. The instructions in this text are generally
based on Sharp calculators, such as the EL‐738. If you are using another financial calculator, consult the
user manual for your calculator.
For future value problems, we need to use only four of the five keys: N for the number of periods, I/Y for
the interest rate (or growth rate), PV for the present value (at time zero), and FV for the future value in n
periods. The PMT key is not used at this time, but when doing a problem always enter a zero to effectively
clear the register. (The PMT key is used for annuity calculations, which we will discuss in module 6.)
It is important to clear the calculator memory before any calculation. To clear the memory of a Sharp
EL‐738, follow these steps.
Procedure
Key operation
Display
How to clear the memory
[2nd F] [ALPHA]
MEM RESET
Important before any calculation.
0 1
0
CLR_MEMORY?
0
THE MEMORY IS NOW CLEAR
MODULE 5 Time value of money 127
To solve a future value problem, enter the known data into your calculator. For example, if you know
that the number of periods is five, key in 5 and press the N key. Repeat the process for the remaining
known values. Once you have entered all of the values you know, then press the COMP key followed by
the FV key for the unknown quantity, and you have your answer.
Let’s try a problem to see how this works. Suppose you invest $5000 at 15 per cent for 10 years. How
much money will you have in 10 years? To solve the problem, we enter data on the keys as displayed
in the following table and solve for FV. Note that the initial investment of $5000 is a negative number
because it represents a cash outflow. Use the +/– key to make a number negative.
If you did not get the correct answer of $20 227.79, you may need to consult the instruction manual
for your financial calculator. However, before you do that you may want to look through figure 5.5,
which lists the most common problems when using financial calculators. Also, note again that the PMT
is entered as zero, which effectively clears the register.
Procedure
Key operation
Display
Enter cash flow data
[+/−] 5000 [PV]
(−5000) ⇒ PV
10 [N]
10 ⇒ N
10.00
15 [I/Y]
15 = ⇒ I/Y
15.00
[COMP] [FV]
FV = 20 227.79
Calculate FV
FIGURE 5.5
−5000.00
20 227.79
Tips for using financial calculators
Use the correct compounding period. Make sure your calculator is set to compound one payment per period
or per year. Because financial calculators are often used to calculate monthly payments, some will default to
monthly payments unless you indicate otherwise. You will need to consult your calculator’s instruction manual,
because procedures for changing settings vary by manufacturer. Most of the problems you will work in other
modules will compound annually.
Clear the calculator before starting. Be sure you clear the data out of the financial register before starting to
work a problem, because most calculators retain information between calculations. Since the information may
be retained even when the calculator is turned off, turning it off and on again will not clear the data. Check your
instruction manual for the correct procedure for clearing the financial register of your calculator.
Negative signs on cash outflows. For certain types of calculations, it is critical that you input a negative
sign for all cash outflows and a positive sign for all cash inflows. Otherwise, the calculator cannot make the
calculation and the answer screen will display some type of error message.
Putting a negative sign on a number. To create a number with a negative sign, enter the number and then press
the ‘change of sign’ key (or the ‘change of sign’ key first, then the number). This key is typically labelled ‘+/–’.
Interest rate as a percentage. Most financial calculators require interest rate data to be entered in percentage
form, not in decimal form. For example, enter 7.125 per cent as 7.125 and not 0.07125. Unlike non‐financial
calculators, financial calculators assume that rates are stated as percentages.
Rounding off numbers. Never round off any numbers until all your calculations are complete. If you round off
numbers along the way, you can generate significant rounding errors.
Adjust decimal setting. Most calculators are set to display two decimal places. You will find it convenient at
times to display four or more decimal places when making financial calculations, especially when working with
interest rates or present value factors. Again, consult your instruction manual.
Have correct BEG or END mode. In finance, most problems that you solve will involve cash payments
that occur at the end of each time period, such as with the ordinary annuities discussed in module 6. Most
calculators normally operate in this mode, which is usually designated ‘END’ mode. However, for annuities due,
which are also discussed in module 6, the cash payments occur at the beginning of each period. This setting is
designated ‘BEG’ mode. Most leases and rent payments fall into this category. When you bought your financial
calculator, it was set in END mode. Financial calculators allow you to switch between END and BEG modes.
128 Finance essentials
One advantage of using a financial calculator is that, if you have values for any three of the four vari­
ables in equation 5.1, you can solve for the remaining variable at the press of a button. Suppose that
you have an opportunity to invest $5000 in a bank and the bank will pay you $20 227.79 at the end of
10 years. What interest rate does the bank pay? The time line for your situation is as follows:
0
i=?
1
2
3
9
−$5000
10
Year
$20 227.79
We know the values for N (10 years), PV ($5000) and FV ($20 227.79), so we can enter these values
into the financial calculator:
Press COMP and then the interest rate (I/Y) key, and 15.00 per cent appears as the answer. Note that
the cash outflow ($5000) was entered as a negative value and the cash inflow ($20 227.79) as a posi­
tive value. If both values were entered with the same sign, your financial calculator algorithm could not
­calculate the equation and an error message would result. Go ahead and try it.
Procedure
Key operation
Enter cash flow data
[+/−] 5000 [PV]
(−5000) ⇒ PV
10 [N]
10 ⇒ N
20227.79 [FV]
20227.79 ⇒ FV
[COMP] [I/Y]
I/Y =
Calculate I/Y
Display
−5000.00
10.00
20227.79
15.00
BEFORE YOU GO ON
1. What is compounding and how does it affect the future value of an investment?
2. What is the difference between simple interest and compound interest?
3. How does changing the compounding period affect the amount of interest earned on an investment?
5.3 Present value decisions
LEARNING OBJECTIVE 5.3 Explain the concept of present value and how it relates to future value, and
use the present value formula to make business decisions.
We have noted that, while future value calculations involve compounding an amount forwards into the
future, present value (PV) calculations involve the reverse. That is, present value calculations involve
determining the current value (or present value) of a future cash flow. The process of calculating the
present value is called discounting and the interest rate i is known as the discount rate. Accordingly,
the present value (PV) can be thought of as the discounted value of a future amount. The present value is
simply the current value of a future cash flow that has been discounted at the appropriate discount rate.
The FV equation (equation 5.1) can be manipulated so that it will give the present value (PV) of a
future sum.
FVn = PV(1 + i)n
PV =
where:
FVn
(1 + i)n
(5.3)
PV = the value today (t = 0) of a cash flow
FVn = the future value at the end of nth period
i = the discount rate, which is the interest rate per period
n = the number of periods, which could be years, quarters, months, days or some other unit
of time
MODULE 5 Time value of money 129
Just as we have a future value factor, (1 + i), we also have a present value factor, which is more com­
monly called the discount factor. The discount factor, which is 1/(1 + i), is the reciprocal of the future
value factor. This expression may not be obvious in the equation above, but note that we can write that
equation in two ways:
1. PV =
FVn
(1 + i)n
2. PV = FVn ×
1
(1 + i)n
These equations amount to the same thing; the discount factor is explicit in the second equation.
Future and present value equations are the same
As mentioned above, the present value equation, equation 5.3, is just a restatement of the future
value equation, equation 5.1. That is, to get the future value (FVn) of funds invested for n years, we
multiply the original investment by (1 + i)n. To find the present value of a future payment (FVn), we
divide FVn by (1 + i)n. Stated another way, we can start with the future value equation (equation 5.1,
FVn = PV × (1 + i)n) and then solve it for PV; the resulting equation is the present value equation
(equation 5.3, PV = FVn/(1 + i)n).
Figure 5.6 illustrates the relationship between the future value and present value calculations for $100
invested at 10 per cent interest. You can see that present value and future value are just two sides of the
same coin. The formula used to calculate the present value is really the same as the formula for future
value, just rearranged.
FIGURE 5.6
Comparing future value and present value calculations
Future value
$110 = $100 × (1 + 0.10)
$100
0
1 Year
10%
$110
$100 = $110 / (1 + 0.10)
Present value
Note: The future value and present value formulas are one and the same; the present value factor, 1/(1 + i)n, is just the reciprocal
of the future value factor, (1 + i)n.
Applying the present value formula
Let’s work through some examples to see how the present value equation is used. Suppose you are inter­
ested in buying a new BMW convertible a year from now. You estimate that the car will cost $120 000. If
your local bank pays 5 per cent interest on savings deposits, how much money will you need to save in
order to buy the car as planned? The time line for the car purchase problem is as follows:
0
PV = ?
130 Finance essentials
5%
1 Year
$120 000
The problem is a direct application of equation 5.3. What we want to know is how much money you
have to put in the bank today to have $120 000 a year from now to buy your BMW. To find out, we
­calculate the present value of $120 000 using a 5 per cent discount rate:
FV1
1+ i
$120 000
=
1 + 0.05
$120 000
=
1.05
= $114 285.71
PV =
If you put $114 285.71 in a bank savings account at 5 per cent today, you will have the $120 000 to buy
the car in 1 year.
Since that’s a lot of money to come up with, your mother suggests that you leave the money in the
bank for 2 years instead of 1 year. If you follow her advice, how much money do you need to invest?
The time line is as follows:
0
1
5%
2 Year
PV = ?
$120 000
For a 2‐year waiting period, assuming the car price will stay the same, the calculation is:
FV1
1
( + i )n
$120 000
=
(1 + 0.05)2
$120 000
=
1.1025
= $108 843.54
PV =
Given the time value of money, the result is exactly what we would expect. The present value of
$120 000 in 2 years is lower than the present value of $120 000 in 1 year — $108 843.54 compared with
$114 285.71. Thus, if you are willing to leave your money in the bank for 2 years instead of 1, you can
make a smaller initial investment to reach your goal.
Now suppose your rich neighbour says that if you invest your money with him for 1 year, he will pay
you 15 per cent interest. The time line is:
0
1 Year
15%
PV = ?
$120 000
The calculation for the initial investment at this new rate is as follows:
FV1
1+ i
$120 000
=
1 + 0.15
$120 000
=
1.15
= $104 347.83
PV =
MODULE 5 Time value of money 131
Thus, when the interest rate, or discount rate, is 15 per cent, the present value of $120 000 to be
received in 1 year’s time is $104 347.83, compared with $114 285.71 at a rate of 5 per cent and a time
period of 1 year. Holding maturity constant, an increase in the discount rate decreases the present value
of the future cash flow. This makes sense because, when interest rates are higher, it is more valuable to
have dollars in hand today to invest; thus, dollars in the future are worth less.
DEMONSTRATION PROBLEM 5.3
Backpacking around Europe
Problem:
Suppose you plan to go backpacking around Europe after you finish university in 2 years. If your savings
account at the bank pays 6 per cent, how much money do you need to set aside today to have $10 000
when you leave for Europe?
Approach:
The money you need today is the present value of the amount you will need for your trip in 2 years.
Thus, the value of FV2 is $10 000. The interest rate is 6 per cent. Using these values and the present
value equation, we can calculate how much money you need to put in the bank at 6 per cent to generate $10 000. The time line is:
0
1
6%
PV = ?
2 Year
$10 000
Solution:
FVn
(1 + i )n
10 000
=
(1.06)2
10 000
=
1.1236
= $8899.96
PV =
Thus, if you invest $8899.96 in your savings account today, at the end of 2 years you will have exactly
$10 000.
Relationship between time, discount rate and present value
From our discussion so far, we can see that: (1) the further in the future a dollar will be received, the less
it is worth today; and (2) the higher the discount rate, the lower the present value of a dollar. Let’s look
a bit more closely at these relationships.
Recall from figure 5.4 that the future value of a dollar increases with time because of compounding.
In contrast, the present value of a dollar becomes smaller the farther into the future that dollar is to be
received. The reason is because the present value factor 1/(1 + i)n is the reciprocal of the future value
factor (1 + i)n. Thus, the present value of $1 must become smaller the farther into the future that dollar
is to be received. This relationship is consistent with our view of the time value of money. That is, the
longer you have to wait for money, the less it is worth today.
Figure 5.7 shows the present values of $1 for different time periods and discount rates. For example,
at 10 years the present value of $1 discounted at 5 per cent is 61 cents, at 10 per cent it is 39 cents
and at 20 per cent just 16 cents. Thus, the higher the discount rate, the lower the present value of $1
132 Finance essentials
for a given time period. Figure 5.7 also shows that, just as with future value, the relationship between
the present value of $1 and time is not linear, but exponential. Finally, it is interesting to note that,
if interest rates are zero, the present value of $1 is $1; that is, there is no time value of money. In
this situation, $1000 today has the same value as $1000 a year from now or, for that matter, 10 years
from now.
FIGURE 5.7
Present value of $1 for different time periods and discount rates
$1.00
Interest
rate
Value today
(PV0) of $1 to
be received
10 years
in the future
0%
$1.00
5%
$0.61
10%
$0.39
15%
$0.25
20%
$0.16
$0.90
$0.80
Present value of $1
$0.70
$0.60
$0.50
$0.40
$0.30
$0.20
$0.10
$0.00
0
1
2
3
4
5
6
Time (years)
7
8
9
10
DECISION‐MAKING EX AMPLE 5.2
Picking the best lottery pay‐off option
Situation:
Congratulations! You have won $1 million on Lotto. You have been presented with several payout alternatives, and you have to decide which one to accept. The alternatives are as follows:
• $1 million today
• $1.2 million lump sum in 2 years
• $1.5 million lump sum in 5 years
• $2 million lump sum in 8 years.
You are intrigued by the choice of collecting the prize money today or receiving double the amount of
money in the future. Which payout option should you choose?
MODULE 5 Time value of money 133
Your cousin, a fund manager, advises you that over the long term you should be able to earn
12 per cent on an investment portfolio. Based on that rate of return, you make the following calculations:
Alternative
Nominal value
Present value
Today
$1 million
$1 million
2 years
$1.2 million
$956 632.65
5 years
$1.5 million
$851 140.28
8 years
$2 million
$807 766.46
Decision:
As appealing as the higher amounts may sound, waiting for the big payout is not worthwhile in this
case. Applying the present value formula has enabled you to convert future dollars into present, or
current, dollars. Now the decision is simple — you can directly compare the present values. Given the
above choices, you should take the $1 million today.
Calculator tips for present value problems
Calculating the discount factor (present value factor) on a calculator is similar to calculating the future
value factor, but requires an additional keystroke on most advanced‐level calculators. The discount
factor, 1/(1 + i)n, is the reciprocal of the future value factor, (1 + i)n. The additional keystroke involves
use of the reciprocal key (1/x) to find the discount factor. For example, to calculate 1/(1.08)10, first enter
1.08, press the yx key and enter 10, then press the equal (=) key. The number on the screen should be
2.159. This is the future value factor. It is a calculation you have made before. Now press the 1/x key,
then the equal key, and you have the present value factor, 0.4632!
Calculating present value (PV) on a financial calculator is the same as calculating future value (FVn)
except that you solve for PV rather than FVn. For example, what is the present value of $1000 received
10 years from now at a 9 per cent discount rate? To find the answer on your financial calculator, enter
the following keystrokes:
Procedure
Key operation
Enter cash flow data
1000 [FV]
1000 ⇒ FV
10 [N]
10 ⇒ N
10.00
9 [I/Y]
9 ⇒ I/Y
9.00
[COMP] [PV]
PV =
Calculate PV
Display
1000.00
−422.41
The PV is −$422.41. Note that the answer has a negative sign. As we have discussed previously, the
$1000 represents an inflow and the $442.41 represents an outflow.
Future value versus present value
We can analyse financial decisions using either future value or present value techniques. Although the
two techniques approach the decision differently, both result in the same answer. Both techniques focus
on the valuation of cash flows received over time. In corporate finance, future value problems typically
measure the value of cash flows at the end of a project, whereas present value measures the value of cash
flows at the start of a project (time zero).
Compounding converts a present value into its future value, taking into account the time value of money.
Discounting is just the reverse — it converts a future cash flow into its present value. Figure 5.8 compares
the $10 000 investment decision shown in figure 5.1 in terms of future value and present value. When
managers are making a decision about whether to accept a project, they must look at all of the cash flows
associated with that project with reference to the same point in time. As figure 5.8 shows, for most busi­
ness decisions that point is either the start (time zero) or the end of the project (in this example, year 5).
134 Finance essentials
In module 6 we will discuss calculation of the future value or present value of a series of cash flows like
that illustrated in figure 5.8.
FIGURE 5.8
Future value and present value compared
Compounding
Future
value
0
−$10 000
1
2
3
4
$5000
$4000
$3000
$2000
5%
5 Year
$1000
Present
value
Discounting
BEFORE YOU GO ON
1. What is the present value and when is it used?
2. What is the discount rate? How does the discount rate differ from the interest rate in the future
value equation?
3. What is the relationship between the present value factor and the future value factor?
4. Explain why you would expect the discount factor to become smaller, the longer the time to payment.
5.4 Future value decisions
LEARNING OBJECTIVE 5.4 Discuss how the future value formula can be used to make business
decisions when the interest rate or number of periods is unknown.
In this final section, we discuss several additional issues concerning present and future value, including
how to find an unknown discount rate and how to calculate the length of time it will take for your money
to grow to a certain amount.
Finding the interest rate
In finance, some situations require you to determine the interest rate (or discount rate) for a given future
cash flow. These situations typically arise when you want to determine the return on an investment. For
example, an interesting financial market innovation is the zero coupon bond. These bonds pay no peri­
odic interest; instead, at maturity the issuer (the company that borrows the money) makes a payment that
includes repayment of the amount borrowed plus interest. Needless to say, the issuer must prepare in
advance to have the cash to pay off the bondholders.
MODULE 5 Time value of money 135
Suppose a company is planning to issue $10 million worth of zero coupon bonds with 20 years to
maturity. The bonds are issued in denominations of $1000 and sold for $90 each. In other words, you
buy the bond today for $90 and 20 years from now the company pays you $1000. If you bought one of
these bonds, what would be your return on investment?
0
i=?
1
2
3
19
−$90
20
Year
$1000
To find the return, we need to solve equation 5.1, the future value equation, for i, the interest, or dis­
count, rate. The $90 you pay today is the PV (present value), the $1000 you get in 20 years is the FV
(future value) and 20 years is n (the compounding period). The resulting calculation is as follows:
FVn = PV(1 + i)n
$1000 = $90 (1 + i )
20
$1000
20
= (1 + i )
$90
 $1000 


$90 
1/ 20
= 1+ i
11.11111/ 20 − 1 = i
i = 1.1279 − 1
= 0.1279 or 12.79%
The rate of return on your investment, compounded annually, is 12.79 per cent. Using a financial calcu­
lator, we arrive at the following solution:
Procedure
Key operation
Enter cash flow data
[+/−] 90 [PV]
(−90) ⇒ PV
−90.00
20 [N]
20 ⇒ N
20.00
1000 [FV]
1000 ⇒ FV
1000.00
[COMP] [I/Y]
I/Y =
12.79
Calculate I/Y
Display
DEMONSTRATION PROBLEM 5.4
Interest rate on a loan
Problem:
Greg and Joan Hubbard are getting ready to buy their
first house. To help make the deposit, Greg’s aunt offers
to lend them $30 000, which can be repaid in 10 years. If
Greg and Joan borrow this money, they will have to repay
Greg’s aunt the amount of $47 500. What rate of interest
would Greg and Joan be paying on the 10‐year loan?
Approach:
In this case, the present value is the value of the loan
($30 000) and the future value is the amount due at the end
of 10 years ($47 500). To solve for the rate of interest on
the loan, we can use the future value equation, equation 5.1. Alternatively, we can use a financial calculator to calculate the interest rate. The time line for the loan is as follows:
0
i=?
−$30 000
136 Finance essentials
1
2
3
9
10
$47 500
Year
Solution:
Using equation 5.1:
FVn = PV(1+ i )n
$47 500 = $30 000 (1+ i )
10
$47 500
10
= (1+ i )
$30 000
 $47 500 
 $30 000 
1/10
= 1+ i
1.583 331/10 − 1 = i
i = 1.047 03 − 1
= 0.047 03 or 4.703%
Using a financial calculator, the steps are:
Procedure
Key operation
Enter cash flow data
[+/−] 30 000 [PV]
(−30 000) ⇒ PV
10 [N]
10 ⇒ N
47 500[FV]
47 500 ⇒ FV
[COMP] [I/Y]
I/Y =
Calculate I/Y
Display
−30 000.00
10.00
47 500.00
4.703
Using Excel, the steps are:
MODULE 5 Time value of money 137
Finding how many periods it takes an investment to grow
to a certain amount
Up to this point we have used variations of equation 5.1:
FVn = PV(1 + i)n
to calculate the future value of an investment (FVn), the present value of an investment (PV) and the
interest rate necessary for an initial investment (the PV) to grow to a specific value (the FV) over a cer­
tain number of periods (n). Note that equation 5.1 has a total of four variables. You may have noticed
that, in all of the previous calculations, we took advantage of the mathematical principle that if we know
the values of three of these variables we can calculate the value of the fourth.
The same principle allows us to calculate the number of periods (n) that it takes an investment to
grow to a certain amount. This is a more complicated calculation than the calculations of the values of
the other three variables, but is an important one for you to be familiar with. Suppose you would like to
purchase a new motocross bike to ride on the dirt trails in the state park near your home. The motorcycle
dealer will finance the bike that you want if you make a deposit of $1175. Right now you have only
$1000. If you can earn 5 per cent by investing your money in a term deposit, how long will it take for
your $1000 to grow to $1175?
To find this length of time, we must solve equation 5.3, the future value equation, for n:
FVn = PV(1 + i)n
$1175 = $1 000 (1 + 0.05)
n
$1175
n
= (1.05)
$1 000
 $1175 
ln 
 = n × ln1.05
 $1 000 
ln1.1175 = n × ln1.05
0.1613 = n × 0.0488
0.1613
0.0488
= 3.31 years
n=
It will take 3.31 years for your investment to grow to $1175. If you don’t want to wait this long to get
your motorcycle, you cannot rely on your investment earnings alone. You will have to put aside some
additional money.
Note that because n is an exponent in the future value formula, we have to calculate the natural logar­
ithm, ln(x), of both sides of the equation in the fourth line of the above series of calculations to calculate
the value of n directly. Your financial calculator should have a key that allows you to calculate natural
logarithms. Just enter the value in the parentheses, hit the LN key and press Enter.
Using a financial calculator, we obtain the same solution:
Procedure
Key operation
Enter cash flow data
[+/−] 1000 [PV]
(−1000) ⇒ PV
5 [I/Y]
5 ⇒ 1/Y
1175[FV]
1175 ⇒ FV
[COMP] [N]
N=
Calculate N
138 Finance essentials
Display
−1000.00
10.00
1175.00
3.31
Using Excel, the steps are:
Solving time value problems
On first delving into the area, some students find financial mathematics rather daunting. There is no need
for it to be. As we have shown, the use of a time line can be of great help in defining what information
is available, what information is missing and what type of problem it is. Thus, we have developed a few
steps in solving these problems.
1. Draw a time line and insert the cash flows, both in and out, at the appropriate places.
2. Identify which three variables are known and what the missing fourth one is.
3. Put the variables into the FV/PV equation and solve for the unknown as per the examples shown.
4. Use your financial calculator to solve the question/check your answer. Clear the memory, enter your
three knowns and solve for the unknown.
This module has introduced the basic principles of present value and future value. The table at the end
of the module summarises the key equations developed in the module. The basic equations for present
value (equation 5.3) and future value (equation 5.1) are two of the most fundamental relationships in
finance and will be applied throughout the balance of the text.
BEFORE YOU GO ON
1. The future value formula has four variables. What are they?
2. Give an example of a situation when the number of periods may be unknown.
MODULE 5 Time value of money 139
SUMMARY
5.1 Explain what the time value of money is and why it is so important in the field of finance.
The idea that money has a time value is one of the most fundamental concepts in the field of
finance. This concept is based on the idea that most people prefer to consume goods today, rather
than waiting to have similar goods in the future. Since money buys goods, you would rather have
money today than in the future. Thus, a dollar today is worth more than a dollar received in the
future. Another way of viewing the time value of money is that your money is worth more today
than at some point in the future because, if you had the money now, you could invest it and earn
interest. Thus, the time value of money is the opportunity cost of forgoing consumption today.
Applications of the time value of money focus on the trade‐off between current dollars and dollars
received at some future date. This is an important element in financial decisions because most invest­
ment decisions require the comparison of cash invested today with the value of expected future cash
inflows. Time value of money calculations facilitate such comparisons by accounting for both the
magnitude and timing of cash flows. Investment opportunities are undertaken only when the value
of future cash inflows exceeds the cost of the investment (the initial cash outflow).
5.2 Explain the concept of future value, including the meaning of the terms principal, simple
interest and compound interest, and use the future value formula to make business decisions.
The future value is the sum to which an investment will grow after earning interest. The principal
is the amount of the investment. Simple interest is the interest paid on the original investment; the
amount of money earned on simple interest remains constant from period to period. Compound
interest includes not only simple interest, but also interest earned on the reinvestment of previ­
ously earned interest, the so‐called interest on interest. For future value calculations, the higher
the interest rate, the faster the investment will grow. The application of the future value formula in
­business decisions is presented in section 5.2.
5.3 Explain the concept of present value and how it relates to future value, and use the present
value formula to make business decisions.
The present value is the value today of a future cash flow. Calculating the present value involves
discounting a future cash flow back to the present at an appropriate discount rate. The process of
discounting cash flows adjusts the cash flows for the time value of money. Mathematically, the
present value factor is the reciprocal of the future value factor, or 1/(1 + i). The calculation and
application of the present value formula in business decisions are presented in section 5.3.
5.4 Discuss how the future value formula can be used to make business decisions when the
interest rate or number of periods is unknown.
The future value formula can be used to make business decisions when three of the four variables
are known. The four variables are: (1) FV; (2) PV; (3) interest rate; and (4) number of periods. You
can use the future value formula or a financial calculator to solve for the unknown variable.
SUMMARY OF KEY EQUATIONS
Equation
Description
Formula
5.1
Future value of an n‐period investment with annual compounding
FVn = PV × (1+ i )n
5.2
Future value with continuous compounding
FV∞ = PV × e i × n
5.3
Present value
PV =
140 Finance essentials
FVn
(1+ i )n
KEY TERMS
compound interest interest calculated on the actual amount outstanding each period
compounding process by which interest earned on an investment is reinvested so in future periods
interest is earned on the interest as well as the principal
discount rate the interest rate used in the discounting process to find the present value of future cash
flows
discounting the process by which the present value of future cash flows is obtained
future value (FV) the value of an investment after it earns interest for one or more periods
interest on interest interest earned on interest that is earned in previous periods
present value (PV) the value today of a future stream of cash payments discounted at the appropriate
discount rate
principal amount of money on which interest is paid
simple interest interest earned on the original principal amount only
time line a diagrammatic representation of cash flows, either received or paid or both
time value of money the concept that a dollar is worth more the sooner it is received
time zero the beginning of a transaction; often the current point in time
ACKNOWLEDGEMENTS
Photo: © SergeyP / Shutterstock.com
Photo: © Andresr / Shutterstock.com
Photo: © bikeriderlondon / Shutterstock.com
MODULE 5 Time value of money 141
MODULE 6
Discounted cash
flows and valuation
LEA RN IN G OBJE CTIVE S
After studying this module, you should be able to:
6.1 explain why cash flows occurring at different times must be adjusted to reflect their value at a common
date before they can be compared, and calculate the present value and future value for multiple cash flows
6.2 describe how to calculate the present value and future value of an ordinary annuity, and how an
ordinary annuity differs from an annuity due
6.3 explain what perpetuities are and where we see them in business, and calculate the present values
of perpetuities
6.4 describe how to calculate the periodic payments, number of periods and interest rate for a range
of annuity problems and prepare a loan amortisation schedule
6.5 discuss why the effective annual interest rate (EAR) is the appropriate way to annualise interest rates
and calculate EAR.
Module preview
In the previous module, we introduced the concept of the time value of money: dollars today are more
valuable than dollars to be received in the future. Starting with that concept, we developed the basics
of simple interest, compound interest and future value calculations. We then went on to discuss present
value and discounted cash flow analysis. This was all done in the context of a single cash flow.
In this module, we consider the value of multiple cash flows. Most business decisions, after all, involve
cash flows over time. For example, if Mrs Mac’s, a Perth‐based company that makes frozen fruit pies,
wants to consider adding a production line, the decision will require analysis of the project’s expected
cash flows over a number of periods. Initially, there would be large cash outlays to build the new line
and get it operational. Thereafter, the project should produce cash inflows for many years. Because these
cash flows occur over time, the analysis must consider the time value of money, discounting each of the
cash flows using the present value formula we discussed in module 5.
We begin this module by describing calculations of future and present values for multiple cash flows.
We then examine some situations in which future cash flows are level over time: these involve annuities,
in which the cash flow stream goes on for a finite period, and perpetuities, in which the stream goes
on forever. We then explain how to solve annuity problems when the value of the payment, number of
periods or discount rate is unknown. This is followed by demonstrating how to prepare a loan amor­
tisation schedule suitable for car, housing and business loans. Finally, we describe the effective annual
interest rate and compare it with the annual percentage rate (APR), which is a rate that is used to describe
the interest rate in consumer loans.
MODULE 6 Discounted cash flows and valuation 143
6.1 Multiple cash flows
LEARNING OBJECTIVE 6.1 Explain why cash flows occurring at different times must be adjusted to
reflect their value at a common date before they can be compared, and calculate the present value and
future value for multiple cash flows.
We begin our discussion of the time value of multiple cash flows by calculating the future value and
then the present value of multiple cash flows. These calculations, as you will see, are nothing more than
applications of the techniques you learned in module 5.
Future value of multiple cash flows
In module 5, we worked through several examples that involved the future value of a lump sum of money
invested in a savings account that paid 10 per cent interest per year. But suppose you are investing more
than one lump sum. Let’s say you put $1000 in your bank savings account today and another $1000 a
year from now. If the bank continues to pay 10 per cent interest per year, how much money will you
have at the end of 2 years?
To solve this future value problem, we can use equation 5.1: FVn = PV × (1 + i)n. First, however, we
construct a time line so that we can see the magnitude and timing of the cash flows. As figure 6.1 shows,
there are two cash flows into the savings plan. The first cash flow is invested for 2 years and compounds
to a value that is calculated as follows:
FV2 = PV × (1 + i )2
= $1000 × (1 + 0.10)2
= $1000 × 1.21
= $1210
The second cash flow earns simple interest for a single period only and grows to:
FV1 = PV × (1 + i )
= $1000 × (1 + 0.10)
= $1000 × 1.10
= $1100
As seen in figure 6.1, the total amount of money in the savings account after 2 years is the sum of
these two amounts, which is $2310 ($1100 + $1210).
FIGURE 6.1
Future value of two cash flows
0
$1000
10%
1
2
Year
$1000
$1100 = $1000 × 1.10
$1210 = $1000 × (1.10)2
Total future value $2310
Now suppose that you expand your investment horizon to 3 years and invest $1000 today, $1000 a
year from now and $1000 at the end of 2 years. How much money will you have at the end of 3 years?
First, we draw a time line to be sure that we have correctly identified the time period for each cash flow.
This is shown in figure 6.2.
144 Finance essentials
FIGURE 6.2
Future value of three cash flows
0
10%
$1000
1
2
$1000
$1000
3
Year
$1100 = $1000 × 1.10
$1210 = $1000 × (1.10)2
$1331 = $1000 × (1.10)3
Total future value $3641
Then we calculate the future values of each of the individual cash flows using equation 5.1. Finally,
we add up the future values. The total future value is $3641. The calculations are as follows:
FV1 = PV × (1 + i)   = $1000 × (1 + 0.10)   = $1000 × 1.100 = $1100
FV2 = PV × (1 + i)2 = $1000 × (1 + 0.10)2 = $1000 × 1.210 = $1210
FV3 = PV × (1 + i)3 = $1000 × (1 + 0.10)3 = $1000 × 1.331 = $1331
Total future value
$3641
To summarise, solving future value problems with multiple cash flows involves a simple process.
First, draw a time line to make sure that each cash flow is placed in the correct time period. Second,
calculate the future value of each cash flow for its time period. Third, add up the future values. It’s that
simple!
Let’s use this process to solve a practical problem. Suppose you want to buy an apartment in 3 years
and estimate that you will need $40 000 for a deposit. If the interest rate you can earn at the bank is
8 per cent and you can save $6000 now, $8000 at the end of the first year and $10 000 at the end of
the second year, how much money will you have to come up with at the end of the third year to have a
$40 000 deposit?
The time line for the future value calculation in this problem looks like this:
0
$6000
8%
1
2
3
$8000
$10 000
FV = ?
Year
To solve the problem, we need to calculate the future value for each of the expected cash flows, add
up these values, and find the difference between this amount and the $40 000 needed for the deposit.
Using equation 5.1, we find that the future values of the cash flows at the end of the third year are:
FV1 = PV × (1 + i)  = $10 000 × 1.08  = $10 000 × 1.080 0 = $ 10 800.00
FV2 = PV × (1 + i)2 = $8000 × (1.08)2 = $8000 × 1.166 4  = $ 9331.20
FV3 = PV × (1 + i)3 = $6000 × (1.08)3 = $6000 × 1.259 7  = $ 7558.27
Total future value
$ 27 689.47
At the end of the third year, you will have $27 689.47, so you will need an additional $12 310.53
($40 000 − $27 689.47) at that time to make the deposit.
Calculator tip: calculating the future value of multiple cash flows
To calculate the future value of multiple cash flows with a financial calculator, we calculate the future
value of each of the individual cash flows, write down each calculated future value and add them up.
Present value of multiple cash flows
In business situations, we often need to calculate the present value of a series of future cash flows. We do
this, for example, to determine the market price of a bond, to decide whether to purchase a new machine
MODULE 6 Discounted cash flows and valuation 145
or to assess the value of a business. Solving present value problems involving multiple cash flows is
similar to solving future value problems involving multiple cash flows. First, we prepare a time line
to identify the magnitude and timing of the cash flows. Second, we calculate the present value of each
individual cash flow using equation 5.3: PV = FVn/(1 + i)n. Finally, we add up the present values. The
sum of the present values of a stream of future cash flows is their current market price, or value. There
is nothing new here!
Using the present value equation
Next, we work through some examples to see how we can use equation 5.3 to find the present value of
multiple cash flows. Suppose that your best friend needs cash and offers to pay you $1000 at the end
of each of the next 3 years if you will lend him $3000 cash today. You realise, of course, that because
of the time value of money, the cash flows he has promised to pay are worth less than $3000. If the
interest rate on similar loans is 7 per cent, how much should you lend for the cash flows your friend is
offering?
To solve the problem, we first construct a time line, as shown in figure 6.3. Then, using equation 5.3
we calculate the present value for each of the three cash flows, as follows:
PV = FV1 × 1/(1 + i) = FV1 × 1/1.07    = $1000 × 0.934 6 =
PV = FV2 × 1/(1 + i)2 = FV2 × 1/(1.07)2 = $1000 × 0.873 4 =
PV = FV3 × 1/(1 + i)3 = FV3 × 1/(1.07)3 = $1000 × 0.816 3 =
$ 934.58
$ 873.44
$ 816.30
Total present value
$ 2624.32
If you view this transaction from a purely business perspective, you should not lend your friend more
than $2624.32, which is the sum of the individual discounted cash flows.
FIGURE 6.3
Present value of three cash flows
0
7%
PV = ?
1
2
3
$1000
$1000
$1000
Year
$1000 × 1/1.07 = $934.58
$1000 × 1/(1.07)2 = $873.44
$1000 × 1/(1.07)3 = $816.30
$2624.32 Total present value
Now let’s consider another example. Suppose you have the opportunity to buy a small business while
you are at university. The business involves selling sandwiches, soft drinks and snack foods to students
from a truck that you drive around campus. The annual cash flows from the business have been pre­
dictable. You believe you can expand the business and you estimate that cash flows will be as follows:
$2000 the first year, $3000 the second and third years, and $4000 the fourth year. At the end of the
fourth year, the business will be closed down because the truck and other equipment will need to be
replaced. The total of the estimated cash flows is $12 000. You have done some research at university
and found that a 10 per cent discount rate would be appropriate. How much should you pay for the
business?
To value the business, we calculate the present value of the expected cash flows, discounted at
10 per cent. The time line for the investment is:
0
PV = ?
146 Finance essentials
10%
1
2
3
4
$2000
$3000
$3000
$4000
Year
We calculate the present value of each cash flow and then add them up:
PV
PV
PV
PV
=
=
=
=
FV1
FV2
FV3
FV4
×
×
×
×
1/(1
1/(1
1/(1
1/(1
+
+
+
+
i)  = $2000 × 1/1.10    = $2000 × 0.909 1 =
i)2 = $3000 × 1/(1.10)2 = $3000 × 0.826 4 =
i)3 = $3000 × 1/(1.10)3 = $3000 × 0.751 3 =
i)4 = $4000 × 1/(1.10)4 = $4000 × 0.683 0 =
$1818.18
$2479.34
$2253.94
$2732.05
Total present value
$9283.51
This calculation tells us that the value of the business is $9283.51. If you pay $9283.51 for the busi­
ness, you will earn a return of exactly 10 per cent. Of course, you should buy the business for the lowest
price possible; however, you should never pay more than the $9283.51 value today of the expected cash
flows. If you do, you will be paying more for the investment than it is worth.
Calculator tip: calculating the present value of multiple cash flows
To calculate the present value of future cash flows with a financial calculator, we use exactly the same
process that we used in finding the future value, except that we solve for the present value instead of
the future value. We can calculate the present values of the individual cash flows, save them in the
­calculator’s memory and then add them up to obtain the total present value.
You should note that from this point forward we will use a different notation. Up to this point, we have
used the notation FVn to represent a cash flow in period n. We have done this to stress that, for n > 0,
we were referring to a future value. From this point on, we will use the notation CFn, instead of FVn
because the CFn notation is more commonly used by financial analysts.
DECISION‐MAKING EX AMPLE 6.1
The investment decision
Problem:
You are thinking of buying a business and your investment adviser presents you with two possibilities. Both
businesses are priced at $60 000 and you have only $60 000 to invest. She has provided you with the cash
flows for each business, along with the present value of the cash flows discounted at 10 per cent, as follows:
Cash flow per year ($ thousands)
Business
1
2
3
Total
PV at 10%
A
$50
$30
$ 20
$100
$85.27
B
$ 5
$ 5
$100
$110
$83.81
Which business should you acquire?
Decision:
At first glance, business B may look to be the best choice because its undiscounted cash flows for the
3 years total $110 000, versus $100 000 for A. However, to make the decision on the basis of the undiscounted cash flows ignores the time value of money. By discounting the cash flows, we convert them
to current dollars, or their present values. The present value of business A is $85 270 and that of B is
$83 810. While both of these investment opportunities are attractive, you should acquire business A if
you only have $60 000 to invest. Business A is expected to produce more valuable cash flows for your
investment, as it provides the greater addition to wealth.
BEFORE YOU GO ON
1. Explain how to calculate the future value of a stream of cash flows.
2. Explain how to calculate the present value of a stream of cash flows.
3. Why is it important to adjust all cash flows to a common date?
MODULE 6 Discounted cash flows and valuation 147
6.2 Annuities
LEARNING OBJECTIVE 6.2 Describe how to calculate the present value and future value of an ordinary
annuity, and how an ordinary annuity differs from an annuity due.
In finance we commonly encounter contracts that call for the payment of equal amounts of cash over
several time periods. For example, most business term loans and insurance policies require the holder
to make a series of equal payments, usually monthly. Similarly, nearly all consumer loans, such as car,
personal and home loans, call for equal monthly payments. Any financial contract that calls for equally
spaced and level cash flows over a finite number of periods is called an annuity. Some annuities are
structured so that the cash payments are received or paid at the beginning of each period (such as rent
or insurance). These annuities are known as an annuity due. Most annuities are structured so that cash
payments are received at the end of each period. Because this is the most common structure, these annu­
ities are often called ordinary annuities. If the cash flow payments continue forever, the contract is
called a perpetuity.
Present value of an ordinary annuity
We frequently need to find the present value of an annuity (PVA). Suppose, for example, that a finan­
cial contract pays $2000 at the end of each year for 3 years and the appropriate discount rate is 8 per cent.
The time line for the contract is:
0
8%
PV = ?
1
2
3
$2000
$2000
$2000
Year
What is the most we should pay for this annuity? Of course, we have worked problems like this one
before. All we need to do is calculate the present value of each individual cash flow (CFn) and add them
up, as shown in the previous section of this module.
This approach to calculating the PVA works as long as the number of cash flows is relatively small. In
many situations that involve annuities, however, the number of cash flows is large and doing the calcu­
lations by hand would be tedious. For example, a typical 25‐year home loan has 300 monthly payments
(12 months × 25 years = 300 months).
Fortunately, our problem can be simplified because the cash flows (CF) for an annuity are all the same
(CF1 = CF2 = . . . CFn = CF). Thus, the present value of an annuity (PVAn) with n equal cash flows (CF)
at interest rate i is the sum of the individual present value calculations:
1  
1 
1 

+  CF ×
PVA n =  CF ×
n
2  + +  CF ×

(
(
)
1+ i  
1 + i ) 
1+ i 


With some mathematical manipulations that are beyond the scope of this discussion, we can simplify
this equation to yield a useful formula for the present value of an annuity:
CF 
1 
× 1 −
n
(
i
i ) 
+
1

 1 − 1 / (1 + i )n 
= CF × 

i


PVA n =
where:
PVAn =
CF =
i=
n=
present value of an n period annuity
level and equally spaced cash flow
discount rate, or interest rate
number of periods (often called the annuity’s maturity)
148 Finance essentials
(6.1)
Let’s apply equation 6.1 to the example involving a 3‐year annuity with a $2000 annual cash flow at
8 per cent. To solve for PVAn we first plug our values into the equation and then solve for PVA.
 1 − 1 / (1 + i)n 
PVA n = CF × 

i


3
 1 − 1 / 1.08 
= 2000 × 

0.08


 1 − 1 / 1.2597 
= 2000 × 

0.08

 1 − 0.7938 
= 2000 × 
 0.08 
0.2062 
= 2000 × 
 0.08 
= 2000 × 2.5771
= $5154.19
Even though we have only shown the figures to four decimal places, we did not round them during
the calculation. If you rounded during the calculation, you would get rounding differences. These differ­
ences can be quite large when working with large values. By not rounding, you will get the same answer
as you would using a financial calculator.
These equations may look complicated, but they really are not. It’s just a matter of practice. If you
are calculating a PVA using a calculator and your maths is a bit rusty, start with the (1 + i)n part. The
discount rate, i, is 8 per cent and the n is 3 years. Input 1.08 and hit the y x button, then input 3 and
hit the = sign. Next press the 1/x button (to give you the 1/(1 + i)n value). Then hit the +/− sign to
make the displayed value negative. Press + and 1, then = to get 0.2062 (you have subtracted 0.7938
from 1), then divide by 0.08 to get 2.5771. Next, as your CF is $2000, multiply the 2.5771 by 2000
to get 5154.19. The PVA of $2000 for 3 years at an 8 per cent discount rate is $5154.19. After you
have tried a number of problems, your finger will dance over the calculator and find its own way onto
the right buttons.
Calculator tip: finding the present value of an ordinary annuity
There are four variables in a PVA equation (PVAn, CF, n and i) and if you know three of them, you
can solve for the fourth in a few seconds with a financial calculator. The calculator key that you have
not used so far is the PMT (payment) key, which is the key for level cash flows, CF, over the life of an
annuity.
To illustrate problem‐solving with a financial calculator, we will revisit the financial contract that paid
$2000 per year for 3 years, discounted at 8 per cent. To find the present value of the contract, we enter
8 per cent for the interest rate (I/Y), $2000 for the payment (PMT) and 3 for the number of periods (N).
The key for FV is not relevant for this calculation, so we just need to clear the memory as usual before
any calculation, to clear the registers. The key entries and the answer are as follows:
Procedure
Enter cash flow data
Calculate PV
Key operation
Display
3 [N]
3⇒N
3.00
8 [I/Y]
8 ⇒ I/Y
8.00
2000 [PMT]
2000 ⇒ PMT
[COMP] [PV]
PV =
2000.00
−5154.19
MODULE 6 Discounted cash flows and valuation 149
The price of the contract is $5154.19, which agrees with our other calculations. The negative sign in
the financial calculator box indicates that $5154.19 is a cash outflow. Recall that, when using a calcu­
lator, it is common practice to enter cash outflows as negative numbers and cash inflows as positive
numbers. See module 5 for discussion of the importance of assigning the proper sign (+ or −) to cash
flows when using a financial calculator.
USING EXCEL
Finding the present value of an annuity
We build on the Excel examples provided in the previous module, starting with solving the present value
of an annuity. We now have the addition of the payments made during the holding period. We will use
the same information used in the calculator problem above to demonstrate how to solve this problem
using Excel.
DEMONSTRATION PROBLEM 6.1
Buying equipment for a business
Problem:
You offer a repair and customisation service. You need to buy a new piece of equipment for this side of
the business and think you will net $10 000 each year for 5 years. After 5 years, the equipment will be
worn out with no residual value. What is the PV of these future cash flows? (You want to know this so
that you can compare this figure and the current cost of the machine.) The business’s funds can earn
6 per cent per annum in the next best alternative use, so you want to earn at least this rate of
return. Suppose the current cost of the equipment is $30 000. Should you go ahead with buying the
equipment?
Approach:
By using this best alternative rate in the calculation, you are ensuring this alternative opportunity is
allowed for in the calculations. Then, if the PV of the cash flows exceeds the cost now of the machine,
you are ensuring the wealth of the firm is increased as much as possible in the circumstances. First, we
draw a time line to show the flow of funds over the 5‐year period.
PVA
10
10
10
10
$'000
10
0
1
2
3
4
5
150 Finance essentials
Next, we plug the figures into equation 6.1 to find the present value of the future cash flows, discounting at 6 per cent per annum.
Solution:
 1− 1/ (1 + i )n 
PVA = CF× 

i

 1 − 1/ 1.065 
PVA = 10 000 

0.06

= 10 000 × 4.2124
= $42123.64
Based on these figures and assuming the data is correct, you should go ahead with buying the
equipment because there is more than a $12 000 ($42 123.64 − $30 000) gain in present‐value terms.
Generally speaking, projects should be undertaken where the PV of future cash inflows is greater than
the initial outlay.
Future value of an ordinary annuity
Generally, when we are working with annuities, we are interested in calculating their present value. On
occasion, we do need to calculate the future value of an annuity (FVA). Such calculations typically
involve some type of saving activity, such as a monthly savings plan. Another application is calculating
terminal values for retirement or superannuation plans with constant contributions.
We will start with a simple example. Suppose you plan to save $100 by the end of every year for
4 years with the goal of buying a racing bicycle. The bike you want is a BMC Roadmachine RM02 that
costs around $4500. If your bank pays 8 per cent interest a year, will you have enough money to buy the
bike at the end of 4 years?
To solve this problem, we first lay out the cash flows on a time line, as discussed earlier in this
module. We then calculate the future value for each cash flow using equation 5.1, FVn = PV × (1 + i)n.
Finally, we add up all the cash flows. The time line and calculations are shown in figure 6.4. Given that
the total future value of the four payments is $4506.11, as shown in the figure, you should have just
enough money to buy the bike.
FIGURE 6.4
0
Future value of a 4‐year annuity: BMC Roadmachine RM02
1
2
3
$1000
$1000
$1000
4 Year
$1000.00 = $1000 × (1.08)0
$1080.00 = $1000 × 1.08
$1166.40 = $1000 × (1.08)2
$1259.71 = $1000 × (1.08)3
Total future value
$4506.11
Of course, most business applications involve longer periods of time than the BMC bike example.
One way to solve more complex problems involving the future value of an annuity is first to calculate the
PVA using equation 6.1 and then use equation 5.3 to calculate the future value of the PVA. In practice,
MODULE 6 Discounted cash flows and valuation 151
many analyses condense this calculation into a single step by using the FVA formula, which we obtain
by substituting PVA for PV in equation 5.1:
FVA n = PVA n × (1 + i )
n
CF 
1 
(
)n
× 1 −
n  × 1+ i
(
)
i
i
1
+


CF
n
=
× [(1 + i ) − 1]
i
=
(6.2)
 (1 + i )n − 1 
F VA n = CF × 

i


where:
FVAn = future value of an annuity at the end of n periods
PVAn = present value of an n period annuity
CF = level and equally spaced cash flow
i = discount rate, or interest rate
n = number of periods
Using equation 6.2 to calculate FVA for the BMC bike problem is straightforward. The calculation
and process are similar to those we developed for PVA problems. We plug our values into the equation:
 (1 + i )n − 1 
FVA n = CF × 

i


 (1 + i )n − 1 
= CF × 

i


4
1.08
1
−

= $1000 × 
 0.08 
0.360 49
= $1000 ×
0.08
= $1000 × 4.5061
= $4506.11
This value is the same as we calculated in figure 6.4.
Calculator tip: finding the future value of an ordinary annuity
The procedure for calculating the FVA on a financial calculator is precisely the same as the procedure
for calculating the PVA discussed earlier. The only difference is that we use the FV (future value) key
instead of the PV (present value) key. The PV key will be entered as a zero in the register once you clear
the calculator memory before you perform the calculation.
Let’s work the BMC bicycle problem on a calculator. Recall that we decided to put $1000 in the bank
at the end of each year for 4 years. The bank pays 8 per cent interest. Clear the financial register and
make the following entries:
Procedure
Key operation
Enter cash flow data
4 [N]
4⇒N
4.00
8 [I/Y]
8 ⇒ I/Y
8.00
[+/−]1000 [PMT]
1000 ⇒ PMT
[COMP] [FV]
FV =
Calculate FV
152 Finance essentials
Display
−1000.00
4506.11
The calculated value of $4506.11 is the same as in figure 6.4.
USING EXCEL
Finding the future value of an annuity
Annuities due
So far we have discussed only annuities whose cash flow payments occur at the end of the period, so‐called
ordinary annuities. Another type of annuity that is fairly common in business is known as an annuity due.
Here, cash payments start immediately, at the beginning of the first period. For example, when you rent an
apartment, the first rent payment is typically due immediately. The second rent p­ ayment is due on the first of
the second month and so on. In this kind of payment pattern, you are effectively prepaying for the service.
MODULE 6 Discounted cash flows and valuation 153
Present value of an annuity due
Figure 6.5 compares the cash flows for an ordinary annuity and an annuity due. Note that both annuities
are made up of four $1000 cash flows and carry an 8 per cent interest rate. Part A shows an ordinary
annuity, in which the cash flows take place at the end of the period, and part B shows an annuity due, in
which the cash flows take place at the beginning of the period. There are several ways to calculate the
present and future values of an annuity due, and we discuss them next.
FIGURE 6.5
Ordinary annuity versus annuity due
A. Ordinary annuity (present value: 4 years at 8 per cent)
With an ordinary annuity, the first cash flow occurs
at the end of the first year.
0
1
2
3
4
$1000
$1000
$1000
$1000
Year
8%
$1000/1.08 = $926
$1000/(1.08)2 = $857
$1000/(1.08)3 = $794
$1000/(1.08)4 = $735
Total PV = $3312
B. Annuity due (present value: 4 years at 8 per cent)
With an annuity due, the first cash flow occurs
at the beginning of the first year.
0
$1000
8%
1
2
3
$1000
$1000
$1000
4
Year
$1000/(1.08)0 = $1000
$1000/1.08 = $926
$1000/(1.08)2 = $857
$1000/(1.08)3 = $794
Total PV = $3577
The difference between an ordinary annuity (part A) and an annuity due (part B) is that with an ordi­
nary annuity, the cash flows take place at the end of each period, while with an annuity due, the cash
flows take place at the beginning of each period. As you can see in this example, the PV of the annuity
due is larger than the PV of the ordinary annuity. The reason is that the cash flows of the annuity due are
shifted forwards 1 year and thus are discounted less.
Annuity transformation method
An easy way to work annuity due problems is to transform the formula for the PVA (equation 6.1)
so that it will work for annuity due problems. To do this, we pretend that each cash flow occurs at
154 Finance essentials
the end of the period (although it actually occurs at the beginning of the period) and use equation
6.1. Since equation 6.1 discounts each cash flow by one period too many, we then correct for the
extra discounting by multiplying our answer by (1 + i), where i is the discount rate or interest
rate.
The relationship between an ordinary annuity and an annuity due can be formally expressed as:
Annuity due value = Ordinary annuity value × (1 + i ) (6.3)
This relationship is especially helpful because it works for both present value and future value calcula­
tions. Calculating the value of an annuity due using equation 6.3 involves three steps.
1. Adjust the problem time line as if the cash flows were an ordinary annuity.
2. Calculate the present or future value as though the cash flows were an ordinary annuity.
3. Finally, multiply the answer by (1 + i).
Let’s calculate the value of the annuity due shown under the annuity transformation method above
using equation 6.3, the transformation technique. First, we restate the time line as if the problem were
an ordinary annuity; the revised time line looks like the one in figure 6.5A. Second, we calculate
the PVA as if the problem involved an ordinary annuity. The value of the ordinary annuity is $3312,
as shown in part A of the figure. Finally, we use equation 6.3 to make the adjustment to an annuity
due:
Annuity due value = Ordinary annuity value × (1 + i )
= $3312 × 1.08
= $3577
As they should, the answers for the two methods of calculation agree.
Calculator tip: annuity due
The easy way to calculate the present value or future value of an annuity due is using the BGN/END
switch in your financial calculator. All financial calculators have a key that switches the cash flow from
the end of each period to the beginning of each period. The keys are typically labelled ‘BGN’ for cash
flows at the beginning of the period and ‘END’ for cash flows at the end of the period. To calculate the
PV of an annuity due: (1) switch the calculator to BGN mode; (2) enter the data; and (3) press COMP
and then the PV key for the answer. As an example, work the problem from figure 6.5B using your
financial calculator.
Recall that we decided to put $1000 in the bank at the beginning of each year for 4 years. The bank
pays 8 per cent interest. Clear the financial register and make the following entries:
Procedure
Key operation
Display
Set to BGN mode
BGN
BGN
Enter cash flow data
4 [N]
8 [I/Y]
[+/−]1000 [PMT]
4⇒N
8 ⇒ I/Y
1000 ⇒ PMT
Calculate PV
[COMP] [PV]
PV =
4.00
8.00
−1000.00
3577.10
Don’t forget to reset your financial calculator back to payments at the end of the period, END mode,
so that you don’t make errors with future problems.
MODULE 6 Discounted cash flows and valuation 155
USING EXCEL
Finding the present value of an annuity due
The method used in Excel to solve for annuity values can easily be adjusted when dealing with annuity
due values. The time value of money functions assume payments occur at the end of each period.
However, Excel includes a variable named ‘Type’ that it takes into account when solving for annuity due.
Enter 1 in the cell for ‘type’ and include this cell in your formula, as shown below.
DEMONSTRATION PROBLEM 6.2
Scratch lottery win
Problem:
During a break between classes, you head to the local shops to buy a snack. You notice the scratch
lottery tickets for sale in the newsagent and decide to have a go — after all, it has been a good day so
far. You buy a ticket, scratch it and wow! You’ve won $60 000 a year for 21 years! Needless to say, you
don’t go back to class that day!
A few days later you go to the head office of the lotteries corporation to claim your prize. You have
two options: (1) take the $60 000 per year for 21 years with the first payment received today; or (2) take
an upfront lump sum of $1 000 000. What should you do, assuming the appropriate discount rate is
5 per cent?
Approach:
First calculate the PVA and then compare it to the upfront lump sum. If the PV of the future cash flows
(PVA) exceeds the upfront lump sum option, you are ensuring your wealth will be maximised.
First, we draw the time line to show the future cash flows over the 21‐year period.
PVAD
$'000
60
60
60
60
60
60
60
0
1
2
3
4
19
20
156 Finance essentials
21
Next, we plug the figures into equation 6.3 to find the present value of the future cash flows, discounting at 5 per cent per annum.
Solution:
Annuity due value = Ordinary annuity value × (1+ i )
 1− 1/ (1 + i )n 
= CF 
 × (1+ i )

i
 1 − 1/ 1.0521 
= 60 000 
× (1.05)


0.05
= 60 000(12.8212)(1.05)
= $80 7732.62
Calculator solution:
Procedure
Key operation
Set to BGN mode
BGN
BGN
Enter cash flow data
21 [N]
21 ⇒ N
5 [I/Y]
5 ⇒ I/Y
60 000 [PMT]
60 000 ⇒ PMT
[COMP] [PV]
PV =
Calculate PV
Display
21.00
5.00
60 000.00
−807 732.62
Now that you have calculated the PVA of the future cash flows, you can compare it to the alternative
option of $1 000 000. As $1 000 000 > $80 7732.62, you are better off taking the $1 000 000 upfront
today, rather than receiving the $60 000 annual payments over the next 21 years.
BEFORE YOU GO ON
1. Unless we are explicitly told otherwise, what do we generally assume about the timing of cash
flows in present and future value problems?
2. The payments in an annuity due occur when in each of the equal‐length periods?
3. What is the difference between an ordinary annuity and an annuity due?
6.3 Perpetuities
LEARNING OBJECTIVE 6.3 Explain what perpetuities are and where we see them in business, and
calculate the present values of perpetuities.
The final type of annuity to be considered, and the simplest to understand, is the perpetuity. A perpetuity
is a series of regular, cash flows that continue forever. While forever is a long time and you might argue
that nothing lasts forever, which is true, the concept of perpetuity is still a useful one. Some cash flows
have no determined limit.
The most important perpetuities in the securities markets today are preference share issues. The issuer
of preference shares promises to pay investors a fixed dividend forever unless a retirement date for the
preference shares has been set. If preference share dividends are not paid, all previous unpaid dividends
must be repaid before any dividends are paid to ordinary shareholders. This preferential treatment is one
source of the term preference share.
It is worth noting that, as a company can have an indefinite life, its expected cash flows might also go
on forever. When these expected cash flows are constant, they can be viewed as a perpetuity.
MODULE 6 Discounted cash flows and valuation 157
From equation 6.1, we can calculate the present value of a perpetuity by setting n, which is the number
of periods, equal to infinity (∞).When that is done, the value of the term 1/(1 + i)∞ approaches 0, and thus:
PVP =
CF i
(6.4)
where:
PVP = present value of a perpetuity
CF = periodic cash flow
i = discount rate, or interest rate
As you can see, the present value of a perpetuity is the promised constant cash payment (CF) divided
by the interest rate (i). A nice feature of the final equation (PVP = CF/i) is that it is algebraically very
simple to work with, since it allows us to solve for i directly rather than by trial and error, as is required
with equations 6.1 and 6.2. This is discussed further later in this module.
For example, suppose you had a great experience during university at the faculty of business and
decided to endow a scholarship fund for finance students. The goal of the fund is to provide the univer­
sity with $100 000 of financial support for finance students each year forever. If the rate of interest is
8 per cent, how much money will you have to give the university to provide the desired level of support?
Using equation 6.4, we find that the present value of the perpetuity is:
PVP =
CF $100 000
=
= $1 250 000
i
0.08
Thus, a gift of $1.25 million will provide a constant annual payment of $100 000 to the university
forever.
There is one subtlety that you should be aware of. In our calculation, we made no adjustment for
inflation. If the economy is expected to experience inflation, which is generally the case, the real value
of the scholarship you are funding will decline each year.
Before we finish our discussion of perpetuities, we should point out that the present value of a
­perpetuity is typically not very different from the present value of a very long annuity. For example, sup­
pose that instead of funding the scholarship forever, you plan to fund it for 100 years. If you calculate
the present value of a 100‐year annuity of $100 000 using an interest rate of 8 per cent, you will find that
it equals $1 249 431.76, which is only slightly less than the $1 250 000 value of the perpetuity; making a
gift a perpetuity would only cost you an additional $568.24. This is because the present value of the cash
flows to be received after 100 years is extremely small. The key point here is that cash flows that are to
be received far into the future can have very small present values.
DEMONSTRATION PROBLEM 6.3
Preference share dividends
Problem:
Suppose that you are the CEO of a public company and your investment banker recommends that you
issue some preference shares at $50 per share. Similar preference share issues are yielding 6 per cent. What
annual cash dividend does the company need to offer in order to be competitive in the marketplace? In
other words, what cash dividend paid annually forever would be worth $50 with a 6 per cent discount rate?
Approach:
As we have already mentioned, preference shares are a type of perpetuity; thus, we can solve this
problem by applying equation 6.4. As usual, we begin by laying out the time line for the cash flows:
0 6% 1
PVA∞
158 Finance essentials
CF
2
3
4
5
6
CF
CF
CF
CF
CF
∞ Year
CF
For preference shares, PVA∞ is the value of one share, which is $50. The discount rate is 6 per cent.
CF is the fixed‐rate cash dividend, which is the unknown value. Knowing all this information, we can use
equation 6.4 and solve for CF.
Solution:
CF
i
CF
$50 =
0.06
CF = $50 × 0.06
PVP =
= $3
The annual dividend on the preference shares would be $3 per share.
BEFORE YOU GO ON
1. How do an ordinary annuity and a perpetuity differ?
2. Give two examples of perpetuities.
6.4 Additional concepts and applications
LEARNING OBJECTIVE 6.4 Describe how to calculate the periodic payments, number of periods and
interest rate for a range of annuity problems and prepare a loan amortisation schedule.
So far this module, we have focused on finding the PV or FV for a range of annuities and perpetuities.
However, often in finance it is necessary to calculate the periodic payment amount or the length of time
required to pay or receive a certain dollar amount. We show you how to solve these types of problems in
this section, as well as how to create a loan amortisation schedule which shows the balance outstanding
after each payment is made during the term of the loan. Lastly, we discuss how to find the appropriate
interest rate when solving annuity problems.
Finding the value of periodic payments
A very common problem in finance is determining the payment schedule for a loan on a consumer
asset, such as a car or a home that is purchased on credit. Nearly all consumer credit loans call for equal
monthly payments. Suppose, for example, that you have just purchased a $450 000 apartment on the
Gold Coast. You were able to provide a deposit of $50 000 and obtain a 25‐year home loan at 8 per cent
for the balance. What are your monthly payments?
In this problem we know the present value of the annuity. It is $400 000, the price of the apartment
less the deposit ($450 000 − $50 000). We also know the number of payments; since the payments will
be made monthly for 25 years, you will make 300 payments (12 months × 25 years). Because the pay­
ments are monthly, both the interest rate and maturity must be expressed in monthly terms. For consumer
loans, to get the monthly interest rate we divide the annual interest rate by 12. Thus, the monthly interest
rate equals 0.66667 per cent (8 per cent/12 months = 0.66667 per cent per month). What we need to
calculate is the monthly cash payment (CF) over the loan period. The time line looks like the following:
0 0.666 67%
$400 000
1
2
3
300
CF1
CF2
CF3
CF300
Month
MODULE 6 Discounted cash flows and valuation 159
To find CF (remember that CF1 = CF2 = … CF300 = CF), we plug all the data into equation 6.1 and
solve it for CF:
 1 − 1 / (1 + i )n 
PVA = CF × 

i


 1 − 1 /1.006667 300 
$400 000 = CF × 

0.006667


$400 000
CF =
129.5645
= $3087.26
Your home loan repayments will be about $3087.28 per month.
To solve the problem on a financial calculator takes only a few seconds once the time line is ­prepared.
The most common error students make when using financial calculators is failing to convert all c­ ontract
variables to be consistent with the compounding period. Thus, if the contract calls for monthly p­ ayments,
the interest rate and contract duration must also be stated in monthly terms.
Having converted our data to monthly terms, we enter into the calculator: N = 300 months (25 years ×
12 months per year = 300 months), I/Y = 0.66667 (8 per cent/12 months = 0.66667 per cent per month),
PV = $400 000 and FV = 0 (to clear the register). Then, pressing COMP and then the payment button
(PMT), we find the answer, which is −$3087.26. The necessary keystrokes are:
Procedure
Key operation
Enter cash flow data
300 [N]
300 ⇒ N
8/12 [I/Y]
0.66666667 ⇒ I/Y
0.66666667
[+/−]400 000 [PV]
(−400 000) ⇒ PV
−400 000.00
[COMP] [PMT]
PMT =
Calculate PMT
Display
300.00
3087.26
Notice that the hand and calculator answers differ by only 2 cents. This is because when we did the hand
calculations, we carried six to eight decimals places through the entire set of calculations. Had we rounded
off each number as the calculations were made, the errors between the two calculation methods would have
been about $2.00. The moral of the story is to round as few numbers as possible when making a series of hand
calculations. The more numbers that are rounded during calculations, the greater the possible rounding error.
DEMONSTRATION PROBLEM 6.4
What are your monthly car repayments?
Problem:
You have decided to buy a new car and the dealer’s best price is $19 750. The dealer agrees to provide financing with a 5‐year car loan at 12 per cent interest. Using a financial calculator, calculate your
monthly repayments.
Approach:
All the problem data must be converted to monthly terms. The number of periods is 60 months
(5 years × 12 months per year = 60 months) and the monthly interest charge is 1 per cent (12 per cent/
12 months = 1 per cent per month). The time line for the car purchase is as follows:
0
$19 750
1%
1
2
3
60
CF1
CF2
CF3
CF60
Month
Having converted our data to monthly terms, we enter the following values into the calculator:
N = 60 months, I/Y = 1, PV = $19 750 and FV = 0 (to clear the register). Pressing the COMP key and
then the payment (PMT) key will give us the answer.
160 Finance essentials
Solution:
Procedure
Key operation
Enter cash flow data
60 [N]
60 ⇒ N
60.00
1 [I/Y]
1 ⇒ I/Y
1.00
19 750 [PV]
19 750 ⇒ PV
[COMP] [PMT]
PMT =
Calculate PMT
Display
19 750.00
−439.33
Note that since we entered $19 750 as a positive number (because it is a cash inflow to you), the
monthly repayment of $439.33 is a negative number.
USING EXCEL
Finding the periodic payment
Finding the number of payments
Another important financial calculation is determining the number of payments for an annuity. The number
of payments tells us the time required on an annuity contract to repay a debt. For example, suppose you
decide to purchase a motor vehicle for $35 000 and you agree to pay $700 per month. The bank charges
an annual rate of 7.42 per cent compounding monthly. How long will you need to pay off the loan?
As we did when we found the payment amount, we can insert these values into equation 6.1 and solve
for n:
 1 − 1 / (1 + i)n 
PVA = CF × 

i


 1 − 1 / 1.006183n 
$35 000 = $700 × 

0.006183


$35 000  1 − 1 / 1.006183n 
=

$700
0.006183


MODULE 6 Discounted cash flows and valuation 161
50 × 0.006183 = 1 − 1 / 1.006183n
1 / 1.006183n = 1 − 0.3092
1.006183n = 1 / 0.69083
n × ln1.006183 = ln1.4475
n × 0.006164 = 0.3699
0.3699
0.006164
= 60 months ∴ 5 years
n=
To determine the number of payments for the annuity, we need to solve the equation for the unknown
value n. First, we need to calculate the monthly interest rate (7.42% ÷ 12 = 0.6183%). You will need
to use natural logarithms (ln on your calculator) to solve this equation. Solving this problem as shown
above, we find that it will take 60 months for you to pay off this loan, which equals 5 years.
Naturally, this problem is much easier when solved using a financial calculator. Using a calculator,
the steps are:
Procedure
Key operation
Enter cash flow data
35 000 [PV]
35 000 ⇒ PV
[+/−]700 [PMT]
(−700) ⇒ PMT
−700.00
0.6183 [I/Y]
0.6183 ⇒ I/Y
0.6183
[COMP] [N]
N=
Calculate N
Display
Note: remember to convert the value of N to the number of years by dividing by 12.
USING EXCEL
Finding the number of periods
162 Finance essentials
35 000.00
60
Finding the interest rate
Another important calculation in finance is determining the interest, or discount, rate for an annuity.
The interest rate tells us the rate of return on an annuity contract. For example, suppose your parents are
getting ready to retire and decide to convert some of their superannuation into an annuity that guarantees
them a fixed annual income. Their superannuation fund manager asks for $350 000 for an annuity that
guarantees to pay them $50 000 a year for 10 years. What is the rate of return on the annuity?
As we did when we found the payment amount, we can insert these values into equation 6.1:
 1 − 1 / (1 + i)n 
PVA = CF × 

i


 1 − 1 / (1 + i )10 
$350 000 = $50 000 × 

i


To determine the rate of return for the annuity, we need to solve the equation for the unknown value i.
Unfortunately, it is not possible to solve the resulting equation for i algebraically. The only way to solve
the problem is manually by trial and error. We normally solve this kind of problem using a financial
calculator or computer spreadsheet program that finds the solution for us. However, it is important to
understand how the solution is arrived at by trial and error, so let’s work this problem without such aids.
To start the process, we must select an initial value for i, plug it into the right‐hand side of the equation
and solve the equation to see if the present value of the annuity stream equals $350 000, which is the
left‐hand side of the equation. If the present value of the annuity is too large (PVA > $350 000), we need
to select a higher value for i. If the present value of the annuity stream is too small (PVA < $350 000),
we need to select a smaller value. We continue the trial‐and‐error process until we find the value for i at
which PVA = $350 000.
The key to getting started is to make the best guess we can as to the possible value of the interest
rate, given the information and data available to us. We will assume that the current bank deposit rate
is 4 per cent. Since the annuity rate of return should exceed the bank rate, we will start our calculations
with a 5 per cent discount rate. The present value of the annuity is:
 1 − 1 / (1 + i)n 
PVA n = CF × 

i


 1 − 1 / (1.05)10 
PVA 5% = $50 000 × 

0.05


= $50 000 × 7.7217
= $386 087
That’s a pretty good first guess, but our present value is greater than $350 000, so we need to try a
higher discount rate. Let’s try 7 per cent:
 1 − 1 / (1 + i)n 
PVA = CF × 

i


PVA 7%
 1 − 1 / (1.07 )10 
= $50 000 × 

0.07


= $50 000 × 7.0236
= $351 179
MODULE 6 Discounted cash flows and valuation 163
The present value of the annuity is still slightly higher than $350 000, so we still need a larger value
of i. How about 7.1 per cent:
 1 − 1 / (1 + i)n 
PVA = CF × 

i


 1 − 1 / (1.071)10 
PVA 7.1% = $50 000 × 

0.071


= $50 000 × 6.9912
= $349561
The value is too small, but we now know that i is between 7.00 and 7.1 per cent. On the next try, we
need to use a slightly smaller value of i — say, 7.073 per cent:
 1 − 1 / (1 + i)n 
PVA = CF × 

i


 1 − 1 / (1.07073)10 
PVA 7.073% = $50 000 × 

0.07073


= $50 000 × 6.9999
= $349 997
The cost of the annuity, $350 000, is now very close to being the same as the present value of the annuity
stream ($349 997); thus, 7.073 per cent is slightly higher than the rate of return earned by the annuity.
It typically takes many more guesses to solve for the interest rate than it did in this example. Our
‘guesses’ were good because we knew the answer before we started! Clearly, solving for i by trial and
error can be a long and tedious process. Fortunately, as mentioned, these types of problems are easily
solved with a financial calculator or computer spreadsheet program. Next, we describe how to calculate
the interest rate or rate of return on an annuity on a financial calculator.
Calculator tip: finding the interest rate
To illustrate how to find the interest rate for an annuity on a financial calculator, we will enter the infor­
mation from the previous example (remember to clear the calculator memory first). We know the number
of periods (N = 10), the payment amount (PMT = $50 000) and the present value (PV = −$350 000),
and we want to solve for the interest rate (I/Y):
Procedure
Key operation
Enter cash flow data
[+/−] 350 000 [PV]
(−350 000) ⇒ PV
10 [N]
10 ⇒ N
50 000 [PMT]
50 000 ⇒ PMT
[COMP] [I/Y]
I/Y =
Calculate I/Y
Display
−350 000.00
10.00
50 000.00
7.0728
The interest rate is 7.0728 per cent. Note that we have used a negative sign for the present value of the
annuity contract, representing a cash outflow, and a positive sign for the annuity payments, representing
cash inflows. Using the present value formula, you must always have at least one inflow and one outflow.
If we had entered both the PV and PMT amounts as positive values (or both as negative values), the
calculator would have reported an error since the equation could not be solved. As we have mentioned
before, we could have reversed all of the signs — that is, made cash outflows positive and cash inflows
negative — and still found the correct answer.
164 Finance essentials
DECISION‐MAKING EX AMPLE 6.2
The pizza dough machine
Problem:
As the owner of a pizza restaurant, you are considering whether to buy a fully automated pizza dough
preparation machine. Your staff is wildly supportive of the purchase because it would eliminate a tedious
part of their work. Your accountant provides you with the following information.
• The cost, including shipping, for the Italian Pizza Dough Machine is $25 000.
• Cash savings, including labour, raw materials and tax savings due to depreciation, are $3500 per year
for 10 years.
• Present value of cash savings is $21 506 at a 10 per cent discount rate. (The PVA factor for 10 years
at 10 per cent is 6.1446. Thus, PVA10 = CF × annuity factor = $3500 × 6.1446 = $21 506.10. Using a
calculator, PVA10 = $21 505.98. The difference is due to rounding errors.)
Given the above data, what should you do?
Decision:
As you arrive at the pizza restaurant in the morning, the staff is in a festive mood because word has
leaked that the new machine will save the shop $35 000 and only cost $25 000.
With a heavy heart, you explain that the analysis done at the water cooler by some of the staff is
­incorrect. To make economic decisions involving cash flows, even for a small business such as your pizza
restaurant, you cannot compare cash values from different time periods unless they are adjusted for the
time value of money. The present value formula takes into account the time value of money and converts
the future cash flows into current or present dollars. The cost of the machine is already in current dollars.
The correct analysis is as follows: the machine costs $25 000 and the present value of the cost savings is $21 506. Thus, the cost of the machine exceeds the benefits; the correct decision is not to buy
the new dough preparation machine.
Preparing a loan amortisation schedule
Once you understand how to calculate a monthly or yearly loan payment, you have all of the tools that
you need to prepare a loan amortisation schedule. The term amortisation describes the way in which the
principal (the amount borrowed) is repaid over the life of a loan. With an amortising loan, some portion
of each month’s loan payment goes to reducing the principal. When the final loan payment is made, the
unpaid principal is reduced to zero and the loan is paid off. The other portion of each loan payment is
interest, which is payment for the use of outstanding principal (the amount of money still owed). Thus,
with an amortising loan, each loan payment contains some repayment of principal and some interest
payment. Nearly all loans to consumers are amortising loans.
A loan amortisation schedule is just a table that shows the loan balance at the beginning and end of
each period, the payment made during that period, and how much of that payment represents interest and
how much represents repayment of principal. To see how an amortisation schedule is prepared, consider
an example. Suppose that you have just borrowed $10 000 at a 5 per cent interest rate from a bank to
purchase a car. Typically, you would make monthly payments on such a loan. For simplicity, however,
we will assume that the bank allows you to make annual payments and that the loan will be repaid over
5 years. Figure 6.6 shows the amortisation schedule for this loan.
To prepare a loan amortisation schedule, we must first calculate the loan repayment. Since, for con­
sumer loans, the amount of the loan payment is fixed, all the payments are identical in amount. Applying
equation 6.1, we calculate as follows:
 1 − 1 / (1 + i)n 
PVA n = CF × 

i


 1 − 1 / 1.055 
$10 000 = CF × 

0.05


MODULE 6 Discounted cash flows and valuation 165
$10 000
4.3295
= $2309.75
CF =
Alternatively, we enter the values N = 5 years, I/Y = 5 per cent and PV = $10 000 in a financial calculator
and press COMP and then the PMT key to solve for the loan payment amount. The answer is −$2309.75 per
year. If you rounded during your calculation, your answer may be slightly different. For the amortisation
table calculation, it is best to use the answer from the financial calculator as it will be more precise.
FIGURE 6.6
Year
1
2
3
4
5
Amortisation table for a 5‐year, $10 000 loan at 5 per cent interest
(1)
(2)
(3)
Beginning
balance
Total annual
paymenta
$10 000.00
8190.25
6290.02
4294.77
2199.76
$2309.75
2309.75
2309.75
2309.75
2309.75
Interest
paidb
(4)
Principal
paid
(2)–(3)
(5)
Ending
balance
(1)–(4)
$500.00
409.51
314.50
214.74
109.99
$1809.75
1900.24
1995.25
2095.01
2199.76
$8190.25
6290.02
4294.77
2199.76
0.00
$3 000
Total annual payment
$2 500
$2 000
The total annual payment is calculated
using the formula for the present value
of an annuity, equation 6.1.
The total annual payment is CF in
PVAn = CF × PV annuity factor.
b
Interest paid equals the beginning
balance times the interest rate.
a
Principal paid
$1 500
$1 000
Interest paid
$500
$0
1
2
3
Year
4
5
Turning to figure 6.6, we can work through the amortisation schedule to see how the table is prepared.
For the first year, the values are determined as follows:
1. The amount borrowed, or the beginning principal balance, is $10 000.
2. The annual loan payment, as calculated earlier, is $2309.75.
3. The interest payment for the first year is $500 and is calculated as follows:
Interest payment = i × P0
= 0.05 × $10 000
= $500
4. The principal paid for the year is $1809.75, calculated as follows:
Principal paid = Loan payment − Interest payment
= $2309.75 − $500
= $1809.75
5. The ending principal balance is $8190.25, calculated as follows:
Ending principal balance = Beginning principal balance − Principal paid
= $10 000 − $1809.75
= $8190.25
166 Finance essentials
Note that the ending principal balance for the first year ($8190.25) becomes the beginning principal
balance for the second year ($8190.25), which in turn is used in calculating the interest payment for the
second year:
Interest payment = i × P0
= 0.05 × $8 190.25
= $409.51
This calculation makes sense because each loan payment includes some principal repayment. This is
why the interest in column 3 declines each year. We repeat the calculations until the loan is fully amor­
tised, at which point the principal balance goes to zero and the loan is paid off.
If we are preparing an amortisation table for monthly payments, all of the principal balances, loan pay­
ments and interest rates must be adjusted to a monthly basis. For example, to calculate monthly payments
for our car loan, we would make the following adjustments: n = 60 payments (12 months per year ×
5 years = 60 months), I/Y = 0.4167 per cent (5 per cent/12 months per year = 0.4167 per cent per
month) and monthly payment = $188.71.
USING EXCEL
Loan amortisation table
Loan amortisation tables are most easily constructed using a spreadsheet program. Here, we have
reconstructed the loan amortisation table shown in figure 6.6 using Excel.
Note that all the values in the amortisation table are obtained using formulas. Once you have built an
amortisation table like this one, you can change any of the input variables, such as the loan amount,
and all of the other numbers will automatically be updated.
Note, in figure 6.6 the amounts of interest and principal that are paid each year change over time.
Interest payments are the greatest in the early years of an amortising loan because much of the principal
has not yet been repaid (see columns 1 and 3). However, as the principal balance is reduced over time,
the interest payments decline and more of each monthly payment goes towards paying the principal
(see columns 3 and 4). The final loan payment repays just enough principal to pay off the loan in full.
MODULE 6 Discounted cash flows and valuation 167
BEFORE YOU GO ON
1. How could you reduce the term of a loan?
2. Explain why a financial calculator is ideal for calculating the discount rate for annuity problems.
3. Describe how you would prepare an amortisation schedule for a 4‐year loan of $25 000.
6.5 Comparing interest rates
LEARNING OBJECTIVE 6.5 Discuss why the effective annual interest rate (EAR) is the appropriate way
to annualise interest rates and calculate EAR.
In this module and the preceding one, there has been little question about which interest rate to use in a
particular calculation. In most cases, a single interest rate was supplied. When working with real market
data, however, the situation is not so clear‐cut. We often encounter interest rates that can be calculated
in different ways. In this final section, we try to untangle some of the issues that can cause problems.
Why the confusion?
To better understand why interest rates can be so confusing, consider a familiar situation. Suppose you
borrow $100 on your bank credit card and plan to keep the balance outstanding for 1 year. The credit card’s
stated interest rate is 1 per cent per month. The National Consumer Credit Protection Act requires the bank
and other credit providers to disclose to consumers the annual percentage rate (APR) charged on a loan.
The APR, otherwise known as the nominal rate, is the annualised interest rate using simple interest. Thus, the
APR is defined as the simple interest charged per period multiplied by the number of periods per year. For the
bank credit card loan, the APR is 12 per cent (1 per cent per month × 12 months = 12 per cent).
At the end of the year, you go to pay off the credit card balance as planned. It seems reasonable to
assume that with an APR of 12 per cent, your credit card balance at the end of one year would be $112
(1.12 × $100 = $112). Wrong! The bank’s actual interest rate is 1 per cent per month, meaning that the
bank will compound your credit card balance monthly, 12 times over the year. The bank’s calculation
168 Finance essentials
for the balance due is $112.68 [$100 × (1.01)12= $112.68]. The bank is actually charging you 12.68 per
cent per year, and the total interest paid for the 1‐year loan is $12.68 rather than $12.00. (If you have any
doubt about the total credit card debt at the end of 1 year, make the calculation 12 times on your calcu­
lator: the first month is $100 × 1.01 = 101.00; the second month is $101.00 × 1.01 = $102.01; the third
month is $102.01 × 1.01 = $103.03; and so on for 12 months.)
This example raises a question: What is the correct way to annualise an interest rate?
Calculating the effective annual interest rate
In making financial decisions, the correct way to annualise an interest rate is to calculate the effective
annual interest rate. The effective annual interest rate (EAR) is defined as the annual growth rate that
takes compounding into account. Mathematically, the EAR can be stated as follows:
Quoted interest rate 

1 + EAR =  1 +


m
m
m
(6.5)
Quoted interest rate 

EAR =  1 +
 − 1 
m
where m is the number of compounding periods during a year.
The quoted interest rate is by definition a simple annual interest rate, like the APR or nominal rate.
That means that the quoted interest rate has been annualised by multiplying the rate per period by the
number of periods per year. The EAR conversion formula accounts for the number of compounding
periods and thus effectively adjusts the annualised quoted interest rate for the time value of money.
Because the EAR is the true cost of borrowing and lending, it is the rate that should be used for making
all finance decisions.
We will use our bank credit card example to illustrate the use of equation 6.5. Recall that the credit card
has an APR of 12 per cent (1 per cent per month). The APR is the quoted interest rate and the number of com­
pounding periods (m) is 12. Applying equation 6.5, we find that the effective annual interest rate is:
m
Quoted interest rate 

EAR =  1 +
 − 1

m
12
0.12 

EAR =  1 +
 −1

12 
= 1.0112 − 1
= 1.1268 − 1
= 0.1268 or 12.68%
The EAR value of 12.68 per cent is the true cost of borrowing the $100 on the bank credit card for one
year. The EAR calculation adjusts for the effects of compounding and, hence, the time value of money.
Finally, note that interest rates are quoted in the marketplace in three ways.
1. The quoted interest rate. This is an interest rate that has been annualised by multiplying the rate per
period by the number of compounding periods. The APR is an example. All consumer borrowing and
lending rates are annualised in this manner.
2. The interest rate per period. The bank credit card rate of 1 per cent per month is an example of
this kind of rate. You can find the interest rate per period by dividing the quoted interest rate by the
number of compounding periods.
3. The effective annual interest rate (EAR). This is the interest rate actually paid (or earned), which
takes compounding into account. Sometimes it is difficult to distinguish a quoted rate from an EAR.
Generally, however, an annualised consumer rate is an APR rather than an EAR.
MODULE 6 Discounted cash flows and valuation 169
Comparing interest rates
When borrowing or lending money, it is sometimes necessary to compare and select among interest
rate alternatives. Quoted interest rates are comparable when they cover the same overall time period,
such as 1 year, and have the same number of compounding periods. If quoted interest rates are not
comparable, we must adjust them to a common time period. The easiest way, and the correct way,
to make interest rates comparable for making finance decisions is to convert them to effective annual
interest rates.
Consider an example. Suppose you are the chief financial officer of a manufacturing company. The
company is planning a $1 billion plant expansion and will finance it by borrowing money for 5 years.
Three financial institutions have submitted interest rate quotes; all are APRs:
Lender A: 10.40 per cent compound monthly
Lender B: 10.90 per cent compounded annually
Lender C: 10.50 per cent compounded quarterly.
Although all the loans have the same maturity, the loans are not comparable because the APRs
have different compounding periods. To make the adjustments for the different time periods, we apply
equation 6.5 to convert each of the APR quotes into an EAR:
m
Quoted interest rate 

EAR =  1 +
 − 1

m
12
0.104 

EAR Lender A =  1 +
 −1

12 
= 1.008712 − 1
= 1.1091 − 1
= 0.1091 or 10.91%
1
0.109 

EAR Lender B =  1 +
 −1

1 
= 1.109 − 1
= 0.109 or 10.9%
4
0.105 

EAR Lender C =  1 +
 −1

4 
= 1.026254 − 1
= 1.1092 − 1
= 0.1092 or 10.92%
As shown, Lender B offers the lowest interest cost at 10.90 per cent.
Note the shift in rankings that takes place as a result of the EAR calculations. When we initially
looked at the APR quotes, it appeared that Lender A offered the lowest rate and Lender B the highest.
After ­calculating the EAR, we find that after accounting for the effect of compounding, Lender B
­actually offers the lowest interest rate.
Another important point is that, if all the interest rates are quoted as APRs with the same annualising
period, such as monthly, the interest rates are comparable and you can select the correct rate by simply
comparing the quotes. That is, the lowest APR corresponds with the lowest cost of funds. Thus, it is cor­
rect for borrowers or lenders to make economic decisions with APR data as long as interest rates have
both the same maturity and the same compounding period. To find the true cost of the loan, however, it
is still necessary to calculate the EAR.
170 Finance essentials
DEMONSTRATION PROBLEM 6.5
What is the true cost of a loan?
Problem:
During a period of economic expansion, Fran Singh became financially overextended and was forced
to consolidate her debt with a loan from a consumer finance company. The consolidated debt provided
Fran with a single loan and lower monthly payments than she had previously been making. The loan
agreement quotes an APR of 20 per cent and Fran must make monthly payments. What is the true cost
of the loan?
Approach:
The true cost of the loan is the EAR, not the APR. Thus, we must convert the quoted rate into the EAR,
using equation 6.5, to get the true cost of the loan.
Solution:
m
 Quoted interest rate 
EAR =  1+
 − 1

m
0.20 
EAR =  1+


12 
12
−1
= (1+ 0.0167)12 − 1
= (0.0167)12 − 1
= 1.219 4 − 1
= 0.219 4, or 21.94%
The true cost of Fran’s loan is 21.94 per cent, not the 20 per cent APR.
Using a financial calculator, the steps are:
Procedure
Key operation
Enter cash flow data
12 [P/YR]
12 ⇒ P/YR
12
20 [NOM%]
20 ⇒ NOM%
20
[COMP] [EFF%]
EFF% =
Calculate I/Y
Display
21.94
USING EXCEL
Loan amortisation table
MODULE 6 Discounted cash flows and valuation 171
Consumer protection acts and interest rate disclosure
The Commonwealth Government passed the National Consumer Credit Protection Act in 2009 to ensure
that all borrowers receive meaningful information about the cost of credit, so that they can make intelligent
economic decisions. (Prior to the introduction of this Act, the Uniform Consumer Credit Code (UCCC) per­
formed the same function but was administered on a state/territory basis.) The Act applies to all legal entities
that provide credit to consumers and it covers car loans, home loans, residential investment property loans,
personal loans, credit cards, overdrafts and consumer leases. Provisions within the Corporations Act apply
to the disclosure of interest rates in relation to consumer savings vehicles such as term deposits. Combined,
these two pieces of legislation require by law that the APR be disclosed on consumer loans and savings prod­
ucts, and that the APR be prominently displayed in advertising and contractual material. In the case of an
advertisement of a credit product stating a repayment amount, then a comparison rate may also be disclosed.
The comparison rate reflects the total cost of credit arising from interest charges and other fees and charges,
and hence the comparison rate is an EAR. The objective of the comparison rate is to help consumers identify
the true cost of credit, which allows for easier comparison among the thousands of different credit products.
We know that the EAR, and not the APR, represents the true economic interest rate. So why do these
two pieces of legislation specify the APR as the disclosed rate? The APR was selected because it is easy
to calculate and easy to understand. Historically, before personal computers and handheld calculators
existed, financiers and salespeople needed an easy way to explain and annualise the monthly interest
charge. The APR provided just such a method. And most important, if all the financiers and salespeople
were quoting monthly APR, consumers could then select the loan with the lowest economic interest cost.
Today, although lenders and borrowers are legally required to quote the APR, they run their businesses
using interest rate calculations based on the present value and future value formulas. Consumers are bom­
barded with both APR and EAR comparison rates, and confusion reigns. At a car dealership, for example,
you may find that your car loan’s APR is 5 per cent but the ‘actual borrowing rate’ is 5.12 per cent. And at
the bank where your grandmother gets free coffee and cake, she may be told that the bank’s 1‐year term
deposit has an APR of 5 per cent, but it really pays 5.14 per cent. Because of confusion arising from con­
flicting interest rates in the marketplace, some observers believe that the APR calculation has outlived its
usefulness and should be abandoned by regulators and replaced by the EAR or comparison rate.
Appropriate interest rate factor
Here is a final question to consider: What is the appropriate interest rate to use when making future or
present value calculations? The answer is simple — use the EAR. Under no circumstance should the
APR or any other quoted rate be used as the interest rate in present or future value calculations.
Consider an example of using the EAR in such a calculation. Steffi, an MBA student at Adelaide
University, has purchased a $100 savings note with a 2‐year maturity from a small consumer finance
company. The contract states that the note has a 20 per cent APR and pays interest quarterly. The quar­
terly interest rate is thus 5 per cent (20%/4). Steffi has several questions about the note: (1) What is the
note’s actual interest rate (EAR)? (2) How much money will she have at the end of 2 years? (3) When
making the future value calculation, should she use the quarterly interest rate or the annual EAR?
To answer Steffi’s questions, we first calculate the EAR, which is the actual interest earned on the note:
m
APR 

EAR =  1 +
 −1

m 
4
0.20 

= 1 +
 −1

4 
= (1 + 0.05)4 − 1
= 1.21551 − 1
= 0.21551, or 21.551%
172 Finance essentials
Next, we calculate the future value of the note using the EAR. Because the EAR is an annual rate, for
this problem we use a total of two compounding periods. The calculation is as follows:
FV2 = PV × (1 + i)n
= $100 × (1 + 0.215 51)2
= $100 × 1.477 5
= $147.75
We can also calculate the future value using the quarterly rate of interest of 5 per cent with a total of
eight compounding periods. In this case, the calculation is as follows:
FV2 = $100 × (1 + 0.050)8
= $100 × 1.477 5
= $147.75
The two calculation methods yield the same answer, $147.75.
In summary, any time you do a future value or present value calculation, you must use either the
interest rate per period (quoted rate/m) or the EAR as the interest rate factor. It does not matter which
of these you use. Both properly account for the impact of compounding on the value of cash flows.
Interest rate proxies such as the APR should never be used as interest rate factors for calculating future
or present values. Because they do not properly account for the number of compounding periods, their
use can lead to answers that are economically incorrect.
BEFORE YOU GO ON
1. What is the APR and why are lending institutions required to disclose this rate?
2. What is the correct way to annualise an interest rate in financial decision‐making?
3. Distinguish between quoted interest rate, interest rate per period and effective annual interest rate.
MODULE 6 Discounted cash flows and valuation 173
SUMMARY
6.1 Explain why cash flows occurring at different times must be adjusted to reflect their value at a
common date before they can be compared, and calculate the present value and future value for
multiple cash flows.
When making decisions involving cash flows over time, we should first identify the magnitude
and the timing of the cash flows, and then adjust each individual cash flow to reflect its value at a
common date. For example, the process of discounting (compounding) the cash flows adjusts them
for the time value of money, because today’s dollars are not equal in value to dollars in the future.
Once all of the cash flows are in present (future) value terms, they can be compared in order to
make decisions. Section 6.1 discusses the calculation of present values and future values of multiple
cash flows.
6.2 Describe how to calculate the present value and the future value of an ordinary annuity, and
how an ordinary annuity differs from an annuity due.
An ordinary annuity is a series of equally spaced, level cash flows over time. The cash flows for an
ordinary annuity are assumed to take place at the end of each period. To find the present value of an
ordinary annuity, we multiply the present value of an annuity factor, which is equal to (1 − present
value factor)/i, by the amount of the constant cash flow. An annuity due is an annuity in which the
cash flows occur at the beginning of each period. A lease is an example of an annuity due. In this
case, we are effectively prepaying for the service. To calculate the value of an annuity due, we
calculate the present value (or future value) as though the cash flows were an ordinary annuity.
We then multiply the ordinary annuity value times (1 + i). Section 6.2 discusses the calculation of
present value and future value of an ordinary annuity and present value of an annuity due.
6.3 Explain what perpetuities are and where we see them in business, and calculate the present
values of perpetuities.
A perpetuity is like an annuity except that the cash flows are perpetual — they never end. The
most common example of a perpetuity today is preference shares. The issuer of preference shares
promises to pay fixed‐rate dividends forever. The cash flows from companies can also look like
perpetuities. To calculate the present value of a perpetuity, we simply divide the promised constant
payment (CF) by the interest rate (i). Section 6.3 demonstrates the calculation of the present value
of perpetuities.
6.4 Describe how to calculate the periodic payments, number of periods and interest rate for a
range of annuity problems and prepare a loan amortisation schedule.
To calculate the periodic payments, number of periods or interest rate for an annuity, we use the appro­
priate annuity equation (PV or FV) and solve for the unknown. To solve for the interest rate, we need
to use trial and error unless we have a financial calculator or are able to use Excel or a similar program.
An example of periodic payments is calculating the value of the monthly payment for a housing loan.
A loan amortisation schedule is a table that shows the loan balance at the beginning and end of each
period, the payment made during that period, and how much of that payment represents interest and
how much represents repayment of the principal. The schedule shows these values for the entire term of
the loan. Amortisation schedules are commonly used for housing loans. This is covered in section 6.4.
6.5 Discuss why the effective annual interest rate (EAR) is the appropriate way to annualise interest
rates and calculate EAR.
The EAR is the annual growth rate that takes compounding into account. Thus, the EAR is the
true cost of borrowing or lending money. When we need to compare interest rates, we must make
sure the rates to be compared have the same time and compounding periods. If interest rates are
not comparable, they must be converted into common terms. The easiest way to convert rates into
common terms is to calculate the EAR for each interest rate. The use and calculations of EAR are
discussed in section 6.5.
174 Finance essentials
SUMMARY OF KEY EQUATIONS
Equation
Description
Formula
6.1
Present value of an ordinary annuity
 1− 1/ (1+ i )n 
PVA n = CF × 

i

6.2
Future value of an ordinary annuity
 (1+ i ) n −1
FVA n = CF × 

i

6.3
Value of an annuity due — transformation
method
Annuity due value =
Ordinary annuity value × (1+ i )
6.4
Present value of a perpetuity
PVP =
6.5
Effective annual interest rate
 Quoted interest rate 
EAR =  1+
 − 1

m
CF
i
m
KEY TERMS
amortisation schedule with regards to a loan, a table that shows the loan balance at the beginning and
end of each period, the payment made during that period, and how much of that payment represents
interest and how much represents repayment of principal
amortising loan a loan for which each loan payment contains repayment of some principal and a
payment of interest that is based on the remaining principal to be repaid
annual percentage rate (APR) the simple interest rate charged per period multiplied by the number
of periods per year (also known as the nominal rate)
annuity a series of equally spaced and level cash flows extending over a finite number of periods
annuity due the first payment is made at the inception of the annuity
effective annual interest rate (EAR) the annual interest rate that reflects compounding within a year
future value of an annuity (FVA) the value of an annuity at some point in the future
ordinary annuity an annuity in which payments are made at the ends of the periods
perpetuity a series of level cash flows that continue forever
present value of an annuity (PVA) the present value of the cash flows from an annuity, discounted at
the appropriate discount rate
quoted interest rate a simple annual interest rate, such as the APR or nominal rate
ACKNOWLEDGEMENTS
Photo: © Shawn Talbot / Shutterstock.com
Photo: © Nisakorn Neera / Shutterstock.com
Photo: © Kudla / Shutterstock.com
MODULE 6 Discounted cash flows and valuation 175
MODULE 7
Risk and return
LEA RN IN G OBJE CTIVE S
After studying this module, you should be able to:
7.1 explain the relationship between risk and return
7.2 describe the two components of a total holding period return and calculate this return for an asset
7.3 explain what an expected return is and calculate the expected return for an asset
7.4 explain what the standard deviation of returns is, explain why it is especially useful in finance and be
able to calculate it
7.5 explain the concept of diversification
7.6 discuss which type of risk matters to investors and why
7.7 describe what the Capital Asset Pricing Model (CAPM) tells us and how to use it to evaluate whether
the expected return of an asset is sufficient to compensate an investor for the risks associated with
that asset.
Module preview
Up to this point, we have often mentioned the rate of return that we use to discount cash flows, but
we have not explained how that rate is determined. We have now reached the point where it is time to
examine key concepts underlying the discount rate. This module introduces a quantitative framework for
measuring risk and return. This framework will help you develop an intuitive understanding of how risk
and return are related and which risks matter to investors. The relationship between risk and return has
implications for the rate we use to discount cash flows because the time value of money that we have
discussed in modules 5 and 6 is directly related to the returns that investors require. We must understand
these concepts in order to determine the correct present value for a series of cash flows and to be able to
make investment decisions that create value for shareholders.
We begin this module with a discussion of the general relationship between risk and return, to
i­ntroduce the idea that investors require a higher rate of return from riskier assets. This is one of the
most fundamental relationships in finance. We next develop the statistical concepts required to quantify
holding period returns, expected returns and risk. We then apply these concepts to portfolios with a
single asset, two assets and more than two assets to illustrate the benefit of diversification. From this
discussion, you will see how investing in more than one asset enables an investor to reduce the total risk
associated with their investment portfolio and you will learn how to quantify this benefit.
After we have discussed the concept of diversification, we examine what it means for the relationship
between risk and return. We find that the total risk associated with an investment consists of two com­
ponents: (1) unsystematic risk; and (2) systematic risk. Diversification enables investors to eliminate the
unsystematic risk, or unique risk, associated with an individual asset. Investors do not require higher
returns for the unsystematic risk that they can eliminate through diversification. Only systematic risk
— risk that cannot be diversified away — affects expected returns on an investment. The distinction
MODULE 7 Risk and return 177
between unsystematic and systematic risk and the recognition that unsystematic risk can be diversified
away are extremely important in finance. After reading this module, you will understand precisely
what the term risk means in finance and how it is related to the rates of return that investors require.
7.1 Risk and return relationship
LEARNING OBJECTIVE 7.1 Explain the relationship between risk and return.
The rate of return that investors require for an investment depends on the risk associated with that invest­
ment. The greater the risk, the larger the return investors require as compensation for bearing that risk.
This is one of the most fundamental relationships in finance. The rate of return is what you earn on an
investment, stated in percentage terms. We will be more specific later, but for now you can think of risk
as a measure of how certain you are that you will receive a particular return. A higher risk means you
are less certain.
To get a better understanding of how risk and return are related, consider an example. You are trying
to select the best investment from among the following three shares:
Share
Expected return (%)
Risk level (%)
A
12
12
B
12
16
C
16
16
Which should you choose? If you were comparing only shares A and B, you should choose Share A:
both shares have the same expected return, but Share A has less risk. It does not make sense to invest in
the riskier share if the expected return is the same. Similarly, you can see that Share C is clearly superior
to Share B: shares B and C have the same level of risk, but Share C has a higher expected return. It
would not make sense to accept a lower return for taking on the same level of risk.
But what about the choice between shares A and C? This choice is less obvious. Deciding this requires
understanding the concepts that we discuss in the rest of this module.
More risk means a higher expected return
The greater the risk associated with an investment, the greater the return investors expect from it. A con­
sequence of this idea is that investors want the highest return for a given level of risk, or the lowest risk
for a given level of return. When choosing between two investments that have the same level of risk,
investors prefer the investment with the higher return. Alternatively, if two investments have the same
expected return, investors prefer the less risky alternative.
7.2 Measures of return
LEARNING OBJECTIVE 7.2 Describe the two components of a total holding period return and calculate
this return for an asset.
Before we begin a detailed discussion of the relationship between risk and return, we should define
more precisely what these terms mean. We begin with holding period returns and then look at expected
returns.
Holding period returns
When people refer to the return from an investment, they are generally referring to the total return
over some investment period or holding period. The total holding period return consists of two
178 Finance essentials
components: (1) capital appreciation; and (2) income. The capital appreciation component of a return,
RCA, arises from a change in the price of the asset over the investment or holding period and is calculated
as follows:
R CA =
Capital appreciation P1 − P0 ∆P
=
=
P0
P0
Initial price
where P0 is the price paid for the asset at time zero and P1 is the price at a later point in time.
The income component of a return arises from income that an investor receives from the asset while
they own it. For example, when a company pays a cash dividend on its shares, the income component of
the return on that share, RI, is calculated as follows:
RI =
Cash flow CF1
=
Initial price P0
where CF1 is the cash flow from the dividend.
The total holding period return is simply the sum of the capital appreciation and income components
of return:
P1 − P0 + CF1
(7.1)
R T = R CA + R I =
P0
Let’s consider an example of calculating the total holding period return on an investment. One year
ago today, you purchased a share of Computershare Limited for $26.50. Today it is worth $29.00.
Computershare paid no dividend on its shares. What total return did you earn on this share over the past year?
If Computershare paid no dividend and you received no other income from holding the share, the total
return for the year equals the return from the capital appreciation, calculated as follows:
P1 = P0 + CF1
P0
$29.00 − $26.50 + $0.00
=
$26.50
= 0.0943, or 9.43%
R T = R CA + R1 =
What return would you have earned if Computershare had paid a $1 dividend and today’s price was
$28.00? With the $1 dividend and a correspondingly lower price, the total return is the same:
R T = R CA + R I =
P1 + P0 + CF1 $28.00 − $26.50 + $1.00
=
= 0.0943, or 9.43%
P0
$26.50
You can see from this example that a dollar of capital appreciation is worth the same as a dollar of income.
DEMONSTRATION PROBLEM 7.1
Calculating the return on an investment
Problem:
You purchased a beat‐up 1974 Datsun 240Z sports car a year ago for $1500. Datsun is what Nissan, the
Japanese car company, was called in the 1970s. The 240Z was the first in a series of cars that led to the
Nissan 370Z being sold today. Recognising that a mint‐condition 240Z is a much sought‐after car, you
have invested $7000 and a lot of your time in fixing up the car. Last week, you sold it to a collector for
$18 000. Not counting the value of the time you spent restoring the car, what is the total return you
earned on this investment over the 1‐year holding period?
MODULE 7 Risk and return 179
Approach:
Use equation 7.1 to calculate the total holding period return. To calculate RT using equation 7.1, you
must know P0, P1 and CF1. In this problem, you can assume that the $7000 was spent at the time you
bought the car to purchase parts and materials. Therefore, your initial investment, P0, was $1500 +
$7000 = $8500. Since there were no other cash inflows or outflows between the time when you bought
the car and the time when you sold it, CF1 equals $0.
Solution:
The total holding period return is:
RT = RCA + RI =
P1 − P0 + CF1 $18 000 − $8500 + $0
=
= 1.118, or 111.8%
P0
$8500
7.3 Expected returns
LEARNING OBJECTIVE 7.3 Explain what an expected return is and calculate the expected return for
an asset.
Let’s look at expected returns with the help of an example. Suppose that you are Steve Smith, who plays
cricket for the Rising Pune Supergiants in the Indian Premier League (IPL). Furthermore, suppose that
you are coming up for what you expect to be your last game. This fact is important because you have
signed a very unusual contract with the Supergiants. Your signing bonus will be determined solely by
whether the Supergiants make the semifinals. If they do make the semifinals, then your signing bonus
will be $800 000; otherwise, it will be $400 000. You believe there is a 32.5 per cent likelihood that the
Supergiants will make the semifinals.
What is the expected value of your bonus? If you have taken a statistics course, you may recall that
an expected value represents the sum of the products of the possible outcomes and the probabilities that
those outcomes will be realised. In our example, the expected value of the bonus can be calculated using
the following formula:
E(Bonus) = (pSF × BSF ) + (pNSF × BNSF )
where E(Bonus) is your expected bonus, pSF is the probability of making the semifinals, pNSF is the
probability of not making the semifinals, BSF is the bonus you receive if the Supergiants do make the
semifinals and BNSF is the bonus you receive if the Supergiants do not make the semifinals. Since pSF
equals 0.325, pNSF equals 0.675, BSF equals $800 000 and BNSF equals $400 000, the expected value of
your bonus is:
E(Bonus) = ( pSF × BSF ) + ( pNSF × BNSF )
= (0.325 × $800 000) + (0.675 × $400 000) = $530 000
Note that the expected bonus of $530 000 is not equal to either of the two possible payoffs. Neither is
it equal to the simple average of the two possible payoffs. This is because the expected bonus takes into
account the probability of each event occurring. If the probability of each event had been 50 per cent,
then the expected bonus would have equalled the simple average of the two payoffs:
E(Bonus) = (0.5 × $800 000) + (0.5 × $400 000) = $600 000
180 Finance essentials
However, since it is more likely that the Supergiants will not reach the semifinals (a 67.5 per cent
chance) than that they will reach them (a 32.5 per cent chance), and the payoff is lower if you do not
reach them, the expected bonus is less than the simple average.
What would your expected payoff be if you were 99 per cent certain of reaching the semifinals?
We intuitively know that the expected bonus should be much closer to $800 000 in this case. In fact,
it is:
E(Bonus) = (0.99 × $800 000) + (0.01 × $400 000) = $796 000
The key point here is that the expected value reflects the relative likelihoods of the possible outcomes.
We calculate an expected return in finance in the same way that we calculate any expected value. The
expected return is a weighted average of the possible returns from an investment, where each of these
returns is weighted by the probability that it will occur. In general terms, the expected return on an asset,
E(RAsset), is calculated as follows:
n
E ( R Asset ) = ∑ ( pi × R i ) = ( p1 × R1 ) + ( p2 × R 2 ) + + ( pn × R n )
(7.2)
i =1
where Ri is the possible return i and pi is the probability that you will actually earn return Ri. The sum­
mation symbol in this equation
n
∑
i =1
is mathematical shorthand indicating that n values are added together. In equation 7.2, each of the n
possible returns is multiplied by the probability that it will be realised, and these products are then added
together to calculate the expected return.
It is important to make sure that the sum of the n individual probabilities, all of the pi, always equals
1, or 100 per cent, when you calculate an expected value. The sum of the probabilities cannot be less
than 100 per cent because you must account for all possible outcomes in the calculation.
The expected return on an asset reflects the return that you can expect to receive from investing in that
asset over the period that you plan to own it. It is your best estimate of this return, given the possible
outcomes and their associated probabilities.
Note that if each of the possible outcomes is equally likely (that is, p1 = p2 = p3 = . . . = pn = p = 1/n),
this formula reduces to the formula for a simple (equally weighted) average of the possible returns:
n
E ( R Asset ) =
∑(R )
i
i =1
n
=
R1 + R2 + + Rn
n
(7.3)
To see how we calculate the expected return on an asset, suppose you are considering purchasing a
share of Computershare Limited for $29.00. You plan to sell the share in 1 year. You estimate there is
a 30 per cent chance that Computershare shares will sell for $28.00 at the end of 1 year, a 30 per cent
chance that they will sell for $30.50, a 30 per cent chance that they will sell for $32.50 and a 10 per cent
chance that they will sell for $36.00. If Computershare pays no dividends on its shares, what is the return
that you expect from this share in the next year?
Since Computershare pays no dividends, the total return on its shares equals the return from capital
appreciation:
R T = R CA =
P1 − P0
P0
MODULE 7 Risk and return 181
Therefore, we can calculate the return from owning shares in Computershare under each of the four
possible outcomes using the approach we used for the similar Computershare problem we solved earlier
in the module. These returns are calculated as follows:
Computershare share
price in 1 year
Total return
(1) $28.00
$28.00 − $29.00
= −0.0345
$29.00
(2) $30.50
$30.50 − $29.00
= −0.0517
$29.00
(3) $32.50
$32.50 − $29.00
= 0.1207
$29.00
(4) $36.00
$36.00 − $29.00
= 0.2414
$29.00
Applying equation 7.2, the expected return on a share of Computershare over the next year is there­
fore 6.55 per cent, calculated as follows:
n
E ( R CPU ) = ∑ ( pi × R i ) = ( p1 × R1 ) + ( p2 × R 2 ) + + ( pn × R n )
i =1
E ( R CPU ) = (0.3 × −0.0345) + (0.3 × 0.0517) + (0.3 × 0.1207) + (0.1 × 0.2414)
= −0.01035 + 0.01551 + 0.03621 + 0.02414 = 0.0655, or 6.55%
Note that the negative return is entered into the formula just like any other. Also note that the sum of
all the pi equals 1.
DECISION‐MAKING EX AMPLE 7.1
Using expected values in decision‐making
Situation:
You are deciding whether you should advertise your pizza business on the internet or on billboards
placed on local taxis. For $1000 per month, you can either buy 20 ads on the internet or place your ad
on 40 taxis.
There is some uncertainty regarding how many new customers will visit your restaurant after seeing one
of your internet ads. You estimate there is a 30 per cent chance that 35 people will visit, a 45 per cent
chance that 50 people will visit and a 25 per cent chance that 60 people will visit. Therefore, you expect
the following number of new customers to visit your restaurant in a month in response to each internet ad:
E(New customers per adRadio ) = (0.30 × 35) + (0.45 × 50) + (0.25 × 60) = 48
This means that you expect 20 ads to bring in 20 × 48 = 960 new customers.
Similarly, you estimate there is a 20 per cent chance that you will get 20 new customers in response to
an ad placed on a taxi, a 30 per cent chance that you will get 30 new customers, a 30 per cent chance
that you will get 40 new customers and a 20 per cent chance that you will get 50 new customers. Therefore, you expect the following number of new customers in response to each ad that you place on a taxi:
E(New customers per adTaxi ) = (0.2 × 20) + (0.3 × 30) + (0.3 × 40) + (0.2 × 50) = 35
Placing ads on 40 taxis is therefore expected to bring in 40 × 35 = 1400 new customers.
Which of these two advertising options is more attractive? Is it cost effective?
182 Finance essentials
Decision:
You should advertise on taxis. For a monthly cost of $1000, you expect to attract 1400 new customers
with taxi ads but only 960 new customers if you advertise on the internet.
The answer to the question of whether advertising on taxis is cost effective depends on how much
gross profits (profits after variable costs) are increased by those 1400 customers. Gross profits will have
to increase by $1000, or an average of 72 cents per new customer ($1000/1400), to cover the cost of
the advertising campaign.
BEFORE YOU GO ON
1. What are the two components of a total holding period return?
2. How is the expected return on an investment calculated?
7.4 Variance and standard deviation
LEARNING OBJECTIVE 7.4 Explain what the standard deviation of returns is, explain why it is especially
useful in finance and be able to calculate it.
We turn next to a discussion of the two most basic measures of risk used in finance — the variance
and the standard deviation. These are the same variance and standard deviation measures that you have
studied if you have taken a course in statistics.
Calculating the variance and standard deviation
Let’s begin by revisiting our Indian Premier League cricket example. Recall that you will receive a bonus
of $800 000 if your side reaches the semifinals and a bonus of $400 000 if it does not. The expected value
of your bonus is $530 000. Suppose you want to measure the risk, or uncertainty, associated with the
payoff. How can you do this? One approach would be to calculate a measure of how much, on average,
the bonus payoffs deviate from the expected value. The underlying intuition here is that the greater the
difference between the actual payoff and the expected value, the greater the risk. For example, you could
calculate the difference between each individual bonus payment and the expected value and then sum
these differences. If you do this, you will get the following result:
Risk = ($800 000 − $530 000) + ($400 000 − $530 000)
= $270 000 + ( − $130 000)
= $140 000
Unfortunately, using this calculation to obtain a measure of risk presents two problems. First, since
one difference is positive and the other difference is negative, one difference partially cancels the other.
As a result, you do not get an accurate measure of total risk. Second, this calculation does not take into
account the number of potential outcomes or the probability of each potential outcome.
A better approach would be to square the differences (this makes all the numbers positive) and
multiply each difference by its associated probability before summing them. This calculation yields the
variance (σ2) of the possible outcomes. The variance does not suffer from the two problems mentioned
earlier and provides a measure of risk that has a consistent interpretation across different situations or
assets. Note that the square of the Greek symbol sigma, σ2, is generally used to represent the variance.
For the original bonus arrangement, the variance is:
2
Var(Bonus) = σ (Bonus)
= {pSF × [BSF − E(Bonus)]2 } + {pNSF × [BNSF − E(Bonus)]2 }
= [0.325 × ($800 000 − $530 000)2 ] + [0.675 × ($400 000 − $530 000)2 ]
= 35 100 000 000 dollars 2
MODULE 7 Risk and return 183
Because it is somewhat awkward to work with units of squared dollars, in a calculation such as this
we would typically take the square root of the variance. The square root gives us the standard deviation
(σ) of the possible outcomes. For our example, the standard deviation is:
2
σ (Bonus) = (σ (Bonus)
)1/2 = (35 100 000 000 dollars 2 )1/2 = $187 349.94
As you will see when we discuss the normal distribution, the standard deviation has a natural interpret­
ation that is very useful for assessing investment risks.
The general formula for calculating the variance of returns can be written as follows:
n
Var(R) = σ R2 = ∑ { pi × [R i − E(R)]2 }
(7.4)
i =1
Equation 7.4 simply extends the calculation illustrated above to the situation where there are n poss­
ible outcomes. Like the expected return calculation (equation 7.2), equation 7.4 can be simplified if all
of the possible outcomes are equally likely. In this case, it becomes:
n
σ R2 =
∑ [R
− E ( R )]
2
i
i =1
n
However, if you are working with a finite sample rather than the entire population of outcomes, such
as a sample of historical data, we substitute n – 1 for n as the denominator in this formula:
n
σ R2 =
∑ [R
− E ( R )]
2
i
i =1
(7.5)
n −1
In both the general case and the case where all possible outcomes are equally likely, the standard
deviation is simply the square root of the variance.
1
σ R = (σ R2 ) 2 = σ R2
(7.6)
DEMONSTRATION PROBLEM 7.2
Calculating expected return and standard deviation of returns
Problem:
The last four years of returns for an ABC Ltd share are as follows:
Year
Return
1
2
3
4
−2%
5%
8%
3%
What is the average annual return for ABC Ltd shares over this period?
What is the variance of the shares’ returns?
What is the standard deviation of the shares’ returns?
Approach:
Use equation 7.3 first, to calculate the average annual return. Next use equation 7.5 to calculate the variance of returns. Lastly, use equation 7.6 to find the standard deviation of returns.
184 Finance essentials
Solution:
The average return is:
n
∑ (R )
i
R + R2 + + Rn
= 1
n
n
−0.02 + 0.05 + 0.08 + 0.03 0.14
=
=
= 0.035 or 3.5%
4
4
E (R Asset ) =
i =1
The variance of returns is:
n
σ R2 =
=
=
=
=
=
∑ (R
i =1
i
− E (R ))
n−1
[R i − E (R)]2 + [R i − E (R)]2 + [R i − E (R)]2 + [R i − E (R)]2
4−1
[ −0.02 − 0.035]2 + [ 0.05 − 0.035]2 + [ 0.08 − 0.035]2 + [ 0.03 − 0.035]2
3
−0.0552 + 0.0152 + 0.0452 + −0.0052
3
0.003 025 + 0.000 225 + 0.002 025 + 0.000 025
3
0.0053
= 0.001767 or 17.67%2
3
The standard deviation of returns is:
1
σ R = (σ R2 ) 2 = σ R2
= 0.001767 = 0.042 or 4.2%
Using a financial calculator, we can obtain the same solution. However, while financial functions on
calculators are similar, you will find that statistical functions vary widely. Please check your calculator
manual if you are unsure how to do this.
Using Excel, the steps are:
MODULE 7 Risk and return 185
Interpreting the variance and standard deviation
The variance and standard deviation are especially useful measures of risk for variables that are nor­
mally distributed — they can be represented by a normal distribution. The normal distribution is a
symmetrical frequency distribution that is completely described by its mean (average) and standard
­deviation. Figure 7.1 illustrates what this distribution looks like.
FIGURE 7.1
Normal distribution
0.45%
0.40%
Probability
0.35%
0.30%
−1σ to 1σ includes
68.26%
0.25%
0.20%
0.15%
−1.645σ to 1.645σ includes 90%
0.10%
−1.960σ to 1.960σ includes 95%
0.05%
0.00%
−2.575σ to 2.575σ includes 99%
−4
−3
−2
−1
Mean
Standard deviations
1
2
3
4
This distribution is very useful in finance because the returns for many assets tend to be approximately
normally distributed. This makes the variance and standard deviation practical measures of the uncertainty
associated with investment returns. Since the standard deviation is more easily interpreted than the vari­
ance, we focus on the standard deviation as we discuss the normal distribution and its application in finance.
In figure 7.1, you can see that the normal distribution is symmetrical: the left and right sides are
mirror images of each other. The mean falls directly in the centre of the distribution, and the probability
that an outcome is less than or greater than a particular distance from the mean is the same whether the
outcome is on the left or the right side of the distribution. For example, if the mean is 0, the probability
that a particular outcome is −3 or less is the same as the probability that it is +3 or more (both are 3 or
more units from the mean). This enables us to use a single measure of risk for the normal distribution.
That measure is the standard deviation.
The standard deviation tells us everything we need to know about the width of the normal distribution
or, in other words, the variation in the individual values. This variation is what we mean when we talk
about risk in finance. In general terms, risk is a measure of the range of potential outcomes. The stan­
dard deviation is an especially useful measure of risk because it tells us the probability that an outcome
will fall a particular distance from the mean, that is, within a particular range. You can see this in the
following table, which shows the fraction of all observations in a normal distribution that are within the
indicated number of standard deviations from the mean.
Number of standard
deviations from the mean
Fraction of total
observations
1.000
68.26%
1.645
90%
1.960
95%
2.575
99%
186 Finance essentials
Since the returns on many assets are approximately normally distributed, the standard deviation pro­
vides a convenient way of calculating the probability that the return on an asset will fall within a par­
ticular range. In these applications, the expected return on an asset equals the mean of the distribution,
and the standard deviation is a measure of the uncertainty associated with the return.
For example, if the expected return for a real estate investment in Caulfield, Victoria is 10 per cent
with a standard deviation of 2 per cent, there is a 90 per cent chance that the actual return will be within
3.29 of 10 per cent. How do we know this? As shown in the table, 90 per cent of all outcomes in a
normal distribution have a value that is within 1.645 standard deviations of the mean value, and 1.645 ×
2 per cent = 3.29 per cent. This tells us there is a 90 per cent chance that the realised return on the
investment in Caulfield will be between 6.71 per cent (10 per cent − 3.29 per cent) and 13.29 per cent
(10 per cent + 3.29 per cent), a range of 6.58 per cent (13.29 per cent − 6.71 per cent).
You may be wondering what is standard about the standard deviation. The answer is that this statistic
is standard in the sense that it can be used to directly compare the uncertainties (risks) associated with
the returns on different investments. For instance, suppose you are comparing the real estate invest­
ment in Caulfield with a real estate investment in Sydney, NSW. Assume that the expected return on the
Sydney investment is also 10 per cent. If the standard deviation for the returns on the Sydney invest­
ment is 3 per cent, there is a 90 per cent chance that the actual return is within 4.935 per cent (1.645 ×
3 per cent = 4.935 per cent) of 10 per cent. In other words, 90 per cent of the time the return will be
between 5.065 per cent (10 per cent − 4.935 per cent) and 14.935 per cent (10 per cent + 4.935 per
cent), a range of 9.87 per cent (14.935 per cent − 5.065 per cent).
This range is exactly 9.87 per cent/6.58 per cent = 1.5 times as large as the range for the Caulfield
investment opportunity. Note that the ratio of the two standard deviations also equals 1.5 (3 per cent/
2 per cent = 1.5). This is not a coincidence. We could have used the standard deviations to directly
­calculate the relative uncertainty associated with the Sydney and Caulfield investment returns. The
relationship between the standard deviation of returns and the width of a normal distribution (the uncer­
tainty) is illustrated in figure 7.2.
FIGURE 7.2
Standard deviation and width of the normal distribution
25%
Probability
20%
Distribution for return on
Caulfield investment
(σ = 2%)
15%
Distribution for
return on Sydney
investment
(σ = 3%)
10%
5%
0%
0%
2%
4%
6%
8%
Mean
= 10%
Return
12%
14%
16%
18%
20%
Let’s consider another example of how the standard deviation is interpreted. Suppose customers
at your pizza restaurant have complained that there is no consistency in the number of slices of
salami that your cooks are putting on large meat lovers’ pizzas. One night you decide to work in
the area where the pizzas are made so that you can count the number of salami slices on the large
MODULE 7 Risk and return 187
pizzas to get a better idea of just how much variation there is. After counting the slices of salami on
50 pizzas, you estimate that, on average, your pizzas have 18 slices of salami and the standard deviation is
3 slices.
With this information, you estimate that 95 per cent of the large meat lovers’ pizzas sold in your res­
taurant have between 12.12 and 23.88 slices. You are able to estimate this range because you know that
95 per cent of the observations in a normal distribution fall within 1.96 standard deviations of the mean.
With a standard deviation of 3 slices, this implies that the number of salami slices on 95 per cent of
your pizzas is within 5.88 slices of the mean (3 slices × 1.96). This, in turn, indicates a range of 12.12
(18 − 5.88) to 23.88 (18 + 5.88) slices.
Since you put only whole slices of salami on your pizzas, 95 per cent of the time the number of slices
is somewhere between 12 and 24. No wonder your customers are up in arms! In response to this infor­
mation, you decide to implement a standard policy regarding the number of salami slices that go on each
type of pizza.
DEMONSTRATION PROBLEM 7.3
Understanding the standard deviation
Problem:
You are considering investing in BHP Billiton and want to evaluate how risky this potential investment
is. You know that share returns tend to be normally distributed, and you have calculated the expected
return on BHP Billiton shares to be 4.67 per cent and the standard deviation of the annual return to be
23 per cent. Based on these statistics, what range would you expect the return on BHP shares to fall
within during the next year? Calculate this range for a 90 per cent level of confidence (that is, 90 per
cent of the time, the returns will fall within the specified range).
Approach:
Use the values in the previous table or figure 7.1 to calculate the range which BHP Billiton’s share return
will fall within 90 per cent of the time. First, find the number of standard deviations associated with a
90 per cent level of confidence in the table or figure 7.1 and multiply this number by the standard
deviation of the annual return for BHP Billiton’s shares. Then subtract the resulting value from the
expected return (mean) to obtain the lower end of the range and add it to the expected return to
obtain the upper end.
Solution:
From the table, you can see that we would expect the return over the next year to be within 1.645 standard deviations of the mean 90 per cent of the time. Multiplying this value by the standard deviation of
BHP Billiton’s shares (23 per cent) yields 23 per cent × 1.645 = 37.835 per cent. This means there is a
90 per cent chance that the return will be between −33.165 per cent (4.67 per cent − 37.835 per cent)
and 42.505 per cent (4.67 per cent + 37.835 per cent).
While the expected return of 4.67 per cent is relatively low, the returns on BHP Billiton shares vary
considerably and there is a reasonable chance that the share return in the next year could be quite
high or quite low (even negative). As you will see shortly, this wide range of possible returns is similar
to the range we observe for typical shares in any world share markets, such as those of the USA
and Australia.
Historical market performance
Now that we have discussed how returns and risks can be measured, we are ready to examine the charac­
teristics of the historical returns earned by securities such as shares and bonds. Figure 7.3 illustrates the
distributions of historical returns for some securities in Australia and shows the average and standard
deviations of these annual returns for the period 1974–2015.
188 Finance essentials
FIGURE 7.3
Distributions of annual total returns for Australian equities and bonds 1974–2015
Australian equity returns
20
15
10
5
0
−0.35 −0.3 −0.25 −0.2 −0.15 −0.1 −0.05 0
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65
Australian Government bond returns
20
15
10
5
0
−0.35 −0.3 −0.25 −0.2 −0.15 −0.1 −0.05 0
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65
90-day bank accepted bills returns
20
15
10
5
0
−0.35 −0.3 −0.25 −0.2 −0.15 −0.1 −0.05 0
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65
Source: Reserve Bank of Australia 2015.
Higher standard deviations of return have historically been associated with higher returns. For
example, between 1974 and 2015 the standard deviation of the annual returns for equities was higher
than the standard deviation of the returns earned by government bonds and 90‐day bank accepted bills,
and the average return that investors earned from equities was also higher. At the other end of the spec­
trum, the returns on the 90‐day bank accepted bills had the smallest standard deviation and smallest
average return.
Note that the statistics reported in figure 7.3 are for indices that represent total average returns for
the indicated types of securities, not total returns on individual securities. We generally use indices to
represent the performance of the share or bond markets. For instance, when media services report on the
performance of the share market, they often report whether the All Ordinaries Index or the S&P/ASX
200 Index rose or fell for the Australian market and whether the Dow Jones Industrial Average (DJIA)
rose or fell for the US market, on any particular day.
The plots in figure 7.3 contrast the returns on the riskier share market (average return 13.81 per cent,
standard deviation 20.86 per cent) with safer government bonds (average return 9.78 per cent, standard
deviation 7.81 per cent) and 90‐day bank accepted bills (average return 8.87 per cent, standard deviation
4.60 per cent). The key point to note in figure 7.3 is that, on average, annual returns have been higher for
riskier securities.
The statistics in figure 7.3 describe actual investment returns, as opposed to expected returns. In other
words, they show what has happened in the past. Financial analysts often use historical numbers such
as these to estimate the returns that might be expected in the future. That is what we did in the cricket
example earlier in this module: we estimated the likelihood of reaching the semifinals of the Indian
MODULE 7 Risk and return 189
Premier League. And we would undoubtedly have done this using past team performances as reasonable
indicators of future performances.
To see how historical numbers are used in finance, let’s suppose that you are considering investing
in a fund that mimics the S&P/ASX 200 Index (this is what we call an index fund) and you want to
estimate what the returns on the S&P/ASX 200 Index are likely to be in the future. If you believe the
1974–2015 period provides a reasonable indication of what we can expect in the future, then the average
historical return on the index of 13.81 per cent provides a perfectly reasonable estimate of the return
you can expect from your investment in the S&P/ASX 200 Index fund. In module 12 we will explore in
detail how historical data can be used in this way to estimate the discount rate used to evaluate projects
in the capital budgeting process.
Comparing the historical returns for individual shares with the historical returns for an index can also
be instructive. Figure 7.4 shows just such a comparison for BHP Billiton and the All Ordinaries Index
using monthly returns for the period from July 2005 to June 2015. Note in the figure that the returns on
BHP Billiton shares are far more volatile than the average returns on the companies represented in the
All Ordinaries Index. In other words, the standard deviation of returns for BHP Billiton is higher than
that for the All Ordinaries Index. This is not a coincidence; we discuss shortly why returns on individual
shares tend to be riskier than returns on indices.
One last point is worth noting while we are examining historical returns: the value of a $100 invest­
ment in 1974 would have varied greatly by 2015 depending on where that dollar was invested. Figure 7.5
shows that $100 invested in Australian equities in 1974 would have been worth $15 472.06 by 2015. In
contrast, that same $100 invested in 90‐day bank accepted bills would have been worth only $3125.30
by 2015. (From a practical standpoint, it was not really possible to grow $100 to $15 472.06 by investing
in Australian equities because it assumes the investor was able to rebalance the share portfolio by buying
and selling shares as necessary at no cost. But, since buying and selling shares is costly, the final wealth
would have been lower. Nevertheless, even after transaction costs it would have been much more profit­
able to invest in shares than in 90‐day bank accepted bills.) Over a long period of time, earning higher
rates of return can have a dramatic impact on the value of an investment. This huge difference reflects
the impact of compounding of returns (returns earned on returns), much like the compounding of interest
we discussed in module 5.
FIGURE 7.4
Monthly returns for BHP Billiton and the ASX All Ordinaries Index July 2005 – June 2015
25%
20%
15%
BHP Billiton
Monthly return
10%
5%
0%
−5%
−10%
All ordinaries index
−15%
−20%
Month
Source: Thomson Reuters 2015.
190 Finance essentials
Jul. 15
Jan. 15
Jul. 14
Jan. 14
Jul. 13
Jan. 13
Jul. 12
Jan. 12
Jul. 11
Jan. 11
Jul. 10
Jan. 10
Jul. 09
Jan. 09
Jul. 08
Jan. 08
Jul. 07
Jan. 07
Jul. 06
Jan. 06
−30%
Jul. 05
−25%
FIGURE 7.5
Cumulative value of $100 invested in 1974
Australian equity
Australian Government bonds
90-day bank accepted bills
$18 000.00
$16 000.00
$15 472.06
$14 000.00
Value
$12 000.00
$10 000.00
$8 000.00
$6 000.00
$4593.93
$4 000.00
$3125.30
$2 000.00
2014
2012
2010
2008
2006
2004
2002
2000
1998
1996
1994
1992
1990
1988
1986
1984
1982
1980
1978
1976
1974
$0.00
Year
Source: Reserve Bank of Australia 2015; Thomson Reuters 2015.
BEFORE YOU GO ON
1. What is the relationship between the variance and the standard deviation?
2. What relationship do we generally observe between risk and return when we examine historical returns?
3. How would we expect the standard deviation of the return on individual shares to compare with the
standard deviation of the return on a share index?
7.5 Risk and diversification
LEARNING OBJECTIVE 7.5 Explain the concept of diversification.
It does not generally make sense to invest all of your money in a single asset. The reason is directly related
to the fact that returns on individual shares tend to be riskier than returns on indices. By investing in two or
more assets whose values do not always move in the same direction at the same time, an investor can reduce
the risk of their collection of investments, or portfolio. This is the idea behind the concept of diversification.
MODULE 7 Risk and return 191
This section develops the tools necessary to evaluate the benefits of diversification. We begin with a
discussion of how to quantify risk and return for a single‐asset portfolio, and then we discuss more real­
istic and complicated portfolios that have two or more assets. Although our discussion focuses on share
portfolios, it is important to recognise that the concepts discussed apply equally well to portfolios that
include a range of assets, including shares, bonds and real estate, among others.
Single‐asset portfolios
Returns for individual shares from one day to the next have been found to be largely independent of each
other and approximately normally distributed. In other words, the return for a share on any one day is
largely independent of the return on that same share the next day, 2 days later, 3 days later and so on.
Each daily return can be viewed as having been randomly drawn from a normal distribution where the
probability associated with the return depends on how far the return is from the expected value. If we
know what the expected value and standard deviation are for the distribution of returns for a share, it
is possible to quantify the risks and expected returns that an investment in the share might yield in the
future.
To see how we can do this, assume that you are considering investing in one of two shares for the
next year: BHP Billiton or Rio Tinto. Also, to keep things simple, assume that there are only three poss­
ible economic conditions (outcomes) a year from now and that the returns on BHP Billiton or Rio Tinto
shares under each of these outcomes are as follows:
Economic outcome
Poor
Neutral
Good
Probability
BHP Billiton return
Rio Tinto return
0.2
0.5
0.3
−0.13
0.10
0.25
−0.10
0.07
0.22
With this information, we can calculate the expected returns for BHP Billiton and Rio Tinto by using
equation 7.2:
E(R BHP ) = (pPoor × R Poor ) + (pNeutral × R Neutral ) + (pGood × R Good )
= (0.2 × − 0.13) + (0.5 × 0.10) + (0.3 × 0.25)
= 0.099, or 9.9%
and
E(R Rio ) = (pPoor × R Poor ) + (pNeutral × R Neutral ) + (pGood × R Good )
= (0.2 × − 0.10) + (0.5 × 0.07) + (0.3 × 0.22)
= 0.081, or 8.1%
Similarly, we can calculate the standard deviations of the expected returns for BHP Billiton and Rio Tinto
in the same way that we calculated the standard deviation for our cricket bonus example in section 7.2:
σ R2 BHP = {pPoor × [R Poor − E(R BHP )]2} + {pNeutral × [R Neutral − E(R BHP )]2} + {pGood × [R Good − E(R BHP )]2}
= [0.2 × ( − 0.13 − 0.099) 2 ] + [0.5 × (0.10 − 0.099) 2 ] + [0.3 × (0.25 − 0.099) 2 ]
= 0.01733
σ
= (σ R2 BHP )1/2 = (0.01733)1/2 = 0.13164, or 13.16%
R BHP
and
σ R2 Rio = {pPoor × [R Poor − E(R Rio )]2} + {pNeutral × [R Neutral − E(R Rio )]2} + {pGood × [R Good − E(R Rio )]2}
= [0.2 × ( − 0.1 0 − 0.0 81)2 ] + [0.5 × (0. 07 − 0.0 81)2 ] + [0.3 × (0.2 2 − 0.0 81)2 ]
= 0.01241
σ R Rio = (σ R2 Rio )1/2 = (0.01241)1/2 = 0.11140, or 11.14%
192 Finance essentials
Having calculated the expected returns and standard deviations for the expected returns on BHP
Billiton and Rio Tinto shares, the natural question to ask is which provides the highest risk‐adjusted
return. Before we answer this question, let’s go back to the example at the beginning of section 7.1.
Recall that, in this example, we proposed choosing among three shares: A, B and C. We stated that
investors would prefer the investment that provides the highest expected return for a given level of risk
or the lowest risk for a given expected return. This made it fairly easy to choose between Shares A and
B, which had the same return but different risk levels, and between Shares B and C, which had the
same risk but different returns. We were stuck when trying to choose between Shares A and C, however,
because they differed in both risk and return. Now, armed with tools for quantifying expected returns
and risk, we can at least take a first pass at comparing shares such as these.
The coefficient of variation (CV) is a measure of risk that can help us in making comparisons such as
that between Shares A and C. The coefficient of variation for share i is calculated as follows:
CVi =
σ Ri
E (Ri )
(7.7)
In this equation, CV is a measure of the risk associated with an investment for each 1 per cent of
expected return.
Recall that Share A has an expected return of 12 per cent and a risk level of 12 per cent, while Share C
has an expected return of 16 per cent and a risk level of 16 per cent. If we assume that the risk level for
each share is equal to the standard deviation of its return, we can find the coefficients of v­ ariation for the
two shares as follows:
CV(RA) =
0.12
0.16
= 1.00 and CV(RC) =
= 1.00
0.12
0.16
Since these values are equal, the coefficient of variation measure suggests that these two investments
are equally attractive on a risk‐adjusted basis.
Going back to our BHP Billiton and Rio Tinto example, we find that the coefficients of variation for
those shares are:
σ R BHP
0.13164
CVBHP =
=
= 1.330
0.099
E(R BHP )
and
CVRio =
σ R Rio
0.11140
=
= 1.375
0.081
E(R Rio )
So we can see that, while BHP Billiton shares have a higher expected return (9.9 per cent versus
8.1 per cent) and a higher standard deviation of returns (13.154 per cent versus 11.140 per cent), they
have a lower coefficient of variation than Rio Tinto shares. This tells us that the amount of risk for
each 1 per cent of expected return is lower for BHP Billiton shares than for Rio Tinto shares. On a
risk‐adjusted basis, then, the expected returns from BHP Billiton shares are more attractive.
DEMONSTRATION PROBLEM 7.4
Calculating and using the coefficient of variation
Problem:
You are trying to choose between two investments. The first investment, a painting by Picasso, has an
expected return of 14 per cent with a standard deviation of 30 per cent over the next year. The second
investment, a pair of blue suede shoes once worn by Elvis Presley, has an expected return of 20 per cent
MODULE 7 Risk and return 193
with a standard deviation of return of 40 per cent. What is the coefficient of variation for each of these
investments and what do these coefficients tell us?
Approach:
Use equation 7.7 to calculate the coefficients of variation for the two investments.
Solution:
The coefficients of variation are:
CV(RPainting ) =
0.3
0.4
= 2.14 and CV(RShoes ) =
= 2.00
0.14
0.2
The coefficient of variation for the Picasso painting is slightly higher than for Elvis’s blue suede shoes.
This indicates that the risk for each 1 per cent of expected return is higher for the painting than for the
shoes.
Portfolios with more than one asset
It may seem like a good idea to evaluate investments by calculating a measure of risk for each 1 per cent
of expected return. However, the coefficient of variation has a critical shortcoming that is not evident
when we are considering only a single asset. In order to explain this shortcoming, we must discuss the
more realistic setting in which an investor has constructed a two‐asset portfolio.
Expected return on a portfolio with more than one asset
Suppose that you own a portfolio that consists of $500 of BHP Billiton shares and $500 of Rio Tinto
shares, and that over the next year you expect to earn returns on the BHP Billiton and Rio Tinto shares
of 9.9 per cent and 8.1 per cent, respectively. How would you calculate the expected return for the
overall portfolio?
Let’s try to answer this question using our intuition. If half of your funds are invested in each share,
it would seem reasonable that the expected return for this portfolio should be a 50–50 mixture of the
expected returns from the two shares, or:
E(R Portfolio ) = (0.5 × 0.099) + (0.5 × 0.081) = 0.09, or 9.0%
Note that this formula is just like the expected return formula for an individual share. However, in
this case, instead of multiplying outcomes by their associated probabilities, we are multiplying expected
returns for individual shares by the fraction of the total portfolio value that each of these shares ­represents.
In other words, the formula for the expected return for a two‐asset portfolio is:
E(R Portfolio ) = x1E(R1 ) + x 2 E(R 2 )
and for n assets is:
E(R Portfolio ) = [x1 × E(R1 )] + [x 2 × E(R 2 )] + . . . + [x n × E(R n )]
where xi represents the fraction of the portfolio invested in asset i. The corresponding equation for a
portfolio with n assets is:
n
E(R Portfolio ) = ∑ [x1 × E(R i )
i =1
194 Finance essentials
(7.8)
This equation is just like equation 7.2, except that: (1) the returns are expected returns for individual
assets; and (2) instead of multiplying by the probability of an outcome, we are multiplying by the frac­
tion of the portfolio invested in each asset. Note that this equation can be used only if you have already
calculated the expected return for each asset.
To see how equation 7.8 is used to calculate the expected return on a portfolio with more than
two assets, consider an example. Suppose your organisation was recently awarded a $500 000 grant
from the Department of Economic Development to fund your project to secure sustainable employ­
ment for disadvantaged people. Since your grant is intended to support your activities for 5 years,
you have kept $100 000 to cover your organisation’s expenses for the next year and invested the
remaining $400 000 in Australian Government bonds and shares. Specifically, you’ve invested:
$100 000 in government bonds (GB) that yield 4.5 per cent; $150 000 in ANZ Bank shares, which have
an expected return of 7.5 per cent; and $150 000 in Automotive Technology Group Limited (ATJ)
shares, which have an expected return of 9.0 per cent. What is the expected return on this $400 000
portfolio?
In order to use equation 7.8, we must first calculate xi, the fraction of the portfolio invested in asset i,
for each investment. These fractions are as follows:
$100 000
= 0.25
$400 000
$150 000
= x ATJ =
= 0.375
$400 000
x GB =
x ANZ
Therefore, the expected return on the portfolio is:
E(R Portfolio ) = [x GB × E(R GB )] + [x ANZ × E(R ANZ )] + [x ATJ × E(R ATJ )]
= (0.25 × 0.045) + (0.375 × 0.075) + (0.375 × 0.090)
= 0.0731, or 7.31%
DEMONSTRATION PROBLEM 7.5
Calculating the expected return on a portfolio
Problem:
You are concerned that you have too much of your money invested in your pizza restaurant and have
decided to diversify your personal portfolio. Right now the pizza restaurant is your only investment.
To diversify, you plan to sell 45 per cent of your restaurant and invest the proceeds from the sale,
in equal proportions, into a share market index fund and a bond market index fund. Over the next
year, you expect to earn a return of 15 per cent on your remaining investment in the pizza restaurant,
12 per cent on your investment in the share market index fund and 8 per cent on your investment
in the bond market index fund. What return will you expect from your diversified portfolio over the
next year?
Approach:
First, calculate the fraction of your portfolio that will be invested in each type of asset after you have
diversified. Then use equation 7.8 to calculate the expected return on the portfolio.
Solution:
After you have diversified, 55 per cent (100 per cent − 45 per cent) of your portfolio will be invested in
your restaurant, 22.5 per cent (45 per cent × 0.50) will be invested in the share market index fund
MODULE 7 Risk and return 195
and 22.5 per cent (45 per cent × 0.50) will be invested in the bond market index fund. Therefore, from
equation 7.8, we know that the expected return for your portfolio is:
E(RPortfolio ) = [xRest × E(RRest )] + [ xShare × E(RShare )] + [xBond × E(RBond )]
= (0.550 × 0.15) + (0.225 × 0.12) + (0.225 × 0.08)
= 0.1275, or 12.75%
At 12.75 per cent, the expected return is an average of the returns on the individual assets in your
­portfolio, weighted by the fraction of your portfolio that is invested in each.
Risk of a portfolio with more than one asset
Now that we have calculated the expected return on a portfolio with more than one asset, the next ques­
tion is how to quantify the risk of such a portfolio. Before we discuss the mechanics of doing this, it
is important to have some intuitive understanding of how volatilities in the returns for different assets
interact to determine the volatilities of the overall portfolio.
The prices of two shares in a portfolio will rarely, if ever, change by the same amount and in the same
direction at the same time. Normally, the price of one share will change by more than the price of the
other. In fact, the prices of two shares will frequently move in different directions. These differences in
price movements affect the total volatility in the returns for a portfolio.
Figure 7.6 shows the monthly returns for the shares of Woolworths Limited (a retailer) and Qantas (an
airline) over the period from July 2010 to June 2015. Note that the returns on these shares are generally
different and the prices of the shares can move in different directions in a given month (one share has a
positive return when the other has a negative return). When the share prices move in opposite directions,
the change in the price of one share offsets at least some of the change in the price of the other share. As
a result, the level of risk for a portfolio of the two shares is less than the average of the risks associated
with the individual shares.
FIGURE 7.6
Monthly returns for Woolworths and Qantas July 2010 – June 2015
30%
Monthly returns
20%
Woolworths
10%
0%
−10%
−20%
Qantas
−30%
Date
Source: Thomson Reuters 2015.
196 Finance essentials
Apr. 15
Jan. 15
Oct. 14
Jul. 14
Apr. 14
Jan. 14
Oct. 13
Jul. 13
Apr. 13
Jan. 13
Oct. 12
Jul. 12
Apr. 12
Jan. 12
Oct. 11
Jul. 11
Apr. 11
Jan. 11
Oct. 10
Jul. 10
−40%
This means that we cannot calculate the variance of a portfolio containing two assets simply by calcu­
lating the average of the variances of the individual shares using a formula such as:
σ R2 2 Asset portfolio = x12σ R21 + x 22σ R2 2
where xi represents the fraction of the portfolio invested in share i and σ R2i is the variance of the return
on share i. We need to account for the fact that the returns on different shares in a portfolio tend to par­
tially offset each other. We do this by adding a third term to the formula. For a two‐asset portfolio, we
calculate the variance of the returns using the following formula:
σ R2 2 Asset portfolio = x12σ R21 + x 22σ R2 2 + 2 x1 x 2σ R1,2
(7.9)
where σ R21,2 is the covariance between shares 1 and 2. The covariance is a measure of how the returns
on two assets covary, or move together. The third term in equation 7.9 accounts for the fact that the
returns from the two assets will offset each other to some extent. The covariance is calculated using the
following formula:
n
Cov ( R1 ,R 2 ) = σ R1,2 = ∑ { pi × [ R1,i − E ( R1 )] × [ R 2,i − E ( R 2 )]}
i =1
(7.10)
where i represents outcomes rather than assets. Compare this equation with equation 7.4, reproduced
here:
n
Var(R) = σ R2 = ∑ { pi × [R i − E(R)]2}
i =1
You can see that the covariance calculation is very similar to the variance calculation. The difference is
that, instead of squaring the difference between the value from each outcome and the expected value for
an individual asset, we calculate the product of this difference for two different assets. (When we have
historical returns, pi is replaced in equations 7.4 and 7.10 by 1n .)
Just as it is difficult to directly interpret the variance of the returns for an asset — recall that the
variance is in units of squared dollars — it is difficult to directly interpret the covariance of returns
between two assets. We get around this problem by dividing the covariance by the product of the stan­
dard deviations of the returns for the two assets. This gives us the correlation, ρ, between the returns
on those assets:
ρ =
σ R1, 2
σ R1σ R 2
(7.11)
The correlation between the returns on two assets will always have a value between −1 and +1.
This makes the interpretation of this variable straightforward. A negative correlation means that the
returns tend to have opposite signs. For example, when the return on one asset is positive, the return
on the other asset tends to be negative. If the correlation is exactly −1, the returns on the two assets are
perfectly negatively correlated. In other words, when the return on one asset is positive, the return on
the other asset will always be negative. A positive correlation means that when the return on one asset
is positive, the return on the other asset also tends to be positive. If the correlation is exactly equal to
+1, then the returns of the two assets are said to be perfectly positively correlated: the return on one
asset will always be positive when the return on the other asset is positive. Finally, a correlation of 0
means that the returns on the assets are not correlated. In this case, the fact that the return on one asset
is positive or negative tells you nothing about how likely it is that the return on the other asset will be
positive or negative.
MODULE 7 Risk and return 197
Let’s work an example to see how equation 7.9 is used to calculate the variance of a portfolio that
consists of 80 per cent Woolworths shares and 20 per cent Qantas shares. Using the data graphed in
figure 7.6, we can calculate the variance of the monthly returns for Woolworths and Qantas shares,
σ R2 , to be 0.00195 and 0.01016, respectively. The covariance between the annual returns on these two
shares is 0.00076. We do not show the calculations for the variances and the covariance because each of
these numbers was calculated using 60 different monthly returns; these calculations are too cumbersome
to illustrate. Rest assured, however, that they have been calculated using equations 7.4 and 7.10. With
these values, we can calculate the variance of a portfolio that consists of 80 per cent Woolworths shares
and 20 per cent Qantas shares as:
2
2
σ R2Portfolio of Woolworths and Qantas = x Woolworths
σ R2Woolworths + x Qantas
σ R2Qantas + 2 x Woolworths x Qantasσ RWoolworths, Qantas
= (0.8)2 (0.00195) + (0.2)2 (0.01016) + 2(0.8)(0.2)(0.00076)
= 0.00190
You can see that this portfolio variance is smaller than the variances of either Woolworths shares or
Qantas shares on their own.
If we calculate the standard deviations by taking the square roots of the variances, we find that the
standard deviations for Woolworths, Qantas and the portfolio consisting of these two shares are 0.0442
(4.42 per cent), 0.01008 (10.08 per cent) and 0.0433 (4.33 per cent), respectively.
Figure 7.7 illustrates the monthly returns for the portfolio of Woolworths and Qantas shares,
along with the monthly returns for the individual shares. You can see in this figure that, while the
returns on the portfolio vary quite a bit, this variation is slightly less than for the individual company
shares.
FIGURE 7.7
Monthly returns for Woolworths shares, Qantas shares and a portfolio with 80 per cent
Woolworths shares and 20 per cent Qantas shares July 2010 – June 2015
Woolworths
30%
Qantas
portfolio
20%
Monthly returns
10%
0%
−10%
−20%
−30%
Date
Source: Thomson Reuters 2015.
198 Finance essentials
Apr. 15
Jan. 15
Oct. 14
Jul. 14
Apr. 14
Jan. 14
Oct. 13
Jul. 13
Apr. 13
Jan. 13
Oct. 12
Jul. 12
Apr. 12
Jan. 12
Oct. 11
Jul. 11
Apr. 11
Jan. 11
Oct. 10
Jul. 10
−40%
Using equation 7.11, we can calculate the correlation of the returns between Woolworths and Qantas
shares as:
ρWoolworths , Qantas =
σ Woolworths, Qantas
σ RWoolworths σ RQantas
=
0.000 76
= 0.1706
0.0442 × 0.1008
The positive correlation tells us that the returns on Woolworths and Qantas shares tend to move in
the same direction. However, the correlation of less than +1 tells us that they do not always do so.
The fact that the returns on these two shares do not always move together is the reason that the returns
on a portfolio of the two shares have less variation than the returns on the individual company shares.
This example illustrates the benefit of diversification — how holding more than one asset with different
risk characteristics can reduce the overall risk of a portfolio. Note that if the correlation of the returns
between Woolworths and Qantas shares equalled exactly +1, holding these two shares would not reduce
risk because their prices would always move up or down together.
As we add more and more assets to a portfolio, calculating the variance using the approach illustrated
in equation 7.9 becomes increasingly complex. The reason for this is that we must account for the covari­
ance between each pair of assets. These more extensive calculations are beyond the scope of this text,
but they are conceptually the same as those for a portfolio with two assets.
DEMONSTRATION PROBLEM 7.6
Calculating the variance of a two‐asset portfolio
Problem:
You are still planning to sell 45 per cent of your pizza restaurant in order to diversify your personal
portfolio. However, you have now decided to invest all of the proceeds in the share market index fund.
After you diversify, you will have 55 per cent of your wealth invested in the restaurant and 45 per cent
invested in the share market index fund. You have estimated the variances of the returns for these two
investments and the covariance between their returns to be as follows:
σ R2Restaurant
0.0625
σ
0.0400
2
RShare market index
σ RRestaurant, Share market index
0.0250
What will be the variance and standard deviation of your portfolio after you have sold the 45 per cent
ownership interest in your restaurant and invested in the share market index fund?
Approach:
Use equation 7.9 to calculate the variance of the portfolio and then take the square root of this value to
obtain the standard deviation.
Solution:
The variance of the portfolio is:
σ R2Portfolio = xR2Restaurant σ R2Restaurant + xR2Share market index σ R2Share market index
+ 2 xRestaurant xShare market indexσ RRestaurant, Share market index
= [(0.55)2 × 0.0625] + [(0.45)2 × 0.0400] + (2 × 0.55 × 0.45 × 0.0250)
= 0.0394
and the standard deviation is (0.0394)1/2 = 0.1985, or 19.85 per cent.
Comparing the portfolio variance of 0.0394 with the variances of the restaurant, 0.0625, and the
share market index fund, 0.0400, shows once again that a portfolio with two or more assets tends to
have a smaller variance (and thus a smaller standard deviation) than any of the individual assets in the
portfolio.
MODULE 7 Risk and return 199
The limits of diversification
In the sample calculations for the portfolio containing Woolworths and Qantas shares, we have seen that
the standard deviation of the returns for a portfolio consisting of 80 per cent Woolworths shares and
20 per cent Qantas shares was 4.33 per cent from July 2010 to June 2015 and that this figure was lower
than the standard deviation for either of the individual shares (4.42 per cent and 10.08 per cent). You
may wonder how the standard deviation for the portfolio is likely to change if we increase the number of
assets in it. The answer is simple: if the returns on the individual shares added to our portfolio do not all
change in the same way, then increasing the number of shares in the portfolio will reduce the standard
deviation of the portfolio returns even further.
Let’s consider a simple example to illustrate this point. Suppose that all assets have a standard devi­
ation of returns that is equal to 40 per cent and that the covariance between the returns for each pair of
assets is 0.048. If we form a portfolio in which we have an equal investment in two assets, the standard
deviation of returns for the portfolio will be 32.25 per cent. If we add a third asset, the portfolio stan­
dard deviation of returns will decrease to 29.21 per cent. It will be even lower, at 27.57 per cent, for a
four‐asset portfolio. Figure 7.8 illustrates how the standard deviation for the portfolio declines as more
assets are added.
FIGURE 7.8
Unique and systematic risk in a portfolio as the number of assets increases
40.0%
35.0%
Standard deviation of the portfolio returns
Total portfolio risk
(standard deviation)
30.0%
Diversifiable, unsystematic or unique risk
25.0%
21.9%
20.0%
15.0%
Nondiversifiable or
systematic risk
10.0%
5.0%
0.0%
1
6
11
16
21
Number of assets (securities) in the portfolio
26
In addition to showing how increasing the number of assets decreases the overall risk of a portfolio,
figure 7.8 illustrates three other very important points. First, the decrease in the standard deviation for
the portfolio becomes smaller and smaller as more assets are added. You can see this effect by looking
at the distance between the straight horizontal line and the plot of the standard deviation of the portfolio
returns.
The second important point is that, as the number of assets becomes very large, the portfolio standard
deviation does not approach zero. It decreases only so far. In the example in figure 7.8, it approaches
21.9 per cent. The standard deviation does not approach zero because we are assuming that the vari­
ations in the asset returns do not completely cancel each other out. This is a realistic assumption,
because in practice investors can rarely diversify away all risk. They can diversify away risk that is
unique to the individual assets, but they cannot diversify away risk that is common to all assets. The
200 Finance essentials
risk that can be diversified away is called diversifiable, unsystematic or unique risk and the risk
that cannot be diversified away is called non‐diversifiable or systematic risk. In the next section, we
discuss systematic risk in detail.
The third key point illustrated in figure 7.8 is that most of the risk‐reduction benefits from diversi­
fication can be achieved in a portfolio with 15 to 20 assets. Of course, the number of assets required to
achieve a high level of diversification depends on the covariances between the assets in the portfolio.
However, in general, it is not necessary to invest in a very large number of different assets.
BEFORE YOU GO ON
1. What does the coefficient of variation tell us?
2. What are the two components of total risk?
3. Why does the total risk of a portfolio not approach zero as the number of assets in a portfolio
becomes very large?
7.6 Systematic risk
LEARNING OBJECTIVE 7.6 Discuss which type of risk matters to investors and why.
The objective of diversification is to eliminate variations in returns that are unique to individual assets.
We diversify our investments across a number of different assets in the hope that these unique variations
will cancel each other out. With complete diversification, all of the unique risk is eliminated from the
portfolio. An investor with a diversified portfolio still faces systematic risk, however, and we now turn
our attention to that form of risk.
Why systematic risk is all that matters
The idea that unique or unsystematic risk can be diversified away has direct implications for the relation­
ship between risk and return. If the transaction costs associated with constructing a diversified portfolio
are relatively low, then rational, informed investors, such as the students who are taking this course, will
prefer to hold diversified portfolios.
Diversified investors face only systematic risk, whereas investors whose portfolios are not well diver­
sified face systematic risk plus unsystematic risk. Because they face less risk, the diversified investors
will be willing to pay higher prices for individual assets than the other investors. Therefore, expected
returns on individual assets will be lower than the total risk (systematic plus unsystematic risk) of those
assets suggests that they should be.
To illustrate, consider two individual investors, Yuan and Jing. Each of them is trying to decide whether
she should purchase shares in your pizza restaurant. Yuan holds a diversified portfolio and Jing does not.
Assume your restaurant’s shares have five units of systematic risk and nine units of total risk. You can see
that Yuan faces less risk than Jing and so will require a lower expected rate of return. Consequently, Yuan
will be willing to pay a higher price than Jing.
If the market includes a large number of diversified investors such as Yuan, competition among these
investors will drive the price of your shares up further. Competition among these investors will ulti­
mately drive the price up to the point where the expected return only just compensates all investors
for the systematic risk associated with your shares. The bottom line is that, because of competition
among diversified investors, only systematic risk is rewarded in asset markets. For this reason, we are
concerned only about systematic risk when we think about the relationship between risk and return in
finance.
MODULE 7 Risk and return 201
Measuring systematic risk
If systematic risk is all that matters when we think about expected returns, then we cannot use the standard
deviation as a measure of risk. (This is true in the context of how expected returns are determined. However,
the standard deviation is still a very useful measure of the risk faced by an individual investor who does not
hold a diversified portfolio. For example, the owners of most small businesses have much of their personal
wealth tied up in their businesses. They are certainly concerned about the total risk because it is directly
related to the probability that they will go out of business and lose much of their wealth.) But the standard
deviation is a measure of total risk. We need a way of quantifying the systematic risk of individual assets.
A natural starting point for doing this is to recognise that the most diversified portfolio possible will come
closest to eliminating all unique risk. Such a portfolio provides a natural benchmark against which we can
measure the systematic risk of an individual asset. What is the most diversified portfolio possible? The
answer is simple: it is the portfolio that consists of all assets, including shares, bonds, real estate, precious
metals, commodities, art and so forth from all over the world. In finance, we call this the market portfolio.
Unfortunately, we do not have very good data for most of these assets for most of the world, so we use
the next best thing, depending on which market we are interested in. For example, if we are interested in
the Australian market then we use data from the Australian Securities Exchange (ASX); if we were inter­
ested in the US market we would use data from the US public share market. The reason that we use share
market information is that a large number of companies from a broad range of industries trade in each
market, and the companies that issue shares in these markets own a wide range of assets all over the world.
These characteristics, combined with the facts that share markets have been operating for a very long time
and that we have very reliable and detailed information on prices for shares around the world, make the
share market a natural benchmark for estimating systematic risk in the market we are interested in. (If
we were interested in estimating the systematic risk for the world market, then we could use a specialised
world share market index such as the FTSE World Index, rather than using a single country share index.)
202 Finance essentials
Since systematic risk is, by definition, risk that cannot be diversified away, the systematic risk of an
individual asset is really just a measure of the relationship between the returns on the individual asset
and the returns on the market. In fact, systematic risk is often referred to as market risk. To see how
we can use data from the ASX to estimate the systematic risk of an individual asset, look at figure 7.9,
which plots 60 historical monthly returns for Woolworths against the corresponding monthly returns
for the S&P/ASX All Ordinaries Index (a proxy for the Australian share market). In this plot, you can
see that returns on Woolworths shares tend to be higher when returns on the S&P/ASX All Ordinaries
Index tend to be higher. The measure of systematic risk that we use in finance is a statistical measure
of this relationship.
FIGURE 7.9
Plot of monthly Woolworths shares and S&P/ASX All Ordinaries Accumulation Index returns
July 2010 – June 2015
15%
Return on Woolworths shares
10%
5%
−8%
−6%
−4%
−2%
0%
2%
4%
6%
8%
−5%
−10%
−15%
Return on S&P/ASX All Ordinaries index
Source: Thomson Reuters 2015.
We can quantify the relationship between the monthly returns on Woolworths shares and on
the general market by finding the slope of the line that best represents the relationship illustrated in
figure 7.9. Specifically, we estimate the slope of the line of best fit. We do this using the statistical tech­
nique called regression analysis. If you are not familiar with regression analysis, don’t worry; the details
are beyond the scope of this course. All you have to know is that this technique gives us the line that fits
the data best.
Figure 7.10 illustrates the line that has been estimated for the data in figure 7.9 using regression
analysis. Note that the slope of this line is 0.50. Recall from your maths classes that the slope of a line
equals the ratio of the rise (vertical distance) divided by the corresponding run (horizontal distance).
In this case, the slope is the change in the return on Woolworths shares divided by the change in the
MODULE 7 Risk and return 203
return on the Australian share market. A slope of 0.50 therefore means that, on average, the change in
the return on Woolworths shares was 0.50 times as large as the change in the return on the S&P/ASX
All Ordinaries Accumulation Index. Thus, if the S&P/ASX All Ordinaries Accumulation Index goes up
1 per cent, the average increase in Woolworths shares is 0.50 per cent. This is a measure of systematic
risk, because it tells us that the volatility of the returns on Woolworths shares is 0.50 times as large as
that for the S&P/ASX All Ordinaries Accumulation Index as a whole.
FIGURE 7.10
Slope of relationship between Woolworths’ monthly share returns and S&P/ASX All Ordinaries
Accumulation Index returns July 2010 – June 2015
15%
Return on Woolworths shares
10%
5%
−8%
−6%
−4%
y = 0.0005 + 0.0505x
−2%
0%
2%
4%
6%
8%
−5%
−10%
−15%
Return on S&P/ASX All Ordinaries index
Source: Thomson Reuters 2015.
To explore this idea more completely, let’s consider another, simpler example. Suppose that you have
data for Caltex Australia shares and for the Australian share market for the past 2 years. In the first year,
the return on the market was 10 per cent and the return on Caltex Australia shares was 15 per cent. In
the second year, the return on the market was 12 per cent and the return on Caltex Australia shares was
19 per cent. From this information, we know that the return on Caltex Australia shares increased by
4 per cent while the return on the market increased by 2 per cent. If we graphed the returns for Caltex
Australia shares and for the general market for each of the last two periods, as we did for Woolworths
shares and the market in figures 7.9 and 7.10, and estimated the line that best fitted the data, it would be a
line that connected the dots for the two periods. The slope of this line would equal 2, calculated as follows:
Slope =
204 Finance essentials
Rise Change in caltex Australia return 19% − 15% 4%
=
=
=
=2
Run
Change in market return
12% − 10% 2%
Although we have to be careful about drawing conclusions when we have only two data points, we
might interpret the slope of 2 to indicate that new information that causes the market return to increase
by 1 per cent will tend to cause the return on Caltex Australia shares to increase by 2 per cent. Of course,
the reverse might also be true. That is, new information that causes the market return to decrease by
1 per cent may also cause the return on Caltex Australia shares to go down by 2 per cent. To the extent
that the same information is driving the changes in returns on Caltex Australia shares and on the market,
it would not be possible for an investor in Caltex Australia shares to diversify this risk away. It is
non‐diversifiable or systematic risk.
In finance, we call the slope of the line of best fit beta. Often we simply use the corresponding Greek
letter β to refer to this measure of systematic risk. As shown below, a beta of 1 tells us that an asset has
just as much systematic risk as the market. A beta higher than or lower than 1 tells us that the asset has
more or less systematic risk than the market, respectively. A beta of 0 indicates a risk‐free security, such
as Australian Government bonds.
β =1
Same systematic risk as market
β >1
More systematic risk than market
β <1
Less systematic risk than market
β =0
No systematic risk
Now you might ask yourself what happened to the unique risk of Woolworths or Caltex Australia
shares. This is best illustrated by the Woolworths example, where we have more than two observations.
As you can see in figure 7.10, the line of best fit does not go right through each data point. That
is because some of the change in Woolworths’ share price each month reflected information that did
not affect the S&P/ASX All Ordinaries as a whole. That information is the unsystematic, or unique,
component of the risk of Woolworths’ shares. The distance between each data point and the line
of best fit represents variation in Woolworths’ share return that can be attributed to this unique
risk.
The positive slope (β) of the regression line in figure 7.10 tells us that returns for the S&P/ASX
All Ordinaries Accumulation Index and for Woolworths shares will tend to move in the same direc­
tion. Returns on the S&P/ASX All Ordinaries Accumulation and on Woolworths’ shares will not always
change in the same direction, however, because the unique risk associated with Woolworths shares can
more than offset the effect of the market in any particular period. In the next section, we discuss the
implications of beta for the level (as opposed to the change) in the expected return for shares such as
Woolworths’.
Compensation for bearing systematic risk
Now that we have identified the measure of the risk that diversified investors care about — systematic
risk — we are in a position to examine how this measure relates to expected returns. Let’s begin by
thinking about the rate of return that you would require for an investment. First, you would want to
make sure that you were compensated for inflation. It would not make sense to invest if you expected
the investment to return an amount that did not at least allow you to have the same purchasing power
that the money you invested had when you made the investment. Second, you would want some
compensation for the fact that you are giving up the use of your money for a period of time. This
compensation may be very small if you are forgoing the use of your money for only a short time,
such as when you invest in a 30‐day Treasury note, but it may be relatively large if you are investing
for several years. Finally, you would also want compensation for the systematic risk associated with
the investment.
MODULE 7 Risk and return 205
When you invest in an Australian Government security such as a Treasury note or bond, you are
investing in a security that has no risk of default. After all, the Australian Government can always
increase tax or print more money to pay you back. Changes in economic conditions and other factors
that affect the returns on other assets do not affect the default risk of Australian Government securities.
As a result, these securities do not have systematic risk and their returns can be viewed as risk free. In
other words, returns on government bonds reflect the compensation required by investors to account for
the impact of inflation on purchasing power and for their inability to use the money during the life of
the investment.
It follows that the difference between required returns on government securities and required returns
for risky investments represents the compensation investors require for taking on risk. Recognising this
allows us to write the expected return for an asset i as:
E(R i ) = R rf + Compensation for taking on risk i
where Rrf is the return on a security with a risk‐free rate of return, which analysts typically estimate by
looking at returns on government securities. The compensation for taking on risk, which varies with the
risk of the asset, is added to the risk‐free rate of return to get an estimate of the expected rate of return
for an asset. If we recognise that the compensation for taking on risk varies with asset risk and that
­systematic risk is what matters, we can rewrite the preceding equation as follows:
E(R i ) = R rf + (Units of systematic risk i × Compensation per unit of systematic risk)
where Units of systematic riski is the number of units of systematic risk associated with asset i. Finally,
if beta, β, is the appropriate measure for the number of units of systematic risk, we can also define com­
pensation for taking on risk as follows:
Compensation for taking on risk i = β i × Compensation per unit of systematic risk
where βi is the beta for asset i.
Remember that beta is a measure of systematic risk that is directly related to the risk of the market as
a whole. If the beta for an asset is 2, that asset has twice as much systematic risk as the market. If the
beta for an asset is 0.5, then the asset has half as much systematic risk as the market. Recognising this
natural interpretation of beta suggests that the appropriate ‘unit of systematic risk’ is the level of risk
in the market as a whole and the appropriate ‘compensation per unit of systematic risk’ is the expected
return required for the level of systematic risk in the market as a whole. The required rate of return on
the market, over and above that of the risk‐free return, represents compensation required by investors for
bearing a market (systematic) risk. This suggests that:
Compensation per unit of systematic risk = E(R m ) − R rf
where E(Rm) is the expected return on the market. The term E(Rm) − Rrf is called the market risk
­premium. Consequently, we can now write the equation for expected return as:
E(R i ) = R rf + β i [E(R m ) − R rf ]
BEFORE YOU GO ON
1. Why are returns on the share market used as a benchmark in measuring systematic risk?
2. How is beta estimated?
3. How would you interpret a beta of 1.5 for an asset? A beta of 0.75?
206 Finance essentials
(7.12)
7.7 Capital Asset Pricing Model
LEARNING OBJECTIVE 7.7 Describe what the Capital Asset Pricing Model (CAPM) tells us and how to
use it to evaluate whether the expected return of an asset is sufficient to compensate an investor for the
risks associated with that asset.
In deriving equation 7.12, we intuitively arrived at the Capital Asset Pricing Model (CAPM).
Equation 7.12 is the CAPM, a model that describes the relationship between risk and expected return.
We discuss the predictions of the CAPM in more detail shortly, but first let’s look more closely at how
it works.
Suppose that you want to estimate the expected return for a share that has a beta of 1.5 and the
expected return on the market and risk‐free rate are 10 per cent and 4 per cent, respectively. We can use
equation 7.12 (the CAPM) to find the expected return for this share:
E(R i ) = R rf + βi [E(R m ) − R rf ]
= 0.04 + [1.5 × (0.10 − 0.04)] = 0.13, or 13%
Note that we must have three pieces of information in order to use equation 7.12: (1) the risk‐free rate;
(2) beta; and (3) either the market risk premium or the expected return on the market. Recall that the
market risk premium is the difference between the expected return on the market and the risk‐free rate
[E(Rm) − Rrf], which is 6 per cent in the above example.
DEMONSTRATION PROBLEM 7.7
Expected returns and systematic risk
Problem:
You are considering buying 100 Woolworths shares. Value Line (a financial reporting service) reports
that the beta for Woolworths is 0.53. The risk‐free rate is 4 per cent and the market risk premium is
6 per cent. What is the expected rate of return on Woolworths shares according to the CAPM?
Approach:
Use equation 7.12 to calculate the expected return on Woolworths shares.
Solution:
The expected return is:
E(R Woolworths ) = Rrf + β Woolworths [E(Rm ) − Rrf ]
= 0.04 + (0.53 × 0.06) = 0.0718, or 7.18%
Security Market Line
Figure 7.11 displays a plot of equation 7.12 to illustrate how the expected return on an asset varies with
systematic risk. This plot shows that the relationship between the expected return on an asset and beta is
both positive and linear. In other words, it is a straight line with a positive slope. The line in figure 7.11
is known as the Security Market Line (SML).
In figure 7.11 you can see that the expected rate of return equals the risk‐free rate when beta equals
0. This makes sense because, when investors do not face systematic risk, they will only require a return
that reflects the expected rate of inflation and the fact that they are giving up the use of their money for
a period of time. Figure 7.11 also shows that the expected return on an asset equals the expected return
on the market when beta equals 1. This is not surprising given that both the asset and the market would
have the same level of systematic risk if this were the case.
MODULE 7 Risk and return 207
FIGURE 7.11
The Security Market Line
E(Ri) = Rrf + β[E[Rm] – Rrf]
Security
Market Line
E(Ri)
E(Rm)
Market portfolio
Rrf
0.0
0.5
1.0
Beta
1.5
2.0
It is important to recognise that the SML illustrates what the CAPM predicts the expected total return
should be for various values of beta. The actual expected total return depends on the price of the asset.
You can see this from equation 7.1:
RT =
∆P + CF1
P0
where P0 is the price that the asset is currently selling for. If an asset’s price implies that the expected
return is greater than predicted by the CAPM, that asset will plot above the SML in figure 7.11. This
means that the asset’s price is lower than the CAPM suggests it should be. Conversely, if the expected
return on an asset plots below the SML, this implies that the asset’s price is higher than the CAPM sug­
gests it should be. The point at which a particular asset plots relative to the SML, then, tells us ­something
about whether the price of that asset is low or high. Recognising this fact can be helpful in evaluating the
attractiveness of an investment, such as the Woolworths shares in demonstration problem 7.7.
Capital Asset Pricing Model and portfolio returns
The expected return for a portfolio can also be predicted using the CAPM. The expected return on a
portfolio with n assets is calculated using the equation:
E(R n Asset portfolio ) = R rf + β n Asset portfolio [E(R m ) − R rf ]
Of course, this should not be surprising since investing in a portfolio is simply an alternative to
investing in a single asset.
208 Finance essentials
The fact that the SML is a straight line turns out to be rather convenient if we want to estimate the
beta for a portfolio. Recall that the equation for the expected return for a portfolio with n assets is given
by equation 7.8:
E(R Portfolio ) =
n
∑ [x
i
× E(R i )]
i =1
= [x1 × E(R 1 )] + [x 2 × E(R 2 )] + + [x n × E(R n )]
If we substitute equation 7.12 into equation 7.8 for each of the n assets and rearrange the equation, we
find that the beta for a portfolio is simply a weighted average of the betas for the individual assets in the
portfolio. In other words:
n
β n Asset portfolio = ∑ xi β i = x1β1 + x 2 β 2 + x3 β 3 + + x n β n
(7.13)
i =1
where xi is the proportion of the portfolio value that is invested in asset i, βi is the beta of asset i and n
is the number of assets in the portfolio. This equation makes it simple to calculate the beta of any port­
folio of assets once you know the betas of the individual assets. As an exercise, you might prove this to
­yourself by using equations 7.8 and 7.12 to derive equation 7.13.
Let’s consider an example to see how equation 7.13 is used. Suppose that you invested 25 per cent of
your wealth in a fully diversified market fund, 25 per cent in risk‐free Treasury notes and 50 per cent
in a house with twice as much systematic risk as the market. What is the beta of your overall portfolio?
What rate of return would you expect to earn from this portfolio if the risk‐free rate was 4 per cent and
the market risk premium was 6 per cent?
We know that the beta for the market must equal 1 by definition and that the beta for a risk‐free
asset equals 0. The beta for your home must be 2 since it has twice the systematic risk of the market.
Therefore, the beta of your portfolio is:
β Portfolio = x Fund β Fund + x TB β TB + x House β House
= (0.25 × 1.0) + (0.25 × 0.0) + (0.50 × 2.0)
= 1.25
Your portfolio has 1.25 times as much systematic risk as the market. Based on equation 7.12, you
would therefore expect to earn a return of 11.5 per cent, calculated as follows:
E(R Portfolio ) = R rf + β Portfolio [E(R m ) − R rf ]
= 0.04 + (1.25 × 0.06) = 0.115, or 11.5%
DEMONSTRATION PROBLEM 7.8
Portfolio risk and expected return
Problem:
You have recently become very interested in real estate. To gain some experience as a real estate
investor, you have decided to get together with nine of your friends to buy three small apartments near
campus. If you and your friends pool your money, you will have just enough to buy the three properties.
Since each investment requires the same amount of money and you will have a 10 per cent interest in
each, you will effectively have one‐third of your portfolio invested in each apartment.
While the apartments cost the same, they are different distances from campus and in different suburbs.
You believe this causes them to have different levels of systematic risk and you estimate that the betas for
the individual apartments are 1.2, 1.3 and 1.5. If the risk‐free rate is 4 per cent and the market risk premium is
6 per cent, what will be the expected return on your real estate portfolio after you buy all three investments?
MODULE 7 Risk and return 209
Approach:
There are two approaches that you can use to solve this problem. First, you can estimate the expected
return for each apartment using equation 7.12 and then calculate the expected return on the portfolio
using equation 7.8. Alternatively, you can calculate the beta for the portfolio using equation 7.13 and
then use equation 7.12 to calculate the expected return.
Solution:
Using the first approach, we find that equation 7.12 gives us the following expected returns:
E(R i ) = Rrf + β i [E(Rm ) − Rrf ]
= 0.04 + (1.2 × 0.06) = 0.112, or 11.2%, for apartment 1
= 0.04 + (1.3 × 0.06) = 0.118, or 11.8%, for apartment 2
= 0.04 + (1.5 × 0.06) = 0.130, or 13.0%, for apartment 3
Therefore, from equation 7.8 the expected return on the portfolio is:
E(RPortfolio ) = [x1 × E(R1 )] + [x 2 × E(R2 )] + [x 3 × E(R3 )]
= (1/3 × 0.112) + (1/3 × 0.118) + (1/3 × 0.13) = 0.12, or 12.0%
Using the second approach, from equation 7.13 the beta of the portfolio is:
βPortfolio = x1β1 + x 2β 2 + x 3β 3 = (1/3)(1.2) + (1/3)(1.3) + (1/3)(1.5) = 1.33333
and from equation 7.12 the expected return is:
E(RPortfolio ) = Rrf + βPortfolio [E(Rm ) − Rrf ]
= 0.04 + (1.33333 × 0.06) = 0.120, or 12.0%
210 Finance essentials
DECISION‐MAKING EX AMPLE 7.2
Choosing between two investments
Situation:
You are trying to decide whether to invest in one or both of two different shares. Share 1 has a beta of
0.8 and an expected return of 7.0 per cent. Share 2 has a beta of 1.2 and an expected return of 9.5 per
cent. You remember learning about the CAPM and believe it does a good job of telling you what the
appropriate expected return should be for a given level of risk. Since the risk‐free rate is 4 per cent and
the market risk premium is 6 per cent, the CAPM tells you the appropriate expected rate of return for
an asset with a beta of 0.8 is 8.8 per cent. The corresponding value for an asset with a beta of 1.2 is
11.2 per cent. Should you invest in either or both of these shares?
Decision:
You should not invest in either share. The expected returns for both of them are below the values predicted by the CAPM for investments with the same level of risk. In other words, both would plot below
the line in figure 7.11. This implies that they are both overpriced.
Up to this point, we have focused on calculating the expected rate of return for an investment in any
asset from the perspective of an investor, such as a shareholder. A natural question that might arise is
how these concepts relate to the rate of return that should be used within a company to evaluate a project.
The short answer is that they are the same: the rate of return used to discount the cash flows for a project
with a particular level of systematic risk is exactly the same as the rate of return that an investor would
expect to receive from an investment in any asset having the same level of systematic risk. In module 11
we will explore the relationship between the expected return and the rate used to discount project cash
flows in much more detail. By the time we finish that discussion, you will understand thoroughly how
businesses determine the rate that they use to discount the cash flows from their investments.
BEFORE YOU GO ON
1. How is the expected return on an asset related to its systematic risk?
2. What name is given to the relationship between risk and expected return implied by the CAPM?
3. If an asset’s expected return does not plot on the line in question 2 above, what does that imply
about its price?
MODULE 7 Risk and return 211
SUMMARY
7.1 Explain the relationship between risk and return.
Investors require greater returns for taking on greater risk. They prefer the investment with the
highest possible return for a given level of risk or the investment with the lowest risk for a given
level of return.
7.2 Describe the two components of a total holding period return and calculate this return for an
asset.
The total holding period return on an investment consists of a capital appreciation component and
an income component. This return is calculated using equation 7.1. It is important to recognise that
investors do not care whether they receive a dollar of return through capital appreciation or as a
cash dividend. Investors value both sources of return equally.
7.3 Explain what an expected return is and calculate the expected return for an asset.
An expected return is a weighted average of the possible returns from an investment where each of
these returns is weighted by the probability that it will occur. It is calculated using equation 7.2.
7.4 Explain what the standard deviation of returns is, explain why it is especially useful in finance
and be able to calculate it.
The standard deviation of returns is a measure of the total risk associated with the returns from
an asset. It is useful in evaluating returns in finance because the returns on many assets tend to
be normally distributed. The standard deviation of returns provides a convenient measure of the
dispersion of returns. In other words, it tells us about the probability that a return will fall within a
particular distance from the expected value or within a particular range. To calculate the standard
deviation, the variance is first calculated using equation 7.4. The standard deviation of returns is
then ­calculated by taking the square root of the variance.
7.5 Explain the concept of diversification.
Diversification is a strategy of investing in two or more assets whose values do not always move
in the same direction at the same time, in order to reduce risk. Investing in a portfolio containing
assets whose prices do not always move together reduces risk because some of the changes in the
prices of individual assets offset each other. This can cause the overall volatility in the value of the
portfolio to be lower than if it were invested in a single asset.
7.6 Discuss which type of risk matters to investors and why.
Investors only care about systematic risk. This is because they can eliminate unique risk by holding
a diversified portfolio. Diversified investors will bid up prices for assets to the point at which they
are just being compensated for the systematic risks they must bear.
7.7 Describe what the Capital Asset Pricing Model (CAPM) tells us and how to use it to evaluate
whether the expected return of an asset is sufficient to compensate an investor for the risks
associated with that asset.
The CAPM tells us that the relationship between systematic risk and return is linear, and that the
risk‐free rate of return is the appropriate return for an asset with no systematic risk. From the
CAPM we know what rate of return investors will require for an investment with a particular
amount of systematic risk (beta). This means that we can use the expected return predicted by
the CAPM as a benchmark for evaluating whether expected returns for individual assets are
­sufficient. If the expected return for an asset is less than that predicted by the CAPM, then the
asset is an unattractive investment because its return is lower than the CAPM indicates it should
be. By the same token, if the expected return for an asset is greater than that predicted by the
CAPM, then the asset is an attractive investment because its return is higher than the CAPM
­indicates it should be.
212 Finance essentials
SUMMARY OF KEY EQUATIONS
Equation
Description
Formula
7.1
Total holding period return
RT = RCA + R1 =
7.2
Expected return on an asset
E(R Asset ) = ∑ ( pi × Ri )
P1 − P0 + CF1
P0
n
i =1
n
∑ (R )
i
R1 + R2 + + Rn
n
7.3
Average return on an asset
E(R Asset ) =
7.4
Variance of return on an asset
Var(R) = σ R2 = ∑ { pi × [R i − E(R)]2 }
i =1
n
=
n
i =1
n
7.5
Variance of return on an asset (sample)
∑ [R
Var(R) = σ =
i =1
2
R
1
2 2
R
)
− E (R )]
2
i
n−1
7.6
Standard deviation of return
σ R = (σ
7.7
Coefficient of variation
CVi =
7.8
Expected return for a portfolio
E(RPortfolio ) = ∑ [ x i × E(R i )]
7.9
Variance for a two‐asset portfolio
σ
7.10
Covariance between two assets
σ R1, 2 = ∑ { pi × [R1, i − E(R1 )] × [R2, i − E(R2 )]}
= σ R2
σ Ri
E(R i )
n
i =1
2
R2Asset portfolio
= x12σ R21 + x 22σ R22 + 2 x1x 2σ R1, 2
n
i =1
σ R1, 2
7.11
Correlation between two assets
ρ=
7.12
Expected return and systematic risk
E(R i ) = Rrf + β i [E(Rm ) − Rrf ]
7.13
Portfolio beta
β n Asset portfolio = ∑ x i β i
σ R1σ R2
n
i =1
KEY TERMS
beta (β) measure of non‐diversifiable, systematic or market risk
Capital Asset Pricing Model (CAPM) model that describes the relationship between risk and
expected return
coefficient of variation (CV) measure of the risk associated with an investment for each 1 per cent of
expected return
covariance measure of how the returns on two assets covary, or move together
diversifiable, unsystematic or unique risk risk that can be eliminated through diversification
diversification strategy of reducing risk by investing in two or more assets whose values do not
always move in the same direction at the same time
MODULE 7 Risk and return 213
expected return average of the possible returns from an investment, where each return is weighted by
the probability that it will occur
market portfolio portfolio of all assets
market risk term commonly used to refer to non‐diversifiable, or systematic, risk
non‐diversifiable or systematic risk risk that cannot be eliminated through diversification
normal distribution a symmetrical frequency distribution that is completely described by its mean
and standard deviation; also known as a bell curve due to its shape
portfolio collection of assets that an investor owns
Security Market Line (SML) plot of the relationship between expected return and systematic risk
standard deviation (σ) square root of the variance
total holding period return total return on an asset over a specific period of time or holding period
variance (σ2) measure of the uncertainty surrounding an outcome
ACKNOWLEDGEMENTS
Photo: © solarseven / Shutterstock.com
Photo: © Mateusz Zagorski / iStockphoto
Photo: © Blend Images / Moxie Productions / Getty Images
Photo: © Alex Slobodkin / iStockphoto
Figure 7.3: © Reserve Bank of Australia
Figure 7.4: © Thomson Reuters
Figure 7.5: © Reserve Bank of Australia
Figure 7.6: © Thomson Reuters
Figure 7.7: © Thomson Reuters
Figure 7.9: © Thomson Reuters
Figure 7.10: © Thomson Reuters
214 Finance essentials
MODULE 8
Bond valuation
LEA RNIN G OBJE CTIVE S
After studying this module, you should be able to:
8.1 explain what Commonwealth Government Securities (CGS) and semi‐government securities (semis) are,
where they are issued and their relative liquidity
8.2 describe the features of corporate bonds and differentiate between the three types of corporate bonds
8.3 explain how to calculate the value of a bond and why bond prices vary negatively with interest rate
movements
8.4 distinguish between a bond’s coupon rate, yield to maturity and effective annual yield, and be able to
calculate their values
8.5 explain why investors in bonds are subject to interest rate risk and why it is important to understand
the bond theorems
8.6 discuss the concept of default risk and know how to calculate a default risk premium
8.7 describe the factors that determine the level and shape of the yield curve.
Module preview
This module is all about bonds and how they are valued, or priced, in the marketplace. As you may suspect,
the bond valuation models presented in this module are derived from the present value concepts discussed
in the modules on the time value of money and discounted cash flows and valuation. The market price of a
bond is simply the present value of the promised cash flows (coupon and principal payments), discounted
at the current market rate of interest for bonds of similar risk.
First, we explain what Commonwealth Government and semi‐government securities are and their rela­
tive liquidity. Next, we discuss the features of corporate bonds and the types of bonds found in the market.
Then we develop the basic equation used to calculate bond prices and show how to calculate the following
characteristics of a bond: (1) yield to maturity; and (2) effective annual yield. We next discuss interest rate
risk and identify three bond theorems that describe how bond prices respond to changes in interest rates.
In the following section, we explain why companies have different borrowing costs. We find that four
factors affect a company’s cost of borrowing: (1) the debt’s marketability; (2) default risk; (3) call risk; and
(4) term to maturity. Finally, we describe the factors that determine the level and shape of the yield curve.
8.1 Government securities
LEARNING OBJECTIVE 8.1 Explain what Commonwealth Government Securities (CGS) and
semi‐government securities (semis) are, where they are issued and their relative liquidity.
Commonwealth Government Securities (CGS) are Treasury bonds and Treasury notes (T‐notes) issued by
the Australian Office of Financial Management (AOFM) and they are backed by the full faith and credit
of the Commonwealth Government. They are considered to be free of default risk. Treasury bonds differ
from T‐notes in that they are coupon instruments (paying interest semiannually). T‐notes, however, are
short‐term discount securities redeemable at face value on maturity. As such this security provides the pur­
chaser with a single payment on maturity without the coupon income stream associated with government
bonds. The Commonwealth also issues Treasury indexed bonds (TIBs) that adjust for inflation.
216 Finance essentials
Treasury bonds
Over the decade leading up to 2008, fiscal surpluses and proceeds from asset sales eliminated the need
for the Commonwealth to issue debt for budget financing purposes. In 2002–03 the government under­
took a review to examine whether it was desirable to continue to reduce the level of outstanding CGS
debt. It was announced in the 2003–04 budget that sufficient Treasury bonds would be issued to support
the Treasury bond futures market. From then on, the issuance of Treasury bonds continued at a steady
rate of around $5 billion each year. Many investors view Treasury bonds as attractive long‐term invest­
ments because of their low credit risk. In announcing its decision in 2003 to maintain the Treasury bond
market, the government noted that this would maintain the ability of such investors, including super­
annuation funds, to hold Commonwealth Government bonds.
The global financial crisis (GFC), however, has drastically altered the government plans of issuing
Treasury bonds at a steady rate. The federal budget ran into deficit in 2009–10 and continues to be in
deficit at the time of writing. To fund the growing deficit, the government had to issue bonds in large
quantities. The total amount of Commonwealth Treasury bonds outstanding in September 2016 was
approximately $420 billion and, when added to State government bonds outstanding, the gross total
reached around $673 billion,1 a three‐fold increase from the level at end June 2012. Table 8.1 shows the
increase in CGS issued since the GFC. By comparison, the government bond market in New Zealand
was worth slightly less than NZ$77 billion at the end of October 2016.2
TABLE 8.1
Increase in Commonwealth Government Securities issued since the GFC
Face value
2008 $m
2009 $m
2010 $m
2011 $m
2012 $m
2013 $m
2014 $m
2015 $m
2016 $m
Treasury bonds
49 395.1
78 403.1
124 695.1
161 242.9
205 387.9
233 539.5
290 936.2
335 186.2
385 219.8
6 020.0
6 020.0
11 415.3
13 929.0
16 069.0
18 319.0
23 531.4
27 530.8
30 179.1
6.7
6.4
5.8
5.8
5.7
5.6
5.7
5.6
5.6
—
16 700.0
11 000.0
16 100.0
12 500.0
5 500.0
5 000.0
6 000.0
5 000.0
4.0
—
—
—
—
—
—
—
—
55 425.9
101 129.5
147 116.2
191 277.7
233 962.6
257 364.1
319 473.2
368 722.6
420 404.5
5 019.7
—
—
—
—
—
—
—
—
60 445.5
101 129.5
147 116.2
191 277.7
233 962.6
257 364.1
319 473.2
368 722.6
420 404.5
Treasury indexed
bonds
Overdue securities
Treasury notes
Other
Sub total
Treasury bonds
Held by the
Commonwealth
Source: Data from Australian Office of Financial Management, ‘Australian government securities on issue – table H12’.
The primary market for Treasury bonds is similar to that for T‐notes discussed in the module on
financial markets: new issues are sold through a tender system following the requirements of the AOFM.
Bids are expressed in terms of yield‐to‐maturity to three decimal places but must be a whole multiple
of 0.005 per cent. The yield‐to‐maturity calculation is the same as that presented in the module on the
time value of money (using semiannual coupon payments). Conceptually, the yield‐to‐maturity is the
interest rate that makes the price of the security equal to the present value of the coupon payments and
the security’s face value (principal). Bids must also be for a minimum parcel of face value $1 000 000
and in multiples of $1 000 000 thereafter.
In New Zealand, the government directly sells some securities to retail investors, known as Kiwi bonds.
The coupon rates offered for Kiwi bonds are less than for bank term deposits of similar maturities, to
reflect the lower risk associated with government securities. The minimum amount that may be invested
is $1000. Recently, the New Zealand government offered a four‐year Earthquake Kiwi bond. While
this is like the other Kiwi bonds, the money invested in this offering goes towards meeting the costs
MODULE 8 Bond valuation 217
to the government of the recovery in Christchurch following the earthquakes of 4 September 2010 and
22 February 2011.
Treasury indexed bonds
In addition to the fixed‐principal bonds discussed, the Commonwealth also issues bonds that adjust for
inflation. These securities are referred to as Treasury indexed bonds (TIBs). Just like the fixed‐coupon
Treasury bonds, issues are sold through the tender process, taking the lowest yield bids first. Unlike the
fixed‐principal securities, interest is paid quarterly and the principal amount on which the coupon pay­
ments are based changes with the inflation rate. Specifically, the principal amount adjusts in response
to changes in the Consumer Price Index (CPI) called the ‘Weighted Average of Eight Capital Cities:
All‐Groups Index’ as maintained and published by the Australian Bureau of Statistics.
For example, consider an investor who purchases a TIB with an original principal amount of $100 000,
a 4 per cent annual coupon rate (1 per cent quarterly coupon rate) and 10 years to maturity. If the quar­
terly inflation rate during the first three months is 2 per cent, the principal amount for the first coupon
payment will be adjusted upwards by 2 per cent, or $2000, to $102 000. Therefore, the first coupon
payment will be $1020 (1 per cent of $102 000). This adjustment in the principal amount will take
place before each and every coupon payment. At maturity, the investor receives the greater of the final
­principal amount or the initial par amount.
TIBs are designed to provide investors with a way to protect their investment against inflation.
Issuance of the inflation‐indexed bonds was suspended after the 2003–04 Commonwealth budget, as
they had not proved popular with investors. However, issuance of TIBs resumed in 2009–10 and has
continued since. In New Zealand, inflation‐indexed bonds were introduced in 1996 but their issuance
was suspended in 1999. However, issuance resumed in New Zealand in October 2012 and, at the end of
October 2016, there were three issues outstanding with issuance totalling NZ$13.86 billion.3
TIBs provide government policymakers with a simple way to calculate the expected rate of inflation
in the economy. The reason is that the principal and interest payments on TIBs are adjusted for changes
in price levels and, therefore, the interest rate on these bonds provides a direct measure of the real rate
of interest. The expected rate of inflation can be obtained by subtracting the real rate of interest from the
nominal interest rate of a comparable security, which is equation 4.1 algebraically rearranged. That is:
∆Pe = i − r
For example, on 31 October 2016 the yield on a 5‐year Treasury bond was 1.87 per cent and the yield
on a long‐term TIB was 0.78 per cent.4 Therefore, the implied expected rate of inflation for the next
5 years is:
∆Pe = 1.87 − 0.78 = 1.09 per cent
The calculation tells us that as of 31 October 2016, 1.09 per cent is approximately the market’s best esti­
mate of the inflation rate for the next 5 years. Needless to say, this is valuable information for government
policymakers, investors and others in the private sector. However, as with any expectations, this may not
be realised. The calculated value of 1.09 per cent is the market’s best estimate at a point in time. As new
­information becomes available, the market participants will more than likely revise their estimate.
Investors in Commonwealth Government Securities
The Reserve Bank of Australia (RBA) holds large amounts of CGS mainly for the purpose of open‐
market operations to set the overnight cash rate. It normally does this through transactions known as
repurchase agreements (repos).
Other banks and other private financial institutions are also large holders of CGS. Other private financial
institutions include investment banks, insurance offices, superannuation funds and trustee companies. These
financial companies hold CGS because of the deep and liquid nature of the market. This lets them manage
218 Finance essentials
their liquidity requirements because these securities can be sold quickly and turned into cash. Foreign inves­
tors, however, are the biggest holders of CGS. In 2009, the federal government made important changes in
taxation for interest payable on these bonds to attract more investments in CGS from overseas.
TABLE 8.2
Holders of Commonwealth Government Securities (2009–2013, 30 June, $ million)
2009
Reserve Bank
Other banks
Life assurance offices
2010
2011
2012
2013
2 698
4 615
4 025
9 047
15 142
27 991
21 254
30 388
25 848
38 255
169
220
304
240
589
Private fire, marine and general insurance offices
1 459
1 963
1 998
2 638
1 925
Other private financial institutions
1 799
1 966
3 416
4 136
4 421
321
325
368
488
69
Government financial institutions
Other public authorities
Other including foreign investors
Total holdings
937
968
2 944
422
799
65 766
115 815
147 844
191 153
196 172
101 140
147 126
191 287
233 972
257 372
Source: Data from RBA, ‘Commonwealth government securities classified by holder as at 30 June’, RBA Bulletin, statistical
tables, table E09.
State government bonds
The states and territories of Australia have responsibility for government‐administered services such as
hospitals, schools, policing, roads, electricity and water. In case of funding shortfall, state and ­territory
borrowing authorities issue bonds called semi‐government securities or semis backed by their respec­
tive governments for the same reasons as the Commonwealth Government. Some examples of state
borrowing authorities include: Queensland Treasury Corporation (QTC), New South Wales Treasury
Corporation (NSW T‐corp) and Treasury Corporation of Victoria (TCV).
Semis differ from CGS in important ways. Their trading price is lower than that for an otherwise
identical CGS. In other words, semis trade at a higher yield. This occurs because, although states can
be rated ‘AAA’ (the same rating as for the Commonwealth Government), their debt is not considered
risk free. In the Australian capital markets, only Commonwealth debt receives this endorsement. Semis
are also not as highly traded as CGS and, therefore, trade with a liquidity premium in their yields. This
lower liquidity also means that the spreads between the bid and ask prices quoted for semis by market
dealers are larger than those for CGS. Trading occurs through Austraclear.
As the bulk of state government bonds is used to develop infrastructure assets of the states, the state
treasury corporations often seek to borrow at the longest possible maturities. Since CGS primarily sets
the yield curve, it is difficult for state government bonds to be issued at longer maturities than CGS.
Unlike CGS, semis are not issued through a tender system but are instead issued to a dealer panel.
This is a small set of bond dealers of up to 12 members. They agree to buy semis from state governments
either in closed auctions (in which stock is assigned to the best bids) or through agreeing to buy a given
amount at a given price. State borrowing authorities use dealer panels to sell semis because they increase
the stocks’ liquidity by finding other dealers to sell bonds to and making a market for them by quoting
bid and ask prices on the stock to other dealers.
Although semis are mainly issued to wholesale investors, they are also sold to retail individual inves­
tors as well as individual overseas investors. In the past, semis were also regularly issued into offshore
markets. These bonds are known as global exchangeable bonds and are free of interest withholding
tax (IWT) for foreign investors. Significantly, offshore issues can be exchanged at any time for dom­
estic Australian benchmark issues with corresponding maturity dates and semiannual interest cou­
pons. This gave foreign investors access to the greater liquidity for semis in the Australian market. It
also ensured that the prices of global exchangeable bonds closely track those of the domestic issues.
MODULE 8 Bond valuation 219
However, following tax changes in December 2008, state treasury corporations are no longer issuing
global exchangeable bonds and have instead actively sought to repurchase outstanding stock of these
securities. This has led to a decline in the outstanding stock of global exchangeable bonds in recent
years. Semis issued offshore are traded through clearinghouses such as Cedel, Euroclear and the
Depository Trust Company.
New Zealand has recently formed the Local Government Funding Agency (LGFA) to act as a central
borrowing vehicle for all city councils and municipalities, to consolidate the local government issuer
market. Like Australian semis, these bonds are not explicitly guaranteed by the federal government.
However, the rating agencies usually consider an implied government guarantee when assigning their
rating. There is a joint guarantee built into the legal framework of the LGFA, which means the councils
have joint liability if an individual borrowing entity is unable to meet its obligations.
BEFORE YOU GO ON
1. Discuss the risk characteristics of Treasury bonds.
2. What is a unique feature of Treasury indexed bonds that other government securities do not have?
3. How do semis differ to Commonwealth Government Securities?
8.2 Corporate bonds
LEARNING OBJECTIVE 8.2 Describe the features of corporate bonds and differentiate between the
three types of corporate bonds.
Corporate bonds are debt contracts requiring borrowers to make periodic payments of interest and
to repay principal at the maturity date. Corporate bonds can be unsecured notes or debentures. An
unsecured note is a bond that has no specified security attached as collateral in the case of default.
Debentures come in two forms, fixed and floating. Fixed‐charge debenture holders have the right to the
proceeds of the sale of the assets specified in the debenture should the bond default. A floating‐charge
debenture holder has the right to the proceeds of sale of the assets specified in the debenture that are not
already pledged against a fixed charge in any other debenture in the case of default as well. This usually
ends up being capital assets and produced goods. It should also be noted that a floating charge ranks
behind a fixed charge in the case of default; that is, the holders of fixed charges have first right to the
specified assets, with floating‐charge holders having access to what remains once fixed‐charge holders’
debts have been satisfied. Holders of unsecured notes and other debentures have equal‐ranking claims to
the proceeds of company assets that are not specified in a debenture in the case of default.
Examples of assets that can be pledged in a debenture include land and buildings; specific industrial
equipment or ‘rolling stock’, such as railroad cars, trucks and aeroplanes; and even stocks and bonds
issued by other corporations or government units. Bond contracts that pledge assets in the event of
default have lower yields than similar bonds that are unsecured.
Corporate bonds are usually issued in denominations of $1000 and pay coupon interest semiannually.
Corporate debt can be sold in the domestic bond market or in the Australian dollar eurobond market,
which is a market for the debt of Australian companies denominated in Australian dollars but traded
overseas. Bonds can also be classified as either senior debt, giving the bondholders first priority to the
firm’s assets (after secured claims are satisfied) in the event of default, or subordinated (junior) debt,
in which bondholders’ claims to the company’s assets rank behind senior debt.
Corporate bonds are secured with a trust deed or unsecured note deed that formalises the company’s
obligations to investors. The trust deed is the legal contract that states the covenants and undertakings
made by the bond issuer which are designed to ensure that the issuer can meet its obligations to bond
investors, and it protects the security of the debenture investors in terms of the seniority of their claims
on the proceeds of asset sales in case of default. Provisions may entail financial covenants which limit
220 Finance essentials
the total liabilities or other liabilities a company may take on, and may include terms related to the rights
of bond investors to convert their bond holdings under certain circumstances.
In addition, some corporate bonds have sinking fund provisions or call provisions. This requires that the
bond issuer provide funds to a trustee to retire a specific dollar amount (face amount) of bonds each year.
The trustee may retire the bonds either by purchasing them in the open market or by calling them, if a call
provision is present. It is important to note the distinction between an ordinary sinking fund provision and
a call provision. With an ordinary sinking fund provision, the issuer must retire a portion of the bond as
promised in the bond indenture. In contrast, a call provision is an option that grants the issuer the right to
retire bonds before their maturity. Most security issues with sinking funds have call provisions, because this
guarantees the issuer the ability to retire bonds as they come due under the sinking fund retirement schedule.
Hybrid securities are financial products issued that have characteristics of both debt and equity.
Traditionally, they have a set coupon or ‘dividend’ rate and set conversion dates when they can be
exchanged for ordinary equity. But the nature and characteristics of hybrids that are issued have been
evolving very rapidly over the past five years and no two hybrid securities are ever exactly the same. A
feature often found in hybrid securities is a reset date: on this date, the hybrid issuer can elect to change
the terms of the security (by changing either the next reset date or the coupon rate). Hybrid investors
can choose to convert their securities into shares or accept the new terms at the reset date. Hybrids can
also have cumulative or non‐cumulative interest payments. This means that, if a coupon is not paid as
expected, a cumulative hybrid will pay it at the next coupon date while a non‐cumulative hybrid holder
loses that coupon. Redeemable hybrids have the feature that they can be sold back to the issuer at the
original purchase price.
Convertible notes or convertible bonds are hybrid securities
that can be converted into shares of common stock at the dis­
cretion of the holder. Their convertibility feature permits the
holder to share in the good fortune of the firm if the stock
price rises above a certain level. That is, if the market value of
the stock the holder receives at conversion exceeds the market
value of the notes, it is to the investor’s advantage to exchange
the notes for stock, thus making a profit. As a result, converti­
bility is an attractive feature for investors because it gives them
an option to gain additional profits that are not available with
non‐convertible bonds. Typically, the conversion ratio will
be set so that the stock price must rise substantially, usually
15 per cent to 20 per cent, before it is profitable to convert the
notes into equity.
Because convertibility gives investors an opportunity for
profits not available with non‐convertible bonds, convertible
notes usually have lower yields than similar non‐convertible
bonds. In addition, convertible notes usually include a call pro­
vision so that the bond issuer can force conversion by calling the
bond, rather than continue to pay coupon payments on a security
that has greater value on conversion than the face amount of
the notes.
Another class of hybrid securities which are a lot like ordinary equity are called redeemable preference
shares. These are preference shares that the company states it will buy back on a specified maturity date.
Because they are preference shares, they rank ahead of ordinary shares in a claim on assets of the company,
but they rank behind debentures and other purer forms of debt. As such, they have the most equity‐like
characteristics of the hybrid securities. Because hybrids have these unusual features, their prices are often
correlated with the share price and they are sometimes classified as debt and sometimes as equity by the
Australian Taxation Office. Preference shares will be discussed further in the module on share valuation.
MODULE 8 Bond valuation 221
Financial guarantees have emerged in recent years. These are unconditional offers from a private
sector guarantor to cover the payment of principal and interest to investors in debt securities in the event
of a default. In Australia, bonds with financial guarantees are called credit‐wrapped bonds. Credit
wrapping is primarily used by lower rated (generally BBB) investment‐grade corporates — typically air­
ports, utilities and infrastructure‐related issuers — to obtain a higher rating on their bonds. Bond ratings
are discussed further later in this module.
Types of corporate bonds
Corporate bonds are long‐term IOUs that represent claims against a company’s assets. Unlike share­
holders’ returns, most bondholders’ returns are fixed; they receive only the interest payments that are
promised plus the repayment of the loan amount at the end of the contract. Debt instruments where
the interest paid to investors is fixed for the life of the contract are called fixed‐income securities. We
examine three types of fixed‐income securities in this section.
Coupon bonds
The most common bonds issued by companies are called coupon bonds, or vanilla bonds. These bonds
have coupon payments that are fixed for the life of the bond, and at maturity the entire original principal
is paid and the bonds are retired. Coupon bonds have no special provisions and the provisions they do
have follow convention.
0
PB
8%
1
2
3
Year
$80
$80
$80 + $1000
This time line shows the cash payments for a 3‐year coupon bond with a $1000 face value and an
8 per cent coupon rate. PB is the price (value) of the bond, which is discussed in the next section. The
$80 cash payments ($1000 × 8 per cent) made each year are called the coupon payments, the periodic
interest payments made to bondholders. These payments are usually made annually or semiannually, and
the payment amount (or rate) remains fixed for the life of the bond contract, which in our example is
3 years. The face value or par value for most corporate bonds is $1000, and it is the principal amount
owed to the bondholder at maturity. Finally, the bond’s coupon rate is the annual coupon payment (C)
divided by the bond’s face value (F). Our coupon bond pays $80 coupon interest annually and the face
value is $1000. The coupon rate is thus:
C
F
$80
=
$1000
= 8%
Coupon rate =
Zero coupon bonds
At times, corporations issue bonds that have no coupon payments but promise a single payment at maturity.
The interest paid to a bondholder is the difference between the price paid for the bond and the face amount
received at maturity. These bonds are sold at a price well below their face value because all of the interest
is ‘paid’ when the bonds are retired at maturity, rather than in semiannual or yearly coupon payments.
The most frequent and regular issuer of zero coupon securities is the US Department of Treasury
and perhaps the best‐known zero coupon bond is a United States Saving Bond. Companies also issue
zero coupon bonds from time to time. Companies that are expanding operations but have little cash
on hand are especially likely to use zero coupon bonds for funding. In the 1990s, the US bond market
was ‘flooded’ with zero coupon bonds issued by telecommunications companies. These companies were
spending huge amounts to build fibre‐optic networks, which generated few cash inflows until they were
completed. Zero coupon bonds are not frequently issued in Australia.
222 Finance essentials
Convertible bonds
As discussed above, corporate convertible bonds can be converted into ordinary shares at some pre­
determined ratio at the discretion of the bondholder. For example, a bond of $1000 face value may be
convertible into 100 ordinary shares. The convertible feature allows the bondholders to share in the good
fortunes of the company if the company’s share price rises above a certain level. Specifically, it is to the
bondholders’ advantage to exchange their bonds for shares if the market value of the shares they receive
exceeds the market value of the bonds.
As you would expect from our discussion, bondholders pay a premium (a higher price) for bonds
with a conversion feature, which means the issuing company is able to issue the bonds with a lower
interest rate.
BEFORE YOU GO ON
1. What is the main difference between a coupon bond and a zero coupon bond?
2. A certain bond has a 7 per cent coupon rate, a face value of $1000 and a maturity of 4 years. On a
time line, lay out the cash flows for this bond.
3. Explain what a convertible bond is.
8.3 Bond valuation
LEARNING OBJECTIVE 8.3 Explain how to calculate the value of a bond and why bond prices vary
negatively with interest rate movements.
We turn now to the topic of bond valuation — how bonds are priced. Throughout the text, we have
stressed that the value, or price, of any asset is the present value of its future cash flows. The steps
necessary to value an asset are as follows.
1. Estimate the expected future cash flows.
2. Determine the required rate of return, or discount rate. This rate depends on the riskiness of the cash
flow stream.
3. Calculate the discounted present value of the future cash flows. This present value is what the asset is
worth at a particular point in time.
For bonds, the valuation procedure is relatively easy. The cash flows (coupon and principal payments)
are contractual obligations of the company and are known by market participants, since they are stated
in the bond contract. Thus, market participants know the magnitude and timing of the expected cash
flows promised by the borrower (the bond issuer). The required rate of return, or discount rate, for a
bond is the market interest rate, called the bond’s yield to maturity (or more commonly, simply its yield).
This rate is determined from the market prices of bonds that have features similar to those of the bond
being valued; by ‘similar’, we mean bonds that have the same term to maturity and the same bond rating
(default risk class), and are similar in other ways.
Note that the required rate of return is really investors’ opportunity cost, which is the highest alter­
native return that is sacrificed if a certain investment is made. For example, if bonds identical to the bond
being valued — having the same risk — yield 9 per cent, the threshold yield or required return on the
bond being valued is 9 per cent. Why? Because an investor would not buy a bond with an 8 per cent
yield when an identical bond yielding 9 per cent was available.
Given the above information, we can calculate the current value, or price, of a bond (PB) by calcu­
lating the present value of the bond’s expected cash flows:
PB = PV(Coupon payments) + PV(Principal payment)
Next, we examine this calculation in detail.
MODULE 8 Bond valuation 223
The bond valuation formula
To begin, refer to figure 8.1, which shows the cash flows for a 3‐year corporate bond with an 8 per cent
coupon rate and a $1000 face value. If the market rate of interest on similar bonds is 10 per cent and
interest payments are made annually, what is the market price of the bond? In other words, how much
should you be prepared to pay for the promised cash flow stream?
There are a number of ways to solve this problem. Probably the simplest is to write the bond valuation
formula in terms of the individual cash flows. Thus, the price of the bond (PB) is the sum of the present
value calculations for the coupon payments (C) and the principal amount (F) discounted at the required
rate (i). This calculation follows:
PB = PV (Each coupon payment) + PV(Principal payment)
1  
1  
1 
1  
C ×
F ×
=  C1 ×
 +  C2 ×
2 +  3
3 +  3

(1 + i )  
(1 + i )  
(1 + i )3 
1+ i

1  
1  
1 
1  
=  $80 ×
+ $80 ×
+ $1000 ×
 + $80 ×

(1.10 )3 
(1.10 )2  
(1.10 )3  
1.10  
= ($80 × 0.9091) + ($80 × 0.8264) + ($80 × 0.7513) + ($1000 × 0.7513)
= $72.73 + $66.11 + $60.10 + $751.30
= $950.24
Note that you could have simplified this calculation by combining the final coupon payment and the
principal payment (C3 + F3), since both cash flows occur at time t = 3.
FIGURE 8.1
0
Cash flows for a 3‐year bond
10%
PB
1
2
$80
$80
3 Year
$80 + $1000
$72.73
$66.11
$60.10
$751.30
$950.24 Total price of bond
To develop the general bond pricing formula, we can write the equations for the prices of a 4‐year,
5‐year and 6‐year maturity bond as follows:
1 
1  
 C +F × 1 
( 4 4)
PB =  C1 ×
 +  C2 ×
2  ++ 

(1 + i ) 
(1 + i )4 
1+ i


1 
1 
1  

PB =  C1 ×
+ + ( C5 + F5 ) ×
 + C2 ×

(1 + i )2 
(1 + i )5 
1 + i  

1 
1  
 C +F × 1 
( 6 6)
PB =  C1 ×
 +  C2 ×
2  ++ 

(
)
(1 + i )6 
1+ i 
1+ i


224 Finance essentials
If we continue the process for n periods, we arrive at the general equation for the price of the bond:
1 
1  
 C +F × 1 
( n n)
PB =  C1 ×
 +  C2 ×
2  ++ 

(1 + i ) 
(1 + i )n 
1+ i


An alternative, and preferred, approach is to recognise that the coupon payment stream is an annuity —
each coupon payment is the same amount, with the same amount of time between each payment. Hence
we can use the present value of an ordinary annuity equation from module 6 to value the coupon p­ ayment
stream. Thus the general equation for the price of a bond can be simplified to:
PB =
1 
C
Fn
1−
(8.1)
n +

i  (1 + i )  (1 + i )n
where:
PB = price of the bond, or present value of the stream of cash payments
C = coupon payment in all periods
Fn = par value or face value (principal amount) to be paid at maturity
i = market interest rate (discount rate or market yield)
n = number of periods to maturity.
Note that there are five variables in the bond pricing equation. If we know any four of them, we can
solve for the fifth.
Calculator tip: bond valuation problems
We can easily calculate bond prices using a financial calculator or a spreadsheet program. We solve for
bond prices and bond yield in exactly the same way that we solved for present value (bond price) and
discount rate (bond yield) in the module on discounted cash flows and valuation. There is nothing new to
learn! We solve our example problem (figure 8.1) on a financial calculator as follows:
Procedure
Enter cash flow data
Calculate PV
Key operation
Display
1000 [FV]
1000 ⇒ FV
3 [N]
3⇒N
10 [I/Y]
10 ⇒ I/Y
10.00
80 [PMT]
80 ⇒ PMT
80.00
[COMP] [PV]
PV =
1000.00
3.00
−950.26
Several points are worth noting.
1. Always draw a time line for the cash flows. This simple step will significantly reduce mistakes.
2. The PMT key enters the dollar amount of an ordinary annuity for n periods. In our example, keying
in 3 with the N key and $80 with the PMT key enters an $80 annuity with the final payment made at
the end of year 3.
3. Be sure that you enter the coupon and principal payments separately. Do not enter the final coupon
payment ($80) and principal amount ($1000) as a single entry of $1080 on the FV key. The reason is
that the PMT key is the annuity key and, when you enter N = 3, the $80 is entered in the calculator as
a 3‐year ordinary annuity with a final payment of $80 in period t = 3. If you then enter $1080 on the
FV key, you will have an extra $80 in the final period (t = 3). For the example problem, we correctly
entered the $80 coupon payments with the PMT key and the $1000 principal payment with the
FV key.
4. Finally, as we have mentioned in earlier modules, you must be consistent throughout a problem in how
you enter the signs (positive or negative) for cash inflows and cash outflows. For example, if you are a
bond investor and decide to enter all cash inflows with a positive sign, then you must enter all coupon
MODULE 8 Bond valuation 225
and principal payments with a positive sign. The price you paid for the bond, which is a cash outflow,
must be entered as a negative number. This is the convention we will follow.
Par, premium and discount bonds
One of the mathematical properties of the bond formula is that whenever a bond’s coupon rate is equal
to the market rate of interest on similar bonds (the bond’s yield), the bond will sell at par. We call such
bonds par‐value bonds. For example, say that you own a 3‐year bond with a face value of $1000 and an
annual coupon rate of 5 per cent, when the yield or market rate of interest on similar bonds is 5 per cent.
The price of the bond, based on equation 8.1 is:
1  $1000
$50 
× 1−
3 +
0.05  (1.05)  (1.05)3
= $136.16 + $863.84
PB =
= $1000
As predicted, the bond’s price equals its par value.
Now assume that the market rate of interest rises overnight to 8 per cent. What happens to the price of
the bond? Will the bond’s price be below, above or at par?
1  $1000
$50 
× 1 −
3 +
0.08  (1.08 )  (1.08 )3
= $128.85 + $793.83
PB =
= $922.68
When i is equal to 8 per cent, the price of the bond declines to $922.68. The bond will sell below par;
such bonds are called discount bonds.
Whenever a bond’s coupon rate is lower than the market rate of interest on similar bonds, the bond
will sell at a discount. This is true because of the fixed nature of a bond’s coupon payments. Let’s return
to our 5 per cent coupon bond. If the market rate of interest is 8 per cent and our bond pays only 5 per
cent, no economically rational person would buy the bond at its par value. This would be like choosing
a bond with a 5 per cent yield over one with an 8 per cent yield. We cannot change the coupon rate to
8 per cent because it is fixed for the life of the bond. That is why bonds are called fixed‐income securities!
The only way to increase our bond’s yield to 8 per cent is to reduce the price of the bond to $922.68.
At this price, the bond’s yield will be precisely 8 per cent, which is the current market rate for similar
bonds. Through the price reduction of $77.32 ($1000 − $922.68), the seller provides the new owner with
additional ‘interest’ in the form of a capital gain.
What would happen to the price of the bond if interest rates on similar bonds declined to 2 per cent and
the coupon rate remained at 5 per cent? The price of our bond would rise to $1086.52. At this price, the
bond’s yield would be precisely 2 per cent, which is the current market yield. The $86.52 ($1086.52 −
$1000) premium that the investor paid adjusts the bond’s yield to 2 per cent, which is the current market
yield for similar bonds. Bonds that sell above par are called premium bonds. Whenever a bond’s coupon
rate is higher than the market rate of interest, the bond will sell at a premium.
Our discussion of bond pricing can be summarised as follows, where i is the market rate of interest:
1. i > coupon rate — the bond sells for a discount
2. i < coupon rate — the bond sells for a premium
3. i = coupon rate — the bond sells at par value.
This negative relationship between changes in the level of interest rates and changes in the price
of a bond (or any fixed‐income security) is one of the most fundamental relationships in corporate
226 Finance essentials
finance. The relationship exists because the coupon payments on most bonds are fixed and the only
way that bonds can pay the current market rate of interest to investors is through adjustment of the
price of the bond.
DEMONSTRATION PROBLEM 8.1
Pricing a bond
Problem:
Your financial adviser is trying to sell you a 15‐year bond with a face value of $1000 and a 7 per cent
coupon, and the interest, or yield, on similar bonds is 10 per cent. Is the bond selling for a premium,
at par or at a discount? Answer the question without making any calculations and then prove that your
answer is correct. The time line is as follows:
0
10%
PB
Year
1
2
14
15
$70
$70
$70
$70 + $1000
Approach:
Since the market rate of interest is greater than the coupon rate (i > coupon rate), the bond must sell at
a discount.
Solution:
To prove that the answer is correct (or wrong), we can calculate the bond’s price with a financial
­calculator as follows:
Procedure
Key operation
Enter cash flow data
Calculate PV
Display
1000 [FV]
1000 ⇒ FV
15 [N]
15 ⇒ N
15.00
10 [I/Y]
10 ⇒ I/Y
10.00
70 [PMT]
70 ⇒ PMT
70.00
[COMP] [PV]
PV =
1000.00
−771.82
The bond is selling at a discount, and it should. Why? Because the market rate of interest is 10 per cent
and our bond is paying only 7 per cent. Since the bond’s coupon rate is fixed, the only way we can
bring the bond’s yield up to the current market rate of 10 per cent is to reduce the price of the bond.
USING EXCEL
Bond prices and yields
Calculating bond prices and yields using a spreadsheet may seem daunting at first. However,
understanding the terminology used in the formulas will make the calculations a matter of common sense.
• Settlement date — the date a buyer purchases the bond.
• Maturity date — the date the bond expires; if you know only the n (number of years remaining) of the
bond, use a date that is n years in the future in this field.
• Redemption — the security’s redemption value per $10 face value; in other words, if the bond has a
par of $1000, you enter 100 in this field.
• Frequency — the number of coupon payments per year.
Here is a spreadsheet showing the setup for calculating the price of the discount bond described in
demonstration problem 8.1.
We first use the Excel formula:
= PRICE(settlement, maturity, rate, yield, redemption, frequency)
MODULE 8 Bond valuation 227
to calculate the bond price as a percentage of par. We then multiply this percentage (77.18 in the above
example) by $1000 to obtain the bond price in dollars. A bond yield, which is discussed in the next section, is calculated in a similar manner using the formula:
= YIELD(settlement, maturity, rate, price, redemption, frequency).
Semiannual compounding
In Europe, bonds generally pay coupon interest on an annual basis. In contrast, in Australia and the
USA, most bonds pay coupon interest semiannually — that is, twice a year. Thus, if a bond has an
8 per cent coupon rate (paid semiannually), the bondholder will in 1 year receive 2 coupon payments of
$40 each, totalling $80 ($40 × 2). We can modify equation 8.1 as follows to adjust for coupon payments
made more than once a year:
PB =
1
C/m
Fmn

1−
mn  +

i / m  (1 + i / m )  (1 + i / m )mn (8.2)
where C is the annual coupon payment, m is the number of times coupon payments are made each year,
n is the number of years to maturity and i is the annual interest rate. In the case of a bond with semi­
annual coupon payments, m equals 2.
Whether we are calculating bond prices annually, semiannually, quarterly or for some other period,
the calculation is the same. We need only be sure that the bond’s yield, coupon payment and maturity are
adjusted to be consistent with the bond’s stated compounding period. Once that information is converted
to the correct compounding period, it can simply be entered into equation 8.1. Thus, there is really no
need to memorise or use equation 8.2 unless you find it helpful.
Let’s work an example to demonstrate. Earlier we determined that a 3‐year, 5 per cent coupon bond
will sell for $922.68 when the market rate of interest is 8 per cent. Our calculation assumed that coupon
payments were made annually. What is the price of the bond if the coupon payments are made semi­
annually? The time line for the semiannual bond situation follows:
0
PB
8%/2
1
2
3
4
5
$50/2
$50/2
$50/2
$50/2
$50/2
228 Finance essentials
6 Semiannual period
$50/2 + $1000
We convert the bond data to semiannual compounding as follows: (1) the market yield is 4 per cent
semiannually (8 per cent per year/2); (2) the coupon payment is $25 semiannually ($50 per year/2); and
(3) the total number of coupon payments is 6 (2 per year × 3 years). Plug the data into equation 8.1 and
the bond price is:
1  $1000
$25 
1−
6 +

0.04  (1.04 )  (1.04 )6
= $131.05 + $790.31
PB =
= $921.37
Note that the price of the bond is slightly lower with semiannual compounding than with annual
­compounding ($921.37 < $922.68). The slight difference in price reflects the change in the timing of
the cash flows and the interest rate adjustment. (If the bond sold at a premium, the reverse would be
true; that is, the price with semiannual compounding would be slightly more than the price with annual
compounding.)
DEMONSTRATION PROBLEM 8.2
Bond pricing with semiannual coupon payments
Problem:
A corporate treasurer decides to purchase
a 20‐year Treasury bond with a 4 per cent
coupon rate. If the current market rate
of interest for similar Treasury securities
is 4.5 per cent, what is the price of the
bond?
Approach:
Treasury securities pay interest semiannually, so we first convert the bond data
to semiannual compounding as follows:
(1) the bond’s semiannual yield is 2.25 per
cent (4.5 per cent per year/2); (2) the semiannual coupon payment is $20 [($1000 ×
4 per cent)/2 = $40/2]; and (3) the total
number of compounding periods is 40 (2 per year × 20 years). Note that at maturity, the bond pays its principal, or face value, of $1000 to the investor. Thus, the bond’s time line for the cash payments is as follows:
0 4.5%/2 1
PB
$20
2
3
4
39
$20
$20
$20
$20
Semiannual
40 period
$20 + $1000
Using equation 8.2, we enter the appropriate value into the equation:
PB =
$20 
1
$1000

1−
+
0.0225  (1.0225)40  (1.0225)40
= $523.87 + $410.65
= $934.52
MODULE 8 Bond valuation 229
Solution:
To confirm, we can enter the appropriate values in the financial calculator and solve for the present
value as follows:
Procedure
Key operation
Enter cash flow data
Calculate PV
Display
1000 [FV]
1000 ⇒ FV
40 [N]
40 ⇒ N
2.25 [I/Y]
2.25 ⇒ I/Y
2.25
20 [PMT]
20 ⇒ PMT
20.00
[COMP] [PV]
PV =
1000.00
40.00
−934.52
The bond sells for a discount and its price is $934.52.
Zero coupon bonds
As previously mentioned, zero coupon bonds have no coupon payments but promise a single payment at
maturity. The price (or yield) of a zero coupon bond is simply a special case of equation 8.2 in which all
the coupon payments are equal to zero.
Hence, the pricing equation is:
Fn
(8.3)
PB =
(1 + i )n where:
PB = price of the bond
Fn = amount of the cash payment at maturity (face value)
i = interest rate (yield) for n periods
n = number of periods until the payment is due
This is similar to the annual bond pricing equation, equation 8.1.
Note that if a zero coupon bond compounds semiannually (or more than once per year), equation 8.3
becomes:
Fmn
PB =
(1 + i / m )mn
where:
Fmn = the amount of the cash payment at maturity (face value)
m = number of times interest is compounded each year
Now let’s work an example. What is the price of a zero coupon bond with a $1000 face value, 10‐year
maturity and semiannual compounding when the market interest rate is 12 per cent? Since the bond
compounds interest semiannually, the number of compounding periods is 20 (m × n = 2 × 10 = 20). The
semiannual interest is 6 per cent (12 per cent/2). The time line for the cash flows is as follows:
0
12%/2
PB
1
2
3
19
20
0
0
0
0
$1000
Plugging the data into equation 8.3, we find that the price of the bond is $311.80:
$1000
(1.06 )20
= $1000 × 0.3118 = $311.80
PB =
230 Finance essentials
Period
Note that the zero coupon bond is selling at a deep discount. This should come as no surprise, since
the bond has no coupon payment and all the dollars paid to investors are paid at maturity. Why are zero
coupon bonds so heavily discounted compared with similar bonds that do have coupon payments? From
module 5 we know that, because of the time value of money, dollars to be received in the future have
less value than current dollars. Thus, zero coupon bonds, for which all the cash payments are made at
maturity, must sell for less than similar bonds that make coupon payments before maturity.
DEMONSTRATION PROBLEM 8.3
The price of a bond
Problem:
An investor is considering buying an Australian corporate bond with an 8‐year maturity, $1000 face
value and coupon rate of 6 per cent. Similar bonds in the marketplace yield 14 per cent. Coupons are
paid semiannually. How much should the investor be willing to pay for the bond? Using equation 8.2,
set up the equation to be solved and then solve the problem using your financial calculator. Note that
the discount rate used in the problem is the 14 per cent market yield on similar bonds (bonds of similar
risk), which is the investor’s opportunity cost.
Approach:
Since Australian corporate bonds pay coupon interest semiannually, we first need to convert all of the
bond data to reflect semiannual compounding: (1) the annual coupon payment is $60 per year (6 per
cent × $1000) and the semiannual payment is $30 per period ($60/2); (2) the appropriate semiannual
yield is 7 per cent (14 per cent/2); and (3) the total number of compounding periods is 16 (2 per year ×
8 years). The time line for the semiannual cash flows is as follows:
0
1
2
3
15
$30
$30
$30
$30
14%/2
PB
16
Semiannual period
$30 + $1000
Solution:
Using equation 8.1, the setup is as follows:
PB =
$30 
1  $1000
1−
+
0.07  (1.07)16  (1.07)16
= $283.40 + $338.73
= $662.13
To solve the problem using a financial calculator, we enter the appropriate values and solve for PV as
follows:
Procedure
Enter cash flow data
Calculate PV
Key operation
Display
1000 [FV]
1000 ⇒ FV
16 [N]
16 ⇒ N
16.00
7 [I/Y]
7 ⇒ I/Y
7.00
30 [PMT]
30 ⇒ PMT
[COMP] [PV]
PV =
1000.00
30.00
−622.13
The investor should be willing to pay $622.13 because the bond’s yield at this price would be exactly
14 per cent, which is the current market yield on similar bonds. If the investor pays more than $622.13,
the investment will yield a return of less than 14 per cent. In this situation the investor would be better
off buying the similar bonds in the market that yield 14 per cent. Of course, if the investor can buy the
bond for less than $622.13, the price is a bargain and the return on investment will be greater than the
market yield.
MODULE 8 Bond valuation 231
BEFORE YOU GO ON
1. Explain conceptually how bonds are priced.
2. What is the compounding period for most bonds sold in Australia?
3. What are zero coupon bonds and how are they priced?
8.4 Bond yields
LEARNING OBJECTIVE 8.4 Distinguish between a bond’s coupon rate, yield to maturity and effective
annual yield, and be able to calculate their values.
In dealing with bonds, we frequently know the bond’s price but not its yield — or, more formally, the
bond’s yield to maturity. In this section, we discuss how to calculate the yield to maturity and some other
important bond yields.
Yield to maturity
The yield to maturity of a bond is the discount rate that makes the present value of the coupon and
principal payments equal to the price of the bond. The yield to maturity can be viewed as the ‘promised
yield’ because it is the yield that the investor earns if the bond is held until maturity and all the coupon
and principal payments are made as promised. A bond’s yield to maturity changes daily as interest rates
increase or decrease, but its calculation is always based on the issuer’s promise to make interest and
principal payments as stipulated in the bond contract.
Let’s work through an example to see how a bond’s yield to maturity is calculated. Suppose you
decide to buy a 3‐year bond with a face value of $1000 and a 6 per cent coupon rate for $960.99. For
simplicity, we will assume that the coupon payments are made annually. The time line for the cash flows
is as follows:
0
−$960.99
i=?
Year
1
2
3
$60
$60
$60 + $1000
To calculate the yield to maturity, we apply equation 8.1 and solve for i as follows:
$960.99 =
1  1000
60 
1−
3 +

i  (1 + i )  (1 + i )3
As we discussed in the module on discounted cash flows and valuation, we cannot solve for i mathemat­
ically; we must find it by trial and error. We know the bond is selling for a discount because its price is
below par, so the yield must be higher than the 6 per cent coupon rate. Let’s try 7 per cent:
1  1000
60 
1−
= $973.76
3 +

(
0.07 
1.07 )  (1.07 )3
The calculated price of $973.76 is still greater than our market price of $960.99; thus, we need to use a
slightly larger discount rate. Let’s try 7.7 per cent:
1
60 
1000

1−
= $955.95
3 +

0.077  (1.077 )  (1.077 )3
232 Finance essentials
Our calculated value of $955.95 is now less than the market price of $960.99, so we need a lower
­discount rate. We’ll try 7.5 per cent:
1
60 
1000

1−
= $960.99
3 +

0.075  (1.075)  (1.075)3
At a discount rate of 7.5 per cent the price of the bond is exactly equal to the market price, and thus the
bond’s yield to maturity is 7.5 per cent.
We can, of course, also calculate the bond’s yield to maturity using a financial calculator. Calculating
the yield in this way is no different from calculating the price, except that the unknown is the bond’s
yield. As with calculating the price of a bond, the major source of calculation errors is failing to make
sure that all the bond data is consistent with the bond’s compounding period. The three variables that
may require adjustment are: (1) the coupon payment; (2) the yield; and (3) the bond maturity.
For the 3‐year corporate bond discussed earlier, the bond data is already in a form that is consistent
with the annual compounding period, so we enter the values into the calculator and solve for i, which is
the yield to maturity, remembering to enter the present value as a negative.
Procedure
Key operation
Enter cash flow data
Calculate I/Y
Display
1000 [FV]
1000 ⇒ FV
3 [N]
3⇒N
−960.99 [PV]
(−960.99) ⇒ PV
60 [PMT]
60 ⇒ PMT
[COMP] [I/Y]
I/Y =
1000.00
3.00
−960.99
60.00
7.50
The bond’s yield to maturity is 7.5 per cent, which is identical to the answer from our hand calculation.
Effective annual yield
Up to now, when pricing a bond with a semiannual compounding period, we have assumed the bond’s
annual yield to be twice the semiannual yield. This is the convention used by practitioners who deal
in bonds. However, note that bond yields quoted in this manner are just like the bank credit card APR
calculations discussed in module 6: to get a credit card’s APR, we multiplied the monthly interest rate
of 1 per cent by 12, for an APR of 12 per cent. As you recall, interest rates (or yields) annualised in
this manner do not take compounding into account. Hence, the values calculated are not the true cost of
funds and their use can lead to decisions that are economically incorrect.
As a result, annualised yields calculated by multiplying a period yield by the number of com­
pounding periods are only acceptable for decision‐making purposes when comparing bonds that have
the same compounding frequencies. Thus, for example, an investor must be careful when evaluating
yields between European and Australian bonds, since the European is compounded annually while the
Australian bond compounds interest twice a year.
The correct way to annualise an interest rate is to calculate the effective annual rate (EAR). In industry,
the EAR is called the effective annual yield (EAY); thus, EAR = EAY. Drawing on equation 6.5
(see module 6), we find that the correct way to annualise the yield on a bond is as follows:
m
Quoted interest rate 

EAY =  1 +
 − 1

m
where:
(8.4)
Quoted interest rate = simple annual yield (semiannual yield × 2)
m = number of compounding periods per year
MODULE 8 Bond valuation 233
We can work through an example to clarify how the EAY differs from the yield to maturity. Suppose
an investor buys a 30‐year bond with a $1000 face value for $800. The bond’s coupon rate is 8 per cent
and interest payments are made semiannually. What is the bond’s yield to maturity and what is its effec­
tive annual yield? To find out, we first need to convert the bond’s annual data into semiannual data:
(1) the 30‐year bond has 60 compounding periods (30 years × 2 periods per year); and (2) the bond’s
semiannual coupon payment is $40 [($1000 × 0.08)/2 = $80/2]. The time line for this bond is:
0
i=?
−$800
1
2
3
59
$40
$40
$40
$40
60
Period
$40 + $1000
We can set up the problem using equation 8.1:
$800 =
$40
$40
$40
$40
$1040
+
+
++
+
2
3
59
(1 + i / 2 )
(1 + i / 2 )60
1 + i / 2 (1 + i / 2 ) (1 + i / 2 )
However, solving an equation with so many terms can be time consuming. Therefore, we will solve
for the yield to maturity using the yield function in a financial calculator as follows:
Procedure
Enter cash flow data
Calculate I/Y
Key operation
Display
1000 [FV]
1000 ⇒ FV
60 [N]
60 ⇒ N
−800 [PV]
(−800) ⇒ PV
40 [PMT]
40 ⇒ PMT
[COMP] [I/Y]
I/Y =
1000.00
60.00
−800.00
40.00
5.07
The answer is 5.07 per cent. We then multiply the semiannual yield by 2 to convert it to an annual yield:
2 × 5.07 = 10.14 per cent. This is the bond’s yield to maturity.
Now we will enter the appropriate values into equation 8.4 and calculate the EAY for the bond:
m
Quoted interest rate 

EAY =  1 +
 − 1

m
2
0.1014 
−1
2 
= (1.0507 )2 − 1 = 0.1040, or 10.40%
= 1 +

The EAY is 10.40 per cent, compared with the annual yield to maturity of 10.14 per cent. The EAY
is greater because it takes into account the effects of compounding — earning interest on interest. As
mentioned earlier, calculating the EAY is the proper way to annualise the bond’s yield exactly because
it takes compounding into account.
Using a financial calculator:
Procedure
Key operation
Enter cash flow data
2 [P/YR]
2 ⇒ P/YR
10.14 [NOM%]
10.14 ⇒ NOM%
10.14
[COMP] [EFF%]
EFF% =
10.40
Calculate I/Y
234 Finance essentials
Display
2.00
DEMONSTRATION PROBLEM 8.4
A bond’s yield to maturity
Problem:
You can purchase a corporate bond from your broker for $1099.50. The bond has a maturity of 6 years
and an annual coupon rate of 5 per cent. Another broker offers you an Australian dollar eurobond (a
dollar‐denominated bond sold overseas) with a yield of 3.17 per cent which is denominated in Australian
dollars and has the same maturity and credit rating as the corporate bond. Which bond should you buy?
Approach:
Solving this problem involves two steps. First, we must calculate the corporate bond’s yield to maturity.
The bond pays coupon interest semiannually, so we have to convert the bond data to semiannual
periods: (1) the number of compounding periods is 12 (6 years × 2 periods per year); and (2) the semiannual coupon payment is $25 [($1000 × 0.05)/2 = $50/2]. Second, we must annualise the yield for the
corporate bond so that we can compare its yield with that of the eurobond.
Solution:
We can solve for the yield to maturity using a financial calculator as follows:
Procedure
Key operation
Enter cash flow data
1000 [FV]
1000 ⇒ FV
12 [N]
12 ⇒ N
−1099.50 [PV]
(−1099.50) ⇒ PV
25 [PMT]
25 ⇒ PMT
[COMP] [I/Y]
I/Y =
Calculate I/Y
Display
1000.00
12.00
−1099.50
25.00
1.5831
The answer, 1.5831 per cent, is the semiannual yield. Since the eurobond’s yield, 3.17 per cent, is
an annualised yield because of that bond’s yearly compounding, we must annualise the yield on the
corporate bond in order to compare the two. (Note that, for annual compounding, the yield to maturity
equals the EAY; for the eurobond, the yield to maturity = 3.17 per cent and the EAY = (1 + Quoted
interest rate/m)m − 1 = (1 + 0.0317/1)1 − 1 = (1 + 0.0317) − 1 = 0.0317, or 3.17 per cent. We annualise
the yield on the corporate bond by computing its effective annual yield:
m
 Quoted interest rate 
EAY =  1+
 − 1

m
2
 0.031661
=  1+
 − 1

2
= (1.015831)2 − 1 = 0.03191, or 3.19%
So the corporate bond is a better deal because of its higher EAY (3.191 per cent > 3.17 per cent). Note
that if we had just annualised the yield on the corporate bond by multiplying the semiannual yield by 2
(1.5831 per cent × 2 = 3.166 per cent) and compared the simple yields for the eurobond and the corporate bond (3.170 per cent > 3.166 per cent), we would have selected the eurobond. This would have
been the wrong economic decision.
Realised yield
The yield to maturity tells the investor the return on a bond if the bond is held to maturity and all the
coupon and principal payments are made as promised. More than likely, however, the investor will sell
the bond before maturity. The realised yield is the return earned on a bond given the cash flows actually
received by the investor. More formally, it is the interest rate at which the present value of the actual
MODULE 8 Bond valuation 235
cash flows generated by the investment equals the bond’s price. The realised yield allows investors to
see the return they have actually earned on their investment. It is the same as the holding period return
discussed in module 7.
Let’s return to the situation involving a 3‐year bond with a 6 per cent coupon rate that was purchased
for $960.99 and had a promised yield of 7.5 per cent. Suppose that interest rates increased sharply and
the price of the bond plummeted. Disgruntled, you sold the bond for $750.79 after having owned it for
2 years. The time line for the realised cash flows looks like this:
0
i=?
−$960.99
1
2
3
$60
$60 + $750.79
Year
$60 + $1000
Relevant cash flows to calculate realised yield
Substituting the cash flows into equation 8.1 yields the following:
PB = $960.99 =
1  $750.79
$60 
1−
2 +

i  (1 + i )  (1 + i )2
We can solve this equation for i either by trial and error or with a financial calculator, as described
earlier. Using a financial calculator, the solution is as follows:
Procedure
Enter cash flow data
Calculate I/Y
Key operation
Display
750.79 [FV]
750.79 ⇒ FV
2 [N]
2⇒N
−960.99 [PV]
(−960.99) ⇒ PV
60 [PMT]
60 ⇒ PMT
60.00
[COMP] [I/Y]
I/Y =
−4.97
750.79
2.00
−960.99
The result is a realised yield of negative 4.97 per cent. The difference between the promised yield of
7.50 per cent and the realised yield of negative 4.97 per cent is 12.47 per cent [7.50 − (−4.97)], which can
be accounted for by the capital loss of $210.20 ($960.99 − $750.79) from the decline in the bond price.
BEFORE YOU GO ON
1. Explain how bond yields are calculated.
2. What is the difference between the yield to maturity and the realised yield?
3. What is the purpose of calculating the effective annual yield (EAY)?
8.5 Interest rate risk
LEARNING OBJECTIVE 8.5 Explain why investors in bonds are subject to interest rate risk and why it is
important to understand the bond theorems.
As discussed previously, the prices of bonds fluctuate with changes in interest rates, giving rise to
interest rate risk. Anyone who owns bonds is subject to interest rate risk because interest rates are
always changing in financial markets. A number of relationships exist between bond prices and changes
in interest rates. These relationships are often called the bond theorems, but they apply to all fixed‐
income securities. It is important that investors and financial managers understand these relationships.
236 Finance essentials
Bond theorems
The bond theorems are the relationships between bond prices and changes in interest rates. Three of
these are now explained.
1. Bond prices are negatively related to interest rate movements. As interest rates decline, the prices of
bonds rise; and as interest rates rise, the prices of bonds decline. As mentioned earlier, this negative
relationship exists because the coupon rate on most bonds is fixed at the time the bonds are issued.
Note that the negative relationship is observed not only for bonds, but also for all other financial
claims that pay a fixed rate of interest to investors.
2. For a given change in interest rates, the prices of long‐term bonds will change more than the prices
of short‐term bonds. In other words, long‐term bonds have greater price volatility than short‐term
bonds. Thus, all other things being equal, long‐term bonds are more risky than short‐term bonds.
Figure 8.2 illustrates the fact that bond values are not equally affected by changes in interest rates.
The figure shows how the prices of a 1‐year bond and a 30‐year bond change with changing interest
rates. As you can see, the long‐term bond has much greater price swings than the short‐term bond.
Why? The answer is that long‐term bonds receive much of their cash flows far into the future and,
because of the time value of money, these cash flows are heavily discounted.
3. For a given change in interest rates, the prices of lower coupon bonds change more than the prices
of higher coupon bonds. Table 8.3 illustrates the relationship between bond price volatility and
coupon rates. The table shows the prices of three 10‐year bonds: a zero coupon bond, a 5 per cent
coupon bond, and a 10 per cent coupon bond. Initially, the bonds are priced to yield 5 per cent
(see column 2). The bonds are then priced at yields of 6 and 4 per cent (see columns 3 and 6). The
dollar price changes for each bond given the appropriate interest rate change are recorded in columns
4 and 7, and the percentage price changes (price volatilities) are shown in columns 5 and 8.
FIGURE 8.2
Relationship between bond price volatility and maturity
$2000
$1900
$1800
$1769
$1700
$1600
30-year bond
$1500
Bond price
$1400
$1295
$1300
The price of the 1-year
bond varies slightly with
changes in interest rates.
$1200
$1100
$1048
$1023
$1000
$900
$800
1-year bond
$700
$1000
$978
$958
$936
$671
The price of the 30-year
bond changes much more
as interest rates change.
$579
$806
$600
$916
$502
$500
$400
5%
7.5%
10%
12.9%
15%
Market interest rate
17.9%
20%
Note: Plots are for a 1-year bond and a 30-year bond with a 10 per cent coupon rate and annual payment.
As shown in column 5, when interest rates increase from 5 to 6 per cent, the zero coupon bond experi­
ences the greatest percentage price decline and the 10 per cent bond experiences the smallest percentage
MODULE 8 Bond valuation 237
price decline. Similar results are shown in column 8 for interest rate decreases. In sum, the lower a bond’s
coupon rate, the greater its price volatility, and hence lower coupon bonds have greater interest rate risk.
The reason for the higher interest rate risk for low coupon bonds is essentially the same as the reason
for the higher interest rate risk for long‐term bonds. The lower a bond’s coupon rate, the greater the
amount of the bond’s cash flow that investors will receive at maturity. This is clearly seen with a zero
coupon bond, where all of the bond’s cash flows are received at maturity. The further into the future
the cash flows will be received, the greater the impact of a change in the discount rate will have on
their present value. Thus, all other things being equal, a given change in interest rates will have a
greater impact on the price of a low coupon bond than a higher coupon bond with the same maturity.
TABLE 8.3
(1)
Coupon
rate
Relationship between bond price volatility and coupon rate
Price change if yield increases
from 5% to 6%
(2)
(3)
(4)
Loss from
Bond price
Bond price
increase in
at 5% yield
at 6%
yield
(5)
% Price
change
Price change if yield decreases
from 5% to 4%
(6)
(7)
(8)
Gain from
Bond price
decrease in
% Price
at 4%
yield
change
0%
$ 613.91
$ 558.39
$55.52
−9.04%
$ 675.56
$ 61.65
10.04%
5%
$1000.00
$ 926.40
$73.60
−7.36%
$1081.11
$ 81.11
8.11%
10%
$1386.09
$1294.40
$91.69
−6.62%
$1486.65
$100.56
7.25%
Note: Calculations are based on a bond with a $1000 face value and a 10‐year maturity and assume annual compounding.
The price changes shown are consistent with the third bond theorem: the smaller the coupon rate,
the greater the percentage price change for a given change in interest rates.
Bond theorem applications
The bond theorems provide important information about bond price behaviour for financial managers.
For example, if you are the financial officer of a company and are investing cash temporarily — say, for
a few days — the last security you want to purchase is a long‐term zero coupon bond. In contrast, if you
are an investor and you expect interest rates to decline, you may well want to invest in long‐term zero
coupon bonds. This is because, as interest rates decline, the price of long‐term zero coupon bonds will
increase more than that of any other type of bond.
Make no mistake, forecasting interest rate movements and investing in long‐term bonds is a very high‐risk
strategy. In addition, since the GFC, government securities no longer carry the risk‐free status of the past.
For example, following the downgrading of Greece’s government bonds in 2011, speculating hedge fund
managers purchased bonds for 36 euro cents for each euro of their face value in anticipation that the Euro­
pean Union and International Monetary Fund would bail out Greece again to prevent another global finan­
cial disaster.5 A few months earlier, as part of Europe’s rescue plan, Greece had agreed to swap a substantial
portion of its existing bonds into new, longer term securities valued at more than 70 euro cents to the euro.
The increase in value reflects the reduced risk (lower interest rates) due to the influx of bailout funds. The
debt swap is expected to cover about 135 billion euros in existing bonds. Hedge funds that bought the bonds
at the distressed prices stand to double their money if their expectations come to fruition. On the other hand,
bondholders who have sold their bonds for the distressed price have crystallised their losses in preference to
taking on the risk that the Greek bonds may go into default should the needed funds not be received (in this
scenario the interest rates would increase, thereby reducing the bond’s value further).
The moral of the story is simple. Long‐term bonds carry substantially more interest rate risk than
short‐term bonds and investors in long‐term bonds need to fully understand the magnitude of the risk
involved. Furthermore, no one can predict interest rate movements consistently, in line with the weak‐
form market efficiency discussed in the module on the financial system.
238 Finance essentials
DECISION‐MAKING EX AMPLE 8.1
Risk taking
Situation:
You work for the chief financial officer (CFO) of
a large manufacturing company where earnings are down substantially for the year. The
CFO’s staff are convinced that interest rates are
going to decline over the next 3 months and
they want to invest in fixed‐income securities
to make as much money as possible for the
company. They recommend investing in one of
the following securities: 90‐day bank accepted
bill, 20‐year corporate bond, or 20‐year zero
coupon Treasury bond.
The CFO asks you to answer the following
questions about the staff plan. (1) What is the
underlying strategy of the proposed plan?
(2) Which investment should be selected if the
plan were to be executed? (3) What should the
CFO do?
Decision:
First, the staff strategy is based on the negative
relationship between interest rates and bond
prices. Thus, if interest rates decline, bond prices will rise and the company will earn a capital gain.
Second, to maximise earnings the CFO should select bonds that will have the largest price swing for
a given change in interest rates. Bond theorems 2 and 3 suggest that, for a given change in interest
rates, low coupon, long‐term bonds will have the largest price swing. Thus, the CFO should invest in the
20‐year zero coupon Treasury bond. With respect to the plan’s merits, the intentions are good but the
investment plan is pure folly. Generating ‘earnings’ from risky financial investments is not the company’s
line of business nor one of its core competencies. As discussed in module 1, the CFO’s primary investment function is to invest idle cash in safe investments such as money market instruments that have
very low default and interest rate risks.
BEFORE YOU GO ON
1. What is interest rate risk?
2. Explain why long‐term bonds with zero coupons are riskier than short‐term bonds that pay coupon
interest.
8.6 The structure of interest rates
LEARNING OBJECTIVE 8.6 Discuss the concept of default risk and know how to calculate a default
risk premium.
In module 4 we discussed the economic forces that determine the level of interest rates, and so far in this
module we have discussed how to price various types of debt securities. Armed with this knowledge, we
now explore why, on the same day, different businesses have different borrowing costs. As you will see,
market analysts have identified four risk characteristics of debt instruments that are responsible for most
of the differences in company borrowing costs: the security’s marketability, call provision, default risk,
and term to maturity.
MODULE 8 Bond valuation 239
Marketability
The interest rate, or yield, on a security varies with its degree of marketability. Recall from module 2
that marketability refers to the ease with which an investor can sell a security quickly at a low trans­
action cost. The transaction costs include all fees and the cost of searching for information. The lower
the costs, the greater a security’s marketability. Because investors prefer marketable securities, they must
be paid a premium to purchase similar securities that are less marketable. The difference in interest rates,
or yields, between a marketable security (ihigh mkt) and a less marketable security (ilow mkt) is known as the
marketability risk premium (MRP):
MRP = ilow mkt − ihigh mkt > 0
Unlike the US market, where US Treasury bills have the largest and most active secondary market and
are considered the most marketable of all securities, bank‐accepted bills have the largest and most active
secondary market in Australia. (The Australian T‐note market was non‐existent from October 2003 to
March 2009 as the Commonwealth Government ran a budget surplus and hence had no need to raise
short‐term funding by issuing T‐notes. The size of the Australian market for bank certificates of deposit,
bank bills and commercial paper was $263.5 billion at June 2016; at the same date the T‐note market
was $23.8 billion.6) Investors can sell virtually any dollar amount of these bank‐accepted securities
quickly without disrupting the market. Similarly, the securities of many well‐known businesses enjoy
a high degree of marketability, especially companies whose securities are traded on the major stock
exchanges. For thousands of other companies whose securities are not traded actively, marketability can
pose a problem and can raise borrowing costs substantially.
Call provision
Most corporate bonds contain a call provision in their contract. As discussed above, call provision gives
the company issuing the bonds the option to purchase the bond from an investor at a predetermined
price (the call price), and the investor must sell the bond at that price. Bonds with a call provision sell
at higher market yields than comparable non‐callable bonds. Investors require the higher yield because
call provisions work to the benefit of the borrower and to the detriment of the investor. For example, if
interest rates decline after the bond is issued, the issuer can call (retire) the bonds at the call price and
refinance with a new bond issued at the lower prevailing market rate of interest. The issuing company
will be delighted because the refinancing has lowered its interest expense, but investors will be less
gleeful. When bonds are called, investors suffer a financial loss because they are forced to surrender their
high‐yielding bonds and reinvest their funds at the lower prevailing market rate of interest.
The difference in interest rates between a callable bond and a comparable non‐callable bond is called
the call interest premium (CIP) and it can be defined as follows:
CIP = icall − incall > 0
where CIP is the call interest premium, icall is the yield on a callable bond and incall is the yield on a
non‐callable bond of the same maturity and default risk. Thus, the more likely a bond is to be called,
the higher the CIP and the higher the bond’s market yield. Bonds issued during periods when interest
rates are high are likely to be called when interest rates decline and, as a result, these bonds have a high
CIP. Conversely, bonds sold when interest rates are relatively low are less likely to be called and have a
smaller CIP.
Default risk
Recall that any debt, such as a bond or a bank loan, is a formal promise by the borrower to make peri­
odic interest payments and pay the principal as specified in the debt contract. Failure on the borrower’s
240 Finance essentials
part to meet any condition of the debt or loan contract constitutes default. Recall also from module 2 that
default risk refers to the possibility that the lender may not receive payments as promised.
Default risk premium
Because investors are risk averse, they must be paid a premium to purchase a security that exposes them
to default risk. The size of the premium has two components: (1) compensation for the expected loss
if a default occurs; and (2) compensation for bearing the risk that a default could occur. The degree of
default risk that a security possesses can be measured as the difference between the interest rate on a
risky security and the interest rate on a default‐free security — all other factors, such as maturity and
marketability, held constant. The default risk premium (DRP) can thus be defined as follows:
DRP = idr − irf
where idr is the interest rate (yield) on a security that has default risk and irf is the interest rate (yield)
on a risk‐free security. In Australia, Commonwealth Government Treasury securities are the best proxy
measure for the risk‐free rate. The larger the default risk premium, the higher the probability of default
and the higher the security’s market yield.
Bond ratings
Many investors, especially individuals and smaller businesses, do not have the expertise to formulate
the probabilities of default themselves, so they must rely on credit rating agencies to provide this infor­
mation. The two most prominent credit rating agencies are Moody’s Investors Service (Moody’s) and
Standard & Poor’s (S&P). Both rank bonds in order of their expected probability of default and publish
these ratings as letter grades. The rating schemes used are shown in table 8.4. The highest grade bonds
— those with the lowest default risk — are rated Aaa (or AAA). The default risk premium on corporate
bonds increases as the bond rating becomes lower.
TABLE 8.4
Corporate bond rating systems
Moody’s
Standard &
Poor’s
Default risk
premium
Regulatory
designation
Best quality, smallest degree of risk
Aaa
AAA
Lowest
High quality, slightly more long‐term
risk than top rating
Aa
AA
Investment
grade
Upper‐medium grade, possible
impairment in the future
A
A
Medium grade, lacks outstanding
investment characteristics
Baa
BBB
Speculative, protection may be very
moderate
Ba
BB
Very speculative, may have small
assurance of interest and principal
payments
B
B
Issues in poor standing, may be in
default
Caa
CCC
Speculative in a high degree, with
marked shortcomings
Ca
CC
Lowest quality, poor prospects of
attaining real investment standing
C
C
Explanation
Noninvestment
grade
Highest
MODULE 8 Bond valuation 241
Table 8.4 also shows that bonds in the top four rating categories are called investment‐grade bonds.
Moody’s calls bonds rated below Baa (or BBB) noninvestment‐grade bonds, but most financial market
participants refer to them as speculative‐grade bonds, high‐yield bonds or junk bonds. The distinction
between investment‐grade and noninvestment‐grade bonds is important, as most financial institutions,
such as banks and insurance companies, and trustees of superannuation funds and other managed invest­
ment companies typically will not invest in bond issues of noninvestment grade. This is usually stated in
their product disclosure statements. Likewise, government agencies usually specify that any monies to
be invested into bonds are to be invested in bonds of investment grade.
Table 8.5 shows the default risk premiums associated with selected 10‐year bonds with­
investment‐grade bond ratings in October 2016. The premiums measure the difference between yields
on Australian government securities — which, as mentioned, are the proxy for the risk‐free rate — and
yields on riskier securities of similar maturity. (Default risk premiums are typically quoted in terms
of basis points: a basis point is simply 1/100 of 1 per cent. Thus 50 basis points equal 0.5 per cent,
100 basis points equal 1.0 per cent and so on.) The 159 basis‐point (1.59 per cent) default risk premium
on A‐rated corporate bonds represents the market consensus of the amount for which investors must be
compensated to induce them to purchase typical A‐rated bonds instead of a risk‐free security. As credit
quality declines from A to BBB, the default risk premiums increase from 159 basis points to 223 basis
points.
TABLE 8.5
Default risk premiums for selected bond ratings, October 2016
Security yield (%)
Default risk spread
over bonds issued by
Australian government (%)
A
3.94
1.59
BBB
4.58
2.23
Security: Standard & Poor’s
credit rating
BEFORE YOU GO ON
1. What are default risk premiums and what do they measure?
2. Describe the two most prominent bond rating systems.
8.7 The term structure of interest rates
LEARNING OBJECTIVE 8.7 Describe the factors that determine the level and shape of the yield curve.
The term to maturity of a loan is the length of time until the principal amount is payable. The relation­
ship between yield to maturity and term to maturity is known as the term structure of interest rates.
We can view the term structure visually by plotting the yield curve, a graph with the term to maturity
on the horizontal axis and the yield to maturity on the vertical axis. Yield curves show graphically how
market yields vary as term to maturity changes.
For yield curves to be meaningful, the securities used to plot the curves should be similar in all
features (for example, default risk and marketability) except for maturity. We do not want to confound
the relationship between yield and term to maturity with other factors that also affect interest rates. We
can best see the term structure relationship by examining yields on Australian government securities,
because they have similar default risk (none) and marketability.
Figure 8.3 shows data and yield curve plots for Australian government securities from 2008 to
2016. As you can see, the shape of the yield curve is not constant over time. As the general level of
interest rises and falls, the yield curve shifts up and down and has different slopes. We can observe
242 Finance essentials
three basic shapes (slopes) of yield curves in the marketplace. First is the ascending or upward‐
sloping yield curve (June 2010, June 2014 and June 2016), which is the yield curve most commonly
observed. Descending or downward‐sloping yield curves (June 2008) appear periodically and are char­
acterised by short‐term rates (e.g. 6‐month yield) exceeding long‐term rates (e.g. 5‐ or 10‐year rates).
Downward‐sloping yield curves often appear before the beginning of a recession. Flat yield curves are
not common, but do occur from time to time. The yield curve for June 2012 is relatively flat where
short‐term (6 month rates) and long‐term (10‐year rates) are similar, but it is downward‐sloping for
shorter term maturities (1‐ to 5‐year rates).
Australian zero coupon yield curve at five different points in time7
FIGURE 8.3
8
The June 2008 yield curve is downward-sloping, which means that
shorter term security yields are higher than longer term security yields.
7
Interest rates %
6
June 2008
June 2010
June 2012
June 2014
The June 2012 yield curve is downward-sloping for bonds with five or less years
to maturity, but upward-sloping for bonds with more than five years to maturity.
5
June 2016
4
3
2
1
0
The other three yield curves are upward-sloping, which means that yields are higher for
longer term securities than for shorter term securities. This is the more common situation.
0
1
2
3
4
5
6
Years to maturity
7
8
9
10
Time to maturity
June 2008
June 2010
Interest rate (%)
June 2012
June 2014
June 2016
6 months
7.35
4.49
3.08
2.47
1.56
1 year
7.26
4.47
2.77
2.44
1.50
5 years
6.44
4.70
2.56
3.02
1.69
10 years
6.29
5.11
3.10
3.60
2.03
Three factors affect the level and the shape (the slope) of the yield curve over time: the real rate of
interest, the expected rate of inflation, and interest rate risk.
The real rate of interest is the base interest rate in the economy and is determined by individuals’
time preference for consumption; that is, it tells us how much individuals must be paid in order to forgo
spending their money today. The real rate of interest varies with the business cycle, with the highest rates
seen at the end of a period of business expansion and the lowest at the bottom of a recession. The real
rate is not affected by the term to maturity. Thus, the real rate of interest affects the level of interest rates
but not the shape of the yield curve.
The expected rate of inflation can influence the shape of the yield curve. If investors believe that
inflation will increase in the future, the yield curve will be upward‐sloping because long‐term interest
rates will contain a larger inflation premium than do short‐term interest rates. This inflation premium is
the market’s best estimate of future inflation. Conversely, if investors believe inflation will decrease in
the future, the prevailing yield will be downward‐sloping.
MODULE 8 Bond valuation 243
Finally, the presence of interest rate risk affects the shape of the yield curve. As discussed earlier,
long‐term bonds have greater price volatility than short‐term bonds. Because investors are aware of this
risk, they demand compensation in the form of an interest rate premium. It follows that the longer the
maturity of a security, the greater its interest rate risk and so the higher the interest rate. It is impor­
tant to note that the interest rate risk premium always adds an upward bias to the slope of the yield
curve.
The shape, or slope, of the yield curve is not constant over time. The figure shows three shapes:
(1) the curves for June 2010, June 2014 and June 2016 are upward‐sloping, the shape most commonly
observed; (2) the curve for June 2008 is downward‐sloping; and (3) the curve for June 2012 is­
downward‐sloping for bonds with 5 years or less to maturity, but upward‐sloping for bonds with more
than 5 years to maturity.
In sum, the cumulative effect of three economic factors determines the level and shape of the yield
curve: (1) the cyclical movements of the real rate of interest affect the level of the yield curve; (2) the
expected rate of inflation can bias the slope of the yield curve either positively or negatively, depending
on market expectations of inflation; and (3) interest rate risk always provides an upward bias to the slope
of the yield curve.
BEFORE YOU GO ON
1. What are the key factors that most affect the level and shape of the yield curve?
244 Finance essentials
SUMMARY
8.1 Explain what Commonwealth Government Securities (CGS) and semi‐government
securities (semis) are, where they are issued and their relative liquidity.
CGS are Treasury bonds and T‐notes, issued by the Australian Office of Financial Management.
Semis are bonds issued by state and territory borrowing authorities backed by their respective govern­
ments. The amount of CGS on issue has been declining from 1996. However, this trend is now
reversing as the federal government is expected to run budgetary deficits for the next several years and
needs to fund these by issuing new CGS. The Commonwealth Government has decided to support
the Treasury bond futures market by maintaining current levels of securities in the market. Treasury
bonds are important instruments because they carry no default risk and so are useful in managing
interest rate risk across the economy. Semis are often issued offshore and can be exchanged for dom­
estic issues. Although they are not as liquid as CGS domestically, their ability to be exchanged raises
their liquidity offshore and makes them more attractive to investors. Dissimilarly to CGS, semis are
issued through dealer panels and not open tender.
8.2 Describe the features of corporate bonds and differentiate between the three types of
corporate bonds.
Corporate bonds are debt contracts requiring borrowers to make periodic payments of interest and
to repay principal at the maturity date. Corporate bonds can be either unsecured notes or deben­
tures. An unsecured note is a bond that has no specified security attached as collateral in the case
of default. Debentures come in two forms, fixed and floating. Corporate bonds are usually issued in
denominations of $1000 and pay coupon interest semiannually. Corporate debt can be sold in the
domestic bond market or in the Australian dollar eurobond market.
A coupon bond has fixed regular coupon payments over the life of the bond and the entire prin­
cipal is repaid at maturity. A zero coupon bond pays all interest and all principal at maturity. Since
there are no payments before maturity, zero coupon bonds are issued at prices well below their face
value. Convertible bonds can be exchanged for ordinary shares at a predetermined ratio.
8.3 Explain how to calculate the value of a bond and why bond prices vary negatively with interest
rate movements.
The value of a bond is equal to the present value of the future cash flows (coupons and prin­
cipal repayment) discounted at the market rate of interest for bonds with similar characteristics.
Bond prices vary negatively with interest rates, because the coupon rate on most bonds is fixed
at the time the bond is issued. Therefore, as interest rates go up, investors seek other forms of
investment that will allow them to take advantage of the higher returns. Because a bond’s coupon
payments are fixed, the only way its yield can be adjusted to the current market rate of interest is
to reduce the bond’s price. Similarly, when interest rates are declining, the yield on fixed‐income
securities will be higher relative to yield on similar securities price to market; the favourable yield
will increase the demand for these securities, increasing their price and lowering their yield to
the market yield.
8.4 Distinguish between a bond’s coupon rate, yield to maturity and effective annual yield, and be
able to calculate their values.
A bond’s coupon rate is the stated interest rate on the bond when it is issued. Australian bonds typi­
cally pay interest semiannually, whereas European bonds pay once a year. The yield to maturity is
the expected return on a bond if it is held until its maturity date. The effective annual yield is the
yield that an investor actually earns in 1 year, adjusting for the effects of compounding. If the bond
pays coupon payments more often than annually, the effective annual yield will be higher than the
simple annual yield because of compounding. Work through demonstration problems 8.2, 8.3 and
8.4 to master these calculations.
MODULE 8 Bond valuation 245
8.5 Explain why investors in bonds are subject to interest rate risk and why it is important to
understand the bond theorems.
Because interest rates are always changing in the market, all investors who hold bonds are subject
to interest rate risk. Interest rate risk is uncertainty about future bond values caused by fluctuations
in interest rates. Three of the most important bond theorems can be summarised as follows.
1. Bond prices are negatively related to interest rate movements.
2. For a given change in interest rates, the prices of long‐term bonds will change more than the
prices of short‐term bonds.
3. For a given change in interest rates, the prices of lower coupon bonds will change more than the
prices of higher coupon bonds.
Understanding these relationships is important because it helps investors to better understand why
bond prices change and, thus, to make better decisions regarding the purchase or sale of bonds and
other fixed‐income securities.
8.6 Discuss the concept of default risk and know how to calculate a default risk premium.
Default risk is the risk that an issuer will be unable to pay its debt obligation. Since investors are risk
averse, they must be paid a premium to purchase a security that exposes them to default risk. The
default risk premium has two components: (1) compensation for the expected loss if a default occurs;
and (2) compensation for bearing the risk that a default could occur. All factors being held constant, the
degree of default risk that a security possesses can be measured as the difference between the interest
rate on a risky security and the interest rate on a default‐free security. The default risk is also reflected
in the company’s bond rating. The highest grade bonds, those with the lowest default risk, are rated Aaa
(or AAA). The default risk premium on corporate bonds increases as the bond rating becomes lower.
8.7 Describe the factors that determine the level and shape of the yield curve.
The level and shape of the yield curve are determined by three factors: (1) the real rate of interest;
(2) the expected rate of inflation; and (3) interest rate risk. The real rate of interest is the base
interest rate in the economy and varies with the business cycle. The real rate of interest affects only
the level of the yield curve and not its shape. The expected rate of inflation does affect the shape
of the yield curve. If investors believe inflation will increase in the future, for example, the curve
will be upward sloping, as long‐term rates will contain a larger inflation premium than short‐term
rates. Finally, interest rate risk, which increases with a security’s maturity, adds an upward bias to
the slope of the yield curve.
SUMMARY OF KEY EQUATIONS
Equation
Description
Formula
8.1
Price of a bond
PB =
1 
C
Fn
1−
+
i  (1 + i )n  (1 + i )n
8.2
Price of a bond making multiple payments
each year
PB =
1
C/ m
Fmn

1−
mn +
i / m  (1 + i / m)  (1 + i / m)mn
8.3
Price of a zero coupon bond
PB =
Fn
(1 + i )n
8.4
Effective annual yield
Quoted interest rate 

EAY =  1 +
 − 1

m
m
246 Finance essentials
KEY TERMS
coupon payments the periodic interest payments in a bond contract
coupon rate the annual coupon payment of a bond divided by the bond’s face value
credit‐wrapped bonds bonds with financial guarantees
dealer panel a small set of bond dealers, mostly comprising banks, that agree to buy semis from state
governments either in closed auctions (where stock is assigned to the best bids) or through agreeing
to buy a given amount at a given price
debentures debt instruments usually issued by corporate borrowers; they may be unsecured and hence
rely on the creditworthiness of the issuer, or secured by charges over the corporate borrower’s assets
discount bonds bonds that sell at below par (face) value
effective annual yield (EAY) the annual yield that takes compounding into account; another name for
the effective annual interest rate (EAR)
face value or par value the amount on which interest is calculated and that is owed to the bondholder
when a bond reaches maturity
financial guarantees unconditional offers from a private sector guarantor to cover the payment of
principal and interest to investors in debt securities in the event of a default
fixed‐income securities debt instruments that pay interest in amounts that are fixed for the life of the
contract
hybrid securities financial products with characteristics of both debt and equity
interest rate risk risk that changes in interest rates will cause an asset’s price and realised yield to
differ from the purchase price and initially expected yield
interest withholding tax (IWT) a 10 per cent tax levied on interest payments from bonds issued by
Australian companies that are held by offshore investors
investment‐grade bonds bonds with low risk of default that are rated Baa (BBB) or above
noninvestment‐grade bonds bonds rated below Baa (or BBB) by rating agencies; often called
speculative‐grade bonds, high‐yield bonds or junk bonds
opportunity cost the return from the best alternative investment with similar risk that an investor
sacrifices when they make a certain investment
par‐value bonds bonds that sell at par value, or face value; whenever a bond’s coupon rate is equal to
the market rate of interest on similar bonds, the bond will sell at par
premium bonds bonds that sell at above par (face) value
realised yield for a bond, the interest rate at which the present value of the actual cash flows generated
by a bond equals the bond’s price
senior debt debt that has priority in the event of default
sinking fund a provision that requires that the bond issuer provide funds to a trustee to retire a specific
dollar amount (face amount) of bonds each year
subordinated (junior) debt debt that ranks behind senior debt in the event of default
term structure of interest rates the relationship between yield and term to maturity
Treasury indexed bonds (TIBs) Commonwealth‐issued bonds that adjust for inflation
unsecured note a bond for which there is no underlying specified security as collateral in the case of
default
yield curve a graph representing the term structure of interest rates, with term to maturity on the
horizontal axis and yield on the vertical axis
yield to maturity for a bond, the discount rate that makes the present value of the coupon and
principal payments equal to the price of the bond
MODULE 8 Bond valuation 247
ENDNOTES
1.
2.
3.
4.
5.
6.
7.
Reserve Bank of Australia 2016, Statistics, table D4, www.rba.gov.au.
NZ Debt Management Office 2016, ‘Government securities on issue’, 31 October, www.nzdmo.govt.nz/publications/data.
ibid.
Reserve Bank of Australia 2016, Statistics, table F2, www.rba.gov.au.
Thomas, L 2011, ‘Greek bonds lure some, despite risk’, New York Times, 28 September, www.nytimes.com.
Reserve Bank of Australia 2016, tables F7, D4.
Reserve Bank of Australia 2016, Statistical table F17, www.rba.gov.au.
ACKNOWLEDGEMENTS
Photo: © AlexRaths / iStockphoto
Photo: © DNY59 / Getty Images
Photo: © Morganka / Shutterstock.com
Photo: © vectorfusionart / Shutterstock.com
Table 8.1: © Australian Office of Financial Management
Table 8.2 © Reserve Bank of Australia
Figure 8.3: © Reserve Bank of Australia
248 Finance essentials
MODULE 9
Share valuation
LEA RNIN G OBJE CTIVE S
After studying this module, you should be able to:
9.1 describe the four types of secondary markets
9.2 explain why many financial analysts treat preference shares as a special type of bond rather than an
equity security
9.3 describe how the general dividend valuation model values a share
9.4 discuss the assumptions necessary to make the general dividend valuation model easier to use, and
use the model to calculate the value of a company’s ordinary shares
9.5 explain how valuing preference shares with a stated maturity differs from valuing preference shares with
no maturity date, and calculate the price of a preference share under both conditions.
Module preview
This module focuses on equity securities and how they are valued. We first examine the fundamental
factors that determine a share’s value, then we discuss several valuation models. These models tell us what
a share’s price should be. We can compare our estimates from such models with actual market prices.
FIGURE 9.1
All Ordinaries 5‐year trend chart
All ordinaries
ˆAORD
6 Dec. 2016
6000
5800
5600
5400
5200
5000
4800
4600
4400
4200
Jan-12
Jan-13
Jan-14
Jan-15
Jan-16
Volume
4000
3.0
1.0
Billions
2.0
0.0
Sources: Adapted from Dow Jones and New York Stock Exchange.
Why are share‐valuation formulas important for you to study in a corporate finance course? First, company management may want to know whether a company’s shares are undervalued or overvalued. For
example, if the shares are undervalued, management may want to buy back shares to reissue in the future
or postpone an equity offering until the share prices increase. Second, as we mentioned in module 1,
the overarching goal of financial management is to maximise the current value of the company’s
shares. To make investment or financing decisions that increase shareholder value, you must understand
the fundamental factors that determine the market value of the company’s shares.
We begin this module with a discussion of the secondary markets for equity securities and their efficiency,
explain how to read share market price listings in the financial news sources, and introduce the types of
equity securities that companies typically issue. Then we develop a general valuation model and demonstrate
that the value of a share is the present value of all expected future cash dividends. We use some simplifying
assumptions about dividend payments to implement this valuation model. These assumptions correspond to
actual practice and allow us to develop several specific valuation models that are theoretically sound.
9.1 The market for shares
LEARNING OBJECTIVE 9.1 Describe the four types of secondary markets.
Equity securities are certificates of ownership of a company. Equities are the most visible securities
on the financial landscape. At the end of November 2016, more than $1.69 trillion of public equity
securities were outstanding in Australia alone.1 Every day Australians eagerly track the ups and downs
250 Finance essentials
of the share market. Most people believe that the performance of the share market is an important
barometer of the country’s economic health. Also fuelling interest is the large number of people (36 per cent
of the adult population) who own equity securities either directly or indirectly.2
Secondary markets
Recall from module 2 that the share market consists of primary and secondary markets. In the primary
market, companies sell new shares to investors in order to raise money. In secondary markets, outstanding shares are bought and sold among investors. We will discuss the primary markets for bonds and
equity securities in another module. Our focus here is on secondary markets.
Any trade of a security after its primary offering is said to be a secondary market transaction. Most
secondary market transactions do not directly affect the company that issues the securities. For example,
when an investor buys 100 shares in Woolworths Limited on the Australian Securities Exchange (ASX),
the exchange of money is only between the investors buying and selling the securities; Woolworths
Limited’s cash position is not affected.
The presence of a secondary market does, however, affect the issuer indirectly. Simply put, investors
will pay a higher price for primary securities that have an active secondary market because of the marketability this secondary market provides. As a result, companies whose securities trade on a secondary
market can sell their new debt or equity issues at a lower funding cost than can companies selling similar
securities that have no secondary market.
Secondary markets and their efficiency
In Australia, virtually all secondary equity market transactions take place on the ASX. In terms of total
volume of activity and total equity value of the companies listed, the ASX is the world’s 14th largest
share market as at September 2016.3 Of course the world’s largest equity market by market value is the
New York Stock Exchange (NYSE).
MODULE 9 Share valuation 251
The role of these and other secondary markets is to bring buyers and sellers together. Ideally we want
security markets to be as efficient as possible. Markets are efficient when the current market prices of
securities traded reflect all available information relevant to the security. If this is the case, security prices
will be near or at their true value. The more efficient the market, the more likely this is to be the case.
There are four types of secondary markets and each type differs according to the amount of price
information available to investors, which in turn affects the efficiency of that market. We discuss the four
types of secondary markets — direct search, brokered, dealer and auction — in order of their increasing
market efficiency.
Direct search
The secondary markets furthest from the ideal of complete availability of price information are those in
which buyers and sellers must seek each other out directly. In these markets, individuals bear the full
cost of locating and negotiating, and it is typically too costly for them to conduct a thorough search in
order to locate the best price. Securities that sell in direct search markets are usually bought and sold
so infrequently that few third parties, such as brokers or dealers, find it profitable enough to serve these
markets. In these markets, sellers often rely on word‐of‐mouth communication to find interested buyers.
The ordinary shares of small private companies are a good example of a security that trades in this manner.
Brokered
When trading in a security issue becomes sufficiently heavy, brokers find it profitable to offer specialised
search services to market participants. Brokers bring buyers and sellers together in order to earn a fee,
called a commission. To provide investors with an incentive to hire them, brokers may charge a commission that is less than the cost of a direct search. Brokers are not passive agents, but aggressively seek
out buyers or sellers and try to negotiate acceptable transaction prices for their clients. The presence of
active brokers increases market efficiency because brokers are in frequent contact with market participants and so are likely to know what constitutes a ‘fair’ price for a security. The ASX is best described
as a quote‐driven broker market.
Dealer
If the trading in a given security has sufficient volume, market efficiency is improved when there
is someone in the marketplace to provide continuous bidding (selling or buying) for the security. Dealers
provide this service by holding inventories of securities which they own, and then buying new securities
and selling from their inventories in order to earn a profit. Unlike brokers, dealers have their own capital at
risk. Dealers earn their profits from the spread on the securities they trade — the difference between their
bid price (the price at which they buy) and their offer (ask) price (the price at which they sell). NASDAQ
is the best known example of a dealer market.
The advantage of a dealer market over a brokered market is that brokers cannot guarantee that an
order to buy or sell will be executed promptly. This uncertainty about the speed of execution creates
price risk. During the time a broker is trying to sell a security, its price may change and their client could
suffer a loss. A dealer market eliminates the need for time‐consuming searches for a fair deal because
buying and selling take place immediately from the dealer’s inventory of securities.
Dealers make markets in securities using computer networks to quote prices at which they are willing
to buy or sell a particular security. These networks enable dealers to electronically survey the prices
quoted by different dealers to help establish their sense of a fair price and to trade.
Auction
In an auction market, buyers and sellers confront each other directly and bargain over price. Participants
can communicate verbally if they are located in the same place, or the information can be transmitted
electronically. The ASX did originally operate as an ‘open out‐cry’ market, but the trading floors were
phased out in 1990 following the introduction of the Stock Exchange Automatic Trading System (SEATS)
in 1987.4 The NYSE is the best‐known example of an auction market. In the NYSE, the auction for a
252 Finance essentials
security takes place at a specific location on the floor of the exchange, called a post. The auctioneer in this
case is the specialist, who is designated by the exchange to represent orders placed by public customers.
Specialists, as the name implies, handle a small set of securities and are also allowed to act as dealers.
Thus, in reality, the NYSE is an auction market that also has some features of a dealer market. In recent
years, the NYSE has been moving towards electronic trading with the SuperDOT system (DOT stands
for ‘designated order turnaround’), which allows orders to be transmitted electronically to specialists.
Reading the share market listings
The Australian Financial Review and other financial news sources provide share listings for the ASX
as well as other security market information. Table 9.1 shows a small section of a listing from the
Australian Financial Review market wrap for the ASX.
TABLE 9.1
(1)
52 Wk
High
(2)
52 Wk
Low
ASX 100 leading industrial shares5
(3)
Company Name
(4)
Last
Sale
(5)
+ or
− (¢)
(6)
(7)
(8)
(9)
(10)
Quote Quote Div ¢ per
Div Tms
Buy
Sell
Share
Franking
Cov
(11)
NTA
(12)
(13)
Div Yld P/E
%
ratio
11.00
8.19
9.04
−6.0   9.02   9.05
42
p
0.85
1.76
4.65
25.4
93.97
62.41
Cochlear
90.24
−169.0 90.08 90.24
217
p
1.17
1.58
2.40
35.7
96.69
73.57
C’wlth Bank of Aust
86.35
26.0 86.30 86.38
416
f
1.33
24.46
4.82
15.6
13.56
10.875
Computershare
11.91
−19.0 11.89 11.91
30
p
0.78
−2.69
2.52
51.0
1.34
0.74
7.18
10.4
1.76
4.14
2.78
20.4
2.27
5.52
1.45
30.4
1.24
2.17
5.52
14.5
1.20
0.935
Coca‐Cola Amatil
Cromwell Property stp
1.095
1.09 1.095
16.47
11.66
Crown Resorts
13.30
−18.0 13.26 13.30
96.60
63.77
CSL
96.17
152.0 96.17 96.32
4.43
3.15
CSR
3.62
8.25
1.10
DEXUS Prop Grp stp
41.64
20.08
5.22
3.93
Downer EDI
2.589
2.14
DUET Grp forus
6.88
5.11
5.07
3.08
1.11
3.19
48.20
31.41
37
p
139.23
10.0
3.61
3.63
20
−9.0
7.61
7.64
41.04
1.03
6.47
5.37
18.1
−57.0 38.63 38.67
43.6
f
1.44
−0.01
1.13
61.6
4.49
−11.0
4.47
4.49
24
f
1.97
2.54
5.35
9.5
2.15
−1.0
2.14
2.15
17.5
0.18
1.37
8.14
66.6
Dulux Group
5.82
−10.0
5.81
5.82
21.5
f
1.15
0.25
3.69
23.6
Echo Entertainment
4.81
−9.0
4.80
4.83
9
f
2.12
1.87
25.2
0.725
Fairfax Media
0.83
−1.5   0.825 0.835
4
f
0.60
0.29
4.82
34.6
2.48
Federation Cntres stp
2.96
2.94
16.9
1.81
2.44
5.71
9.7
f
1.28
7.66
4.29
18.1
f
3.14
Domino’s Pizza
7.64
7.86
38.64
2.96
−75.0 35.40 35.44
Flight Centre Travel
35.40
4.131
2.905
Genworth Mortg Ins
3.57
7.0
3.55
3.57
152
15.9
6.70
5.045
Goodman Grp stp
6.46
−4.0
6.44
6.46
22.2
4.89
3.77
GPT Grp stp
4.46
−2.0
4.45
4.46
21.7
10.36
7.83
GrainCorp
8.64
1.0
8.61
8.65
12.5
f
4.45
7.2
2.63
3.15
3.44
11.1
1.76
3.94
4.87
11.7
1.07
5.63
1.45
64.5
Source: © Fairfax Syndications.
In the table, go to the entry for Domino’s Pizza, which is highlighted. Domino’s is the largest worldwide franchise pizza‐delivery company. Columns 1 and 2 show the highest price ($41.64) and the lowest
price ($20.08) over the past 52 weeks. Column 4 shows that Domino’s last sale price before the day’s
closing was $38.64. Column 6 indicates the highest price bid for a share of Domino’s at closing, while
column 7 shows the lowest sell price at which a Domino’s share is offered for sale at closing.
Column 8 shows Domino’s annual cash dividend per share paid to shareholders, which is $0.436.
Although the annual dividend is shown, most Australian‐listed companies including Domino’s pay
MODULE 9 Share valuation 253
dividends twice yearly. In Column 9 you will see that some companies have an ‘f’ or ‘p’ noted next to their
dividend. These symbols indicate whether the company has already paid tax on the dividend: ‘f’ denotes
that the dividend is 100% franked, which means the company has fully paid tax on the dividend; ‘p’ denotes
that the dividend is partly franked; and a blank space in this column indicates that the dividend is unfranked,
or no tax has been paid on the dividend. Dividend imputation is covered further in coming modules.
Column 10 indicates the dividend times covered ratio; that is, the number of times the company’s profit
covers the company’s latest dividend. In this case, Domino’s profit per share covers its dividend 1.44 times.
Column 11 shows Domino’s net tangible assets (NTA) per share ratio. This is the total assets of a
company less its total liabilities, not including intangible items such as goodwill. In Domino’s case, the
NTA ratio is –0.01. Column 12 shows Domino’s dividend yield, which is 1.13 per cent. The dividend
yield is calculated by dividing the annual dividend payout by the current share price. For Domino’s this
calculation is 0.436/38.64 = 0.0113 or 1.13 per cent. If you scan the dividend yields, you will note that
most of the 100 leading Australian industrial companies pay dividends and these are generally fully
franked. As you will learn, most companies under dividend imputation pay a fully franked dividend. For
companies that do not pay a dividend, investors are still willing to purchase shares in those companies as
long as they believe that they will receive dividends and/or a higher share price in the future.
Finally, column 13 indicates Domino’s price–earnings (P/E) ratio, which is the current price per share
divided by the earnings per share. For Domino’s, the P/E ratio is 61.6 times, which is very high. This
tells us that investors are willing to pay a price per share 61.6 times the earning per share for Domino’s
shares. To justify a high P/E ratio, investors must believe that the company has good prospects for future
earnings growth. We will have more to say about the P/E ratio in later modules.
BEFORE YOU GO ON
1. How do dealers differ from brokers?
2. What does the price–earnings (P/E) ratio tell us?
9.2 Ordinary and preference shares
LEARNING OBJECTIVE 9.2 Explain why many financial analysts treat preference shares as a special
type of bond rather than an equity security.
Equity securities take several forms. The most common type of equity security is ordinary shares.
Ordinary shares represent the basic ownership claim in a company. One of the basic rights of the owners
is to vote on all important matters that affect the life of the company, such as election of the board of
directors or a proposed merger or acquisition. Owners of ordinary shares are not guaranteed any dividend payments and have the lowest priority claim on the company’s assets in the event of insolvency.
Legally, ordinary shareholders enjoy limited liability; that is, their losses are limited to the original
amount of their investment in the company and their personal assets cannot be taken to satisfy the obligations of the company. Finally, ordinary shares are perpetuities in the sense that they have no maturity.
Ordinary shares can be retired only if management buys them in the open market from investors or if the
company is liquidated, in which case its assets are sold, as described in the next section.
Like ordinary shares, preference shares represent an ownership interest in the company but, as the
name implies, preference shares receive preferential treatment over ordinary shares. Specifically, preference shareholders take precedence over ordinary shareholders in the payment of dividends and in the
distribution of corporate assets in the event of liquidation. Unlike the interest payments on bonds, which
are contractual obligations, preference share dividends are declared by the board of directors and, if a
dividend is not paid, the lack of payment is not legally viewed as a default.
Preference shares are legally a form of equity. Thus, preference share dividends are paid by the
issuer with after‐tax dollars. Even though preference shares are an equity security, the owners have no
254 Finance essentials
voting privileges unless the preference shares are convertible into ordinary shares. Preference shares are
generally viewed as perpetuities because they have no maturity. However, most preference shares are not
true perpetuities because their share contracts often contain call provisions and can even include sinking
fund provisions, which require management to retire a certain percentage of the share issue annually
until the entire issue is retired.
Preference shares: debt or equity?
One of the ongoing debates in finance is whether preference shares are debt or equity. As explained in
module 8, a strong case can be made that preference shares are a special type of bond. The argument
behind this case goes as follows. First, regular (non‐convertible) preference shares confer no voting
rights. Second, preference shareholders receive a fixed dividend regardless of the company’s earnings
and, if the company is liquidated, they receive a stated value (usually par) and not a residual value.
Third, preference shares often have ‘credit’ ratings that are similar in nature to those issued to bonds.
Fourth, preference shares are sometimes convertible into ordinary shares. Finally, most preference share
issues are not true perpetuities. For these reasons, many investors consider preference shares to be a
special type of debt rather than equity.
Ordinary share valuation
In earlier modules we have emphasised that the value of any asset is the present value of its future cash
flows. The steps in valuing an asset are as follows.
1. Estimate the future cash flows.
2. Determine the required rate of return, or discount rate, which depends on the riskiness of the future
cash flows.
3. Calculate the present value of the future cash flows to determine what the asset is worth.
It is relatively straightforward to apply these steps in valuing a bond, because the cash flows are
stated as part of the bond contract and the required rate of return, or discount rate, is just the yield to
maturity on bonds with comparable risk characteristics. However, ordinary share valuation is more difficult for several reasons. First, while the expected cash flows for bonds are well documented and easy
to determine, ordinary share dividends are much less certain. These dividends are declared by the board
of directors, which may or may not decide to pay a cash dividend at a particular time. Thus, the size
and the timing of dividend cash flows are less certain. Second, ordinary shares are true perpetuities in
that they have no final maturity date. Thus, companies never have to redeem them. In contrast, bonds
have a finite maturity. Finally, unlike the rate of return, or yield, on bonds, the rate of return on ordinary
shares is not directly observable. Thus, grouping ordinary shares into risk classes is more difficult than
grouping bonds. Keeping these complexities in mind, we now turn to a discussion of ordinary share
valuation.
A one‐period model
Let’s assume that you have a genie who can tell the future with perfect certainty. You are thinking about
buying a share and selling it after a year. The genie volunteers that in 1 year you will be able to sell the share
for $100 (P1) and it will pay an $8 dividend (D1) at the end of the year. The time line for the transaction is:
0
1
Year
Buy share
$8 + $100
If you and the other investors require a 20 per cent return on investments in securities in this risk class,
what price would you be willing to pay for the share today?
The value of the share is the present value of the future cash flows you can expect to receive from it.
The cash flows you will receive are as follows: (1) the $8 dividend; and (2) the $100 sale price. Using a
MODULE 9 Share valuation 255
20 per cent rate of return, we see that the value of the share equals the present value (PV) of the dividend
plus the present value of the cash received from the sale of the share:
PV(share) = PV(dividend) + PV(sale price)
=
$8
$100
+
1 + 0.2 1 + 0.2
$8 + $100
$108
=
1.2
1.2
= $90
=
Thus, the value of the share today is $90. If you pay $90 for the share, you will have a 1‐year holding
period return of exactly 20 per cent. More formally, the time line and the current value of the share for
our one‐period model can be as shown:
0
1
P0
D1 + P1
P0 =
where:
Year
D1 + P1
1+ R
P0 = current value, or price, of the share
D1 = dividend paid at the end of the period
P1 = price of the share at the end of the period
R = required return on ordinary shares, or discount rate, in a particular risk class
Note that P0 denotes time zero, which is today; P1 is the price one period later; P2 is two periods in
the future and so on. Note also that when we speak of the price (P) in this context, we mean the value —
what we have determined is what the price should be, given our model — not the actual market price.
Our one‐period model provides an estimate of what the market price should be.
Now what if, at the beginning of year 2, we are again asked to determine the price of an ordinary
share with the same dividend pattern and a 1‐year holding period. As in our first calculation, the current
price (P1) of the share is the present value of the dividend and the share’s sale price, both received at the
end of the year (P2). Specifically, our time line and the share pricing formula are as follows:
1
2
P1
D2 + P2
P1 =
Year
D 2 + P2
1+ R
If we repeat the process again at the beginning of year 3, the result is similar:
P2 =
D3 + P3
1+ R
P3 =
D 4 + P4
1+ R
and at the beginning of year 4:
Each single‐period model discounts the dividend and sale price at the end of the period by the
required return.
256 Finance essentials
A perpetuity model
Unfortunately, although our one‐period model is correct, it is not very realistic. We need a share‐
valuation formula for perpetuity, not for one or two periods. However, we can string together a series of
one‐period share‐pricing models to arrive at a share perpetuity model. Here is how we do it.
First, we construct a two‐period share‐valuation model. The time line for the two‐period model follows:
0
1
2
Period
P0
(D1 + P1)
P1
(D2 + P2)
To construct our two‐period model, we start with our initial single‐period valuation formula:
P0 =
D1 + P1
1+ R
Now we substitute into this equation the expression derived earlier for P1 = (D2 + P2)/(1 + R), which is
as follows:
P0 =
D1 + [(D 2 + P2 ) / (1 + R)]
1+ R
Solving this equation results in a share‐valuation model for two periods:
P0 =
D1
D2
P2
+
+
2
1+ R
(1 + R)
(1 + R)2
Finally, we combine the second‐period terms, resulting in this two‐period share‐valuation equation:
P0 =
D 2 + P2
D1
+
1+ R
(1 + R)2
This equation shows that the price of a share for two periods is the present value of the dividend in
period 1 (D1) plus the present value of the dividend and sale price in period 2 (D2 and P2).
Now let’s construct a three‐period model. The time line for the three‐period model is:
0
1
P0
(D1 + P1)
P1
2
3
Period
(D2 + P2)
P2
(D3 + P3)
If we substitute the equation for P2 into the two‐period valuation model shown above, we have a three‐
period model which is shown in the following equations. Recall that P2 = (D3 + P3)/(1 + R). This model
is developed in precisely the same way as our two‐period model:
P0 =
D1
D2
P2
+
+
1+ R
(1 + R)2
(1 + R)2
(D3 + P3 )/(1 + R)
D1
D2
+
+
2
1+ R
(1 + R)
(1 + R)2
D1
D2
D3
P3
=
+
+
+
1+ R
(1 + R)2
(1 + R)3
(1 + R)3
D3 + P3
D1
D2
=
+
+
2
1+ R
(1 + R)
(1 + R)3
=
MODULE 9 Share valuation 257
By now, it should be clear that we could go on to develop a four‐period model, a five‐period model, a
six‐period model and so on. The ultimate result is the following equation:
P0 =
D1
D2
D3
Dt
Pt
+
+
++
+
1+ R
(1 + R)2
(1 + R)3
(1 + R)t
(1 + R)t
Here, t is the number of time periods, which can be any number from one to infinity (∞).
In summary, we have developed a model showing that the value, or price, of a share today (P0) is
the present value of all future dividends and the share’s sale price in the future. Although theoretically
sound, this model is not practical to apply because the number of dividends could be infinite. It is
unlikely that we can successfully forecast an infinite number of dividend payments or a share’s sale price
far into the future. What we need are some realistic simplifying assumptions.
BEFORE YOU GO ON
1. Why are preference shares often viewed as a special type of a bond rather than a share?
9.3 General dividend valuation model
LEARNING OBJECTIVE 9.3 Describe how the general dividend valuation model values a share.
In the preceding equation, note that the final term, as in the earlier valuation models, is always the sale
price of the share in period t (Pt) and that t can be any number including infinity. The model assumes
that we can forecast the sale price of the share far into the future, which does not seem very likely in
real life. However, as a practical matter, as Pt moves further out in time towards infinity, the value of Pt
approaches zero. Why? Because, no matter how large the sale price of the share, the present value of Pt
will approach zero because the discount factor approaches zero. Therefore, if we go out to infinity, we
can ignore the Pt/(1 + R)t term and write our final equation as:
P0 =
D1
D2
D3
D4
D5
D∞
+
+
+
+
++
1+ R
(1 + R)2
(1 + R)3
(1 + R)4
(1 + R)5
(1 + R)∞
∞
Dt
=∑
(1
+
R)t
t =1
where:
(9.1)
P0 = current value, or price, of the share
Dt = dividend received in period t, where t = 1, 2, 3, ⋯ ∞
R = required return on ordinary shares or discount rate
The above equation is a general expression for the value of a share. It says that the price of a share is
the present value of all expected future dividends:
Share price = PV (All future dividends)
This formula does not assume any specific pattern for future dividends, such as a constant growth rate.
Nor does it make any assumption about when the share will be sold in the future. Furthermore, the
model says that, to calculate a share’s current value, we need to forecast an infinite number of dividends,
which is a daunting task at best.
The above equation provides some insight into why share prices are changing all the time and why,
at certain times, these price changes can be dramatic. It implies that the underlying value of a share is
determined by the market’s expectations of the future cash flows (from dividends) that the company can
generate. In efficient markets, share prices change constantly as new information becomes available and
258 Finance essentials
is incorporated into the company’s market price. For publicly traded companies, the market is inundated
with facts and rumours, such as when a company fails to meet sales projections, the CEO resigns or is
fired, or a class‐action suit is filed against one of its products. Some events may have little or no impact
on the company’s cash flows and hence its share price. Others can have very large effects on cash flows.
Examples include the impact on BHP Billiton of the downward commodity price cycle over recent years,
which culminated in a loss of $8.3 billion in the 2016 financial year. Consequently, its share price more
than halved from a high of over $100 in April 2011 to around $40 in December 2016.
Growth share pricing paradox
An interesting issue concerning growth shares arises out of the fact that the share‐valuation equation
is based on dividend payments. Growth shares are typically defined as the shares of companies whose
earnings are growing at above‐average rates and are expected to continue to do so for some time. A company of this type typically pays little or no dividends on its shares because management believes that the
company has a number of high‐return investment opportunities and that both the company and its investors will be better off if earnings are reinvested, rather than paid out as dividends.
To illustrate the problem with valuing growth shares, let’s suppose that the earnings of Acme Ltd are
growing at an exceptionally high rate. The company’s shares pay no dividends and management states
that there are no plans to pay any dividends. Based on our share valuation equation, what is the value of
Acme Ltd’s shares?
Obviously, since all the dividend values are zero, the value of our growth share is zero!
P0 =
0
0
0
+
+
+= 0
2
1+ R
(1 + R)
(1 + R)3
How can the value of a growth share be zero? What is going on here?
The problem is that our first definition of growth shares was less than precise. Our application of
equation 9.1 assumes that Acme Ltd will never pay a dividend. If Acme Ltd had an article of association
MODULE 9 Share valuation 259
that stated it would never pay dividends and would never liquidate itself (unless it became insolvent),
the value of its shares would indeed be zero. Equation 9.1 predicts, and common sense says, that if you
own shares in a company that will never pay you any cash, the market value of those shares is absolutely
nothing. As you may recall, this is a point we emphasised in module 1.
What we should have said is that a growth share is a share in a company that currently has exceptional
investment opportunities and thus is not currently paying dividends because it is reinvesting earnings.
At some time in the future, growth share companies will pay dividends or will liquidate themselves (for
example, by selling out to other companies) and will then pay a single large ‘cash dividend’. People who
buy growth shares expect rapid price appreciation because management reinvests the cash flows from
earnings internally in investment projects believed to have high rates of return. If these internal investments succeed, the share’s price should go up significantly and investors can sell their shares at a price
that is higher than the price they paid.
BEFORE YOU GO ON
1. What is the general formula used to calculate the price of a share? What does it mean?
2. What are growth shares and why do they typically pay little or no dividends?
9.4 Share valuation: some simplifying assumptions
LEARNING OBJECTIVE 9.4 Discuss the assumptions necessary to make the general dividend valuation
model easier to use, and use the model to calculate the value of a company’s ordinary shares.
Conceptually, our general dividend model is consistent with the notion that the value of an asset is
the discounted value of future cash flows. Unfortunately, at a practical level, the model is not easy to
use because of the difficulty of estimating future dividends over a long period of time. We can, however, make some simplifying assumptions about the pattern of dividends that will render the model
more manageable. Fortunately, these assumptions closely resemble the way many companies manage
their dividend payments. We have a choice among three different assumptions: (1) Dividend payments
remain constant over time; that is, they have a growth rate of zero. (2) Dividends have a constant
growth rate; for example, they grow at 3 per cent per year. (3) Dividends have a mixed growth rate
pattern; that is, they have one payment pattern and then switch to another. Next, we discuss each
assumption in turn.
Zero growth dividend model
The simplest assumption is that dividends have a growth rate of zero. Thus, the dividend payment pattern remains constant over time:
D1 = D 2 = D3 = … = D ∞
In this case, the general dividend discount model becomes:
P0 =
D
D
D
D
D
D
+
+
+
+
++
2
3
4
5
1+ R
(1 + R)
(1 + R)
(1 + R)
(1 + R)
(1 + R)∞
This cash flow pattern essentially describes a perpetuity with a constant cash flow. You may recall that
we developed an equation for such a perpetuity in module 6. Equation 6.4 said that the present value of a
perpetuity with a constant cash flow is CF/i, where CF is the constant cash flow and i is the interest rate.
In terms of our share‐valuation model, we can represent the same relationship as follows:
P0 =
260 Finance essentials
D
R
(9.2)
where:
P0 = current value, or price, of the share
D = constant cash dividend received in each time period
R = required return on ordinary shares or discount rate
This model fits the dividend pattern for ordinary shares of a company that is not growing and has little
growth potential, and for preference shares, which we discuss in the next section.
For example, Great Southern Print & Copy is a small printing company in Albany, Western Australia.
The town’s economic base has remained constant over the years and Great Southern’s sales and earnings
reflect this trend. The company pays a $5 dividend per year and the board of directors has no plans to
change the dividend. The company’s investors are mostly local businesspeople who expect a 20 per cent
return on their investment. What should be the price of the company’s shares?
Since the cash dividend payments are constant, we can use equation 9.2 to find the price of the shares:
P0 =
D
$5
=
= $25 per share
R
0.20
DEMONSTRATION PROBLEM 9.1
The value of a small business
Problem:
For the past 15 years, a family has operated the gift shop in a luxury hotel in Cairns, Queensland. The
hotel management wants to sell the gift shop to the family members, rather than paying them to operate
it. The family’s accountant will incorporate the new business and estimates that it will generate an
annual cash dividend of $150 000 for the shareholders. The hotel will provide the family with an infinite
guarantee for the space and a generous buyout plan in the event that the hotel closes its doors. The
accountant estimates that a 20 per cent discount rate is appropriate. What is the value of the shares?
Approach:
Assuming that the business will operate indefinitely and that its growth is constrained by its circumstances, the zero growth discount model can be used to value the shares. Thus, we can use equation
9.2. Since the number of shares outstanding is not known, we can simply interpret P0 as being the total
value of the outstanding ordinary shares.
Solution:
P0 =
D
$150 000
=
= $750 000
R
0.20
The value of the shares is $750 000.
Constant growth dividend model
Under the next dividend assumption, cash dividends do not remain constant but instead grow at some average
rate g from one period to the next forever. This rate of growth can be positive or negative. And, as it turns out,
a constant growth rate is not a bad approximation of the actual dividend pattern for some companies. Constant dividend growth is an appropriate assumption for mature companies with a history of stable growth.
You may have concerns about the assumption of an infinite time horizon. In practice, this does not
present a problem. It is true that most companies do not continue forever. We know, however, that the
further in the future a cash flow will occur, the smaller its present value. Thus, far‐distant dividends have
a small present value and contribute very little to the share price. For example, as shown in figure 9.2,
with constant dividends and a 15 per cent discount rate, dividends paid during the first 10 years account
for more than 75 per cent of the value of a share, while dividends paid after the 20th year contribute less
than 6 per cent of the value.
MODULE 9 Share valuation 261
Impact on share prices of near and distant future dividends
FIGURE 9.2
$2.50
PV of expected dividends
$2.00
More than 75% of the present
value of a share comes
from expected dividends in
the first 10 years.
$1.50
$1.00
About 20% of the present
value comes from years 11–20.
$0.50
$0.00
Less than 6% comes
from all other years.
0
5
10
15
20
25
Year
30
35
40
45
50
Note: Calculations based on discount rate of 15% and constant dividends.
Identifying and applying the constant‐growth dividend model is fairly straightforward. First, we need
a model to calculate the value of dividend payments for any time period. We will assume that the cash
dividends grow at a constant rate g from one period to the next forever. This situation is an application
of the compound growth rate formula:
FVn = PV × (1 + g)n
where g is the compound growth rate and n is the number of compounding periods. We can apply this
formula to our dividend payments. We note that D0 is the current dividend, paid at time t = 0, and it
grows at a constant growth rate g. The next dividend, paid at time t = 1, is D1, which is just the current
dividend (D0) multiplied by the growth factor, (1 + g). Thus, D1 = D0 × (1 + g). The general formula for
dividend values over time is stated as follows:
Dt = D 0 × (1 + g)t where:
(9.3)
Dt = dividend payment in period t, where t = 1, 2, 3, … ∞
D0 = dividend paid in the current period, t = 0
g = constant growth rate for dividends
Equation 9.3 allows us to calculate the dividend payment for any time period.
Dividends expected far in the future have a smaller present value than dividends expected in the next
few years, and so they have less effect on the share price. As you can see in the figure, with constant
dividends more than 75 per cent of the current price of a share comes from expected dividends in the
first 10 years.
Note that to calculate the dividend for any period, we multiply D0 by the growth rate factor to some
power, but we always start with D0.
262 Finance essentials
We can now develop the constant growth dividend model, which is easy to do because it is just an
extension of equation 6.4 from module 6. Equation 6.4 says that the present value of a perpetuity (PVP)
is the cash flow value (CF1) from period 1, divided by the discount rate (i):
CF1
i
We can now extend this relationship to include growing cash flows. The present value of a growing
perpetuity (PVP) is the growing cash flow value (CF1) from period 1, divided by the difference between
the discount rate (i) and the rate of growth (g) of the cash flow (CF1) as follows:
CF1
PVP =
i −g
PVP =
We can represent this same relationship as follows:
D1
P0 =
R −g
where:
P0 =
D1 =
g=
R=
(9.4)
current value, or price, of the shares
dividend paid in the next period (t = 1)
constant growth rate for dividends
required return on ordinary shares or discount rate
In other words, the constant growth dividend model tells us that the current price of a share is the next
period dividend divided by the difference between the discount rate and the dividend growth rate. Note that
PVP is the current value or price of the share (P0), which is the present value of the dividend cash flows.
The growing perpetuity model is valid only as long as the growth rate is less than the discount rate,
or required rate of return. In terms of equation 9.4, then, the value of g must be less than the value of R
(g < R). If the equation is used in situations where R is equal to or less than g (R ≤ g), the calculated
results will be meaningless.
Finally, note that if g = 0 there is no dividend growth, the dividend payment pattern becomes a constant no‐growth dividend stream and equation 9.4 becomes P0 = D/R. This equation is precisely the
same as equation 9.2, which is our zero growth dividend model. Thus, equation 9.2 is just a special case
of equation 9.4 where g = 0.
Let’s work through an example using the constant growth dividend model. Blue Oval Motor Wreckers is
an automotive parts supplier based in Geelong. At the company’s year‐end shareholders meeting, the CFO
announces that this year’s dividend will be $4.81. The announcement conforms to Blue Oval’s d­ ividend
policy, which sets dividend growth at a 4 per cent annual rate. Investors who own shares in similar types
of companies expect to earn a return of 18 per cent. What is the value of the company’s shares?
First, we need to calculate the cash dividend payment for next year (D1). Applying equation 9.3 for
t = 1 yields the following:
D1 = D 0 × (1 + g) = $4.81 × (1 + 0.04) = $4.81 × 1.04 = $5.00
Next, we apply equation 9.4 to find the value of the company’s shares, which is $35.71 per share:
D1
P0 =
R −g
=
$5.00
0.18 − 0.04
$5.00
0.14
= $35.71
=
MODULE 9 Share valuation 263
DEMONSTRATION PROBLEM 9.2
Blue Oval grows faster
Problem:
Using the information given in the text, calculate the value of Blue Oval’s shares if dividends grow at
12 per cent, rather than 4 per cent. Explain why the answer makes sense.
Approach:
First calculate the cash dividend payment for next year (D1) using the 12 per cent growth rate. Then
apply equation 9.4 to solve for the company’s share price.
Solution:
D1 = $4.81 × 1.12 = $5.39
P0 =
$5.39
$5.39
=
= $89.83
0.18 − 0.12
0.06
The higher share value of $89.93 is no surprise because dividends are now growing at a rate of 12 per cent
rather than 4 per cent. Hence, the value of cash payments to investors (dividends) is expected to be larger.
Calculating future share prices
The constant growth dividend model (equation 9.4) can be modified to determine the value, or price, of a
share at any point in time. In general, the price of a share, Pt, can be expressed in terms of the dividend
in the next period (Dt+1), g and R, when the dividends from Dt+1 forward are expected to grow at a constant rate. Thus, the price of a share at time t is as follows:
Pt =
Dt + 1
(9.5)
Note that equation 9.5 is just a special case of equation 9.4 in which t = 0. To be sure that you understand this, set up equation 9.5 to calculate a share’s current price at t = 0. When you are finished, the
resulting equation should look exactly like equation 9.4.
An example will illustrate how equation 9.5 is used. Suppose that a company has a current dividend
(D0) of $2.50, R is 15 per cent and g is 5 per cent. What is the share price today (P0), and what will it be
in 5 years (P5)? To help visualise the problem, we lay out a time line and identify some of the important
variables necessary to solve the problem:
0
Dividend: $2.50
Share price: P0
R −g
1
2
3
4
5
6
D1
D2
D3
D4
D5
P5
D6
Year
To find the current share price we can apply equation 9.3, but we must first calculate the dividend for the
next period (D1), which is at t = 1. Using equation 9.3, we calculate the company’s dividend for next year:
D1 = D 0 × (1 + g) = $2.50 × 1.05 = $2.625
Then we can use equation 9.4 to find the price of the share today:
P0 =
D1
$2.625
$2.625
=
=
= $26.25
R −g
0.15 − 0.05
0.10
Now we will find the value of the share in 5 years. In this situation equation 9.5 is expressed as:
P5 =
264 Finance essentials
D6
R −g
We need to calculate D6 and we do so by using equation 9.3:
D6 = D 0 × (1 + g)6 = 2.50 × (1.05)6 = 2.50 × 1.34 = $3.35
The price of the share in 5 years is therefore:
P5 =
$3.35
$3.35
=
= $33.50
0.15 − 0.05
0.10
Finally, note that $33.50/(1.05)5 = $26.25, which is the value today.
DEMONSTRATION PROBLEM 9.3
David Jones’ current share price
Problem:
Suppose that the current cash dividend on David Jones’ ordinary shares is $0.27. Financial analysts
expect the dividends to grow at a constant rate of 6 per cent per year and investors require a 12 per
cent return on this class of shares. What should be the current share price of David Jones?
Approach:
In this scenario, D0 = $0.27, R = 0.12 and g = 0.06. We first find D1 using equation 9.3 and then calculate the value of a share using equation 9.4.
Solution:
Dividend: D1 = D0 × (1 + g ) = $0.27 × 1.06 = $0.2862
Value of a share: P0 =
D1
$0.2862
$0.2862
=
= $4.77
=
R − g 0.12 − 0.06
0.06
The current share price for David Jones should be $4.77.
DEMONSTRATION PROBLEM 9.4
David Jones’ future share price
Problem:
Continuing the example in demonstration problem 9.3, what should David Jones’ share price be 7 years
from now (P7)?
Approach:
This is an application of equation 9.5. We first need to calculate David Jones’ dividend in period 8, using
equation 9.3. Then we can apply equation 9.5 to calculate the estimated price of the share 7 years in
the future.
Solution:
Dividend in period 8: D8 = D0 × (1 + g )8 = $0.27 × (1.06)8 = $0.27 × 1.594 = 0.43
Price of a share in 7 years: P7 =
D8
$0.43
$0.43
=
=
= $7.17
R − g 0.12 − 0.06
0.06
Alternatively, we could calculate the price of a share in 7 years using the compound growth rate formula.
Value of a share in year 0: P0 = $4.77
Price of a share in 7 years: P7 = PV0 × (1 + g)n = $4.77 × 1.067 = $4.77 × 1.5036 = $7.17
The share price of David Jones in 7 years should be $7.17.
MODULE 9 Share valuation 265
Relationship between R and g
We have previously mentioned that the dividend growth model provides valid solutions only when g < R.
Students frequently ask what happens to equations 9.4 or 9.5 when this condition does not hold (when
g ≥ R). Mathematically, as g approaches R the share price becomes larger and larger, and when g = R
the value of the share is infinite, which is nonsense. When the growth rate (g) is larger than the discount
rate (R), the constant growth dividend model tells us that the value of the share is negative. However,
this is not possible; the value of a share can never be negative.
From a practical perspective, the growth rate in the constant growth dividend model cannot be greater
than the sum of the long‐term rate of inflation and the long‐term real growth rate of the economy. Since
this model assumes that the company will grow at a constant rate forever, any growth rate that is greater
than this sum would imply that the company will eventually take over the entire economy. Of course, we
know this is not possible. Since the sum of the long‐term rate of inflation and the long‐term real growth
rate has historically been less than 7 to 8 per cent, the growth rate (g) is virtually always less than the
discount rate (R) for the shares that we would want to use the constant growth dividend model to value.
It is possible for companies to grow faster than the long‐term rate of inflation plus the real growth rate
of the economy — just not forever. A company that is growing at such a high rate is said to be growing
at a supernormal growth rate. We must use a different model to value the shares of a company like this.
We discuss one such model next.
Mixed (supernormal) growth dividend model
For many companies, it is not appropriate to assume that dividends will grow at a constant rate. Companies
typically go through life cycles and, as a result, exhibit different dividend patterns over time.
During the early part of their lives, successful companies experience a supernormal rate of growth
in earnings. These companies tend to pay lower dividends or no dividends at all, because many good
investment projects are available to them and management wants to reinvest earnings in the company
to take advantage of these opportunities. If a growth company does not pay regular dividends, investors receive their returns from capital appreciation of the company’s shares (which reflects increases in
expected future dividends), from a cash or share payout if the company is acquired, or possibly from a
large special cash dividend. As a company matures, it will settle into a growth rate at or below the long‐
term rate of inflation plus the long‐term real growth rate of the economy. When a company reaches this
stage, it will typically be paying a fairly predictable regular dividend.
Figure 9.3 shows several dividend growth curves. In the top curve, dividends figure a supernormal
growth rate of 25 per cent for 4 years, then a more sustainable nominal growth rate of 5 per cent (this
might, for example, be made up of 2.5 per cent growth from inflation plus a 2.5 per cent real growth
rate). By comparison, the remaining curves show dividends with a constant nominal growth rate of
5 per cent, a zero growth rate and a negative 10 per cent growth rate.
As mentioned earlier, successful companies often experience supernormal growth early in their life
cycles. During 2014, for example, companies such as Kloud Solutions, Metro Property Development and
Prime Build experienced supernormal growth.6 Older companies that reinvent themselves with new products or strategies may also experience periods of supernormal growth. Between the return of Steve Jobs to
the helm of Apple in 1997 and his death in 2011, both earnings growth and shareholder returns exceeded
30 per cent per annum.7 Not long after Tim Cook took over as CEO, Apple announced that net profit had
increased by 85 per cent in the financial year ending 27 September 2011. Apple’s annual net profit growth
has varied considerably since 2011, fluctuating between −11.25 per cent (in 2013) and 60.99 per cent
(in 2012). In the September 2016 quarter, Apple posted a negative net profit growth of −3 per cent. This
decline in growth has been attributed to a drop in sales of Apple’s iPhone, which is the main contributor to
the company’s profits. This pattern reflects a supernormal positive impact on financial performance of new
technology followed by a decline in growth as competitors catch up with their own rival technologies.8
Following Apple’s initial introduction of the iPhone to the market, its stock price rose dramatically from
266 Finance essentials
$60 in January 2011 to $117 in October 2016 and subsequently stabilised as profits normalised.9 Apple has
since returned some of its profits to shareholders in the form of dividends and share buybacks, whereas in
the past Jobs preferred to retain earnings for further investments in profitable projects.
FIGURE 9.3
$6.0
Supernormal 25% growth
Normal 5% growth
Normal 5% growth
Zero growth
Declining –10% growth
$5.0
$4.0
Dividends
Dividend growth rate patterns
Dividends exhibit a supernormal growth rate of 25%
for 4 years and then a
more normal growth rate
of 5%.
$3.0
Dividends exhibit a
constant growth rate of 5%.
$2.0
Dividends exhibit zero
growth.
$1.0
$0.0
0
1
2
3
Year
4
5
6
Dividends exhibit a
negative growth rate
of 10%.
To value a share for a company with supernormal dividend growth patterns, we do not need to develop
any new equations. Instead, we can apply equation 9.1, our general dividend model, and equation 9.5,
which gives us the price of a share with constant dividend growth at any point in time.
We illustrate with an example. Suppose a company’s expected dividend pattern for 3 years is as
follows: D1 = $1, D2 = $2, D3 = $3. After 3 years, the dividends are expected to grow at a constant rate
of 6 per cent a year. What should the current share price (P0) be if the required rate of return demanded
by investors is 15 per cent?
We begin by drawing a time line, as shown in figure 9.4. We recommend that you prepare a time line
whenever you solve a problem with a complex dividend pattern so that you can be sure the cash flows
are placed in the proper time periods. The critical elements in working these problems are to correctly
identify when the constant growth starts and to value it properly.
FIGURE 9.4
Time line for non‐constant dividend pattern
Non-constant growth
Time
0
Constant growth at 6%
1
2
3
4
5
Dividends
$1.00
$2.00
$3.00
$3.18
$3.37
Key variables P0
D1
D2
D3
D4
Year
Looking at figure 9.4, it is easy to see that we have two different dividend patterns. (1) D1 to D3 represents a mixed dividend pattern, which can be valued using equation 9.1, the general dividend valuation
model. (2) After the third year, dividends show a constant growth rate of 6 per cent and this pattern can be
valued using equation 9.5, the constant growth dividend valuation model. Thus, our valuation model is:
P0 = PV (Mixed dividend growth) + PV (Constant dividend growth)
MODULE 9 Share valuation 267
Combining these present values yields the following result:
D1
D2
D3
+
+
+
P0 =
(1 + R) (1 + R)2
(1 + R)3
PV of mixed growth
dividend payments
P3
(1 + R)3
Value of constant
growth
dividend payments
The value of the constant growth dividend stream is P3, which is the value, or price, at time t = 3.
More specifically, P3 is the value of the future cash dividends discounted to time period t = 3. With a
required rate of return of 15 per cent, the value of these dividends is calculated as follows:
D 4 = D3 × (1 + g) = $3.00 × 1.06 = $3.18
P3 =
D4
$3.18
=
R− g
0.15 − 0.06
$3.18
0.09
= $35.33
=
We find the value of P3 using equation 9.5, which allows us to calculate share prices in the future for
shares with constant dividend growth. Note that the equation gives us the value, as of year 3, of a constant growth perpetuity that begins in year 4. This formula always gives us the value as of one period
before the first cash flow.
Now, since P3 is at time period t = 3, we must discount it back to the present (t = 0). This is accomplished by dividing P3 by the appropriate discount factor — (1 + R)3.
Plugging the values for the dividends, P3 and R into the above mixed growth equation results in the
following:
$1.00
$2.00
$3.00
$35.33
P0 =
+
+
+
2
3
1.15
(1.15)
(1.15)
(1.15)3
= $0.87 + $1.51 + $1.97 + $23.23
= $27.58
Thus, the value of the share is $27.58.
We can write a general equation for the supernormal growth situation, where dividends grow first at a
non‐constant rate until period t and then at a constant rate, as follows:
P0 =
D1
D2
Dt
Pt
+
++
+
1 + R (1 + R)2
(1 + R)t (1 + R)t
(9.6)
If the supernormal growth period ends and dividends grow at a constant rate, g, then Pt is calculated
from equation 9.5 as follows:
Pt =
Dt + 1
R − g
The two preceding equations can also be applied when dividends are constant over time, since we know
that g = 0 is just a special case of the constant growth dividend model (g > 0).
Let’s look at another example, this time using equation 9.6. Suppose that AusBiotech Ltd is a high‐tech
medical device company located in Melbourne. The company is 3 years old and has experienced spectacular growth since its inception. You are a financial analyst for a share brokerage company and have just
returned from a two‐day visit to the company. You learned that AusBiotech plans to pay no dividends for
the next 5 years. In year 6, management plans to pay a large special cash dividend, which you estimate
to be $25 per share. Then, beginning in year 7, management plans to pay a constant annual dividend of
268 Finance essentials
$6 per share for the foreseeable future. The appropriate discount rate for the shares is 12 per cent and
the current market price is $25 per share. Your boss doesn’t think that the shares are worth the price. You
think that they are a bargain and that you should recommend them to the company’s clients. Who is right?
Our first step in answering this question is to lay out on a time line the expected dividend payments:
0
5
No dividends
through year t = 5
P0
6
7
$25
$6
(D6 + P6)
D7
8
9
Year
Constant dividend forever
Constant after year 7
This situation is a direct application of equation 9.6, which is the mixed dividend model. That is,
there are two different dividend cash streams: (1) the mixed dividends, which in this case comprise a
single dividend paid in year 6 (equation 9.5); and (2) the constant dividend stream (g = 0) of $6 per year
­forever (equation 9.5). The value of the ordinary shares can be calculated as follows:
P0 = PV (Mixed dividend growth) + PV (Constant dividends with no growth)
Applying equation 9.6 to the cash flows presented in the problem yields:
D1
D2
Dt
Pt
+
+…+
+
1+ R
(1 + R)2
(1 + R)t
(1 + R)t
D6
P6
=
+
6
(1 + R)
(1 + R)6
D6 + P6
=
(1 + R)6
P0 =
Note that the first term in the second line calculates the present value of the large $25 dividend paid in
year 6. In the second term, P6 is the discounted value of the constant $6 dividend payments made in
perpetuity, valued to period t = 6. To calculate the present value of P6, we divide it by the appropriate
discount factor, which is (1 + R)6.
Next, we plug the data given earlier into the above equation:
P0 =
$25 + P6
(1.12)6
We can see that we still need to calculate the value of P6 using equation 9.5:
Pt =
Dt + 1
R − g
Equation 9.5 is easy to apply since the dividend payments remain constant over time. Thus, Dt+1 = $6
and g = 0. P6 is calculated as follows:
P6 =
D7
$6
$6
=
=
R − g
0.12 − 0
0.12
= $50
The calculation for P0 is, therefore:
$25 + $50
(1.12)6
$75
=
1.9738
= $38.00
P0 =
MODULE 9 Share valuation 269
The share’s current market price is $25 and, if your estimates of dividend payments are correct, the
share’s value is $38 per share. This suggests that the share is a bargain and so your boss is incorrect.
BEFORE YOU GO ON
1. Which three different models are used to value shares based on different dividend patterns?
2. Explain why the growth rate g must always be less than the rate of return R.
9.5 Valuing preference shares
LEARNING OBJECTIVE 9.5 Explain how valuing preference shares with a stated maturity differs from valuing
preference shares with no maturity date, and calculate the price of a preference share under both conditions.
As mentioned earlier in the module, preference shares are hybrid securities, falling somewhere between
bonds and ordinary shares. For example, preference shares are a higher priority claim on the com­pany’s
assets than ordinary shares, but a lower priority claim than the company’s creditors in the event of
default. In calculating the value of preference shares, however, the critical issue is whether the preference shares have an effective ‘maturity’. If the preference share contract has a sinking fund that calls for
the mandatory retirement of the shares over a scheduled period of time, financial analysts will tend to
treat the shares as if they were a bond with a fixed maturity.
The most significant difference between a preference share with a fixed maturity and a bond is the risk
of default. Bond coupon payments are a legal obligation of the company and failure to pay them results
in default, whereas preference share dividends are declared by the board of directors and failure to pay
dividends does not result in default. Even though it is not a legal default, the failure to pay a preference share dividend as promised is not a trivial event. It is a serious financial breach that can signal to
the market that the company is in financial difficulty. As a result, managers make every effort to pay
­preference share dividends as promised.
Preference shares with a fixed maturity
Because a preference share with an effective maturity is considered similar to a bond, we can use the bond
valuation model developed in module 8 to determine its price, or value. Applying equation 8.2 requires only
that we recognise that the coupon payments (C) are now dividend payments (D) and the preference share
dividends are paid semiannually. Thus, equation 8.2 can be restated as the price of a preference share (PS0):
Preference share price = PV(Dividend payments) + PV(Par value)
PS0 =
where:
D=
P=
i=
m=
n=
D/ m
i/m


1
Pmn
+
1 −
mn 
(1
i
/
m
)
(1
i / m)mn
+
+


(9.7)
annual preference share dividend payment
stated (par) value of the preference share
yield to maturity of the preference share
number of times dividend payments are made each year
number of years to maturity
For preference shares with semiannual dividend payments, m equals 2.
Consider an example of how this equation is used. Suppose that an energy company’s preference
shares have an annual dividend payment of $10 (paid semiannually), a stated (par) value of $100 and
an effective maturity of 20 years owing to a sinking fund requirement. If similar preference share issues
have market yields of 8 per cent, what is the value of these preference shares?
270 Finance essentials
First, we convert the data to semiannual compounding as follows: (1) the market yield is 4 per cent
semiannually (8 per cent per year/2); (2) the dividend payment is $5 semiannually ($10 per year/2);
and (3) the total number of dividend payments is 40 (2 per year × 20 years). Plugging the data into
equation 9.7, we find that the value of the preference shares is:
1 
$100

1 − (1.04)40  + (1.04)40


$100
= (125 × 0.7917) +
4.801
= 98.96 + 20.83
PS0 =
$5
0.04
= $119.79
We can, of course, also solve this problem on a financial calculator, as follows.
Procedure
Key operation
Enter cash flow data
Calculate PV
Display
4 [I/Y]
4 ⇒ I/Y
4.00
40 [N]
40 ⇒ N
40.00
100 [FV]
100 ⇒ FV
100.00
5 [PMT]
5 ⇒ PMT
5.00
[COMP] [PV]
PV =
−119.79
DEMONSTRATION PROBLEM 9.5
Calculating the yield on preference shares
Problem:
AGL Energy Ltd has a preference share issue outstanding that has a stated value of $100 which
will be retired by the company in 15 years and
which pays a $4 dividend each 6 months. If the
preference shares are currently selling for $95,
what is the share’s yield to maturity?
Approach:
We calculate the yield to maturity on this preference
share in exactly the same way that we calculate the
yield to maturity on a bond. We already know that
the semiannual dividend rate is $4, but we must
convert the number of periods to allow for semiannual compounding. The total number of compounding periods is 30 (2 per year × 15 years). Using equation 9.7, we can enter the data and find i, the
share’s yield to maturity, through trial and error. Alternatively, we can solve the problem easily on a financial
calculator.
Solution:
Applying equation 9.7:


1
Pmn
1 −
 +
mn
(1 + i / m) 
(1 + i / m)mn

PS0 =
D/m
i/m
$95 =

$4 
1
$100
+
1 −
30 
i 
(1 + i ) 
(1 + i )30
MODULE 9 Share valuation 271
Financial calculator steps are as follows.
Procedure
Key operation
Enter cash flow data
[+/−] 95 [PV]
(−95) ⇒ PV
30 [N]
30 ⇒ N
100 [FV]
100 ⇒ FV
100.00
4 [PMT]
4 ⇒ PMT
4.00
[COMP] [I/Y]
I/Y =
4.30
Calculate I/Y
Display
−95.00
30.00
The preference share’s yield is 4.30 per cent per half‐year and the annual yield is 8.60 per cent
(4.30 per cent × 2).
Perpetuity preference shares
Some preference share issues have no maturity. These securities have dividends that are constant over
time (g = 0) and the fixed dividend payments go on forever. Thus, these preference shares can be valued
as perpetuities using equation 9.2:
P0 =
D
R
where D is a constant cash dividend and R is the interest rate, or required rate of return.
Let’s work an example. Suppose that Qantas has a perpetual preference share issue that pays a dividend of $5 per year. Investors require an 18 per cent return on such an investment. What should be the
value of the preference share? Applying equation 9.2, we find that the value is:
P0 =
D $5.00
=
= $27.78
R
0.18
BEFORE YOU GO ON
1. Why can skipping payment of a preference share dividend be a bad signal?
2. How is a preference share with a fixed maturity valued?
272 Finance essentials
SUMMARY
9.1 Describe the four types of secondary markets.
The four types of secondary markets are: (1) direct search; (2) broker; (3) dealer; and (4) auction.
In direct search markets, buyers and sellers seek each other out directly. In broker markets, brokers
bring buyers and sellers together for a commission fee. Trades in dealer markets go through dealers
who buy securities at one price and sell at a higher price. The dealers face the risk that prices could
decline while they own the securities. Auction markets have a fixed location where buyers and
sellers confront each other directly and bargain over the transaction price.
9.2 Explain why many financial analysts treat preference shares as a special type of bond rather
than an equity security.
Preference shares represent ownership in a company and entitle the owner to a dividend which must
be paid before dividends are paid to ordinary shareholders. Similar to bonds, preference share issues
have credit ratings, are sometimes convertible to ordinary shares and are often callable. Unlike
owners of ordinary shares, owners of non‐convertible preference shares do not have voting rights
and do not participate in the company’s profits beyond the fixed dividends they receive. Because
of their strong similarity to bonds, many financial analysts treat preference shares that are not true
perpetuities as a form of debt, rather than equity.
9.3 Describe how the general dividend valuation model values a share.
The general dividend valuation model values a share as the present value of all future cash dividend
payments, where the dividend payments are discounted using the rate of return required by investors for a particular risk class.
9.4 Discuss the assumptions necessary to make the general dividend valuation model easier to
use, and use the model to calculate the value of a company’s ordinary shares.
The problems with the general dividend valuation model are that the exact discount rate that should
be used is unknown, dividends are often uncertain and some companies do not pay dividends at all.
To render the model easier to apply, we make assumptions about the dividend payment patterns of
businesses. These simplifying assumptions allow the development of more manageable models and
they also conform with the actual dividend policies of many companies. Dividend patterns include
the following: (1) dividends are constant (zero growth), as calculated in demonstration problem 9.1;
(2) dividends have a constant growth pattern (they grow forever at a constant rate g), as calculated
in demonstration problem 9.2; and (3) dividends grow first at a non‐constant rate, then at a constant
rate, as calculated in the AusBiotech example at the end of 9.4.
9.5 Explain how valuing preference shares with a stated maturity differs from valuing preference
shares with no maturity date, and calculate the price of a preference share under both
conditions.
When a preference share has a maturity date, financial analysts value it as they value any other
fixed obligation — that is, like a bond. To value such a preference share, we can use the bond
valuation model from module 8. Before using the model, we need to recognise that we will be
using dividends in the place of coupon payments and the par value of the share will replace the par
value of the bond. Additionally, in Australia both bond coupons and preference share dividends are
paid semiannually. When a preference share has no stated maturity it becomes a perpetuity, with
the dividend becoming the constant payment that goes on forever. We use the perpetuity valuation
model represented by equation 9.2 to price such shares. The calculations appear in demonstration
problem 9.5.
MODULE 9 Share valuation 273
SUMMARY OF KEY EQUATIONS
Equation
Description
Formula
P0 =
D1
D2
D3
D4
D5
D∞
+
+
+
+
++
1+ R
(1 + R)2
(1 + R)3
(1 + R)4
(1 + R)5
(1 + R)∞
9.1
The general dividend
valuation model
9.2
Zero growth dividend
model
P0 =
9.3
Value of a dividend at
time t in a
constant‐growth scenario
Dt = D0 × (1 + g )t
9.4
Constant growth dividend
model
P0 =
9.5
Value of a share at time t
when dividends grow at a
constant rate
Pt =
9.6
Supernormal growth share
valuation model
P0 =
9.7
Value of a preference
share with a fixed maturity
PS0 =
∞
Dt
+
(1
R)t
t =1
=∑
D
R
D1
R − g
Dt + 1
R− g
D1
D2
Dt
Pt
+
++
+
1+ R
(1 + R)2
(1 + R)t
(1 + R)t

D/ m 
1
Pmn
1 −
 +
i/m 
(1 + i / m)mn 
(1 + i / m) mn
KEY TERMS
bid price price that a securities dealer will pay for a given share
dividend yield share’s dividend payout divided by its current price
offer (ask) price price at which a securities dealer seeks to sell a given share
ordinary shares equity shares that represent the basic ownership claim in a company
post specific location on the floor of a securities exchange at which auctions for a particular security
take place
preference shares shares that confer preference over ordinary shares in terms of dividend payments
and the claim against the firm’s assets in the event of bankruptcy or liquidation
ENDNOTES
1. ASX, ‘No. of companies and securities listed on ASX’, www.asx.com.au/about/historical-market-statistics.htm.
2. ASX 2014, ‘Australian share ownership study’, www.asx.com.au.
3. Business Insider 2016, ‘The 17 most valuable stock exchanges in the world’, http://economictimes.indiatimes.com/markets/
stocks/news/the-17-most-valuable-stock-exchanges-in-the-world/articleshow/54013184.cms.
4. The ASX replaced SEATS with the CLICK XT integrated trading system in 2006, which incorporated SEATS and other
trading platforms for securities other than shares.
5. Australian Financial Review 2015, ‘Daily summary table: 100 leading industrial stocks’ (online), 29 July, www.afr.com/
share_tables.
6. Business Review Weekly 2014, ‘BRW Fast 100’, www.brw.com.au.
7. F.A.S.T. Graphs 2010, ‘10 super‐fast growth stocks with explosive returns’, 24 November, www.fastgraphs.com.
274 Finance essentials
8. CNBC 2016, ‘Apple falls 2% as it posts 3rd straight quarter of year‐on‐year revenue declines’, www.cnbc.com/2016/10/25/
apple‐reports‐fiscal‐fourth‐quarter‐2016‐earnings.html.
9. Yahoo!7 Finance 2016, ‘Interactive charts: Apple Inc.’, https://au.finance.yahoo.com.
ACKNOWLEDGEMENTS
Figure 9.1: © Fairfax Syndications
Photo: © epa european pressphoto agency b.v. / Alamy Stock Photo
Photo: © ramcreations / Shutterstock.com
Photo: © NAN104 / iStockphoto
MODULE 9 Share valuation 275
MODULE 10
Capital budgeting
and cash flows
LEA RN IN G OBJE CTIVE S
After studying this module, you should be able to:
10.1 discuss why capital budgeting decisions are the most important investment decisions made by a
company’s management
10.2 evaluate capital budgeting projects using the net present value (NPV), payback period, accounting
rate of return and internal rate of return methods
10.3 explain why incremental after‐tax free cash flows are relevant in evaluating a project and calculate
them for a project
10.4 discuss the five general rules for incremental after‐tax free cash flow calculations.
Module preview
This module is about capital budgeting, a topic we first visited in module 1. Capital budgeting is the pro­
cess of deciding which capital investments a company should make.
We begin the module with a discussion of the types of capital projects that companies undertake
and how the capital budgeting process is managed within a company. When making capital investment
decisions, management’s goal is to select projects that will increase the value of the company.
Next we examine some of the techniques used to evaluate capital budgeting decisions. We first discuss
the net present value (NPV) method, which is one of the most popular methods of project evaluation in
practice. The NPV method takes into account the time value of money and provides a direct measure of
how much a capital project will increase the value of the company.
We then examine the payback method and the accounting rate of return. As methods of selecting
capital projects, both of these methods have some serious deficiencies. Finally, we discuss the internal
rate of return (IRR), which is the expected rate of return for a capital project. Like the NPV, the IRR
involves discounting a project’s future cash flows. It is a popular and important alternative to the NPV
technique. However, in certain circumstances the IRR can lead to incorrect decisions. We then discuss
evidence of the techniques that financial managers actually use when making capital budgeting decisions.
The next part of this module focuses on the cash flows from a project. We first discuss how to ­calculate
the cash flows used to calculate the NPV of a project and how these cash flows differ from accounting
earnings. We then present five rules to follow when you calculate free cash flows. Since the cash flows
generated by a project will almost certainly differ from the forecasts, it is important to have a framework
that helps minimise errors and ensures forecasts are internally consistent. We also address some concepts
that will help you better understand cash flow calculations.
10.1 Introduction to capital budgeting
LEARNING OBJECTIVE 10.1 Discuss why capital budgeting decisions are the most important investment
decisions made by a company’s management.
We begin with an overview of capital budgeting, followed by a discussion of some important concepts
you will need to understand in this and later modules.
MODULE 10 Capital budgeting and cash flows 277
Importance of capital budgeting
Capital budgeting decisions are the most important investment decisions made by company manage­
ment. The objective of these decisions is to select investments in real assets that will increase the value
of the company. These investments create value when they are worth more than they cost. Capital invest­
ments are important because they can involve substantial cash outlays and, once made, are not easily
reversed. They also define what the company is all about — the company’s lines of business and its
inherent business risk. For better or worse, capital investments produce most of a typical company’s
revenues for years to come. The growth of BHP Billiton highlights the importance of a well‐developed
capital budgeting plan to keep the company competitive and to increase shareholders’ wealth.
Capital budgeting techniques help management systematically analyse potential business opportunities
in order to decide which are worth undertaking. As you will see, not all capital budgeting techniques are
equal. The best techniques are those that determine the value of a capital project by discounting all of the
cash flows generated by the project and thus accounting for the time value of money. We focus on these
techniques in this module.
In the final analysis, capital budgeting is really about management’s search for the best capital ­projects
— those that add the greatest value to the company. Over the long term, the most successful companies
are those whose managements consistently search for and find capital investment opportunities that
increase company value.
Capital budgeting process
The capital budgeting process starts with a company’s strategic plan, which spells out its strategy for
the next 3 to 5 years. Division managers then convert the company’s strategic objectives into business
plans. These plans have a 1–2‐year time horizon, provide a detailed description of what each division
should accomplish during the period covered by the plan and have quantifiable targets that each division
is expected to achieve. Behind each division’s business plan is a capital budget that details the resources
that management believes it needs to get the job done.
The capital budget is generally prepared jointly by the Chief Financial Officer’s staff and financial
staff at the divisional and lower levels and reflects, in large part, the activities outlined in the divisional
business plans. Many of these proposed expenditures are routine in nature, such as the repair or purchase
of new equipment at existing facilities. Less frequently, companies face broader strategic decisions, such
as whether to launch a new product, build a new plant, enter a new market or buy a business. Table 10.1
identifies some reasons that companies initiate capital projects.
TABLE 10.1
Key reasons for making capital expenditures
Reason
Description
Renewal
Over time, equipment must be repaired, overhauled, rebuilt or retrofitted with new
technology to keep the company’s manufacturing or service operations going. For example,
a company that has a fleet of delivery trucks may decide to overhaul the trucks and their
engines, rather than purchasing new trucks. Renewal decisions typically do not require an
elaborate analysis and are made on a routine basis.
Replacement
At some point, an asset will have to be replaced rather than repaired or overhauled.
This typically happens when the asset is worn out or damaged. The major decision is
whether to replace the asset with a similar piece of equipment or to purchase equipment
that would require a change in the production process. Sometimes replacement
decisions involve equipment that is operating satisfactorily but has become obsolete. The
new or retrofitted equipment may provide cost savings with respect to labour or material
usage, and/or may improve product quality. These decisions typically originate at the plant
level.
278 Finance essentials
Reason
Description
Expansion
Strategically, the most important motive for capital expenditures is to expand the level
of operating output. One type of expansion decision involves increasing the output of
existing products. This may mean new equipment to produce more products or expand the
company’s distribution system. These types of decisions typically require a more complex
analysis than a renewal or replacement decision. Another type of expansion decision
involves producing a new product or entering a new market. This type of expansion often
involves large dollar amounts and significant business risk, and so requires the approval of
the company’s board of directors.
Regulatory
Some capital expenditures are required by federal and state regulations. These mandatory
expenditures usually involve meeting workplace safety standards and environmental standards.
Other
This category includes items such as parking facilities, office buildings and executive aircraft.
Many of these capital expenditures are hard to analyse because it is difficult to estimate their
cash inflows. Ultimately, such decisions can be more subjective than analytical.
Sources of information
Where does a company get all of the information it needs to make capital budgeting decisions? Most of
this information is generated within the company and, for expansion decisions, it often starts with sales
representatives and marketing managers, who are in the marketplace talking to potential and current cus­
tomers on a day‐to‐day basis. For example, a sales manager with a new product idea might present the
idea to management and the marketing research group. If the product idea looks promising, the marketing
research group will estimate the size of the market and a market price. If the product requires new
technology, the company’s research and development group must decide whether to develop the tech­
nology or to buy it. Next, cost accountants and production engineers determine the cost of producing
the product and any capital expenditures necessary to manufacture it. Finally, the CFO’s staff takes the
data and estimates the cost of the project and the cash flows it will generate over time. The project is a
viable candidate for the capital budget if the present value of the cash benefits exceeds the project’s cost.
Classification of investment projects
Potential capital budgeting projects can be classified into three types: (1) independent projects;
(2) mutually exclusive projects; and (3) contingent projects.
Independent projects
Projects are independent when their cash flows are unrelated. With independent projects, accepting or
rejecting one project does not eliminate the other projects from consideration (assuming the company
has unlimited funds to invest). For example, suppose a company has unlimited funding and management
wants to: (1) build a new parking ramp at its headquarters; (2) acquire a small competitor; and (3) add
manufacturing capacity to one of its plants. Since the cash flows for each project are unrelated, accepting
or rejecting one of the projects will have no effect on the others.
Mutually exclusive projects
When projects are mutually exclusive, acceptance of one project precludes acceptance of the others.
Typically, mutually exclusive projects perform the same function and thus only one project needs to be
accepted. For example, a food manufacturing company is considering two possible new manufacturing
sites (or capital projects) at Altona and Bendigo in Victoria. Once management has selected Bendigo, the
other possible location, Altona, is out of the running.
Contingent projects
With contingent projects, the acceptance of one project is contingent on the acceptance of another. There
are two types of contingency situations. In the first type of situation, the contingent product is mandatory. For example, when a public utility company (such as your local electricity company) builds a
MODULE 10 Capital budgeting and cash flows 279
power plant, it must also invest in suitable pollution‐control equipment to meet government environ­
mental standards. The pollution‐control investment is a mandatory contingent project. When faced with
mandatory contingent projects, it is best to treat all of the projects as a single investment for the purpose
of evaluation. This provides management with the best measure of the value created by these projects.
In the second type of situation, the contingent project is optional. For example, suppose Dell invests
in a new computer for the home market. This computer has a feature that allows Dell to bundle a pro­
prietary gaming system. The gaming system is a contingent project but is an optional add‐on to the new
computer. In these situations, the optional contingent project should be evaluated independently and be
accepted or rejected on its own merits.
Basic capital budgeting terms
In this section we briefly introduce two terms that you need to be familiar with — cost of capital and
opportunity cost of capital.
Cost of capital
The cost of capital is the rate of return that a capital project must earn in order to be accepted by manage­
ment. The cost of capital can be thought of as an opportunity cost. Recall from earlier modules that an
opportunity cost is the value of the most valuable alternative given up if a particular investment is made.
Let’s consider the opportunity cost concept in the context of capital budgeting decisions. When inves­
tors buy shares in a company or lend money to a company, they are giving management money to invest
on their behalf. Thus, when a company’s management makes capital investments, it is really investing
shareholders’ and creditors’ money in real assets — property, plant and equipment. Since shareholders
and creditors could have invested their money in financial assets, the minimum rate of return they are
willing to accept on an investment in a real asset is the rate they could have earned investing in financial
assets that have similar risk. The rate of return that investors can earn on financial assets with similar risk
is an opportunity cost because investors lose the opportunity to earn that rate if the money is invested
in a real asset instead. It is therefore the rate of return that investors will require for an investment in a
capital project. In other words, this rate is the cost of capital. It is also known as the opportunity cost of
capital. We discuss how we estimate the opportunity cost of capital in practice in a later module.
Investment decisions have opportunity costs
When any investment is made, the opportunity to earn a return from an alternative investment is lost. This
lost return can be viewed as a cost that arises from a lost opportunity. For this reason, it is called an oppor­
tunity cost. The opportunity cost of capital is the return an investor gives up when their money is invested
in one asset rather than the best alternative asset. For example, suppose that a company invests in a piece
of equipment rather than returning money to shareholders. If shareholders could have earned an annual
return of 12 per cent on a share with cash flows that are as risky as the cash flows the equipment will
produce, this is the opportunity cost of capital associated with the investment in the piece of equipment.
BEFORE YOU GO ON
1. Why are capital investments the most important decisions made by a company’s management?
2. What are the differences between capital projects that are independent, mutually exclusive and
contingent?
10.2 Capital budgeting methods
LEARNING OBJECTIVE 10.2 Evaluate capital budgeting projects using the net present value (NPV),
payback period, accounting rate of return and internal rate of return methods.
In this section we discuss four capital budgeting methods that are commonly used to evaluate capital
budgeting projects. The first, the net present value (NPV) method, is one of the most basic concepts
280 Finance essentials
underlying corporate finance. It is the capital budgeting technique recommended in this text. The second
method, the payback period, is one of the most commonly used methods due to its simplicity — it
tells us how long a project’s cash flows will take to recoup the initial outlay. We turn next to a capital
budgeting technique based on the accounting rate of return (ARR), sometimes called the book value
rate of return. The final method we discuss is the internal rate of return (IRR), which is closely related
to the NPV method. It tells us the rate of return that a project earns when the NPV is equal to zero.
Net present value
The NPV method tells us the amount by which the benefits from a capital expenditure exceed its costs. It
is consistent with the goal of financial management — to maximise the wealth of the shareholders. The
NPV of a project is the difference between the present value of the project’s future cash flows and the
present value of its cost. The NPV can be expressed as follows:
NPV = PV(Project’s future cash flows) – PV(Cost of the project)
If a capital project has a positive NPV, the value of the cash flows the project is expected to generate exceeds
the project’s cost. Thus, a positive NPV project increases the value of the company and, hence, shareholders’
wealth. If a capital project has a negative NPV, the value of the cash flows from the project is less than its
cost. If accepted, a negative NPV project will decrease the value of the company and shareholders’ wealth.
To illustrate these important points, consider an example. Suppose a company is considering building
a new marina for pleasure boats. The company has a genie that can tell the future with perfect certainty.
The finance staff estimates that the marina will cost $3.50 million. The genie volunteers that the market
value of the marina is $4.25 million.
Assuming this information is correct, the NPV for the marina project is a positive $750 000
($4.25 million – $3.50 million). Management should accept the project, because the excess of market
value over cost increases the value of the company by $750 000. Why is a positive NPV a direct measure
of how much a capital project will increase the value of the company? If management wanted to, the
company could sell the marina for $4.25 million, pay the $3.50 million in expenses and deposit $750 000
in the bank. The value of the company would increase by the $750 000 deposited in the bank. In sum,
the NPV method tells us which capital projects to select and how much value they add to the company.
Net present value technique
The NPV of a capital project can be stated in equation form as the present value of all net cash flows
(inflows – outflows) connected with the project, whether in the current period or in the future. The NPV
equation can be written as follows:
NCF1
NCF2
NCFn
+
++
1+ k
(1 + k )2
(1 + k )n
n
NCFt
=∑
(1
+ k )t
t=0
NPV = NCF0 +
(10.1)
where:
NCFt = net cash flow (cash inflows – cash outflows) in period t, where t = 1, 2, 3, . . . n
k = the cost of capital
n = the project’s estimated life
Next, we provide an example to see how the NPV is calculated for a capital project. Suppose you are the
president of a small regional company located in Shepparton that manufactures frozen pizzas which are
sold to grocery stores and to companies in the hospitality and food service industry. Your market research
group has developed an idea for a ‘pocket’ pizza that can be used as an entrée with a meal or as an ‘on the
go’ snack. The sales manager believes that, with an aggressive advertising campaign, sales of the product
MODULE 10 Capital budgeting and cash flows 281
will be about $300 000 per year. The cost to modify the existing production line will also be $300 000
according to the plant manager. The marketing and plant managers estimate that the cost to produce the
pocket pizzas, to market and advertise them, and to deliver them to customers will be about $220 000 per
year. The product’s life is estimated to be 5 years and the specialised equipment necessary for the project
has an estimated salvage value of $30 000. The appropriate cost of capital is 15 per cent.
When analysing capital budgeting problems, we typically have a lot of data to sort through. The work­
sheet approach is helpful in keeping track of the data in an organised format. Figure 10.1 shows the time
line and relevant cash flows for the pocket pizza project. The steps in analysing the project’s cash flows
and determining its NPV are as follows.
1. Determine the cost of the project. The cost of the project is the cost to modify the existing production
line, which is $300 000. This is a cash outflow (negative sign).
2. Estimate the project’s future cash flows over its expected life. The project’s future cash inflows come
from sales of the new product. Sales are estimated at $300 000 per year (positive sign). The cash
outflows are the costs to manufacture and distribute the new product, which are $220 000 per year
(negative sign). The life of the project is 5 years. The project has a salvage value of $30 000, which
is a cash inflow (positive sign). The net cash flow (NCF) per time period is just the sum of the cash
inflows and the cash outflows for that period. For example, the NCF for period t = 0 is –$300 000, the
NCF for period t = 1 is $80 000 and so on, as you can see in figure 10.1.
3. Determine the riskiness of the project and appropriate cost of capital. The discount rate is the cost of
capital, which is 15 per cent.
4. Calculate the project’s NPV. To calculate the project’s NPV, we apply equation 10.1 by plugging in
the NCF values for each time period and using the cost of capital, 15 per cent, as the discount rate.
The equation looks like this (the figures are in thousands of dollars):
NPV =
n
NCFt
∑ (1 + k )
t=0
t
(80 + 30)
80
80
80
+
++
+
2
4
(1.15)5
1.15 (1.15)
(1.15)
= − $300 + $69.57 + $60.49 + $52.60 + $45.74 + $54.69
= − $300 +
= − $300 + $283.09
= − $16.91
The NPV for the pocket pizza project is therefore –$16 910.
5. Make a decision. The pocket pizza project has a negative NPV, which indicates that the project is not a
good investment and should be rejected. If management undertook this project, the value of the company
would decrease by $16 910, and if the company had 100 000 shares outstanding, we can estimate that the
project would decrease the value of each share by about 17 cents ($16 910/100 000 shares).
FIGURE 10.1
Pocket pizza project time line and cash flows ($ thousands)
0
1
2
3
4
5 Year
Time line
Cash flows:
Initial cost
–$300
Inflows
Outflows
$300
$300
$300
$300
$300
–$220
–$220
–$220
–$220
–$220
$80
$80
$80
$80
$110
30
Salvage
Net cash flow –$300
282 Finance essentials
Calculator tip: calculating NPV
Using a financial calculator is an easier way to calculate the present value of the future cash flows. In this
example you should recognise that the cash flow pattern is a 5‐year ordinary annuity with an additional cash
inflow in the 5th year. This is exactly the cash pattern for the bond with annual coupon payments and pay­
ment of principal at maturity we saw in an earlier module. We can find the present value using a financial
calculator, with $80 being the annuity stream for 5 years and $30 the salvage value at year 5, as follows:
Procedure
Key operation
Enter cash flow data
30 [FV]
30 ⇒ FV
5 [N]
5⇒N
15 [I/Y]
15 ⇒ I/Y
80 [PMT]
80 ⇒ PMT
[COMP] [PV]
PV =
Calculate PV
Display
30.00
5.00
15.00
80.00
–283.09
The PV of the future cash flows is –$283.09. With that information, we can calculate the NPV using
equation 10.1 as follows:
n
NCFt
NPV = ∑
− NCF0
(1
+ k )t
t =1
= $283.09 − 300.00
= − $16.91
DEMONSTRATION PROBLEM 10.1
The dough’s up: the self‐rising pizza project
Problem:
Let’s continue our frozen pizza example. Suppose the head of the research and development (R&D)
group announces that R&D engineers have developed a breakthrough technology — self‐rising frozen
pizza dough that, when baked, rises and tastes exactly like fresh‐baked dough.
The cost is $300 000 to modify the production line. Sales of the new product are estimated at $200 000
for the first year, $300 000 for the next 2 years and $500 000 for the final 2 years. It is estimated that
production, sales and advertising costs will be $250 000 for the first year and then decline to a constant
$200 000 per year. There is no salvage value at the end of the product’s life and the appropriate cost of
capital is 15 per cent. Is the project, as proposed, economically viable?
Approach:
To solve the problem, work through the steps for NPV analysis given in the text.
Solution:
Figure 10.2 shows the project’s cash flows.
1. The cost to modify the production line is $300 000, which is a cash outflow and the cost of the project.
FIGURE 10.2
Self‐rising pizza dough project time line and cash flows ($ thousands)
0
1
2
3
4
5 Year
Time line
Cash flows:
Initial cost
–$300
Inflows
Outflows
$200
$300
$300
$500
$500
–$250
–$200
–$200
–$200
–$200
–$50
$100
$100
$300
$300
Salvage
Net cash flow
–$300
MODULE 10 Capital budgeting and cash flows 283
2. The future cash flows over the expected life of the project are laid out on the time line in figure 10.2.
The project’s life is 5 years. The NCFs for the capital project are negative at the beginning of the pro­
ject and in the first year (−$300 000 and −$50 000) and thereafter positive. The worksheet shows the
time line and cash flows for the self‐rising pizza dough project. As always, it is important to assign
each cash flow to the appropriate year and to give it the proper sign. Once you have calculated the
net cash flow for each time period, solving for NPV is just a matter of plugging the data into the NPV
formula.
3. The appropriate cost of capital is 15 per cent.
4. The values are substituted into equation 10.1 to calculate the NPV:
NPV = NCF0 +
NCF1
NCF2
NCFn
+
++
1+ k
(1 + k )2
(1 + k )n
= −$300 000 −
$50 000 $100 000 $100 000 $300 000 $300 000
+
+
+
+
1.15
(1.15)2
(1.15)3
(1.15)4
(1.15)5
= −$300 000 − $43 478 + $75 614 + $65752 + $171526 + $149153
= $118 567
5. The decision is based on the NPV. The NPV for the self‐rising pizza dough project is $118 567.
Because the NPV is positive, management should accept the project. The project is estimated to
increase the value of the company by $118 567.
USING EXCEL
Net present value
Net present value problems are most com­
monly solved using a spreadsheet program
like Excel. The program is designed to keep
track of all the cash flows and the periods in
which they occur. The following spreadsheet
setup shows how to calculate the NPV for the
self‐rising pizza dough project.
Note that the NPV formula does not take
into account the cash flow in year zero. There­
fore, you only enter into the NPV formula the
cash flows in years 1 to 5, along with the dis­
count rate. You then add the cash flow in year
zero to the total from the NPV formula calcu­
lation to get the NPV for the investment.
DECISION‐MAKING EX AMPLE 10.1
The IT department’s capital projects
Situation:
Suppose you are the manager of the information technology (IT) department of the frozen pizza manu­
facturer we have been discussing. Your department has identified four possible capital projects with the
following NPVs: (1) $4500; (2) $3000; (3) $0; and (4) –$1000. What should you decide about each project
if the projects are independent? What should you decide if the projects are mutually exclusive?
284 Finance essentials
Decision:
If the projects are independent, you should accept projects 1 and 2, both of which have a positive NPV,
and reject project 4. Project 3, with an NPV of zero, could be either accepted or rejected. If the pro­
jects are mutually exclusive and you can accept only one of them, it should be project 1, which has the
largest NPV.
Concluding comments on NPV
Some concluding comments about the NPV method are in order. First, as you may have noticed,
the NPV calculations are rather mechanical once we know the cash flows and have determined the
cost of capital. The real difficulty is in estimating or forecasting the future cash flows. Although this
may seem a daunting task, companies with experience in producing and selling a particular type of
product can usually generate fairly accurate estimates of sales volumes, prices and production costs.
However, problems can arise with cash flow estimates when a project team becomes enamoured with
a project. Wanting the project to succeed, the project team can be too optimistic about the cash flow
projections.
Second, we must recognise that the calculated values for NPV are estimates based on management’s
informed judgement; they are not real market data. Like any estimate, they can be too high or too
low. The only way to determine a project’s ‘true’ NPV is to put the asset up for sale and see what
price market participants are willing to pay for it. An example of this approach is the sale of our pizza
­restaurant; however, situations such as this are the exception, not the rule.
Finally, there is nothing wrong with using estimates to make business decisions as long as they are
based on informed judgements and not guesses. Most business managers are routinely required to make
decisions that involve expectations about future events. In fact, that is what business is really all about —
dealing with uncertainty and making decisions that involve risk.
In conclusion, the NPV approach is the method we recommend for making capital investment
decisions. The following table summarises the NPV decision rules and the method’s key advantages and
disadvantages.
Summary of net present value (NPV) method
Decision rule:
NPV > 0 → Accept the project.
NPV < 0 → Reject the project.
Key advantages
Key disadvantages
1. Uses the discounted cash flow valuation technique
to adjust for the time value of money.
2. Provides a direct (dollar) measure of how much
a capital project will increase the value of the
company.
3. Is consistent with the goal of maximising
shareholder value.
1. Can be difficult to understand without
an accounting and finance background.
Payback period
The payback period is one of the most widely used tools for evaluating capital projects. The payback
period is defined as the number of years it takes for the cash flows from a project to recover the project’s
initial investment. With the payback method for evaluating projects, a project is accepted if its payback
period is below some specified threshold. Although it has serious weaknesses, this method does provide
insight into a project’s risk and liquidity; the more quickly you recover the cash, the less risky is the
­project. This insight cannot be obtained from the other project evaluation techniques.
MODULE 10 Capital budgeting and cash flows 285
Calculating the payback period
To calculate the payback period, we need to know the project’s cost and to estimate its future net cash
flows. The net cash flows and the project cost are the same values that we use to calculate the NPV. The
payback (PB) equation can be expressed as follows:
PB = Years before cost recovery +
Remaining cost to recover
Cash flow during the year
(10.2)
Figure 10.3 shows the net cash flows (row 1) and cumulative net cash flows (row 2) for a proposed
capital project with an initial cost of $70 000. The payback period calculation for our example is:
PB = Years before cost recovery +
= 2 years +
$70 000 − $60 000
$20 000
= 2 years +
$10 000
$20 000
Remaining cost to recover
Cash flow during the year
= 2.5 years
FIGURE 10.3
Payback period cash flows and calculations
0
1
2
3
4 Year
Time line
Net cash flow (NCF)
−$70 000
$30 000
$30 000
$20 000
$15 000
Cumulative NCF
−$70 000
−$40 000
−$10 000
$10 000
$25 000
Let’s look at this calculation in more detail. Note in figure 10.3 that the company recovers cash
flows of $30 000 in the first year and $30 000 in the second year, for a total of $60 000 over the 2 years.
During the third year, the company needs to recover only $10 000 ($70 000 – $60 000) to pay back
the full cost of the project. The third‐year cash flow is $20 000, so it will only have to wait 0.5 year
($10 000/$20 000) to recover the final amount. Thus, the payback period for this project is 2.5 years
(2 + 0.5).
The idea behind the payback period method is simple: the shorter the payback period, the faster the
company gets its money back and so the more desirable the project. However, there is no economic
rationale that links the payback method to shareholder value maximisation. Companies that use the
payback method accept all projects with a payback period under some threshold and reject those with a
payback period over this threshold. If a company has a number of projects that are mutually exclusive,
the projects are selected in order of their payback rank: projects with the shortest payback period are
selected first. Figure 10.3 shows the net and cumulative net cash flows for a proposed capital project
with an initial cost of $70 000. The cash flow data is used to calculate the payback period, which is
2.5 years.
286 Finance essentials
DEMONSTRATION PROBLEM 10.2
A payback calculation
Problem:
A company has two capital projects, A and B, which are under review for funding. Both projects cost
$500 and they have the following cash flows.
Year
Project A
Project B
0
–$500
–$500
1
100
400
2
200
300
3
200
200
4
400
100
What is the payback period for each project? If the projects are independent, which project should man­
agement select? If the projects are mutually exclusive, which project should management accept? The
company’s payback cut‐off point is 2 years.
Approach:
Use equation 10.2 to calculate the number of years it takes for the cash flows from each project to recover
the project’s initial investment. If the two projects are independent, you should accept the p
­ rojects that
have a payback period less than or equal to 2 years. If the projects are mutually exclusive, you should
accept the project with the shortest payback period if that is also less than or equal to 2 years.
Solution:
The payback period for project A requires only that we calculate the first term in equation 10.2 —
years before recovery. The first year recovers $100, the second year $200 and the third year $200, for
a total of $500 ($100 + $200 + $200). Thus, in three years the $500 investment is fully recovered, so
PBA = 3.00:
PB = Years before cost recovery +
Remaining cost to recover
Cash flow during the year
PBA = 3 years
For project B, the first year recovers $400 and the second year $300. Since we need only part of the
second‐year cash flow to recover the initial cost, we calculate both terms in equation 10.2 to obtain the
payback time:
$500 − $400
$300
$100
= 1 year +
$300
= 1.33 years
PBB = 1 year +
Whether the projects are independent or mutually exclusive, management should accept only project B
since project A’s payback period exceeds the 2‐year cut‐off point.
Evaluating the payback rule
In spite of its lack of sophistication, the standard payback period is widely used in business, in part
because it provides an intuitive and simple measure of a project’s liquidity risk. This makes sense
MODULE 10 Capital budgeting and cash flows 287
because projects that pay for themselves quickly are less risky than projects whose paybacks occur
further in the future. There is a strong feeling in business that ‘getting your money back quickly’ is an
important standard when making capital investments. Probably the greatest advantage of the payback
period is its simplicity; it is easy to calculate and easy to understand, making it especially attractive to
business executives with little training in accounting and finance.
When compared with the NPV method, however, the payback method has some serious shortcomings.
First, the standard payback method does not use discounting; hence, it ignores the time value of money.
Second, it does not adjust or account for differences in the riskiness of projects. Another problem is that
there is no economic rationale for establishing cut‐off criteria. Who is to say that a particular cut‐off,
such as 2 years, is optimal with regards to maximising shareholder value?
Finally, perhaps the greatest shortcoming of the payback method is its failure to consider cash flows
after the payback period. This is true whether or not the cash flows are discounted. As a result of this
feature, the payback method is biased towards shorter term projects, which tend to free up cash more
quickly. Consequently, projects for which cash inflows tend to occur further in the future, such as
research and development investments, new product launches and entry into new lines of business, are
at a disadvantage when the payback method is used. The following table summarises the major features
of the payback method.
Summary of payback method
Decision rule:
Payback period ≤ Payback cut‐off point → Accept the project.
Payback period > Payback cut‐off point → Reject the project.
Key advantages
Key disadvantages
1. Is easy to calculate and understand for people
without a strong finance background.
2. Is a simple measure of a project’s liquidity.
1. Most common version does not account for time value
of money.
2. Does not consider cash flows past the payback period.
3. Is biased against long‐term projects such as research
and development and new product launches.
4. Has an arbitrary cut‐off point.
Accounting rate of return
This method calculates the return on a capital project using accounting numbers — the project’s net
income (NI) and book value (BV) — rather than cash flow data. The accounting rate of return (ARR)
can be calculated in a number of ways, but the most common definition is:
ARR =
where:
Average net income
Average book value
(10.3)
Average net income = (NI1 + NI 2 + + NI n )/n
Average book value = (BV1 + BV2 + + BVn )/n
n = the project’s estimated life
Similarly to the payback period method, the ARR is easy to calculate and understand for people
without a strong finance background. It is still used in business as a screening measure of a project on
company profitability. However, it has a number of major flaws as a tool for evaluating capital expendi­
ture decisions. Besides the fact that the ARR is based on accounting numbers rather than cash flows, it
is not really even an accounting‐based rate of return. Instead of discounting a project’s cash flows over
time, it simply gives us a number based on average figures from the income statement and balance sheet.
Thus, the ARR ignores the time value of money. Also, as with the payback method, there is no econ­
omic rationale that links a particular acceptance criterion to the goal of maximising shareholder value.
288 Finance essentials
Because of these major shortcomings, the ARR technique should not be used as the only method to
evaluate the viability of capital projects.
Internal rate of return
The internal rate of return, known in practice as the IRR, is an important and legitimate alternative to the
NPV method. The NPV and IRR techniques are closely related in that both involve discounting the cash
flows from a project; thus, both account for the time value of money. When we use the NPV method to
evaluate a capital project, the discount rate is the rate of return required by investors for investments with
similar risk, which is the project’s opportunity cost of capital. When we use the IRR, we are looking for
the rate of return associated with a project so that we can determine whether this rate is higher or lower
than the project’s opportunity cost of capital.
We can define the IRR as the discount rate that equates the present value of a project’s expected cash
inflows to the present value of the project’s outflows:
PV(Project’s future cash flows) = PV(Cost of the project)
This means that we can also describe the IRR as the discount rate that causes the NPV to equal zero.
This relationship can be written in a general form as follows:
NCF1
NCF2
NCFn
+
++
2
1 + IRR (1 + IRR)
(1 + IRR)n
n
NCFt
=∑
=0
t
t = 0 (1 + IRR)
NPV = NCF0 +
(10.4)
Because of their close relationship, it may seem that the IRR and the NPV are interchangeable — that
is, either should accept or reject the same capital projects. After all, both methods are based on whether
the project’s return exceeds the cost of capital and, hence, whether the project will add value to the com­
pany. In many circumstances, the IRR and NPV methods do give us the same answer. As you will see
later, however, some of the mathematical properties of the IRR equation can lead to incorrect decisions
concerning whether to accept or reject a particular capital project.
Calculating the IRR
The IRR is an expected rate of return like the yield to maturity we calculated for bonds in module 8.
Thus, in calculating the IRR, we need to apply the same trial‐and‐error method we used in module 8.
We begin by doing some IRR calculations by trial and error so that you understand the process, and
then switch to the financial calculator, which provides an answer more quickly and is less prone
to mistakes.
Trial‐and‐error method
Problem: Larry’s Gelato in Lygon Street, Melbourne is famous for its gelato. However, some customers
have asked for a healthier, low‐fat frozen yoghurt. The machine that best makes this confection is
­manufactured in Italy and costs $5000 plus $1750 for installation. Larry estimates that the machine will
generate a net cash flow of $2000 per year (the shop closes from March to September of each year). He
also estimates the machine’s life to be 10 years and that it will have a $400 salvage value. His cost of
capital is 15 per cent. Larry thinks the machine is overpriced. Is he right?
MODULE 10 Capital budgeting and cash flows 289
Using equation 10.4, we substitute various values for IRR into the equation to calculate the project’s IRR
by trial and error. We continue this process until we find the IRR value that makes equation 10.4 equal zero.
A good starting point is to use the cost of capital as the discount rate. Note that when we discount the
NCFs by the cost of capital, we are calculating the project’s NPV.
The IRR for an investment is the discount rate at which the NPV is zero. Thus, we can use equation 10.4
to solve for the IRR and then compare this value with Larry’s cost of capital. If the IRR is greater than
the cost of capital, the project has a positive NPV and should be accepted.
The total cost of the machine is $6750 ($5000 + $1750), and the final cash flow at year 10 is $2400
($2000 + $400).
0
1
2
3
9
$2000
$2000
$2000
$2000
15%
–$6750
10 Year
$2400
NCF1
NCF2
NCFn
+
++
=0
2
1 + IRR (1 + IRR)
(1 + IRR)n
$2000 $2000
$2400
= −$6750 +
+
++
= $3386.41
2
1.15 (1.15)
(1.15)10
$2000
$2000
$2400
= −$6750 +
+
++
= $0.00
2
1.2708 (1.2708)
(1.2708)10
NPV = NCF0 +
NPV15.00%
NPV27.08%
The hand trial‐and‐error calculations are shown in these equations. The first calculation uses
15 per cent, the cost of capital, our recommended starting point, and the answer is $3386.41 (which is
also the project’s NPV). Because the value is a positive number, we need to use a larger discount rate
than 15 per cent. Our guess is 27.08 per cent. At that value, NPV = 0; thus, the IRR for the yoghurt
machine is 27.08 per cent.
290 Finance essentials
Since the IRR is higher than Larry’s cost of capital, the IRR criterion indicates the project should be
accepted. As the project’s NPV is positive $3386.41, it also indicates that Larry should accept the pro­
ject. Thus, the IRR and NPV methods have reached the same conclusion.
Financial calculator method
Because the project’s future cash flow pattern resembles that for a bond, we can also solve for the IRR on a
financial calculator, just as we would solve for the yield to maturity. Enter the data directly into the corre­
sponding keys on the calculator and press the interest key and we have our answer — 27.08 per cent.
Procedure
Key operation
Enter cash flow data
[+/–] 6750 [PV]
(–6750) ⇒ PV
10 [N]
10 ⇒ N
400 [FV]
400 ⇒ FV =
400.00
2000 [PMT]
2000 ⇒ PMT
2000.00
[COMP] [I/Y]
I/Y
Calculate PV
Display
–6750.00
10.00
27.08
As with present value calculations, for projects with unequal cash flows you should consult your
financial calculator’s manual.
Because the project’s IRR exceeds Larry’s cost of capital of 15 per cent, the project should be
accepted. Larry is wrong.
USING EXCEL
Internal rate of return
You now see that calculating the IRR by hand
can be tedious. The trial‐and‐error method can
take a long time and can be quite frustrating.
Knowing all the cash flows and an approximate
rate will allow you to use a spreadsheet formula
to get an answer instantly.
The spreadsheet shows the setup for cal­
culating the IRR for the low‐fat frozen yoghurt
machine at Larry’s Gelato that is described above.
Here are a couple of important points to
note about IRR calculations using spreadsheet
programs:
1. Unlike the NPV formula, the IRR formula
accounts for all cash flows, including the ini­
tial investment in year 0, so there is no need
to add this cash flow later.
2. In order to calculate the IRR, you need to
provide a ‘guess’ value, or a number that
you estimate is close to the IRR. A good
value to start with is the cost of capital. To
learn more about why this value is needed,
you should go to your spreadsheet’s help
manual and search for ‘IRR’.
When IRR and NPV methods agree — independent projects
and conventional cash flows
In the Larry’s Gelato example, the IRR and NPV methods agree. These two methods will always agree
when you are evaluating independent projects and the projects’ cash flows are conventional. As discussed
MODULE 10 Capital budgeting and cash flows 291
previously, an independent project is one that can be selected with no effect on any other project, assuming
the company faces no resource constraints. If two projects are independent, a positive NPV project will
have an IRR greater than the cost of capital. A project with a conventional cash flow is one with an initial
cash outflow followed by one or more future cash inflows. Put another way, after the initial investment is
made (cash outflow), all the cash flows in each future year are positive (inflows). For example, the pur­
chase of a bond involves a conventional cash flow. You purchase the bond for a price (cash outflow) and in
the future you receive coupon payments and a principal payment at maturity (cash inflows).
Let’s look more closely at the kinds of situations in which the NPV and the IRR methods agree. A good
way to visualise the relationship between the IRR and NPV methods is to graph NPV as a function of the
discount rate. The graph, called an NPV profile, shows the NPV of the project at various costs of capital.
Figure 10.4 shows a basic NPV profile. We have placed the NPV value on the vertical axis, or y‐axis,
and the discount rate on the horizontal axis, or x‐axis.
As you can see, as the discount rate increases, the NPV curve declines smoothly. Not surprisingly, the
curve intersects the x‐axis at precisely the point where the NPV is 0. At this point k is equal to the pro­
ject’s IRR. The IRR precisely marks the point at which the NPV changes from a positive to a negative
value. Whenever a project is independent and has conventional cash flows, the result will be as shown
in the figure. The NPV will decline as the discount rate increases, and the IRR and NPV methods will
result in the same capital expenditure decision.
NPV $ for a given project
FIGURE 10.4
NPV profile
Positive NPV – accept
(NPV decreases as k increases)
IRR for project
0
k (%)
Negative NPV – reject
(k is so large that NPV is negative)
When IRR and NPV methods disagree — mutually exclusive
projects and unconventional cash flows
We have seen that the IRR and NPV methods lead to identical investment decisions for capital projects
that are independent and that have conventional cash flows. However, if either of these conditions is not
met, the IRR and NPV methods can produce different accept–reject decisions.
Mutually exclusive projects
The NPV and IRR methods may lead to inconsistent accept–reject decisions when capital projects are mutu­
ally exclusive — that is, when accepting one project means rejecting the other. For example, suppose you
own a small store in the central business district of Sydney that is currently vacant. You are looking at two
business opportunities: opening an upscale coffee shop or opening a photocopying and printing centre.
Clearly you cannot pursue both projects at the same location; these two projects are mutually exclusive.
292 Finance essentials
When you have mutually exclusive projects, how do you select the best alternative? If you are using
the NPV method, the answer is easy. You select the project that has the highest NPV because it will
increase the value of the company by the largest amount. If you are using the IRR method, it would
seem logical to select the project with the highest IRR. In this case, though, the logic is wrong! You
cannot tell which mutually exclusive project to select just by looking at the projects’ IRRs.
Let’s consider another example to illustrate the problem. The cash flows for two projects, A and B,
are as follows:
Year
Project A
Project B
0
−$100
−$100
1
50
20
2
40
30
3
30
50
4
30
65
The IRR is 20.7 per cent for project A and 19.0 per cent for project B. Because the two projects are mutu­
ally exclusive, only one project can be accepted. If you were following the IRR decision rule, you would
accept project A. However, as you will see, it turns out that project B might be the better choice.
The following table shows the NPVs for the two projects at several discount rates.
Discount rate
NPV of project A
NPV of project B
0%
$50.0
$65.0
5%
34.5
42.9
10%
21.5
24.9
13%
14.8
15.7
15%
10.6
10.1
20%
1.3
−2.2
25%
−6.8
−12.6
30%
−13.7
−21.3
IRR
20.7%
19.0%
Note that the project with the higher NPV depends on what rate of return is used to discount the cash
flows. Our example shows a conflict in ranking order between the IRR and NPV methods at discount
rates between 0 and 13 per cent. In this range, project B has the lower IRR, but it has the higher NPV and
should be the project selected. If the discount rate is above 15 per cent, however, project A has the higher
NPV as well as the higher IRR. In this range there is no conflict between the two evaluation methods.
Another conflict involving mutually exclusive projects concerns comparisons of projects that have
significantly different costs. The IRR does not adjust for these differences in size. What the IRR gives us
is a rate of return on each dollar invested. In contrast, the NPV method calculates the total dollar value
created by the project. The difference in results can be significant.
Unconventional cash flows
Unconventional cash flows can cause a conflict between the NPV and IRR decision rules. In some
instances the cash flows for an unconventional project are just the reverse of those of a conventional
project: the initial cash flow is positive and all subsequent cash flows are negative. For example, con­
sider a life insurance company that sells a lifetime annuity to a retired person. The company receives a
single cash payment, which is the price of the annuity (cash inflow), and then makes monthly payments
to the retiree for the rest of their life (cash outflows). In this case, we need only reverse the IRR decision
rule and accept the project if the IRR is less than the cost of capital to make the IRR and NPV methods
MODULE 10 Capital budgeting and cash flows 293
agree. The intuition in this example is that the life insurance company is effectively borrowing money
from the retiree and the IRR is a measure of the cost of that money. The cost of capital is the rate at
which the life insurance company can borrow elsewhere. An IRR less than the cost of capital means that
the lifetime annuity provides the insurance company with money at a lower cost than alternative sources.
When a project’s future cash flows include both positive and negative cash flows, the situation is more
complicated. An example of such a project is an assembly line that will require one or more major renovations
over its lifetime. Another common business situation is a project that has conventional cash flows except for
the final cash flow, which is negative. The final cash flow might be negative because extensive environmental
cleanup is required at the end of the project, such as the cost for decommissioning a nuclear power plant, or
because the equipment originally purchased has little or no salvage value and is expensive to remove.
Consider an example. Suppose a company invests in a gold‐mining operation that costs $55 million
and has an expected life of 2 years. In the first year, the project generates a cash inflow of $150 million.
In the second year, extensive environmental and site restoration is required, so the expected cash flow is
a negative $100 million. The time line for these cash flows follows:
0
1
Cash flow –$55
(millions)
2 Year
–$100
$150
Once again, the best way to understand the effect of these cash flows is to look at an NPV profile.
Shown here are NPV calculations we made at various discount rates:
Discount rate
NPV ($ millions)
0%
−$5.00
10
−1.28
20
0.56
30
1.21
40
1.12
50
0.56
60
−0.31
70
−1.37
Looking at the data in the table, you can probably spot a problem. The NPV is initially negative (–$5.00);
then, at a discount rate of 20 per cent, switches to positive ($0.56); and then, at a discount rate of
60 per cent, switches back to negative (–$0.31).
We have two IRRs, one at 16.05 per cent and the other at 55.65 per cent. Which is the correct IRR or
are both correct? Actually, there is no correct answer; these results are meaningless and you should not
try to interpret them. Thus, in this situation the IRR technique provides information that is suspect and
should not be used for decision‐making.
How many IRR solutions can there be for a given cash flow? The maximum number of IRR solu­
tions is equal to the number of sign reversals in the cash flow stream. For a project with a conventional
cash flow, there is only one cash flow sign reversal; thus, there is only one IRR solution. In our mining
example, there are two cash flow sign reversals; thus, there are two IRR solutions.
Finally, for some cash flow patterns, it is impossible to calculate an IRR. These situations can occur when
the initial cash flow (t = 0) is either a cash inflow or outflow and is followed by cash flows with two or more
sign reversals. An example of such a cash flow pattern is NCF0 = $15, NCF1 = –$25 and NCF2 = $20. This
type of cash flow pattern might occur on a building project where the contractor is given a prepayment,
usually the cost of materials and supplies ($15); then does the construction and pays the labour cost (–$25);
and on completion of the work, receives the final payment ($20). Note that when it is not possible to calculate
an IRR, the project either has a positive NPV or a negative NPV for all possible discount rates.
294 Finance essentials
IRR versus NPV: a final comment
The IRR method, as noted, is an important alternative to the NPV method. As we have seen, it accounts for
the time value of money, which is not true of methods such as the payback period and the ARR. Further­
more, the IRR technique has great intuitive appeal. Many business practitioners are in the habit of thinking
in terms of rates of return, whether the rates relate to their ordinary share portfolios or to their companies’
capital expenditures. To these practitioners, the IRR method just seems to make sense. Indeed, we suspect
that the IRR’s popularity with business managers results more from its simple intuitive appeal than its merit.
We believe that the NPV should be the primary method used to make capital budgeting decisions.
Decisions made by the NPV method are consistent with the goal of maximising the value of the com­
pany’s shares and the NPV tells management the dollar amount by which each project is expected to
increase the value of the company.
The following table summarises the major features of the IRR method:
Summary of internal rate of return (IRR) method
Decision rule: IRR > Cost of capital ⇒ Accept the project.
IRR < Cost of capital ⇒ Reject the project.
Key advantages
Key disadvantages
1. Is intuitively easy to understand. 1. With non‐conventional cash flows, can yield no usable answer or
2. Is based on discounted cash
multiple answers.
flow technique.
2. A lower IRR can be better if a cash inflow is followed by cash outflows.
3. With mutually exclusive projects, can lead to incorrect investment
decisions.
Capital budgeting in practice
Capital expenditures are big‐ticket items in the Australian economy. According to the Australian Bureau
of Statistics, the total new capital expenditure in the Australian economy for 2015–16 was estimated
to be $127 455 million as at August 2016. This includes capital expenditure on building and structures
($77 232 million) and on equipment, plant and machinery ($50 223 million). Given the large dollar
amounts and the strategic importance of capital expenditures, it is no surprise that corporate managers
spend considerable time and energy analysing them.
MODULE 10 Capital budgeting and cash flows 295
Practitioners’ methods of choice
Because of the importance of capital budgeting, over the years a number of surveys have asked financial
managers what techniques they actually use in making capital investment decisions. Table 10.2 sum­
marises the results of a survey of company executives in Australia regarding their companies’ capital
budgeting practices in 2014. The respondents were asked to indicate whether they frequently or mostly
used major capital budgeting methods. Executives ranked NPV and IRR as the most‐used techniques
for evaluating projects. As you can see from table 10.2, most companies use all of the major capital
budgeting tools discussed in this module:
TABLE 10.2
Importance of various capital budgeting techniques
Capital budgeting technique
NPV
Payback
period
ARR
IRR
Frequently/mostly used
98%
83%
51%
98%
Source: Pratheepkanth, P, Hettihewa, S, Wright, CS 2015, ‘Capital budgeting practices in Australia and Sri Lanka: a comparative
study’, Global Review of Accounting and Finance, September.
Ongoing and post‐audit reviews
Management should systematically review the status of all ongoing capital projects and perform post‐
audit reviews on all completed capital projects. In a post‐audit review, management compares the
actual performance of a project with what was projected in the capital budgeting proposal. For example,
suppose a new microchip was expected to earn a 20 per cent IRR, but the product’s actual IRR turned
out to be 9 per cent. A post‐audit review would determine why the project failed to achieve its expected
financial goal. Project reviews keep all people involved in the capital budgeting process honest because
they know that the project and their performance will be reviewed and they will be held accountable for
the results.
Managers should also conduct ongoing reviews of capital projects in progress and make adjustments
to reflect changing business conditions. Such a review should challenge the business plan, including
the cash flow projections and the operating cost assumptions. Business plans are management’s best
estimates of future events at the time they are prepared, but as new information becomes available, the
decision to undertake a capital project and the nature of that project must both be reassessed.
Management must also evaluate the people responsible for implementing a capital project. It should
monitor whether the project’s revenues and expenses are meeting projections. If the project is not
meeting the plan, the difficult task for management is to determine whether the problem is a flawed plan
or poor execution by the implementation team. Good plans can fail if they are poorly executed at the
operating level.
BEFORE YOU GO ON
1. If a company accepts a project with a $10 000 NPV, what is the effect on the value of the company?
2. Why does the payback period provide a measure of a project’s liquidity risk?
3. Why should the NPV method be the primary decision tool used in making capital investment
decisions?
10.3 Project cash flows
LEARNING OBJECTIVE 10.3 Explain why incremental after‐tax free cash flows are relevant in evaluating
a project and calculate them for a project.
We begin our discussion of cash flows in capital budgeting by describing the mechanics of cash flow
calculations and the rules for estimating the cash flows for individual projects. You will see that the
296 Finance essentials
approach we use to calculate cash flows is similar to that used to prepare the accounting statement of
cash flows. However, there are three very important differences.
1. Most importantly, the cash flows used in capital budgeting calculations are based on forecasts of
future cash revenues, expenses and investment outlays. In contrast, the accounting statement of cash
flows is a record of past cash flows that might not reflect what can be expected in the future.
2. The accounting statement of cash flows reports a measure of the cash flows for the company as a
whole. In capital budgeting, we generally forecast cash flows associated with an individual project.
3. The capital budgeting cash flow calculation is designed to estimate total cash flows, while the
accounting statement of cash flows is intended to reconcile changes in the balance sheet cash accounts
(for example, bank account balances). If there are any cash outflows or inflows to or from debtholders
or shareholders, total cash flows will differ from the changes in the cash balances because the total
cash flow calculation does not include these inflows or outflows.
Capital budgeting is forward looking
In capital budgeting, we estimate the NPV of the cash flows that a project is expected to produce in the
future. In other words, all of the cash flow estimates are forward looking. This is very different from the
accounting statement of cash flows, which provides a record of historical cash flows.
Cash flow versus accounting earnings
It is worth stressing that cash flow is what matters to investors. The impact of a project on a company’s
overall value or its share price does not depend on how the project affects the company’s accounting
earnings. It depends only on how the project affects the company’s cash flow.
Recall that accounting earnings can differ from cash flows for a number of reasons, making accounting
earnings an unreliable measure of the costs and benefits of a project. For example, as soon as a company
sells a good or provides a service, its income statement will reflect the associated revenue and expenses
regardless of whether the customer has made any actual payments.
Accounting earnings also reflect non‐cash charges, such as depreciation and amortisation, which are
intended to account for the costs associated with deterioration of the assets in a business as those assets
are used. Depreciation and amortisation rules can cause substantial differences between cash flows and
reported income, because the assets acquired for a project are generally depreciated over several years,
even though the actual cash outflow for their acquisition typically takes place at the beginning of the
project.
Incremental after‐tax free cash flows
The cash flows we discount in an NPV analysis are the incremental after‐tax free cash flows that are
expected from the project. The term incremental refers to the fact that these cash flows reflect how much
the company’s total after‐tax free cash flows will change if the project is adopted. Thus, we define the
incremental after‐tax free cash flows (FCF) for a project as the total after‐tax FCF the company would
produce with the project, less the total after‐tax FCF the company would produce without the project:
FCF Project = FCF Company with project − FCF Company without project
(10.5)
In other words, FCFProject equals the net effect the project will have on the company’s cash revenues,
costs, tax and investment outlays. This is what shareholders care about.
Throughout the rest of this module, we refer to the total incremental after‐tax free cash flows associ­
ated with a project simply as the FCF from the project. For convenience, we will drop the ‘Project’ sub­
script from the FCF in equation 10.5.
The FCF for a project is what we generically referred to as NCF earlier in this module. The term free
cash flows, which is commonly used in practice, refers to the fact that the company is free to distribute
these cash flows to debtholders and shareholders because these are the cash flows that are left over after
MODULE 10 Capital budgeting and cash flows 297
a company has made necessary investments in working capital and non‐current assets. The cash flows
associated with financing a project (cash outflows or inflows to or from debtholders or shareholders) are
not included in the FCF calculation because, as we will discuss in a later module, these are accounted
for in the discount rate that is used in an NPV analysis. All of these points will become clearer as we
discuss the FCF calculation next.
FCF calculation
The FCF calculation is illustrated in table 10.3. Let’s begin with an overall review of how the calcu­
lation is done. After that, we will look more closely at details of the calculation. The FCF equals the
change in the company’s cash income, excluding interest expense, that the project is responsible for, plus
depreciation and amortisation for the project, minus all required capital expenditures and investments in
working capital. FCF also equals the incremental after‐tax cash flow from operations, minus the capital
expenditures and investments in working capital required for the project.
TABLE 10.3
{
Incremental after‐tax free cash flow calculation
Explanation
The change in the company’s cash income,
excluding interest expense, resulting from
the project.
Adjustments for the impact of depreciation
and amortisation and investments on FCF.
{
Calculation
Formula
Revenue
− Cash operating expenses
Earnings before interest, tax,
depreciation and amortisation
− Depreciation and amortisation
Earnings before interest and tax
× (1 − Company’s marginal tax rate)
Net operating profit after tax
+ Depreciation and amortisation
Revenue
− Op Ex
EBITDA
Cash flow from operations
− Capital expenditures
− Additions to working capital
− CF Opns
− Cap Exp
− Add WC
Free cash flow
− D&A
EBIT
× (1 − tc)
NOPAT
+ D&A
FCF
When we calculate the FCFs for a project, we first calculate the incremental cash flow from
o­ perations (CF Opns) for each year during the project’s life. This is the cash flow that the project is
expected to generate after all operating expenses and tax have been paid. To obtain the FCF, we then
subtract the incremental capital expenditures (Cap Exp) and the incremental additions to working
capital (Add WC) required for the project. Cap Exp and Add WC represent the investments in non‐
current assets, such as property, plant and equipment, and in working capital items, such as accounts
­receivable, ­inventory and accounts payable, which must be made if the project is pursued.
Since the FCF calculation gives us the after‐tax cash flows from operations over and above what is
necessary to make any required investments, the FCFs for a project are the cash flows that the security
holders can expect to receive from the project. This is why we discount the FCFs when we calculate
the NPV.
The formula for the FCF calculation can also be written as:
FCF = [(Revenue – Op Ex – D&A) × (1 – tc )] + D&A – Cap Exp – Add WC (10.6)
where Revenue is the incremental revenue (net sales) associated with the project, D&A is the incremental depreciation and amortisation (D&A) associated with the project and tc is the company’s
marginal tax rate.
298 Finance essentials
Let’s use equation 10.6 to work through an example. Suppose you are considering purchasing a new
truck for your plumbing business. This truck will increase revenues by $50 000 and operating expenses
by $30 000 in the next year. Depreciation and amortisation charges for the truck will equal $10 000 next
year and your company’s marginal tax rate will be 30 per cent. Capital expenditures of $3000 will be
required to offset wear and tear on the truck, but no additions to working capital will be required. To
calculate the FCF for the project in the next year, you can simply substitute the appropriate values into
equation 10.6:
FCF = [(Revenue – Op Ex – D&A) × (1 – tc )] + D&A – Cap Exp – Add WC
= [($50 000 – $30 000 – $10 000) × (1 – 0.30)] + $10 000 – $3000 – $0
= $14 000
The FCF calculated with equation 10.6 equals the total cash flow the company will produce with the
project less the total cash flow the company will produce without the project. Even so, it is important to
note that it is not necessary to actually estimate the company’s total cash flows in an NPV analysis. We
need only estimate the cash outflows and inflows that arise as a direct result of the project in order to
value it. The idea that we can evaluate the cash flows from a project independently of the cash flows for
the company is known as the standalone principle. The standalone principle says that we can treat the
project as if it were a standalone company that has its own revenue, expenses and investment require­
ments. NPV analysis compares the present value of the FCF from this standalone ‘company’ with the
cost of the project.
To fully understand the standalone principle, it is helpful to consider an example. Suppose that you
own shares in Finco and these shares are currently selling for $29.35. Now suppose that Finco’s manage­
ment announces it will immediately invest $2.3 billion in a new production and distribution centre that
is expected to produce after‐tax cash flows of $0.6 billion per year forever. Since Finco has 2.3 billion
shares outstanding and uses no debt, this means the investment will equal $1.00 per share ($2.3/2.3)
and the annual increase in the cash flows is expected to be $0.26 per share ($0.6/2.3). How should this
announcement affect the value of a Finco share?
If the appropriate cost of capital for the project is 10 per cent, then from equation 9.2 and the dis­
cussion in this module we know the value of a Finco share should increase by D/R = $0.26/0.10 = $2.60
less the $1.00 invested, or $2.60 – $1.00 = $1.60, making each Finco share worth $29.35 + $1.60 =
$30.95 after the announcement. This example illustrates how the standalone principle allows us to simply
add the value of a project’s cash flows to the value of the company’s other cash flows to obtain the total
value of the company with the project.
Incremental after‐tax free cash flows are what shareholders care about
When evaluating a project, managers focus on the FCF that the project is expected to produce, because
that is what shareholders care about. The FCFs reflect the impact of the project on the company’s overall
cash flows. They also represent the additional cash flows that can be distributed to shareholders if the
project is accepted. Only after‐tax cash flows matter, because these are the cash flows that are actually
available for distribution after tax is paid to the government.
Cash flows from operations
Let’s examine table 10.3 in more detail to better understand why FCF is calculated as it is. First, note
that the incremental cash flow from operations, CF Opns, equals the incremental net operating profits
after tax (NOPAT) plus D&A.
If you refer back to the earlier discussion of the income statement, you will notice that NOPAT
is essentially a cash measure of the incremental profit from the project without interest expenses.
In other words, it is the impact of the project on the company’s cash profit, excluding the effects
of any interest expenses associated with financing the project. We exclude interest expenses when
MODULE 10 Capital budgeting and cash flows 299
calculating NOPAT because, as mentioned earlier, the cost of financing a project is reflected in the
discount rate.
We use the company’s marginal tax rate, tc, to calculate NOPAT because the profits from a project
are assumed to be incremental to the company. Since the company already pays tax, the appropriate
tax rate for FCF calculations is the tax rate that the company will pay on any additional profits that are
earned because the project is adopted. This rate is the marginal tax rate. We discuss tax in more detail
later in this module.
We add D&A to NOPAT when calculating CF Opns because, as in the accounting statement of cash
flows, D&A represents a non‐cash charge that reduces the company’s tax obligation. Note that we subtract
D&A before calculating the tax that the company would pay on the incremental earnings for the project.
This accounts for the ability of the company to deduct D&A when calculating tax. However, since D&A
is a non‐cash charge, we have to add it back to NOPAT in order to get the cash flow from operations right.
The net effect of subtracting D&A, calculating the tax and then adding D&A back is to reduce the
tax attributable to earnings from the project. For example, suppose that the earnings before interest, tax,
depreciation and amortisation (EBITDA) for a project is $100.00, D&A is $50.00 and tc is 30 per cent.
The cash flow from operations would be:
CF Opns = [(EBITDA – D&A) × (1 – tc )] + D&A
= [($100.00 – $50.00) × (1 – 0.30)] + $50.00
= $85.00
Note also that the definition of CF Opns differs from that in the accounting statement of cash flows in
that it ignores changes in working capital accounts and other accounting adjustments. In financial calcu­
lations, investments in working capital are treated separately and there is no need for special accounting
adjustments because CF Opns is based on cash flow estimates, not accounting numbers.
Cash flows associated with investments
Once we have estimated CF Opns, we simply subtract the cash flows associated with the required
­investments to obtain the FCF for a project in a particular period. Investments can be required in order
to purchase non‐current tangible assets, such as property, plant and equipment, to purchase ­intangible
assets, such as a patent, or to fund current assets, such as accounts receivable and inventories. Net
investments in property, plant and equipment, and working capital items are also deducted in the
accounting statement of cash flows. You can see this in the long‐term investing and operating activities
sections of that statement. It is important to recognise that all investments that are incremental to a
­project must be accounted for.
The most obvious investments are those in the land, buildings, machinery and equipment that are
acquired for the project. However, investments in intangible assets can also be required. For example, a
manufacturing company may purchase the right to use a particular production technology. Incremental
investments in non‐current tangible assets and intangible assets are collectively referred to as ­incremental
capital expenditures (Cap Exp).
In addition to tangible and intangible assets, such as those described earlier, it is also necessary to
account for incremental additions to working capital (Add WC). For example, if the product being pro­
duced will be sold on credit, thereby generating additional accounts receivable, the cost of providing that
credit must be accounted for. Similarly, if it will be necessary to hold product in inventory, the cost of
financing that inventory must be considered.
FCF calculation: an example
Let’s work a more comprehensive example to see how FCF is calculated in practice. Suppose that you
work at a performing arts centre and are evaluating a project to increase the number of seats by building
300 Finance essentials
four new luxury box seating areas and adding 5000 seats for the general public. Each box seating area
is expected to generate $400 000 in incremental annual revenue, while each of the new seats for the
general public will generate $2500 in incremental annual revenue. The incremental expenses associated
with the new boxes and seating will amount to 60 per cent of the revenues. These expenses include
hiring additional personnel to handle merchandising, ushering and security. The new construction will
cost $10 million and will be fully depreciated (to a value of zero dollars) on a straight‐line basis over
the 10‐year life of the project. The performing arts centre will have to invest $1 million in additional
working capital immediately, but the project will not require any other working capital investments
during its life. This working capital will be recovered in the last year of the project. The centre’s tax rate
is 30 per cent. What are the incremental cash flows from this project?
When evaluating a project, it is generally helpful to first organise your calculations by setting up a
worksheet such as the one illustrated in table 10.4. A worksheet like this helps ensure that the calcu­
lations are completed correctly. The left‐hand column in table 10.4 shows the actual calculations that
will be performed. Other columns are included for each of the years during the life of the project, from
year 0 (today) to the last year in the life of the project (year 10). In this example, the cash flows will
be exactly the same for years 1 to 9; therefore, for illustration purposes, we will only include a single
column to represent these years. If you were using a spreadsheet program, you would normally include
a column for each year.
Unless there is information to the contrary, we can assume that the investment outlay for this pro­
ject will be made today (year 0). We do this because in a typical project no revenue will be generated
and no expenses will be incurred until after the investment has been made. Consequently, the only cash
flows in year 0 are those for new construction (Cap Exp = $10 000 000) and additional working capital
(Add WC = $1 000 000). The FCF in year 0 will therefore equal –$11 000 000.
In years 1 to 9, incremental revenue (Revenue) will equal:
Box seating ($400 000 × 4)
Public seating ($2 500 × 5 000)
Total incremental net revenue
$ 1 600 000
$12 500 000
$14 100 000
Incremental Op Ex will equal 0.60 × $14 100 000 = $8 460 000. Finally, depreciation (there is no amor­
tisation in this example) is calculated as:
D&A = Cap Exp/Depreciable life of the investment
= $10 000 000/10 years
= $1 000 000
Note that only the Cap Exp are depreciated and these capital expenditures will be depreciated or
written off over the 10‐year life of the project. Working capital is not depreciated because it is an invest­
ment that will be recovered at the end of the project.
The cash flows in year 10 will be the same as those in years 1 to 9 except that the $1 million invested
in additional working capital will be recovered in the last year. The $1 million is added back to (or a
negative number is subtracted from) the incremental cash flows from operations in the calculation of the
year 10 cash flows.
The completed cash flow calculation worksheet for this example is presented in table 10.4. We could
have completed the calculations without the worksheet. However, as mentioned, a cash flow calculation
worksheet is a useful tool because it helps us make sure we don’t forget anything. Once we have set the
worksheet up, calculating the incremental cash flows is simply a matter of filling in the blanks. As you will
see in the following discussion, correctly filling in some blanks can be difficult at times, but the worksheet
keeps us organised by reminding us which blanks have yet to be filled in.
MODULE 10 Capital budgeting and cash flows 301
TABLE 10.4
Completed FCF calculation worksheet for performing arts centre project
Years
1 to 9
Year 10
Revenue
$14 100 000
$14 100 000
− Op Ex
$ 8 460 000
$ 8 460 000
EBITDA
$ 5 640 000
$ 5 640 000
− D&A
$ 1 000 000
$ 1 000 000
EBIT
$ 4 640 000
$ 4 640 000
× (1 − tc)
$0.70
$0.70
NOPAT
$ 3 248 000
$ 3 248 000
+ D&A
$ 1 000 000
$ 1 000 000
$ 4 248 000
$ 4 248 000
0
0
$ 1 000 000
0
−$ 1 000 000
− $11 000 000
$ 4 248 000
$ 5 248 000
Year 0
CF Opns
− Cap Exp
− Add WC
FCF
NPV @ 10%
$10 000 000
$15 487 664
Note: With a discount rate of 10 per cent, the NPV of the cash flows in table 10.4 is $15 487 664. As shown earlier in this
module, the NPV is obtained by calculating the present values of all of the cash flows and adding them up. You could confirm
this by doing this calculation yourself.
USING EXCEL
Performing arts centre project
Cash flow calculations for capital budgeting problems are best set up and solved using a spreadsheet
application. The following is the formula setup for the performing arts centre project.
302 Finance essentials
As in table 10.4, we have combined years 1 to 9 in a single column to save space. As mentioned in
previous modules, note that none of the values in the actual worksheet are hard coded, but instead use
references from the key assumptions list, or specific formulas. This allows for an easy analysis of the
impact of changes in the assumption.
DECISION‐MAKING EX AMPLE 10.2
Free cash flows
Situation:
You have saved $6000 and plan to use $5500 of this money to buy a motorcycle. However, before
you go to visit the motorbike dealer, a friend of yours asks you to invest your $6000 in a local pizza‐
delivery business she is starting. Assuming she can raise the money, your friend has two alternatives
(detailed in the table above) regarding how to market the business. The opportunity cost of capital is
12 per cent. You will receive all free cash flows from the business until you have recovered your $6000
plus 12 per cent interest. After that, you and your friend will split any additional cash proceeds. Which
­alternative would you prefer that your friend choose?
Alternative 1
Alternative 2
Year 1
Year 1
Revenue
−Op Ex
$12 000
4 000
$12 000
6 000
$16 000
8 000
$ 8 000
4 240
EBITDA
D&A
$ 8 000
2 500
$ 6 000
2 500
$ 8 000
2 500
$ 3 760
2 500
EBIT
× (1 − tc)
$ 5 500
0.70
$ 3 500
0.70
$ 5 500
0.70
$ 1 260
0.70
NOPAT
+ D&A
$ 3 850
2 500
$ 2 450
2 500
$ 3 850
2 500
$ 882
2 500
$ 6 350
2 000
$ 4 950
500
(1 000)
$ 6 350
500
$ 3 382
500
( 1 000)
$ 4 350
$ 5 450
$ 5 850
$ 3 882
CF Opns
− Cap Exp
− Add WC
FCF
NPV at 12%
$ 5 000
1 000
−$ 6 000
$ 2 229
$ 5 000
1 000
−$ 6 000
$ 2 614
MODULE 10 Capital budgeting and cash flows 303
Decision:
If you expect no cash from other sources during the next year, you should insist that your friend choose
alternative 2. This is the only alternative that will produce enough FCF next year for you to purchase the
motorcycle. Alternative 1 would produce $6350 in CF Opns but would require $2000 in capital expendi­
tures. You would not be able to take more than $4350 from the business in year 1 under alternative 1
without leaving the business short of cash. Moreover, the NPV of alternative 2 is greater than that of
alternative 1.
BEFORE YOU GO ON
1. Why do we care about incremental cash flows at the company level when we evaluate a project?
2. Why is D&A first subtracted and then added back in FCF calculations?
3. What types of investments should be included in FCF calculations?
10.4 Estimating cash flows in practice
LEARNING OBJECTIVE 10.4 Discuss the five general rules for incremental after‐tax free cash
flow calculations.
Now that we have discussed what FCFs are and how they are calculated, we are ready to focus on some
important issues that arise when we estimate FCFs in practice. The first of these issues is determining
which cash flows are incremental to a project and which are not. In this section, we begin with a dis­
cussion of five general rules that help us do this. We then discuss why it is important to distinguish
between nominal and real cash flows, and to use one or the other consistently in our calculations. Next,
we discuss some concepts regarding tax rates and depreciation that are crucial to the calculation of FCF
in practice. Finally, we describe and illustrate special factors that must be considered when calculating
FCF for the final year of a project.
Five general rules for incremental after‐tax FCF calculations
As discussed earlier, we must determine how a project would change the after‐tax FCF of a company
in order to calculate its NPV. This is not always simple to do, especially in a large company that has a
complex accounting system and many other projects that are not independent of the new project being
considered. Fortunately, there are five rules that can help us isolate the FCFs specific to an individual
project even in the most complicated circumstances.
Rule 1: Include cash flows and only cash flows in your calculations
Do not include allocated costs unless they reflect cash flows. Examples of allocated costs are charges
that accountants allocate to individual businesses to reflect their share of the corporate overhead (the
costs associated with the senior managers of the company, centralised accounting and finance functions
and so forth).
To see how allocated costs can differ from actual costs (and cash flows), consider a company with
$3 million of annual corporate overhead expenses and two identical manufacturing plants. Each of
these plants would typically be allocated one half, or $1.5 million, of the corporate overhead when their
accounting profitability is estimated. Suppose that the company is considering building a third plant
identical to the other two. If this plant is built, it will have no impact on the annual corporate overhead
cash expense. Someone in accounting might argue that the new plant should be able to support its ‘fair
share’ of the $3 million overhead — i.e. $1 million — and that this overhead should be included in the
cash flow calculation. Of course, this person would be wrong. Since total corporate overhead costs will
304 Finance essentials
not change if the third plant is built, no overhead should be included when calculating the incremental
FCFs for this new plant.
Rule 2: Include the impact of the project on cash flows from other
product lines
If the product associated with a new project is expected to affect sales of one or more other products at
the company, you must include the expected impact of the project on the cash flows from the other prod­
ucts when calculating the FCFs. For example, consider the analysis that analysts at Apple would have
done before giving the go‐ahead for the development of the iPhone. Since, like the iPod, the iPhone can
store music, these analysts may have expected that the introduction of the iPhone would reduce annual
iPod sales. If so, they would have had to account for the reduction in cash flows from lost iPod sales
when they forecast the FCFs for the iPhone.
Similarly, if a new product is expected to boost sales of another, complementary product, then the
increase in cash flows associated with the new sales of that complementary product line should also be
reflected in the FCFs. For example, suppose that the introduction of the iPhone will increase the total
number of music‐playing devices (iPhones plus iPods) that Apple sells by 1 million units per year and that
the average purchaser of a music‐playing device buys and downloads 100 digital songs from Apple. The
digital music that Apple sells is a complementary product and the cash flows from the sale of 100 million
(1 million music‐playing devices × 100 songs) additional songs each year should be included in the
analysis of the iPhone project. If Apple did not introduce the iPhone, it would not have those sales.
Rule 3: Include all opportunity costs
By opportunity costs, we mean the cost of giving up another opportunity. (The concept of opportunity
cost here is similar to that discussed earlier in this module in the context of the opportunity cost of
capital.) Opportunity costs can arise in many different ways. For example, a project may require the use
of a building or a piece of equipment that could otherwise be sold or leased out. To the extent that selling
or leasing the building or piece of equipment would generate additional cash flow for the company and
so the opportunity to realise that cash flow must be forgone if the project is adopted, it represents an
opportunity cost.
To see why this is the case, suppose that a project will require the use of a piece of equipment that the
company already has and that could be sold for $50 000 on the used‐equipment market. If the project
is accepted, the company will lose the opportunity to sell the piece of equipment for $50 000. This is a
$50 000 cost that must be included in the project analysis. Accepting the project reduces the amount of
money that the company can realise from selling excess equipment by this amount.
Rule 4: Forget sunk costs
Sunk costs are costs that have already been incurred. All that matters when you evaluate a project at a
particular point in time is how much you must invest in the future and what you can expect to receive in
return for that investment. Past investments are irrelevant.
To see this, consider a situation in which your company has invested $10 million in a project that has
not yet generated any cash inflows. Also assume that circumstances have changed so the project, which
was originally expected to generate cash inflows with a present value of $20 million, is now expected to
generate cash inflows with a value of only $2 million. To receive this $2 million, however, you will have
to invest another $1 million. Should you do it? Of course you should!
If you stop investing now, you will have lost $10 million. If you make the investment, your total
loss will be $9 million. Although neither is an attractive alternative, it should be clear that it is better
to lose $9 million than it is to lose $10 million. The conclusion is the same if you ignore the previous
investment and recognise that the choice is between never receiving anything and receiving an NPV of
$1 million ($1 million investment and $2 million return). The point here is that, while it is often painful
to do, you should ignore sunk costs when calculating FCF.
MODULE 10 Capital budgeting and cash flows 305
Rule 5: Include only after‐tax cash flows in the cash flow calculations
The incremental pre‐tax earnings of a project matter only to the extent that they affect the after‐tax cash
flows that the company’s investors receive. For an individual project, as mentioned earlier, we calcu­
late the after‐tax cash flows using the company’s marginal tax rate, because this is the rate that will be
applied against the incremental cash flows generated by the project.
Applying these rules in practice
Let’s use the performing arts centre project to illustrate how these rules are applied in practice. Suppose
the following requirements and costs are associated with this project.
1. The CFO requires that each project be assessed at 5 per cent of the initial investment to account for
costs associated with the accounting, marketing and information technology departments.
2. It is likely that increasing the number of seats will reduce revenues next door at the cinema that your
employer also owns. Attendance at the cinema is expected to be lower only when the performing arts
centre is staging a big event. The total impact is expected to be a reduction of $500 000 each year,
before tax, in the operating profits (EBIT) of the cinema. The depreciation of the cinema’s assets will
not be affected.
3. If the project is adopted, the new seating will be built in an area where art installations have been
placed in the past when the centre has hosted guest lectures by well‐known painters and sculptors.
The centre will no longer be able to host such events and revenue will be reduced by $600 000 each
year as a result.
4. The centre has already spent $400 000 on researching the demand for new seating.
5. You have just discovered that a new salesperson will be hired if the centre goes ahead with the
expansion. This person will be responsible for sales and service of the four new luxury boxes and will
be paid $75 000 per year, including salary and benefits. The $75 000 is not included in the 60 per cent
figure for operating expenses that was previously mentioned.
306 Finance essentials
What impact will these requirements and costs have on the FCFs for the project?
1. The 5 per cent assessment sounds like an allocated overhead cost. To the extent that this assessment
does not reflect an actual increase in cash costs, it should not be included. It is not relevant to the
project. The analysis should include only cash flows.
2. The impact of the expansion on the operating profits of the cinema is an example of how a project can
erode business in another part of a company. The $500 000 reduction in EBIT is relevant and should
be included in the analysis.
3. The loss of the ability to use the installation area represents a $600 000 opportunity cost. The centre is
giving up revenue from guest lecturers who require installation space in order to build the additional
seating. This opportunity cost will be partially offset by elimination of the operating expenses
associated with the guest lectures.
4. The $400 000 for research has already been spent. The decision about whether to accept or reject the
project will not alter the amount spent on this research. This is a sunk cost that should not be included
in the analysis.
5. The $75 000 annual salary for the new salesperson is an incremental cost that should be included in the
analysis. Even though the marketing department is a corporate overhead department, in this case the
salesperson must be hired specifically because of the new project.
Table 10.5 shows the impact of the changes described earlier on the cash flows outlined in table 10.4.
Note that Revenue and Op Ex after year 0 have been reduced from $14 100 000 and $8 460 000, res­
pectively, in table 10.4 to $13 500 000 and $8 100 000, respectively, in table 10.5. These changes reflect
the $600 000 loss of revenue and the reduction in costs (60 per cent of revenue) associated with the
loss of the ability to host guest lectures. The $75 000 expense for the new salesperson’s salary and
the $500 000 reduction in the EBIT of the cinema are then subtracted from Revenue, along with Op
Ex. These changes result in an EBITDA of $4 825 000 in table 10.5, compared with an EBITDA of
$5 640 000 in table 10.4. The net result is a reduction in the project NPV from $15 487 664 (in table
10.4) to $11 982 189 (in table 10.5). The adjustments described in the text result in changes in the FCF
calculations and a different NPV for the performing arts centre project.
TABLE 10.5
Adjusted FCF calculations and NPV for performing arts centre project
Year 0
Revenue
− Op Ex
− New salesperson’s salary
− Lost cinema EBIT
EBITDA
− D&A
EBIT
× (1 − tc)
NOPAT
+ D&A
CF Opns
− Cap Exp
− Add WC
FCF
NPV @ 10%
$10 000 000
1 000 000
−$11 000 000
$11 982 189
Years 1 to 9
Year 10
$13 500 000
8 100 000
75 000
500 000
$ 4 825 000
1 000 000
$ 3 825 000
0.70
$ 2 677 500
1 000 000
$ 3 677 500
0
0
$ 3 677 500
$13 500 000
8 100 000
75 000
500 000
$ 4 825 000
1 000 000
$ 3 825 000
0.70
$ 2 677 500
1 000 000
$ 3 677 500
0
−1 00 000
$ 4 677 500
Tax rates and depreciation
Tax and depreciation have important implications in capital budgeting decisions. These concepts are
discussed next.
MODULE 10 Capital budgeting and cash flows 307
Tax rates for businesses in Australia
Table 10.6 shows the tax rate schedule faced by a typical Australian company. The tax rate for busi­
nesses in Australia depends on business type. Currently, most Australian companies have a flat tax rate
of 30 per cent.
TABLE 10.6
Australian company tax rates for the financial year July 2015 – June 2016
Tax rate %
Companies
• includes corporate limited partnerships, strata title bodies corporate, trustees of corporate unit
trusts and public trading trusts
• small business entities
Life insurance companies
• ordinary class of taxable income
• complying super class of taxable income
• additional tax on no‐TFN contributions income where the company is a retirement savings
account (RSA) provider
30
28.5
30
15
34
Source: Australian Taxation Office, www.ato.gov.au.
Tax depreciation
From the capital budgeting perspective, depreciation is an important consideration in cash flow analysis.
Generally, assets that a company invests in will lose value (or depreciate) over time. Depreciation
charges are intended to represent the cost of wear and tear on assets in the course of business. Although
depreciation is not a cash flow item, companies can claim depreciation on assets as a deduction in deter­
mining company taxable income. Therefore, depreciation can be regarded as producing tax savings, also
known as the depreciation tax shield. For the purpose of capital budgeting, depreciation charges are
normally calculated based on either the straight‐line method (dividing the total cost of an investment by
its estimated useful life) or the reducing‐balance method (multiplying a fixed percentage of the asset’s
written‐down value). The written‐down value of an asset is the total cost of investment less accumulated
depreciation. The depreciation tax shield is then calculated as:
Depreciation tax shield = Depreciation × tc
The main difference between the straight‐line and reducing‐balance methods of depreciation is that
the reducing‐balance method will result in higher depreciation expense in the early years and lower
depreciation expense in the later years of the asset’s life. The higher depreciation expense leads to
higher depreciation tax shields and consequently higher after‐tax net cash flows, which are important to
­companies as they require more cash in the early years of a project.
DEMONSTRATION PROBLEM 10.3
Calculating depreciation
Problem:
BW Ltd acquired an asset for $300 000 which has an expected economic life of 6 years. If the ­company
tax rate is 30 per cent, what are the depreciation and depreciation tax shield of this asset for each
year, using (a) the straight‐line method and (b) the reducing‐balance method at the rate of 25 per cent
per annum?
308 Finance essentials
Solution:
(a) Straight‐line method
Year
Depreciation
Depreciation tax shield
1
$300 000/6 = $50 000
$50 000 × 0.3 = $15 000
2
$50 000
$15 000
3
$50 000
$15 000
4
$50 000
$15 000
5
$50 000
$15 000
6
$50 000
$15 000
(b) Reducing‐balance method
Year
Written‐down value
Depreciation
Depreciation tax shield
1
$300 000
$300 000 × 0.25 = $75 000
$75 000 × 0.3 = $22 500
2
$300 000 – $75 000 = $225 000
$225 000 × 0.25 = $56 250
$56 250 × 0.3 = $16 875
3
$225 000 – $56 250 = $168 750
$168 750 × 0.25 = $42 188
$42 188 × 0.3 = $12 656
4
$168 750 – $42 188 = $126 562
$126 562 × 0.25 = $31 641
$31 641 × 0.3 = $9 492
5
$126 562 – $31.641 = $94.921
$ 94 921 × 0.25 = $23 730
$23 730 × 0.3 = $7 119
6
$ 94 921 – $23 730 = $71.191
$ 71 191 × 0.25 = $17 798
$17 798 × 0.3 = $5 339
Recall that the FCF calculation, equation 10.5, includes incremental depreciation along with incre­
mental amortisation (D&A). We put depreciation and amortisation together in the calculation because
amortisation is a non‐cash charge (deduction) like depreciation. It is beyond the scope of this text to dis­
cuss amortisation in detail, because the rules that govern it are complex. However, you should know that
amortisation, like depreciation, is a deduction that is allowed under tax law to compensate for the decline
in value of certain, mainly intangible, assets used by a business.
Calculating the terminal‐year FCF
The FCF in the last, or terminal, year of a project’s life often includes cash flows that are not typi­
cally included in the calculations for other years. For instance, in the final year of a project the assets
acquired during the life of the project may be sold and the working capital that has been invested may
be recovered. The cash flows that result from the sale of assets and recovery of working capital must be
included in the calculation of the terminal‐year FCF.
In the performing arts centre example discussed earlier, the cash flows in year 0 are different from
the cash flows in the other years (see table 10.5). The year 0 cash flows include only cash flows associ­
ated with incremental capital expenditures (Cap Exp) and additions to working capital (Add WC). They
do not include incremental cash flows from operations (CF Opns). The principle behind including only
these cash flows in year 0 is that the investments must be made before any cash flows from operations
are realised. In some cases, such as large construction projects, up‐front investments may be required
over several years, but these investments are typically also made before the project begins to generate
revenue.
The year 10, or terminal year, cash flows in the performing arts centre example are also different from
those in the other years. They include both CF Opns and investment cash flows that reflect the recovery
MODULE 10 Capital budgeting and cash flows 309
of net working capital investments. The net incremental additions to working capital (Add WC) that are
due to the project are calculated as follows:
Add WC = Change in cash and cash equivalents + Change in accounts receivable
+ Change in investories − Change in accounts payable
(10.7)
where the changes in cash and cash equivalents, accounts receivable, inventories and accounts payable
represent changes in the values of these accounts that result from the adoption of the project.
Looking at the components of Add WC, we can see that cash and cash equivalents, accounts receiv­
able and inventories require the investment of capital, while accounts payable represent capital provided
by suppliers. When a project ends, the cash and cash equivalents are no longer needed, the accounts
receivable are collected, the inventories are sold and the accounts payable are paid. In other words, the
company recovers the net working capital that has been invested in the project. To reflect this in the
FCF calculation, the cash flow in the last year of the project typically includes a negative investment in
working capital that equals the cumulative investment in working capital over the life of the project. It
is very important to make sure the recovery of working capital is reflected in the cash flows in the last
year of a project. In some businesses, working capital can account for 20 per cent or more of revenue
and excluding working capital recovery from the calculations can cause you to substantially understate
the NPV of a project.
In some projects, there will also be incremental capital expenditures (Cap Exp) in the terminal year.
This is because either the assets acquired for the project are being sold or there are disposal costs
associated with them. In the performing arts centre example, Cap Exp is $0 in year 10. This is because
we assumed that, other than the working capital, the investments at the beginning of the project would
have no salvage value, there would be no disposal costs associated with the assets and there would
be no clean‐up costs associated with the project in year 10. When an asset is expected to have a sal­
vage value, we must include both the salvage value realised from the sale of the asset and the impact
of the sale on the company’s tax in the terminal‐year FCF calculations. Any costs that must
be incurred to dispose of assets should also be included. Finally, clean‐up costs, such as those associated
with restoring the environment after a strip‐mining project, also must be included in the terminal‐year
FCF.
If the salvage value (selling price) of an asset is less than the written‐down value, the company experi­
ences a loss on the sale that will provide a tax saving. However, if the salvage value exceeds the book
value, the company will have a gain on the sale of the asset that will increase its tax liability. In either
case, you must include the proceeds from the sale of the assets and the tax effects in your cash flow
­calculations. The general formula for calculating the tax on the salvage value of an asset is:
Tax on sale of an asset = (Selling price of asset – Book value of asset) × tc
where tc is the company tax rate.
To better understand how taxes affect the terminal‐year cash flow of a project, let’s make the per­
forming arts centre example more realistic. Recall that the initial Cap Exp in the example was $10 million
and we used straight‐line depreciation. Suppose that the salvage value (selling price) in year 10 of the
$10 million investment in the project is expected to be $1 million and the book value of the investment at
year 10 is $0. In this case, the company will pay additional taxes of ($1 000 000 – $0) × 0.3 = $300 000
on the sale of the assets. Deducting this amount from the $1 000 000 that the company receives from the
sale of the assets yields after‐tax proceeds of $700 000 and these cash flows are illustrated in table 10.7.
This shows the FCF calculations and NPV for the performing arts centre project, assuming the salvage
value of the $10 million capital investment is $1 million in year 10. All other assumptions are the same
as in table 10.6.
310 Finance essentials
TABLE 10.7
FCF calculations and NPV for performing arts centre project with $1 million salvage
value in year 10 ($ thousands)
Year 0
CF Opns
−Cap Exp
−Add WC
FCF
NPV @ 10%
$ 10 000
1 000
$ −11 000
15 880.016
Years 1–9
Year 10
$ 4 248
0
0
$ 4 248
$ 4 248
−700
−1 000
$ 5 948
BEFORE YOU GO ON
1. What are the five general rules for calculating FCF?
2. How can FCF in the terminal year of a project’s life differ from FCF in the other years?
MODULE 10 Capital budgeting and cash flows 311
SUMMARY
10.1 Discuss why capital budgeting decisions are the most important investment decisions made by
a company’s management.
Capital budgeting is the process by which management decides which productive assets the com­
pany should invest in. Because capital expenditures involve large amounts of money, are critical to
achieving the company’s strategic plan, define the company’s line of business over the long term
and determine the company’s profitability for years to come, they are considered the most important
investment decisions made by management.
10.2 Evaluate capital budgeting projects using the net present value (NPV), payback period,
accounting rate of return and internal rate of return methods.
The NPV method leads to better investment decisions than the other techniques because the NPV
method does the following: (1) it uses the discounted cash flow valuation approach, which accounts
for the time value of money; and (2) it provides a direct measure of how much a capital project is
expected to increase the dollar value of the company. Thus, NPV is consistent with the top manage­
ment goal of maximising shareholder value.
The payback period is the length of time it will take for the cash flows from a project to recover
the cost of the project. The payback period is widely used, mainly because it is simple to apply and
easy to understand. It also provides a simple measure of liquidity risk because it tells management
how quickly the company will get its money back. The payback period has a number of short­
comings, however. For one thing, the payback period, as most commonly calculated, ignores the
time value of money.
While the accounting rate of return (ARR) method is easy to understand and to calculate, it is
based on accounting numbers such as book value and net income, rather than cash flow data. As
such, it is not a true rate of return. Instead of discounting a project’s cash flows over time, it simply
gives us a number based on average figures from the income statement and balance sheet. Further­
more, as with the payback method, there is no economic rationale for establishing the hurdle rate.
Finally, the ARR does not account for the size of the projects when a choice between two projects
of different sizes must be made.
The internal rate of return (IRR) is the expected rate of return for an investment project; it is
calculated as the discount rate that equates the present value of a project’s expected cash inflows
to the present value of the project’s outflows — in other words, as the discount rate at which the
NPV is equal to zero. If a project’s IRR is greater than the required rate of return, i.e. the cost
of capital, the project is accepted. The IRR rule often gives the same investment decision for a
project as the NPV rule. However, the IRR method does have operational pitfalls that can lead to
incorrect decisions. Specifically, when a project’s cash flows are unconventional, the IRR calcu­
lation may yield no solution or more than one IRR. In addition, the IRR technique cannot be used
to rank projects that are mutually exclusive, because the project with the highest IRR may not be
the project that would add the greatest value to the company if accepted — that is, the project with
the highest NPV.
These capital budgeting methods are demonstrated in 10.2.
10.3 Explain why incremental after‐tax free cash flows are relevant in evaluating a project and
calculate them for a project.
The incremental after‐tax free cash flows, FCFs, for a project equal the expected change in the total
after‐tax cash flows of the company if the project is adopted. The impact of a project on the com­
pany’s total cash flows is the appropriate measure of cash flows, because these are the cash flows
that reflect all of the costs and benefits from the project and only the costs and benefits from the
project. The incremental after‐tax FCFs are calculated using equation 10.6. This calculation is also
illustrated in table 10.7.
312 Finance essentials
10.4 Discuss the five general rules for incremental after‐tax free cash flow calculations.
The five general rules are as follows.
Rule 1: Include cash flows and only cash flows in your calculations. Shareholders care about only
the impact of a project on the company’s cash flows.
Rule 2: Include the impact of the project on cash flows from other product lines. If a project affects
the cash flows from other projects, we must take this fact into account in NPV analysis in order to
fully capture the impact of the project on the company’s total cash flows.
Rule 3: Include all opportunity costs. If an asset is used for a project, the relevant cost of that asset
is the value that could be realised from its most valuable alternative use. By including this cost in
the NPV analysis, we capture the change in the company’s cash flows that is attributable to the use
of this asset for the project.
Rule 4: Forget sunk costs. The only costs that matter are those to be incurred from this point on.
Rule 5: Include only after‐tax cash flows in the cash flow calculations. Since shareholders receive
cash flows after taxes have been paid, they are concerned only about after‐tax cash flows.
SUMMARY OF KEY EQUATIONS
Equation
10.1
Description
Formula
Net present value
NPV = NCF0 +
n
=∑
t=0
NCF1
NCF2
NCFn
+
++
1+ k
(1 + k )2
(1 + k )n
NCFt
(1 + k )t
10.2
Payback period
PB = Years before cost recovery +
10.3
Accounting rate of return
ARR =
10.4
Internal rate of return
NPV = ∑
Remaining cost to recover
Cash flow during the year
Average net income
Average book value
n
t=0
NCFt
=0
(1 + IRR)t
10.5
Incremental free cash flow
definition
FCF Project = FCF Company with project − FCF Company without project
10.6
Incremental free cash flow
calculation
FCF = [(Revenue – Op Ex – D&A) × (1 – tc )] + D&A – Cap Exp – Add WC
10.7
Incremental additions to
working capital
Add WC = Change in cash and cash equivalents
+ Change in accounts receivable
+ Change in inventories – Change in accounts payable
KEY TERMS
accounting rate of return (ARR) rate of return on a capital project based on average net income
divided by average assets over the project’s life; also called book value rate of return
capital budgeting process of choosing the real assets in which the company will invest
company’s marginal tax rate tax rate that is applied to each additional dollar of earnings at a company
contingent projects projects whose acceptance depends on the acceptance of another project
conventional cash flow cash flow pattern made up of an initial cash outflow followed by one or more
cash inflows
MODULE 10 Capital budgeting and cash flows 313
cost of capital required rate of return for a capital investment
current assets assets, such as accounts receivable and inventories, that are expected to be liquidated
(collected or sold) within 1 year
incremental additions to working capital (Add WC) investments in working capital items, such as
accounts receivable, inventory and accounts payable, that must be made if a project is pursued
incremental after‐tax free cash flows (FCF) difference between total after‐tax free cash flows at a
company with a project and total after‐tax free cash flows at the same company without that project;
measure of a project’s total impact on the free cash flows at a company
incremental capital expenditures (Cap Exp) investments in property, plant and equipment and other
non‐current assets that must be made if a project is pursued
incremental cash flow from operations (CF Opns) cash flow that a project generates after all
operating expenses and tax have been paid but before any cash outflows for investments
incremental depreciation and amortisation (D&A) depreciation and amortisation charges that are
associated with a project
incremental net operating profits after tax (NOPAT) measure of the impact of a project on the
company’s cash profit, excluding the effects of any interest expenses associated with financing the project
independent projects projects whose cash flows are unrelated
intangible assets non‐physical assets such as patents, mailing lists and brand names
internal rate of return (IRR) discount rate that equates the present value of a project’s expected cash
inflows to the present value of the project’s outflows
mutually exclusive projects projects for which acceptance of one precludes acceptance of another
net present value (NPV) method method of evaluating a capital investment project which measures
the difference between its cost and the present value of its expected cash flows
net present value (NPV) profile graph showing NPV as a function of the discount rate
opportunity cost of capital return an investor gives up when their money is invested in one asset
rather than the best alternative asset
payback period number of years it takes for cash flows from a project to recover the project’s initial
investment
post‐audit review audit to compare actual project results with the results projected in the capital
budgeting proposal
standalone principle principle that allows us to treat each project as a standalone company when we
perform an NPV analysis
tangible assets physical assets such as property, plant and equipment
ACKNOWLEDGEMENTS
Photo: © pogonici / Shutterstock
Photo: © Petr Jilek / Shutterstock.com
Photo: © bikeriderlondon / Shutterstock.com
Photo: © Ferenc Szelepcsenyi / Shutterstock.com
314 Finance essentials
MODULE 11
Cost of capital and
working capital
management
LEA RNIN G OBJE CTIVE S
After studying this module, you should be able to:
11.1 explain how to calculate the overall cost of capital for a company which uses debt and equity
financing for projects
11.2 calculate the weighted average cost of capital (WACC) for a company and explain the limitations of
using a company’s WACC as the discount rate when evaluating a project
11.3 define and calculate net working capital and discuss the importance of working capital management
11.4 identify three current asset financing strategies and discuss the main sources of short-term financing.
Module preview
Earlier we discussed the general concept of risk and
described what financial analysts mean when they talk
about the risk associated with a project’s cash flows. We
also explained how this risk is related to expected returns.
With this background, we are now ready to discuss the
methods that financial managers use to estimate discount
rates, the reasons that they use these methods and the
shortcomings of each method.
We start this module by introducing the weighted
average cost of capital and explaining how this concept
is related to the discount rates that many financial managers use to evaluate projects. Then we describe various
methods that are used to estimate the three broad types
of financing that companies use to acquire assets — debt,
ordinary shares and preference shares — as well as the
overall weighted average cost of capital for the company.
We next discuss the circumstances under which it is
appropriate to use the weighted average cost of capital for
a company as the discount rate for a project and outline
the types of problems that can arise when the weighted
average cost of capital is used inappropriately.
The next part of this module focuses on short-term activities that involve cash inflows and outflows
that will occur within a year or less. These types of activities are concerned with what is known as
working capital management. Because of the short-term nature of current assets and liabilities, decisions
involving them are more flexible and more easily reversed than capital investment decisions. The greater
flexibility associated with working capital management does not mean that these activities are not important, however. Companies that do not manage their day-to-day operations diligently can suffer severe
financial consequences, including insolvency.
We begin this part of the module by reviewing some basic definitions and concepts. Next, we examine
the individual working capital accounts, and discuss how to determine and analyse the operating and
cash conversion cycles. We finish by considering the alternative means of financing short-term assets and
the risks associated with each.
11.1 Overall cost of capital
LEARNING OBJECTIVE 11.1 Explain how to calculate the overall cost of capital for a company which
uses debt and equity financing for projects.
Our discussions of investment analysis up to this point have focused on evaluating individual projects.
We have assumed that the rate used to discount the cash flows for a project reflects the risks associated
with the incremental cash flows from that project. In an earlier module we saw that since unique risk
can be eliminated by holding a diversified portfolio, systematic risk is the only risk that investors require
compensation for bearing.
Although these ideas help us better understand the discount rate on a conceptual level, they can be
difficult to implement in practice. Companies do not issue publicly traded shares for individual projects.
This means that financial analysts do not have the share returns necessary to estimate the beta ( β) for an
individual project. As a result, they have no way to directly estimate the discount rate that reflects the
systematic risk of the incremental cash flows from a particular project.
316 Finance essentials
In many companies, senior financial managers deal with this problem by estimating the cost of capital
for the company as a whole and then requiring analysts within the company to use this cost of capital to
discount the cash flows for all projects. One problem with this approach is that it ignores the fact that a
company is really a collection of projects with varying levels of risk. A company’s overall cost of capital
is actually a weighted average of the costs of capital for all of these projects, where the weights reflect
the relative values of the projects.
If the risk of an individual project differs from the average risk of the company, the company’s overall
cost of capital is not the ideal discount rate to use when evaluating that project. Nevertheless, since this
is the discount rate that is commonly used, we begin by discussing how a company’s overall cost of
capital is estimated. We then discuss alternatives to using the company’s cost of capital as the discount
rate in evaluating a project.
Estimating the cost of capital
The fact that the market value of a company’s assets must equal the value of the cash flows these assets
are expected to generate, combined with the fact that the value of the expected cash flows also equals the
total market value of the company’s total liabilities and equity, means that we can write the market value
(MV) of assets as follows:
MV of assets = MV of liabilities + MV of equity
This equation is just like the accounting balance sheet identity, except it is based on market values.
To see why the market value of the assets must equal the total market value of the liabilities and
equity, consider a company whose only business is to own and manage an apartment building that was
purchased 20 years ago for $1 000 000. Suppose that there is currently a loan on the building that is
worth $300 000, the company has no other debt and the current market value of the building, based on
the expected cash flows from future rents, is $4 000 000. What is the value of all of the equity (shares) in
this company? The answer is $4 000 000 − $300 000 = $3 700 000. If the cash flows that the apartment
building is expected to produce are worth $4 000 000, then investors would be willing to pay $3 700 000
for the equity in the company. This is the value of the cash flows that they would expect to receive after
making interest and principal payments on the loan. Furthermore, since by definition the loan is worth
$300 000, the value of the debt plus the value of the equity is $300 000 + $3 700 000 = $4 000 000 —
which is exactly equal to the market value of the company’s assets.
A finance balance sheet based on market values is more useful to financial decision-makers than the
ordinary accounting balance sheet. This is because financial managers are far more concerned about the
future than the past when they make decisions.
Analysts do not need to estimate betas for each type of financing that the company has. As long as
they can estimate the cost of each type of financing — either directly, by observing that cost in the
capital markets, or by using equation 7.12 — they can calculate the cost of capital for the company using
the following equation:
n
k Company = ∑ xi ki = x1 k1 + x 2 k 2 + x3 k3 + ... + x n k n (11.1)
i =1
In equation 11.1, kCompany is the cost of capital for a company, ki is the cost of financing type i and xi
is the fraction of the total market value of the financing (or of the assets) of the company represented by
financing type i. This formula simply says that the overall cost of capital for the company is a weighted
average of the cost of each different type of financing used by the company. Note that since we are
specifically talking about the cost of capital, we use the symbol ki to represent this cost, rather than the
more general notation E(Ri) that we used earlier in the text.
To see how equation 11.1 is applied, let’s return to the example of the company whose only business
is to manage an apartment building. Recall that the total value of this company is $4 000 000 and it has
MODULE 11 Cost of capital and working capital management 317
$300 000 in debt. If the company has only one loan and one type of shares, then the fractions of the total
value represented by those two types of financing are as follows:
where x Debt
x Debt = $300 000/$4 000 000 = 0.075, or 7.5%
x Equity = $3 700 000/$4 000 000 = 0.925, or 92.5%
+ x Equity = 0.075 + 0.925 = 1.000
This tells us that the value of the debt claims equals 7.5 per cent of the value of the company and that
the value of the equity claims equals the remaining 92.5 per cent of the value of the company. If the cost
of the debt for this business is 6 per cent and the cost of the equity is 10 per cent, the cost of capital for
the company can be calculated as a weighted average of the costs of the debt and equity:1
k Company = x Debt k Debt + x Equity k Equity = (0.075)(0.06) + (0.925)(0.10) = 0.097, or 9.7%
Note that we have used equation 11.1 to calculate a weighted average cost of capital (WACC) for the
company in this example. In fact, this is what people typically call a company’s cost of capital, kCompany.
From this point on, we will use the abbreviation WACC to represent a company’s overall cost of capital.
In our discussion of how the WACC for a company is calculated, we have assumed that the costs of
the different types of financing were known. This assumption allowed us to simply plug those costs into
equation 11.1 once we had calculated the weight for each. Unfortunately, life is not that simple. In the
real world, analysts have to estimate each of the individual costs. In other words, the discussion initially
glossed over a number of concepts and issues that you should be familiar with. We now discuss those
concepts and issues, and show how the costs of the different types of financing can be estimated.
Before we move on to the specifics of how to estimate the costs of different types of financing, we
must stress an important point: all of these calculations depend in some part on financial markets being
efficient.2 The reason for this is that analysts often cannot directly observe the rate of return that investors require for a particular type of financing. Instead, analysts must rely on the security prices they can
observe in the financial markets to estimate the required rate.
It makes sense to rely on security prices only if you believe that the financial markets are r­easonably
efficient at incorporating new information into these prices. If the markets were not efficient, estimates
of expected returns that were based on market security prices would be unreliable. Of course, if the
returns that are plugged into equation 11.1 are flawed, the resulting estimate for WACC will also be
inappropriate. With this caveat, we can now discuss how to estimate the costs of the various types
of financing.
A company’s cost of capital is a weighted average of all of its financing costs
The cost of capital for a company is a weighted average of the costs of the different types of financing
used by a company. The weights are the proportions of the total company value represented by the different types of financing. By weighting the costs of the individual financing types in this way, we obtain
the overall average opportunity cost of each dollar invested in the company.
Debt financing
Virtually all companies use some form of debt financing. Company financial managers typically arrange
for revolving lines of credit to finance working capital items such as inventories or accounts receivable.
These lines of credit (such as an overdraft) are very much like the lines of credit that come with your
credit cards. Companies also obtain private fixed-term loans, such as bank loans, or sell bonds to the
public to finance ongoing operations or the purchase of non-current assets — just as you might finance
your living expenses while at university with a student loan or a car with a car loan. For example, an
electricity utility company such as AGL Energy Limited in Australia will sell bonds to finance a new
power plant, and a rapidly growing retailer such as JB Hi-Fi Limited will use debt to finance new stores
and distribution centres. Companies use three general types of debt financing: lines of credit, private
fixed-term loans and bonds sold in the public markets.
318 Finance essentials
There is a cost associated with each type of debt that a company uses. However, when we estimate
the cost of capital for a company, we are particularly interested in the cost of the company’s long-term
debt. Companies generally use long-term debt to finance their non-current assets, and it is the noncurrent assets that concern us when we think about the value of a company’s assets. By long-term debt,
we usually mean the debt that, when it was borrowed, was set to mature in more than 1 year. This typically includes fixed-term bank loans used to finance ongoing operations or non-current assets, as well
as the bonds that a company sells in the public debt markets. Although 1 year is not an especially long
time, debt with a maturity of more than 1 year is typically viewed as permanent debt. This is because
companies often borrow the money to pay off this debt when it matures.
We do not normally worry about lines of credit when calculating the cost of debt because these lines
tend to be temporary. Banks typically require that the outstanding balances be periodically paid down to
$0 (just as we are sure you pay your entire credit card balance from time to time).
When analysts estimate the cost of a company’s long-term debt, they are estimating the cost on a particular date — the date on which they are doing the analysis. This is a very important point to keep in
mind, because the interest rate that the company is paying on its outstanding debt does not necessarily
reflect its current cost of debt. Interest rates change over time and so does the cost of debt for a company.
The rate that a company was charged 3 years ago for a 5-year loan is unlikely to be the same rate that
it would be charged today for a new 5-year loan. For example, suppose that AGL Energy issued bonds
5 years ago for 7 per cent. Since then, interest rates have recently fallen, so the same bonds could be sold
at par value today for 6 per cent. The cost of debt today is 6 per cent, not 7 per cent, and so 6 per cent
is the cost of debt that management will use in current WACC calculations. This is because the WACC
is driven by market valuations. If you looked at the company’s financial statements, you would see that
it is paying an interest rate of 7 per cent. This is what the financial managers of the company agreed to
pay 5 years ago, not what it would cost to sell the same bonds today. The accounting statements reflect
the cost of debt that was sold at some time in the past.
Estimating the cost of debt
We have now seen that we should not use historical costs of debt in WACC calculations. Let’s discuss
how we can estimate the current costs of bonds and other fixed-term loans by using market information.
Current cost of a bond
You may not realise it, but we have already discussed how to estimate the current cost of debt for a publicly traded bond. This cost is estimated using the yield to maturity calculation. Recall that we defined
the yield to maturity as the discount rate that makes the present value of the coupon and principal
­payments equal to the price of the bond.
For example, consider a 10-year $1000 bond that was issued 5 years ago. This bond has 5 years
remaining before it matures. If the bond has an annual coupon rate of 7 per cent, pays coupon interest
semiannually and is currently selling for $1042.65, we can calculate its yield to maturity by using
equation 8.1 and solving for i or by using a financial calculator. Let’s use equation 8.1 for this example.
To do this, as discussed in the section on semiannual compounding in a previous module, we first
convert the bond data to reflect semiannual compounding: (1) the total number of coupon payments is
10 (2 per year × 5 years); and (2) the semiannual coupon payment is $35 [($1000 × 7 per cent)/2 = $70/2].
We can now use equation 8.1 and solve for i to find the yield to maturity:
PB =
$1042.65 =
C
i

1 
Fn
+
1 −
n 
(1 + i)  (1 + i)n


35 
1
1000
1 −
+
i 
(1 + i )10  (1 + i )10
MODULE 11 Cost of capital and working capital management 319
Now, by trial and error or with a financial calculator, we solve for i and find:
i = k Bond = 0.030, or 3.0%
This semiannual rate could be quoted as an annual rate of 6 per cent (2 × 0.03 = 0.06, or 6 per cent).
However, as previously explained, this annual rate fails to account for the effects of compounding. We
must therefore use equation 8.4 to calculate the effective annual yield (EAY) in order to obtain the actual
current annual cost of this debt:
m
2
Quoted interest rate 
0.06 


EAY =  1 +
 − 1 =  1 +
 −1

m
2 
= (1.03) 2 − 1 = 0.0609, or 6.09%
If this bond was sold at par, it paid 7 per cent when it was issued 5 years ago. Someone who buys it
today will expect to earn only 6.09 per cent per year. This is the annual rate of return required by the
market on this bond, which is known as the EAY.
Note that the above calculation takes into account the interest payments, the face value of the debt (the
amount that will be repaid in 5 years) and the current price at which the bond is selling. It is necessary to
account for all of these characteristics of the bond. The return received by someone who buys the bond
today will be determined by both the interest income and the capital appreciation (or capital depreciation
in this case, since the price is higher than the face value).
We must also account for one other factor when we calculate the current cost of bond financing to a
company — the cost of issuing the bond. In the above example, we calculated the return that someone
who buys the bond can expect to receive. Since a company must pay fees to investment bankers,
lawyers and accountants, along with various other costs, in order to actually issue a bond, the cost to
the company is higher than 6.09 per cent.3 Therefore, in order to obtain an accurate estimate of the
cost of a bond, analysts must incorporate issuance costs into their calculations. Issuance costs are an
example of direct out-of-pocket costs, the actual out-of-pocket costs that a company incurs when it
raises capital.
The way that issuance costs are incorporated into the calculation of the cost of a bond is quite simple.
Analysts use the net proceeds that the company receives from the bond, rather than the price that is paid
by the investor, on the left-hand side of equation 8.1. Suppose the company in our example sold 5-year
bonds with a 7 per cent coupon today and paid issuance costs equal to 2 per cent of the total value of the
bonds. After paying the issuance costs, the company would receive only 98 per cent of the price paid by
the investors. Therefore, the company would actually receive only $1042.65 × (1 − 0.02) = $1021.80 for
each bond it sold and the semiannual cost to the company would be:
PB =
C 
1 
Fn
+
1 −
n 
i 
(1 + i)  (1 + i)n


1
1000
+
1 −
10 
i
+
+ i )10
(1
)
(1


i = k Bond = 0.0324, or 3.24%
$1021.80 =
35
i
Converting the adjusted semiannual rate to an EAY, we see that the actual annual cost of this debt
financing is:
EAY = (1.0324)2 − 1 = 0.0658, or 6.58%
In this example the issuance costs increase the effective cost of the bonds from 6.1 per cent to 6.6 per cent
per year.
320 Finance essentials
Current cost of an outstanding loan
Conceptually, calculating the current cost of long-term bank or other private debt is not as straightforward as estimating the current cost of a public bond, because financial analysts cannot observe the
market price of private debt. Fortunately, analysts do not typically have to do this. Instead, they can
simply contact their banker and ask what rate the bank would charge if they decided to refinance the debt
today. A rate quote from a banker provides a good estimate of the current cost of a private loan.
Tax and the cost of debt
It is very important that you understand one additional concept concerning the cost of debt. In Australia,
as well as other countries, companies can deduct interest payments for tax purposes. In other words,
every dollar a company pays in interest reduces its taxable income by one dollar. Thus, if the company’s
marginal tax rate is 30 per cent, its total tax bill will be reduced by 30 cents. A dollar of interest would
actually cost this company only 70 cents because the company would save 30 cents on its tax.
More generally, the after-tax cost of interest payments equals the pre-tax cost times 1 minus the tax
rate. This means that the after-tax cost of debt is:
k Debt after-tax = k Debt pre-tax × (1 − t ) (11.2)
In the previous bond example, the effective pre-tax cost of debt was 6.58 per cent per year. With
kDebt after-tax at 6.58 per cent and t at 30 per cent, equation 11.2 gives us:
k Debt after-tax = k Debt pre-tax × (1 − t ) = 0.0658 × (1 − 0.3) = 0.0461, or 4.61%
Estimating the average cost of debt
Most companies have several different debt issues outstanding at any particular point in time. Just as you
might have both a car loan and a home loan, a company might have several bank loans and bond issues
outstanding. To estimate a company’s overall cost of debt when it has several debt issues outstanding,
we must first estimate the costs of the individual debt issues and then calculate a weighted average of
these costs.
To see how this is done, let’s consider an example. Suppose that your doughnut business has grown
dramatically in the past 3 years from a single doughnut outlet to 30 outlets. To finance this growth,
2 years ago you sold $25 million of 5-year bonds. These bonds pay interest annually and have a coupon
rate of 8 per cent. They are currently selling for $1026.24 per $1000 bond. Just today, you also borrowed
$5 million from your local bank at an interest rate of 6 per cent. Assume that this is all the long-term
debt you have and that there are no issuance costs. What is the overall average after-tax cost of your debt
if your business’s tax rate is 30 per cent?
The pre-tax cost of the bonds as of today is the effective annual yield on those bonds. Since the bonds
were sold 2 years ago, they will mature 3 years from now. Using equation 8.1, we find that the EAY
(which equals the yield to maturity in this example) for these bonds is:
PB =
C 
1 
Fn
1 −
+
i 
(1 + i)n  (1 + i)n
80 
1 
1000
+
1 −
3 
i 
(1 + i)  (1 + i)3
i = k Bond pre -tax = 0.07, or 7%
$1026.24 =
The pre-tax cost of the bank loan you took out today is simply the 6 per cent rate that the bank is
charging you, assuming that the bank is charging you the market rate.
MODULE 11 Cost of capital and working capital management 321
Now that we know the pre-tax costs of the two types of debt that your doughnut business has outstanding, we can calculate the overall average cost of your debt by calculating the weighted average of
their two costs. The weights for the two types of debt are as follows:
x Bonds = $25 000 000/($25 000 000
+ $5 000 000) = 0.833
x Bank debt = $5 000 000/($25 000 000
+ $5 000 000) = 0.167
where x Bonds + x Bank debt = 0.833 + 0.167
= 1.000
The weighted average pre-tax cost of debt is:
k Debt pre-tax = x Bonds k Bonds pre-tax + x Bonds debt k Bonds debt pre-tax
= (0.833)(0.07) + (0.167)(0.06)
= 0.0683, or 6.83%
The after-tax cost of debt is therefore:
k Debt after-tax = k Debt pre-tax × (1 − t ) = 6.83% × (1 − 0.30) = 4.78%
Cost of equity
The cost of equity for a company is a weighted average of the costs of the different types of shares
that the company has outstanding at a particular point in time. We saw in an earlier module that some
companies have both preference shares and ordinary shares outstanding. In order to calculate the cost
of equity for these companies, we need to know how to calculate the costs of both ordinary shares and
preference shares. In this section, we discuss how financial analysts can estimate the costs associated
with these two different share types.
322 Finance essentials
Ordinary shares
Just as information about market rates of return is used to estimate the cost of debt, market information is
also used to estimate the cost of equity. There are several ways to do this. The particular approach that a
financial analyst chooses will depend on what information is available and how reliable the analyst believes
it is. Next we discuss three alternative methods for estimating the cost of ordinary shares. It is important to
remember throughout this discussion that the ‘cost’ we are referring to is the rate of return that investors
require for investing in these shares at a particular point in time, given their ­systematic risk.
Method 1: Capital Asset Pricing Model (CAPM)
The first method for estimating the cost of ordinary equity is one that we discussed earlier in the text.
This method uses equation 7.12:
E(R i ) = R rf + βi [E(R m ) − R rf ]
In this equation, the expected return on an asset is a linear function of the systematic risk associated with
that asset.
If we recognise that E(Ri) in equation 7.12 is the cost of the ordinary share capital used by the company (kos) when we are calculating the cost of equity and that [E(Rm) − Rrf] is the market risk premium,
we can rewrite equation 7.12 as follows:
kos = R rf + (βos × Market risk premium) (11.3)
Equation 11.3 is just another way of writing equation 7.12. It tells us that the cost of ordinary shares
equals the risk-free rate of return plus compensation for the systematic risk associated with the ordinary
shares. You already saw some examples of how to use this equation to calculate the cost of equity in the
discussion of the Capital Asset Pricing Model (CAPM). In those examples you were given the current
risk-free rate, the beta for the shares and the market risk premium, and were asked to calculate kos using
the equation. Now we turn our attention to some practical considerations that you must be concerned
with when choosing the appropriate risk-free rate, beta and market risk premium for this calculation.
Risk-free rate. First, let’s consider the risk-free rate. The current EAY on a risk-free asset should
always be used in equation 11.3. This is because the risk-free rate at a particular point in time reflects the
rate of inflation that the market expects in the future. Since the expected rate of inflation changes over
time, an old risk-free rate might not reflect current inflation expectations.
When analysts select a risk-free rate, they must choose between using a short-term rate, such as that
for Treasury notes (T-notes), or a longer term rate, such as those for Treasury bonds. Which of these
choices is most appropriate? This question has been hotly debated by finance professionals for many
years. We recommend that you use the risk-free rate on a long-term Treasury security when you estimate
the cost of equity capital, because the equity claim is a long-term claim on the company’s cash flows.
As you saw previously, the shareholders have a claim on the cash flows of the company in perpetuity.
By using a long-term Treasury security, you are matching a long-term risk-free rate with a long-term
claim. A long-term risk-free rate better reflects long-term inflation expectations and the cost of getting
investors to part with their money for a long period of time than a short-term rate.
Beta. If the ordinary shares of a company are publicly traded, then you can estimate the beta for these
shares using a regression analysis similar to that illustrated in figure 7.10. However, identifying the
appropriate beta is much more complicated if the ordinary shares are not publicly traded. Since most
companies in Australia are privately owned and do not have publicly traded shares, this is a problem that
arises quite often when someone wants to estimate the cost of ordinary shares for a company.
Financial analysts frequently overcome this problem by identifying a ‘comparable’ company with
publicly traded shares that is in the same business and has a similar amount of debt. For example, suppose you are trying to estimate the beta for your doughnut business. The company has now grown to
include more than 2000 restaurants throughout the world. The frozen-foods business, however, was never
successful and had to be shut down. You know that Doughnut Time, one of your major competitors, has
MODULE 11 Cost of capital and working capital management 323
publicly traded equity and that the proportion of debt to equity for Doughnut Time is similar to the
proportion for your company. Since Doughnut Time has a business similar to yours, in that it is only
in the doughnut business and competes in similar geographic areas, it would be reasonable to consider
Doughnut Time a comparable company.
The systematic risk associated with the shares of a comparable company is likely to be similar to
the systematic risk for the private company because systematic risk is determined by the nature of the
company’s business and the amount of debt that it uses. If you are able to identify a good comparable
company, such as Doughnut Time, you can use its beta in equation 11.3 to estimate the cost of equity
capital for your company. Even when a good comparable company cannot be identified, it is sometimes
possible to use an average of the betas for the public companies in the same industry.
Market risk premium. It is not possible to directly observe the market risk premium. We just do not
know what rate of return investors expect for the market portfolio — E(Rm) — at a particular point in
time. Therefore, we cannot simply calculate the market risk premium as the difference between the
expected return on the market and the risk-free rate — [E(Rm) − Rrf]. For this reason, financial analysts
generally use a measure of the average risk premium that investors have actually earned in the past as an
indication of the risk premium they might require today.
For example, from 1974 to July 2015 actual returns on the Australian equity market exceeded actual
returns on long-term Australian government bonds by an average of 4 (4.03) per cent per year. If, on average,
investors earned the risk premium that they expected, this figure reflects the average market risk premium
over the period 1974–2015. If an analyst believes that the market risk premium in the past is a reasonable estimate of the risk premium today, then they might use 4 per cent as the market risk premium in equation 11.3.
With this background, let’s work an example to illustrate how equation 11.3 is used in practice to estimate
the cost of ordinary shares for a company. Suppose that it is 1 July 2015 and we want to estimate the cost of
ordinary shares for the oil company Woodside Petroleum Limited. Using the yields reported by the Reserve
Bank of Australia (RBA) for that day, we determine that 30-day T-notes have an effective yield of 2 (2.06) per
cent and 10-year Treasury bonds have an effective yield of 3 (3.01) per cent. From Reuters’ website (www.
reuters.com), we find that the beta for Woodside Petroleum is 1.22. We know that the market risk premium
averaged 4 (4.03) per cent from 1974 to 2015. What is the expected rate of return on Woodside Petroleum?
Since we are estimating the expected rate of return on ordinary shares, and ordinary shares are
a long-term asset from the perspective of the market, we use the long-term Treasury bond yield of
3 per cent in the calculation. Notice that the T-note and the Treasury bond rates differed by 0.95 per cent
(3.01 − 2.06 = 0.95) on 1 July 2015. These interest rates often differ by this amount and more, dependent on the market expectation of future inflation and the RBA’s monetary policy stance, so the choice of
which risk-free rate to use can make quite a difference in the estimated cost of equity.
Once we have selected the appropriate risk-free rate, we can plug it, along with the beta and market
risk premium values, into equation 11.3 to calculate the cost of ordinary shares for Woodside Petroleum:
k os = Rrf + ( β os × Market risk premium )
= 0.03 + (1.22 × 0.04 ) = 0.0788, or 7.88%
How would the analysis differ for a private company? The only difference is that we would not be able to
estimate the beta directly. We would have to estimate the beta from betas for similar public companies.
Method 2: Constant-growth dividend model
Earlier in the text we noted that, if the dividends received by the owner of an ordinary share are expected to
grow at a constant rate in perpetuity, then the value of that share today can be calculated using equation 9.4:
P0 =
D1
R − g
where D1 is the dividend expected to be paid one period from today, R is the required rate of return and
g is the annual rate at which the dividends are expected to grow in perpetuity.
324 Finance essentials
We can replace the R in equation 9.4 with kos since we are specifically estimating the expected rate of
return for investing in ordinary shares (also the cost of equity). We can then rearrange this equation to
solve for kos:
kos =
D1
+ g
P0
(11.4)
While equation 11.4 is just a variation of equation 9.4, it is important enough to identify as a separate
equation because it provides a direct way of estimating the cost of equity under certain circumstances.
If we can estimate the dividend that shareholders will receive next period, D1, and we can estimate the
rate at which the market expects dividends to grow over the long run, g, then we can use today’s market
price, P0, in equation 11.4 to tell us what rate of return investors in the company’s ordinary shares are
expecting to earn.
Consider an example. Suppose that the current price for the ordinary shares of AGL Energy is $20,
the company is expected to pay a dividend of $2 per share to its ordinary shareholders next year and the
dividend is expected to grow at a rate of 3 per cent in perpetuity after next year. Equation 11.4 tells us
that the required rate of return for AGL Energy shares is:
kos =
D1
$2
+g=
+ 0.03 = 0.13, or 13%
P0
$20
This approach can be useful for a company that pays dividends when it is reasonable to assume dividends will grow at a constant rate and when the analyst has a good idea what that growth rate will be.
An electricity utility company is an example of this type of company. Some electricity utility companies
pay relatively high and predictable dividends that increase at a fairly consistent rate. In contrast, this
approach would not be appropriate for use by a high-tech company that pays no dividends or pays a
small dividend that is likely to increase at a high rate in the short term. Equation 11.4, like any other
equation, should be used only if it is appropriate for the particular share.
You might be asking yourself at this point where you would get P0, D1 and g in order to use equation
11.4 for a particular share. You can get the current price of a share as well as the dividend that a company is expected to pay next year quite easily from many different websites — for example, Yahoo!
Finance. The financial information includes the dollar value of dividends paid in the past year and the
dividend that the company is expected to pay in the next year.
Estimating the long-term rate of growth in dividends is more difficult, but there are some guidelines
that can help. As we discussed in a previous module, the first rule is that dividends cannot grow faster
than the long-term growth rate of the economy in a perpetuity model such as equations 9.5 or 11.4.
Assuming dividends will grow faster than the economy is the same as assuming that dividends will eventually become larger than the economy itself! We know this is impossible.
What is the long-term growth rate of the economy? Well, historically it has been the rate of inflation
plus about 4 per cent. This means that, if inflation is expected to be 3 per cent in the long term, then
a reasonable estimate for the long-term growth rate in the economy is 7 per cent (3 per cent inflation
plus 4 per cent real growth). This tells us that g in equation 11.4 will not be greater than 7 per cent.
What exactly it will be depends on the nature of the business and the industry it is in. If it is a declining
industry, then g might be negative. If the industry is expected to grow with the economy and the particular company you are evaluating is expected to retain its market share, then a reasonable estimate for
g might be 6 or 7 per cent.
Method 3: Multistage-growth dividend model
Using a multistage-growth dividend model to estimate the cost of equity for a company is very similar
to using a constant-growth dividend model. The difference is that a multistage-growth dividend model
allows for faster dividend growth rates in the near term, followed by a constant long-term growth rate. If
MODULE 11 Cost of capital and working capital management 325
this concept sounds familiar, that is because it is the idea behind the mixed (supernormal) growth dividend model discussed in a previous module. In equation 9.6 this model was written as:
P0 =
D1
D2
Dt
Pt
+
+ +
+
2
t
1+ R
(1 + R)
(1 + R)
(1 + R)t
where Di is the dividend in period i, Pt is the value of constant-growth dividend payments in period t and
R is the required rate of return.
To refresh your memory of how this model works, let’s consider a three-stage example. Suppose that
a company will pay a dividend 1 year from today (D1) and that this dividend will increase at a rate of
g1 the following year, g2 the year after that and g3 per year thereafter. The value of a share today thus
equals:
P0 =

D1 (1 + g1)
D1 (1 + g1)(1 + g2 )  D1 (1 + g1)(1 + g2 )( 1 + g3)  
D1
1
+ 
+
+
 
3 
−
+
1 + kos
(1 + kos )2
(1 + kos )3
k
g
k
(1
)
3
os
os

 

In this equation, we have replaced the R in equation 9.6 with kos since we are specifically estimating the
expected rate of return for ordinary shares. We have also written all of the dividends in terms of D1 to
illustrate how the different growth rates will affect the dividends in each year. Finally, we have written
Pt in terms of the constant-growth model. If we substitute D1, D2, D3 and D4 where appropriate, you can
see that this is really just equation 9.6, where we have replaced R with kos and written Pt in terms of the
constant-growth model:
P0 =
 D4 
D1
D2
D3
+
+
+ 

2
3
1 + kos
(1 + kos )
(1 + kos )
 kos − g3 


1

3 
 (1 + kos ) 
All this equation does is add the present values of the dividends that are expected in each of the next
3 years and the present value of a growing perpetuity that begins in the fourth year.
Note that the fourth term is discounted only 3 years because, as we saw in previous modules, the
­constant-growth model gives the present value of a growing perpetuity as of the year before the first cash
flow. In this case, since the first cash flow is D4, the model gives you the value of the growing perpetuity
as of year 3.
The multistage-growth dividend model is far more flexible than the constant-growth dividend model
because we do not have to assume that dividends grow at the same rate forever. We can use a model such
as this to estimate the cost of ordinary shares, kos, by plugging P0, D1 and the appropriate growth rates
into the model and solving for kos using trial and error — just as we solved for the yield to maturity of
bonds in a previous module and earlier in this module. The two major issues we need to be concerned
about when we use a growth dividend model are: (1) that we have chosen the right model, meaning
that we have included enough stages or growth rates; and (2) that our estimates of the growth rates are
reasonable.
Let’s work an example to illustrate how this model is used to calculate the cost of ordinary shares.
Suppose that we want to estimate the cost of ordinary shares for a company that is expected to pay a
dividend of $1.50 per share next year. This dividend is expected to increase 15 per cent the following
year, 10 per cent the year after that, 7 per cent the year after that and 5 per cent annually thereafter. If the
company’s ordinary shares are currently selling for $24 per share, what is the rate of return that investors
require for investing in these shares?
Because there are four different growth rates in this example, we have to solve a formula with five terms:
P0 =
 D5 
D1
D2
D3
D4
+
+
+
+ 

1 + kos
(1 + kos )2
(1 + kos )3
(1 + kos )4
 kos − g4 
326 Finance essentials


1

4 
(1
+
k
)
os


From the information given in the problem statement, we know the following:
D1 = $1.50
D 2 = D1 × (1 + g1 ) = $1.500 × 1.15 = $1.725
D3 = D 2 × (1 + g2 ) = $1.725 × 1.10 = $1.898
D 4 = D3 × (1 + g3 ) = $1.898 × 1.07 = $2.031
D5 = D 4 × (1 + g4 ) = $2.031 × 1.05 = $2.133
Substituting these values into the previous equation gives us the following, which we solve for kos:
$24 =
 $2.13 
$1.50
$1.73
$1.90
$2.03
+
+
+
+ 

2
3
4
1 + kos
(1 + kos )
(1 + kos )
(1 + kos )
 kos − 0.05 


1

4 
 (1 + kos ) 
As mentioned previously, we can solve this equation for kos using trial and error. When we do this, we
find that kos is 12.2 per cent. This is the rate of return at which the present value of the cash flows equals
$24. Therefore, it is the rate that investors currently require for investing in these shares.
Which method should we use?
We now have discussed three methods of estimating the cost of ordinary equity for a company. You
might be asking yourself how you are supposed to know which method to use. The short answer is that,
in practice, most people use the CAPM (method 1) to estimate the cost of ordinary equity if the result
is going to be used in the discount rate for evaluating a project. One reason is that, assuming the theory
is valid, the CAPM tells managers what rate of return investors should require for equity with the same
level of systematic risk that the company’s equity has. This is the appropriate opportunity cost of equity
capital for an NPV analysis if the project has the same risk as the company overall and will have similar
leverage. Furthermore, the CAPM does not require financial analysts to make assumptions about future
growth rates in dividends, as methods 2 and 3 do.
Used properly, methods 2 and 3 provide an estimate of the rate of return that is implied by the current price of a company’s shares at a particular point in time. If the share markets are efficient, then this
should be the same as the number that we would estimate using the CAPM. However, to the extent that
the company’s shares are mispriced — for example, if investors are not informed or have misinterpreted
the future prospects for the company — deriving the cost of equity from the price at one point in time
can yield a poor estimate of the true cost of equity.
Indeed, it is important to realise that project valuation can never be an exact science. In principle, the
theoretical underpinnings of discounting future cash flows at the opportunity cost of those cash flows are
valid. The point is that both the anticipated cash flows and the appropriate discount rate are imprecise.
Managers aim to have at least some degree of ‘comfort’ and ‘confidence’ in them, however.
Preference shares
As we have discussed, preference shares are a form of equity that has a stated value and specified dividend rate. For example, a preference share might have a stated value of $100 and a 5 per cent dividend
rate. The owner of such a share would be entitled to receive a dividend of $5 ($100 × 0.05) each year.
Another feature of preference shares is that they do not have an expiration date. In other words, preference shares continue to pay the specified dividend in perpetuity, unless the company repurchases them
or goes out of business.
These characteristics of preference shares allow us to use the perpetuity model, equations 6.4 and 9.2,
to estimate the cost of preference shares. Rearranging the formula to solve for kps yields:
k ps =
D ps
Pps
(11.5)
where Pps is the present value of the expected dividends (the current preference share price), Dps is the
annual preference share dividend and kps is the cost of the preference share.
MODULE 11 Cost of capital and working capital management 327
For example, suppose that investors would pay $85 for the preference share mentioned above. Plugging the information from our example into equation 11.5, we see that kps for the preference share in our
example is:
k ps =
D ps
$5
=
= 0.0588, or 5.88%
Pps
$85
This is the rate of return at which the present value of the annual $5 cash flows equals the market price
of $85. Therefore, 5.88 per cent is the rate that investors currently require for investing in this preference
share.
It is easy to incorporate issuance costs into the above calculation to obtain the cost of the preference
share to the company that issues it. As in the previous bond calculations, we use the net proceeds from
the sale, rather than the price that is paid by the investor, in the calculation. For example, suppose that
in order for a company to sell the above preference share, it must pay an investment banker 5 per cent
of the amount of money raised. If there are no other issuance costs, the company would receive $85 ×
(1 − 0.05) = $80.75 for each share sold and the total cost of this financing to the company would be:
k ps =
D ps
$5
=
= 0.0619, or 6.19%
Pps
$80.75
You may recall that certain characteristics of preference shares look a lot like those of debt. The
equation Pps = Dps/kps shows that the value of preference shares also varies with market rates of return
in the same way as debt. Because kps is in the denominator of the fraction on the right-hand side of the
equation, whenever kps increases Pps decreases, and whenever kps decreases Pps increases. That is, the
value of preference shares is negatively related to market rates.
It is also important to recognise that the CAPM can be used to estimate the cost of preference shares,
just as it can be used to estimate the cost of ordinary equity. A financial analyst can simply substitute kps
for kos and βps for βos in equation 11.3 and use it to estimate the cost of preference shares. Remember that
the CAPM does not apply only to ordinary shares; rather, it applies to any asset. Therefore, we can use
it to calculate the rate of return on any asset if we can estimate the beta for that asset.
BEFORE YOU GO ON
1.
2.
3.
4.
How do you estimate the cost of debt for a company with more than one type of debt?
How does tax affect the cost of debt?
What information is needed in order to use the CAPM to estimate kos or kps?
Under what circumstances can you use the constant-growth dividend formula to estimate kos?
11.2 Using the weighted average cost of capital
LEARNING OBJECTIVE 11.2 Calculate the weighted average cost of capital (WACC) for a company and
explain the limitations of using a company’s WACC as the discount rate when evaluating a project.
We have now covered the basic concepts and calculation tools that are used to estimate the WACC. At
this point, we are ready to talk about some of the practical issues that arise when financial analysts calculate the WACC for their companies.
When financial analysts think about calculating the WACC, they usually think of it as a weighted
average of the company’s after-tax cost of debt, cost of preference shares and cost of ordinary shares.
Equation 11.1 is usually written as:
WACC = x Debt k Debt pre -tax (1 − t ) + x ps k ps + x os k os 328 Finance essentials
(11.6)
where xDebt + xps + xos = 1. If the company has more than one type of debt outstanding or more than one
type of preference or ordinary shares, analysts will calculate a weighted average for each of these types of
securities and then plug these averages into equation 11.6. Analysts will also use the market values, rather
than the accounting book values, of the debt, preference shares and ordinary shares to calculate the weights
(the x’s) in equation 11.6. This is because, as we have already seen, the theory underlying the discounting
process requires that the costs of the different types of financing be weighted by their relative market values.
Accounting book values have no place in these calculations unless they just happen to equal the market values.
Calculating WACC: an example
An example provides a useful way of illustrating how the theories and tools that we have discussed are
used in practice. Assume that you are a financial analyst at a manufacturing company that has used three
types of debt, preference shares and ordinary shares to finance its investments.
Debt: The debt includes a $4 million bank loan that is secured by machinery and equipment. This loan has
an interest rate of 6 per cent and your company could expect to pay the same rate if the loan were refinanced
today. Your company also has a second bank loan (a $3 million secured loan on your manufacturing plant)
with an interest rate of 5.5 per cent. Again, this rate would be the same today. The third type of debt is a bond
issue that the company sold 2 years ago for $11 million. The market value of these bonds today is $10 million.
Using the approach we discussed previously, you have estimated that the EAY on these bonds is 7 per cent.
Preference shares: The preference shares pay an annual dividend of 4.5 per cent on a stated value of
$100. A preference share is currently selling for $60 and there are 100 000 shares outstanding.
Ordinary shares: There are 1 million ordinary shares outstanding and they are currently selling for
$21 each. Using a regression analysis, you have estimated that the beta of these shares is 0.95.
The 10-year Treasury bond rate is currently 3.00 per cent and you have estimated the market risk premium to be 4.00 per cent using the returns on shares and Treasury bonds from the period 1974–2015.
The corporate income tax rate is 30 per cent. What is the WACC for your company?
The first step in calculating the manufacturing company’s WACC is to calculate the pre-tax cost of
debt. Since the market value of the company’s debt is $17 million ($4 + $3 + $10), we can calculate the
pre-tax cost of debt as follows:
k Debt pre -tax = x Bank loan 1 k Bank loan 1 pre -tax + x Bank loan 2 k Bank loan 2 pre -tax + x Bonds k Bonds pre -tax
= ( $4 / $17 ) ( 0.06 ) + ( $3 / $17 ) ( 0.055) + ( $10 / $17 ) ( 0.07 )
= 0.065, or 6.5%
MODULE 11 Cost of capital and working capital management 329
Note that because the $4 million and $3 million loans have rates that equal what it would cost to refinance
them today, their market values equal the amount that is owed. Since the $10 million market value of the
bond issue is below the $11 million face value, the rate the company is actually paying must be lower
than the 7 per cent rate you estimated to reflect the current cost of this debt. Recall that as interest rates
increase, the market value of a bond decreases.
We next calculate the cost of the preference shares using equation 11.5, as follows:
D ps
0.045 × $100
=
Pps
$60
$4.5
=
= 0.075, or 7.5%
$60
k ps =
From equation 11.3, we calculate the cost of the ordinary shares to be:
kos = Rrf + (β os × Market risk premium) = 0.03 + (0.95 × 0.04)
= 0.068 or 6.8%
We are now ready to use equation 11.6 to calculate the WACC. Since the company has $17 million
of debt, $6 million of preference shares ($60 × 100 000 shares) and $21 million of ordinary shares
($21 × 1 000 000 shares), the total market value of its capital is $44 million ($17 + $6 + $21). The
company’s WACC is therefore:
WACC = x Debt k Debt pre − tax (1 − t ) + x ps k ps + xos kos
= ( $17 / $44 ) ( 0.065) (1 − 0.3) + ( $6 / $44 ) ( 0.075) + ( $21 / $44 ) ( 0.068 )
= 0.0176 + 0.0102 + 0.0325
= 0.0603 or 6.03%
DEMONSTRATION PROBLEM 11.1
Calculating the WACC with equation 11.6
Problem:
After calculating the cost of the common equity in your doughnut business to be 8.51 per cent, you
have decided to estimate the WACC. You recently hired a business appraiser to estimate the value of
your shares, which includes all of the outstanding ordinary shares. Her report indicates that they are
worth $500 million.
In order to finance the 2000 restaurants that are now part of your company, you have sold three different bond issues.
Based on the current prices of the bonds from these issues and the issue characteristics (face values
and coupon rates), you have estimated the market values and EAY to be:
Bond issue
Value ($ millions)
Effective annual yield
1
2
3
$100
187
154
6.5%
6.9
7.3
Total
$441
Your company has no other long-term debt or any preference shares outstanding. The corporate tax
rate is 30 per cent. What is the WACC for your doughnut business?
330 Finance essentials
Approach:
You can use equation 11.6 to solve for the WACC for your doughnut business. To do so, you must first
calculate the weighted average cost of debt. You can then plug the weights and costs for the debt and
ordinary shares into equation 11.6. Since your business has no preference shares, the value for this term
in equation 11.6 will equal $0.
Solution:
The weighted average cost of the debt is:
k Debt pre -tax = x1k1 Debt pre-tax + x 2 k 2 Debt pre-tax + x 3 k 3 Debt pre-tax
= ( $100 / $441) ( 0.065 ) + ( $187 / $441) ( 0.069 ) + ( $154 / $441) ( 0.073 )
= 0.0695, or 6.95%
and the WACC is:
WACC = x Debt k Debt pre -tax (1− t ) + x ps k ps + x os k os
= ( $441/ $941) ( 0.0695 ) (1− 0.3) + 0 + ( $500/$4941) ( 0.0851)
= 0.0228 + 0 + 0.0452
= 0.068 or 6.8%
Limitations of using WACC as a discount rate
At the beginning of this module, we told you that financial managers often require analysts within the
company to use the company’s current cost of capital to discount the cash flows for individual projects.
They do so because it is very difficult to directly estimate the discount rate for individual projects. You
should recognise by now that the WACC is the discount rate that analysts are often required to use.
Using the WACC to discount the cash flows for a project can make sense under certain circumstances.
However, in other circumstances it can be very dangerous. The rest of this section discusses when it
makes sense to use the WACC as a discount rate and the problems that can occur when the WACC is
used incorrectly.
An earlier module discussed how an analyst forecasting the cash flows for a project is forecasting the
incremental after-tax free cash flows at the company level. These cash flows represent the difference
between the cash flows that the company will generate if the project is adopted and the cash flows that
the company will generate if the project is not adopted.
Financial theory tells us the rate that should be used to discount these incremental cash flows is the
rate that reflects their systematic risk. This means the WACC is the appropriate discount rate for evaluating a project only when the project has cash flows with systematic risks that are exactly the same as
those for the company as a whole. Unfortunately, this is not true for most projects. The company itself is
a portfolio of projects with varying degrees of risk.
When a single rate, such as the WACC, is used to discount cash flows for projects with varying levels
of risk, the discount rate will be too low in some cases and too high in others. When the discount rate
is too low, the company runs the risk of accepting a project with a negative NPV. To see how this might
happen, assume you work at a company that manufactures soft drinks and the managers at your company are concerned about all the competition in the core soft drink business. They are thinking about
expanding into the manufacture and sale of exotic tropical beverages. The managers believe that entering
this market would allow the company to better differentiate its products and earn higher profits. Suppose
also that the appropriate beta for soft drink projects is 1.2, while the appropriate beta for tropical beverage projects is 1.5. Since your company is only in the soft drink business right now, the beta for its
overall cash flows is 1.2.
MODULE 11 Cost of capital and working capital management 331
Since the beta of the tropical beverage project is larger than the beta of the company as a whole, the
expected return (or discount rate) for the tropical beverage project should be higher than the company’s
WACC. The Security Market Line (SML) indicates what this expected return should be. Now, if the
company’s WACC is used to discount the expected cash flows for this project and the expected return
on the project is above the company’s WACC, then the estimated NPV will be positive. So far, so good.
However, some projects may have an expected return that is above the WACC but below the SML. For
projects such as those, using the WACC as the discount rate may actually cause the company to accept
a negative NPV project! The estimated NPV will be positive even though the true NPV is negative. The
negative NPV projects that would be accepted in those situations have returns that fall in the red shaded
area below the SML, above the WACC line and to the right of the company’s beta.
Using the WACC to discount expected cash flows for low-risk projects could result in company managers rejecting projects that have positive NPVs. This problem is, in a sense, the mirror image of the
case where the WACC is lower than the correct discount rate. Financial managers run the risk of turning
down positive NPV projects whenever the WACC is higher than the correct discount rate. The positive
NPV projects that would be rejected are those that are below the WACC but above the SML and have
betas less than that of the company.
To see how these types of problems arise, consider a project that requires an initial investment of $100
and is expected to produce cash inflows of $40 per year for 3 years. If the correct discount rate for this
project is 8 per cent, its NPV will be $3.08:
NPV = FCF0 +
FCF1
FCF2
FCF3
+
+
2
1+ k
(1 + k )
(1 + k )3
= − $100 +
= $3.08
$40
$40
$40
+
+
1 + 0.08 (1 + 0.08)2
(1 + 0.08)3
This is an attractive project because it returns more than the investors’ opportunity cost of capital.
Suppose, however, that the financial managers of the company considering this project require that all
projects be evaluated using the company’s WACC of 11 per cent. When the cash flows are discounted
using a rate of 11 per cent, the NPV is –$2.25.
NPV = − $100 +
$40
$40
$40
+
+
= − $2.25
2
1 + 0.11 (1 + 0.11)
(1 + 0.11)3
As you can see, when the WACC is used to discount the cash flows in this case, the company will
end up rejecting a positive NPV project. It will be passing up an opportunity to create value for its
shareholders.
It is also important to recognise that if a company uses a single rate to evaluate all of its projects, there
will be a bias towards accepting more risky projects. The average risk of the company’s assets will tend
to increase over time. Furthermore, because some positive NPV projects are likely to be rejected and
some negative NPV projects are likely to be accepted, new projects on the whole will probably create
less value for shareholders than if the appropriate discount rate had been used to evaluate all projects.
This, in turn, can put the company at a disadvantage when compared with its competitors and adversely
affect the value of its existing projects.
The key point to take away from this discussion is that it is only really correct to use a company’s
WACC to discount the cash flows for a project if the expected cash flows from that project have the same
systematic risk as the expected cash flows from the company as a whole. You might be wondering how
you can tell when this condition exists. The answer is that we never know for sure. Nevertheless, there
are some guidelines that you can use when assessing whether the systematic risk for a particular project
is similar to that for the company as a whole.
332 Finance essentials
The systematic risk of the cash flows from a project depends on the nature of the business. Revenues
and expenses in some businesses are affected more by changes in general economic conditions than
revenues and expenses in other businesses. While total volatility is not the same as systematic volatility,
we find that businesses with more total volatility (uncertainty or risk) typically have more systematic
volatility. Since beta is a measure of systematic risk and systematic risk is a key factor in determining
a company’s WACC, this suggests that the company’s WACC should be used only for projects with
­business risks similar to those for the company as a whole.
Condition 1: A company’s WACC should be used to evaluate the cash flows for a new project only
if the level of systematic risk for the project is the same as that for the whole portfolio of projects that
currently comprise the company.
You also need to consider the way the project will be financed and how this financing compares with
the way the company’s assets are financed. To better understand why this is important, consider equation
11.6, which provides a measure of the company’s cost of capital that reflects both how the company has
financed its assets — that is, the mix of debt and preference and ordinary shares it has used — and the
current cost of each type of financing. In other words, the WACC reflects both the x’s and the k’s associated with the company’s financing. Why is this important? Because the costs of the different types of
capital depend on the fraction of the total company financing that each represents. If the company uses
more or less debt, the cost of debt will be higher or lower. In turn, the costs of both preference shares
and ordinary shares will be affected. This means that, even if the underlying business risk of the project
is the same as that for the company as a whole, if the project is financed differently than the company the
appropriate discount rate for the project analysis will be different from that for the company as a whole.
Condition 2: A company’s WACC should be used to evaluate a project only if that project uses the
same financing mix — the same proportions of debt, preference shares and ordinary shares — used to
finance the company as a whole.
In summary, the WACC is a measure of the current cost of the capital that the company has used to
finance its projects. It is an appropriate discount rate for evaluating projects only if: (1) the project’s
systematic risk is the same as that of the company’s current portfolio of projects; and (2) the project will
be financed with the same mix of debt and equity as the company’s current portfolio of projects. If either
of these two conditions does not hold, then managers should be careful in using the company’s current
WACC to evaluate a project.
BEFORE YOU GO ON
1. Do analysts use book values or market values to calculate the weights when they use
equation 11.6? Why?
2. Under what conditions is the WACC the appropriate discount rate for a project?
11.3 Working capital basics
LEARNING OBJECTIVE 11.3 Define and calculate net working capital and discuss the importance of
working capital management.
Working capital management involves two fundamental questions: (1) What is the appropriate amount
and mix of current assets for the company to hold? (2) How should these current assets be financed? Companies must carry a certain amount of current assets in order to be able to operate smoothly. For example,
without sufficient cash on hand, a company facing an unexpected expense might not be able to pay its
bills on time. Without an inventory of raw materials, production might be subject to costly interruptions or
shutdowns. Without an inventory of finished goods, sales might be lost because a product is out of stock.
To provide a background for our discussion of working capital management, we first briefly review
some important terminology and ideas.
MODULE 11 Cost of capital and working capital management 333
Working capital terms and concepts
First, we provide a brief review of the basic terms associated with working capital management.
1. Current assets are cash and other assets that a company expects to convert into cash in a year or
less. These assets are usually listed on the balance sheet in order of their liquidity. Typical current
assets include cash, marketable securities (sometimes also called short-term investments), accounts
receivable, inventory and others, such as prepaid expenses.
2. Current liabilities (or short-term liabilities) are obligations that a company expects to repay in a
year or less. They may be interest bearing, such as short-term notes and current maturities of longterm debt, or non-interest bearing, such as accounts payable, accrued expenses or accrued tax and
wages.
3. Working capital (also called gross working capital) includes the funds invested in a company’s
cash and marketable security accounts, accounts receivable, inventory and other current assets. All
companies require a certain amount of current assets in order to operate smoothly and to carry out
day-to-day operations. Note that working capital is defined in terms of current assets, so the two
terms are one and the same.
4. Net working capital (NWC) refers to the difference between current assets and current liabilities:
NWC = Current assets − Current liabilities
NWC is important because it is a measure of a company’s liquidity. It is a measure of liquidity
because it is the amount of working capital that a company would have left over after it paid off
all of its short-term liabilities. The larger the company’s NWC, the greater its liquidity. Almost all
companies have more current assets than current liabilities, so net working capital is positive for most
companies.4
5. Working capital management involves management of current assets and their financing. The financial
manager’s responsibilities include determining the optimum balance for each of the current asset
accounts and deciding what mix of short-term debt, long-term debt and equity to use in financing
working capital. Working capital management decisions are usually fast paced as they reflect the pace
of the company’s day-to-day operations.
6. Working capital efficiency is a term that refers to how efficiently working capital is used. It is most
commonly measured by a company’s cash conversion cycle, which reflects the time between the
point at which raw materials are paid for and the point at which finished goods made from those
materials are converted into cash. The shorter a company’s cash conversion cycle, the more efficient
is its use of working capital.
7. Liquidity is the ability of a company to convert assets — real or financial — into cash quickly without
suffering a financial loss.
Working capital accounts and trade-offs
Short-term cash inflows and outflows do not always match in their timing or magnitude, creating a need
to manage the working capital accounts. The objective of the managers of these accounts is to enable
the company to operate with the smallest possible net investment in working capital. To do this, however, managers must make cost–benefit trade-offs. These trade-offs arise because it is easier to run a
business with a generous amount of net working capital, but it is also more costly to do so. Let’s briefly
look at each working capital account to see what the basic trade-offs are. Keep in mind as you read the
discussion that the more working capital assets a company holds, the greater the cost to the company.
The working capital accounts that are the focus of most working capital management activities are as
follows.
1. Cash (including marketable securities): The more cash a company has on hand, the more
likely it will be able to meet its financial obligations if an unexpected expense occurs. If cash
balances become too small, the company runs the risk that it will be unable to pay its bills;
334 Finance essentials
if this condition becomes chronic, creditors could force the company into insolvency. The downside
of holding too much cash is that the returns on cash are low even when it is invested in an
interest-paying bank account or highly liquid short-term money market instruments such as Treasury
securities.
2. Receivables: The accounts receivable at a company represent the total unpaid credit that the company
has extended to its customers. Accounts receivable can include trade credit (credit extended to
another business) or consumer credit (credit extended to a consumer) or both. Businesses provide
trade and consumer credit because doing so increases sales and because it is often a competitive
necessity to match the credit terms offered by competitors. The downside to granting such credit is
that it is expensive to evaluate customers’ credit applications to ensure they are creditworthy and then
to monitor their ongoing credit performance. Companies that are not diligent in managing their credit
operations can suffer large losses from bad debts, especially during a recession when customers may
have trouble paying their bills.
3. Inventory: Customers like companies to maintain large finished goods inventories because then, when
they go to make a purchase, the item they want will likely be in stock and so they do not have to wait.
Similarly, large raw material inventories reduce the chance that the company will not have access
to raw materials when they are needed, which can cause costly interruptions in the manufacturing
process. At the same time, large inventories are expensive to finance, can require warehouses that are
expensive to build and maintain, must be protected against breakage and theft, and run a greater risk
of obsolescence.
4. Payables: Accounts payable are trade credits provided to companies by their suppliers. Because
suppliers typically grant a grace period before payables must be repaid and companies do not
have to pay interest during this period, trade credit is an attractive source of financing. For this
reason, financial managers do not hurry to pay their suppliers when bills arrive. Of course, suppliers
recognise that they provide attractive financing to their customers and that trade credit is expensive
for them. Consequently, suppliers tend to provide strong incentives (by either providing discounts
for paying on time or charging penalties for late payment) for companies to pay on time. As you
might expect, companies typically wait until near the end of the grace period to repay trade credit.
The financial manager at a company that is having serious financial problems may have no choice
but to delay paying its suppliers. However, besides incurring monetary penalties, a manager who
is consistently late paying trade credit runs the risk that the supplier will no longer sell to their
company.
When the financial manager makes a decision to increase working capital, good things are likely
to happen to the company — sales should increase, relationships with vendors and suppliers should
improve, and work or manufacturing stoppages should be less likely. Unfortunately, the extra working
capital costs money and there is no simple algorithm or formula that determines the optimal level of
working capital that a company should hold. The choice depends on management’s strategic preferences,
its willingness to bear risk and the company’s line of business.
Operating and cash conversion cycles
A very important concept in working capital management is known as the cash conversion cycle. This
is the length of time from the point at which a company actually pays for raw materials until the point
at which it receives cash from the sale of finished goods made from those materials. This is an important concept because the length of the cash conversion cycle is directly related to the amount of working
capital that a company needs.
The sequence of events that occurs from the point in time that a company actually pays for its raw
materials to the point that it receives cash from the sale of finished goods is as follows: (1) the company uses cash to pay for raw materials and the cost of converting them into finished goods (conversion
costs); (2) finished goods are held in the finished goods inventory until they are sold; (3) finished goods
MODULE 11 Cost of capital and working capital management 335
are sold on credit to the company’s customers; and, finally, (4) customers repay the credit the company
has extended to them and the company receives the cash. The cash is then reinvested in raw materials
and conversion costs, and the cycle is repeated. If a company is profitable, the cash inflows increase over
time. Figure 11.1 shows a schematic diagram of the cash conversion cycle. The cash conversion cycle
reflects the average time from the point when cash is used to pay for raw materials until the point when
cash is collected on the accounts receivable associated with the product produced with those raw materials. One of the main goals of a financial manager is to optimise the time between the cash outflows
and the cash inflows.
FIGURE 11.1
The cash conversion cycle
Collection of
accounts
receivable
1
Raw materials
purchased on
credit
4
Cash inflows
Accounts
receivable
Cash
outflows
Payment of
conversion costs
• Labour
• Equipment
Payment of
accounts
payable
3
2
Finished
goods
inventory
Sale of
goods or
services
Clearly, financial managers want to achieve several goals in managing this cycle.
•• Delay paying accounts payable as long as possible without suffering any penalties.
•• Maintain the minimum level of raw material inventories necessary to support production without
causing manufacturing delays.
•• Use as little labour and other inputs to the production process as possible while maintaining product
quality.
•• Maintain the level of finished goods inventory that represents the best trade-off between minimising
the amount of capital invested in finished goods inventory and the desire to avoid lost sales.
•• Offer customers terms on trade credit that are sufficiently attractive to support sales and yet minimise
the cost of this credit — both the financing cost and the risk of non-payment.
•• Collect cash payments on accounts receivable as quickly as possible to close the loop.
All of these goals have implications for a company’s efficiency and liquidity. It is the financial
man­ager’s responsibility to ensure that they make decisions that maximise the value of the company.
­Managing the length of the cash conversion cycle is one aspect of managing working capital to ­maximise
the value of the company.5
Next, we discuss two simple tools to measure working capital efficiency. As you read the discussion,
refer to figure 11.2. The figure shows the cash inflows and outflows and other key events in a company’s
operating cycle and cash conversion cycle, along with calculated values for Whitehaven. Both of these
cycles are used for measuring working capital efficiency.
336 Finance essentials
Time line for operating and cash conversion cycles for Whitehaven Coal Ltd 2014
FIGURE 11.2
Events
Receive
raw
materials
Sell
finished
goods
Collect cash
for finished
goods
Pay cash
for raw
materials
Days’ payables outstanding
Liabilities
(137.53 days)
Days’ sales in inventory
(53.99 days)
Assets
Cycles
Days’ sales outstanding
(33.95 days)
Cash conversion cycle
(–49.59 days)
Operating cycle (87.94 days)
Operating cycle
Throughout the module, we use financial statements and supporting data from Whitehaven Coal Limited to illustrate our discussions. Table 11.1 presents Whitehaven’s balance sheet and income statement for 2014. We have changed some account names from those used by Whitehaven to maintain
consistency with this text. We use this information in illustrating various elements of working capital
management.
TABLE 11.1
Whitehaven Coal Ltd’s financial statements, financial year ended 30 June 2014
($ thousands)
Balance sheet year ended 30 June 2014
Assets
Liabilities and equity
Cash and cash
equivalents
Accounts receivable
Inventories
$ 103 167
Total current assets
$234 551
Non-current receivables
Investments
Property, plant and
equipment
Income statement
70 262
61 122
29 672
568
3 384 937
Accounts payable
$ 155 688
Loans and borrowings
33 084
Current tax liabilities
6 219
Provisions
22 995
Other liabilities
13 366
Revenue
Other income
Cost of sales
Selling and distribution
expenses
Government royalties
Administrative expenses
−24 623
Other expenses
Depreciation and
amortisation
−6 907
−79 491
Exploration and
evaluation
526 914
$ 844 597
Intangible assets
105 843
Total non-current
liabilities
Total non-current
assets
$4 047 934
Total liabilities
$1 075 949
Net tax benefit
Total equity
$3 206 536
Net other comprehensive
income
755 308
29 931
59 358
EBIT
Total liabilities and
equity
−4 177
Net financing costs
−52 157
EBT
−56 334
Profit attributable to
shareholders
$4 282 485
−54 222
Total current liabilities $ 231 352
Loans and borrowings
Deferred tax liabilities
Non-current
provisions
Total assets
$755 406
8 497
−413 183
−189 654
17 949
3 046
−$ 35 339
$4 282 485
Source: Whitehaven Coal Ltd 2014, www.whitehavencoal.com.au/investors/docs/2014-annual-report.pdf.
MODULE 11 Cost of capital and working capital management 337
The operating cycle starts with the receipt of raw materials and ends with the collection of cash
from customers for the sale of finished goods made from those materials. The operating cycle can be
described in terms of two components: days’ sales in inventory (DSI) and days’ sales outstanding (DSO).
The ­formulas for these efficiency ratios are shown below.
Whitehaven’s ratios from 2008 to 2014 are shown in table 11.2.
DSI shows, on average, how long a company holds inventory before selling it. It is calculated by
dividing 365 days by the company’s inventory turnover, which equals the cost of sales divided by the
inventory. The formula for DSI, along with a calculation for Whitehaven in 2014, are as follows:
365 days
365 days
=
Inventory turnover Cost of sales/Inventory
365 days
365 days
=
=
= 53.99 days
$413 183/$61122
6.76
Days’ sales in inventory = DSI =
As shown in table 11.2, Whitehaven’s DSI ranged between 15.69 and 53.99 during the period 2008–14.
Therefore, the 2014 figure of 53.99 days indicates that Whitehaven has been increasing its stockpile each
year. Inventory levels should not be high in the mining industry as the production volume from established
mines is reasonably predictable, reducing the need to build up large stockpiles of raw material. Whitehaven’s
2014 DSI is slightly higher than the 2013 value, which indicates that there may be room to improve
working capital management. When we compare working capital ratios, we see Whitehaven experienced
significant changes from 2008 to 2014. The least variation is in the operating cycle: Whitehaven took
much longer to make payments to suppliers than to collect outstanding balances from debtors.
TABLE 11.2
Selected financial ratios for Whitehaven Coal Ltd 2008–14
Financial ratio
2014
2013
2012
2011
2010
2009
2008
DSI
53.99
49.34
31.23
20.01
28.02
15.69
17.40
DSO
33.95
51.21
41.45
54.19
259.48
129.44
70.97
DPO
137.53
116.30
207.94
119.26
171.95
73.33
70.51
Operating cycle
87.94
100.55
72.68
74.20
287.50
145.13
88.38
Cash conversion cycle
−49.59
−15.75
−135.26
−45.06
115.55
71.80
17.87
DSO indicates how long it takes, on average, for the company to collect its outstanding accounts receivable. DSO is calculated by dividing 365 days by accounts receivable turnover, which equals the net sales
revenue divided by the accounts receivable.6 Sometimes this ratio is called the average collection period.
An efficient company with good working capital management should have a low average collection period
compared with that of its industry. The DSO formula and the calculation for Whitehaven are as follows:
365 days
365 days
=
Accounts receivable turnover Net sales/Accounts receivable
365 days
365 days
=
=
= 33.95 days
$755 406/$70 262 10.7513
Days’ sales outstanding = DSO =
Again, referring to table 11.2 we see that the 2014 DSO is the shortest of the period 2008–14. While
this looks good, we need to recognise that Whitehaven’s 2008 and 2010 figures are quite poor. The
earlier, higher DSO numbers could have been due to the company being too generous with its credit
policy as it tried to increase sales. Similarly, the company may have gone too far in tightening credit
policy to improve the DSO in 2014. However, inspection of Whitehaven’s previous annual reports shows
338 Finance essentials
it has managed lower accounts receivable while increasing sales. Accordingly, its challenge will be to
maintain the lower DSO.
We can now calculate the operating cycle simply by summing the DSO and the DSI:
Operating cycle = DSO + DSI (11.7)
Whitehaven’s operating cycle for 2014 is 87.94 days (53.99 + 33.95 = 87.94), which is a huge improvement on the 2010 value of 287.50 days. The shorter operating cycle is mainly due to the improvement
in DSO, with customers paying much sooner. This also means Whitehaven has far less need to finance
working capital from other sources.
Cash conversion cycle
The cash conversion cycle is related to the operating cycle, but the cash conversion cycle does not begin
until a company actually pays for its inventory. In other words, the cash conversion cycle is the length
of time between the actual cash outflow for materials and the actual cash inflow from sales. To calculate this cycle, we need all of the information used to calculate the operating cycle plus one additional
measure: days’ payables outstanding (DPO).
DPO tells us how long, on average, a company takes to pay its suppliers. It is calculated by dividing
365 days by accounts payable turnover, which equals the cost of sales divided by the accounts payable.
The DPO formula and the calculation for Whitehaven are:
365 days
365 days
=
Accounts payable turnover Cost of sales/Accounts payable
365 days
365 days
=
=
= 137.53 days
$413 183/$155 688
2.6539
Days’ payables outstanding = DPO =
Whitehaven’s 2014 DPO of 137.53 is lower than the 2012 value of 207.94, but still higher than in
earlier years. While a shorter DPO means faster cash outflows, we shouldn’t always see that as a bad
thing, as the significant increase in DPO from 2009 to 2014 was unlikely to keep suppliers happy.
We can calculate the cash conversion cycle by summing the DSO and the DSI and subtracting the
DPO:
Cash conversion cycle = DSO + DSI − DPO (11.8)
In our example:
Cash conversion cycle = 33.95 days + 53.99 days − 137.53 days = −49.59 days
Whitehaven’s cash conversion cycle is −49.59 days. Another way to calculate the cash conversion cycle
is to note that it is simply the operating cycle minus the DPO, as can be seen in table 11.1.
Cash conversion cycle = Operating cycle − DPO (11.9)
Thus, Whitehaven’s cash conversion cycle for 2014 can be calculated as 87.94 − 137.53 = −49.59 days.
A cash conversion cycle of −49.59 days means that Whitehaven pays its suppliers an average of about
49 days after it receives cash from its customers. In other words, instead of Whitehaven needing external
finance to fund inventories and accounts receivable, its suppliers fully finance these current assets.
A direct comparison of the accounts receivable and inventory balances with the accounts payable balance in table 11.1 reveals that the financing provided by Whitehaven’s suppliers is more than the amount
the company has invested in accounts receivable and inventories. One factor that has influenced Whitehaven’s cash conversion rate over and above strong working capital management is that there was a large
amount of capital payment creditors in the 30 June 2014 accounts payable balance.
Whitehaven’s negative cash conversion cycle looks like a great way to finance working capital, but
table 11.2 shows this is only a recent development and the cash conversion cycle was positive and
MODULE 11 Cost of capital and working capital management 339
growing before 2011. For Whitehaven, its cash conversion cycle is highly sensitive to changes in sales
outstanding and payables outstanding, and by maintaining those two factors around current levels it can
keep a negative cash conversion cycle and avoid the need for other sources of finance to pay for working
capital.
Ideally the average company should try to keep its cash conversion cycle as close to zero as possible;
however, this is not usually achieved. Accounts receivable and inventories generally always exceed the
accounts payable.
BEFORE YOU GO ON
1. How do you calculate net working capital and why is it important?
2. What are some of the trade-offs required in the management of working capital accounts?
3. What is the operating cycle and how is it related to the cash conversion cycle?
11.4 Financing working capital
LEARNING OBJECTIVE 11.4 Identify three current asset financing strategies and discuss the main
sources of short-term financing.
So far, we have been discussing the investment side of working capital management. As with other
assets, working capital must be funded in some way. Financial managers can finance working capital
with short-term debt, long-term debt, equity or a mixture of all three. We next explore the main strategies used by financial managers to finance working capital, along with their benefits and costs.
Strategies for financing working capital
In order to fully understand the strategies that can be used to finance working capital, it is important
to recognise that some working capital needs are short term in nature while others are long term, or
permanent, in nature. As suggested earlier, the amount of working capital at a company tends to fluctuate over time as its sales rise and fall with the business season. For example, a toy company might
build up finished goods inventories in winter and spring as it prepares to ship its products to retailers
in early summer for the holiday season. Working capital will remain high through spring as finished
goods inventories are sold and converted into accounts receivable, but will then decline in January as
­receivables are collected — at which point the seasonal pattern begins again. These fluctuations reflect
seasonal working capital needs.
Even during the slowest part of the year, a typical company will hold some inventory, have some outstanding accounts receivable and have some cash and prepaid expenses. This minimum level of working
capital can be viewed as permanent working capital in the sense that it reflects a level of working
capital that will always be on the company’s books.
There are three basic strategies that a company can follow to finance its working capital and property,
plant and equipment. As businesses grow, they need more working capital as well as more long-term
productive assets. We next discuss each of the three strategies.
The maturity matching strategy is when all seasonal working capital needs are funded with shortterm borrowing. As the level of sales varies seasonally, short-term borrowing fluctuates with the level of
seasonal working capital. Furthermore, all permanent working capital and property, plant and equipment
are funded with long-term financing. The principle underlying this strategy is very intuitive: the maturity
of a liability should match the maturity of the asset that it funds. The matching of maturities is one of the
most basic techniques used by financial managers to reduce risk when financing assets.
The long-term funding strategy relies on long-term debt and equity to finance property, plant and
equipment, permanent working capital and seasonal working capital. As shown, when the need for
340 Finance essentials
working capital is at its peak, it is funded entirely by long-term funds. As the need for working capital
diminishes over the seasonal cycle and cash becomes available, the excess cash is invested in short-term
money market instruments to earn interest until the funds are needed again. This strategy reduces the
risk of funding current assets; there is less need to worry about refinancing assets, since all funding is
long term.
The short-term funding strategy funds all seasonal working capital and a portion of the permanent working capital and property, plant and equipment with short-term debt. The benefit of using this
strategy is that it can take advantage of an upward-sloping yield curve and so lower a company’s overall
cost of funding. Recall that yield curves are typically upward sloping, which means that short-term
borrowing costs are lower than long-term rates. The downside to this strategy is that a portion of a
company’s long-term assets must be periodically refinanced over their working lives, which can pose a
significant risk. As discussed in an earlier module, the yield curve can become inverted, making shortterm funds more expensive than long-term funds.
Financing working capital in practice
Each working capital funding strategy has its costs and benefits. A financial manager will typically use
some variation of one of the strategies discussed here to achieve their risk and return objectives.
Matching maturities
Many financial managers try to match the maturities of assets and liabilities when funding the company.
That is, short-term assets are funded with short-term financing while long-term assets are funded with
long-term financing. As suggested in the discussion of the three financing strategies, managers have very
sound reasons for matching assets and liabilities.
Permanent working capital
Many financial managers prefer to fund permanent working capital with long-term funds. They do this
in order to limit the risks associated with the short-term financing strategy. To the extent that permanent
working capital is financed with long-term funds, the ability of the company to finance this minimum
level of working capital is not subject to short-term credit market conditions.
Other managers use short-term debt to finance at least some permanent working capital requirements.
These managers subject their companies to more risk in the hope that they will realise higher returns.
MODULE 11 Cost of capital and working capital management 341
Sources of short-term financing
Now that we have discussed working capital financing strategies, let’s turn our attention to the most
important types of short-term financing instruments used in practice: accounts payable, bank loans and
commercial paper.
Accounts payable (trade credit)
Accounts payable (trade credit) deserve special attention because they comprise a large portion of the
current liabilities of many businesses. Accounts payable arise, of course, when managers do not pay for
purchases with cash on delivery but instead carry the amount owed as an account payable. If a company
orders $1000 of a certain raw material daily and the supplier extends a 30-day credit policy, the company
will be receiving $30 000 of financing from this supplier in the form of trade credit.
Short-term bank loans
Short-term bank loans are also relatively important financing tools. They account for about 20 per cent of
total current liabilities for publicly traded manufacturing companies. When securing a loan, the c­ ompany
and the bank negotiate the amount, the maturity and the interest rate, as well as any binding covenants
that are to be included. After an agreement is reached, both parties sign the debt contract, which is
­sometimes referred to as a promissory note.
The company may also have additional borrowing capacity with a bank through a line of credit. Lines
of credit are advantageous because they provide easy access to additional financing without requiring a
commitment to borrow unnecessary amounts. Lines of credit can be informal or formal.
An informal line of credit is a verbal agreement between the company and the bank allowing the
company to borrow up to an agreed limit. For example, an informal credit line of $1 million for 3 years
allows the company to borrow up to $1 million within the 3-year period. If it borrows $600 000 the first
year, it will still have a limit of $400 000 for the remaining 2 years. The interest rate on an informal
credit line depends on the borrower’s credit standing. In exchange for providing the line of credit, the
bank may require that the company hold a compensating balance.
When required for a loan, a compensating balance represents an implicit cost that must be included in
analysis of the cost of the loan. If a bank requires a compensating balance as a condition for making a
loan, the company must keep a predetermined percentage of the loan amount in a money market account,
which can pay negligible interest. If the rate of return is low, the company is subject to opportunity costs,
which make the effective borrowing rate higher than the percentage stated in the promissory note. For
example, suppose Perth City Bank requires borrowers to hold a 10 per cent compensating balance in an
account that pays no interest. If Zortac Ltd borrows $120 000 from Perth City at a 9 per cent stated rate,
the company will have to maintain a compensating balance of 0.1 × $120 000 = $12 000. Because Zortac
cannot use this money, the effective amount borrowed is equal to only $120 000 − $12 000 = $108 000.
However, since Zortac still must pay interest on the entire loan amount, the company’s interest expense
is 0.09 × $120 000 = $10 800 and the effective rate on the loan is $10 800/$108 000 = 0.1, or 10 per cent,
rather than 9 per cent.
A formal line of credit is also known as revolving credit. Under this type of agreement, the bank has
a contractual obligation to lend funds to the company up to a preset limit. In exchange, the company
pays a yearly fee in addition to the interest expense on the amount borrowed. The yearly fee is commonly a percentage of the unused portion of the entire credit line.
We can illustrate the mechanics of a formal line of credit with an example. Higgins Ltd has a formal
credit line of $20 million for 5 years with Safety Bank. The interest rate on the loan is 6 per cent. Under
the agreement, Higgins has to pay 75 basis points (0.75 per cent) on the unused amount as the yearly fee.
If Higgins does not borrow at all, it will still have to pay Safety Bank 0.0075 × $20 000 000 = $150 000
for each year of the agreement. Suppose Higgins borrows $4 million the first day of the agreement. Then
the fee drops to 0.0075 × ($20 000 000 − $4 000 000) = $120 000. Of course, Higgins will also have to
342 Finance essentials
pay an annual interest expense of 0.06 × $4 000 000 = $240 000. The effective interest rate on the loan
for the first year is ($240 000 + $120 000)/$4 000 000 = 0.09, or 9 per cent.
Another important loan characteristic is whether a loan is secured or unsecured. If a company backs
a loan with an asset, called collateral, the loan is secured; otherwise, the loan is unsecured. Companies
often use current assets such as inventory or accounts receivable as collateral when borrowing in the
short term. These types of working capital tend to be highly liquid and therefore are attractive as collateral to lenders. Secured loans allow the borrower to borrow at a lower interest rate, all else being equal.
The reason is, of course, that if the borrower defaults, the lender can liquidate the collateral and use the
cash generated from the sale to pay off at least part of the loan. The more valuable and liquid the asset
pledged as security, the lower the interest rate on the loan.
Promissory notes
Promissory notes or commercial paper are short-term debt issued by large, financially secure companies
with high credit ratings. The precise number of companies issuing promissory notes varies depending on
the state of the economy. When market conditions and the economy are weak, companies of lesser credit
quality are unable to borrow in the promissory note market.
Most large companies sell promissory notes on a regular basis. A company’s demand for promissory
note financing will depend on the promissory note interest rate relative to other borrowing rates and the
company’s need for short-term funds at the time.
Promissory notes do not have an active secondary market, as nearly all investors hold promissory
notes to maturity. Promissory notes are not secured, which means the lender does not have a claim
on any specific assets of the issuer in the event of default. However, most industrial companies using
promissory notes are backed by a credit line from a commercial bank. If the company does not have the
money to pay off the notes at maturity, the bank will pay it. Therefore, the default rate on promissory
notes is very low, usually resulting in an interest rate that is lower than the rate a bank would charge on
a direct loan.
Accounts receivable financing
For medium-size and small businesses, accounts receivable financing is an important source of funds.
Accounts receivable can be financed in two ways. First, a company can secure a bank loan by pledging
(assigning) its accounts receivable as security. Then, if the company fails to pay the bank loan, the bank can
collect the cash shortfall from the receivables as they come due. If for some reason the assigned receivables
fail to yield enough cash to pay off the bank loan, the company is still legally liable to pay the remaining
bank loan. During the pledging process, the company retains ownership of the accounts receivable.
Second, a company can sell its receivables to a factor or discounter. Factors and discounters are
individuals or financial institutions, such as banks or business finance companies, that buy accounts
receivable. Factors take responsibility for collecting customers’ payments away from the company, while
discounters let the company continue to collect the receivables on behalf of the discounter. D
­ iscounting
can be more efficient than factoring, as it makes use of a company’s existing accounts receivable
­operations instead of having a factor duplicate this function. It is also easier to set up a discounting company than a factoring company, as discounters do not need to handle collections. The other significant
advantage discounting has over factoring is that discounting can be confidential. Customers do not need
to know about discounting and are therefore unlikely to be concerned about doing business with a company that may be experiencing financial difficulties. In Australia over 90 per cent of accounts receivable
financing is through discounting rather than factoring.7
BEFORE YOU GO ON
1. List and briefly describe the three main short-term financing strategies.
2. Give some examples of sources of short-term financing.
MODULE 11 Cost of capital and working capital management 343
SUMMARY
11.1
Explain how to calculate the overall cost of capital for a company which uses debt and equity
financing for projects.
The overall cost of capital for a company is a weighted average of the current costs of the ­different
types of financing that the company has used to finance the purchase of its assets. First, we
­calculate the cost of each source of finance.
The cost of debt can be calculated by solving for the yield to maturity of the debt using the
bond pricing model (equation 8.1), calculating the effective annual yield (EAY) and adjusting
for tax using equation 11.2. The cost of ordinary shares can be estimated using the CAPM,
the ­constant-growth dividend formula and the multistage-growth dividend formula. The cost of
­preference shares can be calculated using the perpetuity model for the present value of cash flows.
When the overall cost of capital is calculated, the cost of each type of financing is weighted
according to the fraction of the total company value represented by that type of financing.
11.2 Calculate the weighted average cost of capital (WACC) for a company and explain the
limitations of using a company’s WACC as the discount rate when evaluating a project.
The weighted average cost of capital (WACC) is estimated using either equation 11.1 or equation
11.6, with the cost of each individual type of financing estimated using the appropriate method.
When a company uses a single rate to discount the cash flows for all of its projects, some project cash flows will be discounted using a rate that is too high and other project cash flows will be
discounted using a rate that is too low. This can result in the company rejecting some positive NPV
projects and accepting some negative NPV projects. It will bias the company towards accepting
more risky projects and can cause the company to create less value for shareholders than it would
have if the appropriate discount rates had been used.
11.3 Define and calculate net working capital and discuss the importance of working capital
management.
Net working capital (NWC) is the difference between current assets and current liabilities. Working
capital management refers to company decisions made regarding the use of current assets and how
they are financed. The goal of working capital management is to ensure that the company can
continue its day-to-day operations and pay its short-term debt obligations. The calculation of net
working capital is illustrated in 11.3.
11.4 Identify three current asset financing strategies and discuss the main sources of short-term
financing.
Three current asset financing strategies are: (1) the maturity matching strategy, which matches
the maturities of assets with the maturities of liabilities; (2) the long-term funding strategy, which
finances both seasonal working capital needs and long-term assets with long-term funds; and
(3) the short-term funding strategy, which uses short-term debt for both seasonal working capital
needs and some permanent working capital and long-term assets. Sources of short-term financing
include accounts payable, short-term bank loans, lines of credit and promissory notes.
SUMMARY OF KEY EQUATIONS
Equation
Description
Formula
General formula for weighted average
cost of capital (WACC) for a company
kCompany = ∑ x i k i = x1k1 + x 2 k 2 + x 3 k 3 + ... + x n k n
11.2
After-tax cost of debt
kDebt after-tax = kDebt pre-tax × (1 − t )
11.3
CAPM formula for the cost of ordinary
shares
kos = Rrf + (βos × Market risk premium)
11.1
344 Finance essentials
n
i=1
Equation
Description
Formula
11.4
Constant-growth dividend formula for the
cost of ordinary shares
kos =
D1
+ g
P0
11.5
Perpetuity formula for the cost of
preference shares
kps =
Dps
Pps
11.6
Traditional WACC formula
WACC = x Debt k Debt pre − tax (1− t ) + x ps k ps + x os k os
11.7
Operating cycle
Operating cycle = DSO + DSI
11.8
Cash conversion cycle
Cash conversion cycle = DSO + DSI − DPO
11.9
Cash conversion cycle
Cash conversion cycle = Operating cycle − DPO
KEY TERMS
cash conversion cycle length of time from the point at which a company pays for raw materials until
the point at which it receives cash from the sale of finished goods made from those materials
consumer credit credit extended by a business to consumers
factor individual or financial institution, such as a bank or business finance company, that buys
accounts receivable
formal line of credit contractual agreement between a bank and a company under which the bank has
a legal obligation to lend funds to the company up to a preset limit
informal line of credit verbal agreement between a bank and a company under which the company
can borrow an amount of money up to an agreed limit
long-term funding strategy financing strategy that relies on long-term debt and equity to finance
property, plant and equipment and working capital
maturity matching strategy financing strategy that matches the maturities of liabilities and assets
multistage-growth dividend model model that allows for varying dividend growth rates in the
near term, followed by a constant long-term growth rate; another term to describe the mixed
(supernormal) dividend growth model
operating cycle average time between receipt of raw materials and receipt of cash for the sale of
finished goods made from those materials
permanent working capital minimum level of working capital that a company will always have on its
books
promissory notes short-term debt issued by large, financially secure companies with high credit ratings
short-term funding strategy financing strategy that relies on short-term debt to finance all seasonal
working capital and a portion of permanent working capital and property, plant and equipment
trade credit credit extended by one business to another
weighted average cost of capital (WACC) weighted average of the costs of the different types of
capital (debt and equity) that have been used to finance a company; the cost of each type of capital is
weighted by the proportion of the total capital that it represents
ENDNOTES
1. We are ignoring the effect of tax on the cost of debt financing for the time being. This effect is discussed in detail later in this
module and explicitly incorporated into subsequent calculations.
2. Recall that we discussed the concept of financial market efficiency in module 2.
MODULE 11 Cost of capital and working capital management 345
3. These types of costs are incurred by companies whenever they raise capital. We only show how to include them in the cost of
bond financing and, later, in estimating the cost of preference shares, but they should also be included in calculations of the
costs of capital from other sources, such as bank loans and common equity.
4. Note that the incremental additions to working capital (Add WC) in equations 10.6 and 10.7 is a measure of the additional
NWC that will be required to fund a project. Equation 10.7 does not include prepaid or accrued expenses because analysts do
not typically forecast these items when they estimate Add WC. Prepaid and accrued expenses tend to be difficult to forecast
and, to the extent that they do not cancel each other out in the calculation, are often quite small. All interest-bearing debt is
also excluded from the calculation in equation 10.7 because these sources of financing are either assumed to be temporary
(for short-term notes) or, for current maturities of long-term debt, assumed to be refinanced with new long-term debt and are
therefore accounted for in the WACC calculation discussed earlier in this module.
5. It is not usually in the best interest of a company’s shareholders for managers to simply minimise the cash conversion cycle. If
it were, companies would stretch out repayment of their payables and not give credit to customers. Of course, this would upset
suppliers, cause the company to incur late-payment penalties and result in lost sales.
6. For simplicity, we assume all sales are credit sales, unless otherwise stated.
7. Debtor and Invoice Finance Association 2015.
ACKNOWLEDGEMENTS
Figure 11.1: © Whitehaven Coal
Photo: © Monkey Business Images / Shutterstock.com
Photo: © Sergey Skleznev / Shutterstock.com
Photo: © Rawpixel / Shutterstock.com
Photo: © Oleksiy Mark / Shutterstock.com
346 Finance essentials
MODULE 12
Capital structure and
dividend policy
LEA RNIN G OBJE CTIVE S
After studying this module, you should be able to:
12.1 discuss some of the practical considerations for managers when they choose a company’s capital
structure, and describe the trade‐off and pecking order theories of capital structure choice
12.2 discuss the benefits and costs of using debt financing
12.3 describe the different types of dividends and the dividend payment process, and discuss the benefits
and costs associated with dividend payments
12.4 define share buy‐backs, bonus share issues and share splits, and explain how they differ
12.5 describe the factors that managers consider when setting the dividend policies for their companies.
Module preview
In this module, we focus on the choice between the various types of financing when choosing a capital
structure. In particular, we examine how a company’s value is affected by the mix of debt and equity used
to finance its investments, and the factors that managers consider when choosing this mix. M
­ anagers use
the concepts and tools discussed in this module to make financing decisions that create value for their
shareholders.
We discuss some of the practical considerations that managers say influence their choice of capital
structure. Then we describe and evaluate two theories about how managers choose the appropriate mix
of debt and equity financing. Next, we discuss the costs and benefits of using debt financing.
Our discussion then turns to dividend decisions — those decisions concerning how and when to return
value (cash or other assets) to shareholders. We first describe the various types of dividends and the dividend payment process. We next discuss the benefits and costs associated with making dividend payments, and
describe how share prices react when a company makes an announcement about future dividend payments.
We then introduce an increasingly popular alternative to dividends — share buy‐backs. Although they
are not technically dividends, share buy‐backs are a potential component of any dividend policy because,
like dividends, they are a means of distributing value to shareholders. We also describe share splits and
bonus share issues, and discuss the reasons that managers might want to split their company’s shares or
distribute bonus shares. Finally, we conclude the module with a discussion of factors that managers and
their boards of directors consider when they set dividend policies.
12.1 Choosing a capital structure
LEARNING OBJECTIVE 12.1 Discuss some of the practical considerations for managers when they choose
a company’s capital structure, and describe the trade‐off and pecking order theories of capital structure choice.
When managers talk about their capital structure choices, their comments are sprinkled with terms
such as financial flexibility, risk and earnings impact. Managers are concerned with how their financing
decisions will influence the practical issues that they must deal with when managing a business.
For example, financial flexibility is an important consideration in many capital structure decisions.
Managers must ensure they retain sufficient financial resources in the company to be able to take
348 Finance essentials
advantage of unexpected opportunities and to overcome unforeseen problems. In theory, if a positive
NPV investment becomes available, managers should be able to obtain financing for it. Unfortunately,
financing might not be available at a reasonable price for all positive NPV projects at all times.
Managers are also concerned about the impact of financial leverage on the volatility of the c­ ompany’s
earnings. Most businesses experience fluctuations in their operating profits over time and we know that
fixed‐interest payments magnify fluctuations in operating profits, thereby causing even greater variation in profit. Managers do not like volatility in reported earnings because it causes problems in their
­relationships with outside investors, who do not like unpredictable earnings.
Furthermore, as we have seen, if a company is too highly leveraged, it runs a greater risk of defaulting
on its debt, which can lead to all sorts of insolvency costs and agency costs. Managers use the term risk
to describe the possibility that normal fluctuations in operating profits will lead to financial distress.
They try to manage their company’s capital structure in a way that limits the risk to a reasonable level —
one that allows them to sleep at night.
A third factor that managers think about when they choose a capital structure is the impact of financial
leverage on the company’s earnings. The interest expense associated with debt financing reduces the reported
dollar value of profit. However, depending on the market value of the company’s shares, using debt instead
of equity to finance a project can increase the reported dollar value of earnings per share. Many managers
are very concerned about the earnings per share that their companies report because they believe this affects
the share price. However, financial theory states that managers should not be so concerned about accounting
earnings because cash flows are what really matter. Whether they are right or wrong, if managers believe that
accounting earnings matter, their capital structure decisions will reflect this belief.
Another factor that managers consider in capital structure decisions is the control implications of
their decisions. The choice between equity and debt financing affects the control of the company. For
example, suppose that a company is controlled by its founding family, which owns 55 per cent of the
ordinary shares, and that it must raise capital to fund a large project. The project has a zero NPV and
will result in a 20 per cent increase in the size of the company. On one hand, using equity financing will
drop the founding family’s ownership (voting rights) below 50 per cent if they do not buy some of the
new shares. In fact, they would end up with 45.8 per cent of the shares [55/(100 + 20) = 0.458]. On
the other hand, their ownership will remain at 55 per cent and they will retain absolute control of the
company if the project is financed entirely with debt. In such a situation, the founding family is likely
to prefer debt financing. Of course, although debt can help a controlling shareholder retain control of a
company, too much debt can cause that shareholder to lose control. This can happen if the company uses
so much debt that fluctuations in business conditions put the company in financial distress. When this
happens, the ability of the creditors to control what happens to the company can overwhelm the ability
of the controlling shareholder to do so.
These are just some examples of the practical considerations that managers must deal with when
choosing the appropriate capital structure for a company. There is no set formula that they can follow
in making financing decisions, because many of these considerations are difficult to quantify and their
relative importance is unique to each company. Nevertheless, it is safe to say that the ultimate objective
of a company’s shareholders — and of managers who have the shareholders’ interests in mind — is to
choose the capital structure that maximises the value of the company.
Capital structure theories
How do managers choose the capital structures for their companies? We consider two theories that
attempt to explain how this choice is made: the trade‐off theory and the pecking order theory.
Trade‐off theory
The trade‐off theory of capital structure states that managers choose a specific target capital structure
based on the trade‐offs between the benefits and the costs of debt. This target structure is the capital
structure that maximises the value of the company, as illustrated in figure 12.1.
MODULE 12 Capital structure and dividend policy 349
Underlying the trade‐off theory is the idea that, when a company uses a small amount of debt financing, it
receives the interest tax shield and possibly some of the other benefits we discuss. Since leverage is low and
the chance that the company will get into financial difficulty is also low, the costs of debt are small relative
to the benefits and so company value increases. However, as more and more debt is added to the company’s
capital structure, the costs of debt increase and eventually reach the point where the cost associated with the
next dollar that is borrowed equals the benefit. Beyond this point, the costs of adding additional debt exceed
the benefits and so any additional debt reduces company value. The trade‐off theory of capital structure says
that managers will increase debt to the point at which the costs and benefits of adding another dollar of debt
are exactly equal because this is the capital structure that maximises company value.
FIGURE 12.1
Trade‐off theory of capital structure
Value of company with only benefits from debt
Company value (VCompany)
Costs of
debt
Value of company with no debt
Value of company
with debt
Capital structure that maximises
company value
0
Debt/Company value (VDebt/VCompany)
1
Pecking order theory
The trade‐off theory makes intuitive sense, but there is another popular theory of how the capital structures of companies are determined. This is known as the pecking order theory, which recognises that
different types of capital have different costs and this leads to a pecking order, or hierarchy, in the
financing choices that managers make. Managers choose the least expensive capital first, then move to
increasingly costly capital when the lower cost sources of capital are no longer available.
Under the pecking order theory, managers view internally generated funds, or cash1 on hand, as the
cheapest source of capital. Debt is more costly to obtain than internally generated funds, but is still relatively
inexpensive. In contrast, raising money by selling shares can be very expensive. The out‐of‐pocket costs of
selling equity are much higher than the comparable costs for bonds. In addition, the regulatory requirements
of government agencies are greater and the share market tends to react negatively to announcements that companies are selling shares. When companies announce that they will sell shares, their share prices often decline
because such sales are often interpreted as evidence that the companies are not profitable enough to fund their
investments internally. Of course, a lower share price reduces the value of everyone’s shares and makes future
share issues even more costly, since more shares will have to be sold to raise the same dollar amount.
The pecking order theory says that companies use internally generated funds as long as they are available. Following that, they tend to borrow money to finance additional projects until they are no longer
able to do so because of restrictions in loan agreements or high interest rates make debt unattractive.
Only then will managers choose to sell equity. Note that the pecking order theory does not assume managers have a target capital structure. Rather, it implies that the capital structure of a company is, in some
sense, a by‐product of the company’s financing history.
350 Finance essentials
The empirical evidence
At this point, you might be asking yourself what we actually know about how capital structures are determined in the real world. A great deal of research has been done in this area and the evidence ­supports
both of the theories we have just described. When researchers compare the capital structures in different
industries, they find evidence that supports the trade‐off theory. Industries with a great many tangible
assets, such as the utilities, real estate, and food and staples retailing industries, typically use relatively
large amounts of debt. In contrast, industries with more intangible assets and numerous growth opportunities, such as the pharmaceuticals, biotechnology and life sciences industries, use relatively little debt.
What accounts for this difference? At least in part, the difference exists because indirect insolvency costs
and agency costs tend to be lower in industries with more tangible assets. The assets in these industries
have higher liquidation values and it is more difficult for shareholders to engage in asset substitution.
Table 12.1 shows the extent of the variation in capital structures across industries.
TABLE 12.1
Average capital structures for selected Australian industries2
Industry description
Number of companies
Debt/company value
Utilities
17
0.40
Real estate
86
0.32
6
0.30
Transportation
14
0.28
Food, beverage and tobacco
37
0.22
Consumer services
32
0.22
Health care equipment and services
40
0.19
Capital goods
71
0.18
Consumer durables and apparel
16
0.18
Commercial and professional services
35
0.17
Technology hardware and equipment
18
0.15
Retailing
28
0.13
Pharmaceuticals, biotechnology and life sciences
45
0.08
5
0.07
Food and staples retailing
Insurance
More general evidence also indicates that the more profitable a company is, the less debt it tends to
have. This is exactly the opposite of what the trade‐off theory suggests we should see. Under the trade‐
off theory, more profitable companies pay more tax so they should use more debt to take advantage of
the interest tax shield. Instead, this evidence is consistent with the pecking order theory. Highly profitable companies have plenty of cash on hand that can be used to finance their projects and, over time,
using this cash will drive down their debt ratios.
The pecking order theory is also supported by the fact that, in an average year, public companies actually buy back more shares than they sell. In Australia, internally generated funds represent the largest
source of financing for new investments, while debt represents the largest source of external financing.
Both the trade‐off theory and the pecking order theory offer some insights into how managers choose
the capital structures for their companies. However, neither of them is able to explain all of the capital
structure choices that we observe. The truth is that capital structure decisions are very complex and it is
difficult to characterise them with a single general theory. In the next section, we briefly discuss some of
the practical issues that managers say they consider when making capital structure decisions.
MODULE 12 Capital structure and dividend policy 351
BEFORE YOU GO ON
1. Why is financial flexibility important in the choice of a capital structure?
2. How can capital structure decisions affect the risk associated with profit?
3. What are the trade‐off and pecking order theories of capital structure?
12.2 Benefits and costs of using debt
LEARNING OBJECTIVE 12.2 Discuss the benefits and costs of using debt financing.
The use of debt in a company’s capital structure involves both benefits and costs. Studies suggest that, for
very low levels of debt, the benefits outweigh the costs and the use of more debt reduces the company’s
WACC. However, as the amount of debt in the company’s capital structure increases, the costs become
relatively greater and eventually begin to outweigh the benefits. The point at which the costs just equal the
benefits is the point at which the WACC is minimised. Understanding the location of this point requires an
understanding of the costs and benefits, and how they change with the amount of debt used by a company.
Benefits of debt
We have noted that including debt in the capital structure has advantages for a company. We now discuss
these benefits in detail.
Interest tax shield benefit
The most important benefit of including debt in a company’s capital structure stems from the fact that, as
we discussed in an earlier module, companies can deduct interest payments for tax purposes, but cannot
deduct dividend payments. This makes it less costly to distribute cash to security holders through interest
payments than through dividends.
Figure 12.2 illustrates three situations, each with varying amounts of debt. As shown in the pie on the
left, if a company is financed entirely with equity, there is no interest expense, the company pays tax on
all of the income from operations and the value of the company equals the present value of the after‐tax
cash flows that the shareholders have a right to receive. Now if the company uses debt, some of the income
from operations will be tax deductible and the tax slice — the present value of the tax that the company
must pay — will be smaller than in the first pie. This is illustrated for one level of debt in the second pie
and for an even greater level of debt in the third pie. Note that the value of the company, which equals
the combined values of the debt and equity slices, increases as the tax slice gets smaller.
FIGURE 12.2
Capital structure and company value with tax
Capital structure 1:
All equity
VTax 1
VEquity 1
Capital structure 2:
Some debt but more equity
VEquity 2
VDebt 2
Capital structure 3:
More debt than equity
VDebt 3
VEquity 3
VTax 3
VTax 2
VCompany 1 = VEquity 1
VCompany 2 = VEquity 2 + VDebt 2
With tax: VCompany 1 < VCompany 2 < VCompany 3
352 Finance essentials
VCompany 3 = VEquity 3 + VDebt 3
Just how large is the value of the interest tax shield? Suppose a company has fixed perpetual debt
equal to D dollars, on which it pays an annual interest rate of kDebt. The total dollar amount of interest
paid each year — and, therefore, the amount that will be deducted from the company’s taxable income
— is D × kDebt. This will result in a reduction in tax paid of D × kDebt × t, where t is the company’s corporate tax rate that applies to the interest expense deduction.
To put this tax reduction in perspective, consider a company that has no debt and annual earnings before
interest and tax, EBIT, of $100, which is expected to remain constant in perpetuity. Because the company has
no debt, it currently pays tax equal to 30 per cent of EBIT. Management is considering borrowing $1000 at an
interest rate of 5 per cent. If the company borrows the money, it will thus pay interest of $50 each year.
The after‐tax earnings for the company without the debt equal $70 [$100 × (1 − 0.30) = $70] and the tax
paid by the company equals $30 ($100 × 0.30 = $30). If the company borrows the $1000, its after‐tax earnings will be $35 [($100 − $50) × (1 − 0.30) = $35] and it will pay taxes of $15 [($100 − $50) × 0.30 = $15].
The new debt will reduce the tax that the company pays each year by $15 (D × kDebt × t = $1000 × 0.05 ×
0.30 = $15). The total cash flows to the government, the shareholders and the debtholders in each situation
are as follows:
No debt
After $1000 loan
Government (tax)
Shareholders
Debtholders
Total
$ 30
$ 15
70
35
0
50
$100
$100
How much is this reduction in tax worth? Since we know the annual dollar value of the tax reduction
and we know this reduction will continue in perpetuity, we can use equation 6.4, the perpetuity model,
to calculate the present value of the tax savings from debt:
VTax-Savings debt = PVP =
D × k Debt × t
CF
=
i
i
All we need now is the appropriate discount rate. In this case, it is reasonable to assume that the
appropriate discount rate equals the 5 per cent cost of debt. This is a reasonable assumption because we
know the discount rate should reflect the risk of the cash flow stream that is being discounted. Since the
company will benefit from the interest tax shield only if it is able to make the required interest payments,
the cash savings associated with the tax shield are about as risky as the cash flow stream associated with
the interest payments. This implies that the value of the future tax savings is:
VTax-Savings debt =
D × k Debt × t
$15
=
= $300
k Debt
0.05
If you look closely at this calculation, you will see that $300 is exactly equal to the product of the
$1000 that the company would borrow and its 30 per cent tax rate (D × t). In other words:
VTax-savings debt = D × t (12.1)
This is because kDebt is in both the numerator and the denominator in the formula and so cancels out.
You can see in the above example that the value of the interest tax shield increases with the amount
of the debt that a company has outstanding and with the size of the corporate tax rate. More debt or a
higher tax rate implies a larger benefit.
It is important to recognise that the income tax benefit we have calculated using the perpetuity model
is an upper limit for this value. This is true for several reasons. The perpetuity model assumes that:
(1) the company will continue to be in business forever; (2) the company will be able to realise the tax
MODULE 12 Capital structure and dividend policy 353
savings in the years in which the interest payments are made (the company’s EBIT will always be at
least as great as the interest expense); and (3) the company’s tax rate will remain at 30 per cent.
In the real world, each of these conditions is likely to be violated. While a company has an indefinite
life, the fact is that companies go out of business. Of course, at that point the tax benefit ends. Even
companies that do not go out of business are unlikely to realise the full benefit of the tax shield. Virtually
all companies sometimes have poor operating performance. This can make it impossible to realise the
benefit of the interest deduction in the year when the payment is made. In such cases, companies must
often carry the tax loss forward and apply it to earnings in a future year. Carrying a tax deduction forward reduces its value by pushing it further into the future. Finally, even if the company is profitable, the
effective tax rate can fall below 30 per cent because earnings are lower than expected or the company
has other deductions that reduce the value of the interest tax shield.
You might be asking yourself, too, whether it is reasonable to assume that a company will borrow
money forever. The consols, issued by the government in the United Kingdom, are the only perpetual
bonds that have been issued that we know of. Nevertheless, it is reasonable to assume that the long‐term
borrowings of a company will be in place as long as the company is in business. While the specific debt
instruments used by companies are not perpetuities, companies do tend to roll over their maturing debt
by borrowing new money to make required principal payments. As long as a company does not shrink,
prompting it to pay down some of its debt, and as long as the company does not currently have too much
debt, long‐term debt can be considered permanent.
The value of the interest tax shield adds to the total value of a company. In other words, the value
of a company with debt equals the value of that company without debt plus the present value of the
interest tax shield. This is illustrated in figure 12.3, where we plot the value of a company with debt, a
financially leveraged company, against the proportion of the company’s total capital represented by debt.
FIGURE 12.3
How company value changes with leverage when interest payments are tax deductible and
dividends are not
Value of company with debt
Company value (VCompany)
Value of the
interest tax shield
Value of company with no debt
0
Debt/Company value (VDebt/VCompany)
1
If we say that the estimated tax benefit realised by Australian companies is 5 per cent and the average
company has debt of, say, 20 per cent, then using equation 12.1 to solve for t gives a tax rate of 25 per
cent — a reasonable estimate of the corporate tax rate given imputation. Both examples suggest that
equation 12.1 gives a reasonable ballpark estimate of the value of the interest tax shield.
To illustrate how tax affects company value, let’s look at an example. Assume that Millennium Motors
must pay corporate tax equal to 30 per cent of its taxable income. The company is financed entirely with ordinary shares and management is considering changing its capital structure by selling a $200 perpetual bond
with an interest rate of 5 per cent and paying a one‐time special dividend of $200. The company produces
354 Finance essentials
annual cash flows of $100 and the appropriate discount rate for these cash flows is 10 per cent. What is the
value of the company without any debt and what will the value be if the restructuring is completed?
We begin by calculating the value of Millennium Motors without any debt. If the entire $100 in pre‐
tax cash flows that the company generates is taxable, its after‐tax cash flows will equal $70 per year
[$100 × (1 − t)]. Using the perpetuity formula, we find that the value of the unleveraged company is
$700 ($70/0.10 = $700) with a 10 per cent discount rate.
We next calculate the value of the interest tax shield that would accompany the new debt. This value
is $60 (D × t = $200 × 0.30 = $60). The total value of the company after the restructuring is equal to
the value of the unleveraged company plus the value of the tax shield. In this case, that is $760 ($700 +
$60 = $760).
We can also calculate the WACC for Millennium Motors after the financial restructuring using
equation 11.6. To do so, we must first calculate the value of the equity (VEquity). In this case, since we
know from module 11 that VCompany = VEquity + VDebt, we can calculate the value of the equity to be $560
(VEquity = VCompany − VDebt = $760 − $200 = $560). Since we also know that the cash flows available to
shareholders after the restructuring will equal $63 [($100 − $10) × (1 − 0.30) = $63], we can calculate
the required return on equity to be 11.25 per cent ($63/$560 = 0.1125). With these values, we are now
ready to calculate the WACC:
WACC = x Debt k Debt pre − tax (1 − t ) + x ps k ps + x os k os
 $560 
 $200 
=
(0.05)(1 − 0.30) + 0 + 
(0.1125) = 0.0921, or 9.21%
 $760 
 $760 
In this example, the cost of ordinary shares increases from 10 per cent to 11.25 per cent. However, with
the interest tax deduction the WACC actually decreases from 10 per cent (recall that the cost of equity
equals the WACC for a company with no debt) to 9.21 per cent.
When we perform the same calculations for other potential debt levels at Millennium, we see how the
value of the company increases and the WACC decreases with the amount of debt in the capital structure.
This is illustrated in table 12.2 for levels of debt ranging from $0 to $800. The calculations assume the cost
of debt remains constant regardless of the amount of leverage, there is no information or transaction cost,
and the real investment policy of the company is not affected by its capital structure.
TABLE 12.2
The effect of tax on the company value and WACC of Millennium Motors
Total debt
Cost of debt
EBIT
Interest expense
$
0.00
5.00%
$100.00
$ 200.00
5.00%
$100.00
$ 400.00
5.00%
$100.00
$ 600.00
5.00%
$100.00
$ 800.00
5.00%
$100.00
0
10
20
30
40
Earnings before tax
$100.00
$ 90.00
$ 80.00
$ 70.00
$ 60.00
Tax (30%)
$ 30.00
$ 27.00
$ 24.00
$ 21.00
$ 18.00
Profit
$ 70.00
$ 63.00
$ 56.00
$ 49.00
$ 42.00
Dividends
$ 70.00
$ 63.00
$ 56.00
$ 49.00
$ 42.00
Interest payments
0
10
20
30
40
Payments to security holders
$ 70.00
$ 73.00
$ 76.00
$ 79.00
$ 82.00
Value of equity
$700.00
$560.00
$420.00
$280.00
$140.00
Cost of equity
Company value
WACC
10.00%
$700.00
10.00%
11.25%
$760.00
9.21%
13.33%
$820.00
8.54%
17.50%
$880.00
7.95%
30.00%
$940.00
7.45%
MODULE 12 Capital structure and dividend policy 355
You should note several other points concerning table 12.2. First, we do not show the calculations
for a company with 100 per cent debt because all companies must have some ordinary equity. Second,
the payments to security holders and company value both increase as the amount of debt financing
increases. This is because the size of the government’s slice of the pie gets smaller. Third, for simplicity
we assume that the cost of debt remains constant. However, even though the cost of equity increases,
the WACC decreases. This decrease is entirely due to the interest tax shield. Finally, while the value of
the company under each scenario is calculated as we have illustrated, you can confirm the answer by
noting that the company value for each capital structure equals the payments to security holders for the
unleveraged company, $70, divided by the WACC. The payments to security holders for the unleveraged
company are used in this calculation, regardless of the company’s capital structure, because, as was the
case for project analysis in an earlier module, the effects of capital structure choices are reflected in the
discount rate rather than the cash flows.
DEMONSTRATION PROBLEM 12.1
Calculating the effect of debt on company value and WACC
Problem:
Up to this point, you have financed your pizza chain entirely with equity. You have heard about the tax
benefit associated with using debt financing and are considering borrowing $1 million at an interest rate
of 6 per cent to take advantage of the interest tax shield. You do not need the extra money, so you will
distribute it to yourself through a special dividend. You are the only shareholder.
Your pizza business generates taxable (pre‐tax) cash flows of $300 000 each year and pays tax at
a rate of 30 per cent; the cost of assets, kAssets (which equals kos for your unleveraged company), is
10 per cent. What is the value of your company without debt and how much would debt increase its
value if you assume that all cash flows are perpetuities and the second and third MM conditions hold
(that is, there are no information or transaction costs, and the real investment policy of the company is
not affected by its capital structure decisions)? Also, what would the WACC for your business be before
and after the proposed financial restructuring?
Approach:
The value of your restaurant chain equals the present value of the after‐tax cash flows that the shareholders and debtholders expect to receive in the future. Without debt, this value equals the present
value of the dividends that you can expect to receive as the only shareholder. The value with debt
equals the value without debt plus the value of the interest tax shield.
The WACC before the financial restructuring equals kos, since your company currently has no preference shares or debt. Equation 11.6 can be used to calculate the WACC with debt.
Solu