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Intro to Fin & Acct - Finance

Introduction to Accounting
and Finance: MBA ACCT 502
King Fahd University of
Petroleum and Minerals
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Introduction to Accounting and Finance:
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Table of Contents
From Financial Management: Theory and Practice, EMEA Edition
Brigham, Ehrhardt & Fox
1. Central Concepts in Finance and Financial Management
3. Understanding Financial Statements Part 2: Analysing and Managing the Accounts
4. The Time Value of Money
5. Bonds and Bond Management
6. Risk and Return
8. Valuation of Shares and Companies
10. Project Cost of Capital
11. Capital Budgeting: Evaluation of Cash Flows
From Principles of Financial Accounting, 12e
Belverd Needles and Marian Powers
1. Accounting Principles and the Financial Statements
2. Analyzing and Recording Business Transactions
3. Adjusting the Accounts
4. Completing the Accounting Cycle
5. Foundations of Financial Reporting and the Classified Balance Sheet
7. Inventories
9. Receivables
13. Accounting for Corporations
15. The Statement of Cash Flows
The content of this text has been adapted from the following product(s):
Principles of Financial Accounting, 12e
Belverd Needles and Marian Powers
Financial Management: Theory and Practice, EMEA Edition
Brigham, Ehrhardt & Fox
Full copyright details and acknowledgements will appear in the aforementioned publications.
Central Concepts in
Finance and Financial
his chapter introduces the connecting features of financial management. We first of all outline the role
of the financial management function in the firm and then we introduce themes and concepts that we
will meet repeatedly throughout the text. The themes form a network, so there is no particular order or
hierarchy but together they make up the foundations of finance and the management task.
Financial Management
Financial management is critical to the success of all companies. No project, activity, investment or contract will
be successful unless it is financially viable. The outcome is more than merely profit. It is income for families and
communities and taxes for social services. Good financial management is at the heart of achieving these outcomes.
The focus of this text is on the free enterprise commercial company. There are other models and other
environments. The value of the one chosen here is twofold: firstly, that it has stood the test of time and is
by far the best wealth-producing vehicle for society. How that wealth is distributed in society is a separate
matter—though some writers, most recently Thomas Picketty,1 would disagree and argue that it is part of the
system. Secondly, this model is transparent. The annual report including the accounts produced by companies gives a financial ‘window’ on a company and enables all to see how the finances are being managed. A government-run institution encounters the same issues as a commercial company, only in a less well defined way.
We begin by considering the scope of the management task. All activities that involve money in the company are subject to financial management. As in society, money in a company serves as a measure of value.
For a firm, valuation is important for measuring performance, valuing projects, valuing plans and investments. The interests of the stakeholders in a company, the shareholders, bondholders and the interests of
potential investors are also concerned with financial valuation and are part of financial management. Money
is a store of value and a means of exchange and in the context of a firm that involves turning revenue into
cash, making payments to suppliers and managing bank overdrafts. There is little in a firm that is not in
some sense concerned with money and which involves in varying degrees financial management.
Who carries out financial management and what do they do? At the top is the finance director whose
main concern is the relationship between the firm and the outside parties; these are the stakeholders, the
investors, creditors and government whose interests are financial, as well as pressure groups affected by the
activities of companies. Below the finance director level are the finance managers who are broadly split into
two roles: the accounting function of recording transactions in the accounts, preparing the year end accounts
and managing the cash flows is the concern of accountants in the main; the second role is more concerned
Picketty, T. (2014) Capital in the Twenty First Century, Cambridge, MA: Harvard University Press.
4 Part 1
The Company and Its Reporting Environment
with the management control and investment by the company. All managers are part of this role—the production, marketing, distribution and administration managers all have to report their performance in financial terms. A knowledge of financial management is important for all managers whatever their specialism.
Clearly, finance encompasses a very large area of company activities. Financial management as a
subject has, over the years, tended to specialize in certain areas. The subject focuses most on cash flow,
funding, investment planning, purchasing and all financial transactions with outside parties, Figure 1-1
presents an overview. Omitted are certain internal aspects such as detailed reports on performance
in relation to the budget, as well as the costing system, which are usually seen as part of the management accounting function in the firm. Whatever your future or current specialism, an understanding of
financial management is essential to being effective in an organization, particularly at senior management and director levels of organizations no matter how large or small.
Common Themes
In this section common themes to the study of financial management are introduced and will be revisited
throughout the text. Here they are given a general introduction and overview.
The Gap Between Theory and Practice
One of the most important themes in the text is the gap that exists between theory (as developed by academics in
universities) and practice (as found in firms both large and small). Theory, as represented by the many models that
we discuss, is important as it abstracts from a very complicated real world and tries to create a logical structure that
helps in the management of finance. Nevertheless, with few exceptions there is a difference between the models and
practice. Sometimes there is even little evidence of the theoretical model in practice! This can be a measurement
problem—some variables, in particular expectations, are difficult if not impossible to measure with any real degree
of accuracy. Analysis therefore needs to be careful not to give the impression that what appears to be the best practice according to a theoretical model should always be applied directly to practice. In some cases we can decide that
F i g u re 1-1
The Role of the Financial Manager
The markets:
stock markets, currency markets,
commodity markets
The stakeholders:
The company finance
and trading
Existing shareholders
transactions and
preparing accounts
Potential investors
Interest groups
(e.g. environmentalists)
The press
The Financial
Making investment
decisions as part of
the management
Chapter 1
Central Concepts in Finance and Financial Management 5
practice is indeed wrong and ought to be changed; in other cases we can decide that theory has not fully captured
the problem. Financial management is a well-rewarded profession precisely because there are few clear prescriptions
as to what is best practice. What is clear is that a good financial manager needs to be aware of theory but also aware
of its problems and the difference with practice. The reader therefore needs to be patient; only a certain amount of
simplicity can be achieved. We will point out the differences between theory and the evidence in practice but there
should be no simple conclusions that either theory or practice is right or wrong. What we can say however is that
one is certainly better off with a good grasp of both theory and practice.
Unless stated otherwise, analysis is based on the assumption that companies seek to maximize shareholder
wealth. This may be regarded as a normative assumption; it is how a company should behave. Of course this
is never entirely true, there is always the suspicion that managers and directors are in part furthering their
own interests. Where there is fraud or embezzlement such activities are illegal but this is an extreme end of a spectrum. The suspicion is that in all companies there is what is called an ‘overconsumption of perquisites’—hotels are
a little more expensive than is needed as are flights, meals, expenses-paid trips to see golf tournaments and
so on. Life on expenses can be very attractive!
Such behaviour is not easy to identify—who can judge what is unnecessary expenditure? Quite simply, the
behavioural assumption of a common goal of shareholder wealth maximization for many seemed unrealistic. In addition, the whole control and reporting mechanism in companies did not seem to sit easily with the
assumption that all were working in the best interests of the company. To express these concerns in a more
formal manner, the accounting and finance literature turned to agency theory. This is a behavioural model
that seeks to link individual wealth maximization with overall company wealth maximization. At the heart
of the model is the relationship between the ‘master’ and ‘servant’, where the master is termed the principal
and the servant the agent. All employees of the company with the exception of the highest level (the shareholders or owners) are agents, that is to say they are working on behalf of their principal. Even the managing
director is an agent in the sense that he or she is employed by the shareholders and is working on their behalf.
With the exception of the lowest level of the workforce, all employees are also principals—that is, they are in
charge of someone. Thus, a company can be seen as a network of principal–agent relationships. The managing director is principal to the other directors who are his or her agents, and the other directors are principals
to the senior management acting as agents, the senior management are principals to the middle management
who are agents to the senior management. In turn the middle management are principals to junior management who are their agents and so on. This enables the problem of control to be reduced to analysing this
common relationship throughout the organization between the principal and the agent.
The problem of control is expressed in terms of agents having individual wealth-maximizing goals that
differ from that of the firm. All agents are subject to moral hazard in that their contract requires them to
work for the goals of the company when their true motive is to work for themselves! The solution is the contract with bonuses to encourage agents to adopt the company goals as a means of furthering their own goals.
History might well record that these models, developed in the 1980s, gave rise to the bonus culture which is
today regarded as standard practice. Certainly, before that time, bonuses were far less common. The study
of bonuses is seen as more of a management accounting subject than one of financial accounting and therefore does not play a great part in this text. Nevertheless, it is important to note that in the background to the
reporting and measurement of financial performance is the concept of agency and the control and motivation issues that it seeks to model. Before agency theory, the individual motives of employees were not considered separately from that of the company. That has now changed and it is the purpose of developments such
as the US Sarbanes–Oxley Act (2002) to address the worst aspects of self-interested behaviour by employees.
The Time Value of Money
One of the principal concerns of the financial manager and a theme that will be addressed at great length
throughout the text is the time value of money. A cash flow in the future is worth less than in the present.
6 Part 1
The Company and Its Reporting Environment
A cash flow now is certain, a cash flow in the future is only a promise, uncertain and risky. How can the
financial manager reconcile the need for cash now to invest and pay bills with the expected future cash flows
to fund these requirements? Much of the financial manager’s role in the organization is to facilitate this process. By the end of this text it is hoped that the reader will have a good grasp of the very many contexts and
issues for which the time value of money is central.
Financial Risk
If the future were known with any degree of assurance, management would be simply a matter of meeting
the known outcomes as efficiently as possible. There is, however, little that can be said to be almost certain.
The share price of a company varies, exchange rates vary, demand for products and services vary, as do interest rates and input prices. As a result, company earnings and the value of the company will also vary over
time. How this problem is addressed is the essence of managing financial risk.
There are two principal models of risk in finance. The first is based on the statistical model of what is
called a random walk. The reasoning is captured in the opening to a seminal paper by Paul Samuelson
in 19652: ‘In competitive markets there is a buyer for every seller. If one could be sure that a price will
rise, it would have already risen’ (p. 41). In other words, the price will be such that the ‘market’ does not
know if the price will rise or fall. The statistical random walk model assumes that over the short term
there is about a 50:50 chance of a rise or a fall. 3 Remarkably, applying this assumption to price changes
results in a distribution of price changes that is the well-known normal distribution as found in many
statistical problems and in nature. Possible future prices do not have all the same probability—the highest short-term probability is that of the current price and the probability of prices that vary from the
current price reduces the further away the possible future price is from the current price. This model of
risk underlies almost all models of risk in finance.
The second model of risk arises from the failings of the first model. In the credit crunch of 2008 the
London Stock Exchange lost 25 per cent, and Queen Elizabeth II famously asked on a visit (in November
to open the New Academic Building at the London School of Economics), ‘Why did nobody notice it?’ (i.e.
predict it). The problem with the random walk model is that it does not take into account the very large and
sudden price changes that take place on far too regular a basis in the financial markets around the world—on
1 December 2014 the Russian rouble fell in value by 4 per cent, in August 2015 the Chinese yuan fell by 3 per
cent against the dollar, the euro fell by 15 per cent against the dollar in 2015 and the dollar fell by more than
19 per cent against the Swiss Franc. Converting foreign earnings to home currency after the foreign currency
devaluations could have easily lost all profit on the transactions. The random walk model does not take into
account such large and sudden changes. Events that are a million to one according to the normal distribution
should not be happening on a one in a thousand basis, but that is the kind of frequency that we see in practice. In the stock market such sudden changes are termed ‘bubbles’ and ‘crashes’ for which there is as yet no
clear predictive model. The problem of financial management is to manage what might be called normal risk
as in the random walk and at the same time use subjective judgement to avoid the possibility of sudden large
movements for which there is no clear predictive model.
The Corporate Life Cycle
Many major companies began life as a single shop (e.g. Tesco) or in a garage or student’s bedroom! How is it
possible for such companies to grow into the giants we see today? No two companies develop in exactly the
same way, but the following sections describe some typical stages in the corporate life cycle.
Samuelson, P. (1965) ‘Proof that properly anticipated prices fluctuate randomly’, Industrial Management Review 6(2):41–49.
Prices have medium- and long-term trends, share prices increase over time through inflation and growth, but such trends are imperceptibly small over a time period such as a day.
Chapter 1
Central Concepts in Finance and Financial Management 7
Starting Up
Many companies begin as unlimited companies owned by one individual. There are three important advantages
to this type of company: (1) it is easily and inexpensively formed, (2) it is subject to few government regulations,
and (3) its income is not subject to corporate taxation but is taxed as part of the proprietor’s personal income.
However, for the proprietor there are three important limitations: (1) it may be difficult to obtain the capital needed for growth; (2) the proprietor has unlimited personal liability for the business’s debts, which can
result in losses that exceed the money invested in the company (creditors may even be able to seize a proprietor’s
house or other personal property); and (3) the life of a business is limited to the life of its founder.
Many Owners: A Company
Most small companies have difficulty attracting substantial amounts of capital. This is generally not a problem for a slow-growing business, but if a business’s products or services really catch on, and if it needs to raise
large sums of money to capitalize on its opportunities, then the difficulty in attracting capital becomes a real
drawback. Thus, many growth companies began life as a small business or partnership, and at some point
their founders decided to convert to a limited company. On the other hand, some companies, in anticipation
of growth, actually begin as limited companies. A limited company is a legal entity that is separate and distinct from its owners and managers. This separation gives the limited company three major advantages:
1. Unlimited life—a company can continue after its original owners and managers are deceased.
2. Easy transferability of ownership interest—ownership interests are divided into shares, which can be
transferred far more easily than can proprietorship or partnership interests.
3. Limited liability—losses are limited to the actual funds invested.
To illustrate limited liability, suppose you invested €10 000 in a partnership that then went bankrupt and
owed €1 million. Because the owners are liable for the debts of a partnership, you could be assessed for a
share of the company’s debt, and you could be held liable for the entire €1 million if your partners could
not pay their shares. On the other hand, if you invested €10 000 in the share of a company that went bankrupt, your potential loss on the investment would be limited to your €10 000 investment. Unlimited life, easy
transferability of ownership interest, and limited liability make it much easier for companies than partnerships to raise money in the financial markets and grow into large companies.
Incorporation—i.e. becoming a limited company—offers significant advantages over unlimited companies and partnerships, but it also has two disadvantages: (1) corporate earnings may be subject to double
taxation—the earnings of the company are taxed at the corporate level, and then earnings paid out as dividends are taxed again as income to the shareholders; (2) setting up a company involves preparing articles
of association, and registering the company, which is more complex and time-consuming than creating a
proprietorship or a partnership.
The articles of association include the following information:
name of the proposed company
types of activities it will pursue
amount of capital share
number of directors
names and addresses of directors
After the company begins operating, annual accounts and other government requirements have to be submitted. The articles together with the memorandum of association form the constitution of the company and
outline how it is to be run. The terms vary between countries but are similar and serve the same purpose.
Growing and Managing a Company
Once a company has been established, how does it evolve? When entrepreneurs start a company, they usually
provide all the financing from their personal resources, which may include savings, home equity loans, or
8 Part 1
The Company and Its Reporting Environment
even credit cards. As the company grows, it will need factories, equipment, inventory, and other resources to
support its growth. In time, the entrepreneurs usually deplete their own resources and must turn to external financing. Many young companies are too risky for banks, so the founders must sell share to outsiders,
including friends, family, private investors or venture capitalists (often called angels). If the company continues to grow, it may become successful enough to attract lending from banks, or it may even raise additional
funds through an initial public offering (IPO) by selling shares to the public at large. After an IPO, companies support their growth by borrowing from banks, issuing debt or selling additional shares. In short, a
company’s ability to grow depends on its interactions with the financial markets, which we describe in much
more detail later in this chapter.
For partnerships, and small companies, the firm’s owners are also its managers. This is usually not true
for a large company, which means that large firms’ shareholders, who are its owners, face a serious problem.
What is to prevent managers from acting in their own best interests, rather than in the best interests of the
shareholders/owners? This is the agency problem, because managers are hired as agents to act on behalf of
the owners, as discussed above. Agency problems can be addressed by a company’s corporate governance,
which is the set of rules that control the company’s behaviour towards its directors, managers, employees,
shareholders, creditors, customers, competitors and community. Corporate governance may reduce but will
not eliminate the problems raised by the agency model.
The Primary Objective of the Company:
Value Maximization
Shareholders are the owners of a company, and they purchase shares because they want to earn a good return
on their investment without undue risk exposure. In most cases, shareholders elect directors, who then hire
managers to run the company on a day-to-day basis. Because managers are supposed to be working on behalf
of shareholders, they should pursue policies that enhance shareholder value. Consequently, throughout this
book we operate on the assumption that management’s primary objective should be shareholder wealth
The market price is the share price that we observe in the financial markets. We later explain in detail how
share prices are determined, but for now it is enough to say that a company’s market price takes account of
the information available to investors. If the market price reflects all relevant information, then the observed
price is termed the fundamental price.
However, investors never have all relevant information. Companies report most major decisions as well
as the information required in the Annual Report (see Chapter 2). Some information that is not part of the
requirements of the Annual Report and are commercially sensitive may be withheld from the market. Any
investor using this information to trade and make a profit would be guilty of insider trading and be liable
for prosecution. For example, if a company has made a medical breakthrough it may well want to keep the
information private until the necessary patent applications have been filed. Anyone who obtains such information either by unfair means, or because they are employees, and who buys the shares on the prospects of
the increased profits would be guilty of insider trading. The market is concerned that all traders should have
access to the same information. Any seller who suspects that the buyer may be in possession of private information would not be happy that the price was fair.
Firms do, of course, have other objectives; in particular, the managers who make the actual decisions are
naturally concerned for their own welfare as expressed in agency theory, in their employees’ welfare, and in
the good of their communities and society at large. It is arguable that these other objectives are ultimately for
the good of the overall profits of the company. It may be argued that these other goals are really part of the
cost that firms face in benefiting from the legal and social systems and infrastructure provided by society.
Still, for the reasons set forth in the following sections, maximizing share value should be the most important objective for most companies. This normative objective (i.e. the objective that ought to be followed)
underlies all subsequent analysis unless specifically stated otherwise.
Chapter 1
Central Concepts in Finance and Financial Management 9
Ethics for Individuals and Businesses
A firm’s commitment to business ethics can be
measured by the tendency of its employees, from
the top down, to adhere to laws, regulations and
moral standards relating to product safety and
quality, fair employment practices, fair marketing
and selling practices, the use of confidential information for personal gain, community involvement,
and illegal payments to obtain business.
Ethical Dilemmas
When conflicts arise between profits and ethics,
sometimes legal and ethical considerations make
the choice obvious. At other times the right choice
isn’t clear. For example, suppose Norfolk Southern’s managers know that its trains are polluting
the air, but the amount of pollution is within legal
limits and further reduction would be costly, causing harm to their shareholders. Are the managers
ethically bound to reduce pollution? Aren’t they
also ethically bound to act in their shareholders’
best interests? This is clearly a dilemma.
Ethical Responsibility
Over the past few years, illegal ethical lapses have
led to a number of bankruptcies, which have raised
this question: Were the companies unethical, or
was it just a few of their employees? Arthur Andersen,
an accounting firm, audited Enron, WorldCom
and several other companies that commit ted
accounting fraud. The US Justice Department concluded that Andersen itself was guilty because it
fostered a climate in which unethical behaviour
was permitted, and it built an incentive system that
made such behaviour profitable to both the perpetrators and the firm itself. As a result, Andersen
went out of business. Andersen was later judged
to be not guilty, but by the time the judgement was
rendered the company was already out of business. People simply did not want to deal with a
tainted accounting firm.
Protecting Ethical Employees
If employees discover questionable activities or
are given questionable orders, should they obey
their bosses’ orders, refuse to obey those orders,
or report the situation to a higher authority, such
as the company’s board of directors, its auditors
or a federal prosecutor? In 2002 the US Congress
passed the Sarbanes – Oxley Act, with a provision designed to protect ‘whistle-blowers’. If an
employee reports corporate wrongdoing and later
is penalized, he or she can ask the Occupational
Safety and Health Administration to investigate
the situation. If the employee was improperly
penalized, the company can be required to reinstate the person, along with providing backpay
and a sizable penalty award. Several big awards
have been handed out since the act was passed.
Share Value Maximization and Social Welfare
If a firm attempts to maximize its share value, is this good or bad for society? In general, it is good. Aside
from such illegal actions as fraudulent accounting, exploiting monopoly power, violating safety codes, and
failing to meet environmental standards, the same actions that maximize share values also benefit society.
Here are some of the reasons:
1. Most individuals have a stake in the share market. When direct share ownership and indirect ownership
through pension funds are also considered, many members of society now have an important stake in
the share market, either directly or indirectly. Therefore, when a manager takes actions to maximize the
share price, this improves the quality of life for millions of ordinary citizens.
2. Share price maximization requires efficient, low-cost businesses that produce high-quality goods and
services at the lowest possible cost. This means that companies must develop products and services
that consumers want and need, which leads to new technology and new products. Also, companies that
maximize their share price must generate growth in sales by creating value for customers in the form of
efficient service.
10 Part 1
The Company and Its Reporting Environment
In a reasonably competitive economy, prices are constrained by competition and consumer resistance. If a firm raises its prices beyond reasonable levels, it will simply lose market share. Of course, firms
want to earn more, and they constantly try to cut costs, develop new products, and so on, and thereby
earn above-normal profits. Note, though, that if they are indeed successful and do earn above-normal
profits, those very profits will attract competition, which will eventually drive prices down. So again, the
main long-term beneficiary is the consumer.
Of course, not all markets can be competitive. In the United Kingdom, for instance, train companies
bid for government contracts to run services on the country’s railway lines. The bidding is competitive
but once the contract is awarded the company in effect has a monopoly over the service. Only a strong
regulatory framework is able to protect the consumer. The problem that society faces is that companies
are able to earn what economists call ‘super normal’ profits by behaving as a monopoly or colluding with
competitors to maintain artificially high prices. There is therefore always the incentive for companies
to try to subvert and degrade the competitive economy. An early example is the Standard Oil Company
in America which in 1909 was sued by the US Department of Justice under federal anti-trust laws. They
found that it engaged in numerous unfair practices such as charging transport costs that discriminated
against competitors and pricing at below cost simply to subvert the competition. It was ruled that Standard Oil was an illegal monopoly and it was broken up into 33 smaller companies. Not all countries manage to take such bold anti-competitive actions. As multinational companies become ever larger, their
power and influence increases and regulation is more problematic.
3. Employees. An often overlooked fact is that companies provide employment. From the salaries and
wages of the workers comes more demand for food, housing and all the other expenses of living that
in turn provides demand for other businesses. Economists call this the ‘multiplier effect’. In addition,
from the salaries and wages of employees comes income tax that helps to fund hospitals, defence, police
and all other government services deemed necessary for a civilized society. A rather more prominent
aspect of employment by companies is the suspicion that in the short term companies have an incentive to underpay their staff in an attempt to maximize short-term profits. In response, many countries
have introduced minimum pay legislation to protect the most vulnerable. Even so, part-time work and
zero hours contracts (work only when requested with no prearranged hours) are evidence of the incentive that companies have to minimize employment costs. In the medium to long run such attitudes to
employees may well reduce the quality of the product or service.
The alternative is to give much greater job security. This is the notion of ‘jobs for life’ that was very
much part of the Japanese employment culture as well as a number of large multinational companies and
government-run commercial organizations. The extreme was the great socialist experiment of the twentieth century whereby all employees were guaranteed jobs for life as in the Soviet Union. This resulted
in wholly uneconomic practices and the stagnation and inefficiency of the economy. Hard though the
profit motive may seem in relation to employees, for society as a whole it would seem to be necessary.
The profit motive and the efficient allocation of resources offers longer-term wealth for society as a
whole even though it may mean individual suffering in the short run.
Managerial Actions to Maximize Shareholder Wealth
What types of actions can managers take to maximize shareholder wealth? To answer this question, we first
need to ask, ‘What determines a firm’s value?’ In a nutshell, it is a company’s ability to generate cash flows
now and in the future.
We address different aspects of this in detail throughout the book, but we can lay out three basic facts
now: (1) Any financial asset, including a company’s share, is valuable only to the extent that it generates cash
flows. (2) The timing of cash flows matters—cash received sooner is better. (3) Investors are averse to risk,
so all else equal, they will pay more for a share whose cash flows are relatively certain than for one whose
cash flows are more risky. Therefore, managers can increase their firm’s value by increasing the size of the
expected cash flows, by speeding up their receipt, and by reducing their risk.
The cash flows that matter are called free cash flows (FCFs), not because they are free, but because they
are available (or free) for distribution to all of the company’s investors, including creditors and shareholders.
Chapter 1
Central Concepts in Finance and Financial Management 11
It is what the company could afford to pay. There are differing ways of defining ‘afford’ and more will be said
in Chapter 2 but a simple definition is:
EBIT (Earnings
before interest
and taxation)
Depreciation and
Required investments
in new operating and
working capital
Brand managers and marketing managers can increase sales (and prices) by truly understanding their customers and then designing goods and services that customers want. Human resource managers can improve
productivity through training and employee retention. Production and logistics managers can improve profit
margins, reduce inventory and improve throughput at factories by implementing supply chain management,
just-in-time inventory management, and lean manufacturing. In fact, all managers make decisions that can
increase FCFs.
One of the financial manager’s roles is to help others see how their actions affect the company’s ability to
generate cash flow. Financial managers also must decide how to finance the firm. In particular, they must
choose the mix of debt and equity to use and the specific types of debt and equity securities to issue. They
also must decide what percentage of current earnings to retain and reinvest rather than pay out as dividends. Along with these financing decisions, the general level of interest rates in the economy, the risk of
the firm’s operations, and share market investors’ overall attitude toward risk determine the rate of return
required to satisfy a firm’s investors. This rate of return from an investor’s perspective is a cost from the
company’s point of view. The rate of return required by investors is called the weighted average cost of capital (WACC).
Corporate Scandals and Maximizing Share Price
The list of corporate scandals seems to go on forever: Sunbeam, Enron, ImClone, WorldCom, Tyco,
Adelphia. . . . At first glance, it’s tempting to say,
‘Look what happens when managers care only about
maximizing share price.’ But closer investigation
reveals a different story. In fact, if these managers
were trying to maximize share price, they failed dismally, given the resulting values of these companies.
Although details vary from company to company, a few common themes emerge. First, managerial compensation was linked to the short-term
performance of the share price via poorly designed
share option and share grant programmes. This
provided managers with a powerful incentive to
drive up the share price at the option vesting date
without worrying about the future. Second, it is virtually impossible to take legal and ethical actions
that drive up the share price in the short term without harming it in the long term, because the value
of a company is based on all of its future free cash
flows and not just cash flows in the immediate
future. Because legal and ethical actions to quickly
drive up the share price didn’t exist (other than the
old-fashioned ones, such as increasing sales, cutting costs or reducing capital requirements), these
managers began bending a few rules. Then, as
they initially got away with bending rules, it seems
that their egos and hubris grew to such an extent
that they felt they were above all rules, so they
began breaking even more rules.
Share prices did go up, at least temporarily, but
as Abraham Lincoln said, ‘You can’t fool all of the
people all of the time.’ As the scandals became
public, the shares’ prices plummeted, and in some
cases the companies were ruined.
There are several important lessons to be learnt
from these examples. First, people respond to
incentives, and poorly designed incentives can
cause disastrous results. Second, ethical violations usually begin with small steps, so if shareholders want managers to avoid large ethical
violations, then they shouldn’t let them make the
small ones. Third, there is no shortcut to creating
lasting value. It takes hard work to increase sales,
cut costs and reduce capital requirements, but this
is the formula for success.
12 Part 1
The Company and Its Reporting Environment
The following equation (Equation 1-1) defines the relationship between a firm’s fundamental value, its
FCFs, and its cost of capital:
Value =
(1 + WACC)1
(1 + WACC)2
(1 + WACC)3
(1 + WACC)∞
We will explain how to use this equation in later chapters, but for now note that (1) a growing firm often
needs to raise external funds in the financial markets, and (2) the actual price of a firm’s share is determined
in those markets. The rest of this chapter focuses on financial markets.
S E L F -T E S T
What should be management’s primary objective?
How does maximizing the fundamental share price benefit society?
Free cash flow depends on what three factors?
How is a firm’s fundamental value related to its free cash flows and its cost of capital?
An Overview of the Capital Allocation Process
Businesses often need capital to implement growth plans; governments require funds to finance building
projects; and individuals frequently want loans to purchase cars, homes and education. Where can they get
this money? Fortunately, there are some individuals and firms with incomes greater than their expenditures.
In spite of William Shakespeare’s advice, most individuals and firms are both borrowers and lenders. For
example, an individual might borrow money with a car loan or a home mortgage but might also lend money
through a bank savings account. In the aggregate, individuals are net savers and provide most of the funds
ultimately used by nonfinancial companies. Although most nonfinancial companies own some financial
securities, such as short-term Treasury bills, nonfinancial companies are net borrowers in the aggregate. In
many countries both local and national governments are also borrowers. Rather than increase taxes to pay
for political promises (so-called fiscal measures) governments have borrowed on the international bond markets (see Chapter 5). This has led to international financial crises such as the Third World Debt Crisis in 1982
and the Greek crisis of 2015.
Banks and other financial companies raise money with one hand and invest (lend) it with the other.
For example, a bank might raise money from individuals in the form of savings accounts and then lend
most of that money to business customers. In the aggregate, financial companies borrow slightly more
than they lend.
Transfers of capital between savers and those who need capital take place in three different ways:
1. Direct transfers of money and securities occur when a business sells its shares or bonds to savers. The
business delivers these securities to savers, who in turn provide the firm with the money it needs. For
example, a privately held company might sell shares directly to a new shareholder, or a government
might borrow by selling Treasury bonds directly to investors.
2. Indirect transfers may go through an investment banking house such as Goldman Sachs, which underwrites the issue. An underwriter serves as a middleman and facilitates the issuance of securities. The
company sells its shares or bonds to the investment bank, which in turn sells these same securities to
savers. Because new securities are involved and the company receives the proceeds of the sale, this is a
‘primary’ market transaction.
3. Transfers also can be made through borrowing from a financial intermediary such as a bank or
mutual fund. Here the intermediary obtains funds from savers in exchange for its own securities. The intermediary then uses this money to purchase and then hold businesses’ securities. For
Chapter 1
Central Concepts in Finance and Financial Management 13
example, a saver might give euros to a bank and receive a certificate of deposit, and then the bank
might lend the money to a small business, receiving in exchange a signed loan. Thus, intermediaries
literally create new types of securities.
There are three important characteristics of the capital allocation process. First, new financial securities
are created. Second, financial institutions are often involved. Third, allocation between providers and users
of funds occurs in financial markets. The following sections discuss each of these characteristics.
S E L F -T E S T
Identify three ways that capital is transferred between savers and borrowers.
Distinguish between the roles played by investment banking houses and financial intermediaries.
Financial Securities
The variety of financial securities is limited only by human creativity, ingenuity and governmental regulations. At the risk of oversimplification, we can classify most financial securities by the type of claim and the
time until maturity. In addition, some securities are actually created from packages of other securities. We
discuss the key aspects of financial securities in this section.
Type of Claim: Debt, Equity or Derivatives
Financial securities are simply pieces of paper with contractual provisions that entitle their owners to
specific rights and claims on specific cash f lows or values. Debt instruments typically have specified
payments and a specified maturity. For example, a Peugeot Citroen bond might promise to pay 10 per
cent interest for 30 years, at which time it promises to make a €1000 principal payment. If debt matures
in more than a year, it is called a capital market security. Thus, the Peugeot Citroen bond in this example is a capital market security.
If the debt matures in less than a year, it is a money market security. For example, a French company
might expect to receive €300 000 in 75 days, but it needs cash now. The company might issue commercial
paper, which is essentially an IOU. In this example, it might agree to pay €300 000 in 75 days in exchange for
€297 000 today, offering a return to the investor. Thus, commercial paper is a money market security.
Equity instruments are a claim upon a residual value. For example, Peugeot Citroen’s shareholders are
entitled to the cash flows generated by Peugeot Citroen after its bondholders, creditors and other claimants
have been satisfied. Because a share has no maturity date, it is a capital market security.
Notice that debt and equity represent claims upon the cash flows generated by real assets, such as the
cash flows generated by Peugeot Citroen’s factories and operations. In contrast, derivatives are securities
whose values depend on, or are derived from, the values of some other traded assets. For example, options
and futures are two important types of derivatives, and their values depend on the prices of other assets. An
option on Peugeot Citroen shares or a futures contract to buy wheat are examples of derivatives.4
Some securities are a mix of debt, equity and derivatives. For example, a preferred share has some features
like debt and some like equity, while convertible debt has both debt-like and option-like features.
We discuss these and other financial securities in detail later in the book, but Table 1-1 provides a summary of the most important conventional financial securities. We discuss rates of return later in this chapter,
but notice now in Table 1-1 that rate of return tends to increase with the maturity and risk of the security.
Some securities are created from packages of other assets, a process called securitization. The misuse
of securitized assets is one of the primary causes of the Global Financial Crisis, so every manager needs to
understand the process of securitization.
See Chapter 9.
14 Part 1
The Company and Its Reporting Environment
Tab l e 1-1
Summary of Major Financial Instruments
Major Participants
Typical Maturity
Typical Return
Treasury bills
Default free
Up to one year
Very low
A firm’s promise to pay
guaranteed by the bank
Up to 180 days
Issued by financially
secure firms to large
Up to 270 days
Loans by banks to
Low to high
Variables (years)
Low to high
Depends on govt
credit rating
2 to 30 years
Low to high
Major companies
Risker than
government bonds
Up to 40 years
Low to high
Issued by companies
to individuals and
Riskier than
corporate bonds
No limit
Issued by companies
to individuals and
Riskier than
preferred shares
No limit
The Process of Securitization—The Case
of Mortgage-Backed Securities
Ownership of assets can be shared and sold in the financial markets by issuing financial instruments, i.e.
financial paper, entitling the holders to the benefits and risks of ownership. Many types of assets can be
securitized, but we will focus on US mortgages (loans to buy houses) because they played such an important
role in the Global Financial Crisis. At one time, most mortgages were made by savings and loan associations
(S&Ls), which took in the vast majority of their deposits from individuals who lived in nearby neighbourhoods. The S&Ls pooled these deposits and then lent money to people in the neighbourhood in the form of
fixed-rate mortgages, which were pieces of paper signed by borrowers promising to make specified payments
to the S&L. The new homeowners paid principal and interest to the S&L, which then paid interest to its
depositors and reinvested the principal repayments in other mortgages. This was clearly better than having
individuals lend directly to aspiring homeowners, because a single individual might not have enough money
to finance an entire house or the expertise to know if the borrower was creditworthy. Note that the S&Ls were
government-chartered institutions. They obtained money in the form of immediately withdrawable deposits
and then invested most of it in the form of mortgages with fixed interest rates and on individual homes. Also,
initially the S&Ls were not permitted to have branch operations—they were limited to one office to maintain
their local orientation.
The S&Ls’ assets consisted mainly of long-term, fixed-rate mortgages, but their liabilities were in the form
of deposits that could be withdrawn immediately. This is the process known as maturity transformation.
Like banks, they convert short-term deposits into long-term loans by assuming that for every €100 deposited
only €8 to €11 need be kept in liquid form (i.e. as cash, or near-cash such as a deposit account) and the rest
can be lent out for a longer time. This is why banks fear a run on the bank—as the money deposited with
the bank has been mostly lent out. The combination of long-term assets and short-term liabilities created
another problem. If the overall level of interest rates increased, the S&Ls would have to increase the rates they
Chapter 1
Central Concepts in Finance and Financial Management 15
paid on deposits or else savers would take their money elsewhere. This they could not readily do, as the interest earned on mortgages (their investments—i.e. what they had done with the money) was fixed, and this led
to their rapid decline.
The demise of the S&Ls created a financial disequilibrium—a higher demand for mortgages than the
supply of available funds from the mortgage lending industry. Savings were accumulating in pension funds,
insurance companies and other institutions, not in S&Ls and banks, the traditional mortgage lenders.
This situation led to the development of ‘mortgage securitization’, a process whereby banks, the remaining
S&Ls and specialized mortgage-originating firms would originate mortgages and then sell them to investment banks, which would bundle them into packages and then use these packages as collateral or security for
bonds. That is, if the bond was not repaid the investor would take ownership of the mortgages. These mortgage-backed bonds were then sold to pension funds, insurance companies and other institutional investors.
Thus, individual loans were bundled and then used to back a bond—a ‘security’—that could be traded in the
financial markets.
To illustrate the securitization process, suppose an S&L or bank is paying its depositors 5 per cent but is
charging its borrowers 8 per cent on their mortgages. The S&L can take hundreds of these mortgages, put
them in a pool, and then sell the pool in the financial market. The mortgagees can still make their payments
to the original S&L, which will then forward the payments (less a small handling fee) to the purchaser of the
bundle of mortgages.
These purchasers of mortgages such as Fannie Mae can take the mortgages it just bought, put them into
a very large pool, and sell bonds backed by the pool to investors. The homeowner will pay the S&L, the S&L
will forward the payment to Fannie Mae, and Fannie Mae will use the funds to pay interest on the bonds it
issued, to pay dividends on its share, and to buy additional mortgages from S&Ls, which can then make additional loans to aspiring homeowners. Notice that the mortgage risk has been shifted from Fannie Mae to the
investors who now own the mortgage-backed bonds.
How does the situation look from the perspective of the investors who own the bonds? In theory, they
own a share in a large pool of mortgages from all over the country, so a problem in a particular region’s real
estate market or job market won’t affect the whole pool. Therefore, their expected rate of return should be
very close to the 8 per cent rate paid by the home-owning mortgagees. (It will be a little less due to handling
fees charged by the S&L and Fannie Mae and to the small amount of expected losses from the homeowners
who could be expected to default on their mortgages.) These investors could have deposited their money
at an S&L where they would earn a virtually risk-free 5 per cent. Instead, they chose to accept more risk in
hopes of the higher 8 per cent return. Note, too, that mortgage-backed bonds are more liquid than individual
mortgage loans, so the securitization process increases liquidity, which is desirable. The bottom line is that
risk has been reduced by the pooling process and then allocated to those who are willing to accept it in return
for a higher rate of return.
Thus, in theory it is a win–win–win situation: more money is available for aspiring homeowners,
S&Ls (and taxpayers) have less risk, and there are opportunities for investors who are willing to take
on more risk to obtain higher potential returns. The cause of the losses was the cause of other financial
crises such as the Third World Debt Crisis of 1982—namely, the underestimation of the risk due to the
independence assumption. Investors assumed that the mortgage risks were independent, but this was
not the case. If the risks were independent and the risk of a mortgagee not paying was 1 in 100, i.e. 0.01,
then an investor in 100 mortgages would expect 1 in 100 to fail with a probability of 0.37 or 37 per cent
(100 C1 × 0.011 × 0.99 99 = 0.3697) and the probability of five failing (again assuming that the risks were
entirely independent/unrelated), would be 0.29 per cent (100 C5 × 0.015 × 0.99 95 = 0.0029). Now consider
a degree of dependence between the mortgages—suppose that if there is one failing then there will
­c ertainly be four others that will also fail. The probability of one failing will now be the probability of
five failing.
What was thought to be a probability of 0.29 per cent is in fact a probability of 1.65 per cent, some
5.7 times higher. What made matters worse was that the risk was separated by a new sort of instrument
termed a collateralized debt obligation (CDO). When applied to subprime (risky) mortgages it created
AAA credit-rated debt by dividing the risk into tranches—the top tranche was rated AAA as it was first
in line for interest payments and would only be liable for bad debts when they reached what was thought
16 Part 1
The Company and Its Reporting Environment
to be an impossibly high level. The market massively under-rated the risk as the economic downturn hit
all mortgagees. Those in the less secure jobs were the first to suffer and were for the most part the subprime mortgagees. What was thought to be a 0.29 per cent type risk was in fact a 37 per cent type risk as
­i llustrated above.
The Cost of Money
In a free economy, capital from those with available funds is allocated through the price system to users who
have a need for funds. The interaction of the providers’ supply and the users’ demand determines the cost
(or price) of money, which is the rate users pay to providers. For debt, we call this price the interest rate. For
equity, we call it the cost of equity, and it consists of the dividends and capital gains (the increase in share
price) shareholders expect. Keep in mind that the ‘price’ of money is a cost from a user’s perspective but a
return from the provider’s point of view.
Notice in Table 1-1 that a financial instrument’s rate of return generally increases as its maturity (length
of time before repayment) and risk increase. Remember that the risk includes delayed repayment and possible nonrepayment, so the advertised rates of return should really be seen as a promise which might not actually happen. We will have much more to say about the risk and return of securities later in the book, but first
we will examine some fundamental factors and economic conditions that affect all financial instruments.
Fundamental Factors that Affect the Cost of Money
The four most fundamental factors affecting the cost of money are (1) production opportunities, (2) time
preferences for consumption, (3) risk and (4) inflation.
By production opportunities, we mean the ability to turn capital into benefits. If a business raises capital,
the benefits are determined by the expected rates of return on its production opportunities. If a student borrows to finance his or her education, the benefits are higher expected future salaries (and, of course, the sheer
joy of learning). If a homeowner borrows, the benefits are the pleasure from living in his or her own home,
plus any expected appreciation in the value of the home. Observe that the expected rates of return on these
‘production opportunities’ put an upper limit on how much users can pay to providers.
Providers can use their current funds for consumption or saving. By saving, they give up consumption
now in the expectation of having more consumption in the future. If providers have a strong preference for
consumption now, then it takes high interest rates to induce them to trade current consumption for future
consumption. Therefore, the time preference for consumption has a major impact on the cost of money.
Notice that the time preference for consumption varies for different individuals, for different age groups and
for different cultures. For example, people in Japan have a lower time preference for consumption than those
in the United States, which partially explains why Japanese families tend to save more than US families even
though interest rates are lower in Japan.
If the expected rate of return on an investment is risky, then providers require a higher expected return to
induce them to take the extra risk, which drives up the cost of money. As you will see later in this book, the
risk of a security is determined by market conditions and the security’s particular features.
Inflation also leads to a higher cost of money. For example, suppose you earned 10 per cent one year on
your investment but inflation caused prices to increase by 10 per cent. Your real return would be 0 per cent.
To earn a real return, investors will want a rate of interest that is higher than the inflation rate.
Economic Conditions and Policies
that Affect the Cost of Money
Economic conditions and policies also affect the cost of money. These include: (1) government monetary
policy, (2) the government budget deficit or surplus, (3) the level of business activity and (4) international
factors, including the foreign trade balance, the international business climate and exchange rates.
Chapter 1
Central Concepts in Finance and Financial Management 17
Government Monetary Policy
If a government wants to stimulate the economy, it most often uses open-market operations to purchase
Treasury securities held by banks. Because banks are selling some of their securities, the banks will have
more cash, which increases their supply of loanable funds, which in turn makes banks willing to lend more
money at lower interest rates. In addition, government purchases represent an increase in the demand for
Treasury securities. As with anything for sale, increased demand causes Treasury securities’ prices to go up
and interest rates to go down, see Chapter 5. The net result is a reduction in interest rates, which stimulates
the economy by making it less costly for companies to borrow for new projects or for individuals to borrow
for major purchases or other expenditures.
When banks sell their holdings of Treasury securities to the government, the banks’ reserves go up, which
increases the money supply. A larger money supply ultimately leads to an increase in expected inflation,
which eventually pushes interest rates up. Thus, the government can stimulate the economy in the short term
by driving down interest rates and increasing the money supply, but this creates longer-term inflationary
pressures. This is the dilemma that faced governments around the world in mid-2012 following the Global
Financial Crisis.
On the other hand, if the government wishes to slow down the economy and reduce inflation, the government reverses the process. Instead of purchasing Treasury securities, the government sells Treasury securities to banks, which causes an increase in short-term interest rates but a decrease in long-term inflationary
Budget Deficits or Surpluses
If the government spends more than it takes in from tax revenues, then it runs a deficit, and that deficit
must be covered either by borrowing or by printing money (increasing the money supply). The government
borrows by issuing new Treasury securities. All else held equal, this creates a greater supply of Treasury securities, which leads to lower security prices and higher interest rates. Other government actions that increase
the money supply also increase expectations for future inflation, which drives up interest rates. Thus, the
larger the government deficit, other things held constant, the higher the level of interest rates. The United
States government has run deficits in 15 of the past 19 years. Annual deficits in the mid-1990s were in the
$250 billion range, but they have ballooned to well over a trillion dollars in recent years. These deficits have
contributed to a cumulative governmental debt which in early 2012 stood at more than $15 trillion.
International Trade Deficits or Surpluses
Businesses and individuals in any one country buy from and sell to people and firms in other countries. If
people in a country buy more than they sell (that is, if the country imports more than it exports), the country is said to be running a foreign trade deficit. When trade deficits occur, they must be financed, and the
main source of financing is debt. In other words, if a country imports €200 billion of goods but exports only
€90 billion, it will run a trade deficit of €110 billion. To attract foreign currency to pay for the net imports,
the country needs to borrow foreign currency. In the case of the United States that is not a problem since
the dollar is close to being a world currency and traders are happy to hold dollar accounts. In less attractive
currencies such as the British pound such money can only be attracted by raising the interest rate. In poorer
countries repayment may only be possible by printing money to buy foreign currency, ultimately leading to
inflation. Of course, in the case of countries in the eurozone that is not possible and countries can only adjust
by austerity measures to repay the foreign loans as in the case of Greece.
The United States has been running annual trade deficits since the mid-1970s. The cumulative effect of
trade deficits and budget deficits is that the United States has become the largest debtor nation of all time. As
noted earlier, the US federal debt exceeds $15 trillion. As a result, US interest rates are influenced by interest
rates in other countries around the world. There are, however, special factors affecting the United States. The
dollar is the most trusted and most traded currency on the international markets. As a result, many countries
and multinationals are happy to invest in dollars in spite of the interest rate. This has enabled the United
States to import more than it exports and borrow from foreign investors to pay for the surplus imports. The
foreign investors are happy to hold dollars because of its special position in world trade. It should also be
18 Part 1
The Company and Its Reporting Environment
noted that the US surplus of imports has provided vital demand for developing economies, helping them to
develop faster than could be achieved by charity—perhaps in this case greed has been good!
International Country Risk
International risk factors may increase the cost of money that is invested abroad. Country risk is the risk that
arises from investing or doing business in a particular country, and it depends on the country’s economic,
political and social environment. Countries with stable economic, social, political and regulatory systems
provide a safer climate for investment and therefore have less country risk than less stable nations. Examples
of country risk include the risk associated with changes in tax rates, regulations, currency conversion and
exchange rates. Country risk also includes the risk that (1) property will be expropriated without adequate
compensation; (2) the host country will impose new stipulations concerning local production, sourcing or
hiring practices; and (3) there might be damage or destruction of facilities due to internal strife.
Exchange Rate Risk
Securities frequently are denominated in a currency other than the home country of the issuing company,
which means that the value of an investment depends on what happens to exchange rates. This is known as
exchange rate risk. For example, if a UK investor purchases a Japanese bond, interest probably will be paid in
Japanese yen, which must then be converted to pounds if the investor wants to spend his or her money in the
United Kingdom. If the yen weakens relative to the pound, then the yen will buy fewer pounds when it comes
time for the investor to convert the Japanese bond’s pay-out. Alternatively, if the yen strengthens relative to
the pound, the investor will earn higher pound returns. It therefore follows that the effective rate of return
on a foreign investment will depend on both the performance of the foreign security in its home market and
on what happens to exchange rates over the life of the investment. We discuss exchange rates in detail in the
final chapter.
S E L F -T E S T
What four fundamental factors affect the cost of money?
Name some economic conditions that influence interest rates, and explain their effects.
Financial Institutions
When raising capital, direct transfers of funds from individuals to businesses are most common for small
businesses or in economies where financial markets and institutions are not well developed. Businesses in
developed economies usually find it more efficient to enlist the services of one or more financial institutions
to raise capital. Most financial institutions don’t compete in a single line of business but instead provide a
wide variety of services and products, both domestically and globally. The following sections describe the
major types of financial institutions and services, but keep in mind that the dividing lines among them are
often blurred. Also, note that the Global Financial Crisis is leading to changes in the structure of our financial institutions, and new regulations are certain to affect those that remain.
Investment Banks and Brokerage Activities
Investment banking houses help companies raise capital. Such organizations underwrite security offerings,
which means they (1) advise companies regarding the design and pricing of new securities, (2) buy these
securities from the issuing company, and (3) resell them to investors. Although the securities are sold twice,
this process is really one primary market transaction, with the investment banker acting as a facilitator to
help transfer capital from savers to businesses. An investment bank often is a division or subsidiary of a
larger company. For example, JPMorgan Chase & Co. is a very large financial services firm, with over $2 trillion in managed assets. One of its holdings is J.P. Morgan, an investment bank.
Chapter 1
Central Concepts in Finance and Financial Management 19
In addition to security offerings, investment banks also provide consulting and advisory services, such as
merger and acquisition (M&A) analysis and investment management for wealthy individuals.
Most investment banks also provide brokerage services for institutions and individuals (called ‘retail’
­customers). For example, Merrill Lynch (acquired in 2008 by Bank of America) has a large retail brokerage
operation that provides advice and executes trades for its individual clients. Similarly, J.P. Morgan helps execute trades for institutional customers, such as pension funds.
Deposit-Taking Financial Intermediaries
Some financial institutions take deposits from savers and then lend most of the deposited money to borrowers. Following is a brief description of such intermediaries.
Savings and Loan Associations or Building Societies
As we explained in earlier, S&Ls originally accepted deposits from many small savers and then loaned this
money to home buyers and consumers. Later, they were allowed to make riskier investments, such as investing in real estate development.
Credit Unions
Credit unions are cooperative associations whose members have a common bond, such as being employees
of the same firm or living in the same geographic area. Members’ savings are lent only to other members,
generally for auto purchases, home-improvement loans, and home mortgages. Credit unions are often the
cheapest source of funds available to individual borrowers.
Commercial Banks
Commercial banks raise funds from depositors and by issuing shares and bonds to investors. For example,
someone might deposit money in a cheque account. In return, that person can write cheques, use a debit card,
and even receive interest on the deposits. Those who buy the banks’ shares expect to receive dividends and
interest payments. Unlike nonfinancial companies, most commercial banks are highly leveraged in the sense
that they owe much more to their depositors and creditors than they raise from shareholders. For example, a
typical bank has about €90 of debt for every €10 of shareholders’ equity. If the bank’s assets are worth €100,
we can calculate its equity capital by subtracting the €90 of liabilities from the €100 of assets: equity capital =
€100 − €90 = €10. But if the assets drop in value by 5 per cent to €95, the equity drops to €5 = €95 − €90, a 50
per cent decline. This scenario may well arise in times of economic hardship when a bank may well experience
loans not being repaid due to bankruptcy. Bad debts are written off against equity. In this example if the assets
of €100 are in the form of loans and there is an 11 per cent bad debt then €11 would be deducted from the €10
equity leaving the bank with equity value of €10 − €11 = −€1. In other words the bank would be in negative
equity and technically bankrupt. To avoid this scenario banks are increasingly ‘stress tested’ against just such
scenarios such as high levels of bad debts or debt impairment. If they are found to be vulnerable then they will
be required to raise reserves and equity in relation to their lending. In our previous example the bank would do
well to issue another €5 in equity and invest the money in something safer than business loans.
Banks are vitally important for a well-functioning economy, and their highly leveraged positions make
them risky. As a result, banks are more highly regulated than nonfinancial firms. Governments will typically
insure the balances of small depositors (in the United Kingdom to the value of £75 000).
Without such insurance, if depositors believed that a bank was in trouble, they would rush to withdraw
funds. This is called a ‘bank run’, which is exactly what happened in the United States during the Great
Depression, causing many bank failures.
Investment Funds
At some financial institutions, savers have an ownership interest in a pool of funds rather than owning a
deposit account. Examples include mutual funds, hedge funds and private equity funds.
20 Part 1
The Company and Its Reporting Environment
Mutual Funds
Mutual funds are companies that accept money from savers and then use these funds to buy financial
instruments. These organizations pool funds, which allows them to reduce risks by diversification and
achieve economies of scale in analysing securities, managing portfolios and buying/selling securities. Different funds are designed to meet the objectives of different types of savers. Hence, there are bond funds
for those who desire safety and share funds for savers who are willing to accept risks in the hope of higher
returns. There are literally thousands of different mutual funds with dozens of different goals and purposes. Some funds are actively managed, with their managers trying to find undervalued securities, while
other funds are passively managed and simply try to minimize expenses by matching the returns on a
particular market index.
Money market funds invest in short-term, low-risk securities, such as Treasury bills and commercial
paper. Many of these funds offer interest-bearing checking accounts with rates that are greater than
those offered by banks, so many people invest in money market funds as an alternative to depositing
money in a bank.
Most traditional mutual funds allow investors to redeem their share of the fund only at the close of business. A special type of mutual fund, the exchange traded fund (ETF), allows investors to sell their share at
any time during normal trading hours. ETFs usually have very low management expenses and are rapidly
gaining in popularity.
Hedge Funds
Hedge funds raise money from investors and engage in a variety of investment activities. Unlike typical
mutual funds, which can have thousands of investors, hedge funds are limited to institutional investors
and a relatively small number of high-net-worth individuals. Because these investors are supposed to be
sophisticated, hedge funds are much less regulated than mutual funds. The first hedge funds literally
tried to hedge their bets by forming portfolios of conventional securities and derivatives in such a way
as to limit their potential losses without sacrificing too much of their potential gains. Many hedge funds
had spectacular rates of return during the 1990s. This success attracted more investors, and thousands
of new hedge funds were created. Much of the low-hanging fruit had already been picked, however, so
the hedge funds began pursuing much riskier (and unhedged) strategies, including the use of high leverage in unhedged positions. Perhaps not surprisingly (at least in retrospect), some funds have produced
spectacular losses. For example, many hedge fund investors suffered losses in 2007 and 2008 when large
numbers of subprime mortgages defaulted.
Private Equity Funds
Private equity funds are similar to hedge funds in that they are limited to a relatively small number of large
investors. They differ in that they own shares (equity) in other companies and often control those companies, whereas hedge funds usually own many different types of securities. In contrast to a mutual fund,
which might own a small percentage of a publicly traded company’s share, a private equity fund typically
owns virtually all of a company’s share. Because the company’s share is not traded in the public markets, it
is called ‘private equity’. In fact, private equity funds often take a public company (or subsidiary) and turn it
private, such as the 2007 privatization of Chrysler by Cerberus (Fiat is now the majority owner). The general
partners who manage private equity funds usually sit on the companies’ boards and guide their strategies
with the goal of later selling the companies for a profit. For example, The Carlyle Group, Clayton Dubilier &
Pace, and Merrill Lynch Global Private Equity bought Hertz from Ford on 22 December 2005, and then sold
shares of Hertz in an IPO less than a year later.
Many private equity funds experienced high rates of return in the last decade, and those returns attracted
enormous sums from investors. A few funds, most notably The Blackstone Group, actually went public themselves through an IPO. Just as with hedge funds, the performance of many private equity funds faltered. For
example, shortly after its IPO in June 2007, Blackstone’s share price was over $31 per share; by early 2009, it
had fallen to about $4. By early 2012 the share price was about $15, still well short of its IPO price.
Chapter 1
Central Concepts in Finance and Financial Management 21
Life Insurance Companies and Pension Funds
Life insurance companies take premiums, invest these funds in shares, bonds, real estate, and mortgages,
and then make payments to beneficiaries. Life insurance companies also offer a variety of tax-deferred savings plans designed to provide retirement benefits.
Traditional pension funds are retirement plans funded by companies or government agencies. Pension
funds invest primarily in bonds, shares, mortgages, hedge funds, private equity and real estate. Most companies now offer self-directed retirement plans, such as 401(k) plans, as an addition to or substitute for traditional pension plans. In traditional plans, the plan administrators determine how to invest the funds; in
self-directed plans, all individual participants must decide how to invest their own funds. Many companies
are switching from traditional plans to self-directed plans, partly because this shifts the risk from the company to the employee.
S E L F -T E S T
What is the difference between a pure commercial bank and a pure investment bank?
List the major types of financial institutions, and briefly describe the original purpose of each.
What are some important differences between mutual funds and hedge funds? How are they similar?
Financial Markets
Financial markets bring together people and organizations needing money with those having surplus funds.
There are many different financial markets in a developed economy. Each market deals with a somewhat different type of instrument, customer, or geographic location. Here are some ways to classify markets:
1. Physical asset markets (also called ‘tangible’ or ‘real’ asset markets) are those for such products as wheat,
autos, real estate, computers and machinery. Financial asset markets, on the other hand, deal with
shares, bonds, notes, mortgages, derivatives and other financial instruments.
2. Spot markets and futures markets are markets where assets are being bought or sold for ‘on-the-spot’
delivery (literally, within a few days) or for delivery at some future date, such as six months or a year into
the future.
3. Money markets are the markets for short-term, highly liquid debt securities, while capital markets are
the markets for corporate shares and debt maturing more than a year in the future. The New York Share
Exchange is an example of a capital market. When describing debt markets, ‘short term’ generally means
less than one year, ‘intermediate term’ means one to five years and ‘long term’ means more than five
4. Mortgage markets deal with loans on residential, agricultural, commercial, and industrial real estate,
while consumer credit markets involve loans for autos, appliances, education, vacations and so on.
5. World, national, regional, and local markets also exist. Thus, depending on an organization’s size and
scope of operations, it may be able to borrow or lend all around the world, or it may be confined to a
strictly local, even neighbourhood, market.
6. Primary markets are the markets in which companies raise new capital. If Microsoft were to sell a new
issue of common shares to raise capital, this would be a primary market transaction. The company selling the newly created shares receives the proceeds from such a transaction. The initial public offering
(IPO) market is a subset of the primary market. Here firms ‘go public’ by offering shares to the public
for the first time. For example, Google had its IPO in 2004. Previously, founders Larry Page and Sergey
Brin, other insiders and venture capitalists owned all the shares. In many IPOs, the insiders sell some of
their shares and the company sells newly created shares to raise additional capital. Secondary markets
are markets in which existing, already outstanding securities are traded among investors. Thus, if you
decided to buy 1000 shares of British Petroleum, the purchase would be in the secondary market. The
New York and London main stock exchanges are secondary markets, because they deal in outstanding
22 Part 1
The Company and Its Reporting Environment
(as opposed to issuing) shares. Secondary markets also exist for bonds, mortgages and other financial
assets. The company whose securities are being traded is not involved in a secondary market transaction
and, thus, does not receive any funds from such a sale.
Private markets, where transactions are worked out directly between two parties, are differentiated from
public markets, where standardized contracts are traded on organized exchanges. Bank loans and private placements of debt with insurance companies are examples of private market transactions. Because
these transactions are private, they may be structured in any manner that appeals to the two parties. In
contrast, securities that are issued in public markets (for example, common shares and corporate bonds)
are ultimately held by a large number of individuals. Public securities must have fairly standardized
contractual features because public investors cannot afford the time to study unique, nonstandardized
contracts. Hence private market securities are more tailor-made but less liquid, whereas public market
securities are more liquid but subject to greater standardization.
The markets in action: companies go to the share and bond markets to raise money. Most important
is the term of the loan, that is to say the length of time before repayment. In the case of shareholders
the term is infinite; the company has no obligation to buy back its own shares or to repay the owners
of the shares. Another major source of funds is a bond (see Chapter 5)—this differs from shares in that
repayment is promised. The term for bondholders varies from short (less than three years), to medium
(three to ten years) and long term (over ten years). Finance for companies—that is, their ability to raise
large amounts of money to finance projects—would be very limited if companies had to seek out investors who wanted to invest permanently or lend large sums of money. The market solves this problem by
creating a financial instrument that is to say a ‘piece of paper’ or other electronic acknowledgement of
ownership. This is normally ownership of part of the debt. So in the case of shares, one share may only
have a nominal value of £1, and in the case of bonds, the nominal value in the United Kingdom is a
standard £100. The term ‘nominal’ can be viewed here as a unit of measurement rather than true market
value. The nominal value may be £100 or £1 but what the market will pay for that nominal value is very
The process of splitting debt up in this way is referred to as debt securitization, as discussed above—creating a legal entitlement to a part of the debt. Companies create securities in the form of shares or bonds
and sell them to investors; this is done in what is known as the primary market where, not surprisingly,
the company has to issue a prospectus stating what it intends to do with the funds in a document that
has to conform to the particular share market regulations.
When the security has been purchased by the investor it can be sold on the secondary market at any
time. The secondary market is a kind of ‘second-hand market’ where purchased shares are traded
between investors. The secondary market is much larger than the primary market. In fact the secondary
market is huge. For example, in October 2014 the value of shares traded on the London Stock Exchange
secondary market was over £1 trillion (i.e. million million). This is over half the UK GDP (that is, the
value of all that is earned in the United Kingdom in one year). In the primary market, issues of shares
totalled £9 billion (i.e. thousand million)—in other words a tiny fraction of the value traded in the secondary market. These types of figures are common to all share markets. The reason for the difference
between the markets is simply that a share is issued once (the primary market) but is traded many times
over the years (the secondary market). A stock exchange consists of many different markets based on
supply and demand, note that exchanges themselves are limited companies.
You should recognize the big differences among types of markets, but keep in mind that the distinctions
are often blurred. Definitions of short and medium term vary, some instruments can have bond-like and
share-like attributes. Innovation is always seeking to challenge these distinctions.
S E L F -T E S T
Distinguish between (1) physical asset markets and financial asset markets, (2) spot and futures
markets, (3) money and capital markets, (4) primary and secondary markets and (5) private and
public markets.
Chapter 1
Central Concepts in Finance and Financial Management 23
Not All Stock Markets are the Same
In July 2015 the Financial Times reported that a
French maker of a possible treatment for peanut allergy DBV Technologies af ter an initial
$93m flotation raised $240m on the New York
Stock Exchange with a share issue that was ten
times oversubscribed. This was for a treatment
that had not yet passed its final trials. So why
was a French company going to New York to
raise money? A number of reasons were offered:
(a) ‘strong US investor demand for risky drug development businesses compared with their European
counterparts; the NASDAQ biotech index has more
than doubled in value over the past two years’;
(b) ‘European companies are t ypically able to
secure higher valuations and more capital in
New York compared with their home markets’;
(c) ‘greater depth of capital and specialist investor
knowledge in the biotech sector ... and follow-on
fundraising’; (d) ‘loosening of rules governing capital raisings’. Some investment communities are
more sophisticated than others, even between
developed countries.
Source: Andrew Ward, Europe’s biotech group’s rush
to list in New York; Pharmaceuticals, the Financial Times
(London), 16 July 2015.
Financial Markets—The Engine of
Successful Economies?
In this section we look at some of the fundamental concepts that lie behind financial markets. Often they are
seen as exploiting societies, places where people make large sums of money without much effort. So why are
they tolerated, why does almost every country have a stock exchange? Some of the concepts here are quite
advanced and the reader may want to refer back to this section having read later chapters. Reading them now
will nevertheless be helpful when encountering them later in the text.
The financial manager has to interact with the financial markets as in Figure 1-1. The share price of the
company on the stock exchange is critical to its shareholders who are the owners of the company. Currency
markets are critical in that exchange rates affect all international transactions. The bond market for raising
funds and the market for derivatives (insurance type contracts on future prices) are again critical to the
company. Often there are scandals associated with such markets. Insider trading (see Chapter 2) and bad
practices (e.g. the LIBOR scandal) are all too frequent. Share market crashes are also seen by some as the
cause of an economic downturn, so it is appropriate to start by pointing out the valuable contribution that
the financial markets make to society.
Information Processing
Financial markets provide a central place where information can be validated, regulated and
disseminated. It is particularly important that the accounts are prepared on a known basis; stock markets
adopt accounting standards to address this need. A certain level of reporting is required so that the performance of one company can be compared to others. Companies prepare annual reports to the stock market
for general release.
An alternative to trading in a market is ‘over the counter’ trading or OTC. Here the information is not
regulated and there is a danger that risk is underestimated. The Dodd Frank Act (2010) in the United States
was part of the OTC derivative market regulation following the global depression in which a clearing
house was set up to regulate OTC transactions. A clearing house is a central location for the monitoring of
­person-to-person sales and can be seen as a very basic form of market place. The need for organized information processing is now generally acknowledged but there remains much to be done in what is a very difficult
environment to regulate given the open nature of the internet.
24 Part 1
The Company and Its Reporting Environment
Maturity Transformation
Maturity transformation is achieved because the company borrowing for the long term can issue shares
or bonds (financial instruments) that after the initial purchase by investors are then typically traded on the
secondary market. Because of the presence of a secondary market the investor does not have to hold
the instrument for the full term of the investment. Thus a long-term borrower can borrow from short-term
lenders. Investors who purchased the newly issued shares on the primary market can sell them whenever they
want on the secondary market. In this way a society where no-one can afford to lend money for a long period
can nevertheless lend to companies that want to borrow and not repay for some time, if ever—an almost
miraculous achievement!
Nevertheless, the relationship between investor and borrower is not without problems. Because the expectations of the investor will be short term, they want to see a positive return to their investment during the,
say, two or three years that they hold the share. The companies’ expectations will however be very different—
they are borrowing for the long term and may not expect to see a positive return for a number of years. Managers from economies such as Germany where the share and financial markets generally are smaller (than in
the United Kingdom and the United States) accuse UK and US management of concentrating too much on
the short term. Certainly, the difference in expectations created by the financial markets is a challenge for
financial management and as we shall see there are ways of mitigating its worse aspects. The benefit of being
able to raise long-term funding from investors who are relatively short term in their investments should however not be underestimated.
From the process of maturity transformation it should now be apparent that in order for companies to
raise money from investors it is important to have a good secondary market. The company itself does not
benefit from shares being sold between investors on the secondary market. When the news is that share
prices rose on the stock exchange, the reference is to investors on the secondary market. It is the price at
which investors are exchanging ownership. The only involvement of the company is to change the names of
the owners on the company share register.
Risk Transformation
A further effect of issuing shares and other financial instruments and trading them on the financial markets
is to reduce risk for the investor. The reduction in risk is achieved in two ways: firstly, by creating a security
that is only a small part of the loan (as in a share) the investor need only invest in a small fraction of their total
savings. The prospect of the share or other financial instrument falling in value is far less damaging if it is
not going to significantly affect the investors’ overall wealth. The second reduction in risk is achieved due to
the ability of the investor to sell on the shares in the secondary market. For most readers it will be intuitively
clear that holding a risky share for a long period is riskier than holding it for a short period. In fact, as will
be shown in later analysis, the risk increases over time in a fairly regular manner (apart from the occasional
From the point of view of society this means that funding can be found for risky projects from investors
who may be quite risk averse—that is, quite conservative. The two risk transformation effects (investing in
only a small share of the investment and not holding the shares for a long period) that are enabled by the
secondary market for shares enables societies or economies to fund long-term risky projects from investors
who do not necessarily want to lend for the long term and only want to take a small risk. This is indeed a
remarkable achievement.
Liquidity is important for both the lender and the borrower. A company goes to the financial markets because
banks and other sources cannot offer sufficient funds. So it is important that the share market attracts sufficient investors to enable companies and indeed governments to raise large funds. Liquidity is also important
for the investor—as mentioned above, a good secondary market enables investors to sell or buy large investments without being adversely affected due to a lack of funds. The terms of the investment, especially the
interest rate, can therefore be due to the nature of the investment and not be affected by the availability of
funds. The market term is that markets should be ‘deep’.
Chapter 1
Central Concepts in Finance and Financial Management 25
Determining a Price—Homogeneous Expectations
Much of analysis in finance refers to ‘the market price’ and ‘expected values’. A fair question is to ask, how
is this price determined? The role of the market is to act as the forum or venue for the valuation process. So
it is important from a market perspective that there are a range of buyers for a particular share when it is
offered for sale. Also it is important that the buyers should be independent in forming a view as to the fair
price of the share. Markets want to avoid a situation where there is only one buyer who can ‘name a price’
and there is no alternative. Such situations are referred to as ‘cornering the market’ and can go disastrously
wrong.5 By contrast, if all investors have differing views then the price could be going up and down purely
due to disagreement over value. A branch of finance termed behavioural finance pursues just such a possibility. Mainstream finance as treated here, however, omits this possibility by assuming that expectations are
homogeneous. In this context homogeneous expectations means roughly that after some debate all investors
are agreed as to the likely future benefits, the possible variation in those benefits and hence the appropriate
current price. Unless stated otherwise this is the basis of the rest of this text and indeed most of the many
Nobel prizes awarded for development in finance.
One of the principal means of managing risk is to diversify. This is the simple concept of ‘not putting all your
eggs in one basket’. To extend the metaphor: with two evenly filled baskets, if one drops then only half the
eggs have been lost, and so in that sense it is safer to spread risk. Accordingly, a firm might engage in developing a range of products and services. A financial manager might invest surplus money in a range of investments; money may be borrowed in differing currencies; production be set up in different countries. The term
portfolio is used to capture the idea of a range of interests. A portfolio of shares is an investment in a range
of shares, financing in a portfolio of currencies implies a range of different currencies. Normally, however,
the term is restricted to investments. Having a portfolio reduces risk in that any failure is highly unlikely to
affect all diversified elements at the same time. This is a fundamental concept in finance and is for instance
the basis of the principal model of share valuation—the Capital Asset Pricing Model. The degree to which a
share diversifies a portfolio is deemed in this model to be the basis of the required return and hence the value
of the share given a stream of expected dividends (see Chapter 6). As a note of caution, diversification relies
on the correct estimation of the degree of independence between the elements of any particular portfolio. For
example, in a stock market crash, the share returns that were thought to be independent all fall together and
the diversification effect suddenly disappears.
Market Efficiency
In finance, efficiency has a special meaning. It is assumed that markets are operationally efficient—that
transactions are properly recorded, that prices are transparent, that credit problems are properly managed.
Efficiency in finance is a concern with how well the market price represents value. It is assumed that unless
stated otherwise, market prices reflect value.
The need for prices to reflect value is common to all markets. A simple case is the second-hand car market. Suppose that in the forecourt of a garage there are four cars lined up for sale that are identical except that
one of the cars costs an extra €1000. The efficient markets assumption maintains that the car that costs and
extra €1000 is offering greater value in the form of more future benefits—it may be more stylish, it may have
better future performance, and so on. The market would be inefficient if there were no difference between
the higher priced car and the other identical cars in the garage. In fact, the second-hand car market as a
whole is not particularly efficient as it is possible to pick up a bargain, a car that is at a lower price than other
identical cars.
A well-known example of cornering the market is that of the Hunt brothers, Nelson ‘Bunker’ Hunt in particular. They bought up
large amounts of silver directly and through futures contracts on which they took delivery rather than close out (see Chapter 9). By
making silver scarce, the price rose from $11 to nearly $50 per ounce. It was estimated that they made around $2 billion to $4 billion
in speculation. The US government stepped in and this led creditors to refuse further loans forcing the Hunts to sell. The price then
collapsed to below $11 an ounce in 1980.
26 Part 1
The Company and Its Reporting Environment
Financial instruments such as shares are fundamentally the same as any other product or service. A share
offers a future benefit in the form of dividends. The difference is one of degree. In the case of a car one can be
reasonably sure about the information that accompanies the product, particularly if it is new. It is possible to
check that the engine is the engine that the manufacturer claims—open the bonnet! Also, that information
does not change over time. One is in effect purchasing a well-defined information set that can be checked
and is stable over time. The information set for a share is very different. The future benefit is the promise of
dividends in the future. There is no means of checking the promise. It is not possible to sue if a promise of
future dividends is broken; a product or service that is different from what is advertised can be the subject
of litigation. Also, the value of the promise changes over time. In good economic conditions the price will
reflect an expectation of high future dividends, in poor economic conditions lower dividends or dividends
that will grow more slowly.
The information set that is the basis of valuation for a share is very much more volatile than for a physical
product. The information that is used as the basis of valuation of a share is not known with any degree of
certainty. One can only speculate or carry out statistical tests to see if potential causal factors such as current
earnings are relevant. The question as to whether the market is efficient is accordingly harder to establish. It
is therefore only an assumption that the market is efficient. This enables us to write about the profit and loss
account, the balance sheet, FCFs and other features as being important to the value of the company based
on the assumption that the market is efficient and that these variables ought to be important to valuation
according to our models of value.
This topic is examined further in Chapter 7 but here it is interesting to think of what a market would look
like if the market for shares were inefficient. One need look no further than the UK economist John Maynard
as a result of the gradual increase in the proportion of the equity in the community’s aggregate capital investment
which is owned by persons who do not manage and have no special knowledge of the circumstances . . . of the
business in question, the element of real knowledge in the valuation of investments by those who own them or contemplate purchasing them has seriously declined . . . It might have been supposed that competition between expert
professionals, possessing judgement and knowledge beyond that of the average private investor, would correct the
vagaries of the ignorant individual left to himself. It happens, however, that the energies and skill of the professional
investor and speculator are mainly occupied otherwise. . . . They are concerned, not with what an investment is really
worth to a man who buys it ‘for keeps’ but with what the market will value it at, under the influence of mass psychology . . . (p. 98 et seq.)
These views, once dismissed as not significant, have a new relevance given the dot com bubble and the
Global Financial Crisis. At the same time, real economic events are clearly important to firm valuation, not
just mass psychology. The role of psychology is the motivating factor for an area of the literature known as
behavioural finance. This is an emerging area that has yet to find evidence that is nearly as strong as the traditional view that mostly prices reflect economic information. Some reference here is made to psychological
aspects but otherwise it is assumed that prices reflect economic information.
Law of One Price
The law of one price maintains that if the same product or service is being offered to the market then it
should have the same price assuming that the market is efficient. Therefore, the same price for a product
implies the same information set about future benefits and if that is the basis for valuation, as is implied by
market efficiency, then it should have the same price. If there are differences then they should quickly disappear. For example, suppose that two shops A and B are reasonably close together and are selling the same
product. If the price is cheaper in shop A than shop B then demand for the product in shop B will fall to zero
and the demand for the product in shop A will be high. This will force shop B to lower its price and shop A
may well think that the price is too low and seek to raise the price. Only when the prices are similar will there
be no pressure for a change in price due to the price differential. The beauty of this process is that the two
Keynes, J. M. (1936) The General Theory of Employment, Interest and Money, Macmillan/Cambridge University Press.
Chapter 1
Central Concepts in Finance and Financial Management 27
shops need not know of each other’s existence, the simple process of demand and supply will ensure that the
prices come into alignment with each other.
This simple process has been the basis for the two most important developments in finance. Modigliani and
Miller showed that company leverage could be replicated by shareholders with a few simplifying assumptions. Therefore the idea that lowering the cost of borrowing through leverage was flawed, as two identical
firms with the same leverage from the shareholder’s perspective (one created by the shareholder, the other
created by the company) would have two different borrowing rates (in effect the price for loans). The second
development was in the pricing of options (a type of insurance contract). It was shown that the outcome of
the contract could be replicated by borrowing and lending, and that therefore, assuming the law of one price,
the cost of the borrowing and lending should be the price of the option. The same could be said for determining movements in the exchange rate for both Purchasing Power Parity and Uncovered Interest Rate Parity
and the pricing of futures. All these instances will be addressed in later chapters.
To generalize, in any reasonably sophisticated market any ‘new’ product can almost certainly be made
up of existing products given the same information set. As the price of the existing products is known, so
the price of the new product can be calculated. The exception is where a scheme is exploiting some unique
regulatory aspect such as created by tax regulations. Does the law of one price have implications for financial management? Certainly, a manager should exercise extreme caution when confronted with any product
claiming to be new or claiming to be cheaper.
The term arbitrage is used rather loosely in the newspapers so we will start with the rather more limited academic
version. Arbitrage is making a profit without taking a risk. In the case of two identical products A and B at different
prices, arbitrage would be the act of buying the product at the lower price and selling it at the higher price. Note that
a profit can only occur if the law of one price is violated—the same product has different prices. A riskless or certain
profit is very attractive—a certain and often immediate return can be augmented infinitely by investing ever greater
amounts. A certain return of 1/100th per cent in one day will earn £0.01 for an investment of £100 but as there is no
risk why not invest £100 000 000 and earn £10 000 in a day? Such was the activity of a hedge fund called Long Term
Capital Management (LTCM) with two Nobel Prize winners on the Board. The strategy was termed ‘hoovering up
the nickels’ and profits were made initially. However, there was a very small risk and to earn the money as our example shows, large sums had to be staked. So when a loss occurred, as in the Russian share market crash of 1998, the
fund collapsed with huge debts. In practice it is very difficult to arrange a transaction with no risk at all. Even in our
example, buying from shop A and selling to shop B entails a small degree of travel. Therefore in practice arbitrage
usually refers to making a profit by taking a small risk. Unless stated otherwise it is assumed here that any such risk is
negligible. It should be readily appreciated that an implication of an efficient market is that there is no arbitrage and
this is the case when the law of one price holds. These assumptions hold jointly.
Trading Procedures in Financial Markets
A large volume of trading occurs in the secondary markets. Although there are many secondary markets
for a wide variety of securities, we can classify their trading procedures along two dimensions: location and
method of matching orders.
Physical Location versus Electronic Network
A secondary market can be either a physical location exchange or a computer/telephone network. For example, the New York Share Exchange, the American Share Exchange (AMEX), the Chicago Board of Trade (the
CBOT trades futures and options), and the Tokyo Share Exchange are all physical location exchanges. In
other words, the traders actually meet and trade in a specific part of a specific building.
In contrast, NASDAQ, which trades a number of US shares, is a network of linked computers. Other network examples are the markets for US Treasury bonds and foreign exchange, which operate via telephone
and/or computer networks. In these electronic markets, the traders never see one another except maybe for
cocktails after work. This is now becoming a standard alternative for all financial markets.
28 Part 1
The Company and Its Reporting Environment
By their very nature, networks are less transparent than physical location exchanges. For example, credit
default swaps are traded directly between buyers and sellers, and there is no easy mechanism for recording,
aggregating and reporting the transactions or the net positions of the buyers and sellers.
Matching Orders: Auctions, Dealers and ECNs
How do buyers and sellers ‘find’ each other? We base the following on the US system but the features are general to all financial markets. Matching can occur through an open outcry auction system, through dealers or
by automated order matching. An example of an outcry auction is the CBOT, where traders actually meet in
a pit and sellers and buyers communicate with one another through shouts and hand signals.
In a dealer market, there are ‘market makers’ who keep an inventory of the share (or other financial
instrument) in much the same way that any merchant keeps an inventory. These dealers list bid quotes and
ask quotes, which are the prices at which they are willing to buy or sell. Computerized quotation systems
keep track of all bid and asked prices, but they don’t actually match buyers and sellers. Instead, traders must
contact a specific dealer to complete the transaction. NASDAQ (US shares) is one such market, as is the
­London SEAQ (UK shares).
The third method of matching orders is through an electronic communications network (ECN). Participants in an ECN post their orders to buy and sell, and the ECN automatically matches orders. For example,
someone might place an order to buy 1000 shares of IBM share—this is called a ‘market order’ because it is
to buy the share at the current market price. Suppose another participant had placed an order to sell 1000
Life in the Fast Lane: High-Frequency Trading!
In the time it takes to blink an eye, a high-frequency
trader’s computer could have made hundreds of
bids, cancelled all but one, purchased shares and
then sold them for a profit of less than a penny. It
may sound like a lot of work for such a small profit,
but a million similar trades a day add up to big bucks.
In fact, high-frequency trading (HFT) firms made
about $7.2 billion total profit in 2009.
Who are these traders? First, there are only
about 400 HTF firms out of the 20 000 or so institutional traders, so there really aren’t very many
of them. Second, many of their employees have
maths and computer science backgrounds rather
than trading experience. Third, they have access to
the very best computer technology. Their demand
for speed is so great that Hibernia Atlantic plans
to lay a new underwater cable along a slightly
shorter route from the United Kingdom to Canada
in order to cut the transmission time from 65 to
60 milliseconds.
Despite the relatively small number of HFT firms,
they have a huge impact on the market, accounting
for over 60 per cent of the share trading volume and
over 40 per cent of the foreign exchange volume.
But are HFT firms good or bad for markets and other
investors? The answer is not clear. On the one hand,
other investors can trade much more quickly now,
with execution time dropping from 10.1 seconds in
2005 to 0.7 seconds in 2010. The cost of trading, as
measured by the spread in bid and ask prices, has
also shrunk dramatically. On the other hand, some
critics say that high-frequency trading distorts prices
and makes markets less stable. Although intuitively
instability might seem to be the obvious outcome,
empirical studies are inconclusive. As Brogaard et al
(2014)7 point out, profit from high-frequency trading is
to be made from trading in the direction of permanent
price changes and in the opposite direction to transitory pricing. This argument for stability suggests that
regulation in the near future seems unlikely.
Sources: Doug Cameron and Jacob Bunge, ‘Under-­
water Options? Ocean Cable Will Serve High-Frequency
Traders’, Wall Street Journal, 1 October 2010, p. C3; and
Kambiz Foroohar, ‘Speed Geeks’, Bloomberg Markets,
November 2010, pp. 111–122.
See Brogaard, J., Hendershott, T. and Riordan, R. (2014) `High-frequency trading and price discovery’, Review of Financial Studies
Chapter 1
Central Concepts in Finance and Financial Management 29
shares of IBM, but only at a price of $91 per share, and this was the lowest price of any ‘sell’ order. The ECN
would automatically match these two orders, execute the trade, and notify both participants that the trade
has occurred. The $91 sell price was a ‘limit order’ as opposed to a market order because the action was limited by the seller. Note that orders can also be limited with regard to their duration. For example, someone
might stipulate that they are willing to buy 1000 shares of IBM at $90 per share if the price falls that low
during the next two hours. In other words, there are limits on the price and/or the duration of the order. The
ECN will execute the limit order only if both conditions are met.
Two of the largest ECNs for trading US shares are INET (owned by NASDAQ) and Area (owned by NYSE
Euronext). Other large ECNs include Eurex (an ECN for derivatives, owned by the Deutsche Borse) and
SETS (a share exchange owned by the SIX Swiss Exchange). Notice that most ‘conventional’ exchanges also
operate ECNs.
S E L F -T E S T
What are the major differences between physical location exchanges and computer/telephone
What are the differences among open outcry auctions, dealer markets and ECNs?
Types of Share Market Transactions
Because the primary objectives of financial management are to maximize the firm’s value and then help
ensure that the current share price equals that value, knowledge of the share market is important to anyone
involved in managing a business. We can classify share market transactions into three distinct types:
(1) IPOs, (2) seasoned equity offerings, and (3) secondary market transactions.
Whenever shares are offered to the public for the first time, the company is said to be going public.
This primary market transaction is called the IPO market. If a company later decides to sell (i.e. issue)
additional shares to raise new equity capital, this is still a primary market, but it is called a seasoned
equity offering. Trading in the outstanding shares of established, publicly owned companies are secondary market transactions. For example, if the owner of 100 shares of publicly held shares sells his or
her shares, the trade is said to have occurred in the secondary market. Thus, the market for outstanding
shares, or used shares, is the secondary market. The company receives no new money when sales occur
in this market.
In the United States, the average first-day return for IPOs was around 13 per cent in 2011. However, some
firms had spectacular first-day price run-ups, such as Linkedln’s 109 per cent gain on its first day of trading.
Not all companies fared so well—indeed, FriendFinder fell by over 21 per cent on its first trading day.
For 2011, some IPOs had big gains for the year, such as Imperva’s 92.8 per cent return. Others had
big annual losses; HCA Holdings fell by over 26 per cent. In fact, the average IPO lost over 13 per cent
during 2011.
Even if you are able to identify a ‘hot’ issue, it is often difficult to purchase shares in the initial
offering. In strong markets, these deals generally are oversubscribed, which means that the demand for
shares at the offering price exceeds the number of shares issued. In such instances, investment bankers
favour large institutional investors (who are their best customers), and small investors find it hard, if
not impossible, to get in on the ground f loor. They can buy the share in the after-market, but evidence
suggests that if you do not get in on the ground floor, the average IPO underperforms the overall market
over the long run.
Before you conclude that it isn’t fair to let only the best customers have the share in an initial offering,
think about what it takes to become a best customer. Best customers are usually investors who have done lots
of business in the past with the investment banking firm’s brokerage department. In other words, they have
paid large sums as commissions in the past, and they are expected to continue doing so in the future. As is so
often true, there is no free lunch, most of the investors who get in on the ground floor of an IPO have, in fact,
paid for this privilege.
30 Part 1
The Company and Its Reporting Environment
S E L F -T E S T
Differentiate between an IPO, a seasoned equity offering and a secondary transaction.
Why is it often difficult for the average investor to make money during an IPO?
The Secondary Share Markets
Secondary share markets are vital to the attractiveness of shares as discussed earlier.
The New York Share Exchange
As stated earlier, stock exchanges are independent companies, they are not government run. Taking the US
stock markets as an example, before March 2006, the New York Share Exchange (NYSE) was a privately held
firm owned by its members. It then merged with Archipelago, a publicly traded company that was one of
the world’s largest ECNs. NYSE members received approximately 70 per cent of the shares in the combined
firm, with Archipelago shareholders receiving 30 per cent. The combined firm, which also owned the Pacific
Exchange, was known as The NYSE Group, Inc., and was traded publicly under the ticker symbol NYX. It
continued to operate the New York Share Exchange (a physical location exchange located on Wall Street) and
Area (comprising the Pacific Exchange and the ECN formerly known as Archipelago). In 2007 the NYSE
Group merged with Euronext, a European company that operates share exchanges (called bourses) in Paris,
Amsterdam, Brussels and Lisbon. The combined company is called NYSE Euronext.
The NYSE still has over 300 member organizations, which are companies, partnerships or LLCs. Membership prices were as high as $4 million in 2005, and the last sale before the Euronext merger was $3.5 million. Member organizations are registered broker-dealers, but they may not conduct trading on the floor of
the exchange unless they also hold a trading licence issued by the NYSE. Before going public, the equivalent
to the trading license was called a seat. Trading licences are now leased by member organizations from the
exchange, with an annual fee of $40 000 for 2012. The NYSE has leased most of its 1500 available trading
Most of the larger investment banking houses operate brokerage departments and are members of the
NYSE with leased trading rights. The NYSE is open on all normal working days, and members meet in large
rooms equipped with electronic equipment that enables each member to communicate with his or her firm’s
offices throughout the country. For example, Merrill Lynch (now owned by Bank of America) might receive
an order in its Atlanta office from a customer who wants to buy shares of Procter & Gamble. Simultaneously,
Edward Jones’ St Louis office might receive an order from a customer wishing to sell shares of P&G. Each
broker communicates electronically with the firm’s representative on the NYSE. Other brokers throughout
the country also communicate with their own exchange members. The exchange members with sell orders
offer the shares for sale, and members with buy orders bid for them. Thus, the NYSE operates as an auction
However, trading on the NYSE floor has declined in importance. In addition to the trading of NYSE
shares on its own ECN area, hundreds of private ECNs and brokers trade NYSE shares. In 2010, about
79 per cent of the trading volume for NYSE-listed shares occurred on these private networks.
The NASDAQ Share Market
The National Association of Securities Dealers (NASD) is a self-regulatory body that licenses brokers and
oversees trading practices. The computerized network used by the NASD is known as the NASD Automated
Quotation System, or NASDAQ. NASDAQ started as a quotation system, but it has grown to become an
organized securities market with its own listing requirements. NASDAQ lists about 5000 shares, although
not all trade through the same NASDAQ system. For example, the NASDAQ National Market lists the larger
NASDAQ shares, such as Microsoft and Intel, while the NASDAQ Small-Cap Market lists smaller companies with the potential for high growth. NASDAQ also operates the NASDAQ OTC Bulletin Board, which
Chapter 1
Central Concepts in Finance and Financial Management 31
lists quotes for shares registered with the Securities and Exchange Commission (SEC) but not listed on any
exchange, usually because the company is too small or not sufficiently profitable. Finally, NASDAQ operates
the Pink Sheets, which provide quotes on companies that are not registered with the SEC.
‘Liquidity’ is the ability to trade quickly at a net price (i.e. after any commissions) that is close to the security’s recent market price. In a dealer market, such as NASDAQ, a share’s liquidity depends on the number
and quality of the dealers who make a market in the share. NASDAQ has more than 400 dealers, most of
whom make markets in a large number of shares. The typical share has about ten market makers, but some
shares have more than 50 market makers. Obviously, there are more market makers, and hence more liquidity, for the NASDAQ National Market than for the Small-Cap Market. Shares listed on the OTC Bulletin
Board or the Pink Sheets have much less liquidity.
Measuring the Market
A share index is designed to show the performance of the stock market. Here we describe some
leading indices.
Dow Jones Industrial Average
Begun in 1896, the Dow Jones Industrial Average
(DJIA) now includes 30 widely held shares that represent almost one-fifth of the market value of all US
shares. See www.dowjones.com for more information.
S&P 500 Index
Created in 1926, the S&P 50 0 Index is widely
regarded as the standard for measuring large-cap
US shares’ market performance. It is value weighted,
so the largest companies (in terms of value) have
the greatest influence. The S&P 500 Index is used
as a comparison benchmark by 97 per cent of all US
money managers and pension plan sponsors. See
www2.standardandpoors.com for more information.
NASDAQ Composite Index
The NASDAQ Composite Index measures the
performance of all common shares listed on the
­NASDAQ stock market. Currently, it includes more
than 3200 companies, many of which are in the technology sector. Microsoft, Cisco Systems and Intel
account for a high percentage of the index’s valueweighted market capitalization. For this reason, substantial movements in the same direction by these
three companies can move the entire index. See
www.NASDAQ.com for more information.
NYSE Composite Index
The NYSE Composite Index measures the performance of all common shares listed on the NYSE. It
is a value-weighted index and is based on just over
2000 shares that represent 77 per cent of the total
market capitalization of all publicly traded companies in the United States. See www.nyse.com
for more information.
Trading the Market
Through the use of exchange traded funds (ETFs),
it is now possible to buy and sell the market in
much the same way as an individual share. For
example, the Standard & Poor’s depository receipt
(SPDR) is a share of a fund that holds the shares of
all the companies in the S&P 500. SPDRs trade during regular market hours, making it possible to buy
or sell the S&P 500 any time during the day. There
are hundreds of other ETFs, including ones for the
NASDAQ, the Dow Jones Industrial Average, gold
shares, utilities and so on.
Recent Performance
Go to the website finance.yahoo.com. Enter the
symbol for any of the indices ( A DJI for the Dow
Jones, AGSPC for the S&P 500, AIXIC for the NASDAQ, and ANYA for the NYSE) and then click GO. This
will bring up the current value of the index, shown
in a table. Click Basic Chart in the panel on the left,
which will bring up a chart showing the historical
performance of the index. Directly above the chart
is a series of buttons that allows you to choose the
number of years and to plot the relative performance
of several indices on the same chart. You can download the historical data in spreadsheet form by clicking Historical Prices in the left panel.
32 Part 1
The Company and Its Reporting Environment
Competition in the Secondary Markets
There is intense competition between the NYSE, NASDAQ and other international share exchanges—they
all want the larger, more profitable companies to list on their exchange. Because most of the largest US companies trade on the NYSE, the market capitalization of NYSE-traded shares is much higher than for shares
traded on NASDAQ (about $13.4 trillion compared with $3.9 trillion at the end of 2010). However, reported
volume (number of shares traded) is often larger on NASDAQ, and more companies are listed on NASDAQ.
For comparison, the market capitalizations for global exchanges are $3.8 trillion in Tokyo, $3.6 trillion in
London, $2.7 trillion in Shanghai, $2.7 trillion in Hong Kong, $1.4 trillion in Germany, and $1.6 trillion in
Interestingly, many high-tech companies such as Microsoft and Intel have remained on NASDAQ even
though they easily meet the listing requirements of the NYSE. At the same time, however, other high-tech
companies such as Iomega have left NASDAQ for the NYSE. Despite these defections, NASDAQ’s growth
over the past decade has been impressive. In an effort to become even more competitive with the NYSE and
with international markets, NASDAQ acquired one of the leading ECNs, Instinet, in 2005. NASDAQ subsequently acquired the Nordic exchange OMX, giving it an international presence. The combined company is
the NASDAQ OMX Group.
Despite the shifting ownerships of exchanges, one thing is clear—there will be a continued consolidation
in the securities exchange industry, with a blurring of the lines between physical location exchanges and
electronic exchanges.
S E L F -T E S T
What are some major differences between the NYSE and the NASDAQ share market?
Share Market Returns
During the period 1968–2011, the average annual return for the share market, as measured by total returns
(dividends plus capital gains) on the S&P 500 index, was about 10.9 per cent, but this average does not
reflect the considerable annual variation. Notice in panel A of Figure 1-2 that the market was relatively
flat in the 1970s, increased somewhat in the 1980s, and has been a roller coaster ever since. In fact, the
market in early 2009 dipped to a level last seen in 1995. Panel B highlights the year-to-year risk by showing
annual returns. Notice that shares have had positive returns in most years, but there have been several years
with large losses. Shares lost more than 40 per cent of their value during 1973–1974 and again during 2000–
2002, and they lost 37 per cent of their value in 2008 alone. We will examine risk in more detail later in the
book, but even a cursory glance at Figure 1-2 shows just how risky investing in shares can be! Note that this
is an example of financial risk as described above in our section on common themes. For much of the time
over the short to medium term, risk behaves according to our relatively well behaved model of ‘normal’ risk;
then on occasions the price will ‘jump’ in a manner that is apparently unpredictable. Note also that there
are longer-term trends which are probably beyond the scope of the financial manager but for which there is
no clear explanation.
Analysts have long touted the benefits of investing overseas, arguing that foreign shares improve diversification and provide good growth opportunities. This has been true for many years, but it wasn’t the case
in 2011. Table 1-2 shows returns in selected countries. Notice that most countries had negative returns. The
table shows how each country’s shares performed in its local currency and in terms of the US dollar. For
example, in 2011 German shares had a −17.3 per cent return in their own currency, but that translated into
a −19.9 per cent return to a US investor; the difference was due to depreciation in the euro relative to the US
dollar. As this example shows, the results of foreign investments depend in part on what happens in the foreign economy and in part on movements in exchange rates. Indeed, when you invest overseas, you face two
risks: (1) that foreign shares will decrease in their local markets and (2) that the currencies in which you will
be paid will fall relative to the dollar.
Chapter 1
Central Concepts in Finance and Financial Management 33
F i g u re 1-2
S&P 500 Share Index Performance
Panel A: End-of-Month Index Value
Panel B: Total Annual Returns: Dividend Yield + Capital Gain or Loss
Sources: Returns data are from various issues of The Wall Street Journal, ‘Investment Scoreboard’ section; the index
level is from http://finance.yahoo.com.
Even though foreign shares have exchange-rate risk, this by no means suggests that investors should avoid
them. Foreign investments do improve diversification, and it is inevitable that there will be years when foreign shares outperform domestic shares. When this occurs, investors will be glad they put some of their
money in overseas markets.
S E L F -T E S T
Explain how exchange rates affect the rate of return on international investments.
34 Part 1
The Company and Its Reporting Environment
TA B L E 1-2
2011 Performance of Selected Dow Jones Global Share Indices, Ranked Highest to Lowest
US Dollars
Local Currency
US Dollars
Local Currency
Hong Kong
South Korea
Source: Adapted from The Wall Street Journal, 3 January, 2012, R17.
Economic Crises
It is a continuing puzzle that despite the increasing sophistication of the financial markets and the development of computing power we still have stock market crashes, sudden falls in the value of currencies and
market price ‘bubbles’—i.e. irrational increases in price, as often occurs in the housing market. Academics are still searching for models that offer some common explanation for these events. Some argue that
the causes are behavioural, that investors are not wholly rational. This has given rise to a whole area of
finance termed ‘behavioural finance’. Although plausible explanations ex post (i.e. after the event) have
been offered, there is little by way of prediction. A more recent approach is to liken markets to a dynamic
(over time) process that evolves slowly, similar to a disease such as diabetes. It is not just the behaviour that
causes the sudden event (diabetes) but also the propensity to the condition. Identifying the faults in markets that may lead to a crisis is an interesting development but it is still in its very early stages of analysis.
Reflecting on past crises merely raises the puzzlement that so few predict the events. Alternatively, there
are many who predict a crisis that does not occur—the collapse of the dollar has for instance been predicted for many years and thankfully for the world economy it has not yet happened. From the perspective
of the financial manager the propensity for crisis means that taking out some form of financial insurance
for large transactions should be seen as sensible modern day management. In later chapters we examine
derivatives that offer just such protection.
The Big Picture
Finance has vocabulary and tools that might be new to you. To help you avoid getting bogged down in the
trenches, the start of each part of the text has a diagram of the role of the financial manager. In words, a
finance manager’s primary job is to work with other managers to invest money to get the highest return for
the risk of that particular activity. The equation in the centre of Figure 1-3 shows one particular model of valuation that plays a central part in the financial manager’s contribution; but it is not the only model. Finance
managers borrow money as cheaply as possible, try to protect against adverse price movements, manage the
flow of money, the receipts and payments, work out if the firms has been profitable, and advise on the value
of future plans.
Chapter 1
Central Concepts in Finance and Financial Management 35
F i g u re 1-3
The Main Determinants of Intrinsic Value: The Big Picture
Sales revenues
Operating costs and taxes
Required investments in operating capital
Free cash flow
Value =
(1 + WACC)1
(1 + WACC)2
(1 + WACC)∞
Weighted average
cost of capital
Market interest rates
Market risk aversion
Cost of debt
Cost of equity
Firm’s debt/equity mix
Firm’s business risk
A financial market is critical to enabling low-risk small investors to finance high-risk large projects.
The primary objective of management should be to maximize shareholders’ wealth, and this means
maximizing the company’s share price.
Transfers of capital between borrowers and savers take place (1) by direct transfers of money and securities; (2) by transfers through investment banking houses, which act as go-betweens; and (3) by transfers
through financial intermediaries, which create new securities.
Four fundamental factors affect the cost of money: (1) production opportunities, (2) time preferences for
consumption, (3) risk and (4) inflation.
Derivatives, such as options, are claims on other financial securities. In securitization, new securities are
created from claims on packages of other securities.
Major financial institutions include commercial banks, savings and loan associations, mutual savings
banks, credit unions, pension funds, life insurance companies, mutual funds, money market funds,
hedge funds and private equity funds.
Spot markets and futures markets are terms that refer to whether the assets are bought or sold for
‘on-the-spot’ delivery or for delivery at some future date.
Money markets are the markets for debt securities with maturities of less than a year. Capital markets
are the markets for long-term debt and corporate shares.
Primary markets are the markets in which companies raise new capital. Secondary markets are markets
in which existing, already outstanding securities are traded among investors.
36 Part 1
The Company and Its Reporting Environment
Markets enable maturity transformation, risk transformation, pricing and liquidity.
Orders from buyers and sellers can be matched in one of three ways: (1) in an open outcry auction,
(2) through dealers and (3) automatically through an ECN.
There are two basic types of markets—the physical location exchanges (such as the NYSE) and computer/telephone networks (such as NASDAQ).
Web Extension 1A discusses derivatives, and Web Extension 1B provides additional coverage of share
( 1-1)
Define each of the following terms:
a. the term of a loan
b. a financial instrument
c. shareholder wealth maximization
d. money market; capital market; primary market; secondary market
e. maturity transformation and risk transformation
f. liquidity
g. diversification
h. law of one price
i. arbitrage
j. agency
k. hedge funds
l. securitization
( 1-2)
What are the principal contributions made by a financial market to an economy?
What are the advantages and disadvantages of each?
What is the basis of valuation in an efficient market?
Edmund Enterprises recently made a large investment to upgrade its technology.
Although these improvements won’t have much of an impact on performance in the
short run, they are expected to reduce future costs significantly. What impact will
this investment have on Edmund Enterprises’ earnings per share this year? What
impact might this investment have on the company’s share price?
Describe the ways in which capital can be transferred from suppliers of capital to
those who are demanding capital.
What are financial intermediaries, and what economic functions do they perform?
Is an initial public offering an example of a primary or a secondary market
Differentiate between dealer markets and share markets that have a physical location.
( 1-3)
( 1- 4 )
( 1-5 )
( 1- 6 )
( 1-7 )
( 1- 8 )
You are required to identify as many common themes in finance from the following memorandum:
To: Earnit Investment Company
From: Mr V. Wealthy
(a) I have been reading some textbooks on share valuation but I am aware that in practice the share price is
not always explained by the textbook models, so I am writing to you to see if you can help with investing
some money on my behalf. (b) I recently saw an advert by NewVenture plc offering shares at £20 each and
for the monies to be used to fund a mining operation in Antarctica. (c) Although they offered a prospectus
Chapter 1
Central Concepts in Finance and Financial Management 37
I thought it a bit risky, after all, some of the territories in Antarctica are disputed. (d) Alternatively I saw an
advert by Try Ltd asking for £100 000 to fund a franchising venture. (e) I have to say I was rather worried
about investing so much in one venture however attractive it seemed. (f) Really I only want to invest my
money for about three years and then I will need it to buy a house. (g) I do not think that Try Ltd could repay
in that short time period. (h) I think that I would rather invest in a range of enterprises and preferably have a
share or bond certificate that I can sell on as and when I want. (i) Now I noticed that shares in Big plc were on
offer at £3.5 on one site and £3.6 on another, I thought of buying at the low price and selling at the higher but
I am sure there was a catch. (j) Anyway as you can see I am a complete amateur and in need of good advice!
Financial Statements
Part 2: Analysing
and Managing the
t is as well to start with a word of caution. The published accounts of companies are highly aggregated. Any
analysis of the accounts must always be aware of the fact that a more detailed set of accounts, not available
outside the company, might well offer differing perspectives. Analysing the published accounts therefore is
best seen as a means of asking questions, determining areas that require further investigation. We need to be
aware that the analysis is only an indication and not a conclusion! Companies also issue ratios of their own.
Where audited, such ratios can be trusted but where there are significant differences between a published ratio
and a ratio calculated from the accounts with no explanation, then caution should be exercised. Differing interpretations are possible and firms naturally enough wish to present the best picture they can. In this spirit, it is
important to beware of value judgements by companies in the annual report. As pointed out in the last chapter,
business people are optimists—analysts need to be more balanced.
In the second part of this chapter we move from the published accounts to what are called the management
accounts—that is, the more detailed accounts that the company does not publish. Obviously we have to abandon the Rolls-Royce example. Looking into a firm’s detailed accounts enables us to have some idea of the kind
of problems and issues that arise in producing the published accounts. Here we tread on the borders of financial
management. Finance is only a part of the management role, as the study of management accounting makes
clear. Nevertheless, we need to understand the business consequences of the published figures and why finance
is only a part of the management role.
Gathering Data
Most educational establishments will subscribe to financial databases such as Fame and Osiris. Companies
likewise are likely to subscribe to information services that offer accounting data. These typically provide
accounts in a standardized format and so make comparison easier. Ratios can be calculated for sectors and
suitable comparison firms selected. Major suppliers and customers are identified. Also, links are provided
62 Part 1
The Company and Its Reporting Environment
to newswires and broker estimates of future earnings and profits. Share price behaviour will include price
trends, betas and correlations with the stock market index. Also, historic share price data are usually accessible. Often such sites will also provide analytical tools, graphing options, etc. This author’s preference is to
download the data onto a spreadsheet or a statistics package for further analysis.
From a financial perspective the most important information is contained in the annual report of companies and in particular the profit and loss account and the balance sheet with accompanying notes. In the UK
these have to be filed at Companies House; in other countries there will be a similar arrangement. These can
be accessed for minimal cost. Alternatively for major companies, the accounts will be freely available on the
Analysis should seek to gather three types of data:
• The accounts along with the notes to the accounts as will be found in the annual report. Having the
accounts in a standardized format to compare with other firms is also useful.
• The directors’ report as may be found in the annual report as well as other nonfinancial data published
by the company such as press releases.
• Third-party views such as broker opinions and articles from newspapers.
The non-accounting information is important for investigating further any issues that arise from
­analysing the accounts.
Determining Objectives
It is important to begin any analysis with a clear statement of objectives. There are a number of stakeholders
or interested parties for whom the accounts will be relevant. Our prime focus here will be the owners of the
company—namely, the shareholders.
The principal interests addressed in the accounts are those of the shareholder. In outline, the question
being addressed is whether continued investment or initial investment is worthwhile. In more detail, shareholders will be interested in:
• The future return on their investment. This can be interpreted as profitability and future prospects for
dividends and share price. This may be short, medium or long term.
• Risk. What is the likely variation to the estimates of profitability? Such analysis should include the influence of factors such as gearing or leverage—that is, the level of borrowing.
• Asset management. The nature and use of assets both long-term and current assets in the form of working capital. This includes issues such as liquidity and cash flows.
• Share valuation. What can the accounts tell us about the value placed on the shares by the stock market?
Other parties will also be interested in these questions but from a different perspective. The Green movement, for instance, will be interested in the profitability of the company—can it afford to be greener and
more ethical?
Creditors will be interested in the current average time taken to pay creditors, the cash flow of the company and the working capital management.
Longer-term lenders such as bondholders will be interested in the assets of the company and their potential use as security (collateral). Also, the profitability of the company, its cash flow and the potential variability in cash flow and profits will be important.
The business press will have a watching brief over any information published by companies partly to
comment on the valuation of the company and partly to consider the implications for other companies in the
same industry. They will also be interested in anything unusual as with any other subject area.
Government will be interested in the accounts and in particular their aggregate values across industries, the
level of sales and their increase or decrease and the implications for overall economic performance. Also, there
are issues concerning taxation: the levels actually being paid, the effect of tax allowances and tax negotiations.
As we have said, the focus here is limited to that of the current and potential investors. Their interests
cover most of the concerns of other parties.
Chapter 3
Understanding Financial Statements Part 2: Analysing and Managing the Accounts 63
Ratio Analysis
Financial ratios are designed to extract important information that might not be obvious simply from examining a firm’s financial statements. For example, suppose Firm A owes €5 million in debt while Firm B owes
€50 million. Which company is in a stronger financial position? It is impossible to answer this question without first comparing each firm’s debt relative to total assets, earnings and interest. Standardized comparisons
are provided through ratio analysis.
This approach can form the basis of a comparison with industry averages, an approach known as the
multiples method. Judgement is then relative to other companies. This is possible at a published accounts
level using commercial databases subscribed to by many educational establishments.
We will calculate the 2013 financial ratios for Rolls-Royce using data from the balance sheet and income
statement given in Figure 3-1 which is an abbreviated version of the accounts in the previous chapter.
F i g u r e 3 -1
Summary Balance Sheet and Income Statement 31/12/2013 for Rolls-Royce (£m)
Income statement
Balance sheet
Non-current assets
15 513
Intangible assets
4 987
Cost of sales
12 197
Property, plant and equipment
3 392
Gross profit
3 316
Investments and other financial assets 1,302
1 302
Other costs and revenues
1 781
Deferred tax assets
Operating profit
1 535
Post-retirement scheme surpluses
Profit on disposal and transfer
10 245
of activities
Current assets
Profit before financing and
3 319
1 870
Trade and other receivables
5 092
Net financing
other items
Profit before taxation
1 759
Cash and cash equivalents
3 990
12 818
Profit for the year
1 379
Total assets
Current liabilities
Other items
2 528
Trade and other payables
7 045
9 780
Non-current liabilities
2 164
Other items
2 678
Trade and other payables
2 138
6 980
Total liabilities
Net assets
16 760
6 303
Called-up share capital
Share premium account
Capital redemption reserve
Other items
Retained earnings
4 804
Non-controlling interests
Total equity
Source: Rolls Royce 2013 Annual Report, http://ar.rolls-royce.com/2013/
64 Part 1
The Company and Its Reporting Environment
Profitability Ratios—Return on Investment
Net Profit Margin
The net profit margin, also called the profit margin on sales, is calculated by dividing net income by sales.
It gives the profit per pound (£) of sales:
Net profit margin 5
Net income available to ordinary shareholders
which in this case is
5 8.9%
This is an overall figure that one would like to compare with other companies. However, comparisons are
difficult because other data are often poorly described and therefore possibly not comparable with RollsRoyce. From the accounting statement in the annual report, sales and profits are broken down into categories. Thus, for Rolls-Royce, Defence returns the highest profit margin followed by Civil Aerospace and
Marine engines. The profit more or less totals the EBIT or earnings before interest and taxation. In the RollsRoyce accounts this is referred to as ‘profit before financing and taxation’. This is termed the operating profit
margin and is defined as:
Operating profit margin 5
which in this case is:
1 870
5 12.0%
The operating profit margin identifies how a company is performing with respect to its operations before the
impact of interest expenses is considered.
Some analysts drill even deeper by breaking operating costs into their components. For example, the gross
profit margin is defined as:
Gross profit margin 5
Sales 2 Cost of goods sold
which in this case is:
3 316
5 21.4%
The gross profit margin identifies the gross profit per pound (in this case) of sales before less direct expenses
are deducted.
Sometimes it is confusing to have so many different types of profit margins. To simplify the situation, we
will focus primarily on the net profit margin as this is the main concern of shareholders. The word ‘net’ is
often omitted and the term used is simply the ‘profit margin’.
Basic Earning Power
The basic earning power (BEP) ratio is calculated by dividing earnings before interest and taxes (EBIT) by
total assets:
Basic earnings power 1 BEP ratio 2 5
Total assets
Chapter 3
Understanding Financial Statements Part 2: Analysing and Managing the Accounts 65
which in this case is:
1 870
5 8.1%
This ratio shows the earning power of the firm’s assets before the influence of taxes and leverage, and it is
useful for comparing firms with different tax situations and different degrees of financial leverage.
Return on Total Assets
The ratio of net income to total assets measures the return on total assets (ROA) after interest and taxes. This
ratio is also called the return on assets and is defined as follows:
Return on total assets 5
Net income to shareholders
Total assets
which in this case is:
1 379
5 6.0%
Rolls-Royce’s 6.0 per cent return then needs to be compared with other similar-risk investments. From
the investor’s point of view the interest is in the returns from the share rather than an interest in a particular
industry. An exception might be where an investor has good knowledge of the industry that he or she feels
enabled to a better understanding of the nonfinancial data.
The World Might Be Flat, but Global Accounting
Is Bumpy! The Case of IFRS versus FASB
In a flat world, distance is no barrier. Work flows to
where it can be done most efficiently, and capital
flows to where it can be invested most profitably.
If a radiologist in India is more efficient than one
in the United States, then images will be emailed
to India for diagnosis; if rates of return are higher
in Brazil, then investors throughout the world will
provide funding for Brazilian projects. One key to
‘flattening’ the world is agreement on common
standards. For example, there are common Internet standards so that users throughout the world
are able to communicate.
A glaring exc eption to s t andardization is
in ac counting. The Securities and Exchange
Commission (SEC) in the United States requires
firms to comply with standards set by the Financial
Accounting Standards Board (FASB). But the European Union requires all EU-listed companies to
comply with the International Financial Reporting
Standards (IFRS) as defined by the International
Accounting Standards Board (IASB).
IFRS tends to rely on general principle s,
whereas FASB standards are rules based. As the
recent accounting scandals demonstrate, many
US companies have been able to comply with US
rules while violating the principle, or intent, underlying the rules. The United States is likely to adopt
IFRS, or a slightly modified IFRS, but the question
is ‘When?’ The SEC estimated that a large company is likely to incur costs of up to $32 million
when switching to IFRS. So even though a survey
by the accounting firm KPMG indicates that most
investors and analysts favour adoption of IFRS, the
path to adoption is likely to be bumpy.
Sources: See the websites of the IASB and the FASB,
www.iasb.org.uk and www.fasb.org. Also see David M.
Katz and Sarah Johnson, ‘Top Obama Advisers Clash
on Global Accounting Standards’, 15 January 2009, at
www.cfo.com, and ‘Survey Favors IFRS Adoption’, 3 February 2009, at www.webcpa.com.
66 Part 1
The Company and Its Reporting Environment
Return on Common Equity
The ratio of net income to common equity measures the return on common equity (ROE):
Return on common equity 5
Net income to shareholders
Common equity
which in this case is:
1 379
5 21.9%
Shareholders invest to earn a return on their money, and this ratio shows how well they are doing in an
accounting sense. Although this figure seems very high, remember that the stock market valuation of the
equity is some 4.5 times higher than the book value. So in terms of the market’s view of return on equity, the
return would be 21.9/4.5 5 4.9%, considerably lower. We have to be careful in drawing too many conclusions
from one year. It may be that investors expect rapid income growth. They may see the possibility of new markets or political and regulatory changes in the future that would imply very promising prospects. Such future
expectations would increase the current valuation. Or it may be that this year is an exception. Much the same
can be said for all these ratios.
The DuPont Equation
Named after the large US multinational this equation attempts to combine business and shareholder interests as follows where ROE represents return on equity:
Net income
Total assets
Total assets
Common equity
which in words for the right-hand side is:
(Profit margin) × (Total assets turnover) × (Equity multiplier)
and in numbers:
1 379
15 513
5 21.9%
6 303
or 8.9% × 67.3% × 3.66 5 21.9%.
The concept of an equity multiplier can be seen as a measure of leverage—the higher the borrowing the
higher the equity multiplier. So the analysis combines a financial measure with operating measures, though
it has to be said that these ratios are normally treated separately in analysis.
Risk Ratios
Debt Management Ratios
The extent to which a firm uses debt financing is called financial leverage. Here are three important
1. Shareholders can control a firm with smaller investments of their own equity if they finance part of the
firm with debt.
2. If the firm’s assets generate a higher pre-tax return than the interest rate on debt, then the share­
holders’ collect the surplus and returns are magnified, or ‘leveraged’. Conversely, shareholders’ losses
Chapter 3
Understanding Financial Statements Part 2: Analysing and Managing the Accounts 67
are also magnified if assets generate a pre-tax return less than the interest rate and the extra has to
be paid.
3. If a company has high leverage, even a small decline in performance might cause the firm’s value to
fall below the amount it owes to creditors. Therefore, a creditor’s position becomes riskier as leverage
Leverage Ratios
Rolls-Royce’s primary types of money owed are notes payable (bonds, see Figure 3-2), but companies also
might report the portion of long-term money owed due within a year, the value of capitalized leases, and
other types of obligations that charge interest.
Is this too much debt (money owed) for Rolls-Royce, not enough, or the right amount? To answer this
question, we begin by calculating the percentage of Rolls-Royce’s assets that are financed by debt. The ratio
of total debt to total assets is called the debt-to-assets ratio. It is usually shortened to the debt ratio. Total debt
is the sum of all short-term debt and long-term debt; it does not include other liabilities such as accounts payable (creditors). Rolls-Royce’s debt ratio is:
Debt-to-assets ratio 5 Debt ratio 5
Total debt
Total assets
which in this case is:
2 164 1 207
5 10.3%
Rolls-Royce’s debt ratio is 10.3 per cent, which is very low. A second ratio is debt-to-equity, defined as
Debt-to-equity ratio 5
Total debt
Total common equity
which in this case is:
2 164 1 207
5 37.6%
6 303
The debt-to-equity ratio shows that Rolls-Royce has £0.376 of debt for every pound of equity, which again is
very low. A comparable firm, United Technologies, has ratios of 21 per cent and 62 per cent for ­debt-to-assets
F i g u r e 3 -2
Long-Term Liabilities for Rolls-Royce, 2013 (£m)
Non-current liabilities
Bank loans
7.125% notes 2016
6.55% notes 2013
6.75% notes 2019
2.125% notes 2021
3.375% notes 2026
Source: Rolls Royce 2013 Annual Report, http://ar.rolls-royce.com/2013/
2 164
68 Part 1
The Company and Its Reporting Environment
and debt-to-equity ratios respectively, approximately twice the Rolls-Royce ratios. Be sure you know how a
ratio is defined before you use it. Some sources, for instance, define the debt ratio using only long-term debt
instead of total debt. Some sources make similar changes in the debt-to-equity ratio. Always be cautious about
your findings and do not report greater detail than is justified by figures.
Sometimes it is useful to express debt ratios in terms of market values. It is easy to calculate the market
value of equity, which is equal to the share price multiplied by the number of shares. Rolls-Royce’s market
value at 31 December 2013 was £23 973m of equity which on the balance sheet is 6303 2 698 5 £5605m. The
market value is therefore over four times greater than the book value (23 973/5605 5 4.3). Often it is difficult
to estimate the market value of debt, so many analysts use the debt reported in the financial statements. The
market debt ratio is defined as:
Market debt ratio 5
Total debt
Total debt 1 Market value of equity
which in this case is:
2 164 1 207
5 9.0%
2 164 1 207 1 23973
Rolls-Royce’s market-to-book ratio in 2012 was 2.9, considerably less than the 4.3 in 2013. A major factor
was a 46 per cent increase in the market capitalization due in the main to a share price increase—so a considerable increase in market expectations as to the future value. Thus, the market-to-debt ratio reflects a source
of risk that is not captured by the conventional debt ratio.
Finally, the ratio of total liabilities to total assets shows the extent to which a firm’s assets are not financed
by equity. The liabilities-to-assets ratio is defined as:
Liabilities-to-assets ratio 5
Total liabilities
Total assets
which in this case is:
5 72.7%
Checking similar ratios is worthwhile to ensure that they are aligned and that there is not some peculiarity that is being missed.
For all the ratios we examined, Rolls-Royce has less leverage and hence less risk than its industry peers.
The next section shows how close Rolls-Royce might be to financial distress!
Ability to Pay Interest
The times-interest-earned (TIE) ratio, also called the interest coverage ratio, is determined by dividing earnings before interest and taxes (EBIT in Figure 3-1) by the interest expense:
which in this case is:
Times-interest-earned 1 TIE 2 ratio 5
Interest expense
1 870
5 32.2 times!
In line with the conservative financing policies there is absolutely no doubt that Rolls-Royce will be able
to meet its interest payments. Nevertheless, the ratio is important in that failure to meet this obligation can
bring legal action by the firm’s creditors, possibly resulting in bankruptcy. Note that earnings before interest
and taxes, rather than net income, is used in the numerator. Because interest is paid with pre-tax pounds, the
firm’s ability to pay current interest is not affected by taxes.
Chapter 3
Understanding Financial Statements Part 2: Analysing and Managing the Accounts 69
Ability to Service Debt: EBITDA Coverage Ratio
The TIE ratio is useful for assessing a company’s ability to meet interest charges on its debt, but this ratio has
two shortcomings:
1. Interest is not the only fixed financial charge—companies must also reduce debt on schedule, and many
firms lease assets and thus must make lease payments. Failure to repay debt or meet lease payments may
force them into bankruptcy.
2. EBIT (earnings before interest and taxes) does not represent all the cash flow available to service debt,
especially if a firm has high depreciation and/or amortization charges. A better coverage ratio would
take into account the ‘cash’ earnings and the other financial charges. A commonly used measure is
EBITDA (earnings before interest, tax, depreciation and amortization).
Perhaps the use of EBITDA is not necessary given the high coverage. Nevertheless, by looking at the notes
to the accounts in the annual report as well as Figure 3-1, Rolls-Royce’s EBITDA coverage ratio is:
EBITDA coverage ratio 5
EBITDA 1 lease payments
Interest 1 Principal payments 1 lease payments
which in this case is:
1 870 1 1 231
5 2.1 times
111 1 133 1 1 231
although in this case due to the complexity of the accounts the figures are not transparent—such is the problem of ratio analysis in practice. In this case however, there is no evidence of cash flow problems from any of
the ratios or from the cash flow statement.
The EBITDA coverage ratio is most useful for relatively short-term lenders such as banks, which rarely
make loans (except real estate-backed loans) for longer than about five years. Over a relatively short period,
depreciation-generated funds can be used to service debt. Over a longer time, those funds must be reinvested
to maintain the plant and equipment or else the company cannot remain in business. Therefore, banks and
other relatively short-term lenders focus on the EBITDA coverage ratio, whereas long-term bondholders
focus on the TIE ratio.
S E L F -T E S T
How does the use of financial leverage affect current shareholders’ control position?
Name six ratios that are used to measure the extent to which a firm uses financial leverage, and
write out their equations.
A company has EBITDA of €600 million, interest payments of €60 million, lease payments of
€40 million, and required principal payments (due this year) of €30 million. What is its EBITDA
coverage ratio? (Answer: 4.9.)
Current Asset Management
Liquidity: Current and Quick Ratios, Debtor and Creditor Days
As shown in Figure 3-1, Rolls-Royce has current liabilities of £9780m that it must pay off within the coming
year. Will it have trouble satisfying those obligations? This depends on how easily Rolls-Royce can change its
sales into cash. Liquidity ratios attempt to answer this type of question.
The current ratio is a very basic measure that asks whether or not there are enough short-term realizable assets on the balance sheet date to pay the creditors in reasonably short time. Current assets normally include cash, marketable securities, accounts receivable and inventories. Current liabilities consist of
accounts payable, short-term notes payable, current maturities of long-term debt, accrued taxes and other
accrued expenses.
70 Part 1
The Company and Its Reporting Environment
The simple calculation is to divide current assets by current liabilities. The basic calculation is:
Current ratio 5
Current assets
Current liabilities
which in this case is:
5 1.3
9 780
Suppose that a supplier is trying to decide whether to extend credit to Rolls-Royce. In general, creditors
like to see a high current ratio. If a company starts to experience financial difficulty, it will begin paying
its bills (accounts payable) more slowly and borrowing more from its bank, so its current liabilities will
be increasing. If current liabilities are rising faster than current assets, then the current ratio will fall,
and this could spell trouble. It cannot be emphasized enough, however, that there is no absolute measure
of current ratio. Unfortunately, some texts say that it should be 2, but this is untrue. It depends on how
quickly customers pay—see the debtor days (in what follows). Thus, a large retail operation where the
customers pay in cash is likely to have a very low current ratio, possibly below 1. This is not a sign of poor
current asset management.
Now consider the current ratio from the shareholder perspective. A high current ratio could mean that
the company has a lot of money tied up in nonproductive assets, such as excess cash or marketable securities.
Or perhaps the high current ratio is due to large inventory holdings, which might become obsolete before
they can be sold. Thus, shareholders might not want a high current ratio.
An industry average is not a magic number that all firms should strive to maintain—in fact, some
well-managed firms will be above the average, while other good firms will be below it. However, if a firm’s
ratios are far from the averages for its industry, this is a red flag, and analysts should be concerned about why
the variance occurs. For example, suppose a low current ratio is traced to low inventories. Is this a competitive advantage resulting from the firm’s mastery of just-in-time inventory management, or is it an Achilles’
heel that is causing the firm to miss shipments and lose sales? Ratio analysis doesn’t answer such questions,
but it does point to areas of potential concern.
The quick ratio, also called the acid test ratio, is calculated by deducting inventories from current assets
and then dividing the remainder by current liabilities:
Quick ratio 5
Current assets 2 Inventories
Current liabilities
which in this case is:
12 818 2 3 319
5 0.97
9 780
A liquid asset is one that trades in an active market, so it can be converted quickly to cash at the going
market price. Inventories are typically the least liquid of a firm’s current assets; hence they are the current
assets on which losses are most likely to occur in a bankruptcy. Therefore, a measure of the firm’s ability to
pay off short-term obligations without relying on the sale of inventories is important. The reference to water
(liquidity) is appropriate in that there has to be a balance between cash coming in from receivables and cash
going out in the form of payments to suppliers. If the rate of going out is greater than the incoming rate the
cash resources of the company will run dry!
An important fact to remember is that companies do not have control over the rate at which their customers pay—they can encourage with discounts but little more. In contrast, companies have total control
over the time they take to pay their suppliers. Their suppliers may tempt them with discounts or threats to
not supply in the future but little more. Quite large companies can be poor payers, taking advantage of their
market position (e.g. when the small supplier relies on the order).
Chapter 3
Understanding Financial Statements Part 2: Analysing and Managing the Accounts 71
As we have said, critical to liquidity is the rate at which the debtors or receivables pay—the money coming
in. This is measured by debtor days1 calculated as:
Debtor days 5
3 365
which in this case is:
5 092
3 365 5 120 days
For United Technologies the debtor days are 66. The type of business must be taken into account. If RollsRoyce were a retail business such as a supermarket operation the debtor days would be extremely poor as
customers should pay on purchase. Rolls-Royce however is engaged in contracts where payment will be made
in stages. Further analysis should look at the dynamic position, whether it has improved, remained static or
worsened over the years. Providing the method of operation has remained relatively constant over the years
we would then be comparing like with like.
Relevant to assessing debtor days is the time taken to pay creditors, i.e. creditor days. This is calculated as:
Creditor days 5
3 365
Purchases are not easily established from the accounts; as a very crude estimate, cost of sales has been
taken along with other costs, so:
7 045
3 365 5 183 days
12197 1 1 781
A reading of the report indicates a special arrangement with suppliers described as: ‘RRSAs (Risk and
Revenue Sharing Arrangements) with key suppliers are a feature of the civil aerospace business. Under
these arrangements the workshare partner shares in the risks and costs of developing an engine and during
the production phase’ (page 11, Rolls-Royce Annual Report 2013). Clearly, cash flow is subject to these
special arrangements and any conclusions should be cautious. All that can be said is that, based on these very
approximate estimates, there is no evidence that suppliers are demanding payment in a shorter time period
than debtors are taking to pay—the ‘money in’ appears to be matching the ‘money out’.
More generally, it should be remembered that the creditor and debtor days are averages—there may be
debtors who are taking longer to pay and creditors having to wait longer for reasons that include disputes,
delivery problems, special agreements as well as reluctance.
S E L F -T E S T
Identify two ratios to use to analyse a firm’s liquidity position, and write out their equations.
What are the characteristics of a liquid asset? Give some examples.
Which current asset is typically the least liquid?
A company has current liabilities of €800 million, and its current ratio is 2.5. What is its level of
current assets? (Answer: €2000 million.) If this firm’s quick ratio is 2, how much inventory does it
have? (Answer: €400 million.)
The inventory turnover ratio is defined as costs of goods sold (COGS) divided by inventories. Occasionally,
where information is limited, ratios use sales instead of COGS. However, sales revenue includes costs and
Also called days sales outstanding (DSO), and the average collection period (ACP).
72 Part 1
The Company and Its Reporting Environment
profits, whereas inventory usually is reported at cost. Therefore, it is better to compare inventory with costs
rather than sales. The figures for Rolls-Royce are:
Inventory turnover 5
Cost of goods sold
Average inventory
The inventory for the previous year was 2726m so the average is (3319 1 2726)/2 5 3023m
5 4.0
so stock on average is sold out and restocked, or ‘turned over’, four times a year or in about 365/4 5 90 days.
This seems very approximately in line with the debtor and creditor days. Clearly production is a slow business. Inventory is not attractive apart from the logistic need as it does not earn money until sold. However,
whether or not inventory can be reduced is a technical matter where a greater knowledge of the business is
required. Some insight can be gained through comparisons. Inventory turnover for United Technologies was
4.4, indicating a slightly lower average holding of stock than Rolls-Royce. This may be due to a number of
factors, not least being a different mix of products, but the difference is not that great.
Other Asset Ratios
The Total Assets Turnover Ratio
The total assets turnover ratio measures the pounds in sales that are generated for each pound that is tied up
in assets:
Total assets turnover ratio 5
Total assets
which in this case is:
15 513
5 0.7
23 063
For United Technologies the ratio is also 0.7. As with engineering firms, the sales per pound investment in
assets are lower but the profit margin is higher. This reflects the high degree of skill and expertise involved in
design and manufacture, selling aircraft engines is not the same as selling beans!
Fixed Assets Turnover Ratio
The fixed assets turnover ratio adjusts for current assets and measures how effectively the firm uses its plant
and equipment. It is the ratio of sales to net fixed assets:
Fixed assets turnover ratio 5
Fixed assets
which in this case is:
15 513
5 1.5
10 245
United Technologies fixed assets ratio is 1.0 so it would appear that Rolls-Royce generates higher sales
from its fixed assets than United Technologies. There could be many reasons for this difference. We know
that the market values the equity at over four times the balance sheet value. Clearly this refers to the fixed
assets whose value in the view of the market is understated, maybe through missing intangible assets such as
engineering expertise. This may be less the case for United Technologies; in fact the market-to-book value is
only 3.3 so perhaps their assets are less understated, hence a lower fixed assets turnover ratio. It should also
be remembered that the products may not be directly comparable.
Chapter 3
Understanding Financial Statements Part 2: Analysing and Managing the Accounts 73
The Price Is Right! (Or Wrong!)
How much is an asset worth if no one is buying
or selling? The answer to that question matters
because an accounting practice called ‘mark to market’ requires that some assets be adjusted on the
balance sheet to reflect their ‘fair market value’. The
accounting rules are complicated, but the general
idea is that if an asset is available for sale, then the
balance sheet would be most accurate if it showed
the asset’s market value. For example, suppose a
company purchased $100 million of Treasury bonds
and the value of those bonds later fell to $90 million.
With mark to market, the company would report
the bonds’ value on the balance sheet as $90 million, not the original purchase price of $100 million.
Notice that marking to market can have a significant
impact on financial ratios and thus on investors’
perception of a firm’s financial health.
But what if the assets are mortgage-backed securities that were originally purchased for $100 million? As defaults increased during 2008, the value
of such securities fell rapidly, and then investors
virtually stopped trading them. How should the
company report them? At the $100 million original price? At a $60 million price that was observed
before the market largely dried up? At $25 million
when a hedge fund in desperate need for cash to
avoid a costly default sold a few of these securities? At $0, because there are no current quotes? Or
should they be reported at a price generated by a
computer model or in some other manner?
The answer to this is especially important during
times of economic stress. The US Congress, the SEC,
FASB and the US Treasury all are working to find the
right answers. If they come up with a price that is too
low, it could cause investors mistakenly to believe
that some companies are worth much less than their
intrinsic values, and this could trigger runs on banks
and bankruptcies for companies that might otherwise survive. But if the price is too high, some ‘walking dead’ or ‘zombie’ companies could linger on and
later cause even larger losses for investors, including
the US government, which is now the largest investor in many financial institutions. Either way, an error
in pricing could perhaps trigger a domino effect that
might affect the entire financial system.
Inflation can cause problems when interpreting the fixed assets turnover ratio because fixed assets are
reported using the historical costs of the assets, whereas sales are at current prices. Therefore, a mature firm with
fixed assets acquired years ago might well have a higher fixed assets turnover ratio than a younger company with
newer fixed assets that are reported at inflated prices relative to the historical prices of the older assets. However,
this would reflect the difficulty accountants have in dealing with inflation rather than inefficiency on the part of
the new firm. You should be alert to this potential problem when evaluating the fixed assets turnover ratio.
S E L F -T E S T
Identify four ratios that measure how effectively a firm is managing its assets, and write out their
What problem might arise when comparing firms’ fixed assets turnover ratios?
A firm has €200 million annual sales, €180 million costs of goods sold, €40 million of inventory, and
€60 million of accounts receivable. What is its inventory turnover ratio? (Answer: 4.5.) What is its DSO
based on a 365-day year? (Answer: 109.5 days.)
Market Value Ratios
Market value ratios relate a firm’s share price to its earnings, cash flow and book value per share. The ratios
are a way of measuring the value of a company’s share relative to that of another company.
74 Part 1
The Company and Its Reporting Environment
Price/Earnings Ratio
The price/earnings (P/E) ratio shows how much investors are willing to pay per pound or euro of reported
earnings. Alternatively, it can be seen as how many years profit is in the share price:
Price/earnings 1P/E 2 ratio 5
Price per share
Earnings per share
Another approach is to use total rather than per share values:
Price/earnings 1 P/E 2 ratio 5
Market capitalization
Earnings due to shareholders
which in both cases equates to:
27 974
5 20.3
1 379
There are a number of interpretations of this ratio. Companies that have a relatively high P/E ratio may be
regarded as very safe, so the share price is a high multiple of earnings. Alternatively, the P/E ratios are higher
for firms with strong growth prospects. The P/E ratio for United Technologies is 18.25, so very similar. The
S&P 500 average for 31 December 2013 was 18.2. One has to be careful to be sure that the earnings figure is
representative of expectations and not an exception.
Price/Cash Flow Ratio
Share prices depend on a company’s ability to generate cash flows. Consequently, investors often look at the
price/cash flow ratio, where cash flow is defined as net income plus depreciation and amortization:
Price/cash flow ratio 5
Market capitalization
Cash flow from operations
which in this case, taking the cash flow statement from Chapter 2, is:
27 974
5 20.0
1 402
A difference would occur if there were significant non-cash items in the income statement that was not
offset by other earnings. This is not the case for Rolls-Royce.
Market Capitalization/EBITDA
The market capitalization/EBITDA ratio (remembering that market capitalization is price × number of
shares) is similar to the market capitalization/cash flow ratio, except the market capitalization/EBITDA ratio
measures performance before the impact of interest expenses and taxes, making it a better measure of operating performance. Rolls-Royce’s market capitalization/EBITDA is 23 974/(1870 1 1231) 5 7.7 so it is again a
high multiple of earning power.
Market/Book Ratio
Much has already been said of the market-to-book ratio.2 It is the ratio of a share’s market price to its book
value, more easily calculated in total terms as:
Market-to-book ratio 5
Sometimes reversed as book-to-market ratio.
Market capitalization
Balance sheet value of shareholder interest
Chapter 3
Understanding Financial Statements Part 2: Analysing and Managing the Accounts 75
which in this case is:
5 4.4
6 303
So the market values the shareholder interest in the company 4.4 times higher than the balance sheet.
Investors are willing to pay £4.4 for every £1 of equity value on the balance sheet. In some respects this
undermines all the valuations on the balance sheet—the market clearly thinks that much is missing.
However, providing that the differences are relatively stable between firms and across time, comparisons can
still be made. So we can say that companies with relatively high rates of return and good prospects generally
sell at higher multiples of book value than those with low returns.
The book value is a record of the past, showing the cumulative amount that shareholders have invested
by purchasing assets. 3 In contrast, the market price of shares is forward looking, incorporating investors’
current expectations of future cash flows. For example, at the end of 2012 Rolls-Royce’s market-to-book ratio
was less than 3, reflecting the lower market expectations for the economy as a whole, and in particular the
airline industry and marine and defence industries.
S E L F -T E S T
Describe three ratios that relate a firm’s share price to its earnings, cash flow and book value per
share, and write out their equations.
What does the price/earnings (P/E) ratio show? If one firm’s P/E ratio is lower than that of another,
what are some factors that might explain the difference?
How is book value per share calculated? Explain why book values often deviate from market values.
A company has €6 billion of net income, €2 billion of depreciation and amortization, €80 billion of
common equity, and 1 billion shares. If its share price is €96 per share, what is its price/earnings ratio?
(Answer: 16.) Its price/cash flow ratio? (Answer: 12.) Its market/book ratio? (Answer: 1.2.)
An Evaluation of the Ratio Approach
Ratios can and are used by companies to compare performance over time. In a wider context, sometimes
referred to as valuation using multiples or the method of multiples, a comparison can include similar companies or the industry or a selected peer group. As noted above, databases make such comparisons increasingly
available at least on published data; but also, firms may subscribe to private comparisons using unpublished
data. There are a number of difficulties with assessment by ratios that have been raised in context above; here
we collect them together:
1. A ratio is susceptible to extremes. A price/earnings ratio may be extremely high if the company has a bad
year that the market regards as an exception, giving the impression of a very safe firm.
2. A ratio has no size measure. High profitability for a very small enterprise is not really comparable with a
much larger enterprise.
3. Comparisons with other companies or with averages are only ever going to be approximate; firms’ activities are never identical.
4. Figures such as debtor days are averages which may conceal large variations—in this case a large number
of long term debts may be offset by short term debts.
5. Ratios are not always relevant. Stock days for a service company is of little value.
6. Values may be inaccurate due to conservative accounting conventions. Items such as assets and goodwill
may have very different market values compared with the balance sheet value. The market-to-book ratio
is an indication of the disparity.
7. Business processes may make a ratio misleading. For example, creditor days might be very high because
suppliers have agreed to offer credit by agreeing to delayed repayment.
Recorded at historic cost, the cost at the time of purchase. Adjustment to current values depends on the accounting standards being
76 Part 1
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8. The ratio time period may not be appropriate. Balance sheet dates may be at a time when stock is especially high or low giving a misleading impression.
Practitioners are well aware of these faults and will make subjective adjustments in meetings. Ratios serve
as a useful starting point for asking further questions, but they should never be regarded as a sufficient basis
for conclusions.
Preparing a Report
Trends and Comparisons
Trends give clues as to whether a firm’s financial condition is likely to improve or deteriorate. A trend analysis examines a ratio over time. Figure 3-3 shows that Rolls-Royce’s profit margin has been very variable but
is much better now than ten years ago. Comparisons can be useful but must be treated with caution. In this
case the profit margin of United Technologies has been used as a comparison; but it must be remembered
that these accounts have not been prepared under the same set of accounting standards. All the other ratios
could be analysed similarly. Whether they should be or not really depends on whether the comparison is
Note that absolute numbers are of limited value, especially in any comparison. Some companies are,
of course, larger than others—that is not a difference that interests us. Using percentages and ratios controls for size and currency differences. A comparison may extend even to converting all the numbers into a
­percentage—so all the income statement as a percentage of sales and all the balance sheet as a percentage of
total assets. Figure 3-4 is an example of the income statement in percentage form.
Comparing the percentage statements as in Figure 3-4 it is tempting to argue that manufacture in United
Technologies is more efficient with an EBITDA of 17.6 per cent as opposed to 15.1 per cent, However, the
F i g u r e 3 -3
Rolls-Royce and United Technologies Profit Margins (%)
United Technologies
Source: Rolls Royce 2013 Annual Report, http://ar.rolls-royce.com/2013/
Chapter 3
Understanding Financial Statements Part 2: Analysing and Managing the Accounts 77
Figur e 3- 4
Rolls-Royce and United Technologies Comparison
Net Sales
Cost of Goods Sold
Research & Development Expenses
Other Operating Items
Total Deprec., Amort. & Depletion
Amortization & Depletion
Operating Income After Depr. & Amort.
Unusual/Exceptional Items
Earnings Before Interest & Tax
Financial Revenue
Financial Expenses
Financial P/L
Other Non Oper./Financial Inc./Exp.
Earnings Before Tax
Income Taxes
Earnings After Tax
Minority Interest
Extraordinary Items After Tax
Preferred Dividends
Net Profit
Source: Rolls Royce 2013 Annual Report, http://ar.rolls-royce.com/2013/
differences are small and it is arguable that the differences in the activities of the two companies might well
be sufficient to explain the gap. So materiality (the size of the differences) and measurement issues should
never be forgotten. Finally, notice that the format has changed from Figure 3-1 simply to enable comparison.
S E L F -T E S T
What is a trend analysis, and what information does it provide?
What is common size analysis?
What is percentage change analysis?
In the analysis so far, the performance of Rolls-Royce has been compared or benchmarked against the US
company United Technologies. No comparison is perfect—in this case products and markets can differ, especially with respect to the defence industry. The industry may be used as a benchmark and databases aid such
comparisons. Comparative ratios are available from a number of sources, including Value Line, Dun and
Bradstreet (D&B), and the Annual Statement Studies published by Risk Management Associates, which is the
national association of bank loan officers. Each data-supplying organization uses a somewhat different set of
ratios designed for its own purposes. For example, D&B deals mainly with small firms, many of which are
proprietorships, and it sells its services primarily to banks and other lenders. Therefore, D&B is concerned
largely with the creditors’ viewpoint, and its ratios emphasize current assets and liabilities, not market value
78 Part 1
The Company and Its Reporting Environment
ratios. So, when you select a comparative data source, you should be sure that your own emphasis is similar
to that of the agency whose ratios you plan to use. Additionally, there are often definitional differences in the
ratios presented by different sources, so before using a source, be sure to verify the exact definitions of the
ratios to ensure consistency with your own work.
S E L F -T E S T
Compare and contrast trend analysis and comparative ratio analysis.
Explain benchmarking.
Writing a Report
Whether as a management report in a company or a report for investment analysts, or even as an academic
exercise, there are a number of issues concerning the preparation of a report:
1. The overall objective of the report should be clearly stated at the start. If the report is being prepared
with a view to investment then the report should address risk and return with liquidity as an important
check. If the report is for a supplier then liquidity is important.
2. Given that the objectives have been set, the overall structure of the report must be clear.
3. The objectives must dominate the ratios. A poor report is one that simply lists out the ratios and then
goes from one to the other making brief comments along the way (the ‘washing line’ approach).
4. If objectives are dominating then simple measures may be used to support the ratios. The sales over the
years, or the percentage movements are often as important as the ratios.
5. Absolute numbers can mean very little. Percentages are far better.
6. Do not use the value judgements that you find in the reports you use. Always be sceptical.
7. Always remember that all measures are subject to measurement problems. Any analysis must address
the possibility that a difference could be due to measurement.
8. It is always better to use your own ratios rather than one prepared by a database. Their descriptions are often
unclear. With your own ratios you will be always able to answer the question: ‘How did you calculate that?’
9. Always remember materiality—if the numbers are small, should you be commenting on them?
10. It is always better to use the databases of your organization where possible. Finding ‘something on the
internet’ does not look good when there are data at least as good readily available in your organization.
11. Good reports are selective, highlighting the important information and keeping it in the main part of
the report and putting less important information in an appendix. But putting all data in appendices
makes a report unreadable.
12. Many large firms operate different divisions in different industries, and for such companies it is difficult
to develop a meaningful set of industry averages. Therefore, industry averages are more meaningful for
small, narrowly focused firms than for large, multidivisional ones.
13. To set goals for high-level performance, it is best to benchmark on the industry leaders’ ratios rather
than the industry average ratios.
14. Inflation may badly distort firms’ balance sheets—reported values are often substantially different from
‘true’ values. Further, because inflation affects depreciation charges and inventory costs, reported profits are also affected. Thus, inflation can distort a ratio analysis for one firm over time or a comparative
analysis of firms of different ages.
15. Seasonal factors can distort a ratio analysis. For example, the inventory turnover ratio for a food processor will be radically different if the balance sheet figure used for inventory is the one just before versus
the one just after the close of the canning season. This problem can be minimized by using monthly
averages for inventory (and receivables) when calculating turnover ratios if possible.
16. Firms can employ ‘window dressing’ techniques to make their financial statements look stronger. To illustrate, suppose a company takes out a two-year loan in late December. Because the loan is for more than
one year, it is not included in current liabilities even though the cash received through the loan is reported
as a current asset. This improves the current and quick ratios and makes the year-end balance sheet look
stronger. If the company pays the loan back in January, then the transaction was strictly window dressing.
Chapter 3
Understanding Financial Statements Part 2: Analysing and Managing the Accounts 79
17. Companies’ choices of different accounting practices can distort comparisons. For example, choices of
inventory valuation and depreciation methods affect financial statements differently, making comparisons among companies less meaningful. As another example, if one firm leases a substantial amount of
its productive equipment, then its assets may appear low relative to sales (because leased assets often do
not appear on the balance sheet).
In summary, conducting ratio analysis in a mechanical, unthinking manner is dangerous. But when ratio
analysis is used intelligently and with good judgement, it can provide useful insights into a firm’s operations
and identify the right questions to ask.
Working Capital Management
We now turn to management issues. Working capital management involves two basic questions:
• What is the appropriate amount of working capital, both in total and for each specific account?
• How should working capital be financed?
Note that sound working capital management goes beyond finance. Indeed, improving the firm’s working capital position generally comes from improvements in the operating divisions. For example, experts in
logistics, operations management and information technology often work with engineers and production
specialists to develop ways to speed up the manufacturing process and thus reduce the goods-in-process
inventory. Similarly, marketing managers and logistics experts co-operate to develop better ways to deliver
the firm’s products to customers. Finance comes into play in evaluating how effective the firm’s operating
departments are relative to other firms in its industry and also in evaluating the profitability of alternative
proposals for improving working capital management. In addition, financial managers decide how much
cash their companies should keep on hand and how much short-term financing should be used to finance
their working capital.
Why is Working Capital a Problem?
To the reader who has not worked in a business, the term working capital may seem rather an abstract concept. So to make it more real we will spend a little time discussing the problems that working capital poses
for an example company. The assets and liabilities are outlined in Table 3-1.
We will start with the least controllable item from a company’s point of view—namely, debtors. Imagine
the company has made the product or delivered the service, staff have been paid, expenses have been met,
Ta b l e 3 -1
An Example of Working Capital
Current Assets
(turned into cash in less than a year)
Accounts receivable (Debtors)
less Current Liabilities
(due in less than a year)
Accounts payable (Creditors)
equals Working Capital
80 Part 1
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suppliers will likely have been paid, the product or service has been delivered, the company has sent the customer the bill . . . and is waiting for payment! So how have these payments been made given that no cash has
been received? Obviously, the company will have to write out the cheques and the bank balance will go into
overdraft. Bank overdraft is a major provider of working capital. Is this a problem? Well, yes! Firstly the bank
will have a limit as to how much can be borrowed. Secondly, it is expensive. A bank overdraft is the most expensive form of borrowing as the bank is providing a valuable service, meeting shortfalls as and when required.
There is no easy solution to trying to turn debtors into cash. A discount can be given for early payment,
but that affects profits. Loan schemes may be offered for high price items. Pressure can be put on the customers for payment, but salesmen are likely to be worried about losing their clients as a result.
The next most difficult item to control is stock. Clearly, for firms engaged in production, stock is often
a necessity. If a company produces 100 fridges a week then how is it going to meet an order for 500 fridges
unless it builds up stock? It cannot say to such a customer ‘please wait five weeks’. So a solution is again not
easy. Can production be increased without excessive investment? Can customers indeed wait? Can the transport logistics be improved?
A service company faces different problems. If it is a restaurant then clearly it cannot store food for long
periods. If it is a consultancy then it will not have significant stock. It is important to understand that net
working capital, namely current assets less current liabilities, is very different from one firm to another.
There is also the issue of cash. A supermarket must keep cash in the tills as must all retail operations.
Finance and banking type operations must keep cash to meet withdrawals. Holding cash itself is an unproductive asset either held physically as cash or on demand in a bank account—in both cases, it is not earning
The most controllable figure is creditors, and this is often forgotten by students when writing about working capital; but it is very clear in practice as the accountant tells the purchasing clerk which bills to pay. We
said earlier, as part of an example, that nonpayment by debtors was a problem because expenses and direct
costs such as materials will have been paid. But in practice this might not be entirely the case. Faced with
nonpayment by customers a firm may well decide to delay payment to its own suppliers. The firm can decide
exactly who is going to be paid, it can decide exactly its outstanding payments and hence the creditor figure
at the end of each month and year. Delaying payment is, however, not an attractive proposition. There may
be discounts for early payment that are being missed. There is the possibility that the suppliers may refuse to
supply in future due to late payment, or they may demand prepayment in future. Even worse, there may be a
meeting of creditors to petition the company for a winding-up order.
So, where the relatively unproductive assets of debtors, stock and cash cannot be financed by creditors, the
balance has to be made up by working capital, which is by its nature expensive. Bank overdrafts and shortterm loans are needed to make the payments for wages, expenses and purchases necessary to keep the firm
going, hence the term working capital.
These matters are important even for large companies such as Rolls-Royce who note in their 2013 accounts
(page 10): ‘Net working capital improved slightly, reflecting a good second half performance on inventory
and higher deposits, mainly in Civil, flowing from the order intake. We made good progress on inventory,
improving turns from 3 to 3.4 times (excluding Power Systems), helped by a consistent focus in the second
half of the year.’
Using and Financing Operating Current Assets
Operating current assets (CA) are used to support sales. High stocks means that the company can meet large
orders, high debtors means that the customers do not have to pay immediately. The drawback is that no
direct profit is being earned on current assets. Having too much invested in operating CA is inefficient, but
having too little might constrain sales.4 Many companies have seasonal, growing sales, so they have seasonal
growing operating CA, which has an implication for the pattern of financing that companies choose. The
next sections address these issues.
For ratio measurement see above.
Chapter 3
Understanding Financial Statements Part 2: Analysing and Managing the Accounts 81
Efficient Use of Operating Current Assets
Most companies can influence their ratios of operating current assets to sales. Some companies choose a
relaxed policy and hold a lot of cash, receivables and inventories relative to sales. On the other hand, if a firm
has a restricted policy, holdings of current assets are minimized and we say that the firm’s policy is tight or
‘lean and mean’. A moderate policy lies between the two extremes.
We can use the DuPont equation (see below) to demonstrate how working capital management affects the
return on equity and hence the routes to efficient management:
Return on equity 5 Profit margin 3 Total assets turnover 3 Equity multiplier
Net income Sales Assets
Assets Equity
Assuming for clarity that the equity multiplier is constant, thus Equity
5 constant, a relaxed policy means a
higher level of assets leads to a lower total assets turnover ratio; this results in a lower ROE, other things held
constant. Conversely, a restricted policy results in lower current assets and a higher assets turnover hence
a higher ROE. However, the restricted policy exposes the firm to risk, because shortages can lead to work
stoppages, unhappy customers and serious long-run problems. The moderate policy falls between the two
extremes. The optimal strategy is the one that management believes will maximize the firm’s long-run free
cash flow and thus the share’s value.
Note that changing technologies can lead to changes in the optimal policy. For example, if a new technology makes it possible for a manufacturer to produce a given product in five rather than ten days, then workin-progress inventories can be cut in half. Similarly, many retailers have inventory management systems that
use bar codes on all merchandise. These codes are read at the cash register, the information is transmitted
electronically to a computer that adjusts the remaining stock of the item, and the computer automatically
places an order with the supplier’s computer when the stock falls to a specified level. This process lowers the
‘safety stocks’ that would otherwise be necessary to avoid running out of stock. Such systems have dramatically lowered inventories and thus boosted profits.
Financing Operating Current Assets
Investments in operating current assets must be financed, and the primary sources of funds include bank
loans, credit from suppliers (accounts payable), accrued liabilities, long-term debt and common equity.
Each of those sources has advantages and disadvantages, so a firm must decide which sources are best for it.
To begin, note that most businesses experience seasonal and/or cyclical fluctuations. For example, construction firms tend to peak in the summer, retailers peak around Christmas, and the manufacturers who
supply both construction companies and retailers follow related patterns. Similarly, the sales of virtually all
businesses increase when the economy is strong, so they increase operating current assets during booms but
let inventories and receivables fall during recessions. However, current assets rarely drop to zero—companies
maintain some permanent operating current assets, which are the operating current assets needed even at
the low point of the business cycle. For a growing firm in a growing economy, permanent current assets tend to
increase over time. Also, as sales increase during a cyclical upswing, current assets are increased; these extra
current assets are defined as temporary operating current assets as opposed to permanent current assets. The
way that permanent and temporary current assets are financed is called the firm’s operating current assets
financing policy. Three alternative policies are discussed next.
Maturity Matching or Self-liquidating Approach
An important principle of financial management is maturity matching. This applies to all investments. For
example, if a project that requires long-term funding is financed by a short-term loan, the loan would have
to be constantly rolled over—that is, new loans would have to be raised to pay for the early maturity of the
82 Part 1
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F i g u r e 3 -5
Current Asset Funding
Short term financing requirements
Temporary Level of Current Assets
Permanent Level of Current Assets
Fixed Assets
Note: expenditure above the dotted line has to be funded by short term sources including creditors.
short-term funding—and this would be a constant and expensive process. Such matching is also important
with working capital. Taking out a five-year loan for a requirement that might be for only a few months
would not be economic and would lead to the holding of excessive cash. For these reasons, temporary current
assets are financed with short-term debt. Inventory expected to be sold in 30 days would be financed with a
30-day bank loan; a machine expected to last for five years would be financed with a five-year loan; a 20-year
building would be financed with a 20-year mortgage bond; and so on.
The process is not exact, as one cannot be precise about the life of current assets. Some requirements will
be more or less constant, such as a certain stock level, and so may be funded by longer-term sources.
The problem of funding current assets is illustrated in Figure 3-5. Asset levels above the dotted line have
to be funded by short-term sources, there are two scenarios, A and B. The funding is needed only on a temporary basis. Line A is a relatively conservative approach whereby there are plenty of funds to support the
requirements and only occasionally is there a need for further short-term funding. Line B represents a more
aggressive approach, where there is a much greater need for short-term funds. This may be because the market is unwilling to lend to the company for longer periods.
Remember that short-term funding may come from delaying payment to creditors and in effect asking
them to fund operations. This is attractive to firms in one respect in that no interest is charged, but as discussed above it risks bankruptcy if funds run so short that the firm cannot pay its creditors.
S E L F -T E S T
Identify and explain three alternative current asset investment policies.
Use the DuPont equation to show how working capital policy can affect a firm’s expected ROE.
What are the reasons for not wanting to hold too little working capital? For not wanting to hold
too much?
Differentiate between permanent operating current assets and temporary operating current assets.
What does maturity matching mean, and what is the logic behind this policy?
What are some advantages and disadvantages of short-term versus long-term debt?
Chapter 3
Understanding Financial Statements Part 2: Analysing and Managing the Accounts 83
The Cash Conversion Cycle
All manufacturing firms follow a ‘working capital cycle’ in which they purchase or produce inventory, hold
it for a time, and then sell it and receive cash. Service companies have no inventory (stock) but apart from
that they have to sell their services and wait to receive payment. This process is known as the cash conversion
cycle (CCC).
For the purposes of illustration we will take the manufacturing company as an example. From a relatively
simple set of figures investors can make an estimate of the length of time taken by each of the processes. We
can get approximate answers to the following questions:
• How long are purchases held as
(a) raw materials?
(b) work in progress?
(c) finished goods?
• How long does it take to manufacture the product?
• How long does it take for customers to pay?
• How long does it take the company to pay its suppliers?
Surprisingly we can get a rough answer from the accounts.
We can answer our ‘How long . . .’ questions by measuring the average days each of the assets and
liabilities in Table 3-2 are held. So, ‘How long are purchases held in stock before becoming part of work in
progress?’ can be estimated by the general formula:
Days held 5
Asset or liability
Related revenue or cost per day
Stock Days
Starting with purchases and working through to finished goods, we have:
Raw materials
Cost of goods sold per day
1 5 12 days
1 013.9 3 365
Days held as raw materials 5
Ta b l e 3 -2
Selected Items from ABC plc Financial Statement (€m)
Annual sales
1 216.7
Cost of goods sold
1 013.9
Raw materials
Work in progress
Finished goods
Inventories (Stock)
Accounts receivable (Debtors)
Accounts payable (Creditors)
84 Part 1
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Days held as work in progress 5
Work in progress
Cost of goods sold per day
1 013.9 3
Days held as finished goods 5
5 22 days
Finished goods
Cost of goods sold per day
1 013.9 3
Stock days 5
5 16 days
Raw materials 1 Work in progress 1 Finished goods
Cost of goods sold per day
34.0 1 60.0 1 45.0
5 50 days
1 013.9 3 365
Hence in the example of Table 3-2 from purchase to finished goods (part of the CCC) takes on average
50 days. It should be remembered that these measures relate to often quite simple real-world facts. For instance,
a pub/restaurant chain such as Wetherspoon may have stock days of about 7 whereas a housebuilder such as
Bovis may have debtor days of over 100. (Why is this? Well, it takes longer to build a house than to make a
Each firm will have particular characteristics and in any analysis comparisons with previous years is
less subject to measurement error than between firms. In this example it may be that the firm feels that raw
material days of 13 is excessive. Why is there stock lying around in the stockyard for nearly two weeks on
Finally, it should be remembered that these figures are averages. It is the average of a range of products
and across a range of days. There may well be items in stock that have been there for over a year; some of the
products may well be in stock as finished goods for many months. We have only the average figure; we do not
know the variation within the sample.
Debtor Days
When a sale is made, often the reader will have paid either in cash or through their credit card. For such
businesses as retail outlets, cash flow and working capital management is not going to be a problem. In business-to-business trade, it is the practice to send an invoice that is in effect a demand for payment that is
normally to be within 30 days. Some customers will take far longer to pay. The annual accounts describes
debtors as ‘trade and other receivables’ or just ‘receivables’ and gives us an idea of the average time to pay by
applying the formula in Equation 3-2 as follows:
Debtor days 5
Sales per day
1 216.7 3
5 134 days
In this example debtor days is greatly in excess of 30 days and this serves as a reminder that each firm
should be evaluated in relation to the business and not against some overall standard. Rolls-Royce, for example, used the formula reported debtor days of 120 in 2014. Payments for a jet engine involves staged payments
and deposits—buying a jet engine is not the same as buying a laptop.
Chapter 3
Understanding Financial Statements Part 2: Analysing and Managing the Accounts 85
Ta b l e 3 -3
Cash Conversion Cycle for ABC plc
Raw materials days
Work in progress days
Finished goods
Inventories (Stock) days
Accounts receivable (Debtors) days
Accounts payable (Creditors) days
Days in cash conversion cycle
Creditor Days
The cycle is completed by considering the creditor days, termed ‘trade and other payables’ in many balance sheets. The buying market for a firm is different from its selling market, but in general if a firm has
high debtor days they are likely to have high creditor days. First let us have a look at the application of
Equation 3-2:
Cost of sales per day
1 5 41 days
1 013.9 3 365
Creditor days 5
For Rolls-Royce in 2014 the creditor days were 211, much higher than its debtor days. There may be
special finance arrangements with suppliers or measurement issues but large companies (not Rolls-Royce)
in general have been accused of being slow payers. A reason for this that is often advanced is that as a large
company they are large customers for their suppliers and they are taking advantage of their suppliers’
­concern that they might lose their business.
The Cash Conversion Cycle
We can now put the measures together to trace the flow of cash in the production process—see Table 3-3.
Such analysis provides the basis for further questions and ultimately the financial short-term policy
of the company. In this case debtor days is very much higher than the other measures and further investigation would seem necessary. As mentioned before, the days measures are just an average. In this case
one would want to know whether the high score may be due to one or two customers. More generally,
it would be useful to have more than just the average. For that we turn to the ageing of the assets and
Ageing Schedules
Ageing schedules answer simple questions such as how many debtors there are over 50, 100, 150 days, and
so on. The same idea can also be applied to stocks. There is no fixed or traditional schedule of time periods.
Table 3-4 illustrates the danger of relying on averages, as the modal figure is over 150 days in this example compared to debtor days of 134 (Equation 3-7). Bad debt policy will be tied to an ageing of debtors—for
example, the auditors may regard debts over 90 days require a 100 per cent provision. The limit will depend
upon traditions in the particular industry; it may be quite normal to pay in 100 days’ time in ABC’s industry.
Or the firm may be operating a credit policy, which we turn to next.
86 Part 1
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Ta b l e 3 - 4
Ageing of Debtors for ABC plc
Days old
% of total
Over 200
Total debtors
The Cost of Trade Credit
Firms that sell on credit have a credit policy that includes their terms of credit. For example, Microchip Electronics sells on terms of 2/10, net 30: It gives customers a 2 per cent discount if they pay within 10 days of the
invoice date, but the full invoice amount is due and payable within a further 20 days if the discount is not taken.
The ‘true price’ of Microchip’s products is the net price, or 0.98 times the list price (i.e. 2 per cent off the
list price), because any customer can purchase an item at that price as long as payment is made within ten
days. Now consider Personal Computer Company (PCC), which buys its memory chips from Microchip.
One chip is listed at €100, so its ‘true’ price to PCC is €98. Now if PCC wants an additional 20 days of credit
beyond the ten-day discount period, it must incur a finance charge of €2 per chip for that credit. Thus, the
€100 list price consists of two components:
List price 5 €98 true price 1 €2 finance charge
The question PCC must ask before it turns down the discount to obtain the additional 20 days of credit is,
could credit be obtained at a lower cost from a bank or some other lender?
So what is the cost of the credit? A 2 per cent charge for 20 days credit is the equivalent5 of 1.02 365
20 days − 1 5
0.435 or 43.5 per cent a year. In borrowing and lending terms it is as if after ten days the buyer (PCC)
­borrowed €98 from Microchip, then paid Microchip €98 for the goods, then repaid the loan from Microchip
€100 in 20 days’ time.6 That is strictly a charge of 100
98 – 1 5 2.04% so 1.0204 20 – 1 5 0.446 or 44.6%. Such
precision is, however, greater than is needed to take decisions. If the bank is charging 15 per cent on overdrafts then increasing the overdraft by making an early payment will be beneficial. Where the differences are
closer, say 5 per cent, then differences in administration costs may be more significant.
S E L F -T E S T
What is trade credit?
How does the cost of costly trade credit generally compare with the cost of short-term bank loans?
A company buys on terms of 2/12, net 28. What is the effective cost? (Answer: 56.1 per cent.)
Managing Short-Term Investments
Part of working capital is the investment needed to finance the operations of the company. We have already
shown in Figure 3-5 that the need for short-term capital can vary with the policy pursued by the firm. In the
following sections we examine the nature of such short-term investments other than creditors.
See Chapter 4 for an explanation of this formula.
Note that from Microchip’s perspective it is simply a payment of €100 in 30 days. It may seem odd to borrow from Microchip and then
immediately pay for the item, but this is an example of a common technique in finance. To price a ‘product’ (in this case the credit terms),
work out an alternative process that reproduces the same cash flows. The cost of this alternative must be the same as the ‘product’ we are
trying to price—i.e. the discount in this case. The law of one price in an efficient market maintains that the same cash flows cannot have
two different valuations (actually this is a requirement of all efficient markets) otherwise traders will be able to make a certain profit.
Chapter 3
Understanding Financial Statements Part 2: Analysing and Managing the Accounts 87
There are three reasons companies hold short-term investments: (1) for liquidation just prior to scheduled
transactions, (2) for unexpected opportunities, and (3) to reduce the company’s risk.
Some future transaction dates and amounts are known with a high degree of certainty. For example,
a company knows the dates on which it will need cash to make interest, principal and dividend payments; if
a company has decided to make a major purchase, such as a new machine or even a new factory, the company
knows the dates on which it will pay for the purchase. A company’s payment isn’t complete until the funds
have been deducted from the company’s bank account and credited to the depositor’s bank account. Because
a company doesn’t actually need a balance in the bank account until the payment is deducted, most companies try to keep their bank account balances (which pay zero or very low interest rates) as low as possible until
the day the payment is deducted. For example, if a company has a scheduled dividend payment, the company
is likely to hold the amount needed for the payment in the form of short-term investments such as T-bills or
other interest-paying short-term securities. The company will liquidate these short-term investments and
deposit the proceeds into its bank accounts just prior to the required payment date.
Short-term investments that are designated for making scheduled payments, such as those just described,
are temporary in the sense that a company acquires these short-term investments and plans to hold them for
a specific period and for a particular use. The following sections describe short-term investments that are
less transitory.
Some companies hold short-term investments even though they have not planned a specific use for them
and the rate of return on short-term investments is very low. For example, some companies compete in businesses that have growth opportunities that arise unexpectedly. If such a company does not have stable cash
flows or ready access to credit markets (perhaps because the company is small or does not have a high credit
rating), it might not be able to take advantage of an unexpected opportunity. Therefore, the company might
hold short-term investments, which are speculative balances in the sense that the company speculates that it
will have an opportunity to use them and subsequently earn much more than the rate on short-term investments. Studies show that such firms do hold relatively high levels of marketable securities. In contrast, cash
holdings are less important to large firms with high credit ratings, because they have quick and inexpensive
access to capital markets. As expected, such firms hold relatively low levels of cash.7
Holding short-term investments reduces a company’s risk of facing a liquidity crisis, such as the ones that
occurred during the economic downturn and credit crunch of the 2007 recession. A stockpile of short-term
investments also reduces transaction costs due to issuing securities because the investments can be liquidated instead.
Although there are good reasons many companies hold short-term investments, there are too many companies holding too much cash. Some companies, such as Apple and Microsoft, have very large cash-to-assets
ratios. Even with the uncertain economic environment, it is hard to believe that investors would not benefit
by cash distributions instead of cash stockpiles.
S E L F -T E S T
Why might a company hold low-yielding marketable securities when it could earn a much higher
return on operating assets?
Short-Term Financing
The three possible short-term financing policies described earlier in the chapter were distinguished by the
relative amounts of short-term debt used under each policy. The aggressive policy called for the greatest use
of short-term debt, and the conservative policy called for using the least; maturity matching fell in between.
Although short-term credit is generally riskier than long-term credit, using short-term funds does have some
significant advantages. The pros and cons of short-term financing are considered in this section.
See Opler, T., Pinkowitz, L., Stulz, R. and Williamson, R. (1999) ‘The determinants and implications of corporate cash holdings’,
Journal of Financial Economics 52(1):3–46.
88 Part 1
The Company and Its Reporting Environment
Advantages of Short-Term Financing
Short-term financing has three advantages. First, a short-term loan can be obtained much faster than long-term
credit. Lenders will insist on a more thorough financial examination before extending long-term credit, and the
loan agreement will have to be spelled out in considerable detail because a lot can happen during the life of a
10- to 20-year loan. Therefore, if funds are needed in a hurry, the firm should look to the short-term markets.
Second, if the need for funds is seasonal or cyclical, then a firm may not want to commit itself to long-term
debt. There are three reasons for this: (1) flotation costs are higher for long-term debt than for short-term credit;
(2) although long-term debt can be repaid early (provided the loan agreement includes a prepayment provision), prepayment penalties can be expensive; accordingly, if a firm thinks its need for funds will diminish in
the near future, it should choose short-term debt; (3) long-term loan agreements always contain provisions, or
covenants, that constrain the firm’s future actions; short-term credit agreements are generally less restrictive.
The third advantage is that, because the yield curve is normally upward sloping,8 interest rates are generally lower on short-term debt. Thus, under normal conditions, interest costs at the time the funds are
obtained will be lower if the firm borrows on a short-term rather than a long-term basis.
Disadvantages of Short-Term Debt
Even though short-term rates are often lower than long-term rates, using short-term credit is riskier for two
1. If a firm borrows on a long-term basis then its interest costs will be relatively stable over time, but if
it uses short-term credit, then its interest expense will fluctuate widely, at times going quite high. For
example, in the United States the rate banks charged large firms for short-term debt more than tripled
over a two-year period in the 1980s, rising from 6.25 per cent to 21 per cent. Many firms that had borrowed heavily on a short-term basis simply could not meet their rising interest costs; as a result, bankruptcies hit record levels during that period.
2. If a firm borrows heavily on a short-term basis, a temporary recession may render it unable to repay
this debt. If the borrower is in a weak financial position, then the lender may not extend the loan, which
could force the firm into bankruptcy.
S E L F -T E S T
What are the advantages and disadvantages of short-term debt compared with long-term debt?
Short-Term Bank Loans
Loans from commercial banks generally appear on balance sheets as notes payable. A bank’s importance is
actually greater than it appears from the amounts shown on balance sheets because banks provide nonspontaneous funds. As a firm’s financing needs increase, it requests additional funds from its bank. If the request
is denied, the firm may be forced to abandon attractive growth opportunities. The key features of bank loans
are discussed in the following paragraphs.
Although banks do make longer-term loans, the bulk of their lending is on a short-term basis—about twothirds of all bank loans mature in a year or less. Bank loans to businesses are frequently written as 90-day
The yield curve is a graph of interest rates for investments of differing terms (or lengths of time to maturity). It is upward sloping in
normal times, reflecting the fact that the market usually charges a higher interest rate per annum the longer the guaranteed length of
time of the investment. Check with your local bank—if you invest for five years you will get a higher interest rate per annum than if
you invest for just one year.
Chapter 3
Understanding Financial Statements Part 2: Analysing and Managing the Accounts 89
notes, so the loan must be repaid or renewed at the end of 90 days. Of course, if a borrower’s financial position
has deteriorated, then the bank may refuse to renew the loan. This can mean serious trouble for the borrower.
Promissory Notes
When a bank loan is approved, the agreement is executed by signing a promissory note. The note specifies
(1) the amount borrowed, (2) the interest rate, (3) the repayment schedule, which can call for either a lump
sum or a series of instalments, (4) any collateral that might have to be put up as security for the loan, and
(5) any other terms and conditions to which the bank and the borrower have agreed. When the note is signed,
the bank credits the borrower’s checking account with the funds; hence both cash and notes payable increase
on the borrower’s balance sheet.
Informal Line of Credit
A line of credit is an informal agreement between a bank and a borrower indicating the maximum credit
the bank will extend to the borrower. For example, on December 31, a bank loan officer might indicate to a
financial manager that the bank regards the firm as being ‘good’ for up to €80 000 during the forthcoming
year, provided the borrower’s financial condition does not deteriorate. If on 10 January the financial manager
signs a 90-day promissory note for €15 000, this would be called ‘taking down’ €15 000 of the total line of
credit. This amount would be credited to the firm’s checking account at the bank, and the firm could borrow
additional amounts up to a total of €80 000 outstanding at any one time.
Revolving Credit Agreement
A revolving credit agreement is a formal line of credit often used by large firms. To illustrate, suppose in
2013 Devon Petroleum Company negotiated a revolving credit agreement for €100 million with a group of
banks. The banks were formally committed for four years to lend the firm up to €100 million if the funds were
needed. Devon Petroleum, in turn, paid an annual commitment fee of 0.25 per cent on the unused balance of
the commitment to compensate the banks for making the commitment. Thus, if Devon Petroleum did not
take down any of the €100 million commitment during a year, it would still be required to pay a €250 000
annual fee, normally in monthly instalments of €20 833.33. If it borrowed €50 million on the first day of the
agreement, then the unused portion of the line of credit would fall to €50 million and the annual fee would fall
to €125 000. Of course, interest would also have to be paid on the money Devon Petroleum actually borrowed.
As a general rule, the interest rate on ‘revolvers’ is pegged to the London Interbank Offered Rate (LIBOR),
the T-bill rate, or some other market rate, so the cost of the loan varies over time as interest rates change. The
interest that Devon Petroleum must pay could for example be the prime lending rate plus 1.0 per cent.
Observe that a revolving credit agreement is similar to an informal line of credit but has an important difference: the bank has a legal obligation to honour a revolving credit agreement, and it receives a commitment
fee. Neither the legal obligation nor the fee exists under the informal line of credit.
Often a line of credit will have a clean-up clause that requires the borrower to reduce the loan balance to
zero at least once a year. Keep in mind that a line of credit typically is designed to help finance seasonal or
cyclical peaks in operations as in Figure 3-5 and not as a source of permanent capital. If the cumulative flows
were always negative, this would indicate that the firm was using its credit lines as a permanent source of
Costs of Bank Loans
Banks calculate interest in several different ways. In this section, we explain the procedure used for most
business loans. For illustration purposes, we assume a loan of €10 000 at the prime rate of 3.25 per cent, with
a 360-day year. Interest must be paid monthly, and the principal is payable ‘on demand’ if and when the bank
wants to end the loan.
90 Part 1
The Company and Its Reporting Environment
The simple approach divides the nominal interest rate (3.25 per cent in this case) by 360 to obtain the rate
per day. This rate is expressed as follows:
Nominal rate
Days in the year
5 0.000089041
Simple interest rate per day 5
5 0.0089041%
Note that in the United States the days in the year figure is normally 360 rather than 365. An alternative
approach is to use the actuarial equivalent of 3.25 per cent. This rate includes interest payment on previous
interest payments:
Actuarial interest rate per day 5 1 1 Nominal rate
5 1.0325
5 0.00008763
5 0.008763%
The actuarial rate is slightly less than the simple rate. The simple rate is favoured by banks for loans such
as mortgages where the difference can be significant—so take care to check the basis of charging.
S E L F -T E S T
What is a promissory note, and what are some terms that are normally included in promissory notes?
What is a line of credit? A revolving credit agreement?
What is the difference between simple interest and add-on interest?
Explain how a firm that expects to need funds during the coming year might make sure that the
needed funds will be available.
How does the cost of costly trade credit generally compare with the cost of short-term bank loans?
If a firm borrowed €500 000 at a rate of 10 per cent simple interest with monthly interest payments and
a 365-day year, what would be the required interest payment for a 30-day month? (Answer: €4109.59.)
If interest must be paid monthly, what would be the effective annual rate? (Answer: 10.47 per cent.)
Commercial Paper
Commercial paper is a type of unsecured promissory note issued by large, strong firms and sold primarily
to other business firms, to insurance companies, to pension funds, to money market mutual funds, and to
banks. In May 2012, there was approximately $1.2 trillion of commercial paper outstanding in the United
States, versus nearly $1.4 trillion of commercial and industrial bank loans. Most, but not all, commercial
paper outstanding is issued by financial institutions.
Maturity and Cost
Maturities of commercial paper generally vary from one day to nine months, with an average of about five
months. The interest rate on commercial paper fluctuates with supply and demand conditions—it is determined in the marketplace, varying daily as conditions change. Recently, commercial paper rates have ranged
from 1.5 to 3.5 percentage points below the stated prime rate and up to half of a percentage point above the
Chapter 3
Understanding Financial Statements Part 2: Analysing and Managing the Accounts 91
T-bill rate. For example, in May 2012, the average rate on three-month commercial paper was 0.20 per cent,
the prime rate was 3.25 per cent, and the three-month T-bill rate was 0.09 per cent.
Use of Commercial Paper
The use of commercial paper is restricted to a comparatively small number of very large companies that are
exceptionally good credit risks. Dealers prefer to handle the paper of firms whose net worth is €100 million
or more and whose annual borrowing exceeds €10 million. One potential problem with commercial paper is
that a debtor who has a temporary financial difficulty may receive little help because commercial paper dealings are generally less personal than are bank relationships. Thus, banks are generally more able and willing
to help a good customer weather a temporary storm than is a commercial paper dealer. On the other hand,
using commercial paper permits a corporation to tap a wide range of credit sources, including financial institutions outside its own area and industrial corporations across the country, and this can reduce interest costs.
S E L F -T E S T
What is commercial paper?
What types of companies can use commercial paper to meet their short-term financing needs?
How does the cost of commercial paper compare with the cost of short-term bank loans? With the
cost of Treasury bills?
Use of Security in Short-Term Financing
Thus far, we have not addressed the question of whether or not short-term loans should be secured. Commercial paper is never secured, but other types of loans can be secured if this is deemed necessary or desirable. Other things held constant, it is better to borrow on an unsecured basis because the bookkeeping costs of
secured loans are often high. However, firms often find that they can borrow only if they put up some type of
collateral to protect the lender, or that, by using security, they can borrow at a much lower rate.
Companies can employ several different kinds of collateral, including marketable shares or bonds, land or
buildings, equipment, inventory and accounts receivable. Marketable securities make excellent collateral, but
few firms that need loans also hold portfolios of shares and bonds. Similarly, real property (land and buildings) and equipment are good forms of collateral, but they are generally used as security for long-term loans
rather than for working capital loans. Therefore, most secured short-term business borrowing involves the
use of accounts receivable and inventories as collateral.
Consider the case of a Parisian hardware dealer (Quincaillerie) who requested a €200 000 bank loan to
­modernize and expand his shop. After examining the business’s financial statements, his bank indicated that it
would lend him a maximum of €100 000 and that the effective interest rate would be 9 per cent. The owner had
a substantial personal portfolio of shares, and he offered to put up €300 000 of high-quality shares to support the
€200 000 loan. The bank then granted the full €200 000 loan at the prime rate of 3.25 per cent. The store owner
might also have used his inventories or receivables as security for the loan, but processing costs would have been
S E L F -T E S T
What is a secured loan?
What are some types of current assets that are pledged as security for short-term loans?
Analysing financial statements provides just one of the many sources of information used to assess
a firm’s future prospects and hence the value of a firm’s current share price. Much of the information
will not be timely and hence serve to confirm other indicators from other sources. This in itself is
an important role. For example, data on consumer sales released during the year in various general
surveys would lead investors to guess at the effect on various companies, but only when the annual
accounts are released can the accuracy of the earlier estimates be confirmed.
92 Part 1
The Company and Its Reporting Environment
This chapter has explained techniques investors and managers use to analyse financial statements. The key
concepts covered are listed below.
Liquidity ratios show the relationship of a firm’s current assets to its current liabilities and thus its ability
to meet maturing debts. Two commonly used liquidity ratios are the current ratio and the quick, or acid
test, ratio.
Asset management ratios measure how effectively a firm is managing its assets. These ratios include
inventory turnover, days sales outstanding, fixed assets turnover and total assets turnover.
Debt management ratios reveal (1) the extent to which the firm is financed with debt, and (2) its likelihood of defaulting on its debt obligations. They include the debt-to-assets ratio (also called the debt
ratio), the debt-to-equity ratio, the times-interest-earned ratio and the EBITDA coverage ratio.
Profitability ratios show the combined effects of liquidity, asset management and debt management policies on operating results. They include the net profit margin (also called the profit margin on sales), the
basic earning power ratio, the return on total assets and the return on common equity.
Market value ratios relate the firm’s share price to its earnings, cash flow and book value per share,
thus giving management an indication of what investors think of the company’s past performance and
future prospects. These include the price/earnings ratio, the price/cash flow ratio and the market/book
Trend analysis, in which one plots a ratio over time, is important because it reveals whether the firm’s
condition has been improving or deteriorating over time.
The DuPont system is designed to show how the profit margin on sales, the assets turnover ratio and
the use of debt all interact to determine the rate of return on equity. The firm’s management can use the
DuPont system to analyse ways of improving performance.
Benchmarking is the process of comparing a particular company with a group of similar successful
Working capital refers to current assets used in operations, and net working capital is defined as current
assets minus all current liabilities. Net operating working capital is defined as operating current assets
minus operating current liabilities.
Under a relaxed working capital policy, a firm would hold relatively large amounts of each type of current
asset. Under a restricted working capital policy, the firm would hold minimal amounts of these items.
A moderate approach to short-term financing involves matching, to the extent possible, the maturities
of assets and liabilities, so that temporary operating current assets are financed with short-term debt
and permanent operating current assets and fixed assets are financed with long-term debt or equity.
Under an aggressive approach, some permanent operating current assets, and perhaps even some fixed
assets, are financed with short-term debt. A conservative approach would be to use long-term sources to
finance all permanent operating capital and some of the temporary operating current assets.
Permanent operating current assets are the operating current assets the firm holds even during slack
times, whereas temporary operating current assets are the additional operating current assets needed
during seasonal or cyclical peaks. The methods used to finance permanent and temporary operating
current assets define the firm’s short-term financing policy.
The cash conversion cycle is the length of time between the firm’s actual cash expenditures to pay for
productive resources and its own cash receipts from the sale of products.
A cash budget is a schedule showing projected cash inf lows and outf lows over some period. The
cash budget is used to predict cash surpluses and deficits, and it is the primary cash management
planning tool.
The primary goal of cash management is to minimize the amount of cash the firm must hold for conducting its normal business activities while at the same time maintaining a sufficient cash reserve to
take discounts, pay bills promptly and meet any unexpected cash needs.
Ratio analysis has limitations, but when used with care and judgement it can be very helpful.
Chapter 3
Understanding Financial Statements Part 2: Analysing and Managing the Accounts 93
Answers to questions 3-11 and 3-12 appear in the Appendix.
( 3 -1)
Define each of the following terms:
a. liquidity ratios: current ratio; quick, or acid test, ratio
b. asset management ratios: inventory turnover ratio; days sales outstanding (DSO);
fixed assets turnover ratio; total assets turnover ratio
c. financial leverage ratios: debt ratio; times-interest-earned (TIE) ratio; coverage
d. profitability ratios: profit margin on sales; basic earning power (BEP) ratio; return
on total assets (ROA); return on common equity (ROE)
e. market value ratios: price/earnings (P/E) ratio; price/cash flow ratio; market/book
(M/B) ratio; book value per share
f. trend analysis; comparative ratio analysis; benchmarking
g. DuPont equation; window dressing; seasonal effects on ratios
( 3 -2)
Financial ratio analysis is conducted by managers, equity investors, long-term creditors and short-term creditors. What is the primary emphasis of each of these groups
in evaluating ratios?
Profit margins and turnover ratios vary from one industry to another. What differences
would you expect to find between a grocery chain such as Morrisons and a steel company?
Think particularly about the turnover ratios, the profit margin and the DuPont equation.
Why is it sometimes misleading to compare a company’s financial ratios with those of
other firms that operate in the same industry?
Define each of the following terms:
a. working capital; net working capital; net operating working capital
b. relaxed policy; restricted policy; moderate policy
c. permanent operating current assets; temporary operating current assets
d. moderate (maturity matching) financing policy; aggressive financing policy;
conservative financing policy
e. inventory conversion period; average collection period; payables deferral period;
cash conversion cycle
f. cash budget; target cash balance
g. trade discounts
h. credit policy; credit period; credit standards; collection policy; cash discounts
i. account receivable; days sales outstanding; aging schedule
j. accruals; trade credit
k. stretching accounts payable; free trade credit; costly trade credit
l. line of credit; revolving credit agreement
m. commercial paper; secured loan
( 3 -5 )
( 3 -7 )
( 3 -9)
( 3 -10 )
What are the two principal reasons for holding cash? Can a firm estimate its target
cash balance by summing the cash held to satisfy each of the two reasons?
What are the advantages of matching the maturities of assets and liabilities? What are
the disadvantages?
From the standpoint of the borrower, is long-term or short-term credit riskier?
Explain. Would it ever make sense to borrow on a short-term basis if short-term rates
were above long-term rates?
Discuss this statement: ‘Firms can control their accruals within fairly wide limits.’ Is
it true that most firms are able to obtain some free trade credit and that additional
trade credit is often available, but at a cost? Explain.
What kinds of firms use commercial paper?
94 Part 1
The Company and Its Reporting Environment
( 3 -11)
( 3 -1 2)
Debt ratio: Argent Corporation has $60 million in current liabilities, $150 million
in total liabilities and $210 million in total common equity; Argent has no preferred
shares. Argent’s total debt is $120 million. What is the debt-to-assets ratio? What is
the debt-to-equity ratio?
Ratio analysis: the following data apply to Jacobus and Associates (millions of
Cash and marketable securities
Fixed assets
Net income
Quick ratio
Current ratio
40.55 days
Jacobus has no preferred shares—only common equity, current liabilities and longterm debt. Find Jacobus’s (1) accounts receivable, (2) current liabilities, (3) current
assets, (4) total assets, (5) ROA, (6) common equity and (7) long-term debt.
( 3 -1)
( 3 -2)
( 3 -3)
( 3 -5 )
Days sales: Outstanding Greene Sisters has a DSO of 20 days. The company’s average
daily sales are $20 000. What is the level of its accounts receivable? Assume there are
365 days in a year.
Debt ratio: Vigo Vacations has $200 million in total assets, $5 million in notes payable, and $25 million in long-term debt. What is the debt ratio?
Market/book ratio: Winston Washers’s shares price is $75 per share. Winston has $10
billion in total assets. Its balance sheet shows $1 billion in current liabilities, $3 billion in long-term debt, and $6 billion in common equity. It has 800 million ordinary
shares outstanding. What is Winston’s market/book ratio?
ROE: Needham Pharmaceuticals has a profit margin of 3 per cent and an equity multiplier of 2.0. Its sales are $100 million and it has total assets of $50 million. What is its
Profit margin and debt ratio: Assume you are given the following relationships for the
Haslam Corporation:
Sales/total assets
Return on assets (ROA)
Return on equity (ROE)
Calculate Haslam’s profit margin and liabilities-to-assets ratio.
Current and quick ratios: The Nelson Company has $1312 500 in current assets and
$525 000 in current liabilities. Its initial inventory level is $375 000, and it will raise
funds as additional notes payable and use them to increase inventory. How much
can Nelson’s short-term debt (notes payable) increase without pushing its current
ratio below 2.0? What will be the firm’s quick ratio after Nelson has raised the maximum amount of short-term funds?
Chapter 3
( 3 -7 )
Understanding Financial Statements Part 2: Analysing and Managing the Accounts 95
Balance sheet analysis: Complete the balance sheet and sales information in the table
that follows for J. White Industries using the following financial data:
Total assets turnover: 1.5
Gross profit margin on sales: (Sales 2 Cost of goods sold)/Sales 5 25%
Total liabilities-to-assets ratio: 40%
Quick ratio: 0.80
Days sales outstanding (based on 365-day year): 36.5 days
Inventory turnover ratio: 3.75
Partial Income
Cost of goods sold
Balance sheet
Accounts payable
Accounts receivable
Long-term debt
Ordinary shares
Fixed assets
Retained earnings
Total assets
$400 000
50 000
100 000
Total liabilities and equity
Comprehensive ratio analysis: The Jimenez Corporation’s forecasted 2014 financial
statements follow, along with some industry average ratios. Calculate Jimenez’s 2014
forecasted ratios, compare them with the industry average data, and comment briefly
on Jimenez’s projected strengths and weaknesses.
Jimenez Corporation: Forecast Balance Sheet, 31 December 2014 ($)
72 000
Accounts receivable
439 000
894 000
Total current assets
Fixed assets
Total assets
1 405 000
431 000
1 836 000
Liabilities and Equity
Accounts payable
332 000
Notes payable
100 000
170 000
Total current liabilities
$602 000
Long-term debt
404 290
Ordinary shares
575 000
Retained earnings
254 710
Total liabilities and equity
$1 836 000
96 Part 1
The Company and Its Reporting Environment
Jimenez Corporation: Forecast Income Statement for 2014 ($)
4 290 000
Cost of goods sold
3 580 000
Selling, general, and administrative expenses
370 320
Depreciation and amortization
159 000
Earnings before taxes (EBT)
180 680
Taxes (40%)
72 272
Net income
108 408
Per Share Data
Cash dividends per share
P/E ratio
Market price (average)
Number of shares outstanding
23 000
Industry Financial Ratios (2013)
Quick ratio
Current ratio
Inventory turnover
Days sales outstanding
32.0 days
Fixed assets turnover
Total assets turnover
Return on assets
Return on equity
Profit margin on sales
( 3 -9)
Debt-to-assets ratio
Liabilities-to-assets ratio
P/E ratio
Price/cash flow ratio
Market/book ratio
Working capital policy: Payne Products’ sales last year were an anaemic €1.6 million, but
with an improved product mix it expects sales growth to be 25 per cent this year,
and Payne would like to determine the effect of various current assets policies on its
financial performance. Payne has €1 million of fixed assets and intends to keep its
debt ratio at its historical level of 60 per cent. Payne’s debt interest rate is currently
8 per cent. You are to evaluate three different current asset policies: (1) a tight policy
in which current assets are 45 per cent of projected sales, (2) a moderate policy with
50 per cent of sales tied up in current assets, and (3) a relaxed policy requiring current
assets of 60 per cent of sales. Earnings before interest and taxes is expected to be
12 per cent of sales. Payne’s tax rate is 40 per cent.
a. What is the expected return on equity under each current asset level?
b. In this problem, we have assumed that the level of expected sales is independent of
current asset policy. Is this a valid assumption? Why or why not?
c. How would the overall riskiness of the firm vary under each policy?
Chapter 3
Understanding Financial Statements Part 2: Analysing and Managing the Accounts 97
Computron Industries incurred a large loss in 2013, rather than the expected profit. As a result, its managers,
directors and investors are concerned about the firm’s survival.
Jenny Cochran was brought in as assistant to Gary Meissner, Computron’s chairman, who had the task of
getting the company back into a sound financial position. Computron’s 2012 and 2013 balance sheets and
income statements, together with projections for 2014, are shown in the following tables. The tables also
show the 2012 and 2013 financial ratios, along with industry average data. The 2014 projected financial statement data represent Cochran’s and Meissner’s best guess for 2014 results, assuming that some new financing
is arranged to get the company ‘over the hump’.
9 000
7 282
14 000
48 600
20 000
71 632
Accounts receivable
351 200
632 160
878 000
715 200
1 287 360
1 716 480
1 124 000
1 946 802
2 680 112
Gross fixed assets
491 000
1 202 950
1 220 000
Less: Accumulated depreciation
146 200
263 160
383 160
Net fixed assets
344 800
939 790
836 840
Total assets
1 468 800
2 886 592
3 516 952
Balance Sheets (in $)
Short-term investments
Total current assets
Liabilities and Equity
Accounts payable
145 600
324 000
359 800
Notes payable
200 000
720 000
300 000
136 000
284 960
380 000
481 600
1 328 960
1 039 800
Long-term debt
323 432
1 000 000
500 000
Ordinary shares (100 000 shares)
460 000
460 000
1 680 936
Total current liabilities
Retained earnings
203 768
97 632
296 216
Total equity
663 768
557 632
1 977 152
1 468 800
2 886 592
3 516 952
Total liabilities and equity
Note: ‘E’ denotes estimated; the 2014 data are forecasts.
3 432 000
5 834 400
7 035 600
Cost of goods sold except depr.
2 864 000
4 980 000
5 800 000
Depreciation and amortization
18 900
116 960
120 000
340 000
720 000
612 960
3 222 900
5 816 960
6 532 960
Income Statements (in $)
Other expenses
Total operating costs
98 Part 1
The Company and Its Reporting Environment
209 100
17 440
502 640
62 500
176 000
80 000
146 600
(158 560)
422 640
Taxes (40%)
58 640
(63 424)
169 056
Net income
87 960
(95 136)
253 584
Interest expense
Other Data
Share price
Shares outstanding
100 000
100 000
250 000
Tax rate
Book value per share
Lease payments
40 000
40 000
40 000
Note: ‘E’ denotes estimated; the 2014 data are forecasts.
Inventory turnover
Days sales outstanding
Fixed assets turnover
Total assets turnover
Ratio Analysis
Debt ratio
Liabilities-to-assets ratio
EBITDA coverage
Profit margin
Price/Earnings (P/E)
Price/Cash flow
Basic earning power
Note: ‘E’ denotes estimated.
Chapter 3
Understanding Financial Statements Part 2: Analysing and Managing the Accounts 99
Cochran must prepare an analysis of where the company is now, what it must do to regain its financial
health, and what actions to take. Your assignment is to help her answer the following questions. Provide clear
explanations, not yes or no answers.
a. Why are ratios useful? What three groups use ratio analysis and for what reasons?
b.Calculate the 2014 current and quick ratios based on the projected balance sheet and income statement
data. What can you say about the company’s liquidity position in 2012, 2013 and as projected for 2014?
We often think of ratios as being useful (1) to managers to help run the business, (2) to bankers for
credit analysis, and (3) to shareholders for share valuation. Would these different types of analysts have
an equal interest in the liquidity ratios?
c.Calculate the 2014 inventory turnover, days sales outstanding (DSO), fixed assets turnover, and total
assets turnover. How does Computron’s utilization of assets stack up against that of other firms in its
d.Calculate the 2014 debt ratio, liabilities-to-assets ratio, times-interest-earned and EBITDA coverage
ratios. How does Computron compare with the industry with respect to financial leverage? What can
you conclude from these ratios?
e.Calculate the 2014 profit margin, basic earning power (BEP), return on assets (ROA) and return on
equity (ROE). What can you say about these ratios?
f.Calculate the 2014 price/earnings ratio, price/cash flow ratio, and market/book ratio. Do these ratios
indicate that investors are expected to have a high or low opinion of the company?
g.Perform a common size analysis and percentage change analysis. What do these analyses tell you about
h.Use the extended DuPont equation to provide a summary and overview of Computron’s financial condition as projected for 2014. What are the firm’s major strengths and weaknesses?
i. What are some potential problems and limitations of financial ratio analysis?
j.What are some qualitative factors that analysts should consider when evaluating a company’s likely
future financial performance?
The Time Value
of Money
uppose you wanted to sell a rare book and you were offered €100 by two purchasers A and B, but B said
that he would pay in one year’s time whereas A said that she would pay you now. Whose offer would you
You would of course select A’s offer. That should be enough to convince you that time has a monetary
value. Delay is unattractive. Now suppose that B, having been told that his offer has been rejected, says
that he will pay €110 in one year’s time? That is a little bit more difficult; what thoughts would go through
your mind?
My guess is that you would look at B and think, what is the risk that he will not pay? You might also think:
wait a minute, there is 3 per cent inflation, I will need €103 just to keep the same value so really B is only offering me about €7 extra in today’s money or 7 per cent. Lastly, and perhaps crucially, you might well think: I need
the money now, I can’t wait a year.
You could go to a money lender, a credit union or a bank and ask to borrow money now and repay with
B’s promised payment. This does not really change matters as the lender would almost certainly have the same
thoughts as yourself.
Now suppose that instead of a single payment the repayments were over a number of years; we need to
know how to calculate the repayment for a given required percentage return. We solve such problems in this
chapter and also show that our solutions are fundamental to all valuation in finance.
The Problem of Valuation
In medieval times banks lent money and had to work out repayments. As there were no calculators they
employed mathematicians who calculated the repayments using their own secret formulae. Fortunately,
we now have calculators and we are able to solve the formulae. So the problem nowadays is to understand
the problem and the solution. Some learners try to memorize the formulae without attempting to understand them. This is a foolish approach. If you understand the formulae then you do not have to remember
them, you can work it out and you can apply them more easily to the many financial problems that they
In Chapter 1, we referred to the time value of money as one of the central concepts in finance. When we
as individuals think of time and money it is usually in the context of saving. In the business context the
104 Part 2
Fixed Income Securities: An Introduction to Valuation
F i g u re 4 -1
Timeline for Cash Flow Valuation
The start of
period 1 (now,
i.e. the present)
End of periods 1, 2, 3. . . n
3 . . . n
Future value
€ 100
Present value
€ 100
opposite is the case. Certainly, businesses save, but their major activity is to borrow to invest. They go to their
shareholders, the lending markets and/or their banks and say, ‘We have these great ideas about the future,
how much will you give us now in order to fund the activity and share in the profits?’ So in money terms the
lender is looking at possible future cash flows and wondering what they are worth today, i.e. their present
value. This will determine how much he or she is willing to lend.
It is essential for financial managers to understand the time value of money and its impact on lenders and
on shareholders. In this chapter we will explain exactly how the timing of cash flows affects asset values and
rates of return.
The principles of time value analysis have many applications, including retirement planning, loan payment schedules, and decisions to invest (or not) in new equipment. In fact, of all the concepts used in finance,
none is more important than the time value of money (TVM), also called discounted cash flow (DCF) analysis. Time value concepts are used throughout the remainder of the book, so it is vital that you understand
the material in this chapter and are able to work the chapter’s problems before you move on to other topics.
The first step in a time value analysis is to set up a timeline to help you visualize what is happening in the
particular problem. All valuation problems can be expressed in terms of a timeline.
To illustrate, consider Figure 4-1, where valuation can be either:
• How much is €100 in three years’ time? (future value, FV)
• How much is the promise of €100 in three years’ time worth now? (present value, PV)
The intervals from 0 to 1, 1 to 2 and 2 to 3 are time periods such as years or months. Time 0 is today or
now, and it is the beginning of period 1; time 1 is one period from today, and it is both the end of period 1 and
the beginning of period 2; and so on. In our example, the periods are years, but they could also be quarters
or months or days or even seconds. So 1 is 11:59pm on 31 December of year 1 and 2 is 11:59pm on 31 December of year 2, and so on. Cash flows are shown directly below the period numbers and unknown cash flows,
which you are trying to find, are indicated by question marks.
Timelines are especially important when you are first learning time value concepts, but even experts use
them to analyse complex problems. Throughout the book, our procedure is to set up a timeline to show what
is happening as the first step to solving a valuation problem.
Future Values
A euro in hand today is worth more than a euro to be received in the future. If you had the euro now you
could invest it, earn interest, and end up with more than one euro in the future. The process of going forward, from present values (PVs) to future values (FVs), is called compounding.
Chapter 4
The Time Value of Money 105
To illustrate, assume that you have €100 in a bank account that pays a guaranteed 5 per cent interest each
year. How much would you have at the end of year 3?
We first define some terms, and then we set up a timeline and show how the future value is calculated:
PV 5 present value, or beginning amount. In our example, PV 5 €100.
FVn 5 f uture value, or ending amount, in the account after n periods. Whereas PV is the value
now, FVn is the value n periods into the future, after interest earned has been added to the
CFt 5 cash flow. The cash flow for a particular period is given a time subscript, CFt, where t is the period.
Cash flows can be positive or negative. For a borrower, the first cash flow is positive and the subsequent cash flows are negative (the repayments), and the reverse holds for a lender. Note that
CF0 5 PV 5 the cash flow at time 0, whereas CF3 would be the cash flow at the end of period 3.
By convention, the cash flows are deemed to be at the end of the period. If one wanted half yearly
cash flows, then the time period should be defined as a half year.
i 5 interest rate, which is in effect the ‘cost of time’. If you are lending then the interest rate is earned
or received, if you are borrowing then it is paid. Interest earned or paid is based on the balance
at the beginning of each year, and we assume that interest is paid at the end of the time period.
In later chapters we use the symbol ‘r’ (for rate of return) in a similar fashion to i, where r is not a contractual return but an expected return. In this chapter we generally assume that interest payments are almost
riskless (i.e. one receives the contractual amount with a small risk of nonpayment). In later chapters we will
deal with risky investments, where there is no contractual repayment and the rate actually earned will often
be different from the rate used in valuation.
Step-by-Step Approach
Let us solve the future value in Figure 4-1. Firstly, look at Figure 4-2.
We start with €100 in the account, which is shown at t 5 0. Assuming a 10 per cent interest rate, we then
multiply the initial amount, and each succeeding beginning-of-year amount, by (1 1 i) 5 (1.10). So over the
three years the future value is
FV0 3 1 1 1 i 2 3 1 1 1 i 2 3 1 1 1 i 2 5 FV3
FV0 3 1 1 1 i 2 3 5 FV3
:100 3 1.13 5 :133.10
In general terms the future value of a single amount invested is:
CF0 3 1 1 1 i 2 n 5 FVn
The interest process is termed compounding, because interest is earned on interest. Compounding is a
very powerful process. If you invested £5 in Shakespearean times at 3 per cent (for example in 1600), then
you would now have:
₤5 3 1 1.03 2 12015–16002 5 ₤1.06m
106 Part 2
Fixed Income Securities: An Introduction to Valuation
F i g u re 4 -2
Calculating Future Value
Future value
invested at
The start of
period 1 (now,
i.e. the present)
End of periods 1, 2, 3…n
So, I invest
€100 now
At the end of
1 year I will have
€100 + 10% ×
€100 = €110
€100 × (1 + 0.1) = €110
If I leave it in at
the end of year 2 I will have
€110 + 10% × €110 = €121
€110 × (1 + 0.1) = €121
If I leave it in for
a third year I will have
€121 + 10% ×
€121 = €133.10
€121 × (1 + 0.1) = €133.1
We can do it in one go!
€100 × 1.13 = 133.1
Applying the Future Value Formula
QUESTION: We have seen that €100 invested for three years at 10 per cent will amount to
€133.1 after three years. What if €200 were invested?
Answer: Rather than recalculate it using Equation 4-1, we can take the €133.1 as the return to
€100 so the return to €200 is simply double, i.e. €133.1 × 2 5 €266.2. If we have a table giving the
return after three years at 10 per cent for €1 it would be €1.331. That is all we would need and we
can multiply that figure by 200.
QUESTION: What if we invested €100 at t0 (i.e. now) then after the first year we invested €50
at the same 10 per cent interest rate. How much would we be owed after three years?
Answer: There are two simple ways of solving this question. We could follow the diagram and
say that after the first year the investment would be worth €100 × 1.1 5 €110, then we would add
the extra €50 so after one year we would have €110 1 €50 5 €160 which is then invested for a
further two years; so using Equation 4-1 we have €160 × 1.12 5 €193.6.
Alternatively, we could say that we are earning €100 for three years and €50 for two years. So
using Equation 4-1 the value is: €100 × 1.13 1 €50 × 1.12 5 €193.6. We shall use this alternative
way when valuing bonds.
QUESTION: What if we invested €100 now and a further €100 at the end of year 1 and a further
€100 at the end of year 2? (Write out the timeline with the payments.)
Answer: Saving regular amounts at regular intervals is a common savings pattern. This is known
as an annuity and we will come across a shorter way of solving the problem later on in the chapter.
Here, we can solve it as €100 for three years, €100 for two years and €100 for one year:
€100(1.1)3 1 €100(1.1)2 1 €100(1.1) 5 €364.1
Chapter 4
The Time Value of Money 107
Clearly if the regular investments were, say, every month for 60 months we would want to apply the
shorter way of calculating the end value. We do just this later when talking about annuities.
Graphic View of the Compounding Process
Figure 4-3 shows how a €100 investment grows over time at different interest rates. Interest rates are normally
positive, but the ‘growth’ concept is broad enough to include negative rates. We developed the curves by solving
Equation 4-1 with different values for n and i. The interest rate is a growth rate: if money is deposited and earns
5 per cent per year, then your funds will grow by 5 per cent per year. Note also that time value concepts can
be applied to anything that grows—sales, population, earnings per share, or your future salary. Also, as noted
before, the ‘growth rate’ can be negative, as was sales growth for a number of auto companies in recent years.
Simple Interest versus Compound Interest
As explained earlier, when interest is earned on the interest earned in prior periods, we call it compound
interest. We will always be using compound interest in this text unless stated otherwise. Occasionally in
practice the simple interest rate is used so it deserves a brief mention. The following example illustrates.
QUESTION: Mr A borrows €100 000 at 10 per cent per year charged monthly. How much is Mr
A charged each month using (a) compound rate and (b) simple rates?
Answer: (a) The monthly compound rate from the annual rate is simply
1 1.10 2 1/12 2 1 5 0.00797 or 0.797%
(b) In practice, the terms and conditions of the loan may well use a simple basis. As the
name implies simple interest is in this case the annual rate divided by 12. So,
5 0.00833 or 0.833%
F i g u re 4 -3
Growth of €100 at Various Interest Rates and Time Periods
Future value of €100
after n years
108 Part 2
Fixed Income Securities: An Introduction to Valuation
There is a small difference. The compound rate is slightly lower because it charges interest on interest and
therefore can reach the end of year €110 000 outstanding on a lower interest rate. The simple rate has to compensate for not doing this by charging slightly more. This is slightly more expensive for Mr A as he has to pay
S E L F -T E S T
Explain why this statement is true: ‘A euro in hand today is worth more than a euro to be received
next year, assuming interest rates are positive.’
What is compounding? What would the future value of €100 be after five years at 10 per cent
compound interest? (Answer: €161.05.)
Suppose you currently have €2000 and plan to purchase a three-year certificate of deposit (CD) that
pays 4 per cent interest, compounded annually. How much will you have when the CD matures?
(Answer: €2249.73.) How would your answer change if the interest rate were 5 per cent, or 6 per cent,
or 20 per cent? (Answer: €2315.25; €2382.03; €3456.00.)
A company’s sales in 2012 were €100 million. If sales grow by 8 per cent annually, what will they be
ten years later? (Answer: €215.89 million.) What would they be if they decline by 8 per cent per year
for ten years? (Answer: €43.44 million.)
How much would €1, growing at 5 per cent per year, be worth after 100 years? (Answer: €131.50.)
What would FV be if the growth rate were 10 per cent? (Answer: €13 780.61.)
Present Values
Money in a nonbusiness context is usually seen in terms of savings and interest rates. Future value is the
normal consideration. The business context is rather different. Businesses need money now in order to create
wealth in the future.
To get money now, they have to borrow and repay with the promised wealth that they are going to create with the money. The popular TV programme ‘The Dragon’s Den’ illustrates the process. Contestants go
before a panel of millionaires (venture capitalists) and ask the millionaires to lend them money (invest) to
fund their business ideas. The millionaires want a return on their investment and so have to assess the promised wealth—is it realistic or fanciful?
The investor therefore has to calculate how much and when the cash will be created from the investment
idea, and then, as a separate exercise, work out how much they are willing to pay for this promised share of
future earnings. The size and timing of the return is one factor in the calculation. A second factor is the risk
of the returns. The riskier the promised profits, the less the venture capitalist will be willing to pay. Risk and
return are positively related: the higher the risk, the higher the return needed in the event of winning to tempt
an investor.
So, instead of working out the future value of a known sum of money, now we need to work out the
­present value of estimated future cash flows. How much are we willing to pay for a potential receipt of cash
in the future, an investment idea?
But how does the investor relate the future cash f lows with the amount that he or she invests now?
This requires a comparison of cash flows at different times—we need to apply a time value of money. To
illustrate the cash flows, consider the problem in Figure 4-4. In the language of finance we want to find
the present value of €100 000—how much is this future promise of value worth now if we want a return
of 25 per cent? The answer is €80 000. Table 4-1 shows how much would be offered for differing levels of
return for the example in Figure 4-4. Note that the expected future value of €100 000 is a business decision
that will not be questioned in this text. The finance role in a company begins from the point of accepting the estimates of those with a knowledge of the enterprise. Applying the appropriate discount rate
(and hence the appropriate return) to get the present value is, however, a financial decision about which we
will have much to say.
Chapter 4
The Time Value of Money 109
F i g u re 4 - 4
Calculating the Present Value of Mr A’s Proposal
Problem: M
r A wants to raise money to fund an Arts festival in one year’s time. How
much are you willing to lend him if he offers you 20 per cent of the net profits?
Mr A estimates that he will earn €500 000
Time line:
year end
0 (now)
0.20 3 €500 000 5 €100 000
Thoughts: €
100 000 is only an expected value. This is a very risky operation. It could be a
flop and earn far less, it could be a huge success and earn far more.
Calculation: I want an expected return of 25 per cent so . . .
year end
0 (now)
€100 000
3 (1 1 0.25)
Invest? 3 1.25 5 €100 000
Invest? 5 €100 000 / 1.25
5 €80 000
So you would be prepared to lend €80 000 and expect a return of:
€100 000 2 € 80 000
5 0.25 or 25%
€ 80 000
Language: ‘Invest?’ (above) is the present value of €100 000 discounted at 25 per cent
TA B L E 4 -1
Present Values at Differing Discount Rates for the Problem in Figure 4-4
Present value
Discount rate
Expected future value
80 000
100 000
83 333
100 000
86 957
100 000
90 909
100 000
110 Part 2
Fixed Income Securities: An Introduction to Valuation
The general formula for single cash flows is:
PV0 5
11 1 i2n
PV0 5 present value which is always at time 0
FVn 5 future cash flow at time n
i 5 interest rate
The extension to multiple cash flows is simply to treat them as a series of single cash flows and add up
their present values, an attribute known as value additivity. Table 4-2 extends the problem of Figure 4-4 to
multiple time periods.
Mr A now wants to raise money for an annual arts festival and offers 20 per cent of the revenues for the
next five years as payment. You still want a 25 per cent return. Mr A estimates that your share (in €’000) for
the next five years is expected to be:
Adding up the individual present values using Equation 4-2 for a 25 per cent discount rate (rate of return) gives:
5 463
1 1
2 1
3 1
4 1
1 1.25 2
1 1.25 2
1 1.25 2
1 1.25 2
1 1.25 2 5
so from Equation 4-3 the amount that would be offered for these expected future cash flows in order to earn
an expected 25 per cent is €463 000.
This problem leads to the general formula for the present value of multiple cash flows as follows:
PV0 5 a
n51 1 1 1 i 2
PV0 5 present value which is always at time 0
FVn 5 future cash flow at time n
i 5 interest rate
a 5 add up the individual discounted cash flows as in Equation 4-3.
S E L F -T E S T
What is discounting, and how is it related to compounding? How is the future value Equation (4-1)
related to the present value Equation (4-2)?
How does the present value of a future payment change as the time to receipt is lengthened?
How does the present value of a future payment change as the interest rate increases? (Hint: Look at
the cash flows in Table 4-1.)
Chapter 4
The Time Value of Money 111
Suppose that a risk-free bond with no interest payments issued by ABC plc promises to pay €1000 in
three years. If the going risk-free discount (interest) rate is 4 per cent, how much is the bond worth
today? (Answer: €889.)
How much is ABC plc’s bond worth if it matures in five rather than three years? (Answer: €821.93.)
If the risk-free interest rate is 6 per cent rather than 4 per cent, how much is ABC plc’s five-year
version of the bond worth today? (Answer: €747.26.)
How much would €1 million due in 100 years be worth today if the discount rate were 5 per cent?
(Answer: €7604.49.)
How much would €1 million due in 100 years be worth today if the discount rate were 20 per cent?
(Answer: €0.012.)
What would be the present value of €100 to be received in five years at 10 per cent discount rate?
(Answer: €62.09.)
What is the present value of the following cash flows:
if a 20 per cent discount rate is deemed appropriate? (Answer: €426.51.)
Graphic View of the Discounting Process
Figure 4-5 shows that the present value of a sum to be received in the future decreases and approaches zero
as the payment date is extended farther and farther into the future; it also shows that, the higher the interest
rate, the faster the present value falls. At relatively high rates, funds due in the future are worth very little
F i g u re 4 -5
Calculating the Present Value
Present value of €100
after n years
112 Part 2
Fixed Income Securities: An Introduction to Valuation
TA B L E 4 -2
Expected Repayments and Return from Mr A’s Proposal Assuming a 25 per cent Interest Rate and
an Initial Investment of €463
Monies owned to lender/investor
Opening balance owed
plus interest charged at (25%)
less estimated repayments
5 closing balance
today, and even at relatively low rates present values of sums due in the very distant future are quite small.
For example, at a 20 per cent discount rate, €100 due in 10 years would be worth less than €16.15 today; at
5 per cent it is worth €61.39.
Finding the Interest Rate
Looking at Equation 4-3 (the NPV calculation of Mr A’s proposal), suppose that someone offering the
expected cash flows as given in Table 4-2 and Equation 4-3 by Mr A of 100, 150, 200, 250 and 250 in successive
years, asks for funding (an immediate payment for this cash flow) of €463—that is, the net present value when
discounted at 25 per cent. Another way of putting this is to say that there would be a return of 25 per cent.
We can see from Table 4-3 that it would indeed be 25 per cent. It is, however, not in the familiar form of borrowing and lending but rather just a figure in an equation. Table 4-2 shows the same return in more familiar
form, that of a bank statement of someone who has lent Mr A €463 at 25 per cent and used the cash flows to
repay the debt.
Table 4-2 shows that should the investor pay €463 for this promised series of future cash flows by Mr A
and should the cash flows materialize, then that will be equivalent to a kind of bank statement where the
lender is being paid 25 per cent on the opening balance of each year plus repayment of the original investment
over the five years. What if the borrower wanted €500? What return would be earned by the lender? There is
TA B L E 4 -3
Present Value of Cash Flows of Mr A’s Proposal at Differing Interest Rates
Discount rate (%)
25% (0.25)
Year »
Cash flows »
Discount values
Total present value
24% (0.24)
23% (0.23)
22% (0.22)
21% (0.21)
20% (0.20)
15% (0.15)
10% (0.10)
5% (0.05)
Chapter 4
The Time Value of Money 113
no formula for finding the discount rate for present values where n > 2. The answer is the interest rate in our
PV0 5 a
n51 1 1 1 i 2
The solution is by trial and error, which is easy when a spreadsheet is used. Table 4-3 shows the present
value of the estimated cash flows for varying discount rates. This was developed using a spreadsheet. For an
investment of €500 the return would be a little under 22 per cent.1
Another term for the discount rate in this context is the internal rate of return (IRR) defined as the interest rate that equates, from the investor’s point of view, the expected positive cash flows (the returns) with the
negative cash flows (the investment). So, from Table 4-3, if the required investment were €511, the (internal)
rate of return would be 21 per cent for the prospective cash flows. In similar manner the other interest rates
are internal rates of return if the outlay exactly equals the present value of the cash flows.
Sometimes the unknown is the number of years. Reconsider the cash flows in Equation 4-3—that is, a businessman is offered the expected cash flows of 100, 150, 200, 250 and 250 and is asked for an investment now
of €450. If you as an investor thought that the cash flows were pretty safe and required only a 10 per cent
return then the present value of the expected cash flows would be €691. A question of interest would be how
many years it would be before the initial outlay of €450 would be recovered including the 10 per cent per year
return. In other words, how long before the investor gets his or her money back?
Again we can solve this problem by trial and error constructing a table as in Table 4-3. This time we need
the discounted values of each year. Reading along the 10 per cent row, the present value (i.e. discounting the
10 per cent per year return requirement in the manner of Equation 4-3) of euros earned over the first three
years would be 91 1 124 1 150 5 €365 and over four years would be €365 1 €171 5 €536. So the €500 total
2 365 2
would be reached in 3 1 500 171
5 3.79 years or three years and 9.5 months.2 This is known as ­discounted
payback and is addressed in more detail later in the text. It may seem rather complicated but it is really just
seeing how many years it takes to get the initial investment back taking into account the cost of time.
This is a very popular valuation method in practice as it is a simple and intuitive measure of risk. The
shorter the payback the less the risk. Academics are not keen on the measure because it looks like double
counting—surely we already have a measure of risk in the discount rate? If the project is judged to be risky
then we apply a higher discount rate. This is one example of the gap between theory and practice. In this
case all one can add is that incorrect rejection of a project through over-estimating risk is less expensive than
accepting a project that subsequently fails, also the discount rate may not fully capture risk in practice.
Surprisingly, we are able to value an infinite series of cash flows, known as a perpetuity. Strictly speaking
we cannot get the exact value but infinitely close to that value or in the language of maths, asymptotically
Why should we want to value an infinite cash flow? Some securities promise to make payments forever.
For example, bonds known as consols promise a regular payment forever. Consols originated in the mid1700s when the British government issued some bonds that never matured and whose proceeds were used
to pay off other British bonds. Because this action consolidated the government’s debt, the new bonds were
called consols. The term stuck, and now any bond that promises to pay interest perpetually is called a consol. If the interest rate on a consol were 2.5 per cent, a consol with a face value of £100 would pay £2.5 per
year forever.
Note in Table 4-3 that the 80 5
Note that the 91 5
1 1.1 2 1
1 1.25 2 1
and the 96 5
and the 124 5
1 1.1 2 2
1 1.25 2 2
and so on.
so on, the 365 refers to euros not days.
114 Part 2
Fixed Income Securities: An Introduction to Valuation
Deriving the Perpetuity Formula
Wherever possible we explain how a formula is derived. Some readers will be happy just to know the formula,
but for the inquisitive we offer a simple derivation of the formula for valuing a perpetuity:
1. We start with the general present value formula for a perpetuity of €1:
PV0 5
2 1
3 1
11 1 i2
11 1 i2
11 1 i2
11 1 i2n
2. Now multiply both sides by (1 1 i):
PV0 1 1 1 i 2 5
3. Which simplifies to
PV0 1 PV0i 5 1 1
11 1 i2
11 1 i2
11 1 i2
c 11i
2 1
3 1
11 1 i2
11 1 i2
11 1 i2
11 1 i2n
1 c1
11 1 i2
11 1 i22
11 1 i23
1 1 1 i 2 n21
4. We now calculate step 3 less step 1, which reduces to
PV0i 5 1
Note that we have ignored 1 1 11 i 2 n as when n is near infinity this value is virtually zero whatever the interest rate or amount.
5. So the present value of a perpetuity of €1 is:
PV0 5
As simple as that.
EXAMPLE: Suppose the British government offers a coupon payment of £3 on a bond (debt) but
states that it will never repay the nominal value (£100). If you want a 4 per cent return on your
investment how much should you offer for the bond?
Answer: You should pay 0.04
5 £75
S E L F -T E S T
A businessman says that his business is worth €20 000 a year in today’s money. How much are you
willing to pay for it if you want a return of 20 per cent?
Answer: 20,000
0.20 5 €100 000.
The government offers you a permanent income to you and your descendants of €150 000 a year in
return for your stately home. What value has been placed on your stately home assuming an interest
rate of 8 per cent?
Answer: 150,000
0.08 5 €1 875 000
You want €100 000 for your business which is earning an expected €20 000 a year. What expected
interest rate (return) would a prospective buyer earn? (solve: €100 000 5 20,000
5 Thus i equals 20%.)
Chapter 4
The Time Value of Money 115
Growing Perpetuities
Often in business when estimating future earnings of a project an element of growth is expected. Also
shareholders expect their dividends to grow. The derivation of the formula is similar to that of the perpetuity. We will leave it to the enthusiasts with the following clues. A constant growth rate of g is treated in
the same way as the3 discount rate, only it is in the numerator rather than the denominator, so for period
11 1 g2
11 1 i2
3 it would be 1 1 1 i 2 3 . In step 2 the factor is 1 1 1 g 2 . The simplification is the same process and the resulting
formula is:
PV0 5
CF0 1 1 1 g 2
1i 2 g2
where CF0 is the cash flow at time 0, the present; note also that the growth rate has to be less than the discount rate.
So, if a company has just paid a dividend of €0.50 per share and there was an expected growth rate of
0.50 1 1.02 2
2 per cent in the dividends, the value of the share given a discount rate of 5 per cent is 1 0.50
2 0.02 2 5 :17.
Business often think in terms of a constant cash flow in making estimates. Contracts involving borrowing
and lending will typically also involve constant payments. Unlike perpetuities, however, these payments are
not continuing indefinitely, they have a fixed period. So the question arises, how can we calculate the present
value of, say, €100 a year for 10 years? One way is to treat each payment as a single cash flow and add up their
present values as in Equations 4-3 and 4-4. Although reasonably easy on a spreadsheet, this would nevertheless be somewhat clumsy and there is in any case a direct formula. As in the previous section some readers
may want simply to go to the formula (Equation 4-7) but the derivation is not too difficult. So for the inquisitive, we shall present its construction as follows:
1. The basic idea is to view the value of an annuity as the difference between two perpetuities of the same
value, one starting now and the other starting at the end of the annuity period.
2. As in Table 4-4, the three-year annuity is row A less row B. The present value in row A is simply Pi. The
valuation of row B is slightly more involved, the simple valuation Pi only values it to the beginning of year
4 (end of year 3). To value it at the beginning of year 1, i.e. the present value, we must further discount
this value as a lump sum, so
11 1 i23
3 which can be written as
11 1 i2
i 3 11 1 i23
3. Now we can return to the idea in step 1 and work out the present value of the annuity in row C as row A
less row B:
Present value of an n-year annuity of :P 5 2
i 3 1 1 i2n
TA B L E 4 - 4
The Idea Behind Valuing an Annuity
A. Perpetuity starting now
B. less perpetuity starting in year 4
C. equals three-year annuity
116 Part 2
Fixed Income Securities: An Introduction to Valuation
The value
Present value of an n-year annuity of :P 5 P 3 a 2
i 3 1 1 i2n
a 2
i 3 11 1 i2n
is an annuity factor and annuity tables are created for different n and i. Such tables seem increasingly
redundant in these days of spreadsheets and calculators. Nevertheless, our purpose here is to understand
the process rather than to merely calculate.
Example: Calculate the present value of a three-year annuity of €100 given a discount rate of
5 per cent. Using Equation 4-7 the value is 100 3 (20 2 17.28) 5 €272. We can check this as it is
1 1
only three years by adding up the present value of each cash flow hence 1.05
1.052 1 1.053 5 €272
so the two methods agree. Obviously if the annuity were for 20 years we would want to use the
formula of Equation 4-7.
What if we wanted the end value rather than the start (or present) value of the annuity. The simple
approach is to work out the present value and then use the future value formula to work out the value at
the end of the annuity or any other period for that matter. Using the previous example, the end value of the
three-year annuity is 272 × €1.053 5 €315. We can check this by again treating the cash flows individually so
100 3 1.052 1 100 3 1.051 1 100 5 €315. Note that as the cash flows are at the end of the period the time to
the end of the annuity is less, the final payment being at the end of the annuity.
EXAMPLE: Suppose you can afford a payment of €5000 a year for 25 years to pay for borrowing
a sum of money (now) at an interest rate of 10 per cent. How much can you borrow?
Answer: This is an annuity so go to the formula:
Present value of an n-year annuity of :P 5 P 3 a 2
i 3 11 1 i2n
and fill in the values:
5000 3 a
b 5 9.077 × 5000 5 €45 385
0.10 3 1 1.10 2 25
Another question. Suppose you can repay €600 a month. How much could you borrow if the bank charges
0.5 per cent a month and offers a 25-year loan?
This is typical of a mortgage, a loan to buy a house. Much of what we have looked at so far has been in
years but so long as the interest rate is for the right time period we proceed as normal with the formula. In
this case the repayment is monthly and the interest rate is monthly so we are OK. We proceed exactly as
before, first of all the formula:
Present value of an n-year annuity of :P 5 P 3 a 2
i 3 11 1 i2n
and fill in the values:
600 3 a
b 5 155.207 3 600 5 93124
0.005 3 1 1.005 2 12325
So you can afford a mortgage of €93 124. The unknown may not be the present value of the annuity, but
the method is the same, write out the formula and fill in the values—there should be only one unknown!
So, if you need to borrow €250 000, how much will you have to repay a month if the interest rate is three
quarters of a per cent a month (0.0075) and you are offered a 25-year loan?
Chapter 4
The Time Value of Money 117
Start with the formula:
Present value of an n-year annuity of :P 5 P 3 a 2
i 3 11 1 i2n
and fill in the values:
250 000 5 P 3 a
b 5 P 3 119.16
0.0075 3 1 1.0075 2 12325
So P 5 250 000/119.16 5 €2098 a month.
Valuation at Other Points in Time
We looked at this briefly when considering the end value of an annuity. With single cash flows we looked at
a present value formula of Equation 4-2 and a future value formula, Equation 4-1. There is a formula for the
value of an annuity at the end of the time period, but it is unnecessary to learn it because we can combine the
present value annuity formula with the future value formula for a single cash flow. In effect this calculates
the present value and then works out the equivalent future value thus ‘moving’ the cash flow to the other end
point of the annuity or any other point in time. Hence:
Future value of an n-year annuity 1 P 2 5 P 3 a 2
b 3 11 1 i2n
i 3 11 1 i2n
QUESTION: If I save €300 a month for 20 years (i.e. 240 months), how much will I have at the
end of 20 years if the interest rate is 0.5 per cent a month?
Answer: The method is the same: start with the right formula, in this case Equation 4-8, and fill
in the missing variables.
Future value of a 240 month €300 annuity:
300 3 a
b 3 1 1 1 0.005 2 240 5 138612
0.005 3 1 1 1 0.005 2 240
So the amount saved after 25 years is €138 612. There are shorter versions of the formula but this one is
conceptually simpler, easier to remember and shows how the formulae can be combined.
Annual, Monthly and Continuous Interest Rates
In publications, unless stated otherwise, the convention is that the interest rate is an annual rate. Often the
interest rate is quoted as an annual rate but the repayments are monthly. Take care, if the time period of payments is in months then the interest rate in any calculation must be in months, a daily interest rate must be
applied to daily payments and so on.
If the rate quoted is annual and the repayments are monthly, then we need to convert the annual interest
rate to a monthly equivalent. We make the normal assumption of a compound interest rate.3 The conversion is:
1 1 1 annual rate 2 1/12 5 1 1 monthly rate
The simple approach would be to multiply the monthly rate by 12; all financial modelling and practice assumes a compound (interest
on interest) approach but in some legal documents of an agreement a simple approach may be stated. In answering questions, the compound approach should be assumed unless clearly stated otherwise.
118 Part 2
Fixed Income Securities: An Introduction to Valuation
Example: If the annual rate is 14 per cent what is the monthly equivalent?
Answer: 1 1 1 0.14 2 1/12 5 1.011 so the monthly rate is 1.1 per cent, the increase over just returning your money (1).
If the rate quoted is monthly and the rate needed is annual (often finance companies have to quote an
annual equivalent (or EAR—equivalent annual rate—in the UK), the formula is:
1 1 1 monthly rate 2 12 5 1 1 annual rate
For example, a monthly rate of 3 per cent is an annual equivalent of (1 1 0.03)12 5 1.426, so
42.6 per cent a year.
From these equations you should be able to convert any time period interest rate into another.
Example: If the annual rate is 250 per cent what is the weekly equivalent?
1 1 1 annual rate 2 1/52 5 1 1 weekly rate
So the weekly rate is 2.44 per cent. That does not sound a great deal and many payday lenders
exploit this feature of interest rates. Compound interest rates mount up very quickly.
Now consider the following problem, which was known about in Elizabethan times (the 1500s). What if we
made the time period shorter and shorter and reduced the interest rate proportionately. So that instead of
charging, say, 10 per cent a year the rate was 0.1/365 5 0.000274 or 0.0274 per cent a day. You would still be
being charged 10 per cent, but the payment would be daily in small amounts. What would be the annual
equivalent on a compound basis? Clearly it will not be 10 per cent as you can invest the first payment for 364
days and the second for 363 days and so on. Applying Equation 4-1 it would be (1.000274)365 5 1.105167 so
10.5167 per cent. What if we divided the payment into infinitely small units, every second? The Elizabethans
noticed that the equivalent annual rate converged to e 0.10 2 1 5 0.105171 or 10.5171 per cent where e is the
mathematical constant 2.71828…. This is known as a continuous interest rate, in other words the annual
equivalent of an infinitely small division of the longer period. As you can see, a division of 365 gets pretty
close to the infinite value. Very occasionally it has been used in practice. Some years ago the UK government
restricted interest rates to something like 8 per cent a year but not as an annual equivalent. One could therefore pay two lots of 4 per cent, four lots of 2 per cent and so on. Soon continuous rates were offered as they
gave the highest annual equivalent. Academic papers often use continuous rates as the maths is more elegant.
Another example: €100 invested at 10 per cent a year for two years yields 100 × (1.10)2 5 121. Using continuous interest rates, €100 invested at 10 per cent a year continuous rate for two years yields 100 × e(0.1 × 2) 5
122—which is similar, but it will always be slightly higher.
What is an Interest Rate? Nominal and Real Rates
Now that we know how to use the interest rate and understand it as a cost of time, it is appropriate to ask,
how is it derived in a free market? The honest answer is we do not know; the interest rate is a market rate, we
can say how we think it should be calculated (the normative approach) but ultimately the market comes to its
own decision as a result of the number of transactions. Here we take the normative approach.
In the introduction we posed the problem as to whether an offer of €110 in one year was better than €100 now.
2 100
In other words, is an interest rate of 110 100
5 10 per cent worth the wait. Three thoughts seem reasonable:
1. Do I want to wait that long: impatience (or more formally time preference)?
2. What if he or she doesn’t pay me (risk)?
3. What about inflation?
Chapter 4
The Time Value of Money 119
All three elements are taken into account by the nominal interest rate. An interest rate that does not
include inflation is known as a real rate of interest. The relationship is approximately additive.
EXAMPLE: If the nominal interest rate is 5 per cent and the rate of inflation is 2 per cent then
the real rate is 5% 2 2% 5 3%. More strictly the relationship is multiplicative thus 1.05
1.02 5 1.0294,
so 2.94 per cent, but there are few contexts where such accuracy is significant.
The interest rates that you see in the media and quoted by banks and credit unions are nominal rates. Unless stated otherwise always assume that the interest rate is in monetary terms—the
nominal rate. Businesses on the other hand often work with real rates, sometimes without realizing, hence the next section.
Working with Real Rates and a Common Error
When estimating future revenues it is normal to think in terms of today’s money. The statement ‘this business is worth €20 000 a year’ does not mean that in ten years’ time it will still be earning €20 000, which
would be unrealistic. Of course, the earnings of the business would increase in line with inflation. In the case
of a financial contract such as a mortgage (a loan to buy a house) requiring, say, a €600 a month repayment,
the repayments will not change with inflation unless there is a specific clause in the contract. The €20 000 is
in real terms (that is, without considering inflation) and the €600 is in monetary terms—it is the actual cash
payment whatever the inflation rate.
The first question in any value problem is therefore, are we dealing in monetary terms or real terms? Until
now problems have all been in monetary terms. So what is the common mistake? As we have seen at the start
of this section there are two types of interest rate: a real rate and a monetary rate. If the cash flows are in real
terms then the interest rate must be the real rate.
However, if the cash flows are in monetary terms (that is, the actual cash flow) then the nominal interest
rate must be used as that includes inflation. Whereas everyone is familiar with the monetary rate as it is the
one in newspapers and advertisements, the real rate is rarely mentioned. The mistake is to estimate cash
flows in terms of current values, today’s money, and then apply the monetary interest rate as that includes
inflation. If there is no inflation in the cash flows then there must be no inflation in the interest rate.4
To repeat, the rule is that if the cash flows are real then the discount (interest) rate must be real. If the cash
flows are in actual monetary terms then the discount rate or interest rate must also be monetary. As a matter
of convention if the interest rate does not specify whether it is real or nominal then assume that it is nominal.
A simple example illustrates the issue:
QUESTION: Suppose that Miss A is seeking funding for the next three years of her fashion
and gardening show. She is prepared to offer a portion of the takings which she estimates will
be €100 000 in the first year and grow in real terms by 20 per cent a year. The interest rate you
require is 18 per cent and the inflation rate is 3 per cent. Work out the amount you would be
prepared to lend using real terms, then do the same using monetary terms—the answer should
be the same.
Answer: We assume that Miss A is talking in terms of today’s money, in real terms unadjusted
for inflation. As we have said, business people normally speak in these terms. Adjusting for
inflation would involve specific calculations and values that would not be familiar to a business
The real interest rate is 1.18
1.03 2 1 5 0.1456 or 14.56%. Applying the real rate to the real cash flows, remembering that they are growing at 20 per cent a year,
PV0 5
100000 3 1 1.2 2
100 000 3 1 1.2 2 2
5 €274503
As a matter of arithmetic, if the numerator is real the denominator must be real in all discounting formulae, otherwise they must both
be monetary; but do not mix the two.
120 Part 2
Fixed Income Securities: An Introduction to Valuation
The monetary cash flows are:
100 000 × 1.03 5 103 000
100 000 × 1.2 × 1.032 5 127 308
100 000 × 1.22 × 1.033 5 157 352
The discount calculation is now:
PV0 5
127 308
5 €274488
The difference of €15 is due to rounding. Note that the valuation is at t0 the present value, the start of the
first period. So inflation begins from that point. Growth is only after the first estimate so it is only applied for
the second and succeeding years.
As should always be the case, real cash flows and a real discount rate give a present value that is the same
as using monetary values, i.e. the actual cash flows and the nominal discount rate. In this case the present
value (amount to borrow) of the calculation using real values (without inflation) is €274 503 and the actual
monetary cash flows and nominal discount rate gives a present value of €274 488 and, as we noted, there is a
difference of €15 which is a rounding error. So the two approaches give the same result.
Capital and Interest Elements
Tax authorities will want to distinguish between the element of repayment that is interest and therefore
­taxable and the element that is capital, i.e. repaying the original amount.
If Mr A is lent €3000 for a year at 10 per cent and is repaid at the end of the year then it is clear that of the
€3300 repayment, €3000 is capital repayment and €300 is interest.
It is less clear if we suppose that Mr A borrows €10 000 for two years at 10 per cent per year charged
semi-annually using the simple method. What are the interest and capital amounts of the repayment?
Answer: We assume that the repayments are of equal amounts and that therefore we need to calculate an annuity with a present value of €10 000. Semi-annual payments using the simple method
is common in practice and is the 10 per cent divided by 2 so 5 per cent a half year. So there are four
equal payments at an interest rate of 5 per cent per period, which in this case is a half year.
We use the annuity formula (Equation 4-7) in Figure 4-6. The closing balance of 20.01 is obviously a
rounding error.
Note that the interest rate is on the capital amount outstanding that reduces over time. So Figure 4-6 is
proof if proof were needed that the annuity formula does indeed work out the constant payment that gives
the investor a 5 per cent return and repays the capital lent.
Interest Rates in the Marketplace:
Spot and Forward Rates
We have assumed so far that interest rates are constant per period. This is the assumption that lies behind
the main valuation models. It seems reasonable to argue that the per period charge (the interest rate) should
be no different whether we are looking at the time period going from the beginning of year 2 to the end of
year 2 or the period from the beginning of year 3 to the end of year 3. Obviously in working out the present
value of the year 3 cash flows there will be three per period charges compared with only two for the second
year cash flow; but the risky events in year 3 are not different from that of year 2—the marketplace however
At the time of writing Barclays Bank offer a one-year bond at 1.2 per cent, a two-year bond at 1.5 per cent
and a three-year bond at 2.0 per cent AER (Annual Equivalent Rate). In other words the per year rate quoted
is constant, but is higher the longer the investment period.
Chapter 4
The Time Value of Money 121
F i g u re 4 - 6
Capital and Interest Elements of an Annuity
10 000.01
A2 5 E1, A3 5 E2 and so on
B 5 A 3 0.05
D 5 10 000/(Annuity Factor, see below) 5 2820.12
10 000 5 Annuity 3 annuity factor
Annuity factor 5 present value of €1 for four periods at 5% per period
5 1/0.05 2 (1/0.05) / (1 1 0.05)4 5 3.54595
So 10 000 5 Annuity 3 3.546 therefore Annuity 5 10 000 / 3.54595 5 2820.12
These rates are known as one-, two- and three-year spot rates. The rates form what is known as the yield
curve, 5 being the rates for investing now (spot) for one, two and three years—the word ‘spot’ means ‘from
now’ in this context. We were, however, thinking of the rate for year 2, starting at the beginning of year 2
rather than now, and the beginning of year 3 rather than now. Such rates are known as forward rates—they
start at some time in the future and are for one year.
We can work out the implied forward rate by asking the question, if a two-year investor at the end of two
years wanted to convert to a three-year investment, what rate would Barclays have to offer the investor for the
third year to give the same return as a three-year investor?
Answer: Assuming that the bank would allow this, €100 invested for two years would earn 100 ×
(1 1 0.015)2 5 €103.0225. If invested for three years it would earn 100 3 (1 1 0.02)3 5 £106.1208.
So if Barclays were to agree, they would have to offer a return of 106.1208
103.0225 2 1 5 0.030071 or
3.007%, to the two-year investor for the extra third year to match the three-year investment. This
is the implied interest rate for the third year, i.e. the forward rate. By a similar argument the forward rate for the second year is 1.801 per cent.
We said that the rate was implied because we imagined that the bank would allow the conversion.
The implication is however more general. Think of these rates as general market rates for borrowing and
­investing—we look at just such an example in the next chapter when looking at bonds. A trader could phone
See Figure 5.6.
122 Part 2
Fixed Income Securities: An Introduction to Valuation
his or her bank and arrange to have one of the following two strategies for the same low risk as both would be
guaranteed by the bank:
• strategy A: borrowing or investing in one-year intervals at the forward rates, or
• strategy B: borrowing or investing for the three years at the three-year spot rate
Using the forward rates would mean paying or receiving €100 × (1.012) (1.01801) (1.03007) 5 €106.121,
whereas borrowing or investing for three years would also yield €106.121 (i.e. 100 × (1.02)3), the amounts
would be the same.6 Note that the two deals are arranged now and therefore have the same risk—the borrower cannot wait a year and hope that the one-year rate is still 1.2 per cent: that would be a different risk.
The two strategies have to come to the same result because if for example strategy A were cheaper, then a
trader could borrow using strategy A and invest using strategy B. This would yield a profit without taking
any risk as all the rates would be agreed now. An efficient market does not allow a profit to be made without
taking a risk. It would be the equivalent of giving money away, if I could borrow €1m and undertake this
trade and be guaranteed a profit, I would get a certain return without damaging my wealth—this would be
no different from someone giving me money!
This result is sometimes termed no-arbitrage profit and is one of the most powerful results in finance.
Alternatively, it can be seen as an instance of the ‘law of one price’. If there are two strategies that have identical outcomes for identical risk then they must offer identical returns. Option pricing relies on this assertion
(or axiom) as do Modigliani and Miller’s propositions. We shall return to this assertion later. For now, it
establishes the link between forward and spot rates.
You should now be able to move cash flows around in time using interest rates. Here is a checklist:
An interest rate is a general term for applying a ‘charge for time’, normally the rate is quoted per year
(annum) unless stated otherwise. It is also called a discount rate when ‘moving’ future values back to the
present. Another term is the rate of return when looking at an investment from the lender’s point of view.
You should be able to move a single cash flow to any point in the future using Equation 4-1.
You should be able to move a single cash flow from any point in the future to the present using Equation 4-2.
Any uneven cash flows over time can be discounted to the present by using the present value formula (again
Equation 4-2) and adding up the individual present values (Equation 4-4, present values are additive).
You should understand what is meant by a perpetuity and how it is valued (Equation 4-5).
You should be able to calculate the present value of an annuity (Equation 4-7) and the future value of
an annuity (Equation 4-8).
You should be able to convert interest rates from monthly to yearly and from yearly to monthly and more
generally from one time period to another using the exact approach and the simple approach (Equation 4-9).
You should understand the difference between a real rate of interest and the nominal rate of interest
and how to apply both to valuation problems.
You should be able to calculate the capital and interest elements of a repayment.
Answers to questions (4-2) to (4-22) appear in the Appendix. Use a spreadsheet if you do not have a
­financial calculator.
(4 -1)
Explain the following terms:
a. compounding; discounting
b. present value; future value
c. perpetuity; annuity
There is a small rounding error.
Chapter 4
(4 -2)
The Time Value of Money 123
annual, semi-annual, quarterly, monthly, and daily compounding.
annual equivalent rate (APR) or effective annual rate (EAR)
real interest rates; nominal interest rates
Future value: Assume that one year from now you plan to deposit €1000 in a savings
account that pays a nominal rate of 8 per cent.
a.If the bank compounds interest annually, how much will you have in your account
four years from now?
b.What would your balance be four years from now if the bank used quarterly compounding (using the simple method) rather than annual compounding?
c.Suppose that you deposited the €1000 in four payments of €250 each at the end of
years 1, 2, 3 and 4. How much would you have in your account at the end of year 4,
based on 8 per cent annual compounding?
d.Suppose that you deposited four equal payments in your account at the end of
years 1, 2, 3 and 4. Assuming an 8 per cent interest rate, how large would each of
your payments have to be for you to obtain the same ending balance as you calculated in (a)? (Hint: Discount your answer to part a to the present and then use the
present value of the annuity formula. Fill out all you can, the annuity should be
the only unknown.)
(4 -3)
Present value: Assume that you want to borrow €100 000 from your local bank to help
your business. Your bank charges interest at an 8 per cent annual rate.
a.If you wanted to repay the borrowing after one year, how much would you have
to pay?
b.You hope to get an inheritance in one year’s time of €70 000 which you will use
to repay the loan. Then in three years’ time you hope to sell your house and use
some of the money to pay off the rest of the loan. How much will you have to pay?
c.You hope to arrange a 25-year repayment period using your parents’ house (which
you are due to inherit) as security. What annual repayments would be required?
d.Work out the interest element and the capital element for the last section.
e.You hope to arrange a 25-year repayment period only with monthly repayments.
The bank uses the simple approach for calculating the monthly interest rate based
on the 8 per cent annual rate. What monthly repayments are required?
f.Work out the interest element and the capital element for the last section and
compare with your answer to part d.
g. What is the effective annual rate (APR) being charged by the bank in part e?
(4 - 4 )
(4 -5 )
(4 - 6 )
(4 -7 )
(4 - 8 )
Future value of a single payment: If you deposit €10 000 in a bank account that pays
10 per cent interest annually, how much will be in your account after five years?
Present value of a single payment: What is the present value of a security that will pay
€5000 in 20 years if securities of equal risk pay 7 per cent annually?
Interest rate on a single payment: Your parents will retire in 18 years. They currently
have €250 000, and they think they will need €1 million at retirement. What annual
interest rate must they earn to reach their goal, assuming they don’t save any additional funds? (Hint: Use a spreadsheet.)
Number of periods of a single payment: If you deposit money today in an account that
pays 6.5 per cent annual interest, how long will it take to double your money?
Present of an uneven cash flow stream: An investment will pay €100 at the end of each
of the next three years, €200 at the end of year 4, €300 at the end of year 5, and €500 at
the end of year 6. If other investments of equal risk earn 8 per cent annually, what is
this investment’s present value?
124 Part 2
Fixed Income Securities: An Introduction to Valuation
(4 -9)
Annuity payment and EAR: You want to buy a car, and a local bank will lend you
€20 000. The loan would be fully repaid over five years (60 months), and the nominal
interest rate would be 12 per cent, with interest paid monthly. What is the monthly
loan payment? (Hint: Use the simple approach in converting annual to monthly rates.)
(4 -10 )
Future value of an annuity: Find the future value of the following annuities. The first
payment in these annuities is made at the end of year 1, so they are ordinary annuities. (Hint: Find the present value and then use this value and the single sum future
value formula to find its future value at the end of the annuity period.)
a. €400 per year for ten years at 10 per cent
b. €200 per year for five years at 5 per cent
c. €400 per year for five years at 0 per cent
d.Now rework parts a, b and c assuming that payments are made at the beginning
of each year. (Hint: Treat the first payment separately.)
Present value of an annuity: Find the present value of the following ordinary
a. €400 per year for ten years at 10 per cent
b. €200 per year for five years at 5 per cent
c. €400 per year for five years at 0 per cent
d.Now rework parts a, b and c assuming that payments are made at the beginning
of each year. (Hint: Again treat the first payment separately.)
Uneven cash flow stream:
a.Find the present values of the following cash flow streams. The appropriate interest rate is 8 per cent. (Hint: It is fairly easy to work this problem dealing with the
individual cash flows.)
(4 -11)
(4 -1 2)
(4 -1 3)
(4 -14 )
Cash stream A
Cash stream B
b. What is the value of each cash flow stream at a 0 per cent interest rate?
Effective rate of interest: Find the interest rate (or rates of return) in each of the
­following situations.
a. You borrow €700 and promise to pay back €749 at the end of one year.
b. You lend €700 and receive a promise to be paid €749 at the end of one year.
c. You borrow €85 000 and promise to pay back €201 229 at the end of ten years.
d.You borrow €9000 and promise to make payments of €2684.80 at the end of each
of the next five years.
Future value for various compounding periods:
Find the amount to which €500 will grow under each of the following conditions.
(Hint: Use the simple approach for dividing the annual rate into semi-annual and so
on, calculate the present value and then use the future value formula to work out the
equivalent end value.)
Chapter 4
(4 -15 )
(4 -16 )
(4 -17 )
(4 -1 8 )
(4 -19)
(4 -2 0 )
(4 -21)
The Time Value of Money 125
a. 12 per cent compounded annually for five years
b. 12 per cent compounded semi-annually for five years
c. 12 per cent compounded quarterly for five years
d. 12 per cent compounded monthly for five years
Amortization schedule:
a.Set up a schedule for a €25 000 loan to be repaid in equal instalments at the end
of each of the next five years. The interest rate is 10 per cent.
b.How large must each annual payment be if the loan is for €50 000? Assume that the
interest rate remains at 10 per cent and that the loan is still paid off over five years.
c.How large must each payment be if the loan is for €50 000, the interest rate is 10
per cent, and the loan is paid off in equal instalments at the end of each of the
next ten years? This loan is for the same amount as the loan in part b, but the
payments are spread out over twice as many periods. Why are these payments not
half as large as the payments on the loan in part b?
Growth rates: Sales for Hanebury Corporation’s just-ended year were €12 million.
Sales were €6 million five years earlier.
a. At what rate did sales grow?
b.Suppose someone calculated the sales growth for Hanebury in part a as follows:
‘Sales doubled in five years. This represents a growth of 100 per cent in five years;
dividing 100 per cent by 5 results in an estimated growth rate of 20 per cent per
year.’ Explain what is wrong with this calculation.
Expected rate of return: Washington-Pacific invested €4 million to buy a tract of land
and plant some young pine trees. The trees can be harvested in ten years, at which
time W-P plans to sell the forest at an expected price of €8 million. What is W-P’s
expected rate of return?
Effective rate of interest: A mortgage company offers to lend you €85 000; the loan
calls for payments of €8273.59 at the end of each year for 30 years. What interest rate
is the mortgage company charging you?
Present value of a perpetuity: What is the present value of a perpetuity of €100 a year
if the appropriate discount rate is 7 per cent? If interest rates in general were to double
and the appropriate discount rate rose to 14 per cent, what would happen to the present value of the perpetuity?
Loan amortization: Assume that your aunt sold her house on 31 December, and to
help close the sale she took a second mortgage in the amount of €10 000 as part of the
payment. The mortgage has a quoted (or nominal) interest rate of 10 per cent; it calls
for payments every six months (using the simple method, i.e. 5 per cent), beginning
on 30 June, and is to be amortized over ten years. Now, one year later, your aunt must
inform the tax authorities and the person who bought the house about the interest
that was included in the two payments made during the year. (This interest will be
income to your aunt and a deduction to the buyer of the house.) To the closest euro,
what is the total amount of interest that was paid during the first year? Note that the
interest element of any payment is the interest rate on the opening capital balance, the
rest is capital repayment.
Loan amortization: Your company is planning to borrow €1 million on a five-year, 15
per cent, annual payment, fully amortized term loan. What fraction of the payment
made at the end of the second year will represent repayment of principal?
126 Part 2
Fixed Income Securities: An Introduction to Valuation
(4 -2 2)
(4 -2 3 )
Required annuity payments: Assume that your father is now 50 years old, plans to
retire in ten years, and expects to live for 25 years after he retires—that is, until age 85.
He wants his first retirement payment to have the same purchasing power at the time
he retires as €40 000 has today. He wants all of his subsequent retirement payments to
be equal to his first retirement payment. (Do not let the retirement payments grow with
inflation: Your father realizes that if inflation occurs the real value of his retirement
income will decline year by year after he retires.) His retirement income will begin the
day he retires, ten years from today, and he will then receive 24 additional annual payments. Inflation is expected to be 5 per cent per year from today forward. He currently
has €100 000 saved and expects to earn a return on his savings of 8 per cent per year
with annual compounding. To the nearest euro, how much must he save during each of
the next ten years (with equal deposits being made at the end of each year, beginning a
year from today) to meet his retirement goal? (Note: Neither the amount he saves nor
the amount he withdraws upon retirement is a growing annuity.)
Spreadsheet problem
Growing annuity payments: You want to accumulate €1 million by your retirement
date, which is 25 years from now. You will make 25 deposits in your bank, with the
first occurring today. The bank pays 8 per cent interest, compounded annually. You
expect to receive annual raises of 3 per cent, which will offset inflation, and you will
let the amount you deposit each year also grow by 3 per cent (i.e. your s­ econd deposit
will be 3 per cent greater than your first, the third will be 3 per cent greater than the
second, etc.). How much must your first deposit be if you are to meet your goal?
Assume that you are nearing graduation and have applied for a job with a local bank. The bank’s evaluation
process requires you to take an examination that covers several financial analysis techniques. The first section
of the test addresses discounted cash flow analysis. See how you would do by answering the following questions.
a.Draw timelines for (1) a €100 lump sum cash flow at the end of year 2, (2) an ordinary annuity of
€100 per year for three years and (3) an uneven cash flow stream of 2€50, €100, €75 and €50 at the
end of years 0 through 3.
b. (1) What is the future value of an initial €100 after three years if it is invested in an account paying
10 per cent annual interest?
(2) What is the present value of €100 to be received in three years if the appropriate interest rate is
10 per cent?
c.We sometimes need to find out how long it will take a sum of money (or something else, such as
­earnings, population or prices) to grow to some specified amount. For example, if a company’s sales are
growing at a rate of 20 per cent per year, how long will it take sales to double?
d.If you want an investment to double in three years, what interest rate must it earn?
e. (1) What is the future value of a three-year ordinary annuity of €100 if the a­ ppropriate interest rate is
10 per cent?
(2) What is the present value of the annuity?
Bonds and Bond
bond is the major means of borrowing large amounts of money. For a company, bonds are second only
to shares in importance as a source of finance. The main part of government borrowing is also in the
form of bonds.
Bonds affect the risk profile of companies as well as its cash flow. Managing bonds, understanding their
value and their effect on the company is of major importance to the subject of financial management.
In this chapter we assume that the reader understands the content of Chapter 4. This chapter is a particularly clear application of the time value of money.
What is a Bond?
A bond is a certificate that is a promise to pay money in the future. As a means of raising money for firms it
has all the features of borrowing generally, hence aspects of bonds are to be found in other forms of finance,
making the analysis of general importance to borrowing. A simple example of a bond will help outline its
basic features.
EXAMPLE: XYZ plc wishes to raise €2m in bonds. The bond it plans to issue promises
to pay €5 after one year and €105 in two years’ time. This is known as a ‘5 per cent twoyear bond’ in the United Kingdom. All UK bonds have an assumed terminal payment of
£100 (par). Par values differ between markets. The annual interest payments are of par
being, in this case, 5% 3 £100 = £5. Thus we have a quick way of describing a stream of
repayments. An independent valuer thinks that the market will discount the bond at 7 per
cent. In the language of the previous chapter, the market will calculate the present value
of the promised cash f lows using an interest rate of 7 per cent. How many bonds should the
­c ompany issue?
Answer: From Chapter 4, using the present value formula of Equation 4.2 the value of such a
bond would be 1.07
1 1.07
2 5 €96.38. So XYZ plc will have to issue 2m/96.38 5 20 751 bonds.
This example enables us to talk about some important features of bonds from both the investor’s and
borrower’s perspective. Firstly, if the company issues the bonds one method is to auction them, inviting bids
from the public and the major investing institutions. It will then allocate the bonds at a price that ensures all
the bonds are sold. Then it will create a register of owners. The bonds can be bought and sold on the world’s
128 Part 2
Fixed Income Securities: An Introduction to Valuation
stock markets. When bonds are sold, XYZ will note the change of ownership. It will not receive any money
from these subsequent sales. Like shares, it only benefits from the initial sale. All further sales are between
bondholders—the company merely notes the change of ownership.
From this process we can see some of the important market concepts in action as outlined in Chapter 1.
No-one will want to lend XYZ plc £2m. However, many may well be willing to lend a smaller amount. This
could be because the investors do not have £2m but collectively by enabling individuals to invest in a small
number of bonds the company can still raise the £2m. Thus, issuing debt in the form of about 20 000 bonds
(2m /1000) helps the liquidity of the market. It can raise large amounts of cash by the collective investment
of many smaller investors.
Another reason for limiting investment in XYZ is that an investor may not want to take the risk of lending
£2m. Buying only a few bonds is a much smaller risk. In this way investors can choose the level of risk that
they want to take. Thus XYZ can take a large risk with its £2m investment financed by investors who are taking only a small risk. In this way the market provides for risk transformation.
Investors may not want to invest for the whole of the two years, yet XYZ wants to borrow for that length
of time. The original purchasers can sell the bonds on the stock market whenever they want; the bonds can
be passed around between bondholders. In this way investors need only invest for a short time yet XYZ can
borrow for the full two years. Thus the market enables maturity transformation from short-term investors
to longer-term borrowers.
As we know from Chapter 4, an element of the interest rate is risk. In coming to the decision that the
market would likely on average charge a 7 per cent interest rate, a judgement about risk is being made. If
there is any suggestion that XYZ might not be able to pay, the risk element of the interest rate would rise
dramatically. For example, if 7 per cent was indeed the discount rate applied on issue and immediately after
issue there were rumours of cash flow problems, the discount (interest) rate could possibly rise to 20 per
cent, then the price of the bond would fall from the opening price of 96.38 to 1.20
1 105/1.202 5 €77.08.
In this way bonds help with the valuation of XYZ plc, particularly with its ability to pay its debts.
Thus, it is clear why bonds are such an attractive form of borrowing to both the borrower and the lender
and to the investment community as a whole. Bonds are still a risk to both borrower and lender but, as a
negotiable financial instrument (a promise of payment that can be sold), the bond does much to reduce the
negative aspects for both parties.
Every manager should have a working knowledge of the types of bonds that companies and government agencies issue, the terms that are contained in bond contracts, the types of risks to which
both bond investors and issuers are exposed, and procedures for determining the values of and rates of
return on bonds.
Who Issues Bonds?
Investors have many choices when investing in bonds, but bonds are classified into four main types: treasury,
corporate, municipal (or local government) and foreign.
Treasury bonds are sometimes referred to as government bonds. It is unfortunately not reasonable to
assume that the government will make good on its promised payments—Greece is a current example but
through the years governments have defaulted on their debts on a regular basis. Nevertheless, in the case of a
developed country such as the members of the OECD (developed countries), default risk is generally considered to be lower than for any other issuer of bonds.
Currently in the developed world there are high levels of government debt: Greek debt is 175 per cent of
GDP, Japan’s is over 200 per cent and the UK’s is 90 per cent.
Corporate bonds are exposed to default risk—if the issuing company gets into trouble, it may be
unable to make the promised interest and principal payments. Different corporate bonds have different
levels of default risk, depending on the issuing company’s characteristics and the terms of the specific
bond. Default risk is often referred to as ‘credit risk’, and the larger the credit risk, the higher the interest rate the issuer must pay.
Chapter 5
Bonds and Bond Management 129
Municipal or local government bonds like government bonds have a relatively low but not negligible
default risk.
Foreign bonds are issued by foreign governments or foreign corporations. Foreign corporate bonds
are, of course, exposed to default risk, and so are some foreign government bonds. An additional risk
exists if the bonds are denominated in a currency other than that of the investor’s home currency. For
example, if a UK investor purchases a corporate bond denominated in Japanese yen, and if the yen subsequently falls relative to the pound, then the investor will lose money even if the company does not
default on its bonds.
S E L F -T E S T
What is a bond?
What are the four main types of bonds?
Are government bonds riskless?
To what types of risk are investors of foreign bonds exposed?
Key Characteristics of Bonds
Although all bonds have some common characteristics, they do not always have identical contractual
features, as described below.
Par Value, Coupon Rate, Maturity and Yield
We start with a description of a basic bond which is by far the most common form traded in the markets.
Bonds are issued for full repayment in a set number of years: a short-term bond might be up to 5 years, a
medium-term bond 6 to 15 years and a long-term bond over 15 years and can be as high as 30 years or even
without a maturity date.
As discussed in the previous section one of the most important features of bonds is that they can be
traded on the markets. It is important therefore that there is a reasonably standard pattern of repayment. If
each bond repaid in its own way, trading would be very difficult. Nevertheless, some differences have to be
allowed—maturity dates for example will differ. The standard payment schedule of a bond has arisen over
time and meets the needs of a bygone age that perhaps may seem odd. Nevertheless, the patterns are now too
well known and there seems no pressing need for change.
So if a company offers a ‘5 per cent ten-year bond’ the market will know exactly what payments will be made
over the next ten years. Once the bond is issued it will no longer be ten years, so it is better described as a 5 per
cent 2026 bond so that traders can work out what term is left. Its current value will be the present value of the
cash flows discounted at the rate that the market determines—in the same way as any other discount cash flow
problem as from the previous chapter. So we need to understand the pattern of cash flows of a standard bond.
A bond has a par value that is the stated face value of the bond. This is the amount that the issuer will
pay at the end of the life of the bond, i.e. the maturity date. The par value varies according to currencies. In
the United Kingdom the par value is £100; in dollars and euros the par value is 1000 unless otherwise stated.
The coupon rate is the amount that the issuer will pay on a regular basis before the maturity date. The
coupon rate is expressed as a percentage of the par value. Thus a 5 per cent bond will, if par value is £100, be
a payment of £5 a year.
A somewhat confusing feature of bonds is the difference between the coupon rate and the discount rate,
especially if they are both referred to as interest rates. They are indeed both interest rates but the coupon
rate is concerned with the cash to be paid by the borrower and the discount rate is the interest rate applied by
the investor in valuing the bond as outlined in Figure 5-1. The discount rate is also referred to as the yield to
maturity (YTM) of the bond as it is the return that an investor would get if the bond were held to maturity.
Note the link with the idea of an internal rate of return (IRR), as both IRR and YTM are discount rates that
equate positive cash flows with the initial outlay.
130 Part 2
Fixed Income Securities: An Introduction to Valuation
F i g u r e 5 -1
Valuing an n-Year Bond (PV 5 Present/Market Value)
PV 5
coupon rate
coupon rate
coupon rate 1 par value
1 c1
1 1 1 discount rate 2 n
1 1 1 discount rate 2 1
1 1 1 discount rate 2 2
85.95 5
c 1 105
1 1.07 2 1
1 1.07 2 2
1 1.07 2 3
1 1.07 2 10
EXAMPLE: The 5 per cent ten-year bond above illustrates the link with valuation. We assume
a yield to maturity (discount rate) of 7 per cent that is deemed appropriate by the market investors. The question is: ‘What is the value of the 5 per cent 10-year bond if investors want a yield of
7 per cent?’
Answer: Note again that the coupon rate refers to the top of the fraction (the regular payments
to the purchaser of the bond) and the discount rate (yield) refers to the bottom of the fraction
(the numerator and denominator respectively). The reader of the previous chapter will appreciate
that one can either discount the individual cash flows, or one can calculate a ten-year £5 annuity
and add the discounted value of the £100 (Equations 4-7 and 4-2 respectively).
S E L F -T E S T
All bonds have a par of £100:
What is the value of a 5 per cent three-year bond with a 4 per cent discount rate? (Answer: £102.78.)
What is the value of a 2 per cent three-year bond with a 5 per cent discount rate? (Answer: £91.83.)
What is the value of a 4 per cent 20-year bond with a 4 per cent discount rate? (Answer: £100.)
What is the value of a 5 per cent 20-year bond with a 7 per cent discount rate? (­Answer:
52.97 1 25.84 5 £78.81.)
The Various Forms of Bonds
In some cases, a bond’s coupon payment will vary over time. For these floating-rate bonds, the coupon rate
is set for, say, the initial six-month period, after which it is adjusted every six months based on some market
rate. Some issues are tied to the Treasury bond rate; other issues are tied to other rates, such as LIBOR (the
London Interbank Offered Rate). Many additional provisions can be included in floating-rate issues. For
example, some are convertible to fixed-rate debt, whereas others have upper and lower limits (‘caps’ and
‘floors’) on how high or low the rate can go.
Floating-rate debt is popular with investors who are worried about the risk of rising interest rates,
because the interest (coupon rate) paid on such bonds increases whenever market rates rise. This stabilizes the market value of the debt, and it also provides institutional buyers, such as banks, with income
that is better geared to their own obligations. Banks’ deposit costs rise with interest rates, so the income
on floating-rate loans they have made rises at the same time as their deposit costs rise. The savings and
loan industry in the United States was almost destroyed as a result of its former practice of making fixedrate mortgage loans but borrowing on floating-rate terms. If you earn 6 per cent fixed but pay 10 per cent
f loating (which they were), you will soon go bankrupt (which they did). Moreover, f loating-rate debt
appeals to companies that want to issue long-term debt without committing themselves to paying a historically high interest rate for the entire life of the loan.
Chapter 5
Bonds and Bond Management 131
Some bonds pay no coupons at all but are offered on issue at a substantial discount below their par values
and hence provide capital appreciation rather than interest income. These securities are called zero coupon
bonds (‘zeros’).1 Some bonds are issued with a coupon rate too low for the bond to be issued at par, so the
bond is issued at a price less than its par value. In general, any bond originally offered at a price significantly
below its par value is called an original issue discount (OID) bond.
Some bonds do not pay cash coupons but pay coupons consisting of additional bonds (or a percentage of
an additional bond). These are called payment-in-kind bonds, or just PIK bonds. PIK bonds are usually
issued by companies with cash flow problems, which makes them risky.
Some bonds have a step-up provision: if the company’s bond rating is downgraded, then it must increase
the bond’s coupon rate. Step-ups are more popular in Europe than in the United States, but that is beginning
to change. Note that a step-up is quite dangerous from the company’s standpoint. The downgrade means that
it is having trouble servicing its debt, and the step-up will exacerbate the problem. This combination has led
to a number of bankruptcies.
Maturity Date
Bonds generally have a specified maturity date on which the par value must be repaid. Most bonds have
original maturities (the maturity at the time the bond is issued) ranging from 10 to 40 years, but any maturity is legally permissible. Of course, the effective maturity of a bond declines each year after it has been
issued. Thus, a bond with a 15-year original maturity will, a year later, have a 14-year maturity, and so on.
As discussed in the previous chapter, some treasury bonds have no maturity date and are called consols. The
coupon rate will be paid forever and the bond is valued as a perpetuity.
Provisions to Call or Redeem Bonds
Most corporate bonds contain a call provision, which gives the issuing company the right to buy back the
bonds. The call provision generally states that the company must pay the bondholders an amount greater
than the par value if they are called. The additional sum, which is termed a call premium, is often set equal
to one year’s interest if the bonds are called during the first year, and the premium declines at a constant rate
of i/n each year thereafter (where i 5 annual interest and n 5 original maturity in years). For example, the
call premium on a €100 par value, ten-year, 10 per cent bond would generally be €10 if it were called during
the first year, €9 during the second year and so on. However, bonds are often not callable until several years
(generally 5 to 10) after they are issued. This is known as a deferred call, and the bonds are said to have call
Suppose a company sold bonds when interest rates were relatively high. Provided the issue is callable, the
company could sell a new issue of low-yielding securities if and when interest rates drop. It could then use
the proceeds of the new issue to retire the high-rate issue and thus reduce its interest expense. This process is
called a refunding operation.
A call provision is valuable to the firm but potentially detrimental to investors. If interest rates go up,
the company will not call the bond, and the investor will be stuck with the original coupon rate on the
bond, even though interest rates in the economy have risen sharply. However, if interest rates fall,
the company will call the bond and pay off investors, who then must reinvest the proceeds at the current
market interest rate, which is lower than the rate they were getting on the original bond. In other words,
the investor loses when interest rates go up but doesn’t reap the gains when rates fall. To induce an
investor to take this type of risk, a new issue of callable bonds must provide a higher coupon rate than
an otherwise similar issue of noncallable bonds.
As the zero bond reaches maturity it will move closer to the par value as the discount shrinks to zero. So a five-year bond with a YTM
of 7 per cent would be issued at 1.07
5 5 €71.30, this would increase to €100 over the five years. With six months to go the price of the
bond would be 1.071/2 5 €96.67.
132 Part 2
Fixed Income Securities: An Introduction to Valuation
Bonds that are redeemable at par at the holder’s option protect investors against a rise in interest rates. If
rates rise, the price of a fixed-rate bond declines. However, if holders have the option of turning their bonds
in and having them redeemed at par, then they are protected against rising rates. If interest rates have risen,
holders will turn in the bonds and reinvest the proceeds at a higher rate.
Event risk is the chance that some sudden event will occur and increase the credit risk of a company, hence
lowering the firm’s bond rating and the value of its outstanding bonds. Investors’ concern over event risk
means that those firms deemed most likely to face events that could harm bondholders must pay extremely
high interest rates. To reduce this interest rate, some bonds have a covenant called a super poison put, which
enables a bondholder to turn in, or ‘put,’ a bond back to the issuer at par in the event of a takeover, merger or
major recapitalization.
Some bonds have a make-whole call provision. This allows a company to call the bond, but it must pay a
call price that is essentially equal to the market value of a similar noncallable bond. This provides companies
with an easy way to repurchase bonds as part of a financial restructuring, such as a merger.
Sinking Funds
Some bonds include a sinking fund provision that facilitates the orderly retirement of the bond issue—
that is, the large repayment by the company made at the end of the life of the bond. On rare occasions
the firm may be required to deposit money with a trustee, which invests the funds and then uses the
accumulated sum to retire the bonds when they mature. Usually, though, the sinking fund is used to
buy back a certain percentage of the issue each year. A failure to meet the sinking fund requirement
throws the bond into default, which may force the company into bankruptcy. The penalties of non-­
repayment are great.
In most cases, the firm is given the right to administer the sinking fund in either of two ways:
• The company can call in for redemption (at par value) a certain percentage of the bonds each year; for
example, it might be able to call 5 per cent of the total original amount of the issue at a price of €1000
per bond. The bonds are numbered serially, and those called for redemption are determined by a lottery
administered by the trustee.
• The company may buy the required number of bonds on the open market.
The firm will choose the least-cost method. If interest rates have risen, causing bond prices to fall, then
it will buy bonds in the open market at a discount; if interest rates have fallen and the bond prices will have
therefore risen, it will call the bonds. Note that a call for sinking fund purposes is quite different from a
refunding call as discussed previously. A sinking fund call typically requires no call premium, but only
a small percentage of the issue is normally callable in any one year.
Although sinking funds are designed to protect bondholders by ensuring that an issue is retired in an
orderly fashion, you should recognize that sinking funds also can work to the detriment of bondholders.
For example, suppose that the bond on purchase had a 10 per cent yield and a 10 per cent coupon rate
but that yields on similar bonds had subsequently fallen to 7.5 per cent. A sinking fund call at par would
require an investor to give up a bond that has a 10 per cent yield and then to reinvest in a bond that
pays only €7.5 per cent yield. This obviously harms those bondholders whose bonds are called. A company should be cautious in taking such action as its reputation in the market would be damaged. On
balance, however, bonds that have a sinking fund are regarded as being safer than those without such a
provision, so at the time they are issued sinking fund bonds have lower coupon rates than similar bonds
without sinking funds.
Other Provisions and Features
Owners of convertible bonds have the option to convert the bonds into a fixed number of shares. Convertibles offer investors the chance to share in the upside if a company does well, so investors are willing to accept
a lower coupon rate on convertibles than on an otherwise identical but nonconvertible bond.
Chapter 5
Bonds and Bond Management 133
Warrants are options that permit the holder to buy shares at a fixed price, thereby providing a gain if the
price of the shares rises. Some bonds are issued with warrants. As with convertibles, bonds with warrants
have lower coupon rates than straight bonds.
An income bond is required to pay interest only if earnings are high enough to cover the interest expense.
If earnings are not sufficient, then the company is not required to pay interest and the bondholders do not
have the right to force the company into bankruptcy. Therefore, from an investor’s standpoint, income bonds
are riskier than ‘regular’ bonds.
Indexed bonds, also called purchasing power bonds, first became popular in Brazil, Israel and a few
other countries plagued by high inflation rates. The interest payments and maturity payment rise automatically when the inflation rate rises, thus protecting the bondholders against inflation. In January 1997, the US
Treasury began issuing indexed bonds called TIPS, short for Treasury Inflation-Protected Securities. Later in
this chapter we show how TIPS can be used to estimate the risk-free rate.
Bond Markets
Corporate bonds are traded primarily in electronic/telephone markets rather than in organized exchanges.
Most bonds are owned by and traded among a relatively small number of very large financial institutions,
including banks, investment banks, life insurance companies, mutual funds and pension funds. Although
these institutions buy and sell very large blocks of bonds, it is relatively easy for bond dealers to arrange
transactions because there are relatively few players in this market as compared with stock markets.
Information on bond trades is not widely published, but a representative group of bonds is listed and traded
on the bond division of the NYSE and is reported on the bond market page of The Wall Street Journal. Bond
trading on the London Stock Exchange is reported in the Financial Times. The most useful website (as of
mid-2015) is provided by the Financial Industry Regulatory Authority (FINRA) at http://cxa.marketwatch.
S E L F -T E S T
Define floating-rate bonds and zero coupon bonds.
Why is a call provision advantageous to a bond issuer?
What are the two ways a sinking fund can be handled? Which method will be chosen by the firm if
interest rates have risen? If interest rates have fallen?
Are securities that provide for a sinking fund regarded as being riskier than those without this type of
provision? Explain.
What are income bonds and indexed bonds?
Why do convertible bonds and bonds with warrants have lower coupons than similarly rated bonds
that do not have these features?
Bond Valuation
The value of any financial asset such as a share, a bond, a lease, or even a physical asset such as an apartment
building or a piece of machinery, is simply the present value of the cash flows the asset is expected to produce.
The cash flows from a specific bond depend on its contractual features which determine when and how
much will be paid. That is all that is required for the market to work out the present value and hence the market value of the bond.
We have outlined the basic features of bond valuation. In this section we extend this analysis, but first
recap on the basic format. Assuming that the terms coupon rate, par value and yield from the previous sections are understood, the value (VB) of a bond at any moment in time is:
VB 5
coupon rate
coupon rate
c 1 coupon rate 1 par value
1 1
2 1
1 1 1 yield 2
1 1 1 yield 2
1 1 1 yield 2 n
134 Part 2
Fixed Income Securities: An Introduction to Valuation
If the coupon payments are treated as an annuity (see previous chapter, Equation 4-7) then valuation can
be expressed as follows:
VB 5
coupon rate
coupon rate
coupon rate 1 par value
1 c1
1 1 1 yield 2 1
1 1 1 yield 2 2
1 1 1 yield 2 n
which reduces to an annuity and the present value of the par:
par value
VB 5 coupon rate 3 a 2
b 1
11 1 r2n
r 3 11 1 r2n
r 5 the market discount rate or yield or return on investment
n 5 number of remaining years of the bond
The box highlights the annuity formula.
An important feature of bond valuation is to note that where the yield equals the coupon rate, the bond
value equals par2. In fact we can say that:
If coupon rate . yield, then VB . par value
If coupon rate , yield, then VB , par value
If coupon rate 5 yield, then VB 5 par value
So a 30-year 5 per cent US bond (par 5 $1000) with a required yield of 5 per cent would have a market
price of $1000. If the market yield was above 5 per cent, then the price of the bond would be below $1000,
and if the market yield was below 5 per cent, the market value of the bond would be above $1000. This serves
as a useful calculation check. On issue, the issuer generally tries to match the coupon rate with the expected
yield demanded by the market. In practice, the coupon payments are often paid semi-annually so a 5 per cent
coupon on a US bond would pay $25 after six months and $25 at the year end, the valuation formula in
­Equation 5-1 merely has n 5 0.5, 1, 1.5, 2, and so on.
Finding the Yield to Maturity
If you have the market price of, say, a four-year 5 per cent bond, it is useful to know what yield the market
is asking for; in many cases this is given as part of a quote. Working out the yield is nevertheless a good way
of understanding valuation behaviour. For all but the shortest of bond payments there is no formula for
working out the yield instead. Instead it has to be estimated by trial and error using a spreadsheet. Figure 5-2
shows an example of such trial and error.
An example of the Excel formula for valuation of a four-year 5 per cent bond is:
55*(1/E21 2 1/E21/(1 1 E21)^4 1 100/(1 1 E21)^4)
where E21 is the yield cell and 4 is the time to maturity as in this example.3 So what is to be learnt? Simply
that as the yield rises so the price of the bond falls it is an inverse relationship. Bonds lose value when the
interest rates (the cost of time) rise and gain value when the interest rates fall.
An outline proof is to take a par value of 1 and coupon rate 5 yield 5 5 per cent, then the valuation formula becomes VB 5 (0.05/0.05 2
0.05/(0.05(1.05n) 1 1/(1.05)n), which reduces to 1 2 1/(1.05)n 1 1/(1.05)n 5 1, thus both par and the market value VB 5 1.
It is a simple matter to change the interest rate E21 until the value of this formula is the same as the market price; E21 is then the yield
of the bond.
Chapter 5
Bonds and Bond Management 135
F i g u r e 5 -2
Trial and Error Approach to Finding the Yield
What is the yield of a 5 per cent four-year bond if the market price is £95?
VB 5 coupon rate 3 a
par value
b 1
11 1 r2n
r 3 11 1 r2n
where r 5 unknown yield
Par value
5 £100
coupon rate 5 £5
5 £95
We know that the yield must be more than 5 per cent because the market value is less than the par
value (see above)
Market price
95.0001 close enough!
So the yield is 6.46 per cent
Managing Bonds: Duration
Simple questions often have interesting answers. In this case, looking at the financial press it is clear that
there are many bonds with differing yields and maturities or duration ranging from short term to long term.
Why are there so many? Why for example is, at the time of writing, Apple thought to be offering a range of
maturities in raising a reputed $6.5bn?
One answer is that firms want to borrow for differing lengths of time. Although this may be true in some
cases, a firm wanting to borrow for say ten years does not have to take out a ten-year bond. It could start with
a five-year bond and at the end of the first five years it could make another issue for the same amount to pay
off the first bond issue. This is very common and is known as rolling over debt.
Another answer is that there is a demand from the market for bonds of differing maturity. The reason
is that bonds with differing maturities have differing sensitivity to changes in interest rates. A bond of long
maturity is more sensitive to changes in interest rates than a short maturity bond. Figure 5-3 illustrates the
sensitivities. A decrease in yield of bonds from 8 per cent to 7 per cent will increase the value of the bond,
having a lower cost of time. That change will depend on the years to maturity of the bond. If the bond has
only one year left the effect of a decrease in yield from 8 per cent to 7 per cent results in an increase in value
of only 0.9 per cent but for a bond with 30 years the increase in value is 13.5 per cent. Thus the longer the
time to maturity of the bond, the more sensitive the price to changes in the interest rate.
The differing sensitivities to changes in the interest rates may be attractive to speculators but a question of
interest is whether it is of value to financial managers? The answer is that it helps managers immunize their
investments against changes in interest rates. In practice this is a complex calculation that is made by computer programs rather than financial managers with calculators! Here we look at the idea of immunization
136 Part 2
Fixed Income Securities: An Introduction to Valuation
and the role of the sensitivity of bonds to interest rate changes to enable the reader to understand how the
programs help in the management of funds and the reduction in risk.
When interest rates change it is mainly the years to maturity that affect the change in price but also the
coupon rate and the yield rate are an influence. The measure of sensitivity to interest rate changes is termed
duration and as a measure it takes into account the yield and the coupon rate though years to maturity is the
dominant factor.
F i g u r e 5 -3
Change in Value of 5 per cent Bonds of Differing Years to Maturity Due to a Decrease in Yield from
8 per cent to 7 per cent
Years to
value of a
5% bond
Years to
value of a
5% bond
% Change in present
value due to a 1%
decrease in yield
% Change
Years to Maturity
Chapter 5
Bonds and Bond Management 137
The Calculation of Duration
The calculation of duration uses the discounting formula that the reader should now be confident with:
Duration 5
PV 1 CF1 2 1 1 PV 1 CF2 2 2 1 PV 1 CF1 2 3 c 1 PV 1 CFn 2 n
1 price of the bond 2
PV 5 present value discounted at the yield rate
CF1, CF2 etc. 5 Cash flow period 1, 2, …, n; remember that the final payment includes the par value.
EXAMPLE: A four-year 5 per cent bond with a yield of 6 per cent will have a market value of:
Market 1 present 2 value 5
5 96.53
which we then apply to the duration formula as in Equation 5-2:
Duration 5
1 5/1.06 2 1 1 PV 1 5/1.062 2 2 1 PV 1 5/1.063 2 3 1 PV 1 105/1.064 2 4
which becomes:
Duration 5
4.72 1 8.90 1 12.59 1 332.68
5 3.72
So the measure of sensitivity to a change in interest rates is 3.72. We can convert this to a percentage
change in the value of the bond using the following formula:
Percentage change in price 5 2D 3
11 1 y2
D 5 duration
y 5 original yield
dy 5 small change in yield
So if the yield of the four-year 5 per cent bond increases from 6 per cent to 7 per cent, the price is estimated to fall by:
Percentage change in price 5 23.72 3
5 23.5%
1 1 1 0.06 2
So the new price should be 96.53 3 (1 2 0.035) 5 93.15. In fact, using a spreadsheet the exact value is
93.23 so it should not fall by as much as predicted by the duration formula. Nevertheless, the duration formula gives an approximation that is sufficiently accurate for most purposes.
We can view duration in diagrammatic form in Figure 5-4. Equation 5-3 represents a straight line (linear)
relationship between a small change in the yield and the percentage change in price. To illustrate, looking at
138 Part 2
Fixed Income Securities: An Introduction to Valuation
Equation 5-4, a 2 per cent change in price instead of a 1 per cent change would result in a 23.72 1 1 10.02
0.06 2 5 27%
change in the value of the bond, twice the −3.5 per cent change.
The duration formula is represented by the tangential dotted line in Figure 5-4. As can be seen, the line
progressively overestimates the fall in value of the bond for larger increases in the yield. Note that in the previous section the increase in the yield resulted in a predicted value of 93.15 when in fact it was 93.23. There
are corrections that no doubt would have been of use in a pre-computer age. Nowadays exact results are as
easy to obtain.
Figure 5-4 also shows the nature of convexity and its effect on bond values. The longer-term bonds
have a steeper curve and that implies that when interest rates in the market place rise the values of the
longer-term bonds fall by more than the shorter-term bonds. Also, the curves are steeper at the lower
levels of yields than at the higher levels. So if the yield on bonds is a lowly 0.5 per cent and it increases
to 1.5 per cent, the fall in value of the bond is more than if the yield on bonds increases from, say, 10 per
cent to 11 per cent. The yield on bonds is, of course, the discount rate demanded by the market for that
level of perceived risk for the contractual coupon and par payments. Figure 5-4 also shows the effect of
increased coupon payments. The differences are larger for longer-term bonds, and for bonds of all terms
the differences decrease as yields increase. Managing these sensitivities for large investments clearly
requires a deal of calculation and simulation.
Summary: Malkiel’s Theorems
The relationships discussed above are usefully summarized by Malkiel’s five theorems:
1. The higher the yield, the lower the bond price (see Figure 5-2). This is the strongest relationship: for
example, the 10-year 3 per cent bond in Figure 5-4 has a value of €119 when discounted at 1 per cent and
€28 when discounted at 20 per cent.
Figur e 5- 4
An Illustration of Convexity
Value s
Duration line
3% 10 year bond
3% 5 year bond
5% 10 year bond
5% 5 year bond
% Yield to Maturity
Chapter 5
Bonds and Bond Management 139
2. Long-term bonds have greater risk: the longer-term bonds have a steeper curve in Figure 5-4 and
are therefore more sensitive to interest rate changes. For corporate bonds there is also a greater risk of
bankruptcy over a longer period.
3. Higher coupon bonds have less risk. This is present in Figure 5-4 but not clearly so. This is not a strong
relationship. For example, a 3 per cent ten-year bond falls in value by 75.8 per cent when discounted at 20
per cent as opposed to 1 per cent, and a 5 per cent bond falls in value by 73.1 per cent when discounted at
20 per cent as opposed to 1 per cent.
4. The difference in risk between long- and short-term bonds diminishes over time. This is shown in
Figure 5-4 by the difference in the slopes between the dashed and continuous lines—they both flatten
out over time to be similarly sloped and hence reflect a similar sensitivity to interest rate changes.
5. At any one point on the curves in Figure 5-4 a fall in the yield will result in a larger change (rise) in the
value of the bond than an increase in the yield (fall). This is an implication of the curvature of the lines
in Figure 5-4.
Why Bond Sensitivity to Interest Rate Changes Matters
Having struggled through the previous sections the reader might well be wondering why bother with duration when one can get the exact figure using a spreadsheet. The reader is probably right, though knowledge
of the duration measure does help in understanding basic behaviour of bond prices. The important point is
that, broadly speaking, the longer the time to maturity of a bond (its duration) the more sensitive its price to
changes in the interest rate as in the graphs of Figures 5-3 and 5-4.
This does not matter if the bond is held to maturity because the maturity price is the guaranteed par
value; but often the bond will be sold before maturity and the return on the bond depends on the value of
the bond at the time of sale. We have already seen that the change in value of the bond due to an interest rate
change can be large depending on the time to maturity (again, see Figures 5-3 and 5-4).
The large investing institutions, the insurance institutions and pension funds are buying a very different
product if the bond has a 30-year maturity compared to a bond with one year to maturity. The value of their
funds fall by 13.5 per cent in the case of a 30-year bond and an increase in interest from 7 per cent to 8 per
cent in the Figure 5-3 example. On the other hand, if interest rates fall by 1 per cent then the value of such
bonds will rise by 13.5 per cent. So they are more risky than the one-year-to-maturity bond with a less than
1 per cent movement in price.
A second more complex reason is concerned with matching durations of assets and liabilities. As this is
part of cash flow management it is of direct concern to financial management. Here we outline the problem
with a simplified example.
EXAMPLE: Suppose that Risky Insurance has a £1m bill to pay in one year and invests the
present value of that amount in the form of six-year 5 per cent bonds with a yield of 7 per cent
purchased at the very start of the six-year period (the next payment will be £5 at the end of the
first year). The value of that bond will be:
5 90.47
The yield is 7 per cent, so in one year when payment is due, the value of the investment
should be 90.47 × (1.07) 5 96.80. This is also called the holding period return, which in this
case is the yield. Just to check this we can calculate it as follows. In one year’s time the bond
will have 5 years left and will be priced at:
c 105 5 91.80
3 1
1 1
2 1
In addition it will receive the £5 at the end of the first year, a total of £91.8 1 £5 5 £96.80
which is the 7 per cent return calculated earlier. For the £1m bill Risky will need £1m/1.07 5
£934 579 worth of bonds or in this case 934 579/90.47 5 10 330 bonds.
140 Part 2
Fixed Income Securities: An Introduction to Valuation
But what happens if the day after purchase of these bonds at the start of the one-year holding
period, the required yield rises to 8 per cent? The price will fall to:
c 105 5 86.13
3 1
1 1
2 1
So if the rate stays at 8 per cent, the value of one bond will be at the end of the first year with
only five years left will be:
c 105 5 88.02
3 1
1 1
2 1
In addition there is the £5 payment so the total value will be £88.02 1 £5 5 93.02 and a total
value of 93.02 3 10 330 5 £960 897 a shortfall of £1m 2 £960 897 5 £30 103.
The cause of the shortfall is the increase in interest rates and the sensitivity of the bond to the
interest rate—that is to say, the duration of the bond.
The solution is to match the duration of the bond to the duration of the liability, which
in this case is one year. In this example a 5 per cent one-year bond would have a price of
105/1.07 5 98.13 at the start of the year but would need 1m/105 5 9524 bonds, and so the
cost would be £934 590 (i.e. 9524 3 98.13), only £11 more expensive than the six-year bonds.
The £105 is however guaranteed, whatever subsequently happens to the interest rate.
As part of the management of cash flows where the duration of the investments is very different from the
duration of the liability (which is simply the time to payment), a change in interest rates will mean purchases
or sales of bonds to match the required investment to pay the future bill. Matching the duration more closely
will reduce the need to buy more bonds in the event of a rise in interest rates but at lower likely yields the
returns on the investment will be less.
The Risk of Default
The risk of investing in bonds is that of default—the failure to pay the contracted amounts. The bond market
therefore offers a range of variations that provide greater security of collateral, reducing such risk.
Bond Contract Provisions That Influence Default Risk
Default risk is affected by both the financial strength of the issuer and the terms of the bond contract,
­especially whether collateral has been pledged to secure the bond. Several types of contract provisions are
discussed next.
Bond Indentures
An indenture is a legal document that spells out the rights of both bondholders and the issuing corporation. A trustee is an official (usually a bank) who represents the bondholders and makes sure the terms
of the indenture are carried out. The indenture may be several hundred pages in length, and it will
include restrictive covenants that cover such points as the conditions under which the issuer can pay
off the bonds prior to maturity, the levels at which certain ratios must be maintained if the company is
to issue additional debt, and restrictions against the payment of dividends unless earnings meet certain
In the United States, the Securities and Exchange Commission (1) approves indentures and (2) makes sure
that all indenture provisions are met before allowing a company to sell new securities to the public. A firm
will have different indentures for each of the major types of bonds it issues, but a single indenture covers
all bonds of the same type. For example, one indenture will cover a firm’s first mortgage bonds, another its
debentures, and a third its convertible bonds.
Chapter 5
Bonds and Bond Management 141
Mortgage Bonds
A corporation pledges certain assets as security for a mortgage bond. The company might also choose to
issue second-mortgage bonds secured by the same assets that were secured by a previously issued mortgage
bond. In the event of liquidation, the holders of these second mortgage bonds would have a claim against the
property, but only after the first mortgage bondholders had been paid off in full. Thus, second mortgages are
sometimes called junior mortgages because they are junior in priority to the claims of senior mortgages, or
first-mortgage bonds. All mortgage bonds are subject to an indenture that usually limits the amount of new
bonds that can be issued.
Debentures and Subordinated Debentures
A debenture is an unsecured bond, and as such it provides no lien against specific property as security for
the obligation. Debenture holders are, therefore, general creditors whose claims are protected by property
not otherwise pledged.
The term subordinate means ‘below’ or ‘inferior to’; thus, in the event of bankruptcy, subordinated debt
has claims on assets only after senior debt has been paid off. Subordinated debentures may be subordinated
either to designated notes payable (usually bank loans) or to all other debt. In the event of liquidation or
reorganization, holders of subordinated debentures cannot be paid until all senior debt, as named in the
debentures’ indentures, has been paid.
Development Bonds
In the United States, some companies may be in a position to benefit from the sale of either development
bonds or pollution control bonds. State and local governments may set up both industrial development
agencies and pollution control agencies. These agencies are allowed, under certain circumstances, to sell
tax-exempt bonds and then make the proceeds available to corporations for specific uses deemed (by Congress) to be in the public interest. For example, a Detroit pollution control agency might sell bonds to provide
Ford with funds for purchasing pollution control equipment. As the income from the bonds would be tax
exempt, the bonds would have relatively low interest rates. Note, however, that these bonds are guaranteed by
the corporation that will use the funds, not by a governmental unit, so their rating reflects the credit strength
of the corporation using the funds.
Zero Coupon Bonds and Bond Stripping
Bonds can of course be issued and have zero coupon rate, so that the only payment is the par value at the
end of the term of the bond. This would be attractive to companies and institutions that seek to invest to
provide for a large future payment. As much business is seasonal and contracts require periodic payments,
such u
­ neven cash flows are common. There is no need for coupon payments for such purposes. Alternatively,
bond traders may buy bonds and then sell the coupon payments and the par value payment at the end to
other parties whilst retaining ownership of the original bond. Buying just the coupons would be similar to
buying an annuity. This again would be attractive to the market where the need is for a regular cash flow
having received a large payment. Thus the original bond made up of coupon payments and par value at the
end can be altered by the market whilst retaining all the other advantages of a bond, its acceptability worldwide and the protection against default risk in particular.
Inflation Index Linked Bonds
These are also known as inflation-proof bonds or inflation-linked bonds or in the United States, ‘Treasury
inflation-protected securities’. Such bonds seek to pay the real value or today’s money value of the coupon and par payments. The previous chapter distinguished between real and monetary payments. A simple example is if the coupon payment is €10 and inflation the following year is 10 per cent then the next
year’s payment will be 10 3 1.1 5 €11, and so on. In these times of deflation such a bond is of course not so
142 Part 2
Fixed Income Securities: An Introduction to Valuation
Fitch Rates Falabella
On 15 August, Fitch upgraded the international
bonds of S.A.C.I. Falabella, a Chilean company
involved in retail, real estate and financial services.
The reasoning given was as follows: its EBITDA
(earnings before interest, taxes, depreciation and
amortization) divided by sales (the margin) had
been 13 to 14 per cent despite varying economic
conditions. Cash flow generation was stable. Free
cash flow was mildly negative but not a problem
as it had a very liquid credit card operation. Leverage ratio is some 2.5 (debt divided by equity) and
is expected to remain steady.
Key assumptions are: EBITDA margin remains
in the 13 per cent range; annual free cash flow
(FCF) margin sustained negative in low single
digit; Capex of USD4 billion up to 2018; Gross
adjusted leverage (including retail, shopping malls
and financial operations) below 5× on a sustained
basis; gross adjusted leverage (excluding real
estate (shopping malls) and financial operations)
of between 2× and 3× on a sustained basis. Future
dangers include: significant deterioration in the
credit quality of the company’s credit card and
banking businesses; FCF consistently reaching levels around 15 per cent of revenues; gross adjusted
leverage (excluding banking and credit card operations and real estate businesses) remain consistently above 3×.
Po s i t i ve a dju s t m e n t may o c c ur i f : gr o s s
adjusted leverage (excluding banking and credit
card operations and real estate businesses) remain
consistently below 2×.
Positive FCF generation after capex and dividends; liquidity ratio, measured as FCF plus cash and
marketable securities over debt service coverage,
consistently in excess of 1.25. This is only part of the
many considerations that make up a bond rating.
S o u r c e : h t t p : // w w w . b u s i n e s s w i r e . c o m / n e w s /
Bond Ratings
Since the early 1900s, bonds have been assigned quality ratings that reflect their probability of going into
default. The three major rating agencies are Moody’s Investors Service (Moody’s), Standard & Poor’s Corporation (S&P) and Fitch Ratings. As shown in columns (3) and (4) of Table 5-1, triple-A and double-A
bonds are extremely safe, rarely defaulting even within five years of being assigned a rating. Single-A and
triple-B bonds are also strong enough to be called investment-grade bonds, and they are the lowest-rated
bonds that many banks and other institutional investors are permitted by law to hold. Double-B and lower
bonds are speculative bonds and are often called junk bonds. These bonds have a significant probability of
Bond Rating Criteria, Upgrades and Downgrades
Bond ratings are based on both quantitative and qualitative factors, as we describe below.
1. Financial Ratios. Many ratios potentially are important, but the return on invested capital, debt ratio
and interest coverage ratio are particularly valuable for predicting financial distress. For example, columns (1), (5) and (6) in Table 5-1 show a strong relationship between ratings and the return on capital
and the debt ratio.
2. Bond Contract Terms. Important provisions for determining the bond’s rating include whether the
bond is secured by a mortgage on specific assets, whether the bond is subordinated to other debt, any
sinking fund provisions, guarantees by some other party with a high credit ranking, and restrictive covenants such as requirements that the firm keep its debt ratio below a given level or that it keep its times
interest earned ratio above a given level.
3. Qualitative Factors. Included here would be such factors as sensitivity of the firm’s earnings to the
strength of the economy, how it is affected by inflation, whether it is having or is likely to have labour
problems, the extent of its international operations (including the stability of the countries in which it
Chapter 5
Bonds and Bond Management 143
TA B L E 5 -1
Bond Ratings, Default Risk and Yields
Rating Agencya
S&P and
Percent Defaulting Within:b
1 year
5 years
Median Ratiosc
Return on Total debt/
capital Total capital
Percent Upgraded or
Downgraded in 2011b
Investment-grade bonds
Junk bonds
Notes: aThe ratings agencies also use ‘modifiers’ for bonds rated below triple-A. S&P and Fitch use a plus and minus system; thus, A+ designates the
strongest A-rated bonds and A- the weakest. Moodys uses a 1, 2, or 3 designation, with 1 denoting the strongest and 3 the weakest; thus, within the
double-A category, Aa1 is the best, Aa2 is average, and Aa3 is the weakest.
Default data are from Fitch Ratings Global Corporate Finance 2011 Transition and Default Study, March 16, 2012: see www.fitchratings.com/
Median ratios are from Standard & Poors 2006 Corporate Ratings Criteria, April 23, 2007: see www2.standardandpoors. com/spf/pdf/
Composite yields for 10-year AAA, AA, A, and BBB bonds can be found at www.bondsonline.com/Todays_Market/ Composite_Bond_Yields_
table.php. Representative yields for 10-year BB, B, and CCC bonds can be found using the bond screener at http://cxa.marketwatch.com/finra/
bondcenter/AdvancedScreener.aspx. Thin markets cause the AAA rate to be unusually high.
operates), potential environmental problems, potential antitrust problems, and so on. An example is the
exposure to subprime loans, including the difficulty of determining the extent of this exposure owing to
the complexity of the assets backed by such loans.
Rating agencies review outstanding bonds on a periodic basis and re-rate if necessary. Columns (7)
and (8) in Table 5-1 show the percentages of companies in each rating category that were downgraded or
upgraded in 2011 by Fitch Ratings. The year 2011 was a difficult one, as more bonds were downgraded than
Over the long run, ratings agencies have done a reasonably good job of measuring the average credit risk
of bonds and of changing ratings whenever there is a significant change in credit quality. However, it is
important to understand that ratings do not adjust immediately to changes in credit quality, and in some
cases there can be a considerable lag between a change in credit quality and a change in rating. For example, Enron’s bonds still carried an investment-grade rating on a Friday in December 2001, but the company
declared bankruptcy two days later, on Sunday. Many other abrupt downgrades occurred in 2007 and 2008,
leading to calls by Congress and the SEC for changes in rating agencies and the way they rate bonds. Clearly,
improvements can be made, but there will always be occasions when completely unexpected information
about a company is released, leading to a sudden change in its rating.
There have also been misleading ratings. This is always a risk given the development of new innovations in bonds and bond-like financial instruments. In 2015 S&P were fined $77m by the Security
Exchange Commission and banned from rating certain mortgage-backed securities for one year. One of
the issues was the AAA rating given by rating agencies to mortgage-backed securities that later turned
out to be worthless.
144 Part 2
Fixed Income Securities: An Introduction to Valuation
Bond Ratings and the Default Risk Premium
Why are bond ratings so important? First, most bonds are purchased by institutional investors rather than
individuals, and many institutions are restricted to investment-grade securities. Thus, if a firm’s bonds fall
below BBB, it will have a difficult time selling new bonds because many potential purchasers will not be
allowed to buy them. Second, many bond covenants stipulate that the coupon rate on the bond automatically
increases if the rating falls below a specified level. Third, because a bond’s rating is an indicator of its default
risk, the rating has a direct, measurable influence on the bond’s yield. Column (9) of Table 5-1 shows that
an AA bond has a yield of 3.38 per cent and that yields increase as the rating falls. In fact, an investor would
earn 9.98 per cent on a CCC bond if it did not default.
F i g u r e 5 -5
Risk Premiums and Ratings of Government Borrowing, Mainly Bonds
Ten-year bond rates
Current inflation rate
S&P Credit
South Africa
United States
United Kingdom
Czech Republic
Source: http: //www.tradingeconomics.com 09/02/2015
Chapter 5
Bonds and Bond Management 145
A bond spread is the difference between a bond’s yield and the yield on some other security of the same
maturity. Unless specified differently, the term ‘spread’ generally means the difference between a bond’s
yield and the yield on a Treasury bond of similar maturity.
Figure 5-5 shows the relationship between credit ratings and ten-year bond ratings. The yield rates for
the bonds clearly includes inflation, we are interested in risk so we have deducted inflation to give the real
rates. The difference between real rates is for the most part due to risk.4 In general, it is clear that the market
demands lower yields from countries with better credit ratings. The same is true for companies. The relationship is not exact as there are other factors taken into account in the credit rating and the inflation figure
is, as stated, not necessarily related to expected inflation. The United Kingdom, for example, has quite a high
real rate of return (i.e. the difference) yet a high credit rating. The Czech Republic has a very low ten-year
bond rating yet a worse credit rating than Germany, perhaps understandably as it is an emerging economy
albeit with high expectations.
S E L F -T E S T
Differentiate between mortgage bonds and debentures.
Name the major rating agencies, and list some factors that affect bond ratings.
What is a bond spread?
How do bond ratings affect the default risk premium?
A ten-year T-bond has a yield of 6 per cent. A ten-year corporate bond with a rating of AA has a yield
of 7.5 per cent. If the corporate bond has excellent liquidity, what is an estimate of the corporate
bond’s default risk premium? (Answer: 1.5 per cent.)
Reinvestment Rate Risk
We have seen so far that the ordinary bond is exposed to default risk, inflation risk and (in examining duration) interest rate risk. To this list we add reinvestment rate risk and note that combined with interest rate
risk it is sometimes termed maturity risk premium (MRP).
Apart from default, the biggest risk is of an increase in interest rates. That will hurt bondholders because
it will lead to a decline in the value of a bond portfolio. But can a decrease in interest rates also hurt bondholders? We know that bond prices will rise but the scenario is not entirely good. If interest rates fall then a
bondholder may suffer a reduction in his or her income. For example, consider a retiree who has a portfolio
of bonds and lives off the income they produce. The bonds, on average, have a coupon rate of 10 per cent.
Now suppose that interest rates decline to 5 per cent. The short-term bonds will mature, and when they do,
they will have to be replaced with lower-yielding bonds. In addition, many of the remaining long-term bonds
may be called (the companies buy them back), and as calls occur, the bondholder will have to replace 10 per
cent coupon rate bonds with 5 per cent bonds. Thus, our retiree will suffer a reduction of income.
Generally, when interest rates fall, firms will offer lower coupon rates as a smaller drain on cash flows.
A firm could nevertheless offer high coupon rates to attract retirees; the cost to the firm would not be greater
as the yield is independent of the coupon rate—bonds would sell at above their par value. To clarify, if XYZ
plc offered a two-year 15 per cent bond and the required market yield for that firm was 6 per cent then the
market value would be 15/(1.07) 1 115/(1.07)2 5 114.46, and the bonds would be issued at about this price if
auctioned or taken up by institutions. Alternatively, the coupon rate could be 5 per cent and the market value
would be 5/(1.07) 1 105/(1.07)2 5 96.38. In both cases XYZ plc is having to pay 7 per cent on its borrowing,
it is just repaying in a different way. As the 15 per cent coupon rate could be attractive to the elderly, the yield
rate might be slightly lower than 7 per cent. Such high coupon rate bonds have been offered by the UK government as ‘Granny bonds’ or ‘651 pensioner bonds’ which have been very successful—companies should
take note!
We assume that time preference is the same between countries.
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Accepting that the normal practice is for coupon rates to follow general interest rates, the risk of an
income decline due to a drop in interest rates is called reinvestment rate risk. Reinvestment rate risk is obviously high on callable bonds. It is also high on short-maturity bonds, because the shorter the maturity of a
bond, the fewer the years when the relatively high old interest rate will be earned and the sooner the funds
will have to be reinvested at the new low rate. Thus, retirees whose primary holdings are short-term securities are hurt badly by a decline in rates, but holders of long-term bonds continue to enjoy their old high rates
but the higher duration would reduce their capital by more than the shorter term bonds.
S E L F -T E S T
To which type of risk are holders of long-term bonds more exposed? Short-term bondholders?
The Yield Curve: The Market Approach
to Interest Rates
In the previous chapter is was noted that the market does not charge a constant per period interest rate. As
a saver you will note that with your local bank, there is a higher annual interest rate the longer you commit
your savings. From the previous chapter recall that spot rates are annual interest rates starting from the first
year. So, a two-year spot rate is the annual rate for the first two years. There is also a forward rate which is the
rate for a particular year in the future, so a two-year forward rate is for the second year only. The previous
chapter showed the relationship between the two. The market rates for spot and forward rates of differing
time periods are determined by examining the yields of bonds of differing maturities.
The Term Structure of Interest Rates
The term structure of interest rates describes the relationship between long-term and short-term rates. The
term structure is important both to corporate treasurers deciding whether to borrow by issuing long-term or
short-term debt and to investors who are deciding whether to buy long-term or short-term bonds.
The Few, the Proud, the . . . AAA-Rated Companies!
A A A-rated companies are members of an elite
group. Over the last 20 years, this cream of the
crop has included such powerhouses as 3M,
Abbott Labs, BellSouth, ExxonMobil, GE, Kellogg,
Microsoft and UPS. Only large companies with
stable cash flows make it into this group, and for
years they guarded their AAA ratings vigilantly. In
recent years, however, the nonfinancial AAA-rated
corporation has become a vanishing breed. In
March 2012, the major ratings agencies (Fitch, S&P
and Moody’s) only agreed on the highest rating for
three nonfinancial companies without government
backing: ExxonMobil, XTO Energy (a subsidiary of
ExxonMobil) and Johnson & Johnson. When the
list is expanded to more than just nonfinancials,
it is interesting to note that many of the powerhouses are not-for-profits. For example, Saddleback Valley Community Church, a megachurch
located in Southern California, has a top rating, as
do MIT and Princeton University.
Why do so few companies have AAA ratings?
One reason may be that the recent financial crisis
and recession have hurt the creditworthiness of
even large, stable companies. A more likely explanation, however, is that in recent years large, stable companies have increased their debt levels
to take greater advantage of the tax savings that
they afford. With higher debt levels, these companies are no longer eligible for the highest rating. In
essence, they have sacrificed their AAA rating for
lower taxes. Does this sound like a good tradeoff
to you? We will discuss how companies choose the
level of debt in Chapter 15.
Source: www.finra.org/lnvestors/lnvestmentChoices/
Chapter 5
Bonds and Bond Management 147
Interest rates for bonds with different maturities can be found in a variety of publications, including
The Wall Street Journal and the Financial Times, as well as on a number of websites, including ­Bloomberg,
Yahoo!, CNN Financial, and national central banks. Using interest rate data from these sources, we can
determine the term structure at any given point in time. For example, Figure 5-6 presents interest rates for
different maturities for the spot and forward rates. The top graph is the typical upward-sloping curve offering the market higher per year interest rates the longer the investment. The bottom graph shows that this
is not always the case in times of uncertainty—as in the years 2005 to 2008 in the UK. Investors may take a
more optimistic view of the long term than the present.
Figur e 5-6
Spot and Forward Rate Yield Curve for Commercial Banks, 9 February 2015, and historic spot rate
curves, Produced by the Bank of England
Spot rate curve
Forward rate curve
Sources: Bloomberg and Bank of England calculations.
148 Part 2
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Historically, long-term rates are generally higher than short-term rates owing to the maturity risk premium. To restate, this is mainly the effect of interest rate changes on the value of the bond—the greater the
length of time for the bond, the larger the effect of an interest rate change, hence the higher rate required; it
is riskier, so the yield curve usually slopes upward. For this reason, people often call an upward-sloping yield
curve a normal yield curve and a yield curve that slopes downward an inverted, or abnormal, curve.
A few academics and practitioners contend that large bond traders who buy and sell securities of different
maturities each day dominate the market. According to this view, a bond trader is just as willing to buy a
30-year bond to pick up a short-term profit as to buy a three-month security. Strict proponents of this view
argue that the shape of the yield curve is therefore determined only by market expectations about future
interest rates, a position that is called the pure expectations theory, or sometimes just the expectations
theory. If this were true, then the maturity risk premium (MRP) would be zero and long-term interest rates
would simply be a weighted average of current and expected future short-term interest rates. See Web Extension 5D for a more detailed discussion of expectations theory.
S E L F -T E S T
What is a yield curve, and what information would you need to draw this curve?
Distinguish between the shapes of a ‘normal’ yield curve and an ‘abnormal’ curve.
If the spot interest rates on 1-, 5-, 20- and 30-year bonds are (respectively) 4 per cent, 5 per cent, 6 per
cent and 7 per cent, then how would you describe the yield curve?
How would you describe it if the rates were reversed?
Financing with Junk Bonds
Recall that bonds rated less than BBB are noninvestment-grade debt, also called junk bonds or high-yield
debt. There are two ways that a bond can become a junk bond. First, the bond might have been investment-grade debt when it was issued but its rating declined because the issuing corporation had fallen on hard
times. Such bonds are called ‘fallen angels’.
Some bonds are junk bonds at the time they are issued, but this was not always true. Prior to the 1980s,
fixed-income investors such as pension funds and insurance companies were generally unwilling to buy risky
bonds, so it was almost impossible for risky companies to raise capital in the public bond markets. Then, in
the late 1970s, Michael Milken of the investment banking firm Drexel Burnham Lambert, relying on historical studies that showed risky bonds yielded more than enough to compensate for their risk, convinced institutional investors that junk bond yields were worth their risk. Thus was born the junk bond market.
In the 1980s, large investors like T. Boone Pickens and Henry Kravis thought that certain old-line, established companies were run inefficiently and were financed too conservatively. These corporate raiders were
able to invest some of their own money, borrow the rest via junk bonds, and take over the target company,
usually taking the company private. The fact that interest on the bonds was tax deductible, combined with
the much higher debt ratios of the restructured firms, increased after-tax cash flows and helped make the
deals feasible. Because these deals used lots of debt, they were called leveraged buyouts (LBOs).
In recent years, private equity firms have conducted transactions similar to the LBOs of the 1980s, taking advantage of historically low junk-bond rates to help finance their purchases. For example, in 2007 the
private equity firm Kohlberg Kravis Roberts and Company (KKR) took the discount retailer Dollar General
private in a $6.9 billion deal. As part of the transaction, Dollar General issued $1.9 billion in junk bonds. So
KKR financed approximately 73 per cent of the deal with its own cash (coming from its own equity and from
money it had borrowed on its own account) and about 27 per cent of the deal with money that Dollar General
raised, for a net investment of about $5 billion. In late 2009, KKR took Dollar General public again at $21 per
share with a resulting market value of equity of $7.1 billion and a very tidy gain!
S E L F -T E S T
What are junk bonds?
Chapter 5
Bonds and Bond Management 149
This chapter described the different types of bonds that governments and corporations issue, explained
how bond prices are established, and discussed how investors estimate the rates of return they can expect to
earn. The rate of return required by debtholders is the company’s pre-tax cost of debt, and this rate depends
on the risk that investors face when they buy bonds.
A bond is a long-term promissory note (the market term for an IOU note). A bond is issued by a business or governmental unit. The issuer receives money in exchange for promising to make interest or
coupon payments and to repay the principal or par value on a specified future date.
Some special types of long-term financing include zero coupon bonds, which pay no annual coupon
rates but are priced at the present value of just the single payment of par at the end of the bond’s life.
There are many types of bonds that are in essence variations of the basic model examined here. A particular variant is the junk bond, which is a high-risk, high-yield instrument issued by firms that use a
great deal of financial leverage. Another is an inflation-proofed bond where the cash flows are in real
terms—the previous chapter addressed this calculation.
A call provision gives the issuing corporation the right to redeem the bonds prior to maturity under
specified terms, usually at a price greater than the maturity value (the difference is a call premium).
A firm will typically call a bond if interest rates fall substantially below the coupon rate.
A sinking fund is a provision that requires the corporation to retire a portion of the bond issue each year.
The purpose of the sinking fund is to provide for the orderly retirement of the issue. A sinking fund typically requires no call premium.
The value of a bond is found as the present value of an annuity (the interest payments) plus the present
value of a lump sum (the principal). The bond is evaluated at the appropriate periodic interest rate over
the number of periods for which interest payments are made.
Coupon payments are often semi-annual using the simple approach (the coupon payment divided by 2).
The expected rate of return on a bond held to maturity is defined as the bond’s yield to maturity
(see Figure 5-4).
Valuation of bonds is simply an application of the present value formulae of the previous chapter.
The nominal (or quoted) interest rate on a debt security should be composed of the real risk-free
rate, plus premiums that ref lect inf lation (IP), default risk (DRP), liquidity (LP) and maturity
risk (MRP).
The longer the maturity of a bond, the more its price will change in response to a given change in interest rates; this is called interest rate risk. However, bonds with short maturities expose investors to high
reinvestment rate risk, which is the risk that income from a bond portfolio will decline because cash
flows received from bonds will be rolled over at lower interest rates.
Duration is a measure of interest rate risk.
Corporate and municipal or local government bonds have default risk. If an issuer defaults, investors
receive less than the promised return on the bond. Therefore, investors should evaluate a bond’s default
risk before making a purchase.
Bonds are assigned ratings that ref lect the probability of their going into default. The highest rating is AAA, and they go down to D. The higher a bond’s rating, the lower its risk and therefore its
interest rate.
The relationship between the yields on securities and the securities’ maturities is known as the term
structure of interest rates, and the yield curve is a graph of this relationship.
The shape of the yield curve depends on two key factors: (1) expectations about future inflation and
(2) perceptions about the relative risk of securities with different durations.
The yield curve is normally upward sloping—this is called a normal yield curve. However, the curve can
slope downward (an inverted yield curve) if the inflation rate is expected to decline.
The expectations theory states that yields on long-term bonds reflect expected future interest rates.
150 Part 2
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Solutions to questions 5-6 to 5-29 appear in the Appendix.
( 5 -1)
Define each of the following terms:
a. bond; treasury bond; corporate bond; municipal bond; foreign bond
b. par value; maturity date; coupon payment; coupon interest rate
c. zero coupon bond; original issue discount bond (OID)
d. call provision; redeemable bond; sinking fund
e. current yield (on a bond); yield to maturity (YTM)
f. indentures; mortgage bond; debenture; subordinated debenture
g. junk bond
h. inflation premium (IP); default risk premium (DRP); liquidity; liquidity
premium (LP)
i. maturity risk premium (MRP); reinvestment rate risk
j. term structure of interest rates; yield curve
k. ‘normal’ yield curve; inverted (‘abnormal’) yield curve
( 5 -2)
‘Short-term interest rates are more volatile than long-term interest rates, so shortterm bond prices are more sensitive to interest rate changes than are long-term bond
prices.’ Is this statement true or false? Explain.
The rate of return on a bond held to its maturity date is called the bond’s yield to
maturity. If interest rates in the economy rise after a bond has been issued, what will
happen to the bond’s price and to its YTM? Does the length of time to maturity affect
the extent to which a given change in interest rates will affect the bond’s price? Why
or why not?
If you buy a callable bond and interest rates decline, will the value of your bond rise by as
much as it would have risen if the bond had not been callable? Explain.
A sinking fund can be set up in one of two ways. Discuss the advantages and disadvantages of each procedure from the viewpoint of both the firm and its bondholders.
Bond valuation: The Pennington Corporation issued a new series of bonds on 1 January
1990. The bonds were sold at par (€1000), had a 12 per cent coupon, and matured in
30 years on 31 December 2019. Coupon payments are made semi-annually (on 30 June
and 31 December).
( 5 -3)
( 5 -5 )
a. What was the YTM on the date the bonds were issued?
b. What was the price of the bonds on 1 January 1995 (five years later), assuming
that interest rates had fallen to 10 per cent?
c. Find the current yield, capital gains yield, and total yield on 1 January 1995, given
the price as determined in (b).
d. On 1 July 2013 (6.5 years before maturity), Pennington’s bonds sold for €916.42.
What are the YTM, the current yield, and the capital gains yield for that date?
e. Now assume that you plan to purchase an outstanding Pennington bond on 1
March 2013, when the going rate of interest given its risk is 15.5 per cent. How
large a cheque must you write to complete the transaction? (Hint: Don’t forget the
accrued interest.)
( 5 -7 )
Bond valuation with annual payments: Jackson Corporation’s bonds have 12 years
remaining to maturity. Interest is paid annually, the bonds have a €1000 par value,
and the coupon interest rate is 8 per cent. The bonds have a yield to maturity of 9 per
cent. What is the current market price of these bonds?
Yield to maturity for annual payments: Wilson Wonders’ bonds have 12 years remaining to maturity. Interest is paid annually, the bonds have a €1000 par value, and the
Chapter 5
( 5 -9)
( 5 -10 )
( 5 -11)
( 5 -1 2)
( 5 -1 3 )
( 5 -1 4 )
( 5 -15 )
Bonds and Bond Management 151
coupon interest rate is 10 per cent. The bonds sell at a price of €850. What is their
yield to maturity?
Current yield for annual payments: Heath Foods’s bonds have seven years remaining to
maturity. The bonds have a face value of €1000 and a yield to maturity of 8 per cent.
They pay interest annually and have a 9 per cent coupon rate. What is their current
Determinant of interest rates: The real risk-free rate of interest is 4 per cent. Inflation is
expected to be 2 per cent this year and 4 per cent during the next two years. Assume
that the maturity risk premium is zero. What is the yield on two-year Treasury securities? What is the yield on three-year Treasury securities?
Default risk premium: A Treasury bond that matures in ten years has a yield of 6 per cent.
A ten-year corporate bond has a yield of 9 per cent. Assume that the liquidity premium on the corporate bond is 0.5 per cent. What is the default risk premium on the
corporate bond?
Maturity risk premium: The real risk-free rate is 3 per cent, and inflation is expected to
be 3 per cent for the next two years. A two-year Treasury security yields 6.3 per cent.
What is the maturity risk premium for the two-year security?
Bond valuation with semi-annual payments: Renfro Rentals has issued bonds that
have a 10 per cent coupon rate, payable semi-annually. The bonds mature in eight
years, have a face value of €1000, and a yield to maturity of 8.5 per cent. What is
the price of the bonds?
Yield to maturity and call with semi-annual payments: Thatcher Corporation’s bonds
will mature in ten years. The bonds have a face value of €1000 and an 8 per cent
coupon rate, paid semi-annually. The price of the bonds is €1100. The bonds are
callable in five years at a call price of €1050. What is their yield to maturity? What
is their yield to call?
Bond valuation and interest rate risk: The Garraty Company has two bond issues outstanding. Both bonds pay €100 annual interest plus €1000 at maturity. Bond L has a
maturity of 15 years, and Bond S has a maturity of one year.
a. What will be the value of each of these bonds when the going rate of interest is
(1) 5 per cent, (2) 8 per cent and (3) 12 per cent? Assume that there is only one
more interest payment to be made on Bond S.
b. Why does the longer-term (15-year) bond f luctuate more when interest rates
change than does the shorter-term bond (one year)?
( 5 -16 )
Yield to maturity and required returns: The Brownstone Corporation’s bonds have five
years remaining to maturity. Interest is paid annually, the bonds have a €1000 par
value, and the coupon interest rate is 9 per cent.
a. What is the yield to maturity at a current market price of (1) €829 or (2) €1104?
b. Would you pay €829 for one of these bonds if you thought that the appropriate
rate of interest was 12 per cent—that is, if rd 5 12 per cent? Explain your answer.
( 5 -17 )
Yield to call and realized rates of return: Seven years ago, Goodwynn & Wolf Incorporated sold a 20-year bond issue with a 14 per cent annual coupon rate and a 9 per
cent call premium. Today, G&W called the bonds. The bonds originally were sold at
their face value of €1000. Compute the realized rate of return for investors who purchased the bonds when they were issued and who surrender them today in exchange
for the call price.
152 Part 2
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( 5 -1 8 )
Bond yields and rates of return: A ten-year, 12 per cent semi-annual coupon bond with a
par value of €1000 may be called in four years at a call price of €1060. The bond sells
for €1100. (Assume that the bond has just been issued.)
( 5 -19)
( 5 -2 0 )
( 5 -21)
( 5 -2 2)
( 5 -2 3)
What is the bond’s yield to maturity?
What is the bond’s current yield?
What is the bond’s capital gain or loss yield?
What is the bond’s yield to call?
Yield to maturity and current yield: You just purchased a bond that matures in five years.
The bond has a face value of €1000 and has an 8 per cent annual coupon. The bond
has a current yield of 8.21 per cent. What is the bond’s yield to maturity?
Current yield with semi-annual payments: A bond that matures in seven years sells for
€1020. The bond has a face value of €1000 and a yield to maturity of 10.5883 per cent.
The bond pays coupons semi-annually. What is the bond’s current yield?
Yield to call, yield to maturity, and market rates: Absalom Motors’ 14 per cent coupon
rate, semi-annual payment, €1000 par value bonds that mature in 30 years are callable
five years from now at a price of €1050. The bonds sell at a price of €1353.54, and the
yield curve is flat. Assuming that interest rates in the economy are expected to remain
at their current level, what is the best estimate of the nominal interest rate on new
Interest rate sensitivity: A bond trader purchased each of the following bonds at a
yield to maturity of 8 per cent. Immediately after she purchased the bonds, interest
rates fell to 7 per cent. What is the percentage change in the price of each bond after
the decline in interest rates? Fill in the following table:
Price at 8%
Price at 7%
10% annual coupon
Bond value as maturity approaches: An investor has two bonds in his portfolio. Each
bond matures in four years, has a face value of €1000, and has a yield to maturity
equal to 9.6 per cent. One bond, Bond C, pays an annual coupon of 10 per cent; the
other bond, Bond Z, is a zero coupon bond. Assuming that the yield to maturity
of each bond remains at 9.6 per cent over the next four years, what will be the price of
each of the bonds at the following time periods? Fill in the following table:
Price of Bond C
Price of Bond Z
Chapter 5
Bonds and Bond Management 153
( 5 -24 )
Determinants of interest rates: The real risk-free rate is 2 per cent. Inflation is
expected to be 3 per cent this year, 4 per cent next year, and then 3.5 per cent there
after. The maturity risk premium is estimated to be 0.0005 3 (t 2 1), where
t 5 number of years to maturity. What is the nominal interest rate on a seven-year
Treasury security?
( 5 -2 5 )
Maturity risk premiums: Assume that the real risk-free rate, r*, is 3 per cent and
that inflation is expected to be 8 per cent in year 1, 5 per cent in year 2, and 4 per
cent thereafter. Assume also that all Treasury securities are highly liquid and free of
default risk. If two-year and five-year Treasury notes both yield 10 per cent, what is
the difference in the maturity risk premiums (MRPs) on the two notes; that is, what is
MRP5 minus MRP2?
( 5 -2 6 )
Inflation risk premiums: Because of a recession, the inflation rate expected for the
coming year is only 3 per cent. However, the inflation rate in year 2 and thereafter is
expected to be constant at some level above 3 per cent. Assume that the real risk-free
rate is r* 5 2 per cent for all maturities and that there are no maturity premiums. If
three-year Treasury notes yield 2 percentage points more than one-year notes, what
inflation rate is expected after year 1?
( 5 -27 )
Bond valuation and changes in maturity and required returns: Suppose Hillard Manufacturing sold an issue of bonds with a ten-year maturity, a €1000 par value, a 10 per
cent coupon rate, and semi-annual interest payments.
a. Two years after the bonds were issued, the going rate of interest on bonds such as
these fell to 6 per cent. At what price would the bonds sell?
b. Suppose that two years after the initial offering, the going interest rate had risen
to 12 per cent. At what price would the bonds sell?
c. Suppose that two years after the issue date, as in (a), interest rates fell to 6 per cent.
Suppose further that the interest rate remained at 6 per cent for the next eight
years. What would happen to the price of the bonds over time?
( 5 -2 8 )
Yield to maturity and yield to call: Arnot International’s bonds have a current market
price of €1200. The bonds have an 11 per cent annual coupon payment, a €1000 face
value, and ten years left until maturity. The bonds may be called in five years at 109
per cent of face value (call price 5 €1090).
( 5 -2 9)
What is the yield to maturity?
What is the yield to call if they are called in five years?
Which yield might investors expect to earn on these bonds, and why?
The bond’s indenture indicates that the call provision gives the firm the right to
call them at the end of each year beginning in year 5. In year 5, they may be called
at 109 per cent of face value, but in each of the next four years the call percentage
will decline by 1 percentage point. Thus, in year 6 they may be called at 108 per
cent of face value, in year 7 they may be called at 107 per cent of face value, and so
on. If the yield curve is horizontal and interest rates remain at their current level,
when is the latest that investors might expect the firm to call the bonds?
Determinants of interest rates: Suppose you and most other investors expect the inflation rate to be 7 per cent next year, to fall to 5 per cent during the following year, and
then to remain at a rate of 3 per cent thereafter. Assume that the real risk-free rate, r*,
will remain at 2 per cent and that maturity risk premiums on Treasury securities rise
from zero on very short-term securities (those that mature in a few days) to a level of
0.2 percentage points for one-year securities. Furthermore, maturity risk premiums
increase 0.2 percentage points for each year to maturity, up to a limit of 1 percentage
point on five-year or longer-term T-notes and T-bonds.
154 Part 2
Fixed Income Securities: An Introduction to Valuation
a. Calculate the interest rate on 1-, 2-, 3-, 4-, 5-, 10- and 20-year Treasury securities,
and plot the yield curve.
b. Now suppose that ExxonMobil’s bonds, rated AAA, have the same maturities as
the Treasury bonds. As an approximation, plot an ExxonMobil yield curve on the
same graph with the Treasury bond yield curve. (Hint: Think about the default
risk premium on ExxonMobil’s long-term versus short-term bonds.)
c. Now plot the approximate yield curve of Long Island Lighting Company, a risky
nuclear utility.
Sam Strother and Shawna Tibbs are vice presidents of Mutual of Seattle Insurance Company and co-directors
of the company’s pension fund management division. An important new client, the North-Western Municipal
Alliance, has requested that Mutual of Seattle present an investment seminar to the mayors of the represented
cities, and Strother and Tibbs, who will make the actual presentation, have asked you to help them by answering the following questions.
a. What are the key features of a bond?
b.What are call provisions and sinking fund provisions? Do these provisions make bonds more or less
c.How does one determine the value of any asset whose value is based on expected future cash flows?
d.How is the value of a bond determined? What is the value of a ten-year, €1000 par value bond with a
10 per cent annual coupon if its required rate of return is 10 per cent?
e. (1) What would be the value of the bond described in part d if, just after it had been issued, the expected
inflation rate rose by 3 percentage points, causing investors to require a 13 per cent return? Would
we now have a discount or a premium bond?
(2) What would happen to the bond’s value if inflation fell and rd declined to 7 per cent? Would we now
have a premium or a discount bond?
(3) What would happen to the value of the ten-year bond over time if the required rate of return
remained at 13 per cent? If it remained at 7 per cent?
f. (1) What is the yield to maturity on a ten-year, 9 per cent annual coupon, €1000 par value bond that
sells for €887.00? That sells for €1134.20? What does the fact that a bond sells at a discount or at a
premium tell you about the relationship between rd and the bond’s coupon rate?
(2) What are the total return, the current yield, and the capital gains yield for the discount bond?
(Assume the bond is held to maturity and the company does not default on the bond.)
g.How does the equation for valuing a bond change if semi-annual payments are made? Find the value of a
ten-year, semi-annual payment, 10 per cent coupon bond if the nominal rd is 13 per cent.
h.Suppose that a ten-year, 10 per cent semi-annual coupon bond with a par value of €1000 is currently selling for €1135.90, producing a nominal yield to maturity of 8 per cent. However, the bond can be called
after five years for a price of €1050.
(1) What is the bond’s nominal yield to call (YTC)?
(2) If you bought this bond, do you think you would be more likely to earn the YTM or the YTC? Why?
i.Write a general expression for the yield on any debt security (rd) and define these terms: real risk-free rate
of interest (r*), inflation premium (IP), default risk premium (DRP), liquidity premium (LP) and maturity
risk premium (MRP).
j. Define the nominal risk-free rate (rf ). What security can be used as an estimate of rf ?
k. Describe a way to estimate the inflation premium (IP) for a t-year bond.
l.What is a bond spread and how is it related to the default risk premium? How are bond ratings related to
default risk? What factors affect a company’s bond rating?
m.What is interest rate (or price) risk? Which bond has more interest rate risk: an annual payment one-year
bond or a ten-year bond? Why?
Chapter 5
Bonds and Bond Management 155
n.W hat is reinvestment rate risk? Which has more reinvestment rate risk: a one-year bond or a ten-year
o. How are interest rate risk and reinvestment rate risk related to the maturity risk premium?
p. What is the term structure of interest rates? What is a yield curve?
q.Briefly describe bankruptcy law. If a firm were to default on its bonds, would the company be liquidated
immediately? Would the bondholders be assured of receiving all of their promised payments?
Risk and Return
e now reach the heart of finance by seeking to answer the questions: how are shares valued and
how do we invest successfully. The possibility of gains are there for all to see. Buying shares when
their value is low and selling them when they rise is surely the way to make a fortune. For some,
such as George Soros and Warren Buffet, this is true. The FTSE index, an average of stock market prices, rose
from 4477 at the end of 2003 to 6220 three years later—a 39 per cent increase. Unfortunately, this is not the
whole story. At the turn of the century the NatWest bank offered the same return as the stock market capped at
8 per cent per annum for a five-year investment with the clause that in the unlikely event of the stock market
falling, the original investment would be returned. The index fell by over 30 per cent during the five years. In
the final chapter of this section we will see NatWest’s offer as a cylinder contract, a form of insurance added to
the rate of return. The possibility of such large movements makes insurance an important part of managing
risk and return.
Introduction With a Caution
The development of finance in the economic literature has been founded on modelling risk and return. We
know that the required return by investors in the market includes risk, from there we can work out prices.
For example, if we feel that a share price will be worth €110 in one year’s time and we are looking for a return
of 15 per cent, then our price for that share would be 1 1 11100.15 2 5 €96.65. If someone else thought that the
return was not as risky and would be happy with a 10 per cent return then they would offer 1 1 11100.10 2 5 €100.0
for the share. Notice that the expected value and risk are separate considerations. In our example the investors agree on the expected future value—it is just that one investor feels that a very different result could well
occur. Of course, investors may also disagree on expected value, but that is really more of a business estimate.
We shall have to assume that there is agreement on the expected values. Our question is therefore how does
the market move from an agreed position on expected values to a valuation? Our basic answer is to discount
using the models in Chapter 4, so the value of the company is the present value of its dividends as in Figure
6-1. Estimating a share price, we argue, is conceptually the same as estimating the value now of future dividends because a future share price is the discounted value of future dividends.
160 Part 3
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F i g u re 6 -1
The Discount Cash Flow Model, Risk, Return and the Present Share Price
The expected dividends estimated
using business knowledge about
the firm and its market
E(share price) =
Subjective estimate of the share
price—a judgement on what
the share price ought to be..
dividend 1
(1 + i )1
dividend 2
(1 + i )2
(1 + i ) n
The required rate of return using
models of financial risk and/or
‘gut feeling’.
Now for some words of caution. The models we examine are elegant and even beautiful. They are nevertheless models and while they are correct within their own assumptions they not wholly accurate descriptions of
reality. If you are required to evaluate risk in finance, it is essential that you understand and make this point.
The models make surprising predictions about practice that are at times extremely accurate and sometimes
inaccurate but are still the best explanation we have. An example of the latter that is of current concern stems
from the common assumption that returns are normally distributed. The normal distribution curve gives the
probability that an observation lies inside a defined range. As an example, taking the daily returns from the FTSE
index from the beginning of 2000 to the end of 2014, and defining a range such that there should be a 99.9 per
cent chance of being in that range, leaves only a 0.1 per cent chance of being outside. That would mean that
only some four days of extreme movements should lie outside the range—but there were in fact 48 such days.
This does not mean that the models are wrong, just that they are the best that we currently have to work with.
Defining a Return
The concept of return provides investors with a convenient way to express the financial performance of an
investment. From Chapter 2 the reader will be familiar with the calculation of a percentage return such as:
return on assets 5 profit / assets. That needs no further explanation. In finance, however, return is often in the
form of an increase in share prices. To illustrate, suppose you buy ten shares for €1000. The share pays no
dividends1, but at the end of one year you sell the share for €1100. How would you describe the return on your
€1000 investment?
Return as a Money Value
One way to express an investment’s return is in currency value:
euro return 5 amount to be received (end value) 2 amount invested (start value)
5 €1100 2 €1000
5 €100
If instead, at the end of the year you sell the share for only €900, your euro return will be 2€100.
Although expressing returns in euros is easy, two problems arise. (1) To make a meaningful judgement
about the return, you need to know the scale (size) of the investment; a €100 return on a €100 investment
We assume throughout this chapter that dividends are included in any end value calculation which can be thought of as no dividends.
Chapter 6
Risk and Return 161
seems a great return, but a €100 return on a €10 0 00 investment seems a poor return. (2) You also need to
know the timing of the return; a €100 return on a €100 investment is a great return if it occurs after one year,
but the same return after 20 years is not very good.
Return as a Percentage
The solution to the size of the original investment problem is to express investment outcomes as rates of
return, or percentage returns. For example, the rate of return on the one-year share investment, when €1100
is received after one year, is 10 per cent:
end value 2 start value
start value
Rate of return 5
5 0.10 5 10%
On a practical note, if the brackets are omitted on a calculator then the answer will be wrong as it will
choose to do the division before the subtraction. To avoid this problem a safer way to calculate is:
end value 2 start value
start value
end value
start value
start value
start value
Rate of return 5
end value
start value
5 0.10 5 10%
So just the ‘end value divided by start value minus 1’ means no need to fiddle with brackets.
The rate of return calculation ‘standardizes’ the euro return by considering the annual return per unit
of investment. That is we standardize all returns to a particular time interval (usually one year) and a particular unit, percentage or per hundred. This may seem obvious but reconsidering the obvious is ­valuable.
In this case, it emphasizes the problems of reporting in absolute terms ‘Company X made a profit of
€1 million’—what does that mean? Is it good is it bad? €1 million a second sounds good, €1 million return
on a €100 million investment sounds bad! We need to know the time interval and the per unit return.
A percentage return also has a weakness. Percentages may seem very impressive but the values may be
small. So comparing a firm that is making an 80 per cent return on its assets when the assets are €10 000
(i.e. €8000) is less impressive than a return of 30 per cent on an investment of €4m (i.e. €1.2m). Note that it is
the return as a monetary value that tells us the truth here. Small firms are more likely to produce high ratios.
This should be taken into account in any analysis and comparisons should be between firms of similar size,
or between divisions of a large company. Figure 6-2 gives an example of return calculated as a percentage
movement of share price giving both methods of calculating the percentage return. In calculations, returns
should always be expressed as fractions—i.e. 0.04 and not 4 per cent. Only when presenting the final data
should you express 0.04 as 4 per cent; this will avoid drastic calculation errors.
So neither absolute nor percentage return is ideal. They both have problems relating the return to the
original investment: a percentage hides the size and the absolute omits the size. Comparisons are therefore
problematic. In a survey of return on assets, for example, to make valid comparisons one might analyse separately companies below a certain size of earnings and companies with exceptionally high percentage returns.
In reporting performance, making statements such as ‘XYZ plc made a profit of 25 per cent on its €2 million
investment’ is better than trying to give just one measure, 25 per cent or €500 000.
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F i g u re 6 -2
Return Calculation
(B2 − B1)/B1
B2/B1 − 1
% Return
Time (t)
Note: the return on time series data is the percentage movement in price over time as calculated in column C or D. Normally share
price data has been adjusted for dividends and share splits. The return on a price index measures inflation.
Measuring Risk: The Single-Investment Case
Risk refers to the chance that some unfavourable event will occur. For an investment in financial assets
or in new projects, the unfavourable event is ending up with a lower return than you expected. An asset’s
risk can be analysed in two ways: (1) on a stand-alone basis, where the asset is considered in isolation,
and (2) on a portfolio basis, where the asset is held as one of a number of assets in a portfolio. Thus, an
asset’s stand-alone risk is the risk an investor would face if she held only this one asset. Most assets are
held in portfolios, but it is necessary to understand stand-alone risk in order to understand risk in a
portfolio context.
S E L F -T E S T
Differentiate between euro returns and rates of return.
In what ways are rates of return superior to euro currency returns when comparing different potential
investments? (Hint: Think about size and timing.)
If you pay €500 for an investment that grows to €600 in one year, what is your annual rate of return?
(Answer: 20 per cent.)
Measuring Risk and Return for Discrete Distributions
Outcomes can be measured either in terms of discrete outcomes (typically high, medium and low) where a
number is given to each outcome (say a profit of €4m or €1m, or a loss of €2m). Alternatively, returns can be
represented as a continuous distribution such as the normal distribution—say, an expected return of €1m
with a standard deviation of €3m. It is tempting to see the continuous distribution as being more accurate.
There is obviously a possibility that returns may be €2m or €0.75m. We can work this out with the continuous distribution but not directly with the discrete distribution.
So why do we bother with discrete distributions? Predictions of the future are inevitably approximate.
In a business setting where risk has to be communicated to staff who are not familiar with the concepts,
it is important that the measurement is easily understood. Representing possible outcomes in a discrete
manner is, in such contexts, a sufficiently accurate measure. As such a representation is more accessible,
other staff can more easily bring their expertise to bear. A discrete outcome can be questioned in terms of
Chapter 6
Risk and Return 163
the business scenario that would produce such a result. In addition, outcomes can be discussed without an
associated probability.
The probabilities in the discrete case are subjective, not frequentist. 2 Subjective probabilities may be
described as degrees of belief, or ‘gut feeling’. Effective use of managerial experience is therefore essential to
getting best estimates.
A continuous outcome approach using the mean and standard deviation and making the assumption of a
normal distribution is more computationally impressive but carries with it the hidden danger that the estimates are failing to make full use of the managerial information set. Managers can identify more easily with
a discrete estimate.
An event’s probability is defined as the chance that the event will occur. For example, a weather forecaster
might state: ‘There is a 40 per cent chance of rain today and a 60 per cent chance that it will not rain.’ If all
possible events, or outcomes, are listed, and if a probability is assigned to each event, then the listing is called
a discrete probability distribution. (Keep in mind that the probabilities must sum to 1.0, or 100 per cent
implying that the outcome will certainly be one of those listed.)
Expected Rate of Return
Suppose an investor is facing a situation where he believes that there are three possible outcomes for the market
as a whole: (1) best case, with a 30 per cent probability; (2) most likely case, with a 40 per cent probability; and (3)
worst case, with a 30 per cent probability. The investor also believes the market would go up by 37 per cent in the
best scenario, go up by 11 per cent in the most likely scenario, and go down by 15 per cent in the worst scenario.
Figure 6-3 shows the probability distribution for these three scenarios. Notice that the probabilities sum
to 1.0 and that the possible returns are dispersed around the most likely (modal) scenario’s return.
We can calculate expected return using the probability distribution. If we multiply each possible outcome
in Figure 6-4 by its probability of occurrence and then sum these products, as in column (3) of Figure 6-4,
the result is a weighted average of outcomes. The weights are the subjective probabilities, this means that the
F i g u re 6 -3
Return Probability Distribution
Probability of
Worst Case
Most Likely
Best Case
They are not a matter of finding out how many times an outcome occurred in the past and then using that as your probability.
Though frequency may inform a subjective estimate there is no compulsion to apply such estimates.
164 Part 3
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F i g u re 6 - 4
The Expected Value Calculated as the Average and Risk as the Standard Deviation
Rate of return
(2) × (3)
(3) −11%
(5) × (5)
(6) × (2)
Best case
Most likely
Worst case
sum to 1
implying that
it is certain
that one of the
outcomes will
E(r) 5 Total 5 11.0%
(5) the difference
from the mean of
the expected
return E(r)
calculated as
the ‘average’.
Variance 5 total 5 4.0%
Standard deviation 5 "4.0% 5 20.0%
(6) squared
difference to
get rid of the
(7) average of the
squared differences
giving the variance
then reversing the
squaring to give the
standard deviation.
probabilities are estimated by human judgement rather like betting odds. The weighted average is viewed as
the expected rate of return and is normally noted as E(r).
What expected means in this context is not entirely clear, as it might not be one of the scenarios and is hence
not part of the distribution, so how can it be expected? One answer is that the discrete distribution is an approximation of the continuous distribution where the outcome does exist. This leaves another problem, namely
that the expected value might not be the most likely, which is what we normally understand from the word
“expected”—i.e. the modal value. Normally, the difference is likely to be trivial given that most distributions have
a single peak, but not always. Perhaps the best understanding is that the expected value is the value that minimizes
the expected difference with the actual, the closest we can get to the actual given our current knowledge.
If there are two distinct outcomes with no real possibility of a midway outcome, the expected outcome
as defined here would have little meaning—preparing for an outcome that you know will not happen! Here
again there is a gap between academic modelling and practice. The academic model is a generalization of risk
that is usually applicable but not always. We need to be aware that there are exceptions which in this case are
better handled by a separate examination of scenarios.
In the example of Figure 6-4 the expected value is one of the discrete outcomes and is 11 per cent and
there is no real conflict with a continuous approach which would place normal distribution ‘over’ the discrete outcomes with no great differences.
The calculation for expected rate of return can also be expressed as an equation:
Expected rate of return 5 E 1 r 2 5 p1 r1 1 p2 r2 1 c1 pn rn
5 a piri
rn 5 return if outcome n occurs
pn 5 subjective probability that outcome n will occur
Chapter 6
Risk and Return 165
Expected rate of return 5 p1(r1) 1 p2(r2) 1 p3(r3)
5 0.3(37%) 1 0.4(11%) 1 0.3(215%)
5 11% as in Figure 6-4
Measuring Stand-Alone Risk: The Standard Deviation of a Discrete Distribution
Investors and businessmen, whether explicitly or implicitly, think of the future in terms of discrete outcomes
typically in the form of scenarios that may not cover all possibilities. For example, it is common to look at
‘worst-case scenarios’—stress testing of banks is one such example. Specific threats may form the basis of a
scenario in a ‘what if’ type of analysis for events such as the debt crisis, the European bond crisis, oil supply
threats and so on.
For simple distributions, it is easy to assess risk by looking at the dispersion of possible outcomes—a distribution with widely dispersed possible outcomes is riskier than one with narrowly dispersed outcomes. For
example, we can look at Figure 6-3 and see that the possible returns are widely dispersed. But when there are
many possible outcomes and we are comparing many different investments, it is not possible to assess risk
simply by looking at the probability distribution, we need a quantitative measure of the width of the probability distribution. One such measure is the standard deviation, the symbol for which is s (pronounced ‘sigma’).
A large standard deviation means that possible outcomes are widely dispersed, whereas a small standard
deviation means that outcomes are more tightly clustered around the expected value.
To calculate the standard deviation, we proceed as shown in Figure 6-4, taking the following steps:
1. Calculate the expected value for the rate of return using column (4) of Figure 6.4.
2. Subtract the expected rate of return (E(r) or 11 per cent in this case from each possible outcome (r i) to
obtain a set of deviations about E(r) as shown in column (5) of Figure 6-4.
3. Square each deviation as shown in column (6) to get rid of the negatives as we are interested in the difference irrespective of it being positive or negative. Then multiply the squared deviations in column (6) by
the probability of occurrence for its related outcome; these products are shown in column (7). Sum these
products to obtain the variance of the probability distribution:
Variance 5 s2i 5 a 1 ri 2 E 1 ri 2 2 2pi
Thus, the variance is essentially a weighted average of the squared deviations from the expected value.
4. Finally, take the square root of the variance to obtain the standard deviation:
Standard deviation 5 si 5
) i51
1 ri 2 E 1 ri 2 2 2pi
The standard deviation provides an idea as to how far above or below the expected value the actual value
is likely to be and hence gives a measure of risk. It may seem odd that the risk of the outcome being higher
than the expected value is included when most would not see this as a risk! So why does this apparently not
matter? Firstly, some useful US terms: variation below the expected value is referred to as downside risk and
variation above the expected value is referred to as upside risk. As we will be assuming a normal distribution
of outcomes which is broadly in agreement with reality (but not exactly, as frequently stressed), the distribution of outcomes will be symmetrical. In other words ‘downside risk’ 5 ‘upside risk’. So upside risk will
always move in line with what we are really interested in, which is the downside risk, and it will not affect our
measure providing that the outcomes are symmetrical about the expected value.
Using the procedure in Figure 6-4, our hypothetical investor believes that the market return has a standard deviation of about 20 per cent. This is a ‘kind of’ average spread around the expected value.
166 Part 3
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S E L F -T E S T
What does ‘investment risk’ mean?
Set up an illustrative probability distribution for an investment.
How does one calculate the standard deviation?
An investment has a 20 per cent chance of producing a 25 per cent return, a 60 per cent chance of
producing a 10 per cent return, and a 20 per cent chance of producing a 215 per cent return. What is
its expected return? (Answer: 8 per cent.) What is its standard deviation? (Answer: 12.9 per cent.)
Risk in a Continuous Distribution
An obvious problem with discrete outcomes (as already stated) is that they do not cover the outcomes
between the chosen set of values. Looking at Figure 6-4, what if the expected return were 8 per cent? That is
not one of the scenarios. One solution is to have a continuous distribution.
The normal distribution is a particularly attractive continuous distribution (see Figure 6-5). The area
under each of the three curves represents probability. The total area for each curve adds up to 1, or 100 per
cent, and hence all outcomes are included. The expected return is 5 per cent for all three curves. One can
see that the area to the left of 0 per cent is largest for the flattest curve; it therefore has a greater probability
of a loss compared to the other two curves. The flatter the curve the greater the standard deviation of the
So why is this especially attractive? Firstly, all outcomes have a probability, so unlike the discrete version,
there are no missing outcomes. Secondly, the normal distribution is completely defined by the mean (average) and standard deviation. This means that given the mean and standard deviation the probability of every
outcome can be calculated. This is useful as the mean is taken as the expected value and the standard deviation is seen as a measure of risk. So the normal curve fully represents our understanding of expected risk and
F i g u re 6 -5
Normal Distributions for Varying Standard Deviations
Chapter 6
Risk and Return 167
return. Thirdly, the normal distribution is easier to manipulate in mathematical models and as a result has
been the basis of financial modelling for the last 50 years. Fourthly, as we will see in the chapter on market
efficiency, we can construct a rationale for the normal distribution of returns from our understanding of
market pricing—it ought to be normal under reasonable conditions!
Normal distributions nevertheless have significant drawbacks. We have already pointed out that in practice extreme values happen far more frequently than implied by the normal distribution. Secondly, there is
something of a hidden assumption that no other activity is considered in measuring the outcome. Significant
exceptions in practice are outcomes that are contingent on the outcome of the investment. For example, a
business might suggest that if a project’s return is above 10 per cent then a second project in another city
can be undertaken—this is termed a real option and is addressed in later chapters. Another outcome that is
not considered is the reaction of competitors—what is the effect of a reaction if the project is successful? For
shares, however, the main problem is that of extreme movements not considered possible (or rather given a
minuscule probability) according to the normal distribution. The term ‘fat tails’ is given to this problem as
the tails of the distributions in Figure 6-5 in practice are more probable than the normal distribution and
hence higher or fatter! We return to this issue when examining behavioural finance.
S E L F -T E S T
For a normal distribution, what is the probability of being within one standard deviation of the
expected value? (Answer: 68.26 per cent.)
Using Historical Data to Estimate Risk
Estimating the standard deviation can be carried out in two ways. Either it can as in the previous sections be
estimated from subjective estimates based on human judgement from experienced and informed investors,
or, where available, information from the past can be used to make an estimate. An obvious assumption in
using historic data is that the past is relevant to the future. In the terminology of statistics the assumption is
that the return is stationary, meaning that it does not change over time, so an estimate from past data is as
good as taking future data. This approach also appeals to the view that if there is no clear reason for a change
then one should assume no change. A dangerous assumption indeed!
The calculation of the expected return and the standard deviation from historic data is the same as in Equations 6-3 and 6-4 except that there is no need for probabilities as we are using the frequentist approach. We ask
the question, what was the average return over the past observations? What was the standard deviation of the
returns over the past observations? The reader will notice that the equations are similar to those based on probability (above) but in place of probabilities we take averages of actual past data adjusted for degrees of freedom:
Variance 5 VAR 5 s2 5
1r 2 r22
n 2 1 i51 i
Standard deviation 5 STDEV 5 s 5
1r 2 r22
) n 2 1 i51 i
ri 5 the sample set of n past returns
r 5 the average or mean of the sample set of past returns
In practice one would use a spreadsheet to input the data and for 100 items use the instruction
‘5 average(a1:a100)’ and ‘5stdev(a1:a100)’.
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How reliable is the stationarity assumption in practice? Are standard deviations and averages truly stable
over time such that the past is a reliable indicator of the future? This does, of course, depend on the return
being considered. In the case of the FTSE index it is not stable over time. The annual return from 2010 to
2014 has been as low as 214 per cent and as high as 52 per cent—which average will be relevant for the future?
The standard deviation is similarly unstable. Little wonder that there are so many employed in the financial
centres to estimate the future prospects of share prices; one needs to look at much more than past prices.
Despite misgivings about making future estimates of expected values and standard deviations from past
data, using past data is nevertheless an important way to understand risk and an important part of making
estimates about the future.
Risk in a Portfolio Context
Most financial assets are actually held as parts of portfolios. Banks, pension funds, insurance companies,
mutual funds and other financial institutions are required by law to hold diversified portfolios. Even individual investors, at least those whose shareholdings constitute a significant part of their total wealth, generally
hold portfolios and not the shares of only one firm.
Creating a Portfolio
A portfolio is a collection of assets. The ‘weight’ of an asset in a portfolio is the percentage of the portfolio’s
total value that is invested in the asset. For example, if you invest €1000 in each of ten shares, your portfolio
has a value of €10 000, and each share has a weight of :10
000 5 10 per cent. If instead you invest €5000 in one
share and €1000 apiece in five shares, the first share has a weight of :10
000 5 50 per cent, and each of the other
five shares has a weight of 10 per cent. Usually it is more convenient to talk about an asset’s weight in a portfolio rather than the euros invested in the portfolio. Therefore, when we create a portfolio, we choose a weight
(or a percentage) for each asset, with the weights summing to 1.0 (or the percentages summing to 100 per cent).
Suppose we have a portfolio of n shares. The actual return on a portfolio in a particular period is the
weighted average of the returns of the shares (however calculated) in the portfolio. The overall expected
value is calculated as:
E 1 r 2 5 w1 r1 1 w2 r2 1 c1 wn rn
5 a wi ri
ri 5 estimated returns of investment i
E(r) 5 the average or mean return of the portfolio
Calculating the Risk of a Portfolio
The tendency of two returns to move together is called correlation, and its measurement lies at the heart of
managing risk and the valuation of shares.
The symbol for the correlation coefficient is the Greek letter rho, r (pronounced ‘row’ as in row a boat).
The correlation coefficient can range from 11.0, denoting that the two variables move up and down in perfect synchronization, to 21.0, denoting that the variables always move in exactly opposite directions. A correlation coefficient of zero indicates that the two variables are not related to each other at all—that is, changes
in one variable are independent of changes in the other.
Chapter 6
Risk and Return 169
F i g u re 6 - 6
Correlation in General: The Percentage Return on Shares A and B
Most share prices
move together and but
not closely. Hence a
positive correlation.
The same direction means
‘if A9 is above its mean is B9
above its mean?’.
Here A9 = 2 3 A* and the
correlation is the same—
size does not matter.
If they always move
in the same direction
then the correlation
will be high.
The concept of correlation is central to the notion of a portfolio. This is simply ‘how do the variables
(share prices or returns in this case) move together?’ Figure 6-6 gives an example—note that the movement
is relative to its own average. It is as if they are attached by a piece of string but the string can be of varying
lengths, so visually the relationship is not always clear, as in the last example of Figure 6-6.
The fundamental element of correlation is covariance. In fact correlation is really a standardized covariance mapped onto a 21 to 11 scale.
Covariance 1 i,j 2 5 COV 1 i,j 2 5 sij 5
1 r 2 ri 2 1 rj,t 2 rj 2
n 2 1 t51 i,t
The correlation is:
a 1 ri,t 2 ri 2 1 rj,t 2 rj 2
ri,j 5 CORR 1 i,j 2 5
) t51
1 ri,t 2 ri 2
ri,rj 5 estimated returns of investments i and j
ri,rj 5 the average or more return of i and j
t 5 time subscript
n 5 number of observations
si,sj 5 standard deviation i and j
ri,j 5 correlation of i and j
) t51
1 rj,t 2 rj 2
si, j
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Note that the n 21 1 in Equation 6-10 cancels out, also, if i 5 j then Equation 6-10 5 1, perfect correlation.
In fact, variance is just a special case of covariance—i.e. covariance with itself. The concept of covariance
therefore lies behind the more familiar ideas of variance and correlation.
The population coefficient estimate of correlation from a sample of historical data is often called ‘R’.
­Fortunately, it is easy to estimate the correlation coefficient in Excel as ‘5CORREL(A1:A100,B1:B100)’ etc.
We can now look at risk using our measures of expected returns and the variance and covariance of
returns to develop a measure of the risk of a portfolio.
Measuring Portfolio Risk
It is common knowledge that diversification reduces risk. If you have a number of part time jobs, you are less
likely to face full unemployment than if you have one full-time job. Businesses like to sell a range of products
so that if the sales of one product falls, other sales are likely to compensate. In finance, holding a collection
(or portfolio) of financial assets (shares, bonds, etc.) has a similar compensating effect; if the returns on one
share falls your hope is that the returns on the other shares will make up for the shortfall.
How does correlation affect diversification? Let us consider the full range of correlation coefficients, from
21 to 11. If two shares have a correlation of 21 (the lowest possible correlation), when one share has a higher
than expected return, then the other share has a lower than expected return, and vice versa. In fact, it would
be possible to choose weights such that one share’s deviations from its mean return completely cancel out
the other share’s deviations from its mean return. Such a portfolio would have a zero standard deviation but
would have an expected return equal to the weighted average of the share’s expected returns. Such a return
would be for a riskless investment in monetary or cash terms.
If the correlation were 11 (the highest possible correlation), the portfolio’s standard deviation would be
the weighted average of the share’s standard deviations. Suppose that the two shares were the same; their
returns would be identical and there would be no offsetting effect through holding two rather than one such
share. In this case, diversification would not help. For any other positive correlation, diversification reduces,
but cannot eliminate, risk. Most correlations in finance are positive as there is a mutual dependence on the
economy. Diversification therefore reduces individual risk: for correlations between 21 and 11 the port­
folio’s standard deviation is less than the weighted average of the shares’ standard deviations.
F i g u re 6 -7
Correlation Calculation of Percentage Returns for A and B
Time (t)
(2) 3 (2)
(5) 3 (5)
(2) 3 (6)
Correlation 5
"23.3333 3 10.8333
5 0.5451
(2) and (5) are the difference from A and B averages
(3) and (6) are the difference from A and B averages squared
(7) is the product of the difference from A and B averages
Chapter 6
Risk and Return 171
F i g u re 6 - 8
Portfolio and the Diversification Effect from Hypothetical Perfect Correlation (Triangle) to Actual
Correlation (Diamond)
Daily Return
Portfolio: mean & actual stdev
Individual: mean & stdev
Portfolio: mean & average stdev
Standard Deviation
The correlation between most pairs of companies is in the range of 0.2 to 0.3, so diversification reduces
risk, but it does not completely eliminate risk.
Figure 6-8 shows the effect of diversification based on a portfolio of equal investments in 15 major
companies quoted on the London Stock Exchange from 2000 to 2014. The triangle represents the nodiversification perfect correlation position where the portfolio standard deviation is just the average of the
standard deviations. The diamond is the actual standard deviation of the portfolio. Note that the expected
value has not changed but the risk is considerably reduced compared to the no-risk position and the individual
Diversification and Multi-share Portfolios
Standard deviation (the square root of the variance) is taken as the measure of risk—standard deviation and
variance are used interchangeably to measure risk.
The risk of a portfolio is calculated using a simple result from statistics. We shall deal with monetary values (not % returns) first for ease of notation. Suppose a portfolio is denoted as P and the constituent shares
are A, B, C, . . . , then the expected return of the portfolio will be E(P) 5 E(A) 1 E(B) 1 E(C). . .expected
values as we have said are additive. The standard deviation of the portfolio will be the square root of its variance. The portfolio in this case is made up of shares so: P 5 A 1 B 1 C. . . . and it is simple to establish that
VAR(P,P) 5 COV(A,A) 1 COV(A,B) 1 COV A,C) . . . COV(B,A) 1 COV(B,B) 1 COV(B,C) . . . and so on, on
an ‘all play all’ basis.3 In case this is not clear, presentation can be simplified by placing the covariances in a
table. So the variance of a portfolio is the total of the matrix in Table 6-1.
The pattern continues with the addition of more investments: D, E, F, etc. The variance of the portfolio is
simply the total of the matrix. Thus, one often sees the formula for a two-share portfolio (of A and B) given
For a proof see p. 20, Dougherty, C. (2011), Introduction to Econometrics, 4th edition, Oxford: Oxford University Press.
172 Part 3
Shares and Derivatives
TA B L E 6 -1
A Variance–Covariance Matrix in Monetary Values
wAw B cov(A,B)
wAwC cov(A,C)
w B2 var(B)
w BwC cov(B,C)
TA B L E 6 -2
A Variance–Covariance Matrix Using Percentages
w A2
w BwA var(B,A)
wCwA var(C,A)
wCw B cov(C,B)
w C2
as: VAR(P) 5 VAR(A) 1 VAR(B) 1 2 COV(A,B) which is simply the total of a two by two matrix (the top
left-hand four entries in Table 6.1). Extending the calculation to three or more shares is simply a matter of
completing the matrix.
Where returns are in percentages, the formula needs to know how much is invested in each share as the
percentage loses the size effect. To overcome this problem ‘weights’ are introduced to the equation. Keeping
to the matrix presentation the calculation becomes: where a weight is calculated as the percentage invested
in a particular share. Thus, if an investor invests €1000 in a portfolio and invests €200 in A then wA 5 1000
0.20 or 20 per cent. All the weights should add up to 1, or 100 per cent.
An example of a matrix calculation is given in Figure 6-9.
S E L F -T E S T
Explain the following statement: ‘An asset held as part of a portfolio is generally less risky than the
same asset held in isolation.’
What is meant by perfect positive correlation, perfect negative correlation and zero correlation?
In general, can the risk of a portfolio be reduced to zero by increasing the number of shares in the
portfolio? Explain.
The Relevant (Relative) Risk of a Share: The CAPM
We have redefined risk from being measured as the standard deviation of the returns of a share to being
the risk of a portfolio, a group of shares. We have noted that the standard deviation of a portfolio is not
simply the weighted average of the individual standard deviations unless there is perfect correlation which
is extremely unlikely. There is therefore an offsetting effect that we have called diversification. That was the
state of knowledge in the 1950s. The main author of this analysis was Harry Markowitz who was awarded a
Nobel Prize for his contribution.4 He is sometimes referred to as the father of modern finance.
Markowitz, H. (1952) ‘Portfolio selection’, Journal of Finance 7(1):77–91.
Chapter 6
Risk and Return 173
F i g u re 6 - 9
Variance–Covariance Matrix: Portfolio (A, B and C) Mean and Variance of Return Calculations for
Given Individual Investments, Returns, Standard Deviations and Correlations
20 000
48 000
12 000
80 000
Variance Covariance Matrix
expected value 5
0.1505 5 15.05%
matrix total 5 variance 5 0.033559
standard deviation = 0.1832 = 18.32%
1) Weights are calculated for example for A is 20 000 / 80 000 = 0.25 = 25%
2) Covariance (A,B) = Covariance(B,A) it is commutative
3) Covariance (A,B) = correlation(A,B) 3 stdev(A) 3 stdev(B)
4) Matrix value for A,B is 0.25 3 0.6 3 0.35 3 0.12 3 0.25 = 0.001575
The question then arose that if an individual share’s standard deviation is no longer to be regarded
as the measure of risk for an individual share, then how should we measure the risk of an individual
share? The answer is the Capital Asset Pricing Model (CAPM, pronounced ‘cap em model’). Note that
we have used the phrase ‘how should we measure risk?’ Within the assumptions of the model, CAPM
remains the normative, logical deduction as to how risk should be measured. The subsequent disputes as to its empirical or practical application are essentially an attack on its assumptions not on its
deductive logic. So it is worthwhile setting out the main assumptions on which the model and most of
finance rests:
• Returns are jointly normally distributed. As our analysis rests on the use of mean and standard deviation to represent risk and return it is a very attractive feature that the normal distribution is fully defined
by the mean and standard deviation. Of course it is far from perfect in practice as there are a disturbing
number of outliers.
• Homogeneous expectations. Clearly, if we are to use standard deviation as our measure of risk then we
are saying that this is the view of the market about the economic prospects of the firm. Put another more
casual way, it is not the outcome of squabbling between investors unable to make up their minds about
the value of a share! Similarly we assume that the market is able to come to a sensible conclusion as to
the expected returns of a share as represented by its future value and dividend payments. We treat the
market therefore as some sort of ethereal being, an obvious point of contention.
• Efficient markets. We assume that the price of a share is a valuation of that share and not the result of
uninformed speculative trading. This is a large area of research in finance which we address in the next
174 Part 3
Shares and Derivatives
• The model is a single-period model; this is not as restrictive as it sounds as multiperiod models can be
seen as successive single-period applications.
• Finally we assume that there are no transaction costs and that there is full and open access to information.
An important implication is that the borrowing and lending rates are the same, there is no trading margin.
The list is not complete and never can be; some of the other assumptions are that investors are overwhelmingly risk averse and return loving and need return to compensate for risk, there are no taxes, no
transaction costs, prices are not affected by individual buying and selling activity; but we assume that this is
relatively clear and not disputed in theory or practice.
If we look again at the variance covariance matrix in Table 6-1, we can see two types of risk. First there is
the risk that we have discussed before looking at portfolios—the variance of expected returns that takes up
the lead diagonal of the matrix from the top left to the bottom right. This is individual risk.
The second type of risk is new, it is the covariance risk: how does the variation of an individual share affect
the overall variation of the portfolio? This depends on the covariance of a share with the other shares in a portfolio. Remember that we use the terms covariance and correlation interchangeably as the latter is a covariance
mapped onto a 21 to 11 scale. So we are also saying that the portfolio risk depends on the correlation of the
returns of an individual share with the rest of the other shares in the portfolio. What is noticeable is that there
are many more covariance terms than variance terms. Even in a small portfolio of three shares there are six
covariance terms and only three variance terms and they are not necessarily smaller (see Figure 6-9). If there
were 10 shares in the portfolio than there would be 10 3 10 5 100 terms in the variance covariance matrix: 90
covariances and only 10 variance terms. So the relevant risk is not the individual risk of the share (the variance)
but what is termed the systematic risk of the share: that is, its covariance or correlation with the other shares in
the portfolio.
The Risk–Return Combination for Portfolios
Combining investments in varying proportions produces an area below an ‘envelope’ curve. To illustrate we
take an example of two shares ABC plc and XYZ plc in Figure 6-10.
The feature here is that the combined standard deviation is not a linear combination (straight line). That
would only be the case if the correlation were perfect. Different correlations will produce different curves.
The combined standard deviations for the two share case is the total of the top left-hand four (A and B) of
Table 6-2. So 60 per cent ABC plc and 40 per cent XYZ plc had a combined standard deviation of 19.9 per
cent (see Figure 6-10) calculated as:
combined stdev 5 sABC,XY Z
5 "w2ABC sABC
5 "0.6020.2662 1 0.420.17802 1 2 1 0.4 2 1 0.6 2 1 0.266 2 1 0.178 2 1 0.4 2 5 0.199
5 19.9%
see Equations 6-9 and 6-10 for the derivation and key to the variables.
Stock Market Risk
The stock market can be regarded as one portfolio. The arrival of a new share is judged in terms of its risk
relative to existing shares. So one view of a share is as part of the market portfolio. If the market is efficient
then the market portfolio must be the best risk for the return that one can get. We locate the market portfolio
in Figure 6-11.
We can draw a line from the risk-free rate to a point just touching the curve; this tangential point is the
market portfolio. The line known as the capital market line offers the highest return for all levels of risk. We
can reach points on this line through a combination of investing in the risk-free investment such as a treasury bond and the market portfolio. It is a straight line as there is assumed to be a zero standard deviation for
Chapter 6
Risk and Return 175
F i g u re 6 -1 0
The Risk–Return Outcomes for Varying Combinations of ABC plc and XYZ plc
Average return
Standard deviation
ABC plc
XYZ plc
Portfolio Effect:
% ABC plc
% XYZ plc
Average return (%)
Combined SD (%)
ABC plc
XYZ plc
Standard Deviation (%)
the risk-free rate. To get to the square point one would invest in both the risk-free investment and the market
portfolio. To get to the triangular point one would construct a levered portfolio by adding borrowing at the
risk-free rate to your own investment and investing the total in the market portfolio. Therefore the market
portfolio is the best investment in the market, implying that all shares are at their best value. This would be
the case in an efficient market.
In this context we can ask the question: What return does the market ask of a firm to be part of the market
portfolio? As we have said, to solve this problem it was realized that the portfolio that supported the capital
market line and gave the highest return for each element of risk must be the market portfolio. All shares are
valued efficiently if the market is efficient. A share offers value and that value must have a price that results
in all the issue being purchased in a free market. The share price determines the return in the sense discussed
before—that for instance a share estimated to be worth €110 in one year for which the market judges should
earn a return of 10 per cent should have a present price of 110
1.1 = 100. That value multiplied by the number of
shares would form part of the market portfolio. It was realized that the return on the market portfolio will
be determined at the point where the curve and the straight line slopes are equal, that of the Capital Market
Line and the Leading Edge as in Figure 6-11. In equation form it is:
176 Part 3
Shares and Derivatives
E 1 ri 2 2 E 1 rm 2
E 1 rm 2 2 rf
1 sim 2 s2m 2 /sm
F i g u re 6 -11
The Market Portfolio and the Capital Market Line
Leading edge
Capital market line
Market portfolio
Standard Deviation
1. σm = standard deviation
rf = risk free rate
rm = market return
2. The leading edge represents portfolios with the highest return for any given risk.
3. All points between the two dots (the square) represent portfolios that combine the risk
free investment and the market portfolio in differing proportions.
4. The triangle represents ‘leveraged investment’ borrowing at the risk-free rate and
investing in the market portfolio.
The left-hand side is the capital market line slope and the right-hand side is the slope of the leading edge at
the point of the market line. Note that the leading edge is in effect a condition imposed on share returns (ri).
Rearranging to isolate (ri), the required return on share i leads to the CAPM:5
E 1 ri 2 5 rf 1 3 E 1 rm 2 2 rf 4
We leave the algebra as a task for the reader.
Chapter 6
Risk and Return 177
normally written as:
E 1 ri 2 5 rf 1 bi 1 E 1 rm 2 2 rf 2
bi 5
COV 1 ri,rm 2
VAR 1 rm 2
So the critical measure of risk is no longer the standard deviation but beta (bi), and all the other elements
of Equation 6-12 and 6-13 are fixed. To understand beta we can break down the covariance thus:
bi 5 CORR 1 ri,rm 2
STDEV 1 rj 2
STDEV 1 rm 2
where correlation can be seen as phasing and the ratio of standard deviations as relative amplitude.
Note the similarity with the variance covariance matrix:
• Firstly, in the beta formula VAR(r m) is a scaling factor common to all firms. The difference in return
between firms is determined by the covariance with the market return.
• Secondly, rather than the covariance with all other shares the market return is used.
• Thirdly, the betas are additive in the same way as the share covariances in the matrix were added together
to form the portfolio risk. For example, an investment of 25 per cent in a share with a beta of 0.8 and
75 per cent in a share with a beta of 1.2 will result in a portfolio beta of 0.25 3 0.8 1 0.75 3 1.2 5 1.1.
This we would expect as there can be no further gain through diversification.
Using Beta as Part of the Language of Risk
Perhaps the best contribution of beta has been to expand our notion of risk in a formal manner. Risk is relative to the market portfolio. In theory that is the value of all the shares on the stock market; in practice this is
measured as a stock market index such as the FTSE or Dow Jones, where
• bi 5 1; the return required on share i is the same as the market portfolio;
• bi . 1; the return required on share i is greater than the market portfolio, the share is riskier than the
• bi , 1; the return required on share i is less than that of the market portfolio, the share is less risky than
the market portfolio.
The unit of risk is the market risk premium which from Equation 6-13 is E(rm) 2 rf ). So beta really determines how much or little of the market risk premium should be charged to the share.
Shares can be placed on a line according to their risk, the slope of the line (known as the security market
line) is determined by the market risk premium as in Figure 6-12.
Those familiar with statistics can see that in practice the shares should lie on a line that is a regression:6
ri 5 ai 1 birm 1 Pi
The total risk can be broken down into systematic risk b2i s2m the variation in E 1 ri 2 that is explained by the
line which cannot be diversified and nonsystematic risk s2P. As nonsystematic risk can be diversified away
In what follows, measured beta and model beta will both be denoted by bi.
178 Part 3
Shares and Derivatives
F i g u re 6 -1 2
The Security Market Line
E (rm )
in a portfolio it does not play a part in the required market return as in Equation 6-13. Put another way, the
covariance measure in 6-14 is not the same as the variance of a share; it is only the covariance element that
is priced, not the variance. Thus one could have shares that appear to be relatively safe in terms of their individual variation but the movements are highly correlated with the market and so would incur a relatively
higher risk than one might expect from the standard deviation. In comparison, there could be a share that
appears to be quite risky with a high standard deviation but the movements are not well correlated with the
market and so the share’s expected benefits are discounted with a relatively lower return than expected from
the standard deviation. Referring back to Figure 6-8, diversification reduces the risk represented by the gap
between perfect positive correlation (1.0) and the actual correlation of that example.
Another common representation is in Figure 6-13 showing the reduction in expected risk when diversification is achieved as it would be in practice by increasing the number of shares in the portfolio.
Finally, there is a more subtle implication of beta analysis to which we devote the next chapter but introduce it here. Although not a financial term as such, it is the idea that ‘you cannot beat the market on a consistent basis’. That is to say that you might be lucky in choosing shares such as Microsoft or Apple and do
much better than the market; but there is no method of regularly beating the market. Look again at Figure
6-11; the market portfolio is an investment in all the shares in proportion to their market value, say, 10 per
cent of every share’s total market value. By using this portfolio, you achieve the best return for every given
level of risk. Therefore every share must be priced at the best return for its risk. This is shown in Figure 6-12.
To the man in the street this may seem obvious. Why should you with limited knowledge of the shares
that you have invested in be able to make a better choice than the rest of the market with all its knowledge
and experience brought to bear. After a moment’s reflection, the man in the street might add, ‘unless you are
cheating!’ Many believe that the market can be beaten, the investment department of banks, stock market
traders and hedge funds are based on the idea of beating the market. Is their success just down to luck? We
can never be sure. What can nevertheless be said is that the analysis of beta does assume that regularly making larger profits than the market is not possible assuming efficient markets.
Estimating Beta
The CAPM is above all a model that elegantly relates the variation of shares in the market as represented in
the model to a price for the share. The question we ask is how realistic is this price?
Chapter 6
Risk and Return 179
F i g u re 6 -1 3
Reduction in Expected Risk (Standard Deviation) by Increasing the Number of Shares
Expected Portfolio
Standard Deviation
Progressive reduction in
expected risk due to increased
number of shares
Market non
diversifiable risk
Number of Shares
EXAMPLE: Suppose we think that
• a plc is going to produce an annual dividend of €10 growing at a rate of 2 per cent; we can use our
D 11 1 g2
perpetuity with growth formula from Chapter 4: share value 5 0i 2 g where D is dividend, g is
growth and i or r is the return;
• we estimate that the expected market return (rm) is 9 per cent
• the risk-free rate rf is 4 per cent and
• the beta is 0.8
then applying the CAPM model of Equation 6-13, the required return is
E 1 ri 2 5 rf 1 bi 1 E 1 rm 2 2 rf 2
5 4% 1 0.8 1 9% 2 4% 2 5 8%
and putting the return of 8 per cent into the dividend growth model gives
share value 5
10 1 1.02 2
5 127.50
so the share value should be €127.50. Thus, we have moved from a theoretical model that includes
the somewhat abstract notion of beta to a very practical conclusion.
How betas are reported in practice is illustrated in Figure 6-14.
The holding period is clearly significant. Beta for short-period holding is sensitive to the index used. Oneyear and five-year holding periods are more stable across indices. The data also show that over the short term
for the FTSE100 it is less risky than the market but over the longer term is as risky as the market (i.e. close
180 Part 3
Shares and Derivatives
F i g u re 6 -14
Rolls-Royce Beta
Beta for the last…
1 month
1 year
5 years
1 month
1 year
5 years
1 year
5 years
Correlation for the last…
STDEV(i)/STDEV(m) for the last…
1 month
Source: Osiris, Bureau van Dijk, http://www.bvdinfo.com/
to 1.0) but this is not true for the other indices. It is disappointing that the results are so variable. Although
the subject of many, many papers, the notion of a true measure of beta remains elusive.
Another view is to ask businesses whether or not they use betas. In a survey of 96 UK companies by Arnold
and Hatzopolous in 2000,7 when they were asked about the techniques used when assessing a major project
responded: sensitivity analysis 85 per cent, raising the required rate of return 52 per cent, subjective assessment 46 per cent, probability analysis 31 per cent, shorten payback period 20 per cent, beta analysis 3 per cent,
other 3 per cent. There is some variation between surveys but the order is similar—beta analysis is rarely used
and is the least popular technique. Given that the model is so dominant in theory and the subject of Nobel
prizes, it is surprising that there is such a gap between theory and practice. The precise reasons are unclear and
difficult to ascertain; businessmen do what works for them and do not have to rationalize their actions.
The model has also been subjected to academic criticism. Roll’s critique was on the problem of measuring
the market portfolio. He pointed out that investment possibilities are not confined to the market—there is
the housing market, the labour market, investment in precious metals, paintings and so on.8 These are capital assets in the sense that they are an investment that produces returns in much the same way as a share.
Measuring the market return is not simply a matter of measuring the movement of the stock market index
such as the FTSE100 index. Roll also proved that the CAPM was no more than a restatement of mean variance efficiency of the portfolio. Mean variance efficiency is in part captured by the security market line, it
is the idea that greater return should only be possible if a greater risk is being taken in an efficient market
(i.e. well priced). We have already made this point but it is worth restating.
EXAMPLE: Suppose OK plc’s share price is currently €100 and is expected to be €105 in one
year’s time and that a dividend would be declared of €5, also that the standard deviation of these
estimates is 15 per cent. We will assume that OK is correctly priced. The return is therefore 1051001 5
5 10 per cent. If the price fell, then the return would increase for set or given future expected cash
flows. For example, if the price fell to €97 then the return would be 105971 5 = 13.4 per cent. In this
way price determines return which in a mean variance efficient world should be related to risk.
See Arnold, G. C. and Hatzopoulos, P. D. (2000) ‘The theory-practice gap in capital budgeting: evidence from the United Kingdom’,
Journal of Business Finance and Accounting 27(5–6):603–26.
See Roll, R. (1977) ‘A critique of the asset pricing theory’s tests’, Journal of Financial Economics 4(2):129–76.
Chapter 6
Risk and Return 181
Table 6 -3
Mean Variance Efficiency of Investments A, B, C and D in Relation to OK plc for Estimated Returns
OK plc
Expected return
Expected risk
F i g u re 6 -1 5
Mean Variance Efficiency in Relation to OK plc for Given Future Expected Returns as in Table 6-3,
Assuming that OK is Correctly Priced
C: Return is too high for
the risk compared to OK–
making it attractive, price
should increase to lower
the return
OK plc
B: Mean variance
effiicient compared to OK–
higher return BUT higher
D: Mean variance
effiicient compared to OK–
lower return BUT lower
A: Return is too low for
the risk compared to OK–
making it unattractive,
price should fall to
increase the return
Risk: Variance or Standard Deviation
We assume that OK is correctly priced and is the centre of Figure 6-15. Investment A in Table 6-3 belongs to the
top left quadrant, B to the top right quadrant, C to bottom right and D to bottom left. Only B and D are mean variance efficient in relation to OK. A’s price should fall taking it into the bottom left quadrant and C’s price should rise
taking it into the top right quadrant. The overall picture should look like the Security Market Line as in Figure 6-12.
There have also been criticisms of the CAPM from academic studies that have found other factors related
to return that are claimed to be better predictors. The best known of these is the Fama–French three-factor
model.9 In brief, the model is:
ri 5 ai 1 bFF 1 rm 2 rf 2 1 bsizerSMB 1 bB/MrHML 5 Pi
bFF 5 beta as measured by the Fama–French model
ri 5 return on the share
ai 5 intercept for share i
rm 5 market return
SMB 5 a measure of size ‘small minus big’
B/M 5 book-to-market ratio
HML 5 ‘high B/M minus low’
Fama, E. F. and French, K. R. (1992) ‘The cross-section of expected share returns’, Journal of Finance 47(2):427–65.
182 Part 3
Shares and Derivatives
To the beta bFF Fama and French add size to reflect the empirical finding that returns tend to be higher
for smaller firms even after adjusting for beta risk. The other measure B/M is the book-to-market ratio,
being the balance sheet value of equity divided by the stock market valuation of equity (the market capitalization). Low book-to-market shares are known as value shares and were found to have had higher returns.
More pointedly, Fama and French test for the relationship between beta and return controlling for size
and find that beta is not related to return. This raises the question as to whether beta has any empirical
The problem is that beta on its own explains some but not all of the risk of portfolio investments and the
Fama–French model explains more. However, the rationale of the Fama–French model is not that clear. Why
should small firms have higher returns without higher beta risk? Why should so-called value shares have a
higher return? Prediction without explanation is not furthering understanding and is in essence a form of
technical analysis (see next chapter). The results raise important questions but not answers.10
S E L F -T E S T
What is the average beta? If a share has a beta of 0.8, what does that imply about its risk relative to
the market?
Why is beta the theoretically correct measure of a share’s risk?
What types of data are needed to calculate a beta coefficient for an actual company?
An investor has a three-share portfolio with €25 000 invested in Dell, €50 000 invested in Ford, and
€25 000 invested in Walmart. Dell’s beta is estimated to be 1.20, Ford’s beta is estimated to be 0.80,
and Walmart’s beta is estimated to be 1.0. What is the estimated beta of the investor’s portfolio?
(Answer: 0.95.)
What is the relationship between risk and return in the CAPM?
This chapter has focused on the trade-off between risk and return. We began by discussing how to estimate risk and return for both individual assets and portfolios. In particular, we differentiated between standalone risk and risk in a portfolio context, and we explained the benefits of diversification. We introduced the
CAPM, which describes how risk affects required rates of return.
Risk can be defined as exposure to the chance of an unfavourable event.
The risk of an asset’s cash flows can be considered on a stand-alone basis (each asset all by itself) or in a
portfolio context, in which the investment is combined with other assets and its risk is reduced through
Most rational investors hold portfolios of assets, and they are more concerned with the risk of their portfolios than with the risk of individual assets.
For further debate on the relationship between risk and return see Kapadia, N. (2011) ‘Tracking down distress risk’, Journal of Financial Economics 102(1):167–82; George, T. J. (2010) ‘A resolution of the distress risk and leverage puzzles in the cross section of share
returns’, Journal of Financial Economics 96(1):56–79; and Garlappi, L. and Yan, H. (2011) ‘Financial distress and the cross-section of
equity returns’, Journal of Finance 66(3):789–822. For studies rejecting the relationship, see Campbell, J. Y., Hilscher, J. and Szilagyi,
J. (2008) ‘In search of distress risk’, Journal of Finance, 63(6):2899–940; and Dichev, I. D. (1998) ‘Is the risk of bankruptcy a systematic
risk?’ Journal of Finance, 53(3):1131–47.
The finding that small companies should have a higher return has also come under much scrutiny, see Knez, P. J. and Ready, M.
J. (1997) ‘On the robustness of size and book-to-market in the cross-sectional regressions’, Journal of Finance 52(4):1355–82; Kim, D.
(1997) ‘A reexamination of firm size, book-to-market, and earnings price in the cross-section of expected share returns’, Journal of
Financial and Quantitative Analysis 32(4):463–89; Shumway, T. and Warther, V. A. (1999) ‘The delisting bias in CRSP’s Nasdaq data
and its implications for the size effect’, Journal of Finance, 54(6):2361–79; and Loughran, T. (1997) ‘Book-to-market across firm size,
exchange, and seasonality: is there an effect?’ Journal of Financial and Quantitative Analysis, 32(3):249–68.
Chapter 6
Risk and Return 183
The expected return on an investment is the mean value of its probability distribution of returns.
The greater the probability that the actual return will be far below the expected return, the greater the
asset’s stand-alone risk.
The average investor is risk averse, which means that he or she must be compensated for holding risky
assets. Therefore, riskier assets have higher required returns than less risky assets.
An asset’s risk has two components: (1) diversifiable risk, which can be eliminated by diversification, and
(2) market risk, which cannot be eliminated by diversification.
Market risk is measured by the standard deviation of returns on a well-diversified portfolio, one that
consists of all shares traded in the market. Such a portfolio is called the market portfolio.
The CAPM defines the relevant risk of an individual asset as its contribution to the risk of a welldiversified portfolio. As market risk cannot be eliminated by diversification, investors must be compensated for bearing it.
A share’s beta coefficient measures how much risk a share contributes to a well-diversified portfolio?
A share with a beta greater than 1 has share returns that tend to be higher than the market when the
market is up but tend to be below the market when the market is down. The opposite is true for a share
with a beta less than 1.
The beta of a portfolio is a weighted average of the betas of the individual securities in the portfolio.
The CAPM’s Security Market Line (SML) equation shows the relationship between a security’s market
risk and its required rate of return. The return required for any security i is equal to the risk-free rate
plus the market risk premium multiplied by the security’s beta.
Answers to questions (6-6) to (6-13) appear in the Appendix.
(6 -1)
(6 -2)
(6 -3)
Define the following terms, using graphs or equations to illustrate your answers
where feasible:
a. risk in general; stand-alone risk; probability distribution and its relation to risk
b. expected rate of return
c. continuous probability distribution
d. standard deviation, s; variance, s2
e. risk aversion; realized rate of return
f. risk premium for share i; market risk premium
g. capital asset pricing model
h. expected return on a portfolio, market portfolio
i. correlation as a concept; correlation coefficient, r
j. market risk; diversifiable risk; relevant risk
k. beta coefficient; average share’s beta
l. security market line (SML); SML equation
m. slope of SML and its relationship to risk aversion
n. equilibrium; efficient markets hypothesis (EMH); three forms of EMH
o. Fama–French three-factor model
p. behavioural finance; herding; anchoring
The probability distribution of a less risky return is more peaked than that of a riskier
return. What shape would the probability distribution have for (a) completely certain
returns and (b) completely uncertain returns?
Security A has an expected return of 7 per cent, a standard deviation of returns of
35 per cent, a correlation coefficient with the market of −0.3, and a beta coefficient of
−1.5. Security B has an expected return of 12 per cent, a standard deviation of returns
of 10 per cent, a correlation with the market of 0.7, and a beta coefficient of 1.0. Which
security is riskier? Why?
184 Part 3
Shares and Derivatives
(6 - 4 )
(6 -5 )
(6 - 6 )
If investors’ aversion to risk increased, would the risk premium on a high-beta share
increase by more or less than that on a low-beta share? Explain.
If a company’s beta were to double, would its expected return double?
Realized rates of return: Shares A and B have the following historical returns:
2012 44 24
–22 –4
2014 22 8
2015 34 56
a. Calculate the average rate of return for each share during the five-year period.
Assume that someone held a portfolio consisting of 50 per cent of share A and
50 per cent of share B. What would have been the realized rate of return on the
portfolio in each year? What would have been the average return on the portfolio
for the five-year period?
b. Now calculate the standard deviation of returns for each share and for the por­t­
folio. Use Equation 6-9.
c. Looking at the annual returns data on the two shares, would you guess that the
correlation coefficient between returns on the two shares is closer to 0.8 or to −0.8?
d. If you added more shares at random to the portfolio, which of the following is the
most accurate statement of what would happen to sp?
(1) sp would remain constant.
(2) sp would decline to somewhere in the vicinity of 20 per cent.
(3) sp would decline to zero if enough shares were included.
(6 -7 )
Beta and required rate of return: ECRI Corporation is a holding company with four
main subsidiaries. The percentage of its business coming from each of the subsidiaries, and their respective betas, are as follows:
Electric utility
Cable company
Real estate
International/special projects
(6 - 8 )
Percentage of
a. What is the holding company’s beta?
b. Assume that the risk-free rate is 6 per cent and that the market risk premium is
5 per cent. What is the holding company’s required rate of return?
c. ECRI is considering a change in its strategic focus: It will reduce its reliance on
the electric utility subsidiary so that the percentage of its business from this subsidiary will be 50 per cent. At the same time, ECRI will increase its reliance on
the international/special projects division, and the percentage of its business from
that subsidiary will rise to 15 per cent. What will be the shareholders’ required
rate of return if management adopts these changes?
Portfolio beta: Your investment club has only two shares in its portfolio. €20 000 is
invested in a share with a beta of 0.7, and €35 000 is invested in a share with a beta of
1.3. What is the portfolio’s beta?
Chapter 6
(6 -9)
(6 -10 )
(6 -11)
(6 -1 2)
Risk and Return 185
Required rate of return: AA Industries’ share has a beta of 0.8. The risk-free rate is
4 per cent and the expected return on the market is 12 per cent. What is the required
rate of return on AA’s share?
Required rates of return: Suppose that the risk-free rate is 5 per cent and that the
market risk premium is 7 per cent. What is the required return on (1) the market,
(2) a share with a beta of 1.0, and (3) a share with a beta of 1.7?
Fama–French three-factor model: An analyst has modelled the share of a company
using the Fama–French three-factor model. The risk-free rate is 5 per cent, the market
return is 10 per cent, the return on the SMB portfolio (rsmb) is 3.2 per cent, and the
return on the HML portfolio (r HML) is 4.8 per cent. If ai 5 0, bi 5 1.2, ci 5 20.4 and
di 5 1.3, what is the share’s predicted return?
Expected return, discrete distribution: A share’s return has the following distribution:
Demand for the Company’s
Probability of This
Demand Occurring
Rate of Return If
This Demand Occurs (%)
Below average
Above average
(6 -1 3)
Calculate the share’s expected return and standard deviation.
Expected return, discrete distribution: Calculate the share’s expected return and
standard deviation.
The market and Share J have the following probability distributions:
a. Calculate the expected rates of return for the market and Share J.
b. Calculate the standard deviations for the market and Share J.
(6 -1)
Start with the partial model in the file Ch06 P15 Build a Model.xls on the textbook’s
website. The file contains hypothetical data for working this problem. Goodman
Industries’ and Landry Incorporated’s share prices and dividends, along with the
Market Index, are shown below. Share prices are reported for December 31 of each
year, and dividends reflect those paid during the year. The market data are adjusted
to include dividends.
186 Part 3
Shares and Derivatives
Goodman Industries
Landry Incorporated
Market Index
Share price
Share price
Includes dividends
17 495.97
13 178.55
13 019.97
9 651.05
8 403.42
7 058.96
a. Use the data given to calculate annual returns for Goodman, Landry and the
Market Index, and then calculate average annual returns for the two shares and
the index. (Hint: Remember, returns are calculated by subtracting the beginning
price from the ending price to get the capital gain or loss, adding the dividend
to the capital gain or loss, and then dividing the result by the beginning price.
Assume that dividends are already included in the index. Also, you cannot calculate the rate of return for 2010 because you do not have 2009 data.)
b. Calculate the standard deviations of the returns for Goodman, Landry, and the
Market Index. (Hint: Use the sample standard deviation formula given in the
chapter, which corresponds to the STDEV function in Excel.)
c. Construct a scatter diagram graph that shows Goodman’s returns on the vertical
axis and the Market Index’s returns on the horizontal axis. Construct a similar
graph showing Landry’s share returns on the vertical axis.
d. Estimate Goodman’s and Landry’s betas as the slopes of regression lines with share
return on the vertical axis (y-axis) and market return on the horizontal axis (x-axis).
(Hint: Use Excel’s SLOPE function.) Are these betas consistent with your graph?
e. The risk-free rate on long-term Treasury bonds is 6.04 per cent. Assume that the
market risk premium is 5 per cent. What is the required return on the market?
Now use the SML equation to calculate the two companies’ required returns.
f. If you formed a portfolio that consisted of 50 per cent Goodman shares and 50 per
cent Landry shares, what would be its beta and its required return?
g. Suppose an investor wants to include some Goodman Industries shares in his portfolio. Shares A, B and C are currently in the portfolio, and their betas are 0.769,
0.985 and 1.423, respectively. Calculate the new portfolio’s required return if it
consists of 25 per cent Goodman, 15 per cent Share A, 40 per cent Share B, and
20 per cent Share C.
Assume that you recently graduated and landed a job as a financial planner with Cicero Services, an investment advisory company. Your first client recently inherited some assets and has asked you to evaluate them.
The client presently owns a bond portfolio with €1 million invested in zero-coupon US Treasury bonds that
mature in ten years. The client also has €2 million invested in the share of Blandy, Inc., a company that produces meat-and-potatoes frozen dinners. Blandy’s slogan is ‘Solid food for shaky times’.
Unfortunately, the US Congress and the President are engaged in an acrimonious dispute over the budget and
the debt ceiling. The outcome of the dispute, which will not be resolved until the end of the year, will have a big
impact on interest rates one year from now. Your first task is to determine the risk of the client’s bond portfolio.
After consulting with the economists at your firm, you have specified five possible scenarios for the resolution of
the dispute at the end of the year. For each scenario, you have estimated the probability of the scenario occurring
and the impact on interest rates and bond prices if the scenario occurs. Given this information, you have calculated the rate of return on 10-year zero coupon for each scenario. The probabilities and returns are shown below:
Chapter 6
Risk and Return 187
Return on a 10-year zero
coupon treasury bond
during the next year
of scenario
Worst Case
Poor Case
Most Likely
Good Case
Best Case
You have also gathered historical returns for the past ten years for Blandy, Gourmange Corporation
(a producer of gourmet specially foods) and the stock market:
Historical share returns
Average return:
Standard deviation:
Correlation with the market:
The risk-free rate is 4 per cent and the market risk premium is 5 per cent.
a. What are investment returns? What is the return on an investment that costs €1000 and is sold after
one year for €1060?
b. Graph the probability distribution for the bond returns based on the five scenarios. What might the
graph of the probability distribution look like if there were an infinite number of scenarios (i.e. if it
were a continuous distribution and not a discrete distribution)?
c. Use the scenario data to calculate the expected rate of return for the ten-year zero-coupon Treasury
bonds during the next year.
d. What is stand-alone risk? Use the scenario data to calculate the standard deviation of the bond’s return
for the next year.
e. Your client has decided that the risk of the bond portfolio is acceptable and wishes to leave it as it is.
Now your client has asked you to use historical returns to estimate the standard deviation of Blandy’s
share returns. (Note: Many analysts use four to five years of monthly returns to estimate risk and many
use 52 weeks of weekly returns; some even use a year or less of daily returns. For the sake of simplicity,
use Blandy’s ten annual returns.)
188 Part 3
Shares and Derivatives
Your client is shocked at how much risk Blandy share has and would like to reduce the level of risk. You
suggest that the client sell 25 per cent of the Blandy share and create a portfolio with 75 per cent Blandy
share and 25 per cent in the high-risk Gourmange share. How do you suppose the client will react to
replacing some of the Blandy share with high-risk share? Show the client what the proposed portfolio
return would have been in each of year of the sample. Then calculate the average return and standard
deviation using the portfolio’s annual returns. How does the risk of this two-share portfolio compare
with the risk of the individual shares if they were held in isolation?
g. Explain correlation to your client. Calculate the estimated correlation between Blandy and Gourmange.
Does this explain why the portfolio standard deviation was less than Blandy’s standard deviation?
h. Suppose an investor starts with a portfolio consisting of one randomly selected share. As more and
more randomly selected shares are added to the portfolio, what happens to the portfolio’s risk?
i. (1) Should portfolio effects influence how investors think about the risk of individual shares? (2) If you
decided to hold a one-share portfolio and consequently were exposed to more risk than diversified
investors, could you expect to be compensated for all of your risk; that is, could you earn a risk premium on that part of your risk that you could have eliminated by diversifying?
j. According to the Capital Asset Pricing Model, what measures the amount of risk that an individual
share contributes to a well-diversified portfolio? Define this measurement.
k. What is the security market line (SML)? How is beta related to a share’s required rate of return?
l. Calculate the correction coefficient between Blandy and the market. Use this and the previously calculated (or given) standard deviations of Blandy and the market to estimate Blandy’s beta. Does Blandy
contribute more or less risk to a well-diversified portfolio than does the average share? Use the SML to
estimate Blandy’s required return.
m. Show how to estimate beta using regression analysis.
n. (1) Suppose the risk-free rate goes up to 7 per cent. What effect would higher interest rates have on the
SML and on the returns required on high- and low-risk securities? (2) Suppose instead that investors’
risk aversion increased enough to cause the market risk premium to increase to 8 per cent. (Assume the
risk-free rate remains constant.) What effect would this have on the SML and on returns of high- and
low-risk securities?
o. Your client decides to invest €1.4 million in Blandy share and €0.6 million in Gourmange share. What are
the weights for this portfolio? What is the portfolio’s beta? What is the required return for this portfolio?
p. Jordan Jones (JJ) and Casey Carter (CC) are portfolio managers at your firm. Each manages a well-­
diversified portfolio. Your boss has asked for your opinion regarding their performance in the past
year. JJ’s portfolio has a beta of 0.6 and had a return of 8.5 per cent; CC’s portfolio has a beta of 1.4 and
had a return of 9.5 per cent. Which manager had better performance? Why?
q. What does market equilibrium mean? If equilibrium does not exist, how will it be established?
r. What is the efficient markets hypothesis (EMH) and what are its three forms? What evidence supports
the EMH? What evidence casts doubt on the EMH?
Valuation of Shares
and Companies
hare brokerage companies, mutual fund companies, financial services institutions, pension funds
and financial advisory firms are among the many companies that employ security analysts to
­estimate the value and risk of shares.
‘Sell side’ analysts work for investment banks and brokerages. They write reports that are distributed to investors, generally through brokers. ‘Buy side’ analysts work for mutual funds, hedge
funds, pension funds and other institutional investors. Those institutions obtain information from
the buy-side analysts, but they also do their own research and ignore the buy side if they disagree.
The analysts on both sides generally focus on specific industries, and many of them are hired as
analysts after working for a time in the industry they cover. Physics PhDs are often electronics analysts, biologists analyse biotech shares, and so on. The analysts pore over financial statements and
Excel models, but they also go on the road and talk with company officials, companies’ customers,
and their suppliers. The analysts’ primary objective is to predict corporate earnings, dividends and
free cash flow, and thus share prices.
Share prices are volatile, so it is difficult to estimate a share’s value. However, some analysts are
better than others, and the material in this chapter can help you be better than average. How much
is a company worth? What can managers do to make a company more valuable? Why are share
prices so volatile? This chapter addresses these questions through the application of two widely used
valuation models: the dividend growth model and the free cash flow valuation model. But before
plunging into share valuation, we begin with a closer look at what it means to be a shareholder.
Legal Rights and Privileges of Ordinary Shareholders
Ordinary shareholders are the owners of a company, and as such they have certain rights and privileges.
Control of the Firm
A firm’s ordinary shareholders have the right to elect its directors, who, in turn, elect the officers who manage the business. In a small firm, the largest shareholder typically serves as president and chairperson of
the board. In a large UK and US publicly owned firm, the managers typically have some shares, but their
210 Part 3
Shares and Derivatives
personal holdings are generally insufficient to give them voting control. Thus, the managers of most publicly
owned firms can be removed by the shareholders if the management team is not effective. In other countries
around the world the major shareholder is far more likely to have voting control and the company is therefore
more likely to resemble a small firm in this respect.
Companies must hold periodic elections to select directors, usually once a year, with the vote taken at the
annual meeting. At some companies, all directors are elected each year for a one-year term. At other companies, the terms are staggered: for example, one-third of the directors may be elected each year for a threeyear term.
Each share has one vote, so the owner of 1000 shares has 1000 votes. Shareholders can appear at the annual
meeting and vote in person, but typically they transfer their right to vote to another party by means of a
proxy. Management always ask for shareholders’ proxies for their own use and usually get them. However, if
earnings are poor and shareholders are dissatisfied, an outside group may ask for the proxies in an effort to
overthrow management and take control of the business. This is known as a proxy fight.
The Pre-emptive Right
Ordinary shareholders often have the right, called the pre-emptive right, to purchase any additional shares
sold by the firm. The pre-emptive right enables current shareholders to maintain control, and it also prevents
a transfer of wealth from current shareholders to new shareholders. If not for this safeguard, the management of a company could issue additional shares at a low price and purchase these shares itself. Management
could thereby seize control of the company and steal value from the current shareholders.
For example, suppose 1000 ordinary shares, each with a price of €100, were outstanding, making the total
market value of the firm €100 000. If an additional 1000 shares were sold at €50 a share, or for €50 000,
this would raise the total market value to €150 000. When total market value is divided by new total shares
outstanding, a value of €75 a share is obtained. The old shareholders thus lose €25 per share, and the new
shareholders have an instant profit of €25 per share. Thus, selling ordinary shares at a price below the market
value would dilute its price and transfer wealth from the present shareholders to those who were allowed to
purchase the new shares. The pre-emptive right prevents such occurrences.
S E L F -T E S T
What is a proxy fight?
What are the two primary reasons for using pre-emptive rights?
Types of Ordinary Shares
Although most firms have only one type of ordinary share, in some instances companies use classified
shares to meet special needs. Generally, when special classifications are used, one type is designated Class A,
another Class B, and so on. Small, new companies seeking funds from outside sources frequently use different types of ordinary share. For example, when Genetic Concepts in the US went public, its Class A shares
were sold to the public and paid a dividend, but these shares had no voting rights for five years. Its Class B
shares, which the firm’s organizers retained, had full voting rights for five years, but the legal terms stated
that the company could not pay dividends on the Class B shares until it had established its earning power
and built up retained earnings to a designated level.1 The use of classified shares thus enabled the public to
take a position in a conservatively financed growth company without sacrificing income, while the founders
retained absolute control during the crucial early stages of the firm’s development. At the same time, outside
investors were protected against excessive withdrawals of funds by the original owners. As is often the case
in such situations, the Class B shares were called founders’ shares.
Note that there is no standard definition of Class A and Class B shares; another firm may have completely different meanings or even
reverse their meaning.
Chapter 8
Valuation of Shares and Companies 211
As these examples illustrate, the right to vote is often a distinguishing characteristic between different
classes of shares. Suppose two classes of shares differ in only one respect: one class has voting rights but the
other does not. As you would expect, the share with voting rights would be more valuable. In the United
States, which has a legal system with fairly strong protection for minority shareholders (that is, noncontrolling shareholders), voting share typically sells at a price 4 per cent to 6 per cent above that of otherwise
similar nonvoting share. Thus, if a share with no voting rights sold for $50, then one with voting rights
would probably sell for $52 to $53. In countries with legal systems that provide less protection for minority
shareholders, the right to vote is far more valuable. For example, a voting share in Israel sells for 45 per cent
more on average than a nonvoting share, and a voting share in Italy has an 82 per cent higher value than a
nonvoting share.
Some companies have multiple lines of business, with each line having different growth prospects.
As cash f lows for all business lines are mingled in the financial statements, some companies worry
that investors are not able to value the high-growth business lines correctly. To separate the cash f lows
and to allow separate valuations, occasionally a company will have classes of share with dividends tied
to a particular part of a company. This is called a tracking share, or a target share. For example, in
2006 Liberty Media Company, a conglomerate that owned such entertainment assets as the Starz movie
channel and investments in Time Warner, issued two different tracking shares to track its two different business lines. One of these, Liberty Interactive tracking share, was designed to track the performance of its QVC home shopping network and other high-growth Internet-based interactive assets. The
other, Liberty Capital Group, comprised slower-growth holdings like the Starz Entertainment Group.
The idea was that investors would assign a higher value to the high-growth portion of the company if it
traded separately.
However, many analysts are sceptical as to whether tracking shares increase a company’s total market
value. Companies still report consolidated financial statements for the entire company and have considerable
leeway in allocating costs, deploying capital and reporting the financial results for the various divisions, even
those with tracking share. Thus, a tracking share is far from identical to the share of an independent, standalone company.
S E L F -T E S T
What are some reasons why a company might use classified shares?
Market Reporting of Shares
Fifty years ago, investors who wanted real-time information would sit in brokerage firms’ offices watching
a ‘ticker tape’ go by that displayed prices of shares as they were traded. Those who did not need current
information could find the previous day’s prices from the business section of a daily newspaper like the
Wall Street Journal. Today, one can get quotes throughout the day from many different Internet sources.
Figure 8-1 shows the quote for Rolls-Royce Holdings as traded on the London Stock Exchange (LSE) under
the symbol RR.L on 11 March 2014. The quote gives the price at which the share can be bought (the Ask
quote, £976.50) or sold (the Bid quote, £975.50). During the previous 52 weeks, the price hit a high of
£1108.00 and a low of £777.00. Details vary depending on the source, as do the abbreviations, in this case
‘ttm’ stands for trailing twelve months. Note that the relatively high price of the share is likely to put off
very small investors, otherwise the price is of no great significance. If Rolls-Royce had a share split of 10:1,
the value of any holding would remain the same—the holder of one share at £979.00 would now have 10
shares at £97.90. Note also that the P/E ratio (share price divided by earnings or how many multiples of
annual earnings are in the share price) was very high but meaningless as the earnings were very low and
did not represent long-term expectations. The dividend and yield is N/A because Rolls Royce do not pay
dividends for those shares.
In addition to basic quote information, typically there are links to financial statements, research reports,
historical ratios, analysts’ forecasts of EPS and EPS growth rates, and a wealth of other data. Note that unless
stated otherwise, quotes are delayed and hence not suitable for active trading.
212 Part 3
Shares and Derivatives
F i g u r e 8 -1
Share quote for Rolls-Royce, 11 March 2014
Rolls-Royce Group PLC (RR.L) – LSE Ticker: 63H849/ISIN: GB00B63H8491
3.00 (0.50%)
f Like
Add to Portfolio
Prev Close:
Day’s Range:
600.75 - 606.50
52wk Range:
02 Dec 16:30 GMT
600.50 3 250000
601.50 3 250000
Avg Vol (3m):
1y Target Est:
Market Cap:
P/E (ttm):
Next Earnings Date:
EPS (ttm):
Div & Yield:
N/A (N/A)
Previous Close
Source: Reprinted with permission from Yahoo. © 2015 Yahoo.
S E L F -T E S T
What information is provided on the Internet in addition to the share’s latest price?
Valuing Ordinary Shares
In this section we describe the traditional cash flow approach to valuing shares using the discounted cash
flow approach that is general to all valuation in financial economics. If you have read Chapter 4 you will
immediately recognize that this is an application of the actuarial formulae in that chapter. For proofs and
further explanations please refer to that chapter.
Ordinary shares are expected to provide a stream of future cash flows that may or may not be distributed.
A share’s value is found in the same way as the values of other financial assets—namely, as the present value
of its expected future cash flow stream. In later sections we will show how to estimate a share’s value as part
of a company’s total value, but we begin here by directly valuing a share’s cash flows to shareholders.
Definitions of Terms Used in Share Valuation Models
We begin by defining key terms:
Dt is the dividend that the shareholder expects to receive at the end of year t. D 0 is the most recent dividend,
which has already been paid; D1 is the first dividend expected, which will be paid at the end of this year;
D2 is the dividend expected at the end of year 2; and so forth. D1 represents the first cash flow that a new
purchaser of the share will receive, because D 0 has just been paid. D 0 is known with certainty, but all
future dividends are expected values. In practice, dividends are often paid half yearly or even quarterly
but the payment over the year approximated as all being at the end of the year is sufficiently accurate.
Pt is the share price at the end of period t. P0 is the actual market price of the share today. As with dividends,
P1, P2, P3, . . . , Pn are estimates or expectations of future share prices at the end of the particular period.
Thus P1 is the valuation at the end of period 1, with P2 the valuation at the end of period 2, and so on.
Note that these are ex-dividend prices—that is, P0 assumes that dividends have just been paid (the day
before), P1 assumes that the first year dividend has just been paid, P2 assumes that the second year dividend had just been paid, and so on.
E(P0) is the estimated value of the share today as seen by the particular investor doing the analysis. It is
likely to differ from the actual price P0.
D1/P0 is the expected dividend yield during the coming year. For example, if a share is expected to pay a
dividend of D1 5 €1 during the next 12 months and if its current price is P0 5 €10, then the expected
dividend yield is :10
5 0.10 5 10%.
Chapter 8
Valuation of Shares and Companies 213
P1 2 P0
5 expected capital gains yield during the coming year. If the share sells for €10 today and
if it is expected to rise to €10.50 at the end of one year, then the expected capital gain is P1 2 P 0 5
: 0.50
€10.50 2 €10.00 5 €0.50, and the expected capital gains yield is :10 5 0.05 5 5%.
g is the expected growth rate of dividends as predicted by a marginal investor (by that we mean an investor
who is prepared to buy or sell at the current price).
rs is the required rate of return on the share. As shown in Chapter 6, the primary determinants of rs include
the risk-free rate and adjustments for the share’s risk. Note that this is a nominal rate, that is to say, it
includes inflation.
E(rs) is the expected rate of return that an investor who buys the share expects to receive in the future. Note
that the expected return is equal to the expected dividend yield (D1 / P0) plus the expected capital gains
yield ([P1 2 P0]/ P0). In our example, E(rs) 5 10% 1 5% 5 15%. Inflation is included in this rate.
ras 5 actual, or realized, after-the-fact rate of return (including inflation) for a risky security (s); the actual
return can differ considerably from the expected return.
Expected Dividends as the Basis for Share Values
Like all financial assets, the value of a share can be modelled as the present value of expected future cash
flows. We start with a simple regular dividend-paying share because of its well-defined cash flows.
What are the cash flows that companies are expected to provide to their shareholders? First, think of
yourself as an investor who buys a share with the intention of holding it (in your family) forever. In this case,
all that you (and your heirs) will receive is a stream of dividends, and the value of the share today is calculated as the present value of an infinite stream of dividends. We would therefore expect to find that:
Value of share 5 present value of future dividends:
P0 5
1 c1
1 1 1 rs 2 1
1 1 1 rs 2 2
1 1 1 rs 2 3
1 1 1 rs 2 `
5 a
t51 1 1 1 rs 2
What about the more typical case, where you expect to hold the share for a finite period and then sell it.
What is the value of the share in this case? Take someone who buys a share and intends to hold it for two years
and then sell the share. The estimated present value of the share in two years’ time is shown in Equation 8-2. It
is the same basis as the valuation in Equation 8-1 but applied to all the dividends after the period 2 dividend.
Our strategy is to sell it after two years so the cash flows are as in Equation 8-3. If we substitute the right-hand
side of Equation 8-2 into P2 in Equation 8-3 we get Equation 8-4, which is the same as Equation 8-1:
P2 5
P0 5
P0 5
1 c1
1 1 1 rs 2 3
1 1 1 rs 2 `
1 P2
1 1 1 rs 2 1
1 1 1 rs 2 2
1 1
2 1
3 1
1 1 1 rs 2
1 1 1 rs 2
1 1 1 rs 2
1 1 1 rs 2 `
The important conclusion is that whether you intend to hold the shares forever or sell them after two or three
years, or any other time period, the valuation at P0 is the same. The future selling price of a share is simply the
discounted value of the future dividends which, as we saw in Equation 8-3, may be discounted into a future price.
214 Part 3
Shares and Derivatives
S E L F -T E S T
What are the two components of most shares’ expected total return?
How does one calculate the capital gains yield and the dividend yield of a share?
lf D1 = €3.00, P0 = €50 and P1 = €52, what are the share’s expected dividend yield, expected capital
gains yield and expected total return for the coming year? (Answer: 6 per cent, 4 per cent, 10 per
Valuing a Share Using the Growth Model
It is tempting to assume that dividends are estimated as a constant over time. This would be wrong for two
reasons. Firstly, the rate is a nominal rate, that is to say, it includes inflation. We know from Chapter 2 that
for every 1 1 1Dt rs 2 t if rs the rate of return includes inflation, then Dt must include inflation as well—it must
therefore grow with inflation. Secondly, returns to share investment are on average higher than the inflation
rate, so the inclusion of real growth in returns is not unreasonable.
The growth model is an application of a perpetuity with growth (see Equation 4-6)—see Chapter 4 for the
full explanation and derivation of the formulae. The equation is as follows:
P0 5
D0 1 1 1 g 2 1
D0 1 1 1 g 2 2
D0 1 1 1 g 2 3
D 11 1 g2`
c1 0
1 1 1 rs 2 1
1 1 1 rs 2 2
1 1 1 rs 2 3
1 1 1 rs 2 `
` D 11 1 g2t
5 a
t51 1 1 1 rs 2
rs 2 g
Note that g is also the expected capital gains yield
1 P1 2 P0 2
as P1 5 P0 1 1 1 g 2 .
EXAMPLE: ABC s.a.2 has just paid a dividend of €0.05 or 5 cents per share. An investment analyst estimates that the growth in dividends will be the equivalent of 3 per cent a year. The estimated required return for a share of that risk class is 12 per cent. What is the value of the share
according to the constant growth model?
P0 5
rs 2 g
0.05 1 1.03 2
0.12 2 0.03
5 : 0.5722
Of course, this then has to be compared with the market price to come to a judgement. As with all such
modelling, one cannot distinguish between whether the real world is wrong or the model is wrong. So if the
actual price were €0.50 what is one to conclude? A simple conclusion is that the real world is wrong and that
the share is underpriced and worth more, so buy! But it could mean that the model is wrong. Either the input
values are wrong or the variables are incomplete and the market is considering the investment taking into
account the future in a different way.
A French company!
Chapter 8
Valuation of Shares and Companies 215
Sensitivity analysis is perhaps a more rigorous way of investigating value.
EXAMPLE: Take the previous example of ABC s.a., but consider the uncertainty around the
estimates. Holding the other estimates as in the example, what growth rate would support the
actual price of €0.50? Answer: 0.018 or 1.8 per cent.3 What interest rate would justify that price?
Answer: 0.133 of 13.3 per cent.
Now to judge whether the share is under-priced we have to consider whether the interest rate of 13.3 per cent
is too high or the growth rate (remembering that it includes inflation) is too low? Or a combination of the two?
In Table 8-1 we can see the share value for various return–growth combinations as well as the percentage error
from the original ‘best’ estimate of €0.5722. Looking at the 3 per cent growth row, the higher the required return
the lower the value, and checking the 12 per cent return column the higher the growth the higher the value. Note
that on the lead diagonal (top left to bottom right) the errors are very small, being 1 per cent or 2 per cent. In this
particular case changing both the return and growth by 1 per cent does not greatly change the valuation—a 1 per
cent greater return is offset by a 1 per cent higher required return. Note also that the potential for quite high errors
in valuation is evident. For example, taking the 12 per cent column as the reasonable required return, if growth
were 5 per cent instead of 3 per cent then the valuation should have been 31 per cent higher! Thus, seemingly small
changes in input estimates can yield large differences in estimates.
Another way of looking at the percentage error figures in Table 8-1 is to see the potential for share volatility. Information coming to the market may change the market’s view of the required return, or change the
economic outlook and hence the growth rate. There is no necessary trade-off—growth could be lower and
the returns riskier and hence higher.
More generally, one can see how sensitive the original €0.5722 valuation is to changes in the estimates. In
this way, subjective judgement sits alongside financial modelling to help in coming to a valuation.
It may be that an investor, whether a company valuing a project or an investor on the stock market, has
particular views about the growth of returns that are not linear. The simple solution is to place the estimates
on a spreadsheet and discount the returns individually. To communicate the results it may nevertheless be
useful to give the equivalent constant growth rate.
Looking at the growth model in Equation 8-5 it seems odd that the main uncertain values are on the
right-hand side—we surely get a reasonable estimate of price P0 in the case of share valuation from the market price.4 The uncertainties are more with growth and the required return than with the share price. In
­Equations 8-6 and 8-7 we rearrange the growth formula to reflect these uncertainties:
rs 5
i.e. required return = expected dividend yield + expected growth rate
TA B L E 8 -1
The Value of ABC S.A. Shares Using Different Growth and Return Combinations. In Parentheses, the
Percentage Difference from the Original Estimate of €0.5722 (in Bold)
10% Return
11% Return
€0.5611 (−2%)
€0.505 (−12%)
€0.4591 (−20%)
12% Return
€0.4208 (−26%)
13% Return
€0.3885 (−32%)
€0.6375 (11%)
€0.5667 (−1%)
€0.51 (−11%)
€0.4636 (−19%)
€0.425 (−26%)
€0.7357 (29%)
€0.6438 (13%)
€0.5722 (0%)
€0.515 (−10%)
€0.4682 (−18%)
€0.8667 (51%)
€0.7429 (30%)
€0.65 (14%)
€0.5778 (1%)
€0.52 (−9%)
€1.05 (83%)
€0.875 (53%)
€0.75 (31%)
€0.6563 (15%)
€0.5833 (2%)
We leave the calculation to the algebra or trial and error skills with a spreadsheet of the reader, but see Table 8-1.
Usually, we seek to predict the variable on the left-hand side from known values of the right-hand side.
15% Return
216 Part 3
Shares and Derivatives
i.e. growth rate = required return − expected dividend yield
g 5 rs 2
The Free Cash Flow Valuation Model
Managers as well as stock market investors need to be able to value investments. For managers those investments may be buying shares in a company but also investments will include what are termed real investments: that is, projects undertaken by the company. The discount cash flow model makes no distinction
between investment in shares and investment in a project. Nevertheless there are differences in determining
the cash flows.
The dividend growth model is unsuitable in many share valuation situations. For example, suppose
a start-up company is formed to develop and market a new product. Its managers will focus on product
development, marketing and raising capital. They will probably be thinking about an eventual IPO or share
issue, or perhaps the sale of the company to a larger firm—for example, Google, Cisco, Microsoft, Intel, IBM
and other industry leaders buy hundreds of successful new companies each year. For the managers of such
a start-up, a decision to initiate dividend payments in the foreseeable future will be unthinkable. Thus, the
dividend growth model is not useful for valuing most start-up companies.
Also, many established firms pay no dividends. This is the case for Rolls-Royce Holdings analysed in
Chapter 3. Investors may expect them to pay dividends sometime in the future—but when, and how much?
As long as internal opportunities and acquisitions are so attractive, the initiation of dividends will be postponed, and this makes the dividend growth model of little use. Even Apple, one of the world’s most successful companies, paid no dividends from 1995 until 2012, when it initiated quarterly dividend payments.
The dividend growth model is generally of limited use for internal management purposes, even for a
­d ividend-paying company. If the firm consisted of just one big asset and if that asset produced all of the
cash flows used to pay dividends, then alternative strategies could be judged through the use of the dividend growth model. However, most firms have several different divisions with many assets, so the company’s
value depends on the cash flows from many different assets and on the actions of many managers. These
managers need a way to measure the effects of their decisions on corporate value, but the discounted dividend model is not very useful because individual divisions do not pay dividends.
An alternative measure of the cash benefit from investment is needed. One response is the free cash flow
valuation model which does not depend on dividends, and can be applied to divisions and subunits as well as
to the entire firm.
Sources of Value and Claims on Value
Companies have two primary sources of value: the value of operations and the value of non-operating assets.
There are three major types of claims on this value: debt, preferred share and ordinary share. Following is a
description of these sources and claims.
Free cash flow (FCF) is the cash flow available for distribution to all of a company’s investors. FCF is
defined as: after-tax operating profit plus depreciation minus the amount of new investment in working capital and fixed assets necessary to sustain the business. A slightly shorter version from Chapter 1 is:
EBIT (Earnings Depreciation Required investments
before interest
and amorti2
in new operating and
and taxation)
working capital
Alternatively, FCF can be taken as the operating cash flow less required capital expenditure, a more convenient measure where a cash flow statement is available. The intuition here is that operating profit is not
the complete definition of what can be distributed. To maintain the current level of operations, investment
has had to be made in the increase in debtors net of the extra creditors. This appears initially as an increase
Chapter 8
Valuation of Shares and Companies 217
in overdraft and is a negative cash flow that is recorded on the balance sheet rather than the income and
expenditure account. Expenditure will also have been needed on fixed assets. The accounting treatment is to
apportion the cost in the form of depreciation and this should be added back to the operating profit. Deducting the expenditure on fixed assets when it happens ensures that the FCF is not already committed to maintain operations and is therefore by our definition not free.
The Weighted Average Cost of Capital—Outline
The weighted average cost of capital (WACC) is the overall return required by a company’s investors, being
mainly the shareholders and bondholders. It is relevant for both share valuation and project valuation. We
discuss its calculation in relation to project valuation in Chapter 10. Here we give an outline of its application
and of issues related to WACC.
A critical question raised in the 1950s was whether the rate of return depends on the mix of investors. After
all, bondholders require a lower rate than shareholders, so is a lower return required when being financed by
bondholders? The implications are important because a lower discount rate means a higher net present value of
the company’s expected future earnings and a higher company value on the stock exchange. In a renowned paper
Modigliani and Miller (MM) in 19585 demonstrated that such a conclusion would be illogical (other than for tax
considerations which were not part of the original question). The argument they advanced depended on the law
of one price, like many financial proofs, and we examine it in Chapter 10. Here we give an intuitive outline.
The argument of Modigliani and Miller is that a project has a set amount of risk defined by its a­ ctivities—a
rocket into space, drilling for an oilfield, researching a new drug. The risk is the risk of future cash flows
from the project. The way it is financed does not make it safer. Bondholders may want a lower return but they
also want greater security. Providing that security (basically, payment in bad times) increases the risk for the
shareholders. MM applied the law of one price, in this case that the same risk should have the same price.
Critical to their argument is that there are two ways of achieving leverage—the company can borrow or the
investor/shareholder can borrow. The risk to the shareholder with a few assumptions is the same. Therefore,
company leverage does not matter because a shareholder can substitute ‘homemade leverage’ by personal
borrowing or investing in risk-free assets as well. They showed that this observation implied that leverage
should not affect the cost of capital as it is controllable by the shareholder rather than the company. Shareholders of the same company can have many differing leverage positions. A firm that does not borrow should
therefore have the same cost of capital as a firm that does borrow. If this were not so, over time we would see
firms being increasingly financed by bondholders to lower their cost of capital and taking on ever riskier
projects because of the lower cost! Modigliani and Miller save us from such a prospect.6
A consequence of the MM analysis is expressed as Fisher’s separation theorem. As investors can determine the risk of their investments in companies by differing levels of borrowing and investing, firms do not
have to consider the risk preferences of their investors. The concern of the firm is to get the best return for
the risk of the projects they are investing in—real investment risk (i.e. in projects) and shareholder risk are
separate. The only connection between investment risk and shareholder risk is that the shareholders need to
be aware of the risks that the company is undertaking. That in part is the role of the annual report.
Another concern is: how do we define a project? One can see the problem. If one manager treats the opening of the next supermarket as a project and another manager regards the opening of the next five supermarkets as a project, who is right? The solution is to invoke the value additivity principle. If we assume that the
projects are independent then in our example the value of the five supermarkets will be the net present value
of each supermarket. If they are not independent than the five must be considered as one project. Again the
concept of independence allows us to value.
We therefore have two stages in valuation: project valuation and company valuation where a company
takes on a range of projects, which is normally the case. In this chapter we are interested in company
A clear proof is to be found in Modigliani, F. and Miller, M. H. (1969) ‘Reply to Heins and Sprenkle’, American Economic Review
Tax deductibility of interest payments does modify this conclusion a little when valuing a firm, but this is a practical rather than a
conceptual adjustment, the result of regulation rather than an alteration to the basic argument.
218 Part 3
Shares and Derivatives
valuation. We can see a company as a project that is made up of a bunch of other projects. An investor in
shares can only ‘see’ the overall returns. Only the managers in the company can see the returns required of
an individual project.7 We examine this in Chapter 10. The overall discount rate at company level is termed
the weighted average cost of capital (WACC) and is the overall discount rate applied to the FCFs from all
the projects together undertaken by the company. The value of a company can be described as follows:
Company value (V) 5 present value of free cash flows (FCF) discounted at the
weighted average cost of capital (WACC)
1 1
2 1
1 1 1 WACC 2
1 1 1 WACC 2
1 1 1 WACC 2 `
5 a
t51 1 1 1 WACC 2
applying the growth model:
WACC 2 g
The formula is the same as that of Equation 8-5. We can now use the model to help to value Rolls-Royce.
Fortunately, Rolls-Royce produce a statement of FCFs. The statement for 2014 is summarized in Table 8-2.
The value of the firm (V) is the market capitalization8 plus the noncurrent liabilities (long-term borrowing,
bonds, etc.). For 2014 the market capitalization was £16 378m and the noncurrent liabilities were £5959m.
Using the growth formula from Equation 8-8 and the free cash flow from Table 8-2 we have V and FCF1 so
we can estimate (WACC 2 g) as £16 378m
1 £5959 5 1.13%. This percentage is the margin over the growth rate.
For 2014 if we estimate the growth rate to be the equivalent of 5 per cent which is the annual growth rate of
revenue over the last five years for Rolls-Royce, then the WACC is estimated to be 5% 1 1.13% 5 6 .13%. If
you feel that the WACC should be 6.0 per cent then (WACC 2 g) 5 6% 2 5% 5 1.0% making the total value
TA B L E 8 -2
Rolls-Royce Free Cash Flow Statement 2014
Reported operating profit plus adjustments
Depreciation add back
Less increase in working capital
Less capital expenditure
Trading cash flow
Less pensions / tax
Free cash flow
Source: Rolls Royce 2013 Annual Report, http://ar.rolls-royce.com/2013/
Many of the larger multinational will report the profits of their separate divisions, Rolls-Royce being one such example.
Market capitalization is share price × number of shares issued. Any over- or underestimate of capitalization is therefore an over- or
underestimate of the share price.
Chapter 8
Valuation of Shares and Companies 219
£254m/0.01 5 £25,400m and the share value £25 400 2 £5959 5 £19 441—implying that the market price is
undervalued by some 18.7 per cent.9
There are some lessons to be learnt from this calculation:
• The WACC has to be greater than the growth rate otherwise our formula will not work.
• What seem to be very small changes in the estimates produce large changes in valuation as we showed above.
• This is only the start of a valuation exercise. We are using the past to estimate the future, which is often
a poor way of estimating. In the case of Rolls-Royce the past results are very variable, making our estimates likely to be inaccurate. What about information that is more directly related to the future? What
have the directors said about their future plans?
• FCF models may be more informative for management who can make future estimates using their plans
which are not yet known to the market. As they know that investors will be using the model they can perform
a ‘see how it looks’ exercise to make sure that they are not opening themselves up to criticism from investors.
Share Valuation and Market Efficiency
Let us reconsider a question that we looked at briefly in the previous chapter. The perceptive reader may
be wondering why the previous chapter on market efficiency claimed that share prices moved randomly
and that the current price was the best estimate as it uses all the known information about the future.
Surely this contradicts this chapter where it is being claimed that shares can be valued in quite a simple
way and that we can apparently come to a judgement about whether the share is over- or undervalued
using data related to the previous year’s performance. What are we to believe: the share valuation model
or the market price? If the share valuation model is to be believed then why are millions being spent in
the large financial capitals of the world in order to get information a few seconds more quickly when
according to the share valuation model one just needs to look at the accounts!
Perhaps we can look to practice and in particular one of the greatest stock market investors, Warren Buffett,
for guidance. Reading through his many comments it is clear that he regards analysis as being effective over
the long term. As he pithily puts it: ‘If you aren’t willing to own a share for ten years don’t even think about
Greek Stock Market Woes
On Monday 3 August 2015 the Greek government
allowed trading on the stock exchange—having
been closed for five weeks due to the economic
uncertainty created by the Greek debt crisis. The
stock market fell 16.2 per cent in one day, its biggest ever fall. Bank shares were particularly badly
hit: Piraeus Bank fell 30 per cent (a cumulative
loss of 87.2 per cent over the previous 12 months),
and National Bank of Greece shares fell 28.45 per
cent. Trading was suspended for a number of
shares whose value fell by more than 30 per cent
in one day. Bank shares continued to fall in the
succeeding days, Tuesday was like Monday and
on the Wednesday bank shares fell an average of
15 per cent. Traders complained about a lack of
liquidity—sellers but no buyers. Financial risk can
£19 441/£16 378 2 1 5 0.187, or 18.7 per cent.
be sudden and extreme. Markets are sometimes
accused of overreacting to bad news but often it
is just uncertainty due to changing interpretations
in a very different situation. In this case the Athens
Stock Exchange General Index closed on Monday
3 August at 668, then fell by 3.7 per cent by the
Wednesday, then rose 9.6 per cent over the next
six days, ending at just 1 per cent over the Monday
valuation by 18 August. A crisis is a period of both
large falls and rises.
Sources: ‘Greek bank shares plunge for a third day’,
­w ww.Telegraph.co.uk, 5 August 2015; ‘The Athens Cup’,
Scottish Daily Mail, 5 August 2015; ‘More woe as Greek
stock market falls’, Scotland Evening Times, 4 August
2015; www.bloomberg.com/quote/ASE:IND
220 Part 3
Shares and Derivatives
owning it for ten minutes’.10 Valuation models are really for the medium to long term—i.e. above three years.
The market efficiency argument works well over the short to medium term—an investor is highly unlikely
to beat the market as a result of using a share valuation model. The efficiency of the market over the medium
to long term is however a far less settled matter. Testing is difficult, as one needs longer time periods. Identifying relevant information is difficult. The short-term impact of a surprise increase in profits will be an
increase in value but does it have long-term significance?
There may be better answers in the future but for the moment it is best to distinguish the two approaches
to valuation as being that the share valuation models of this chapter are really for the medium to long term.
If an investor is looking to buy or sell shares with a holding period of a year and make a profit, market
efficiency says that such an investor is unlikely to beat the market unless they get information before other
traders or unless they are receiving insider information. Valuation models may play a part in longer-term
investment for which there are no clear guides. On this both theory and the best of practice can agree.
A Note on Preferred Shares
A preferred share is a hybrid—it is similar to bonds in some respects and to ordinary shares in others. Like
bonds, a preferred share has a par value, and a fixed amount of dividends must be paid on it before dividends
can be paid on ordinary shares. However, if the preferred dividend is not earned, the directors can omit (or
‘pass’) it without throwing the company into bankruptcy. So, although a preferred share has a fixed payment
like bonds, a failure to make this payment will not lead to bankruptcy.
The dividends on preferred shares are fixed, and if they are scheduled to go on forever, the issue is a perpetuity using the constant dividend growth model for which growth is zero as in Equation 8-5. Some preferred
shares have a stated maturity, say, 50 years. Again we can use the actuarial valuation models to estimate the
current price in much the same way as bond valuation of Chapter 5.
Share valuation models apply the actuarial valuation equations to the valuation of shares. As they demand
estimates of the future they can only really be seen as guiding the valuation process rather than giving
definitive answers.
A proxy is a document that gives one person the power to act for another, typically the power to vote on
behalf of ordinary shares. A proxy fight occurs when an outside group solicits shareholders’ proxies in
an effort to overthrow the current management.
Shareholders often have the right to purchase any additional shares sold by the firm. This right, called
the pre-emptive right, protects the present shareholders’ control and prevents dilution of their value.
Although most firms have only one type of ordinary share, in some instances classified shares are used
to meet the special needs of the company. One type is founders’ shares. These are shares owned by the
firm’s founders that carry sole voting rights but restricted dividends for a specified number of years.
The expected total rate of return from a share consists of an expected dividend yield plus an expected
capital gains yield. For a constant growth firm, both the dividend yield and the capital gains yield are
expected to remain constant in the future.
The valuation of shares is an application of the perpetuity cash flow valuation models in Chapter 4.
Although the variables in a model may not represent actual future estimates they may be seen as a useful
way of thinking about the future and as being ‘equivalent’ to the actual estimates.
The value of operations is the present value of all the future FCFs expected from operations when discounted at the weighted average cost of capital.
The EMH provides convincing evidence that share valuation models are not reliable tools for identifying
short- to medium-term gains. They may be of value for medium- to long-term valuation.
Chairman’s letter, Berkshire Hathaway (1996).
Chapter 8
Valuation of Shares and Companies 221
A preferred share is a hybrid security having some characteristics of debt and some of equity.
A preferred share that has a finite maturity is evaluated with a formula that is identical in form to the
bond value formula.
Solutions to questions (8-5) to (8-28) appear in the Appendix.
( 8 -1)
Define each of the following terms:
a. proxy; proxy fight; pre-emptive right; classified share; founders’ shares
b. required rate of return, rs
c. capital gains yield; dividend yield; expected total return
d. constant growth; nonconstant growth; zero growth share, preferred share
e. Free cash flow valuation model
( 8 -2)
Two investors are evaluating General Electric’s shares for possible purchase. They
agree on the expected value of Di and also on the expected future dividend growth
rate. Further, they agree on the risk of the share. However, one investor normally
holds shares for two years and the other normally holds shares for ten years. On the
basis of the type of analysis done in this chapter, they should both be willing to pay
the same price for General Electric’s share. True or false? Explain.
A bond that pays interest forever and has no maturity date is a perpetual bond, also
called a perpetuity or a consol. In what respect is a perpetual bond similar to (1) a
no-growth ordinary share and (2) a share of preferred share?
Explain how to use the corporate valuation model to find the price per share of ordinary equity.
Constant-growth share valuation: Ewald Company’s current share price is €36, and
its last dividend was €2.40. In view of Ewald’s strong financial position and its consequent low risk, its required rate of return is only 12 per cent. If dividends are expected
to grow at a constant rate g in the future, and if rs is expected to remain at 12 per cent,
then what is Ewald’s expected share price five years from now?
Nonconstant-growth share valuation: Snyder Computer Chips Inc. is experiencing a
period of rapid growth. Earnings and dividends are expected to grow at a rate of 15
per cent during the next two years, at 13 per cent in the third year, and at a constant
rate of 6 per cent thereafter. Snyder’s last dividend was €1.15, and the required rate of
return on the share is 12 per cent.
a. Calculate the value of the share today.
b. Calculate the current price and the price in one year’s time.
c. Calculate the dividend yield and capital gains yield for years 1, 2 and 3.
( 8 -3)
( 8 -5 )
A German company!
Free cash flow valuation model: Watkins GmbH11 has never paid a dividend, and when
the firm might begin paying dividends is not known. Its current FCF is €100 000, and this
FCF is expected to grow at a constant 7 per cent rate. The WACC is 11 per cent. Watkins
currently holds €325 000 of nonoperating marketable securities. Its long-term debt is
€1000 000, but it has never issued preferred shares. Watkins has 50 000 shares outstanding.
a. Calculate Watkins’ value of operations.
b. Calculate the company’s total value.
c. Calculate the estimated value of ordinary equity.
d. Calculate the estimated per share price.
222 Part 3
Shares and Derivatives
( 8 -9)
( 8 -10 )
( 8 -11)
( 8 -1 2)
( 8 -1 3)
( 8 -14 )
DPS calculation: Thress Industries just paid a dividend of €1.50 a share (i.e. D0 5 €1.50).
The dividend is expected to grow 5 per cent a year for the next three years and then
10 per cent a year thereafter. What is the expected dividend per share for each of the
next five years?
Constant-growth valuation: Boehm Incorporated is expected to pay a €1.50 per share
dividend at the end of this year (i.e. D1 5 €1.50). The dividend is expected to grow at a
constant rate of 6 per cent a year. The required rate of return on the share, rs, is 13 per
cent. What is the estimated value per share of Boehm’s shares?
Constant-growth valuation: Woidtke Manufacturing’s share currently sells for €22 a
share. The share just paid a dividend of €1.20 a share (i.e. D 0 5 €1.20), and the dividend is expected to grow forever at a constant rate of 10 per cent a year. What share
price is expected one year from now? What is the estimated required rate of return on
Woidtke’s share (assume the market is in equilibrium with the required return equal
to the expected return)?
Preferred-share valuation: Nick’s Enchiladas Incorporated has preferred shares outstanding that pays a dividend of €5 at the end of each year. The preferred shares sell
for €50 a share. What is a share’s required rate of return (assume the market is in
equilibrium with the required return equal to the expected return)?
Nonconstant-growth valuation: A company currently pays a dividend of €2 per
share (D 0 5 €2). It is estimated that the company’s dividend will grow at a rate of
20 per cent per year for the next two years, and then at a constant rate of 7 per cent
thereafter. The company’s share has a beta of 1.2, the risk-free rate is 7.5 per cent,
and the market risk premium is 4 per cent. What is your estimate of the share’s
current price?
Value of operations of constant-growth firm: EMC Company has never paid a dividend. Its current FCF of €400 000 is expected to grow at a constant rate of 5 per cent.
The WACC is 12 per cent. Calculate EMCs estimated value of operations.
Horizon value: Current and projected free cash flows for Radell Global Operations
are shown below. Growth is expected to be constant after 2017, and the WACC is
11 per cent. What is the horizon (continuing) value at 2018 if growth from 2017
remains constant?
(Free cash flow
(€ million)
( 8 -15 )
( 8 -16 )
Constant growth rate, g: A share is trading at €80 per share. The share is expected to
have a year-end dividend of €4 per share (D1 5 €4), and it is expected to grow at some
constant rate g throughout time. The share’s required rate of return is 14 per cent
(assume the market is in equilibrium with the required return equal to the expected
return). What is your forecast of g?
Constant-growth valuation: Crisp Cookware’s ordinary shares are expected to pay
a dividend of €3 a share at the end of this year (D1 5 €3.00); its beta is 0.8; the riskfree rate is 5.2 per cent; and the market risk premium is 6 per cent. The dividend is
expected to grow at some constant rate g, and the share currently sells for €40 a share.
Assuming the market is in equilibrium, what does the market believe will be the
share’s price at the end of three years (i.e. what is P3)?
Chapter 8
( 8 -17 )
( 8 -1 8 )
( 8 -19)
( 8 -2 0 )
( 8 -21)
Valuation of Shares and Companies 223
Preferred share rate of return: What is the required rate of return on a preferred share
with a €50 par value, a stated annual dividend of 7 per cent of par, and a current market price of (a) €30, (b) €40, (c) €50 and (d) €70? (Assume the market is in equilibrium
with the required return equal to the expected return).
Declining-growth share valuation: Brushy Mountain Mining Company’s coal
reserves are being depleted, so its sales are falling. Also, environmental costs increase
each year, so its costs are rising. As a result, the company’s earnings and dividends are
declining at the constant rate of 4 per cent per year. If D 0 5 €6 and rs 5 14%, what is
the estimated value of Brushy Mountain’s share?
Nonconstant-growth share valuation: Assume that the average firm in your company’s
industry is expected to grow at a constant rate of 6 per cent and that its dividend yield is
7 per cent. Your company is about as risky as the average firm in the industry, but it has
just successfully completed some R&D work that leads you to expect that its earnings and
­dividends will grow at a rate of 50 per cent [D1 5 D0(l 1 g) 5 D0(1.50)] this year and
25 per cent the following year, after which growth should return to the 6 per cent industry
average. If the last dividend paid (D0) was €1, what is the estimated value per share of your
firm’s share?
Nonconstant-growth share valuation: Simpkins Company does not pay any dividends
because it is expanding rapidly and needs to retain all of its earnings. However, investors expect Simpkins to begin paying dividends, with the first dividend of €0.50 coming three years from today. The dividend should grow rapidly—at a rate of 80 per cent
per year—during years 4 and 5. After year 5, the company should grow at a constant
rate of 7 per cent per year. If the required return on the share is 16 per cent, what is
the value of the share today (assume the market is in equilibrium with the required
return equal to the expected return)?
Preferred-share valuation: Several years ago, Rolen Riders issued preferred share with
a stated annual dividend of 10 per cent of its €100 par value. Preferred share of this
type currently yields 8 per cent. Assume dividends are paid annually.
a. What is the estimated value of Rolen’s preferred share?
b. Suppose interest rate levels have risen to the point where the preferred share now
yields 12 per cent. What would be the new estimated value of Rolen’s preferred share?
( 8 -2 2)
Return on ordinary shares: You buy a share of the Ludwig Company share for €21.40.
You expect it to pay dividends of €1.07, €1.1449 and €1.2250 in years 1, 2 and 3, respectively, and you expect to sell it at a price of €26.22 at the end of three years.
a. Calculate the growth rate in dividends.
b. Calculate the expected dividend yield.
c. Assuming that the calculated growth rate is expected to continue, you can add
the dividend yield to the expected growth rate to obtain the expected total rate of
return. What is this share’s expected total rate of return (assume the market is in
equilibrium with the required return equal to the expected return)?
( 8 -2 3)
Constant-growth share valuation: Investors require a 13 per cent rate of return on
Brooks Sisters’ share (rs 5 13%).
a. What would the estimated value of Brooks’ share be if the previous dividend were
D 0 5 €3.00 and if investors expect dividends to grow at a constant annual rate of
(1) 25 per cent, (2) 0 per cent, (3) 5 per cent and (4) 10 per cent?
b. Using data from part a, what is the constant growth model’s estimated value for
Brooks Sisters’ share if the required rate of return is 13 per cent and the expected
growth rate is (1) 13 per cent or (2) 15 per cent? Are these reasonable results? Explain.
c. Is it reasonable to expect that a constant growth share would have g > rs?
224 Part 3
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( 8 -24 )
Value of operations: Kendra Enterprises has never paid a dividend. Free cash flow is
projected to be €80 000 and €100 000 for the next two years, respectively; after the
second year, FCF is expected to grow at a constant rate of 8 per cent. The company’s
weighted average cost of capital is 12 per cent.
a. What is the terminal, or horizon, value of operations? (Hint: Find the value of all
free cash flows beyond year 2 discounted back to year 2.)
b. Calculate the value of Kendra’s operations.
( 8 -2 5 )
Free cash flow valuation: Dozier Company is a fast-growing supplier of office products. Analysts project the following FCFs during the next three years, after which FCF
is expected to grow at a constant 7 per cent rate. Dozier’s WACC is 13 per cent.
FCF (€ million)
a. What is Dozier’s terminal, or horizon, value? (Hint: Find the value of all FCFs
beyond year 3 discounted back to year 3.)
b. What is the current value of operations for Dozier?
c. Suppose Dozier has €10 million in marketable securities, €100 million in debt,
and 10 million shares of share. What is the intrinsic price per share?
( 8 -2 6 )
Constant-growth share valuation: You are analysing Jillian’s Jewellery (JJ) shares for a
possible purchase. JJ just paid a dividend of €1.50 yesterday. You expect the dividend
to grow at the rate of 6 per cent per year for the next three years; if you buy the share,
you plan to hold it for 3 years and then sell it.
a. What dividends do you expect for JJ share over the next three years? In other
words, calculate D1, D2 and D3. Note that D 0 5 €1.50.
b. JJ’s share has a required return of 13 per cent and so this is the rate you will use to
discount dividends. Find the present value of the dividend stream; that is, calculate the PV of D1, D2 and D3, and then sum these PVs.
c. A JJ share should trade for €27.05 three years from now (i.e. you expect
P3 5 €27.05). Discounted at a 13 per cent rate, what is the present value of this
expected future share price? In other words, calculate the PV of €27.05.
d. If you plan to buy the share, hold it for three years, and then sell it for €27.05, what
is the most you should pay for it?
e. Use the constant growth model to calculate the present value of this share. Assume
that g 5 6% and is constant.
f. Is the value of this share dependent on how long you plan to hold it? In other
words, if your planned holding period were two years or five years rather than
three years, would this affect the value of the share today, P0? Explain your answer.
( 8 -27 )
Nonconstant-growth share valuation: Reizenstein Technologies (RT) has just developed a solar panel capable of generating 200 per cent more electricity than any solar
panel currently on the market. As a result, RT is expected to experience a 15 per cent
annual growth rate for the next five years. By the end of five years, other firms will
have developed comparable technology, and RT’s growth rate will slow to 5 per cent
per year indefinitely. Shareholders require a return of 12 per cent on RT’s share. The
most recent annual dividend (D 0), which was paid yesterday, was €1.75 per share.
a. Calculate RT’s expected dividends for t 5 1, t 5 2, t 5 3, t 5 4 and t 5 5.
b. Calculate the estimated intrinsic value of the share today, P0. Proceed by finding
the present value of the dividends expected at t 5 1, t 5 2, t 5 3, t 5 4 and t 5 5
plus the present value of the share price that should exist at t 5 5, namely P5. The
Chapter 8
Valuation of Shares and Companies 225
P5 share price can be found by using the constant growth equation. Note that to
find P5 you use the dividend expected at t 5 6, which is 5 per cent greater than the
t 5 5 dividend.
c. Calculate the expected dividend yield 1 P01 2 , the capital gains yield expected during the first year, and the expected total return (dividend yield plus capital gains
yield) during the first year. (Recognize that the capital gains yield is equal to the
total return minus the dividend yield.) Also calculate these same three yields for
t 5 5 [e.g. P56].
( 8 -2 8 )
Nonconstant-growth share valuation: Conroy Consulting Company (CCC) has been
growing at a rate of 30 per cent per year in recent years. This same nonconstant
growth rate is expected to last for another two years (g0,1 5 g1,2 5 30%).
(g0,1 = g1,2 g2,3 g3,4 g4,5 = 30%)
a. If D 0 5 €2.50, rs 5 12% and g L 5 7%, then what is CCCs share worth today? What
are its expected dividend yield and capital gains yield at this time?
b. Now assume that CCCs period of nonconstant growth is to last another five years
rather than two years (g0,1 = g1,2 g2,3 g3,4 g4,5 = 30%). How would this affect its price,
dividend yield and capital gains yield? Answer in words only.
c. What will CCCs dividend yield and capital gains yield be once its period of nonconstant growth ends? (Hint: These values will be the same regardless of whether
you examine the case of two or five years of nonconstant growth, and the calculations are very easy.)
d. Of what interest to investors is the relationship over time between dividend yield
and capital gains yield?
Your employer, a mid-sized human resources management company, is considering expansion into related
fields, including the acquisition of Temp Force Company, an employment agency that supplies word processor operators and computer programmers to businesses with temporary heavy workloads. Your employer
is also considering the purchase of Biggerstaff & Biggerstaff (B&B), a privately held company owned by two
brothers, each with 5 million shares. B&B currently has FCF of €24 million, which is expected to grow at a
constant rate of 5 per cent. B&B’s financial statements report marketable securities of €100 million, debt of
€200 million, and preferred share of €50 million. B&B’s WACC is 11 per cent. Answer the following questions.
a. Describe briefly the legal rights and privileges of ordinary shareholders.
b. (1)Write out a formula that can be used to value any share, regardless of its dividend pattern.
(2) What is a constant growth share? How are constant growth shares valued?
(3)What happens if a company has a constant g that exceeds its rs? Will many shares have expected
g > rs in the short run (i.e. for the next few years)? In the long run (i.e. forever)?
c. Assume that Temp Force has a beta coefficient of 1.2, that the risk-free rate (the yield on T-bonds12) is 7.0 per cent,
and that the market risk premium is 5 per cent. What is the required rate of return on the firm’s share?
d. Assume that Temp Force is a constant-growth company whose last dividend (D 0, which was paid yesterday) was €2.00 and whose dividend is expected to grow indefinitely at a 6 per cent rate.
(1) What is the firm’s current estimated intrinsic share price?
(2) What is the share’s expected value one year from now?
(3)What are the expected dividend yield, the expected capital gains yield, and the expected total return
during the first year?
Treasury bonds.
226 Part 3
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e. Suppose Temp Force’s share price is selling for €30.29. Is the share price based more on long-term or
short-term expectations? Answer this by finding the percentage of Temp Force’s current share price that
is based on dividends expected during years 1, 2 and 3.
f. Why are share prices volatile? Using Temp Force as an example, what is the impact on the estimated
share price if g falls to 5 per cent or rises to 7 per cent? If rs changes to 12 per cent or to 14 per cent?
g. Now assume that the share is currently selling at €30.29. What is its expected rate of return?
h. Now assume that Temp Force’s dividend is expected to experience nonconstant growth of 30 per cent
from year 0 to year 1, 25 per cent from year 1 to year 2, and 15 per cent from year 2 to year 3. After year 3,
dividends will grow at a constant rate of 6 per cent. What is the share’s intrinsic value under these conditions? What are the expected dividend yield and capital gains yield during the first year? What are the
expected dividend yield and capital gains yield during the fourth year (from year 3 to year 4)?
i. What is free cash flow? What is the weighted average cost of capital? What is the free cash flow valuation
j. Use a pie chart to illustrate the sources that comprise a hypothetical company’s total value. Using
another pie chart, show the claims on a company’s value. How is equity a residual claim?
k. Use B&B’s data and the FCF valuation model to answer the following questions.
(1) What is its estimated value of operations?
(2) What is its estimated total corporate value?
(3) What is its estimated intrinsic value of equity?
(4) What is its estimated intrinsic share price per share?
l. You have just learned that B&B has undertaken a major expansion that will change its expected free cash
flows to 2€10 million in 1 year, €20 million in 2 years, and €35 million in three years. After three years,
FCF will grow at a rate of 5 per cent. No new debt or preferred share was added; the investment was
financed by equity from the owners. Assume the WACC is unchanged at 11 per cent and that there are
still 10 million shares of share outstanding.
(1)What is the company’s horizon value (i.e. its value of operations at year 3)? What is its current value
of operations (i.e. at time 0)?
(2) What is its estimated intrinsic value of equity on a price-per-share basis?
m. Compare and contrast the FCF valuation model and the dividend growth model.
n. What is market multiple analysis?
o. What is preferred share? Suppose a share of preferred share pays a dividend of €2.10 and investors
require a return of 7 per cent. What is the estimated value of the preferred share?
Project Cost of Capital
hen companies consider investing in new projects, the cost of capital plays a major role. In practice
when the cost of capital goes up, it is harder to justify an equipment purchase. The opposite is true
when the cost of capital goes down. Among its businesses, Phoenix Stamping Group LLC produces
components for equipment used in agriculture and transportation. After modernizing two factories, Phoenix
President, Brandyn Chapman, said, ‘The cost of capital certainly helps that decision.’
For these and many other companies, the historically low cost of capital is making possible major investments in machinery, equipment and technology. Many of these investments are designed to increase productivity, which will lead to lower prices for consumers and higher cash flows for shareholders. On the other hand,
productivity gains mean not as many employees are needed to run the business.
Think about these issues as you read this chapter.
Source: Adapted from Timothy Aeppel, ‘Man vs. Machine, a Jobless Recovery’, Wall Street Journal,
17 January 2012.
254 Part 4
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The cost of capital is the discount rate that is part of the by now familiar net present value model (see
Chapter 4). We can see with a few numbers that it is significant. A business that offers a constant stream of
cash flows to shareholders of €20m at a cost of capital of 10 per cent would have a value of 20/0.10 5 €200.
But if the cost of capital increases to 12 per cent, only 2 per cent more, then the value of the business falls to
€167m, a big fall of €33 million for a mere 2 per cent change in the interest rate.
Businesses require capital to develop new products, build factories and distribution centres, install information technology, expand internationally, and acquire other companies. For each of these actions, a company must estimate the total investment required and then decide whether the expected rate of return exceeds
the cost of the capital. The cost of capital is also a factor in compensation plans, with bonuses dependent on
whether the company’s return on invested capital exceeds the cost of that capital. This cost is also a key factor
in choosing the firm’s mixture of debt and equity and in decisions to lease rather than buy assets. As these
examples illustrate, the cost of capital is a critical element in many business decisions.
The cost required by the market for projects is only really measurable via the market where we see shares
being valued dependent on their risk. Therefore, to find the cost of capital for a project we need to look at the
behaviour of shares in the market place and see the return required for shares of varying risk either through
measurement of past share price movements or market opinion about the future.
In relating shareholder return to project return we must be mindful of the effect of leverage. A share
return as we will see in this chapter is influenced by two factors: the risk of the projects that it is financing
and the degree of borrowing by the company, the leverage. In applying a cost of capital to a project we must
be careful to remove the effect of leverage when assessing the net present value of the project itself. The
weighted average cost of capital (WACC) does this in that, as in the Modigliani and Miller propositions, it
is unaffected by the level of borrowing, at least in theory and before adjusting for taxes. The return on shares
however is affected by the degree of leverage and hence we need to use the weighted average cost rather than
a share return with the exception of a company that has no borrowing. Further details are given in this chapter and in Chapter 17.
The Weighted Average Cost of Capital
The value of a company’s operations (Vop) can be modelled as the present value of the expected free cash
flows (FCFs) discounted at the WACC:
Vop 5 a
t51 1 1 WACC 2
We defined FCFs in Chapter 2 and explained how to find present values in Chapter 4. In Chapter 8 we
used the valuation equation and defined a project using the value additivity principle—the present values
of independent cash flows can be added to get to the total value. Here we take the activities of the firm as a
project. Now we define WACC to finance the project:
WACC 5 wdrd 1 1 2 T 2 1 wstdrstd 1 1 2 T 2 1 wpsrps 1 wsrs
where the variables are defined as follows:
rd 5 coupon rate on new long term debt being issued by the firm. We assume that this is roughly equal
to the bond’s yield to maturity
T 5 t he firm’s effective marginal rate of tax, that is the tax rate it would have to pay on any increase in
rstd 5 required return on short term debt
rps 5 required return on preference shares
Chapter 10
Project Cost of Capital 255
rs 5 required return on shares
w 5 proportion of the total market value of finance in the form of the subscript as defined above,
e.g. ws 5 proportion of total finance in the form of shares
In the following sections we explain how to estimate the WACC. But we begin with a few general concepts.
First, companies are financed by several sources of investor-supplied capital, which are called capital components. We have included short-term debt and preferred shares because some companies use them as sources of
funding, but most companies only use two major sources of investor-supplied capital: long-term debt and shares.
Second, investors providing the capital components require rates of return (rd, rstd, rps and rs) commensurate with the risks of the components in order to induce them to make the investments. Previous chapters
defined those required returns from an investor’s view, but those returns are costs from a company’s viewpoint. This is why we call the WACC a cost of capital.
Third, recall that FCF is the cash flow available for distribution to all investors. Therefore, the FCFs must
provide an overall rate of return sufficient to compensate investors for their exposure to risk. Intuitively,
it makes sense that this overall return should be a weighted average of the capital components’ required
returns. This intuition is confirmed by applying algebra to the definitions of required returns, free cash flow,
and the value of operations: The discount rate used in Equation 8-1 onwards is equal to the WACC. In other
words, the correct rate for estimating the present value of a company’s cash flows is the WACC.
S E L F -T E S T
Identify a firm’s major capital structure components and give the symbols for their respective costs
and weights.
What is a component cost?
Calculating the Weighted Average Cost of Capital
The WACC will in theory provide a return that satisfies the requirements of all investors. There are two valuations
of these sources of finance. One is the balance sheet of the firm that is being invested in; the other is the market
price. The superior valuation is the market price as that is the value to the investor. The balance sheet value is a
historic valuation of the investment that will not respond to interest rate variations and economic prospects in
the manner of the market price. The value to investors is not the balance sheet value but the market value. That is
why the market value is the superior valuation. Unfortunately, not all sources of finance are regularly traded and
a market value is not easily estimated. So for want of better, one may have to resort to the balance sheet valuation.
The problem of not always having a market value indicates the problem of determining the WACC—
namely, that it is a process of estimation and not an exact science. Table 10-1 gives data for the kind of calculation required. Where there is a choice of values, the market value is preferred to the balance sheet value.
Balance sheets are the result of purchase prices in the past and we really want the current market price.
Working capital is made up of creditors who in not being paid are in effect lending to the company. However,
this is offset by the debtors who the company are in effect lending to as they have not yet paid the company.
This is often omitted altogether as it will not greatly affect the outcome.
The calculation of the weighted average without tax is from Table 10-1 as follows:
WACC 5 1 10%×0% 2 1 1 42%×4% 2 1 1 4%×6% 2 1 1 44%×15% 2 5 8.52%
We have already pointed out that a lower interest rate lowers the discount rate and increases the value
of the firm. The perceptive reader will be thinking something along the lines of ‘Well, if you want to have
cheaper funding then why not borrow more of the cheaper finance, shares look very expensive so how about
long-term bonds.’ Looking at Equations 10-1 and 10-2 this would seem to be the answer. Why this is not the
answer is the subject that we now address (which earned in part a Nobel prize for the two authors of this refutation, Franco Modigliani and Merton Miller).
256 Part 4
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TA B L E 1 0 -1
Data Required for Calculating the Cost of Capital for MicroDrive (€m)
Liabilities and equity
Balance sheet
Long term bonds
Preferred shares
Working capital
15% (est.)
Market value
Chosen value
Weight % of total
Leverage (Gearing) and the Modigliani and Miller Propositions
Increasing the level of fixed interest borrowing will increase what is termed gearing or leverage. This can be
defined in varying ways including:
Gearing 5
Debt 1 Equity
We prefer the first definition as it is simply the proportion of total financing that is funded by debt. The
significance of this ratio is that the interest rate on debt is a fixed cost that has to be paid in both good and
bad times. The important implication is that the higher borrowing increases the variability of returns to the
shareholders and hence increases the risk to shareholders.
First we need to calculate the cost of debt and the level of gearing; this we do in Table 10-2. Debt can be
calculated in varying way from the balance sheet and one should not be too fixed on a particular definition,
but rather to take all the capital that is a significant and continuing part of the finance of the company. Some
companies may borrow heavily from their creditors. It has even been known for swap deals to be a form of
financing; the notes to the accounts may therefore be significant.
The cost of debt can in practice only be an estimate in many cases. If the bond is deeply discounted (selling for much below its par value—see Chapter 5) then the coupon rate will not be adequate and the rate of
return or yield will have to be calculated if it is not given as part of the quote. If the bond is not frequently
traded then the coupon rate may be the only guide.
The significance of the gearing ratio is, as we have said, that it increases the risk of returns. That means
that for the same prospective earnings, the return to shareholders will be more variable. An illustration is
given in Table 10-3. Here the possible future earnings were designed to fit with the expectation of an overall
rate of 8.52 per cent as calculated in Equation 10-3—being made up of a share return of 15 per cent (Table
10-1) and a cost of debt of 3.4 per cent (Table 10-2). The all-equity financing is if MicroDrive were financed
solely by shares and the gearing ratio were zero. As noted on Table 10-3, the return on shares for the allequity financing are simply the earnings divided by the total finance.
What we can see from Table 10-3 is that with leverage the variability of returns to equity is much greater,
having a high of 29 per cent and a low of 1 per cent, whereas the no-leverage option has a high of only 14.5
per cent and a low of 2.5 per cent for the same earnings. If earnings fell below €54 then the no-leverage option
would still have a positive return whereas the leveraged existing finance for MicroDrive would lead to a negative return for its shareholders. This variability represents risk and in an efficient market greater expected
risk requires a greater expected return. This is exactly what we see in this model: more borrowing leads to
greater risk for shareholders which in turn leads to an increase in their expected return.
So we can now begin to see the Modigliani and Miller (MM) argument against simply funding projects
with the cheapest capital (namely, debt). Funding projects in this way merely increases the risk for the existing shareholders and this must be taken into account.
Chapter 10
Project Cost of Capital 257
TA B L E 1 0 -2
Calculation of Gearing and the Cost of Debt for MicroDrive (€m)
Working capital
Long-term bonds
Preferred shares
Annual cost
Cost of debt
56% 1580
44% 1250
100% 2830
*Cost of dept 1580
5 3.4%
**Gearing 1580
2830 ^ 56%
table 1 0 -3
The Effect of Leverage on Annual Share Returns for MicroDrive (€m)
Possible Future Earnings †
Year 1
Year 2
Year 3
Year 4
Distributed to:
Debt (3.4%)
56% €1580
5 3.4%
44% €1250
5 15%
Annual Share Return
56% 3 3.4%
1 44% 3
15% 5 8.5%
EARNINGS (as above)
Distributed to:
Annual Share Return
† One of many possible, chosen to agree with expected returns for MicroDrive.
* 300/1250, 74/1250 etc. for MicroDrive’s leveraged finance.
**354/2830 ≈ 24%, 128/2830 ≈ 4.5% etc., a no-leverage (all-equity) option.
5 8.5%
258 Part 4
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Before they published their paper in 1958 it was well appreciated in practice that borrowing money was more
risky than funding from one’s own resources. Borrowing too much increased the risk of insolvency as interest payments could become more than earnings and a business might not be able to pay the monies due. The potential for
variability was also appreciated but its effect was thought merely to restrain companies from excessive borrowing.
Some borrowing it was thought did lower the cost of capital quite apart from the tax effect that we address later.
The surprise of the MM paper was that they proved that in a no-tax world and an efficient market, any
increase in borrowing was exactly offset by the increased risk to shareholders and that there would be no
change in the cost of capital.
The key to their argument was the concept of personal leverage. Take the all-equity version of
MicroDrive’s finance as in Table 10-3. What if a shareholder in the all-equity version wanted the same
expected pattern of returns and expected return (15 per cent) as the leveraged version in Table 10-3? MM
pointed out that such a shareholder did not have to sell his shares and buy shares in the leveraged version,
but could obtain the same expected returns (15 per cent) from his or her existing investment in the unleveraged version, even though the expected returns for the shares in the unleveraged version were only 8.5
per cent.
For an investor in the unleveraged version to get the same returns as investors in the leveraged version,
the investor will have to borrow and invest the total in the unleveraged version. To get the same expected
returns, the returns for each year must be the same, otherwise it would just be a coincidence. So the returns
in the first year for the investor of €100 in the leveraged version was 24 per cent or €24 as we are saying that
€100 was invested. How much should the unleveraged investor borrow and invest alongside his or her €100
in the unleveraged version? The calculation needed for the year 1 unleveraged investor returns to match the
leveraged returns as in Table 10-3 is as follows:
Investment of borrowing (€B) 1 €100 Borrowing €B and investing €(100 + B)
in all equity firm 5 24% return on €100
(100 1 B) × 0.125 2 (B × 0.034) 5 €24
12.5 1 B × 0.125 2 (B × 0.034) 5 €24
24 2 12.5
0.125 2 0.034
B 5 €126.37
So from Equation 10-5, to get a return of 24 per cent or €24 on your €100 investment in the unleveraged
version, borrow €126.37, and invest in the unleveraged company alongside €100 of your own money, making a total of €226.37 invested in the unleveraged version. As a check, the return on the leveraged portfolio
would be €226.37 3 0.125 5 €28.30 less the interest rate bill of 126.37 3 0.034 5 €4.30, leaving a return on
the €100 personal investment of €28.30 2 4.30 5 €24 or 24 per cent.1 The personal leverage returns are the
same as that of the leveraged version of MicroDrive, see Table 10-4. It should not therefore be surprising
that the leveraged portfolio earns the same returns to shareholders as an unleveraged portfolio investment
in the leveraged company. In fact, a whole range of expected returns and risk for the shareholder can be
obtained by a mixture of personal borrowing and lending, as we demonstrated with the Capital Market Line
in Chapter 8, where the security was the market portfolio (i.e. the market index, FTSE, Dow Jones, etc.).
As we are interested in shareholder risk and not company risk we can see that shareholder risk has nothing to do with company risk, therefore company leverage cannot affect the shareholder valuation of
the company.
To increase expected return and risk the investor has to borrow and invest; to lower expected return and risk
the investor has to invest some money in a risk-free investment as well as MicroDrive. As we have said, we used
the same argument for obtaining any combination of risk and return on the Capital Market Line, see Chapter 8.
× 0.034
< 6%,
For the second year the leveraged portfolio would earn €226.37 3 0.045 5 €10.19. The share return would be 10.19 2 126.37
the same return as an unleveraged investor (no borrowing) in the leveraged company. Note that all the rates are taken from Table 10-3.
Chapter 10
Project Cost of Capital 259
table 1 0 - 4
Personal and Company Leverage
Personal Leverage
Company Leverage
Personal leverage in the unleveraged version can be the same as MicroDrive’s actual leverage (Table 10-3) and when this is so, it produces the same %
returns to shareholders as the leveraged shares.
As long as the overall return is the same as that calculated by the WACC (in this case 8.32 per cent), the
investor should be indifferent as to the particular leverage chosen by the firm. He or she can always change
the leverage by borrowing and lending.
There are a number of assumptions that are significant in this argument: the main ones are (a) the investor, often an institution, can borrow and lend at the same rate as the company; (b) there are no transaction
costs and (c) there are no taxes. We shall modify the tax assumption later, but we have to note that taxes
paid by companies can be low as Amazon and other major multinationals have recently demonstrated in the
United Kingdom.
How to Invest in Pharmaceuticals?
A knowledge of theory should help to distinguish
good advice from bad advice. Take the example of
Matthew Vincent writing in the Financial Times.
He argues that there are two types of investment
to be made in the pharmaceutical field: small
companies which might become the targets of
takeovers where spectacular gains are possible,
and large companies where very good but not
spectacular profits can be made. He quotes the
example of Bristol-Myers Squibb paying $26 a
share for Inhibitex, a hepatitis C drug developer.
So the question arises, which should you have
invested in: Bristol-Myers Squibb or Inhibitex? It is
­tempting to choose Inhibitex, and have a p
­ ortfolio
of small pharmaceutical firms in the hope that
one or more will be subject to a takeover based on
promising research. He argues that such a policy
is not a good return for the risk. Better to piggy­
back on the knowhow of Bristol-Myers Squibb
and generally invest in large pharmaceutical companies. In the past year (2011) he points out that
the top eight pharmaceuticals have gained by an
average of 34 per cent. This is a smaller return but
a lot safer than trying to choose promising small
companies in the hope that they will turn out to
be like Inhibitex.
Applying theory, this makes sense from a market efficiency point of view. Whereas Bristol-Myers
Squibb will not have insider knowledge, it will have
a better understanding of the science than you
or I. Also, in saying that larger firms have a better return for the risk also implies that if we want
a high return we should make a leveraged investment in the big pharmaceuticals, borrow money
and invest. As an extreme example, if I were to
invest $1 and borrow $99 at 12 per cent (as it is a
US company) and invest the $100 in Bristol-Myers
Squibb, and it made a 34 per cent profit which I
realized, then I would have $134, could repay the
loan at about $99 1 $12 5 $111 and have a return of
$134 2 $111 5 $23 net profit, a great return for my
$1 investment. But I would be taking a risk—if I did
the same the next year and the shares lost value
then I would be out of pocket by more than $12, a
very large negative return.
Source: Matthew Vincent (2012). ‘Big pharma—an investor’s tonic?’, Financial Times, 4 February.
260 Part 4
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Modigliani and Miller and Taxation
In 1963 Modigliani and Miller issued a second paper that adjusted their findings to take account of taxation.
Debt interest is tax deductible. Rates for individual countries are readily available but in general terms vary
from 20 per cent to 30 per cent, with a number of countries with rates at 0 per cent. We shall take 25 per cent
as being a representative rate of taxation.
Making the interest rate on bonds tax deductible means that the government sees it as a necessary cost
of running a business. Firstly, let us consider the effect on the cost of capital. From Table 10-2 the annual
interest rate bill for long-term bonds was recorded as being €48. As this amount is deducted before arriving
at taxable income it means that the tax bill will be lower by 48 3 0.25 5 €22. There are two ways in which we
can represent this tax saving when evaluating a project. The basic data for MicroDrive to value a new project
offering a €10 perpetuity is as follows:
% funding from shares 5 44%
% percentage funding from debt 5 56%
Return on debt 5 3.4%
Return on shares 5 15%
Tax rate (T) 5 25%
WACC, no tax 5 8.504%
New project returns €10 per year as a perpetuity
So the question is, what is the present value of these earnings and by implication the maximum that
MicroDrive should pay for the new project, assuming that the risk of the project is in line with the average
risk of other projects in the company?
There are two possible methods to address this question.
Method 1 Adjust the weighted average cost of capital to reflect the tax saving. In general terms,
Effective interest rate on bonds 5 (1 2 T) 3 bond interest rate
which in this case is (1 2 0.25) 3 0.034 5 2.55%. So the revised rate of return is: 0.56 3 0.0255
1 0.44 3 0.15 5 8.028%. Note that this is the approach taken in Equation 10-2 and is to be found
in most textbooks. The value of the new project cash inflows are therefore: 0.08028 5 €124.5640.2
Method 2 Leave the weighted average cost of capital alone and add the tax advantage to the
returns. The outcome should be the same. In this case, the calculation of the advantage through
tax deductibility is the amount raised in debt multiplied by the return due to the debt (3.4 per
cent) multiplied by the tax relief: 0.56 3 124.5640 3 0.25 3 0.034 5 0.592925. So the value of the
cash inflows from the new project is: 1010.592925
5 €124.5640.3
Lessons to be Learnt from Modigliani and Miller
The papers by Modigliani and Miller established the theoretical no-imperfections position and had an impact on
the study of finance, so it is worthwhile summarizing the revisions to traditional analysis that they brought about:
• The notion that cheap sources of finance of themselves will lower the cost of capital for the firm is wrong.
There will be an offsetting increase in the risk to shareholders. The increased return required by shareholders will be such that the cost of capital will not change.
• The only benefit from greater fixed-interest borrowing is the tax deductibility of interest rates.
Remember that the value of a perpetuity is simply the cash flow divided by the interest rate.
The decimal places were purely to avoid rounding errors; note that we assume no change in the leverage in both methods.
Chapter 10
Project Cost of Capital 261
• Changing the leverage of a company will alter the risk for shareholders and will, if the changes are significant, cause them to have to rebalance the risk of their portfolio. This will incur transaction costs and
will not be welcome.
• The risk of bankruptcy is separate from risk as defined by MM and is unaffected by the MM propositions. Excessive borrowing will lead to a greater risk of being unable to pay. In such a case, the overall
weighted average return will increase. The MM analysis separated variability risk from termination risk.
Although the MM analysis brought clarity to the question of the cost of borrowing to finance operations,
the derivation of the overall cost of financing a project remained. The theoretical answer is the capital asset
pricing model (CAPM) as discussed in Chapter 6. We now consider its application to project finance.
Using the CAPM to Estimate the Discount Rate for
a Project
What is a Project?
Consider the drilling of an oil well at a particular location to be undertaken by a specialist team. The question is, would the project be cheaper if it were undertaken by MicroDrive or another company? The answer
is that in economic theory there should be no difference. Note that this implies that the level of gearing is not
important to valuing a project (as established by MM). Also, that economic theory does not recognize the
concept of a firm for these purposes. The organizational ‘package’ is not important to the valuation. A firm is
a bundle of projects. A project is no more than a series of cash flows both negative and positive, that are independent, unaffected by other projects. The organizational setting is important in many other respects but in
project valuation the analysis is restricted to the cash flow implications. These may come from a company,
a division, a department or just as a project, it matters not—it is a cash flow and that is all we need to know.
Using CAPM to Estimate the Cost of
Ordinary Shares
Before estimating the return required by MicroDrive’s shareholders, it is worth considering the two ways that
a company can raise common equity: (1) sell newly issued shares to the public. (2) reinvest (retain) earnings
by not paying out all net income as dividends.
Does new equity capital raised by reinvesting earnings have a cost? The answer is a resounding ‘yes!’ If
earnings are reinvested, then shareholders will incur an opportunity cost—the earnings could have been
paid out as dividends or used to repurchase shares, and in either case shareholders would have received funds
that they could reinvest in other securities. Thus, the firm should earn on its reinvested earnings as high a
return for the risk of the project as possible. The shareholders can adjust their portfolios to the risk they want
to bear by investing in risk-free assets or borrowing and investing as illustrated earlier in this chapter.
The Capital Asset Pricing Model
In 1964 William Sharpe published a paper that was the first satisfactory modelling of rs in the form of the CAPM.4
To estimate the cost of common shares using the CAPM, as discussed in Chapter 6, we proceed as follows:
1. Estimate the risk-free rate, rf.
2. Estimate the current market risk premium (rm 2 rf ), which is the required market return in excess of the
risk-free rate.
Sharpe, W. (1964) ‘Capital asset prices —a theory of market equilibrium under conditions of risk’, Journal of Finance 19(3):425–42.
262 Part 4
Projects and Their Valuation
3. Estimate the share’s beta coefficient, bi, which measures the share’s relative risk. The subscript i signifies
share i’s beta.
4. Use these three values to estimate the share’s required rate of return:
ri,s 5 rf 1 bi(rm 2 rf )
Equation 10-6 shows that the CAPM estimate of rs for firm i begins with the risk-free rate, rf. We then add
a risk premium that is equal to the risk premium on the market (rm 2 rf ), scaled up or down to reflect the
particular share’s risk as measured by its beta coefficient. The following sections explain how to implement
this four-step process.
Estimating the Risk-Free Rate
The starting point for the CAPM cost-of-equity estimate is rf, the risk-free rate. There is no such thing as
a truly riskless asset in an economy. Treasury securities are essentially free of default risk; however, non­
indexed (against inflation) long-term T-bonds will suffer capital losses if interest rates rise and a portfolio of
short-term T-bills will provide a volatile earnings stream because the rate earned on T-bills varies over time.
As we cannot, in practice, find a truly riskless rate upon which to base the CAPM, what rate should we use?
Keep in mind that our objective is to estimate the cost of capital, which will be used to discount a company’s
FCFs or a project’s cash flows. FCFs occur over the life of the company and many projects last for many years.
As the cost of capital will be used to discount relatively long-term cash flows, it seems appropriate to use a
relatively long-term risk-free rate, such as the yield on a ten-year Treasury bond. Indeed, a survey of highly
regarded companies shows that about two-thirds of them use the rate on ten-year Treasury bonds.5
T-bond rates can be found in the financial press or on the Internet. Although most analysts use the yield on
a 10-year T-bond as a proxy for the risk-free rate, yields on 20- or 30-year T-bonds are also reasonable proxies.
There are three approaches to estimating the market risk premium, RPM: (1) use historical averages, (2)
survey experts and (3) estimate forward-looking expected market returns. If all three approaches provide
estimates in the same ballpark, say around 3 per cent to 7 per cent, the final choice really boils down to
judgement informed by the current state of the market and the estimates provided by the three approaches.
We will use a market risk premium of 6 per cent in this example.
Estimating Beta
Beta in the model is actually an expected value. That means that it is supposed to represent the market
expectation about the future. For a company there is the possibility that the past performance of the firm
will give guidance as to the future performance. Alternatively, if it is a project that is being assessed then
maybe there is a company that is engaged in a similar activity and its historic beta may give an indication
as to the future expected beta. Ultimately, though, managers have to be happy with the estimate of beta as
being realistic either for the firm or the project. The problem is that beta lacks intuitive appeal. A manager would not be particularly pleased to have to estimate the ‘relative risk’ of a project’s return with the
market, or however beta is expressed. Nor would a manager be particularly happy at being given a beta
and hence a cost of capital by a statistician who does not necessarily understand the future that the project or company is facing. To offer some more intuitive appeal to the concept of beta, a share’s beta can be
estimated as:
bi 5 a
sm im
See Bruner, R. E., Eades, K. M., Harris, R. S. and Higgins, R. C. (1998) ‘Best practices in estimating the cost of capital: survey and
synthesis’, Financial Practice and Education 8(1):13–28.
Chapter 10
Project Cost of Capital 263
where rim is the correlation between share i’s return and the market return (m), si is the standard deviation
of share i’s return, and σm is the standard deviation of the market’s return. Beta is therefore a combination of
the correlation of returns with the market return and the relative standard deviation. This definition is also
equal to the estimated slope coefficient in a regression, with the company’s share returns on the y-axis and
market returns on the x-axis.
It is easy to gather historical returns from the Web and then estimate the beta for a company. The same
methodology should be applied to a project; but remember that these are historic figures and it is an assumption that these figures are relevant to the future. Beta estimates may also be found on most databases of
­company information.
A company undertaking a project that is not in the same risk class as its existing projects should look at
the beta of companies engaged in the activity of the project rather than their own beta. Note, though, that
the beta relates to the returns required by the shareholders of that particular comparative company. The
beta must be unleveraged to make a comparison, as it is only the unleveraged beta that is the same return
as the WACC. It is the WACC that reflects the cost of capital of the activities of the firm; the share beta also
includes risk due to leverage, which is nothing to do with the risk of the projects being undertaken.
An Illustration of the CAPM Approach
As a reminder, from Chapter 6,
E 1 ri 2 5 rf 1 bi 1 E 1 rm 2 2 rf 2
where (E(rm) 2 rf ) is termed the market risk premium and is general to all projects.
Estimates of market risk premiums are available on the internet. Alternatively, databases give the stock
market returns for national stock markets and returns on treasury bills. Using these data one may make
estimates based on periods that investors think will be relevant to the future. Often it is assumed that the
previous periods will be relevant to the future. For example, the previous five year’s returns on the stock market are relevant to the future returns. This is not necessarily the case, especially when that period contains
dramatic events such as a crash or a bubble.
Risk premiums vary over time and can vary considerably depending on the currency and the country.
The appropriate premium for international projects is a difficult point. As share prices for international
firms vary predominantly with their home country it is appropriate that the risk premium of that country
should be used.
There are three basic methods for calculating beta.
Method 1 Make subjective estimates. The CAPM model as in Equation 10-8 has a relatively simple message.
On the right-hand side of the equals sign the expected return is the risk-free rate plus a portion of the risk
premium as determined by beta. The behaviour of beta can be described in three parts:
bi . 1. The project is relatively more risky than the market and therefore has a premium that is greater than
the market. So if the risk-free rate is 3 per cent and the risk premium (i.e. (E(rm) 2 rf )) is 5 per cent,
then a beta of 1.4 would imply a required rate of return of 3% 1 1.4 3 5% 5 10%. Note that the market rate is 8 per cent, being the risk-free rate plus the risk premium, so 3% 1 5% 5 8%. Where beta is
above 1 the expected rate of return E(ri) will always be above the expected market rate E(rm).
bi 5 1. Here the project is as risky as the market. So assuming as above a risk-free rate of 3 per cent and
a risk premium of 5 per cent the implied required return would be 3% 1 1.0 3 5% 5 8%. The
same as the market rate.
bi , 1. The project is relatively less risky than the market. So assuming as above a risk-free rate of 3 per
cent, a risk premium of 5 per cent and a beta of 0.8, the implied required return would be 3% 1
0.8 3 5% 5 7%, less than the market rate.
264 Part 4
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Beta is a measure that is centred on the market return and as a subjective process should really be thought
of in relation to the general market return. This measure therefore determines the general diversification
effect for the investor in the ownership of the project. In the case of a company quoted on the stock exchange
the investor is the shareholder and the market return is measured as the Dow Jones or FTSE index.
All analysis should be checked against subjective estimation in the sense that decision makers should
agree that the risk implications of the beta however measured is within the bounds of what they regard
as a possible measure. For example, if an investment in a well-established retail outlet had a beta of 2, i.e.
twice the market premium (an E (ri) of (2 3 5) 1 3 5 13% from the above example) then there may be
something wrong with the calculation. A subjective estimate would suggest a beta of less than 1 as such
an investment is relatively less risky than the average market investment.
Method 2 Use databases. Databases such as OSIRIS (see Figure 10-1) will contain estimates of betas based on
varying time periods and periodicity (weeks, months, years, etc.). Such data may help in making a subjective
estimate, as above. Alternatively, in the case of a project that is not similar to the current activities of the
firm, the database may provide an estimate of the beta of a company that is engaged in a similar activity. If
MicroDrive decided to drill for oil and that was allowed in its articles of association, then it would be appropriate to use the beta of an oil drilling company.
Method 3 Regression. Finally, a company may wish to make its own estimate of beta. Data of share price
movements are readily available from databases. Beta may be estimated from the following regression:
ri 5 rf 1 birm 1 Pi
F ig u re 1 0 -1
Database Beta Estimates for Rolls-Royce Based on Weekly Returns
Rolls-Royce Holdings PLC
SW1E 6AT London (United Kingdom)
Publicly quoted company
This company is the GUO of the Corporate Group
BvD ID number
Ref. index 1 Beta 3 months
Ref. index 1 Beta 1 year
Ref. index 1 Beta 3 years
Ref. index 1 Beta 5 years
Ref. index 1 Correlation coeficient 1 month
Ref. index 1 Correlation coeficient 3 months
Ref. index 1 Correlation coeficient 1 year
Ref. index 1 Correlation coeficient 3 years
Ref. index 1 Correlation coeficient 5 years
Ref. index 2 Beta 1 month
Ref. index 2 Beta 3 months
Ref. index 2 Beta 1 year
Ref. index 2 Beta 3 years
Ref. index 2 Beta 5 years
Ref. index 2 Correlation coeficient 1 month
Ref. index 2 Correlation coeficient 3 months
Ref. index 2 Correlation coeficient 1 year
Ref. index 2 Correlation coeficient 3 years
Ref. index 2 Correlation coeficient 5 years
Reference index 2: FTSE 250
Source: Bureau van Dijk (accessed 2015)
Chapter 10
Project Cost of Capital 265
There are a number of statistical problems associated with measurement, as is illustrated in Figure 10-1.
What index should be chosen? What period should be chosen? Should beta be measured over weeks months
or years? It is clear from Figure 10-1 that the resulting beta can differ greatly.
Beta Usage
Surveys ask firms what valuation techniques are used by the company. The question is somewhat problematic in that firms are sensitive to accusations of not using best practice. Given the extensive literature supporting the use of the CAPM, many managers may think it prudent in surveys to tick the CAPM box; survey
results are very variable—between some 34 per cent and 3 per cent.6
S E L F -T E S T
What are the two primary sources of equity capital?
Explain why there is a cost to using reinvested earnings; that is, why are reinvested earnings not a
free source of capital?
A company’s beta is 1.4, the yield on a ten-year T-bond is 4 per cent, and the market risk premium is
4.5 per cent. What is rs? (Answer: 10.3 per cent.)
Use of Dividend Yield Plus Growth Rate
(Discounted Cash Flow Approach)
Surveys show that businesses use more than one method to value projects and it is sensible for firms to use more
than one method to review the discount rate. It should always be remembered that the discount rate is an expected
figure and not a figure which can be calculated with a guaranteed accuracy. The future is always to some uncertain
extent unknown. All that can be sensibly done is to review the figure and see that it not unreasonable as a measure.
Part of such a review is to use the discounted cash flow (DCF) models and the concept of FCFs of Chapter 2 to
see whether the discount rate is producing a reasonable valuation for a project. Where the company is being used
to measure the appropriate discount rate because the project under consideration is in the same risk class, as will
often be the case, the check is to see that the discount rate produces a reasonable valuation for the company.
The WACC is the discount rate to use for projects that are in the same risk class as the company as a
whole. The assumption is that the company is engaged in broadly similar activities. This is usually the case,
as companies are limited in their articles as to what activities they may undertake. However, in the case of
conglomerates or in the case of Wall’s that sold ice cream and sausages, there may not be a typical project.
In such cases a project’s appropriate discount rate should be that of a company whose activities are similar
to the project being valued. A project to sell food in supermarkets should be discounted at the WACC of
supermarket companies. A project to build cars should be discounted at the WACC for car companies. This
may sound obvious, but it is all too easy to think that a cost of capital is independent of the project it is being
used to finance. It would be wrong to say, for instance, that WACC is an opportunity cost of capital (implying
whatever the risk), return cannot be separated from risk in this way. Where an inappropriate cost of capital
is used, the effect is to place the risk on the other shareholders. For example, suppose a land-owning property decides to venture into medical research and erroneously uses its own very low risk cost of capital in
valuation. If the project is accepted then the overall risk of the company will increase and shareholders who
thought that the income from the property company would be unspectacular (but safe), will find that they
now have an investment in a risky company. It is arguably the responsibility of directors not to change the
risk profile of the company without the full knowledge and consent of the investors.
For the high estimate see Graham, J. R. and Harvey, C. (2001) ‘The theory and practice of corporate finance: evidence from the field’, Journal of Financial Economics 60(2):187–243; and for the low estimate see Arnold, G. C. and Hatzopoulos, P. D. (2000) ‘The theory -practice
gap in capital budgeting: evidence from the United Kingdom’, Journal of Business Finance and Accounting 27(5-6):603–26.
266 Part 4
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Managerial Issues and the Cost of Capital
We describe several managerial issues in this section, starting with how managerial decisions affect the cost
of capital.
How Managerial Decisions Affect the Cost of Capital
The cost of capital is affected by some factors that are under a firm’s control and some that are not.
Four Factors the Firm Cannot Control
Four factors are beyond managerial control: (1) interest rates, (2) credit crises, (3) the market risk premium
and (4) tax rates.
Interest Rates Interest rates in the economy affect the costs of both debt and equity, but they are beyond a
manager’s control. Even the government cannot control interest rates indefinitely. For example, interest rates are
heavily influenced by inflation, and when inflation hit historic highs in the early 1980s, interest rates followed.
Rates trended mostly down for 25 years through the recession accompanying the 2008 financial crisis.
Credit Crisis Although rare, sometimes credit markets are so disrupted that it is virtually impossible for
a firm to raise capital at reasonable rates. This happened in 2008 and 2009. During such times, firms tend to
cut back on growth plans; if they must raise capital, its cost can be extraordinarily high.
Market Risk Premium Investors’ aversion to risk determines the market risk premium. The premium is
in effect a standard cost of risk and the beta is how much of that standard cost a project should be charged.
Individual firms have no control over the premium, which affects the cost of equity and thus the WACC.
Tax Rates Tax rates, which are influenced by government, have an important effect on the cost of capital.
They are used when we calculate the after-tax cost of debt for use in the WACC. In addition, the lower tax
rate on dividends and capital gains than on interest income favours financing with shares rather than bonds.
Three Factors the Firm can Control
A firm can affect its cost of capital through (1) its capital structure policy, (2) its dividend policy and (3) its
investment (capital budgeting) policy.
Capital Structure Policy In this chapter, we assume the firm has a given target capital structure, and
we use weights based on that target to calculate its WACC. However, a firm can change its capital structure,
and such a change can affect the cost of capital. For example, the after-tax cost of debt is lower than the cost
of equity, so if the firm decides to use more debt and less common equity, then this increase in debt will tend
to lower the WACC. However, an increased use of debt will increase the risk of debt and the equity, offsetting
(apart from tax) the effect due to a greater weighting of debt.
Dividend Policy As we will see when discussing dividends, the percentage of earnings paid out in dividends may affect a share’s required rate of return. Also, if the payout ratio is so high that the firm must issue
new shares to fund its capital budget, then the resulting flotation costs will also affect the WACC.
Investment Policy When we estimate the cost of capital, we use as the starting point the required rates
of return on the firm’s outstanding shares and bonds, which reflect the risks inherent in the existing assets.
Therefore, we are implicitly assuming that new capital will be invested in assets with the same degree of risk
as existing assets. This assumption is generally correct, because most firms invest in assets similar to those
they currently use.
Chapter 10
Project Cost of Capital 267
The following section explains how to adjust the cost of capital to reflect the risk of individual divisions
and projects.
Adjusting the Cost of Capital for Risk:
Divisions and Projects
As we have calculated it, the WACC reflects the average risk and overall capital structure of the entire firm.
No adjustments are needed when using the WACC as the discount rate when estimating the value of a company by discounting its cash flows. However, adjustments for risk are often needed when evaluating a division or project. For example, what if a firm has divisions in several business lines that differ in risk? Or what
if a company is considering a project that is much riskier than its typical project? It is not logical to use the
overall cost of capital to discount divisional or project-specific cash flows that don’t have the same risk as
the company’s average cash flows. The following sections explain how to adjust the cost of capital for divisions and for specific projects.
Divisional Costs of Capital
Consider a company (Starlight) with two divisions—a bakery operation and a chain of cafés:
• The bakery division is low-risk and has a 10 per cent WACC.
• The café division is riskier and has a 14 per cent WACC.
Each division is approximately the same size, so Starlight’s overall cost of capital is 12 per cent. The
bakery manager has a project with an 11 per cent expected rate of return, and the café division manager
has a project with a 13 per cent expected return. Should these projects be accepted or rejected? Starlight
will create value if it accepts the bakery’s project, because its rate of return is greater than its cost of
capital (11% . 10%); but the café project’s rate of return is less than its cost of capital (13% , 14%), so
it should reject that project. However, if management simply compared the two projects’ returns with
Starlight’s 12 per cent overall cost of capital, then the bakery’s value-adding project would be rejected
while the café’s value-destroying project would be accepted. This once again emphasizes the simple
point that projects must be charged their own risk based on the covariance of their returns with the
market and hence their betas.
A firm itself may be regarded as a ‘portfolio of assets’ or a ‘bundle of projects’. The beta of a firm is a
weighted average of the betas of its individual projects. Charging all projects the average cost of capital will
introduce the kind of distortions that we see in the bakery and café example above. One size does not fit all
projects. The overall return required by investors in a firm should not be mistaken for the required return on
the individual projects.
Our example suggests a level of precision that is much higher than firms can obtain in the real world. Still,
managers should be aware of this example’s logic, and they should strive to measure the required inputs as
accurately as possible. In this way they can be approximately right rather than being definitely wrong!
Two Mistakes to Avoid
We often see managers and students make the following mistakes when estimating the cost of capital. Although we have discussed these errors previously at separate places in the chapter, they are worth
repeating here.
1. Never base the cost of debt on the coupon rate on a firm’s existing debt. The cost of debt must be based
on the interest rate the firm would pay if it issued new debt today.
2. Never use the WACC for a firm to value a project unless the risk of the firm’s projects is similar to that of
the project being considered.
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S E L F -T E S T
Name some factors that are generally beyond the firm’s control but still affect its cost of capital.
What three policies under the firm’s control affect its cost of capital?
Explain how a change in interest rates in the economy would be expected to affect each component
of the WACC.
Based on the CAPM, how would one adjust the corporation’s overall cost of capital to establish the
required return for most projects in a low-risk division and in a high-risk division?
Describe the pure play and the accounting beta methods for estimating divisional betas.
What are the three types of risk to which projects are exposed? Which type of risk is theoretically the
most relevant? Why?
This chapter has discussed how the cost of capital is developed for use in capital budgeting. The key points
covered are listed below:
The cost of capital used in capital budgeting is a weighted average of the types of capital the firm uses—
typically long-term debt, short-term debt, preferred shares and common equity.
The component cost of debt is the after-tax cost of new debt. It is found by multiplying the interest rate
paid on new debt by 1 − T, where T is the firm’s marginal tax rate: rd(1 − T).
Most debt is raised directly from lenders without the use of investment bankers, hence no flotation
costs are incurred. However, a debt flotation cost adjustment should be made if large flotation costs are
incurred. We reduce the bond’s issue price by the flotation expenses, reduce the bond’s cash flows to
reflect taxes, and then solve for the after-tax yield to maturity.
The cost of common equity, rs, also called the cost of ordinary shares, is the rate of return required by the
firm’s shareholders.
To use the CAPM approach, we (1) estimate the firm’s beta, (2) multiply this beta by the market risk premium to obtain the firm’s risk premium and then (3) add the firm’s risk premium to the risk-free rate to
obtain its cost of ordinary shares.
The best proxy for the risk-free rate is the yield on long-term T-bonds, with ten years the maturity used
most frequently.
To use the dividend-yield-plus-growth-rate approach, which is also called the discounted cash flow
(DCF) approach, add the firm’s expected dividend growth rate to its expected dividend yield.
The growth rate for use in the DCF model can be based on security analysts’ published forecasts, on historical growth rates of earnings and dividends, or on the retention growth model.
Each firm has a target capital structure, which is defined as the mix of debt, preferred shares and common equity that minimizes its WACC.
Various factors affect a firm’s cost of capital. Some are determined by the financial environment, but the
firm can influence others through its financing, investment and dividend policies.
Many firms estimate divisional costs of capital that reflect each division’s risk and capital structure.
The pure play and accounting beta methods can be used to estimate betas for large projects or for
A project’s stand-alone risk is the risk the project would have if it were the firm’s only asset and if shareholders held only that one share. Stand-alone risk is measured by the variability of the asset’s expected
Corporate, or within-firm, risk reflects the effect of a project on the firm’s risk, and it is measured by the
project’s effect on the firm’s earnings variability.
Chapter 10
Project Cost of Capital 269
Market, or beta, risk reflects the effects of a project on shareholders’ risk, assuming they hold diversified
portfolios. Market risk is measured by the project’s effect on the firm’s beta coefficient.
Most decision makers consider all three risk measures in a subjective manner and then classify projects
into risk categories. Using the firm’s WACC as a starting point, risk-adjusted costs of capital are developed for each category. The risk-adjusted cost of capital is the cost of capital appropriate for a given project, given its risk. The greater a project’s risk, the higher its cost of capital.
The cost of capital as developed in this chapter is used in the next two chapters to evaluate potential
­capital budgeting projects, and it is used later in the text to determine the value of a corporation.
Answers to questions (10-6) to (10-23) appear in the Appendix.
( 10 -1)
Define each of the following terms:
a. weighted average cost of capital, WACC; after-tax cost of debt, rd(l 2 T); after-tax
cost of shares-term debt, rstd(l 2 T)
b. cost of preferred shares, rps; shares of common equity (or cost of ordinary shares), rs
c. target capital structure
d. flotation cost, F; cost of new external common equity, re
(10 -2)
How can the WACC be both an average cost and a marginal cost?
How would each of the factors in the following list affect a firm’s cost of debt, rd(l 2 T);
its cost of equity, rs; and its weighted average cost of capital, WACC? Indicate by a plus
(1), a minus (2) or a zero (0) if the factor would increase, reduce or have an indeterminate effect on the item in question. Assume that all other factors are held constant.
a. The corporate tax rate is lowered.
b. The Federal Reserve tightens credit.
c. The firm uses more debt.
d. The firm doubles the amount of capital it raises during the year.
e. The firm expands into a risky new area.
f. Investors become more risk averse.
( 10 -3)
( 10 - 4 )
( 10 -5 )
( 10 - 6 )
Distinguish between beta (i.e. market) risk, within-firm (i.e. corporate) risk and
stand-alone risk for a potential project. Of the three measures, which is theoretically
the most relevant, and why?
Suppose that a firm estimates its overall cost of capital for the coming year to be
10 per cent. What might be reasonable costs of capital for average-risk, high-risk,
and low-risk projects?
WACC: Longstreet Communications Inc. (LCI) has the following capital structure, which
it considers to be optimal: debt 5 25% (LCI has only long-term debt), preferred shares
5 15%, and ordinary shares 5 60%. LCI’s tax rate is 40 per cent, and investors expect
earnings and dividends to grow at a constant rate of 6 per cent in the future. LCI paid a
dividend of $3.70 per share last year (D0), and its shares currently sell at a price of $60 per
share. Ten-year Treasury bonds yield 6 per cent, the market risk premium is 5 per cent,
and LCI’s beta is 1.3. The following terms would apply to new security offerings.
Preferred: New preferred shares could be sold to the public at a price of $100 per
share, with a dividend of $9. Flotation costs of $5 per share would be incurred.
Debt: Debt could be sold at an interest rate of 9 per cent.
270 Part 4
Projects and Their Valuation
Common: New common equity will be raised only by retaining earnings.
a. Find the component costs of debt, preferred shares, and ordinary shares.
b. What is the WACC?
( 10 -7 )
After-tax cost of debt: Calculate the after-tax cost of debt under each of the following
a. rd of 13 per cent, tax rate of 0 per cent
b. rd of 13 per cent, tax rate of 20 per cent
c. rd of 13 per cent, tax rate of 35 per cent
( 10 - 8 )
( 10 -9)
( 10 -10 )
( 10 -11)
( 10 -1 3)
( 10 -15 )
( 10 -16 )
After-tax cost of debt: LL Incorporated’s currently outstanding 11 per cent coupon
bonds have a yield to maturity of 8 per cent. LL believes it could issue new bonds at
par that would provide a similar yield to maturity. If its marginal tax rate is 35 per
cent, what is LL’s after-tax cost of debt?
Cost of preferred shares: Duggins Veterinary Supplies can issue perpetual preferred
shares at a price of $50 a share with an annual dividend of $4.50 a share. Ignoring
flotation costs, what is the company’s cost of preferred shares
Cost of preferred shares with flotation costs: Burnwood Tech plans to issue some $60
par preferred shares with a 6 per cent dividend. A similar share is selling on the market for $70. Burnwood must pay flotation costs of 5 per cent of the issue price. What is
the cost of the preferred shares?
Cost of equity (DCF): Summerdahl Resort’s shares are currently trading at $36 a
share. The shares are expected to pay a dividend of $3.00 a share at the end of the year
(D1 5 $3.00), and the dividend is expected to grow at a constant rate of 5 per cent a
year. What is its cost of equity?
Cost of equity (CAPM): Booher Book Stores has a beta of 0.8. The yield on a threemonth T-bill is 4 per cent, and the yield on a ten-year T-bond is 6 per cent. The market risk premium is 5.5 per cent, and the return on an average share in the market last
year was 15 per cent. What is the estimated cost of equity using the CAPM?
WACC: Shi Importers’ balance sheet shows $300 million in debt, $50 million in preferred shares, and $250 million in total equity. Shi’s tax rate is 40 per cent, rd 5 6%,
rps 5 5.8%, and rs 5 12%. If Shi has a target capital structure of 30 per cent debt, 5 per
cent preferred shares, and 65 per cent ordinary shares, what is its WACC?
WACC: David Ortiz Motors has a target capital structure of 40 per cent debt and 60
per cent equity. The yield to maturity on the company’s outstanding bonds is 9 per
cent, and the company’s tax rate is 40 per cent. Ortiz’s CFO has calculated the company’s WACC as 9.96 per cent. What is the company’s cost of equity capital?
Bond yield and after-tax cost of debt: A company’s 6 per cent coupon rate, semiannual payment, $1000 par value bond that matures in 30 years sells at a price of
$515.16. The company’s federal-plus-state tax rate is 40 per cent. What is the firm’s
after-tax component cost of debt for purposes of calculating the WACC? (Hint: Base
your answer on the nominal rate.)
Cost of equity: The earnings, dividends and share price of Shelby Inc. are expected to grow
at 7 per cent per year in the future. Shelby’s ordinary share sells for $23 per share, its last dividend was $2.00, and the company will pay a dividend of $2.14 at the end of the current year.
a. Using the discounted cash flow approach, what is its cost of equity?
b. If the firm’s beta is 1.6, the risk-free rate is 9 per cent, and the expected return on
the market is 13 per cent, then what would be the firm’s cost of equity based on
the CAPM approach?
Chapter 10
Project Cost of Capital 271
c. If the firm’s bonds earn a return of 12 per cent, then what would be your estimate
of rs using the own-bond-yield-plus-judgmental-risk-premium approach? (Hint:
Use the midpoint of the risk premium range.)
d. On the basis of the results of parts a through c, what would be your estimate of
Shelby’s cost of equity?
( 10 -17 )
Cost of equity: Radon Homes’ current EPS is $6.50. It was $4.42 five years ago. The
company pays out 40 per cent of its earnings as dividends, and the share sells for $36.
a. Calculate the historical growth rate in earnings. (Hint: This is a five-year growth
b. Calculate the next expected dividend per share, D 1 (Hint: D 0 5 0.4($6.50) 5
$2.60.) Assume that the past growth rate will continue.
c. What is Radon’s cost of equity, rs?
( 10 -1 8 )
Calculation of g and EPS: Spencer Supplies’ shares are currently selling for $60 a share. The
firm is expected to earn $5.40 per share this year and to pay a year-end dividend of $3.60.
a. If investors require a 9 per cent return, what rate of growth must be expected for
b. If Spencer reinvests earnings in projects with average returns equal to the share’s
expected rate of return, then what will be next year’s EPS? (Hint: g 5 ROE 3
retention ratio.)
( 10 -19)
The cost of equity and flotation costs: Messman Manufacturing will issue ordinary
shares to the public for $30. The expected dividend and the growth in dividends are
$3.00 per share and 5 per cent, respectively. If the flotation cost is 10 per cent of the
issue’s gross proceeds, what is the cost of external equity, re?
The cost of debt and flotation costs: Suppose a company will issue new 20-year debt
with a par value of $1000 and a coupon rate of 9 per cent, paid annually. The tax rate is
40 per cent. If the flotation cost is 2 per cent of the issue proceeds, then what is the aftertax cost of debt? Disregard the tax shield from the amortization of flotation costs.
WACC estimation: On January 1, the total market value of the Tysseland Company
was $60 million. During the year, the company plans to raise and invest $30 million
in new projects. The firm’s present market value capital structure, shown below, is
considered to be optimal. There is no short-term debt.
( 10 -2 0 )
( 10 -21)
$30 000 000
Common equity
$30 000 000
Total capital
$60 000 000
New bonds will have an 8 per cent coupon rate, and they will be sold at par. Common
shares are currently selling at $30 a share. The shareholders’ required rate of return
is estimated to be 12 per cent, consisting of a dividend yield of 4 per cent and an
expected constant growth rate of 8 per cent. (The next expected dividend is $1.20, so
the dividend yield is $1.20/$30 5 4%.) The marginal tax rate is 40 per cent.
a. In order to maintain the present capital structure, how much of the new investment must be financed by common equity?
b. Assuming there is sufficient cash flow for Tysseland to maintain its target capital
structure without issuing additional shares of equity, what is its WACC?
c. Suppose now that there is not enough internal cash flow and the firm must issue
new shares. Qualitatively speaking, what will happen to the WACC? No numbers
are required to answer this question.
272 Part 4
Projects and Their Valuation
( 10 -2 2)
Market value capital structure: Suppose the Schoof Company has this book value
­balance sheet:
Current assets
$30 000 000
Fixed assets
70 000 000
Current liabilities
$20 000 000
Notes payable
$10 000 000
Long-term debt
Equity (1 million shares)
Retained earnings
Total assets
( 10 -2 3)
$100 000 000
Total liabilities and equity
30 000 000
1 000 000
39 000 000
$100 000 000
The notes payable are to banks, and the interest rate on this debt is 10 per cent, the
same as the rate on new bank loans. These bank loans are not used for seasonal
financing but instead are part of the company’s permanent capital structure. The
long-term debt consists of 30 000 bonds, each with a par value of $1000, an annual
coupon interest rate of 6 per cent, and a 20-year maturity. The going rate of interest
on new long-term debt, rd, is 10 per cent, and this is the present yield to maturity on
the bonds. The ordinary shares sell at a price of $60 per share. Calculate the firm’s
market value capital structure.
WACC estimation: The table below gives the balance sheet for Travellers Inn Inc.
(TII), a company that was formed by merging a number of regional motel chains.
Travellers Inn: 31 December 32013 ($millions)
Accounts payable
Accounts receivable
Short-term debt
Current assets
Current liabilities
Net fixed assets
Long-term debt
Preferred shares
Ordinary shares
Retained earnings
Total equity
Total assets
Total liabilities and equity
The following facts also apply to TII:
(1)Short-term debt consists of bank loans that currently cost 10 per cent, with interest payable quarterly. These loans are used to finance receivables and inventories
on a seasonal basis, so bank loans are zero in the off-season.
(2)The long-term debt consists of 20-year, semi-annual payment mortgage bonds
with a coupon rate of 8 per cent. Currently, these bonds provide a yield to investors of rd 5 12%. If new bonds were sold, they would have a 12 per cent yield to
(3)TII’s perpetual preferred shares has a $100 par value, pays a quarterly dividend
of $2, and has a yield to investors of 11 per cent. New perpetual preferred shares
Chapter 10
Project Cost of Capital 273
would have to provide the same yield to investors, and the company would incur a
5 per cent flotation cost to sell it.
(4)The company has 4 million shares of ordinary shares outstanding. P0 5 $20, but
the shares have recently traded in the price range from $17 to $23. D 0 5 $1 and
EPS0 5 $2. ROE based on average equity was 24 per cent in 2012, but management
expects to increase this return on equity to 30 per cent; however, security analysts
and investors generally are not aware of management’s optimism in this regard.
(5)Betas, as reported by security analysts, range from 1.3 to 1.7; the T-bond rate is 10 per
cent; and RPM is estimated by various brokerage houses to range from 4.5 per cent
to 5.5 per cent. Some brokerage house analysts report forecasted growth dividend
growth rates in the range of l0 per cent to 15 per cent over the foreseeable future.
(6)TII’s financial vice president recently polled some pension fund investment managers who hold TII’s securities regarding what minimum rate of return on TII’s
shares would make them willing to buy the shares rather than TII bonds, given
that the bonds yielded 12 per cent. The responses suggested a risk premium over
TII bonds of 4 to 6 percentage points.
(7)TII is in the 40 per cent federal-plus-state tax bracket.
(8)TII’s principal investment banker predicts a decline in interest rates, with rd
­falling to 10 per cent and the T-bond rate to 8 per cent, although the bank
acknowledges that an increase in the expected inflation rate could lead to an
increase rather than a decrease in interest rates.
Assume that you were recently hired by TII as a financial analyst and that your boss,
the treasurer, has asked you to estimate the company’s WACC under the assumption
that no new equity will be issued. Your cost of capital should be appropriate for use in
evaluating projects that are in the same risk class as the assets TII now operates.
During the last few years, Harry Davis Industries has been too constrained by the high cost of capital to
make many capital investments. Recently, though, capital costs have been declining, and the company has
decided to look seriously at a major expansion program proposed by the marketing department. Assume
that you are an assistant to Leigh Jones, the financial vice president. Your first task is to estimate Harry
Davis’s cost of capital. Jones has provided you with the following data, which she believes may be relevant to
your task:
(1) The firm’s tax rate is 40 per cent.
(2)The current price of Harry Davis’s 12 per cent coupon, semi-annual payment, noncallable bonds with 15
years remaining to maturity is $1153.72. Harry Davis does not use short-term interest-bearing debt on a
permanent basis. New bonds would be privately placed with no flotation cost.
(3)The current price of the firm’s 10 per cent, $100 par value, quarterly dividend, perpetual preferred shares
is $116.95. Harry Davis would incur flotation costs equal to 5 per cent of the proceeds on a new issue.
(4)Harry Davis’s common shares are currently selling at $50 per share. Its last dividend (D 0) was $3.12, and
dividends are expected to grow at a constant rate of 5.8 per cent in the foreseeable future. Harry Davis’s
beta is 1.2, the yield on T-bonds is 5.6 per cent, and the market risk premium is estimated to be 6 per
cent. For the own-bond-yield-plus-judgmental-risk-premium approach, the firm uses a 3.2 per cent risk
(5)Harry Davis’s target capital structure is 30 per cent long-term debt, 10 per cent preferred shares, and 60
per cent common equity.
274 Part 4
Projects and Their Valuation
To help you structure the task, Leigh Jones has asked you to answer the following questions.
a. (1)What sources of capital should be included when you estimate Harry Davis’s weighted average cost
of capital?
(2) Should the component costs be figured on a before-tax or an after-tax basis?
(3) Should the costs be historical (embedded) costs or new (marginal) costs?
b.What is the market interest rate on Harry Davis’s debt, and what is the component cost of this debt for
WACC purposes?
c. (1) What is the firm’s cost of preferred shares?
(2)Harry Davis’s preferred shares are riskier to investors than its debt, yet the preferred shares yield to
investors is lower than the yield to maturity on the debt. Does this suggest that you have made a mistake? (Hint: Think about taxes.)
d. (1) What are the two primary ways companies raise common equity?
(2) Why is there a cost associated with reinvested earnings?
(3)Harry Davis does not plan to issue new shares. Using the CAPM approach, what is Harry Davis’s
estimated cost of equity?
e. (1)What is the estimated cost of equity using the discounted cash flow (DCF) approach?
(2)Suppose the firm has historically earned 15 per cent on equity (ROE) and has paid out 62 per cent
of earnings, and suppose investors expect similar values to obtain in the future. How could you use
this information to estimate the future dividend growth rate, and what growth rate would you get?
Is this consistent with the 5.8 per cent growth rate given earlier?
(3)Could the DCF method be applied if the growth rate were not constant? How?
f.What is the cost of equity based on the own-bond-yield-plus-judgmental-risk premium method?
g. What is your final estimate for the cost of equity, rs?
h. What is Harry Davis’s weighted average cost of capital (WACC)?
i. What factors influence a company’s WACC?
j.Should the company use its overall WACC as the hurdle rate for each of its divisions?
k.What procedures can be used to estimate the risk-adjusted cost of capital for a particular division? What
approaches are used to measure a division’s beta?
1.Harry Davis is interested in establishing a new division that will focus primarily on developing new
Internet-based projects. In trying to determine the cost of capital for this new division, you discover that
specialized firms involved in similar projects have, on average, the following characteristics: (1) their
capital structure is 10 per cent debt and 90 per cent common equity; (2) their cost of debt is typically 12
per cent; and (3) they have a beta of 1.7. Given this information, what would your estimate be for the new
division’s cost of capital?
m.What are three types of project risk? How can each type of risk be considered when thinking about the
new division’s cost of capital?
n.Explain in words why new shares that are raised externally have a higher percentage cost than equity
that is raised internally by retaining earnings.
o. (1)Harry Davis estimates that if it issues new shares the flotation cost will be 15 per cent. Harry Davis
incorporates the flotation costs into the DCF approach. What is the estimated cost of newly issued
shares taking into account the flotation cost?
(2)Suppose that Harry Davis issues 30-year debt with a par value of $1000 and a coupon rate of 10 per
cent, paid annually. If flotation costs are 2 per cent, what is the after-tax cost of debt for the new
bond issue?
p.What four common mistakes in estimating the WACC should Harry Davis avoid?
Capital Budgeting:
Evaluation of Cash
n their annual report (2013), BAE systems state that: ‘In a challenging climate for defence spending, the
executive will continue to focus on disciplined cost management in those markets that are contracting and
increase sales endeavours in those parts of the world where new business opportunities are both appropriate and available.’ Thorntons plc’s annual report of the same year stated: ‘Over the course of the year overall
output has grown by 4 per cent (2012: 3.7 per cent) to record levels. This growth has been achieved whilst
controlling our cost base, retaining excellent customer service levels and substantially improving product quality performance.’ Finally, Morrisons in 2013 reported that: ‘Our capital expenditure programme has three elements: the maintenance of our asset base, the development of our infrastructure and the growth of our new
channels and manufacturing capability. The total of £1.1bn that we spent in 2013/14 represents the peak level
of our capital expenditure investment and will reduce significantly in the years ahead.’
As you read this chapter, think about how capital budgeting methods are a vital part of project
selection and expansion decisions.
276 Part 4
Projects and Their Valuation
A budget is a plan that outlines projected expenditures during future periods. The capital budget is a summary of planned investments in projects that will last for more than a year. The word capital is used to indicate that investment in assets is needed to support the project using shareholder and other funds. The values
will end up on the balance sheet. Capital budgeting is the whole process of analysing projects and deciding
which ones to accept and thus include in the capital budget.
An Overview of Capital Budgeting
A firm’s ability to remain competitive and to survive depends on a constant flow of ideas for new products,
improvements in existing products, and ways to operate more efficiently. Therefore, it is vital for a company
to evaluate proposed projects accurately.
However, analysing project proposals requires skill, effort and time. For certain types of projects, an
extremely detailed analysis may be warranted, whereas simpler procedures are adequate for other projects.
Accordingly, firms generally categorize projects and analyse those in each category somewhat differently:
1. Replacement needed to continue profitable operations. An example would be replacing an essential pump
on a profitable offshore oil platform. The platform manager could make this investment without an elaborate review process.
2. Replacement to reduce costs. An example would be the replacement of serviceable but obsolete equipment in order to lower costs. A fairly detailed analysis would be needed, with more detail required for
larger expenditures.
3. Expansion of existing products or markets. These decisions require a forecast of growth in demand, so a
more detailed analysis is required. Go/no-go decisions are generally made at a higher level in the organization than are replacement decisions.
4. Expansion into new products or markets. These investments involve strategic decisions that could change
the fundamental nature of the business. A detailed analysis is required, and top officers make the final
decision, possibly with board approval.
5. Contraction decisions. Especially during bad recessions, companies often find themselves with more
capacity than they are likely to need. Rather than continue to operate plants at, say, 50 per cent of capacity and incur losses as a result of excessive fixed costs, management decides to downsize. That generally
requires payments to laid-off workers and additional costs for shutting down selected operations. These
decisions are made at the board level.
6. Safety and/or environmental projects. Expenditures necessary to comply with environmental orders,
labour agreements or insurance policy terms fall into this category. How these projects are handled
depends on their size, with small ones being treated much like the Category 1 projects and large ones
requiring expenditures that might even cause the firm to abandon the line of business.
7. Mergers. Buying a whole firm (or division) is different from buying a machine or building a new plant.
Still, basic capital budgeting procedures are used when making merger decisions.
8. Other. This catch-all includes items such as office buildings, parking lots and executive aircraft. How
they are handled varies among companies.
Relatively simple calculations, and only a few supporting documents, are required for most replacement
decisions, especially maintenance investments in profitable plants. More detailed analyses are required as
we move on to more complex expansion decisions, especially for investments in new products or areas. Also,
within each category projects are grouped by their costs: larger investments require increasingly detailed
analysis and approval at higher levels. Thus, a plant manager might be authorized to approve maintenance expenditures up to €10 000 using a simple payback analysis, but the full board of directors might
have to approve decisions that involve either amounts greater than €1 million or expansions into new
products or markets.
If a firm has capable and imaginative executives and employees, and if its incentive system is working
properly, then many ideas for capital investment will be forthcoming. Some ideas will be good and should be
funded, but others should be killed, the finance manager has a big part to play in this process.
Chapter 11
Capital Budgeting: Evaluation of Cash Flows 277
It’s the Top Line that Matters
This is a reminder that in business the revenue
from projects remains the most significant figure
when engaging in capital investment decisions.
The very low oil prices in 2015 severely affected
exploration and production (E&P) companies. An
article in www.arabianoilandgas.com estimates
that E&P companies outside North America will
reduce their spending by between 10 per cent and
20 per cent depending on the price of oil. Capital
budgeting is estimated to be reduced by 25 per cent.
This will have a knock-on effect on oilfield services
and midstream energy operators. Although larger
companies in this field such as Schlumberger,
Halliburton and Baker Hughes can weather this
drop in activity, smaller companies will come
under much greater stress. Major integrated oil
companies according to Moody’s will fare better
and be able to take a longer-term view of capital
budgeting. This judgement is, however, suspect,
in that ExxonMobil, Royal Dutch Shell and Total
have all announced spending reductions for 2015,
including redundancies.
Source: www.arabianoilandgas.com 7 January 2015.
The following measures are common financial techniques for screening projects and deciding which
to accept or reject:
net present value (NPV)
internal rate of return (IRR)
accounting rate of return (ARR)
profitability index (PI)
regular payback (PB)
discounted payback
As we shall see, the NPV relates directly to the theory of asset valuation that we have been employing.
However, when applied to projects, it has measurement problems and evaluation problems that the other
methods help to clarify.
Project Valuation
We begin by outlining our choice of projects and applying the valuation methods outlined above:
Net Present Value
Net present value is the standard valuation model that is the basis of valuation in finance. We have discussed
the role of NPV in financial risk measurement in Chapter 6 and the modelling of differing cash flows in
Chapter 4. The advantage of NPV is that it is a measure of profitability and a measure of the size of the profits. The NPV figures of €804.38, and €1048.02 in Table 11-1 are measures of the expected increase in wealth of
the investor now, i.e. year 0.
The discount rate is a nominal rate and therefore includes an estimate for inflation; the cash flows should
similarly be inclusive of inflation and be estimates of the actual cash flows expected.
A basic rule is that all projects with positive NPVs should be accepted in the sense that they are wealth
increasing. We shall modify this rule later in the chapter. Where capital is rationed then projects according to
this rule should be ranked on the basis of their NPVs.
NPV is a very popular valuation technique, especially in the United States and to a lesser extent in the
EMEA region.1 This is despite some 50 years of advocacy in the financial literature. In all surveys it is clear that
Arnold, G. C. and Hatzopolous, P. D. (2000) ‘The theory–practice gap in capital budgeting: evidence from the United Kingdom’,
­Journal of Business Finance and Accounting, 27(5/6):603–26.
278 Part 4
Projects and Their Valuation
TA B L E 11-1
Valuation of Projects S and L (€’000s)
Cash Flows
0 (now)
Project S
Project L
210 000 1
210 000 1
210 000 1
5 0.00
210 000 1
5 0.00
5 804.38
5 1048.02
10 000 1 804.38
5 1.08
10 000
10 000 1 1048.02
5 1.10
10 000
5 2.21
13055 5 0
5 3.39
220 5 0
5 3.21
4279 5 0
5 3.80
210 000
1400 = 0
210 000
210 000
210 000
NPV is just one of many valuation methods used by any one firm in assessing projects, so although firms say
that they use NPV, its actual role in investment decisions is unclear.
As NPV has not been universally adopted with enthusiasm there are clearly some issues with applying
NPV to projects for practitioners. Unfortunately, surveys do not critique its use, but possibly compared with
other valuation methods it lacks the intuitive attraction of a rate of return and possibly offers a level of precision that mangers may well feel is unwelcome in that it gives an apparent authority to the measure that we
shall see later in this chapter is not warranted. Other methods in varying degrees address these problems.
Internal Rate of Return
A more intuitive way of reporting profitability from a net present value approach is the measure the IRR. The
internal rate of return is the discount rate that results in a zero NPV. It is the highest discount rate that can
be charged whilst not making the project unprofitable. Thus in Table 11-1 the internal rate of return for S is
14.69 per cent and for L is 13.79 per cent. Both S and L are acceptable if they offer a rate of return that is higher
than the required return given their risk. From the use of 10 per cent in the NPV calculations we assume that
10 per cent includes a charge for risk and therefore as both the IRR percentages are above 10 per cent both the
projects are acceptable. In this respect the IRR is giving the same message as the NPV.
In most cases the ranking of return by the IRR is also the same as that for NPV. That is not the case here:
NPV prefers L to S and the internal rate of return prefers S to L. We must be clear that the NPV is giving the
correct ranking.
Chapter 11
Capital Budgeting: Evaluation of Cash Flows 279
The difference between NPV and IRR may be a problem if capital is rationed and there has to be a choice
between S and L. There are ways of correcting IRR but they are unnecessary given that an IRR calculation can so
easily be changed to a NPV calculation using a spreadsheet—only the discount rate has to be changed.
Another problem with the IRR is that there is no size estimate—the cash flows in S could be in cents and the
cash flows in L in millions of euros and S would still appear more attractive! Finally, if there is a change in the cash
flows from positive to negative in later years there will be two IRRs and more if there are more changes.
Despite these problems, for many firms IRR is a more popular measure than NPV. Again, the reasons are
not entirely clear, even though there have been numerous surveys of usage. All that can be assumed is that
the drawbacks are not regarded as critical in practice. The lack of a size measure is clearly not seen as important, and possibly the pattern of cash flows is likely to be very simple in practice. There is no doubt that an
IRR has more appeal to the nonspecialist—saying that a project has a rate of return of x per cent is intuitively
appealing. Provided that it is checked by a NPV calculation, its usage will not mislead.
One of the hidden assumptions of the IRR is the reinvestment rate. If we were to shift a cash flow, say
€1000, from year 1 to year 2, what rate of interest would we have to assume for the project to have the same
IRR? That rate would in fact have to be the IRR, i.e. 14.69 per cent for S and 13.79 per cent for L. This is
clearly unrealistic, whereas for the NPV method the same question would require a rate of interest of only
10 per cent which is the required rate of interest and more realistic. So an investor who decides to reinvest the
net cash flow until the end of the investment is going to have a rather different IRR. This can be calculated as
follows as a modified internal rate of return (MIRR) assuming a reinvestment rate of 10 per cent:
5300 1 1.10 2 3
4300 1 1.10 2 2
1874 1 1.10 2 1
5 0.00
remembering that the cash flows are assumed to be at the end of each period. The rate of return for project S
is therefore 12.15 per cent and is found as with all IRRs by trial and error. We leave it to the reader to confirm
that the MIRR of L is 10.19 per cent. Thus, the MIRR illustrates the importance of the use made of the cash
flows. Again, the NPV assumption is more realistic and gives the correct answer. The example once again
shows the importance of using the IRR only as a way of reporting a choice, and not as a means of making the
actual choice.
The Accounting Rate of Return
Another method of valuing projects is the accounting rate of return, defined as:
average earnings
average investment
where average investment is the:
initial book value-closing book value
We assume in the example of Table 11-1 that the initial investment represents an approximate initial
book value that reduces to zero over the life of the project. Also, we assume that the cash flows approximate
reported earnings from which we deduct depreciation that will amount to €10 000, over the life of the project.
Neither of these assumptions are entirely accurate but in what is an approximate measure, greater accuracy is
unlikely to alter the end result greatly. With these assumptions, the ARR for project S is:
5300 1 4300 1 1874 1 1500 2 10000
5 59.48%
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The reader can check that the same calculation for project L yields an ARR of 94.90 per cent. Why are
these rates of return so high? The simple answer is because the returns are not discounted. The return on L
is very much higher than S because of the high later returns that would be heavily discounted in the NPV
model and even more so in the IRR model. In other words, the average does not measure the effect of time.
Nevertheless, this measure is popular because it gives an idea of the effect that a project will have on
the balance sheet of a company. In the final year of project L the market value of the project should be
5 €7090 but on the balance sheet it will appear as 7800 2 2500 5 €5300 using straight line depreciation
(i.e. there is one more year of depreciation to deduct). Often in practice old assets can be written down to a
nominal €1, making the return seem extremely high. It is not therefore surprising that balance sheet value of
equity interest (the value of shares) is normally less than the valuation of the company on the stock market
when productive assets essentially disappear from the balance sheet.2
Profitability Index
The profitability index is a means of making the NPV more accessible and comparable in the manner of the
IRR but without some of the problems of the IRR. The index is simply:
initial cost 1 net present value
initial cost
and is the profit per €1 or $1 (etc.) of initial cost. A higher net present value will always give a higher PI so
there is no distortion. The drawback is that it does not have the familiarity of a return and hence will almost
without exception not even appear as an option in surveys.
Payback and Discounted Payback
Payback (PB) is simply the number of years taken to repay the initial investment. A project with a lower payback is preferred, being seen as less risky.
Of all the measures, PB has over the years been as popular and in the past more popular that NPV. Obviously it has drawbacks as a measure. It does not include cash flows after the PB period and it is easy to devise
cash flows with a low PB but a poor NPV. The evidence from surveys is that companies use more than one
method of evaluation. As part of a package of measures, PB has attractions. The measure is not pretending to
be a measure of profitability but is a measure of individual risk based on the assumption that risk increases
over time, as is the case with all models based on the random walk. For the projects in Table 11-1, project S is
preferred as it has a PB of 2.21 years whereas L has a PB of 3.39 years. The planning horizon of firms rarely
stretches beyond five years (see footnote 1) according to surveys, so 3.39 is high in absolute terms. Firms as a
policy may impose a maximum PB period.
A common adjustment to PB is to discount the cash flows and in Table 11-1 the numbers are the dis4300
counted values, so for example 4818 5 5300
1.1 , 3554 5 1.12 and so on. This does not cure the basic problem of
using PB as a selection criterion, which as we have said is in any case unlikely as a sole measure.
What Happens in Practice?
Surveys of practice have not been fashionable of late in the research literature following a number of surveys
in the later part of the previous century. A major survey of 296 UK firms was conducted by Glen Arnold in
2000 (see footnote 1) and is reported in Table 11-2.
Over the years there has been a gradual increase in the use of NPV but it is still unclear as to the actual role that
is played by this and other measures in actual decisions. It is also noticeable that smaller firms use NPV less and
payback more than the larger firms. In the Arnold and Hatzopolous survey, 58 per cent of large firms used NPV
compared with 26 per cent of the smaller firms in the sample; whereas 35 per cent of small firms used payback
compared with 24 per cent of large firms. The difficulty of establishing the practice of firms is that businessmen do
not rationalize their actions and interviewing them does not necessarily reveal what actually happens.
Note that project S would report a loss in the final year.
Chapter 11
Capital Budgeting: Evaluation of Cash Flows 281
TA B L E 11-2
Frequency of Use of Financial Analysis Techniques
Rarely %
Often %
Mostly %
Always %
Source: Glen C. Arnold and Panos D. Hatzopolous, 2000, ‘The Theory Practice Gap in Capital Budgeting: Evidence from the
United Kingdom’, Journal of Business Finance & Accounting, 27(5) & (6), June/July, 603–626.
How to Use the Different Capital Budgeting Methods
We have discussed six capital budgeting decision criteria: NPV, IRR, MIRR, PI, payback and discounted
­payback. We compared these methods and highlighted their strengths and weaknesses. In the process, we
may have created the impression that ‘sophisticated’ firms should use only one method, the NPV. However,
virtually all capital budgeting decisions are analysed by computer, so it is easy to use all six methods. In
making the accept–reject decision, most firms usually calculate and consider more than one method because
each method provides a somewhat different piece of information about the decision.
A Comparison of the Methods
NPV is the single best of the methods because it provides a direct measure of the value a project adds to shareholder wealth. IRR and MIRR measure profitability expressed as a percentage rate of return, which decision
makers like to consider. The PI also measures profitability but in relation to the amount of the investment.
Further, IRR, MIRR and PI all contain information concerning a project’s ‘safety margin’. To illustrate, consider a firm, whose WACC is 10 per cent, which must choose between these two mutually exclusive projects:
• SS (for small) has a cost of €10 000 and is expected to return €16 500 at the end of one year;
• LL (for large) has a cost of €100 000 and is expected to return €115 550 at the end of one year.
SS has an IRR of 65 per cent, while LL’s IRR is a more modest 15.6 per cent. The NPV paints a somewhat different picture: at the 10 per cent cost of capital, SS’s NPV is €5000 while LL’s is €5045. By the NPV rule we would
choose LL. However, SS’s IRR indicates that it has a much larger margin for error: even if its cash flow were 39 per
cent below the €16 500 forecast, the firm would still recover its €10 000 investment. On the other hand, if LL’s inflows
fell by only 13.5 per cent from its forecast €115 550, the firm would not recover its investment. Further, if neither project generated any cash flows at all, the firm would lose only €10 000 on SS but would lose €100 000 by accepting LL.
The modified IRR has all the virtues of the IRR, but it avoids the problem of multiple rates of return that
can occur with the IRR. The MIRR also measures the expected return of the project and its reinvested cash
flows, which provides additional insight into the project. So if decision makers want to know projects’ rates
of return, the MIRR is a better indicator than the regular IRR in theory.
The PI tells a similar story to the IRR. Here PILL is only 1.05 while PISS is 1.50. As with the IRR, this indicates that project SS’s cash inflow could fall by a lot before it loses money, whereas a small decline in LL’s cash
flows would result in a loss.
Payback and discounted payback provide indications of a project’s liquidity and risk. A long payback
means that investment euros will be locked up for a long time; hence the project is relatively illiquid. In
addition, a long payback means that cash flows must be forecast far into the future, and that probably makes
the project riskier than one with a shorter payback. A good analogy for this is bond valuation. An investor
should never compare the yields to maturity on two bonds without also considering their terms to maturity,
because a bond’s risk is influenced significantly by its maturity. The same holds true for capital projects.
In summary, the different measures provide different types of useful information. It is easy to calculate
all of them using a spreadsheet. Therefore, many companies consider more than one measure when making
capital budgeting decisions. For most decisions, the greatest weight should be given to the NPV, but it would
be foolish to ignore the information provided by the other criteria.
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A note of caution is needed, however—with both projects we assume that there are no contingent decisions
that are possible. Examples would be expansion if the project proved to be more successful than expected,
or abandonment if it should prove to be a failure (the real options argument). Also, we assume that competitors will not react to the investment if it proves to be a success or a failure (the game theory argument). We
address these problems later in the chapter.
The Decision Process: What is the Source of a Project’s NPV?
Just as it would be foolish to ignore these capital budgeting methods, it would also be foolish to make decisions based solely on them. One cannot know at time 0 the exact cost of future capital or the exact future cash
flows. These inputs are simply estimates, and if they turn out to be incorrect then so will be the calculated
NPVs and IRRs. Thus, quantitative methods provide valuable information, but they should not be used as the
sole criterion for accept–reject decisions in the capital budgeting process. Rather, managers should use quantitative methods in the decision-making process, and should also consider the likelihood that actual results
will differ from the forecasts.
Qualitative factors, such as the chances of a tax increase, or a war, or a major product liability suit, should
also be considered. In summary, quantitative methods such as NPV and IRR should be considered as an aid
to informed decisions but not as a substitute for sound managerial judgement.
The central problem is that all the measures are based on quite restrictive assumptions about the behaviour of the estimates in the future. We have noted in particular that the normal distribution assumption in
practice is often violated through so-called extreme events, the outliers.
In this same vein, managers should ask sharp questions about any project that has a large NPV, or a high
IRR. In a perfectly competitive economy, there would be no positive-NPV projects—all companies would
have the same opportunities, and competition would quickly eliminate any positive NPV. The existence of
positive-NPV projects must be predicated on some imperfection in the marketplace, and the longer the life
of the project, the longer that imperfection must last. Therefore, managers should be able to identify the
imperfection and explain why it will persist before accepting that a project will really have a positive NPV.
Valid explanations might include patents or proprietary technology, which is how pharmaceutical and software firms create positive-NPV projects. Pfizer’s Lipitor (a cholesterol-reducing medicine) and Microsoft’s
Windows operating system are examples. Companies can also create positive NPV by being the first entrant
into a new market or by creating new products that meet some previously unidentified consumer needs.
Post-it notes invented by 3M are an example. Similarly, Dell developed procedures for direct sales of microcomputers and, in the process, created projects with enormous NPV. Also, companies such as Southwest
Airlines have trained and motivated their workers better than their competitors, and this has led to positive-NPV projects. In all of these cases, the companies developed some source of competitive advantage, and
that advantage resulted in positive-NPV projects.
This discussion suggests three things: (1) If you cannot identify the reason a project has a positive projected
NPV, then its actual NPV will probably not be positive. (2) Positive-NPV projects do not just happen—they result
from hard work to develop some competitive advantage. At the risk of oversimplification, the primary job of a
manager is to find and develop areas of competitive advantage. (3) Some competitive advantages last longer than
others, with their durability depending on competitors’ ability to replicate them. Patents, the control of scarce
resources, or large size in an industry where strong economies of scale exist, can keep competitors at bay. However,
it is relatively easy to replicate product features that cannot be patented. The bottom line is that managers should
strive to develop nonreplicable sources of competitive advantage. If such an advantage cannot be demonstrated,
then you should question projects with high NPV—especially if they have long lives.
S E L F -T E S T
Describe the advantages and disadvantages of the six capital budgeting methods.
Should capital budgeting decisions be made solely on the basis of a project’s NPV, with no regard to
the other criteria? Explain your answer.
What are some possible reasons that a project might have a high NPV?
Chapter 11
Capital Budgeting: Evaluation of Cash Flows 283
Other Issues in Capital Budgeting
Three other issues in capital budgeting are discussed in this section: (1) how to deal with mutually exclusive
projects whose lives differ; (2) the potential advantage of terminating a project before the end of its physical
life; and (3) the optimal capital budget when the cost of capital rises as the size of the capital budget increases.
Mutually Exclusive Projects with Unequal Lives
Sometimes the choice is between projects that do not have the same ‘life’ so the comparison is not equal in
the sense that they cover differing time periods. There are two main methods of coping with this problem.
Replacement Chains
The key to the replacement chain, or common life, approach is to analyse both projects over an equal life.
So if a transport contract with one company is for three years and the other is for six years, then we simply
compare two lots of three-year contracts with one lot of six-year contracts. This is problematic in the sense
that we are assuming that the three-year contracts will not change when the shorter-term contract is being
offered precisely because it gives the provider the right to change terms, so it is not an insignificant difference
as it increases the risk.
Equivalent Annual Annuities
Another way of equating the lives of the projects is to convert the NPV of a project to an equivalent annual
annuity (EAA). So if the NPV of project X is €2000, and it will need to be renewed in three years’ time and
the interest rate is 10 per cent then using the annuity formula (A3,0.1, i.e. the present value of an annuity for
three years at 10 per cent):
NPVX 5 2000
A3,0.1 5 a
b 5 2.4869
0.1 1 1.1 2 3
EAAX 5 804.21
so €804.21 would be used as the benefit of project X and compared with other projects valued in the same
way over their respective lives and interest rates. The project with the highest EAA would then be selected.
Conclusions about Unequal Lives
When should we worry about analysis of unequal lives? The unequal life issue (1) does not arise for independent projects but (2) can arise if mutually exclusive projects with significantly different lives are being
compared. However, even for mutually exclusive projects, it is not always appropriate to extend the analysis
to a common life. This should be done if and only if there is a high probability that the projects will actually
be repeated at the end of their initial lives.
We should note several potentially serious weaknesses in this type of analysis. (1) If inflation occurs, then
replacement equipment will have a higher price. Moreover, both sales prices and operating costs would probably change. Thus, the static conditions built into the analysis would be invalid. (2) Replacements that occur
down the road would probably employ new technology, which in turn might change the cash flows. (3) It is
difficult enough to estimate the lives of most projects, and even more so to estimate the lives of a series of projects. In view of these problems, no experienced financial analyst would be too concerned about comparing
mutually exclusive projects with lives of, say, eight years and ten years. Given all the uncertainties in the estimation process, we would assume that such projects would, for all practical purposes, have the same life. Still, it
is important to recognize that a problem exists if mutually exclusive projects have substantially different lives.
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When we encounter situations with significant differences in project lives, we first use a computer spreadsheet
to build expected inflation and/or possible efficiency gains directly into the cash flow estimates and then use the
replacement chain approach. We prefer the replacement chain approach for two reasons. First, it is easier to explain
to those who are responsible for approving capital budgets. Second, it is easier to build inflation and other modifications into a spreadsheet and then go on to make the replacement chain calculations.
More generally, we would argue that using formulae such as annuities and growth rates reflects an age
when calculation was difficult and these short cuts were valuable. The far greater access to powerful calculation tools means that future financial plans can be mapped out on an annual basis. A spreadsheet after all
has some 250 columns and thousands of rows!
Cash Flow Estimation
Having seen how cash flows are valued we now turn to what many businessmen and women would probably
think of as the greater problem: estimating the cash flows themselves. How does one estimate the future?
Can we really look at the past to tell us what the future will look like? One should not lose a certain sense of
wonder when thinking about such questions.
Estimates of cash flows need to be estimates of a proposal’s relevant project cash flows, which are the
differences between the cash flows the firm will have if it implements the project versus the cash flows it will
have if it rejects the project. These are called incremental cash flows:
Incremental cash flow 5
cash flows
with the
cash flows
without the
Often in examples, as quoted earlier in this chapter, it is assumed that if the company does not go ahead
with a project the cash flows will be zero. However, think of the case of a company that is seeking to improve
its computer systems. If the company does not go ahead then it risks falling behind. To the benefits of the
computer system must be added the negative outcomes from not going ahead. At times, therefore, the cost of
a project can seem to outweigh the benefits, but in incremental terms the investment can still be worthwhile.
Estimating incremental cash flows might sound easy, but there are many potential pitfalls. In this section,
we identify the key concepts that will help you avoid these pitfalls and then apply the concepts to an actual
project to illustrate their application to cash flow estimation.
Cash Flow versus Accounting Income
We saw in Chapter 2 that FCF differs from accounting income: FCF is cash flow that is available for distribution to investors, making FCF the basis of a firm’s value. It is common in the practice of finance to speak of
a firm’s FCF and a project’s cash flow (or net cash flow), but these are based on the same concepts. In fact, a
project’s cash flow is identical to the project’s FCF, and a firm’s total net cash flow from all projects is equal to
the firm’s FCF. We will follow the typical convention and refer to a project’s FCF simply as project cash flow,
but keep in mind that the two concepts are identical.3
As net income is not equal to the cash flow available for distribution to investors, in the last chapter we
discounted net cash flows, not accounting income, to find projects’ NPVs. For capital budgeting purposes it
is the project’s net cash flow, not its accounting income, which is relevant. Therefore, when analysing a proposed capital budgeting project, disregard the project’s net income and focus where possible on its net cash
flow. The following details the major differences.
When the financial press refers to a firm’s ‘net cash flow’, it is almost always equal to the definition we provide in Chapter 2 (which simply
adds back depreciation and any other noncash charges to net income). However, as we explained in Chapter 2, the net cash flow from operations (from the statement of cash flows) and the firm’s FCF are much more useful measures of cash flow. When financial analysts within a
company use the term ‘a project’s net cash flow’, they almost always calculate it as we do in this chapter, which is in essence the project’s FCF.
Thus, FCF means the same thing whether you calculate it for a firm or for a project. On the other hand, when the financial press talks about a
firm’s net cash flow or when an internal analyst talks about a project’s net cash flow, those ‘net cash flows’ are not the same.
Chapter 11
Capital Budgeting: Evaluation of Cash Flows 285
The Cash Flow Effect of Asset Purchases and Depreciation
Most projects require assets, and asset purchases represent negative cash flows. Even though the acquisition
of assets results in a cash outflow, accountants do not show the purchase of fixed assets as a deduction from
accounting income. Instead, they deduct a depreciation expense each year throughout the life of the asset.
Depreciation shelters income from taxation, and this has an impact on cash flow, but depreciation itself is
not a cash flow. Therefore, depreciation must be added back when estimating a project’s operating cash flow.
Depreciation is the most common noncash charge, but there are many other noncash charges that might
appear on a company’s financial statements. Just as with depreciation, all other noncash charges should be
added back when calculating a project’s net cash flow.
Changes in Net Operating Working Capital
Normally, additional inventories are required to support a new operation, and expanded sales tie up additional funds in accounts receivable. However, payables and accruals increase as a result of the expansion,
and this reduces the cash needed to finance inventories and receivables. The difference between the required
increase in operating current assets and the increase in operating current liabilities is the change in net
operating working capital. If this change is positive, as it generally is for expansion projects, then additional
financing—beyond the cost of the fixed assets—will be needed.
Toward the end of a project’s life, inventories will be used but not replaced, and receivables will be collected without corresponding replacements. As these changes occur the firm will receive cash inflows; as a
result, the investment in net operating working capital will be returned by the end of the project’s life.
Interest Charges Are Not Included in Project Cash Flows
Interest is a cash expense, so at first blush it would seem that interest on any debt used to finance a project should
be deducted when we estimate the project’s net cash flows. However, this is not correct. Recall from Chapter 10
that we discount a project’s cash flows by its risk-adjusted cost of capital, which is a weighted average (WACC) of
the costs of debt, preferred shares and common equity, adjusted for the project’s risk and debt capacity. This project cost of capital is the rate of return necessary to satisfy all of the firm’s investors, including shareholders and
debtholders. A common mistake made by many students and financial managers is to subtract interest payments
when estimating a project’s cash flows. This is a mistake because the cost of debt is already embedded in the
cost of capital, so subtracting interest payments from the project’s cash flows would amount to double-counting
interest costs. Therefore, you should not subtract interest expenses when finding a project’s cash flows.
Timing of Cash Flows: Yearly versus Other Periods
In theory, in capital budgeting analyses we should discount cash flows based on the exact moment when they
occur. Therefore, one could argue that daily cash flows would be better than annual flows. However, it would
be costly to estimate daily cash flows and laborious to analyse them. In general the analysis would be no better than one using annual flows because we simply cannot make accurate forecasts of daily cash flows more
than a couple of months into the future. Therefore, it is generally appropriate to assume that all cash flows
occur at the end of the various years. For projects with highly predictable cash flows, such as constructing a
building and then leasing it on a long-term basis (with monthly payments) to a financially sound tenant, we
would analyse the project using monthly periods.
Expansion Projects and Replacement Projects
Two types of projects can be distinguished: (1) expansion projects, in which the firm makes an investment
in, for example, a new Home Depot store in Lagos; and (2) replacement projects, in which the firm replaces
existing assets, generally to reduce costs. In expansion projects, the cash expenditures on buildings, equipment and required working capital are obviously incremental, as are the sales revenues and operating costs
associated with the project. The incremental costs associated with replacement projects are not so obvious. For example, Home Depot might replace some of its delivery trucks to reduce fuel and maintenance
expenses. Replacement analysis is complicated by the fact that most of the relevant cash flows are the cash
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flow differences between the existing project and the replacement project. For example, the fuel bill for a
more efficient new truck might be €10 000 per year versus €15 000 for the old truck, and the €5000 fuel savings would be an incremental cash flow associated with the replacement decision.
Sunk Costs
A sunk cost is an outlay related to the project that was incurred in the past and that cannot be recovered
in the future regardless of whether or not the project is accepted. Therefore, sunk costs are not incremental costs and thus are not relevant in a capital budgeting analysis. To quote the economist Stanley Jevons:
‘Bygones are forever bygones.’
Opportunity Costs Associated with Assets the Firm Already Owns
Another conceptual issue relates to opportunity costs related to assets the firm already owns. Suppose
Company X owns land with a current market value of €2 million that can be sold or used for the new store if
it decides to build it. This €2 million is an opportunity cost—it is cash that Company X would not receive if
the land is used for the new store. Therefore, the €2 million must be charged to the new project, and failing to
do so would cause the new project’s calculated NPV to be too high.
Another conceptual issue relates to externalities, which are the effects of a project on other parts of the
firm or on the environment. As explained in what follows, there are three types of externalities: negative
­w ithin-firm externalities, positive within-firm externalities, and environmental externalities.
Negative Within-Firm Externalities
If a retailer like Home Depot opens a new store that is close to its existing stores, then the new store might attract
customers who would otherwise buy from the existing stores, reducing the old stores’ cash flows. Therefore, the
new store’s incremental cash flow must be reduced by the amount of the cash flow lost by its other units. This type
of externality is called cannibalization, because the new business eats into the company’s existing business. Many
businesses are subject to cannibalization. For example, each new iPod model cannibalizes existing models. Those
lost cash flows should be considered, and that means charging them as a cost when analysing new products.
Dealing properly with negative externalities requires careful thinking. If Apple decided not to come out
with a new model of iPod because of cannibalization, another company might come out with a similar new
model, causing Apple to lose sales on existing models. Apple must examine the total situation, and this is
definitely more than a simple, mechanical analysis. We shall use a game theory framework to analyse such
issues later in this chapter.
One of the best examples of a company getting into trouble as a result of not dealing correctly with cannibalization was IBM’s response to the development of the first personal computers in the 1970s. IBM’s mainframes dominated the computer industry, and they generated profits. IBM used its technology to enter the
PC market, and initially it was the leading PC company. However, its top managers decided to de-emphasize
the PC division because they were afraid it would hurt the more profitable mainframe business. That decision opened the door for Apple, Dell, Hewlett Packard, Sony, and Chinese competitors to take PC business
away from IBM. As a result, IBM went from being the most profitable firm in the world to one whose very
survival was threatened. IBM’s experience highlights that it is just as important to understand the industry
and the long-run consequences of a given decision as it is to understand the theory of finance. Good judgement is an essential element for good financial decisions.
Positive Within-Firm Externalities
As we noted earlier, cannibalization occurs when a new product competes with an old one. However, a
new project can also be complementary to an old one, in which case cash flows in the old operation will
Chapter 11
Capital Budgeting: Evaluation of Cash Flows 287
be increased when the new one is introduced. For example, Apple’s iPod was a profitable product, but
when Apple considered an investment in its music store it realized that the store would boost sales of
iPods. So, even if an analysis of the proposed music store indicated a negative NPV, the analysis would
not be complete unless the incremental cash f lows that would occur in the iPod division were credited
to the music store. Consideration of positive externalities often changes a project’s NPV from negative
to positive.
Environmental Externalities
The most common type of negative externality is a project’s impact on the environment. Government rules
and regulations constrain what companies can do, but firms have some flexibility in dealing with environmental issues. For example, suppose a manufacturer is studying a proposed new plant. The company could
meet current environmental regulations at a cost of €1 million, but the plant would still emit fumes that
would cause some bad will in its neighbourhood. Those ill feelings would not show up in the cash flow analysis, but they should be considered. Perhaps a relatively small additional expenditure would reduce the emissions substantially, make the plant look good relative to other plants in the area, and provide goodwill that in
the future would help the firm’s sales and its negotiations with governmental agencies.
Of course, all firms’ profits ultimately depend on the Earth remaining healthy, so companies have some
incentive to do things that protect the environment even though those actions are not currently required.
However, if one firm decides to take actions that are good for the environment but quite costly, then it must
either raise its prices or suffer a decline in earnings. If its competitors decide to get by with less costly but
environmentally unfriendly processes, they can price their products lower and make more money. Of course,
the more environmentally friendly companies can advertise their environmental efforts, and this might—
or might not—offset their higher costs. Alternatively, firms may decide not to adopt environmental factors
because the benefits would be short lived before the competition adopts similar measures and the investment would have a negative return as a result. If all firms think like this then there will be no environmental improvements. We shall show later that this competition-induced conformity can be seen in terms of
the well-known ‘prisoner’s dilemma’. All this illustrates why government regulations are often necessary.
Finance, politics and the environment are all interconnected.
S E L F -T E S T
Why should companies use a project’s net cash flows rather than accounting income when
determining a project’s NPV?
Explain the following terms: incremental cash flow, sunk cost, opportunity cost, externality,
cannibalization, and complementary project.
Provide an example of a ‘good’ externality—that is, one that increases a project’s true NPV over what
it would be if just its own cash flows were considered.
Combining Cash Flow Estimates and Risk
Although the CAPM advocates that projects should be charged with beta risk (see Chapter 10) the analysis is
dependent on certain assumptions:
Estimates are expectations of approximately normal distribution of possible cash flows.
Competitor reactions are not significant.
The project is undertaken immediately.
There are no contingent cash flows (opportunities or closure if cash flows reach a certain level, ­sometimes
termed real options).
5. The project is independent of other projects and not part of a general strategy.
6. Investors are well diversified.
Where the assumptions do not hold, analysis of the risk of an investment and the expected cash flows
has to be considered as a stand-alone risk. These assumptions are common phenomena when applied
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to real investments, by which we mean investments other than in shares. As a result, in practice, all
investments are considered independently of the market return as defined by CAPM as part of the evaluation process.
Three techniques are used in practice to assess stand-alone risk: (1) sensitivity analysis, (2) scenario
analysis and (3) Monte Carlo simulation. We discuss them in the sections that follow.
S E L F -T E S T
What does a project’s stand-alone risk reflect?
What three techniques are used to assess stand-alone risk?
Sensitivity Analysis
Intuitively, we know that a change in a key input variable such as units sold or the sales price will cause
the cash flows to change. Sensitivity analysis measures the percentage change in an output measure (NPV,
earnings, rate of return, PB, etc.) that results from a given percentage change in an input variable when other
inputs are held at their expected values. This is by far the most commonly used type of risk analysis.
Taking accounting profit as our output measure, though it could be any output measure chosen by the
firm, analysis begins with a base-case scenario in which the project’s profit is found using the base-case value
for each input variable.
Figure 11-1 shows a simple base case of an estimated activity. The sensitivity estimates are based on deviations being ‘what if sales price were 30 per cent higher?’ or ‘what if units sold were 30 per cent lower?’ (Unsurprisingly, these are referred to as ‘what ifs’.) In essence they are simple scenario questions. In Figure 11-1 we
can see that the relationship with profit is linear so the 30 per cent deviation, to which there is no particular
significance, does not really matter as we can see easily the outcome of a 10 per cent deviation. Where the
model is more complex, such as where price is seen as a function of the volume sold as in a downward-sloping
demand curve, then it will not be possible to change one variable at a time in this manner and analysis will be
more in the nature of scenario analysis.
Sensitivity analysis serves as a simple first look at the future possibilities. From Figure 11-1 it is not clear
from the base case alone that the price and units sold are the most important inputs to estimate accurately.
The diagram shows that this is the case in a manner clear to nonspecialists. How difficult it is to estimate
these figures is a ­different matter. In Figure 11-1 sales price despite its effect on profits may be fixed, whereas
fixed costs may be s­ ubject to much uncertainty. Such considerations are beyond sensitivity analysis as they
require some e­ stimate of the likelihood of outcomes. For this we turn to scenario analysis.
S E L F -T E S T
What is sensitivity analysis?
Briefly explain the usefulness of a sensitivity graph.
Discuss the following statement: ‘A project may not be very risky in spite of its high sensitivity to
certain variables.’
Scenario Analysis
In the sensitivity analysis just described, we changed one variable at a time. However, it is useful to know
what would happen to the project’s profit if several of the inputs turn out to be better or worse than expected,
and this is what we do in a scenario analysis. Also, scenario analysis allows us to assign probabilities to the
base (or most likely) case, the best case and the worst case; then we can find the expected value and standard
deviation of the project’s profit to get a better idea of the project’s risk.
Chapter 11
Capital Budgeting: Evaluation of Cash Flows 289
F i g ure 11-1
Sensitivity Graph Showing Differing Profits if Variables Differ Independently as Indicated (e.g. Profits
Are €25 000 When Units Sold Are 30 per cent Below the Base Case ( (1 2 30%) 3 30 000 5 21 000)
and There Is a Loss of €110 000 When the Price is 30 per cent Below the Base Case
Base case
Sales price per unit
Variable cost
Fixed cost
500 000
30 000
Annual profit with variables at differing deviations from base
30% unfavourable
30% favourable
700 000
600 000
Sales price
Units sold
Sales price
per unit
Variable cost
per unit
25 000
250 000
475 000
–110 000
250 000
610 000
115 000
250 000
385 000
100 000
250 000
400 000
Fixed costs
Variable cost
500 000
400 000
300 000
200 000
100 000
–100 000
–200 000
30% unfavourable
30% favourable
Change in Variables
In a scenario analysis, we begin with the base-case scenario, which uses the most likely value for each
input variable. We then ask marketing, engineering and other operating managers to specify a worst-case
scenario (low unit sales, low sales price, high variable costs, and so on) and a best-case scenario. Often, the
best and worst cases are defined as having a 25 per cent probability of occurring, with a 50 per cent probability for the base-case conditions. Obviously, conditions could take on many more than three values, but such
a scenario setup is useful to help get some idea of the project’s riskiness.
After much discussion with the marketing staff, engineers, accountants and other experts in the company, a set of worst-case and best-case values would be determined for several key inputs. Figure 11-2, taken
from the example of Figure 11-1, shows the probability and inputs assumed for the base-case, worst-case and
best-case scenarios, along with selected key results.
Valuation of the outcomes may be extended to more than three. Ultimately though, there has to be some
single measure of outcome for managers to take a decision. This may simply be a subjective reaction to a bar
chart such as ‘it looks too risky’ (as in Figure 11-2, a different example from Figure 11-1).
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F i g ure 11-2
Scenario Analysis Showing Outcomes and Their Probability (€)
Annual profit estimates
Sales price per unit
Variable cost
Fixed cost
Expected value
Standard deviation
Coefficient of variation
Base case
20 000
30 000
39 000
550 000
500 000
470 000
–150 000
250 000
505 000
213 750
234 397
–200 –150 –100 –50
100 150 200 250 300 350 400 450 500 550
Profit ‘000 Euro
Other measures are the expected value—in this case €213 750. The problem with the expected value is
firstly that there is no indication of risk and secondly it is not ‘expected’ in the normal sense of the word—
estimates do not include €213 750. For the first problem there are several methods of analysing the risk:
• the standard deviation (€234 397)
standard deviation
• coefficient of variation:
(in this case 1.10)
expected value
• worst-case scenario (€2150 000)
• risk relative to market returns (beta)
In a banking context this is referred to as stress testing. Beta is measured on ex-post data and excludes worstcase scenarios as they are likely to be of companies that have closed down (and hence will not show in the returns
data). Surveys show that firms often apply hurdle rates that seem to be very high compared with ex-post data; but
scenario analysis reminds us that ex-post data suffer from biased selection if they only include survivors.
The second problem is that the expected value is not expected in the normal sense of the word. Other measures may be more appropriate as a measure of expectation (in the normal sense of the word). In this case the
Chapter 11
Capital Budgeting: Evaluation of Cash Flows 291
mode, that is the outcome with the highest probability (in this case €250 000), is actually the most anticipated
and in the normal sense is the expected value. The difference between the mode and the average is, however, not
that great and would always be about the same where the distribution is ‘single peaked’ (i.e. like a pyramid).
Businessmen (and students) sometimes ask, ‘but what if a project is expected to be either a great success or
a complete failure?’ In Figure 11-2 it could be, for instance, that the worst outcome had a probability of 40 per
cent, the base case 20 per cent and the best case 40 per cent. The expected value would be €192 000, which is
very different from outcomes that together have an 80 per cent expectation!
The answer gets to the heart of what we mean by an expectation and has been much disputed in the management science literature. If we see probability in the sense of flipping a coin then the expected value is based
on frequency. This may be a realistic view of the project. It may for instance be opening up a supermarket—
some are successful, others a failure. A food retail company may well accept such projects on the basis that
the expected value will be experienced only across a number of such projects.
Where a frequentist interpretation is not the case, as in the example of a start-up company wanting to
market a new product, we cannot identify a repeating scenario. Probability in this sense is a measure of
strength of feeling, sometimes called Bayesian probabilities. It is a measure of preference and not an actual
outcome that is likely. Decision makers may alternatively want to use other measures to value a project, or
relate the monetary outcome to some subjective measure of benefit, such as utility. The implication here is
that the expected monetary value is not the only rational basis for decisions.
Monte Carlo Simulation
Monte Carlo simulation ties together sensitivities, probability distributions and correlations among the input
variables. It grew out of work in the Manhattan Project to build the first atomic bomb and was so named
because it utilized the mathematics of casino gambling. Although Monte Carlo simulation is considerably
more complex than scenario analysis, simulation software packages make the process manageable. Many of
these packages can be used as add-ins to Excel and other spreadsheet programs.
In a simulation analysis, a probability distribution is assigned to each input variable—sales in units, the
sales price, the variable cost per unit, and so on. The computer begins by picking a random value for each
variable from its probability distribution. Those values are then entered into the model. The outcome measure, be it profit or NPV, is calculated and is stored in the computer’s memory. This is called a trial. After
completing the first trial, a second set of input values is selected from the input variables’ probability distributions, and a second profit or NPV is calculated. This process is repeated many times. The NPVs from the
trials can be charted on a histogram, which shows an estimate of the project’s outcomes. The average of the
trials’ outcomes is interpreted as a measure of the project’s expected value, with the standard deviation (or
the coefficient of variation) as a measure of the project’s risk.
The particular advantage of Monte Carlo simulation is that it is capable of handling both continuous and
discontinuous relationships with instructions such as ‘if statements’ that are difficult to model by any other
method. Commercial packages are one source of modelling; but also for relatively modest talents in Excel,
models can be built using the ‘5NORMINV(RAND(), mean, standard deviation)’ function. This returns a
randomly selected value from a normal distribution with the given mean and standard deviation, the essence
of a Monte Carlo simulation. The advantage of a self-build is a complete understanding of the model; the disadvantage is any modelling mistakes that might occur. In any event it should always be the case that results
are reviewed for reasonableness.
Project Risk: Preliminary Conclusions
We have discussed the three types of risk normally considered in capital budgeting projects: stand-alone
risk, within-firm (or corporate) risk and market risk. However, two important questions remain: (1) Should
firms care about stand-alone and corporate risk, given that finance theory says that market (beta) risk is the
only relevant risk? (2) What do we do when the stand-alone, within-firm, and market risk assessments lead
to different conclusions?
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There are no easy answers to these questions. Strict adherents of the CAPM would argue that well-­
diversified investors are concerned only with market risk, that managers should be concerned only with
maximizing share price, and thus market (beta) risk ought to be the basis of capital budgeting decisions.
However, we know that not all investors are well diversified, that the CAPM does not operate exactly as the
theory says it should, and that measurement problems keep managers from having complete confidence in
the CAPM inputs. In addition, the CAPM ignores bankruptcy costs, even though such costs can be substantial, and the probability of bankruptcy depends on a firm’s corporate risk, not on its beta risk. Therefore,
even well-diversified investors should want a firm’s management to give at least some consideration to a
­project’s corporate risk, and that means giving some consideration to stand-alone project risk.
Although it would be nice to reconcile these problems and to measure risk on some absolute scale, the best we
can do in practice is to estimate risk in a somewhat nebulous, relative sense. For example, we can generally say
with a fair degree of confidence that a particular project has more, less, or about the same stand-alone risk as the
firm’s average project. Assuming that market risk and corporate risk are correlated, as is true for most companies,
a project with a relatively high or low corporate risk will also have a relatively high or low market risk. We wish we
could be more specific, but one simply must use a lot of judgment when assessing projects’ risks.
S E L F -T E S T
In theory, should a firm be equally concerned with stand-alone, corporate and market risk?
Would your answer be the same if we substituted ‘In practice’ for ‘In theory’? Explain your answers.
If a project’s stand-alone, corporate and market risk are known to be highly correlated, would this
make the task of evaluating the project’s risk easier or harder? Explain.
Real Options and the Problem of Valuation
According to traditional capital budgeting theory, a project’s value is the NPV of its expected future cash
flows discounted at a rate that reflects the riskiness of those cash flows. It is a once-and-for-all decision
rather like placing money on the table in roulette. A gambler can choose whether to spin the wheel, but once
the wheel has been spun, nothing can be done to influence the outcome. Once the game begins, the outcome
depends purely on chance, and no skill is involved.
Contrast roulette with a game such as poker. Capital budgeting decisions have more in common with
poker than roulette because (1) chance varies throughout the life of the project as with poker, and (2) as the
poker player can respond to cards dealt during the game, so managers can respond to changing market conditions and to competitors’ actions. Opportunities to respond to changing circumstances are called managerial options (because they give managers a chance to influence the outcome of a project), strategic options
(because they are often associated with large, strategic projects rather than routine maintenance projects),
and embedded options (because they are a part of the project). The general term is real options to differentiate them from financial options because they involve real assets (buildings and machinery), rather than
financial assets (shares and bonds).
One of the features of the traditional NPV model without options is that it can be modelled as a binomial
tree. At each chance node the price can go up or down and in the NPV model this is determined like the roulette wheel by pure chance. Looking at projects in general, one can say that the behaviour of a project’s value
may well look very much like chance increases or falls, so the roulette model would appear to be a good description. If sales are higher than expected the value of the project will increase; or if costs are higher than expected
the project’s value will decrease and so on. Value is therefore modelled as in Figure 11-3 as moving from circle
to circle (the chance nodes). The movement is random because a movement up or down depends on whether
actual events are better or worse than expected; our educated guesses are randomly optimistic or pessimistic.
If we are to add management decisions taken during the project (the real options), then every node also
has a decision node (the square boxes) as in Figure 11-3. These decisions are not the minor operational decisions needed to increase sales because of demand, but are decisions that require significant investment or
disinvestment being the managerial, strategic or operational decisions as outlined above.
Chapter 11
Capital Budgeting: Evaluation of Cash Flows 293
F i g ure 11-3
The Role of Real Options in Capital Investment Projects
Chance node
0a Decision node (real option)
In each box of Figure 11-3 is a small set of decisions that managers might want to implement. In practical
terms this might be a decision to open up a second project or it might be a decision to close the project or
invest in an advertising campaign. For all projects at the start, there is the decision as to whether to go ahead
with the project or to delay the project. These decisions have the potential to add value to the project. An
investment that can be easily closed down if the value of the project falls below a certain level is more valuable than a project where abandonment would be very expensive; but how much more valuable? A car production company that invests in a production line that enables the company to switch to new cars is worth more
than a project with an inflexible production line even though in retrospect that facility may never have been
used; but again, how do we value such a possibility?4
These options have a value that depends on the value of the project at any particular point in time. At point
1a in Figure 11-3 the option to abandon is less valuable than if the project value fell to 1b in Figure 11-3. The
value of abandonment will fall further if the value of the project rises to point 2a simply because the option is
less likely to be taken up. As you may suspect, the valuation problem is very similar to financial options where
the value of the option also depends on the price of the share or currency, for example, as the underlying asset.
The implications for valuing projects are significant. The value of a project should be the net present value
plus the value of options associated with the project. This implies that a project may have a negative net present value but the options available to the project post investment means that the project is worthwhile.
The question that arose in the literature was whether one can apply the financial Black–Scholes valuation
model to real investments. This is where theory and practice diverge. A large theoretical literature showing the
possibilities of real options developed from Stuart Myers’ original paper5 in the late 1980s. Surveys of practice
however showed that companies were not using option valuation techniques. In its place was what was sometimes
termed ‘real options reasoning’ 6 that grew out of papers such as Miller and Waller.7 This state of affairs contrasted greatly with the financial option modelling where the Black–Scholes model was greeted with enthusiasm.
See Linebaugh, K. (2008) ‘Honda’s flexible plants provide edge’, Wall Street Journal, 23 September, p. B1.
Myers, S. C. (1984) ‘Finance theory and financial strategy’, Interfaces 14(1):126–37.
Verbeeten, F. (2006) ‘Do organizations adopt sophisticated capital budgeting practices to deal with uncertainty in the investment
decision? A research note’, Management Accounting Research 17(1):106–20.
Miller, K. D. and Waller, H. G. (2003) ‘Scenarios, real options and integrated risk management’ Long Range Planning 36(1): 93–107.
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In fact Myers himself from the outset suggested that the precision of the financial option applied to market prices
would not be possible. Estimating the benefit of opening up a second store if the first store achieves a certain level
of profitability or the costs of abandonment if a project is unsuccessful involves a degree of uncertainty for most
projects that is greater than can be estimated8. Myers suggested the following as a compromise: 9
Smart managers apply the following check. They know that all projects have zero NPV in long-run competitive equilibrium. Therefore, a positive NPV must be explained by a short-run deviation from equilibrium or by some permanent competitive advantage. If neither explanation applies, the positive NPV is suspect. Conversely, a negative NPV
is suspect if a competitive advantage or short-run deviation from equilibrium favours the project. In other words,
smart managers do not accept positive (or negative) NPVs unless they can explain them.
The main contribution of real options has been to understand that negative NPVs in particular are not necessarily unprofitable. Managers take on projects for their ‘wider’ potential value not necessarily their immediate
returns. This rationale was especially clear at the start of this century when firms spent large sums on developing
computer systems that appeared to be little better than existing systems. It was nevertheless accepted that these
systems would rapidly develop and that upgrades would not be possible without an existing system. It might have
been argued that there is an option to delay or in game theory terms there is second mover advantage but both
considerations are very much additional to NPV. The following sections consider these wider issues.
Investment Timing Options
Conventional NPV analysis implicitly assumes that projects either will be accepted or rejected, which implies
they will be undertaken now or never. In practice, however, companies sometimes have a third choice—delay
the decision until later, when more information is available. Such investment timing options can dramatically affect a project’s estimated profitability and risk.
Keep in mind, though, that the option to delay is valuable only if it more than offsets any harm that might
result from delaying. For example, while one company delays, some other company might establish a loyal
customer base that makes it difficult for the first company to enter the market later. The option to delay
is usually most valuable to firms with proprietary technology, patents, licences or other barriers to entry,
because these factors lessen the threat of competition. The option to delay is valuable when market demand is
uncertain, but it is also valuable during periods of volatile interest rates, because the ability to wait can allow
firms to delay raising capital for a project until interest rates are lower.
Where competitor reaction is a factor, the problem is more one of strategy. Delay can be seen as second-mover
advantage and not delaying as first-mover advantage. This is more a gaming problem—as in tennis there is firstmover advantage (the serve); in golf, possibly a second-mover advantage (seeing the state of the green).
Growth Options
A growth option allows a company to increase its capacity if market conditions are better than expected.
There are several types of growth options. One lets a company increase the capacity of an existing product
line. A ‘peaking unit’ power plant illustrates this type of growth option. Such units have high variable costs
and are used to produce additional power only if demand, thus prices, are high.
The second type of growth option allows a company to expand into new geographic markets. Many companies are investing in China, Eastern Europe and Russia even though standard NPV analysis produces negative
NPVs. However, if these developing markets really take off, the option to open more facilities could be valuable.
The third type of growth option is the opportunity to add new products, including complementary products and successive ‘generations’ of the original product. Car manufacturers are losing money on their first
electric cars, but the manufacturing skills and consumer recognition those cars will provide should help turn
subsequent generations of electric cars into money makers.
See Brealey, R. A., Myers, S. C. and Allen, F. (2008) ‘Real options’, Journal of Applied Corporate Finance 20(4):58–71. A book that
is the model of clarity is: Kodukula, P. and Papudesu, C. (2006) Project Valuation Using Real Options—A Practitioner’s Guide,
J. Ross Publishing.
Myers, S. C. (1984) ‘Finance theory and financial strategy’, Interfaces 14(1): 126–37.
Chapter 11
Capital Budgeting: Evaluation of Cash Flows 295
Abandonment Options
Consider the value of an abandonment option. Standard discounted cash flow analysis assumes that a project’s assets will be used over a specified economic life. But even though some projects must be operated over
their full economic life—in spite of deteriorating market conditions and hence lower than expected cash
flows—other projects can be abandoned. Smart managers negotiate the right to abandon if a project turns
out to be unsuccessful as a condition for undertaking the project.
Note, too, that some projects can be structured so that they provide the option to reduce capacity or temporarily suspend operations. Such options are common in the natural resources industry, including mining,
oil and timber, and they should be reflected in the analysis when NPVs are being estimated.
Flexibility Options
Many projects offer flexibility options that permit the firm to alter operations depending on how conditions change during the life of the project. Typically, either inputs or outputs (or both) can be changed.
BMW’s Spartanburg (South Carolina) car assembly plant provides a good example of output flexibility.
BMW needed the plant to produce sports coupés. If it built the plant configured to produce only these
vehicles, the construction cost would be minimized. However, the company thought that later on it
might want to switch production to some other vehicle type, and that would be difficult if the plant were
designed just for coupés. Therefore, BMW decided to spend additional funds to construct a more flexible plant: one that could produce different types of vehicles should demand patterns shift. Sure enough,
things did change. Demand for coupés dropped a bit and demand for sports utility vehicles (SUVs) soared.
But BMW was ready, and the Spartanburg plant began to produce hot-selling SUVs. The plant’s cash flows
were much higher than they would have been without the flexibility option that BMW ‘bought’ by paying
more to build a more flexible plant.
Electric power plants provide an example of input flexibility. Utilities can build plants that generate electricity by burning coal, oil or natural gas. The prices of those fuels change over time in response to events
in the Middle East, changing environmental policies, and weather conditions. Some years ago, virtually all
power plants were designed to burn just one type of fuel, because this resulted in the lowest construction
costs. However, as fuel cost volatility increased, power companies began to build higher-cost but more flexible plants, especially ones that could switch from oil to gas and back again depending on relative fuel prices.
Options give a formal structure within which these decisions can be taken.
Phased Decisions
Up to this point we have focused primarily on techniques for estimating a project’s risk. Although this is an
integral part of capital budgeting, managers are just as interested in reducing risk as in measuring it. One way
to reduce risk is to structure projects so that expenditures can be made in stages over time rather than all at
once. This gives managers the opportunity to re-evaluate decisions using new information and then to either
invest additional funds or terminate the project. This is in effect structuring a project in order to introduce as
many real options as possible. By taking decisions that otherwise might have been made at the start, one can
more closely match the evolving circumstances and hence reduce the risk. This type of analysis involves the
use of decision trees as in Figure 11-3. Originally, all the nodes on the tree were chance nodes, the probability
of a rise or a fall in value. We have stated that options are conditional decisions that depend on the price of
the underlying asset. This makes them decision nodes that can be more or less decided in advance such as in
‘if the value of the project rises we will think of expansion’. Real options are phased decisions.
Valuing Real Options
A full treatment of real option valuation is beyond the scope of this chapter; but we can nevertheless show
how real options can be valued with examples of sufficient detail for our purposes.
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Valuing Real Options Using Risk-Neutral Probabilities
F i g ure 11- 4
Valuing a Real Option for Salford plc Using Risk-Neutral Probabilities (Four Year Call Option: Strike
Price 145, Present Value 80, Volatility 30 per cent, Risk-Free Rate 5 per cent)
European Call
Risk-free rate 5%
Strike = 145
Volatility 30%
Spot = 80
Term = 4 years
228.6121 179.4160
161.1002 90.6838 178.0433
113.5254 44.0181 125.4650 33.0433
20.7773 88.4137 13.3760 97.7122
18 9.6084
5.4146 68.8566
2.1919 48.5225
0.0000 53.6256
0.0000 37.7893
0.0000 29.4304
24 Log normal tree continuous rates: the basis of the normal tree
25 up = 0.3
down = (0.3)
risk-free rate = 0.05
32 4.3820
First, consider the call option in Figure 11-4 which is a project by Salford plc. We analyse it as follows:
Step 1:
Step 2:
Create the tree in log form (Figure 11-4 row 24 to 36). Start at I32: ln(80) 5 4.3820 the log normal
(ln) of the spot price at the beginning of the first year. Along row 32 each year (the ‘trunk’ of the
tree) the value of the project increases by the risk-free rate of 5 per cent continuous, so 4.3820 1
0.5 5 4.4320 for the first year and 4.4820 54.3820 1 0.05 1 0.05 for the second year and so on.
A risk-neutral investor expects the risk-free rate of return. An increase in value of the project is an
addition of 0.3 from the central value (row 32) by the number of ‘steps’; a decrease is a deduction
of 0.3 in similar fashion. So 4.7320 5 4.4320 1 0.3 (one up step), 3.6320 5 4.5320 2 0.3 3 3
(three down steps), count the net number of up or down steps from the ‘trunk’ figure for that year.
These rates and changes are on a continuous basis and is the basic model of price movement of the
NPV model.
Convert the log values to euro. These are the black numbers from row 13 to row 22. Thus
324.4160 5 e5.7820 and 178.0433 5 e5.1820 and so on throughout the tree.
Chapter 11
Step 3:
Step 4:
Capital Budgeting: Evaluation of Cash Flows 297
Now that we have the basic tree, we can apply the option payoffs to the tree. The strike price is 145
so the call will pay by the amount by which the value of the project will exceed 145 in year 4. There
are two instances: should the value of the project reach 178.0433 the payoff will be 178.0433 2 145
5 33.0433 and should the price reach 324.4160 the payoff will be 324.4160 2 145 5 179.4160.
Value the present value of the payoffs in step 3 (and hence the option’s value) by rollback. We start
at the far end of the tree and work leftwards step by step. First we calculate the risk-neutral probabilities of an increase or a decrease. Because our investor is risk neutral these adjusted probabilities
are the same throughout the tree, no matter the change in the ups and downs created by the option.
Applying Equation 9.2 to any of the ups and downs, the risk-neutral probabilities are:
5 1.4191
down-factor (for example) 5
5 0.7788
e0.05 2 0.7788
risk-neutral up-probability 5
5 0.4256
1.4191 2 0.7788
risk-neutral down-probability 5 1 2 0.4256 5 0.5744
up-factor (for example) 5
Recall from Chapter 4 that e0.05 is approximately 1.05, or 1 plus the interest rate of 5 per cent on a continuous basis. We can now apply these probabilities to the payoffs and discount back at the risk-free rate. Thus
1 33.0433 3 0.5744
90.6838 5 179.4160 3 0.4256e0.05
with a small rounding error of 0.0060; the spreadsheet figures are
exact. We ­continue this process until we arrive at year 1 where we discount back 20.7773 and 2.1919 in simi1 62.3041 3 0.5744
lar f­ ashion to get the option valuation of 9.6084 5 113.5254 3 0.4256e0.05
Although this may appear complicated, once set up on a spreadsheet, variations can be simply applied.
The call value of 9.6804 is approximate in the sense that if we had more steps of say 48 months instead
of the equivalent four years then our answer would be 8.7837. The Black–Scholes continuous version (an
almost infinite number of steps) would be 8.74701. The Figure 11-4 solution is therefore an approximation of
the more accurate Black–Scholes valuation. In context, the difference is not that great as the Black–Scholes
version adjusts the approximate value as a percentage of the present value by only 1 per cent. For practical
applications one would be content with this approximate valuation because, as we will now discuss, greater
inaccuracies lie elsewhere.
Real Options and Project Value: Reassessment
Now that we have a method of valuing real options, we can consider the relevance to project valuation. We
have viewed Figure 11-4 as a project with a present value of €80 000. Let us say that the investors choose to
review and possibly sell the project in four years’ time. If the value of the project has risen to 324.4160 (as in
Figure 11-4) it is estimated that further investments will be seen as attractive to the value of 179.4160 and if the
value of the project is 178.0433 then further expansion will be possible to the value of 33.0433. This is equivalent to the call option in Figure 11-4. In other words, these options add some 12 per cent to the value of the
project. Note that the NPV of the project could be negative, as long as it is not a greater loss than 9.6084, the
value of the project plus the option will be positive and worth taking on. We noted earlier that option values
of investing in computer systems encouraged firms at the start of the century to invest heavily in projects that
seemed to be heavy loss makers.
Combining options with the basic binomial tree enables businessmen to adjust the outcomes to include
the decisions that they are likely to take. It may be, for example, that they feel that the assets of the company
in four years’ time will be worth €60; that would be like a put option with a strike or exercise price of 60
and would increase the present value of the investment from 80 to 84.4093 (calculations not shown). Taken
together, the value of the two options would be 4.4093 1 9.6084 5 14.0177 (this is known as a strangle—a
purchased call and a purchased put at two separate strike prices). Generally, these adjustments are an opportunity to adjust the binomial tree to a more realistic set of outcomes.
298 Part 4
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Adding real option outcomes to the NPV as a full valuation of a project has led some to argue that any
project can have a positive NPV now—all one has to do is to dream up some contingent outcome! It should be
remembered that this is a normative analysis—it is a logical treatment of decisions after the initial go-ahead
limited by assumptions, one of which is that estimates are genuine best estimates!
Given the range of adjustments to the basic NPV calculation, there is clearly a valuation problem. One
response is to argue for an essentially subjective approach and see the contribution of real options as enhancing the subjective estimation rather than the numerical explanation. This has given rise to the idea of ‘real
options reasoning’.10 An alternative approach is to see real options as an additional technique and by implication one that requires a higher level of mathematical ability than net present value. A third response and the
one suggested by Myers (see footnote 9) is that NPV should be treated with extra caution. The recommendations can be confusing, for example, Merton and Bodie11 end their text on finance with: ‘Virtually all future
investment opportunities can be viewed as call options because firms can almost always wait before making
their initial outlay and decide not to proceed with it ... Conventional NPV understates the value of the project
because it ignores the option’s time value.’ Rather than just being cautious, we can now use the real option
model to aid the decision.
We have determined that NPV does not include post-investment decisions; real options provides a solution, albeit problematic. There is, however, another assumption. A project assumes that there is no specific
competitor reaction to the project. Any reaction is fully expressed in the estimate of risk at the start of the
project and is not dependent on decisions by a competitor. We turn to this problem in the next section.
S E L F -T E S T
Explain the relevance of the following statement: ‘Capital budgeting decisions have more in common
with poker than roulette.’
What are managerial options? Strategic options?
Identify some different types of real options and differentiate among them.
Competitors and Game Theory
Consider Table 11-3, which uses the outcomes of a project in NPV terms in a game-setting scenario with a
competitor. The decision is to invest or not to invest, only this time the outcome depends on the reaction of
a competitor.
We assume that the matrix is known to both parties before investment, so there is no restriction on information. Whatever B does, A is better off investing. If B does not invest then A is 255 better off (505 2 250 5 255);
if B does invest then A is 145 better off (25 2 (150) 5 145). By similar reasoning and similar numbers (which
need not necessarily be the case), B is better off investing than not investing. So if they both invest, the outcome will be the bottom right hand values of (25, 25). The outcome is therefore that to maximize their future
expected wealth they should both invest in a project yielding a negative NPV! Not only that, if they were both to
collude and solemnly agree not to invest, they would both be better off!! They would have to agree in this way
because if any party broke the agreement they would profit with an NPV of 505 and the other party would
lose 150. This particular scenario is one of many scenarios that enrich the problem of choosing a course of
Game theory highlights the fact that in ordinary NPV analysis we assume that no competitor either
individually or collectively can have an effect on a decision as to whether to invest or not. Table 11-3 is an
Bulan, L. T. (2005) ‘Real options, irreversible investment and firm uncertainty: New evidence from U.S. firms’, Review of Financial Economics 14(3-4):255279; Miller, K. D. and Waller, H. G. (2003) ‘Scenarios, real options and integrated risk management’ Long
Range Planning 36(1):932107; Triantis, A. and Borison, A. (2001) ‘Real options: state of practice’, Journal of Applied Corporate Finance
14(2):8224; Verbeeten, F. H. M. (2006) ‘Do organizations adopt sophisticated capital budgeting practices to deal with uncertainty in
the investment decision? A research note’, Management Accounting Research 17(1):106–20.
Bodie, Z. and Merton, R. (2000). Finance, Englewood Cliffs, NJ: Prentice Hall, p. 434.
Chapter 11
Capital Budgeting: Evaluation of Cash Flows 299
table 11-3
A Game Theory Approach to Investment
Firm B
Firm A
Do not invest
Do not invest
Note: NPV is reported as (NPVA, NPVB ) so (505,2150) means an NPV of 505 for Firm A and a negative NPV of 150 for Firm B.
instance of the Prisoner’s dilemma which we said earlier could explain why firms invested such amounts in
computer systems when there seemed little prospect of a profit. The investment losses in Table 11-3 could be
2100 and the outcome would still be the same. In other words we do not have to be too accurate in our NPV
calculations to come to a decision.
Project selection in a competitive scenario is much more complex than our simple NPV rule—surveys of
investment selection methods show that firms use a wide variety of techniques.12 Little wonder that businessmen and businesswomen do not regard NPV as being a wholly satisfactory solution to project selection—they
are right. In a sense, theory has caught up with practice, and the contribution of theory is to lend greater clarity to what was otherwise very much an intuitive exercise.
Conclusions on the Status of NPV
There was a time when NPV had the status of being a ‘grand narrative’, a general valuation rule for all future
cash flows whether a share, bond or project. The rule was: invest if the NPV is positive; otherwise do not
invest. Real options and game theory have served as a critique of the simple NPV approach. It might have
been hoped that, as well as providing a critique, these methods would also offer an alternative model of
investment in the cases where these methods identified weaknesses in the NPV approach. This has yet to
happen. The binomial model of real options analysis is promising but, as in the early days of advocacy of
NPV in the 1950s, it is far from a practical implementation. Game theory models are even further from
implementation, and are commonly not even addressed in texts on finance; yet their relevance is simple to
establish. All that can be agreed is that the general applicability of NPV is no longer tenable.
Like all valuation methods, one has to be clear about when NPV is and is not the principal valuation model.
It should be remembered that it has been in use at least since the Middle Ages and will continue to be one of the
principal pricing models in finance. The developments discussed in this chapter do no more than qualify its
use for certain applications. In general:
• For investments where the size and timing of future repayments are part of a contractual agreement,
NPV is the principal valuation model.
• Where there are significant outcomes that depend on the timing or the value of the investment, real options
should be added to the NPV model either as a subjective estimate or as part of the modelling process.
• Where the outcome depends significantly on the reactions of competitors, then game theory scenarios
are relevant.
It should be stressed that real options type analysis and game theory are additional to NPV analysis—
they do not exist independently. It may nevertheless be the case that post-investment decisions and competitor reactions are so significant that NPV analysis can be approximate without greatly affecting the
decision—this aspect was noted in the example based on Table 11-3. A thorough NPV calculation is itself an
expensive exercise in terms of managerial time.
Arnold, G. C. and Hatzopoulos, P. D. (2001) ‘The theory–practice gap in capital budgeting: evidence from the United Kingdom’,
Journal of Business Finance and Accounting 27(5-6):603–26.
300 Part 4
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In this chapter we have developed a framework for analysing a project’s cash flows and its risk. The key
concepts covered are listed below.
Capital budgeting is the process of analysing potential projects. Capital budgeting decisions are probably
the most important ones that managers must make.
The IRR is defined as the discount rate that forces a project’s NPV to equal zero. The project should be
accepted if the IRR is greater than the cost of capital.
The NPV and IRR methods make the same accept–reject decisions for independent projects, but if projects are mutually exclusive then ranking conflicts can arise. In such cases, the NPV method should
generally be relied upon.
It is possible for a project to have more than one IRR if the project’s cash flows change signs more than once.
Unlike the IRR, a project never has more than one modified IRR (MIRR). MIRR requires finding the
terminal value (TV) of the cash inflows, compounding them at the firm’s cost of capital, and then
determining the discount rate that forces the present value of the TV to equal the present value of the
The profitability index is calculated by dividing the present value of cash inf lows by the initial
cost, so it measures relative profitability—that is, the amount of the present value per dollar of
The regular payback period is defined as the number of years required to recover a project’s cost. The
regular payback method has three flaws: it ignores cash flows beyond the payback period, it does not
consider the time value of money, and it doesn’t give a precise acceptance rule. The payback method
does, however, provide an indication of a project’s risk and liquidity, because it shows how long the
invested capital will be tied up.
Discounted payback is similar to regular payback except that it discounts cash flows at the project’s
cost of capital. It considers the time value of money, but it still ignores cash f lows beyond the payback period.
If mutually exclusive projects have unequal lives, it may be necessary to adjust the analysis to put the
projects on an equal-life basis. This can be done using the replacement chain (common life) approach or
the equivalent annual annuity approach.
The most important (and most difficult) step in analysing a capital budgeting project is estimating the
incremental after-tax cash flows the project will produce.
A project’s net cash flow is different from its accounting income. Project net cash flow reflects (1) cash
outlays for fixed assets, (2) sales revenues, (3) operating costs, (4) the tax shield provided by depreciation
and (5) cash flows due to changes in net working capital. A project’s net cash flow does not include interest payments, because they are accounted for by the discounting process. If we deducted interest and
then discounted cash flows at the WACC, this would double-count interest charges.
In determining incremental cash flows, opportunity costs (the cash flows forgone by using an asset)
must be included, but sunk costs (cash outlays that have been made and that cannot be recouped) are not
included. Any externalities (effects of a project on other parts of the firm) should also be reflected in the
analysis. Externalities can be positive or negative and may be environmental.
Cannibalization is an important type of externality that occurs when a new project leads to a reduction
in sales of an existing product.
Price level changes (inflation or deflation) must be considered in project analysis. The best procedure is
to build expected price changes into the cash flow estimates. Recognize that output prices and costs for a
product can decline over time even though the economy is experiencing inflation.
The chapter illustrates both expansion projects, in which the investment generates new sales, and
replacement projects, where the primary purpose of the investment is to operate more efficiently and
thus reduce costs.
Chapter 11
Capital Budgeting: Evaluation of Cash Flows 301
We discuss three types of risk: stand-alone risk, corporate (or within-firm) risk, and market (or beta)
risk. Stand-alone risk does not consider diversification at all; corporate risk considers risk among the
firm’s own assets; and market risk considers risk at the shareholder level, where shareholders’ own diversification is considered.
Risk is important because it affects the discount rate used in capital budgeting; in other words, a project’s WACC depends on its risk.
Assuming the CAPM holds true, market risk is the most important risk because (according to the CAPM)
it is the risk that affects share prices. However, usually it is difficult to measure a project’s market risk.
Corporate risk is important because it influences the firm’s ability to use low-cost debt, to maintain
smooth operations over time, and to avoid crises that might consume management’s energy and disrupt
its employees, customers, suppliers, and community. Also, a project’s corporate risk is generally easier to
measure than its market risk, and, because corporate and market risks are generally thought to be correlated, corporate risk can often serve as a proxy for market risk.
Stand-alone risk is easier to measure than either market or corporate risk. Also, most of a firm’s projects’
cash flows are correlated with one another, and the firm’s total cash flows are correlated with those of
most other firms. These correlations mean that a project’s stand-alone risk generally can be used as a
proxy for hard-to-measure market and corporate risk. As a result, most risk analysis in capital budgeting
focuses on stand-alone risk.
Sensitivity analysis is a technique that shows how much a project’s NPV will change in response to a
given change in an input variable, such as sales, when all other factors are held constant.
Scenario analysis is a risk analysis technique in which the best- and worst-case NPVs are compared with
the project’s base-case NPV.
Monte Carlo simulation is a risk analysis technique that uses a computer to simulate future events and
thereby estimate a project’s profitability and riskiness.
The risk-adjusted discount rate, or project cost of capital, is the rate used to evaluate a particular project.
It is based on the corporate WACC, a value that is increased for projects that are riskier than the firm’s
average project and decreased for less risky projects.
A decision tree shows how different decisions during a project’s life can affect its value.
A staged decision tree divides the analysis into different phases. At each phase a decision is made either
to proceed or to stop the project. These decisions are represented on the decision trees by circles and are
called decision nodes.
Opportunities to respond to changing circumstances are called real options or managerial options because
they give managers the option to influence the returns on a project. They are also called strategic options
if they are associated with large, strategic projects rather than routine maintenance projects. Finally, they
are also called ‘real’ options because they involve ‘real’ (or ‘physical’) rather than ‘financial’ assets. Many
projects include a variety of these embedded options that can dramatically affect the true NPV.
An investment timing option involves the possibility of delaying major expenditures until more information on likely outcomes is known. The opportunity to delay can dramatically change a project’s
estimated value.
A growth option occurs if an investment creates the opportunity to make other potentially profitable
investments that would not otherwise be possible. These include (1) options to expand the original project’s output, (2) options to enter a new geographical market, and (3) options to introduce complementary products or successive generations of products.
An abandonment option is the ability to discontinue a project if the operating cash flow turns out to be
lower than expected. It reduces the risk of a project and increases its value. Instead of total abandonment, some options allow a company to reduce capacity or temporarily suspend operations.
A flexibility option is the option to modify operations depending on how conditions develop during a
project’s life, especially the type of output produced or the inputs used.
Game theory introduces the effect of reaction to the decision as to whether to invest or not. It offers
plausible counter examples to the simple NPV rule to invest only if there is a positive NPV.
302 Part 4
Projects and Their Valuation
Answers to questions (11-12) to (11-34) appear in the Appendix.
( 11-1)
Define each of the following terms:
a. capital budgeting; regular payback period; discounted payback period
b. independent projects; mutually exclusive projects
c. discounted cash flow techniques; net present value (NPV) method; internal rate
of return (IRR) method; profitability index (PI)
d. modified internal rate of return (MIRR) method
e. NPV profile; crossover rate
f. non-normal cash flow projects; normal cash flow projects; multiple IRRs
g. reinvestment rate assumption
h. replacement chain; economic life; capital rationing; equivalent annual annuity
i. project cash flow; accounting income
j. incremental cash flow; sunk cost; opportunity cost; externality; cannibalization;
expansion project; replacement project
k. net operating working capital changes; salvage value
l. stand-alone risk; corporate (within-firm) risk; market (beta) risk
m. sensitivity analysis; scenario analysis; Monte Carlo simulation analysis
n. risk-adjusted discount rate; project cost of capital
o. decision tree; staged decision tree; decision node; branch
p. real options; managerial options; strategic options; embedded options
q. investment timing option; growth option; abandonment option; flexibility option
( 11-2)
Operating cash flows, rather than accounting profits, are used in project analysis.
What is the basis for this emphasis on cash flows as opposed to net income?
Why is it true, in general, that a failure to adjust expected cash flows for expected
inflation biases the calculated NPV downward?
Explain why sunk costs should not be included in a capital budgeting analysis but
opportunity costs and externalities should be included.
Explain how net operating working capital is recovered at the end of a project’s life
and why it is included in a capital budgeting analysis.
How do simulation analysis and scenario analysis differ in the way they treat very bad
and very good outcomes? What does this imply about using each technique to evaluate project riskiness?
Why are interest charges not deducted when a project’s cash flows are calculated for
use in a capital budgeting analysis?
Most firms generate cash inflows every day, not just once at the end of the year. In
capital budgeting, should we recognize this fact by estimating daily project cash flows
and then using them in the analysis? If we do not, will this bias our results? If it does,
would the NPV be biased up or down? Explain.
What are some differences in the analysis for a replacement project versus that for a
new expansion project?
Distinguish among beta (or market) risk, within-firm (or corporate) risk, and standalone risk for a project being considered for inclusion in a firm’s capital budget.
In theory, market risk should be the only ‘relevant’ risk. However, companies focus
as much on stand-alone risk as on market risk. What are the reasons for the focus on
stand-alone risk?
( 11-3)
( 11- 4 )
( 11-5 )
( 11- 6 )
( 11-7 )
(11- 8 )
( 11-9)
( 11-10 )
( 11-11)
Chapter 11
( 11-1 2)
Capital Budgeting: Evaluation of Cash Flows 303
Project analysis: You are a financial analyst for the Hittle Company. The director of
capital budgeting has asked you to analyse two proposed capital investments, Projects
X and Y. Each project has a cost of $10 000, and the cost of capital for each is 12 per cent.
The projects’ expected net cash flows are as follows:
Expected net cash flows
Project X
Project Y
2$10 000
2$10 000
6 500
3 500
3 000
3 500
3 000
3 500
1 000
3 500
a. Calculate each project’s payback period, net present value (NPV), internal
rate of return (IRR), modified internal rate of return (MIRR), and profitability
index (PI).
b. Which project or projects should be accepted if they are independent?
c. Which project should be accepted if they are mutually exclusive?
d. How might a change in the cost of capital produce a conflict between the NPV
and IRR rankings of these two projects? Would this conflict exist if r were 5 per
cent? (Hint: Plot the NPV profiles.)
e. Why does the conflict exist?
( 11-14 )
Unequal lives: Shao Airlines is considering the purchase of two alternative planes.
Plane A has an expected life of five years, will cost $100 million, and will produce
net cash flows of $30 million per year. Plane B has a life of ten years, will cost $132
million, and will produce net cash flows of $25 million per year. Shao plans to serve
the route for only ten years. Inflation in operating costs, airplane costs, and fares is
expected to be zero, and the company’s cost of capital is 12 per cent. By how much
would the value of the company increase if it accepted the better project (plane)?
What is the equivalent annual annuity for each plane?
Project analysis: You have been asked by the president of the Farr Construction
Company to evaluate the proposed acquisition of a new earth mover. The mover’s
basic price is €50 000, and it would cost another €10 000 to modify it for special use.
Assume that the mover is depreciated using the U.S. Modified Accelerated Cost
Recovery System (MACRS) for three years being depreciation calculated as a percentage of the cost for year one 33.33%, year two 44.45%, year three 14.81% and year
four 7.41% (purchase is approximated as being half way through the first year hence
the fourth year, note that these percentages sum to 100 per cent). Also, assume that it
would be sold after three years for €20 000, and that it would require an increase in
net working capital (spare parts inventory) of €2000 at the start of the project. This
working capital will be recovered at year 3. The earth mover would have no effect on
revenues, but it is expected to save the firm €20 000 per year in before-tax operating
costs, mainly labour. The firm’s marginal federal-plus-state tax rate is 40 per cent.
What are the year-0 cash flows?
What are the operating cash flows in years 1, 2 and 3?
What are the additional (nonoperating) cash flows in year 3?
If the project’s cost of capital is 10 per cent, should the earth mover be purchased?
304 Part 4
Projects and Their Valuation
( 11-15 )
Corporate risk analysis: The staff of Porter Manufacturing has estimated the following net after tax cash flows and probabilities for a new manufacturing process:
Net after-tax cash flows
p 5 0.2
p 5 0.6
p 5 0.2
minus € 100 000
minus € 100 000
minus €100 000
20 000
30 000
40 000
20 000
30 000
40 000
20 000
30 000
40 000
20 000
30 000
40 000
20 000
30 000
40 000
20 000
30 000
Line 0 gives the cost of the process, Lines 1–5 give operating cash flows, and Line 5*
contains the estimated salvage values. Porter’s cost of capital for an average-risk
project is 10 per cent.
a. Assume that the project has average risk. Find the project’s expected NPV.
(Hint: Use expected values for the net cash flow in each year.)
b. Find the best-case and worst-case NPVs. What is the probability of occurrence of
the worst case if the cash flows are perfectly dependent (perfectly positively correlated) over time? If they are independent over time?
c. Assume that all the cash flows are perfectly positively correlated. That is, assume
there are only three possible cash flow streams over time—the worst case, the
most likely (or base) case, and the best case—with respective probabilities of 0.2,
0.6 and 0.2. These cases are represented by each of the columns in the table. Find
the expected NPV, its standard deviation, and its coefficient of variation.
( 11-16 )
Investment outlay: Talbot Industries is considering launching a new product. The new
manufacturing equipment will cost €17 million, and production and sales will require
an initial €5 million investment in net operating working capital. The company’s tax
rate is 40 per cent.
a. What is the initial investment outlay?
b. The company spent and expensed €150 000 on research related to the new product
last year. Would this change your answer? Explain.
c. Rather than build a new manufacturing facility, the company plans to install the
equipment in a building it owns but is not now using. The building could be sold
for €1.5 million after taxes and real estate commissions. How would this affect
your answer?
( 11-17 )
Operating cash flow: The financial staff of Cairn Communications has identified the
following information for the first year of the roll-out of its new proposed service:
Projected sales
€ 18 million
Operating costs (not including depreciation)
€ 9 million
€ 4 million
Interest expense
€ 3 million
The company faces a 40 per cent tax rate. What is the project’s operating cash flow for
the first year (t 5 1)?
Chapter 11
( 11-1 8 )
( 11-19)
( 11-2 0 )
Capital Budgeting: Evaluation of Cash Flows 305
Net salvage value: Allen Air Lines must liquidate some equipment that is being
replaced. The equipment originally cost €12 million, of which 75 per cent has been
depreciated. The used equipment can be sold today for €4 million, and its tax rate is
40 per cent. What is the equipment’s after-tax net salvage value?
Replacement analysis: Although the Chen Company’s milling machine is old, it is still
in relatively good working order and would last for another ten years. It is inefficient
compared to modern standards, though, and so the company is considering replacing
it. The new milling machine, at a cost of €110 000 delivered and installed, would also
last for ten years and would produce after-tax cash flows (labour savings and depreciation tax savings) of €19 000 per year. It would have zero salvage value at the end of its
life. The firm’s WACC is 10 per cent, and its marginal tax rate is 35 per cent. Should
Chen buy the new machine?
Depreciation methods: Wendy’s boss wants to use straight-line depreciation for the
new expansion project because he said it will give higher net income in earlier years
and give him a larger bonus. The project will last four years and requires €1700 000
of equipment. The company could use either straight line or the three-year MACRS
(see question 11-14) accelerated method. Under straight-line depreciation, the cost of
the equipment would be depreciated evenly over its four-year life (ignore the half-year
convention for the straight-line method). The applicable MACRS depreciation rates
are 33.33 per cent, 44.45 per cent, 14.81 per cent and 7.41 per cent. The company’s
WACC is 10 per cent, and its tax rate is 40 per cent.
a. What would the depreciation expense be each year under each method?
b. Which depreciation method would produce the higher NPV, and how much
higher would it be?
c. Why might Wendy’s boss prefer straight-line depreciation?
New-project analysis: The Campbell Company is considering adding a robotic paint
sprayer to its production line. The sprayer’s base price is €1080 000, and it would
cost another €22 500 to install it. The machine falls into the MACRS three-year
class (see question 11-14), and it would be sold after 3 years for €605 000. The
MACRS rates for the first three years are 0.3333, 0.4445 and 0.1481. The machine
would require an increase in net working capital (inventory) of €15 500. The
sprayer would not change revenues, but it is expected to save the firm €380 000 per
year in before-tax operating costs, mainly labour. Campbell’s marginal tax
rate is 35 per cent.
a. What is the year 0 net cash flow?
b. What are the net operating cash flows in years 1, 2 and 3?
c. What is the additional year-3 cash flow (i.e. the after-tax salvage and the return of
working capital)?
d. If the project’s cost of capital is 12 per cent, should the machine be purchased?
( 11-2 2)
New-project analysis: The president of the company you work for has asked you
to evaluate the proposed acquisition of a new chromatograph for the firm’s R&D
department. The equipment’s basic price is €70 000, and it would cost another
€15 000 to modify it for special use by your firm. The chromatograph, which falls into
the MACRS (see question 11-14) three-year class, would be sold after three years for
€30 000. The MACRS rates for the first three years are 0.3333, 0.4445 and 0.1481. Use
of the equipment would require an increase in net working capital (spare parts inventory) of €4000. The machine would have no effect on revenues, but it is expected to
save the firm €25 000 per year in before-tax operating costs, mainly labour.
The firm’s marginal federal-plus-state tax rate is 40 per cent.
306 Part 4
Projects and Their Valuation
( 11-2 3)
What is the year-0 net cash flow?
What are the net operating cash flows in years 1, 2 and 3?
What is the additional (nonoperating) cash flow in year 3?
If the project’s cost of capital is 10 per cent, should the chromatograph be
Inflation adjustments: The Rodriguez Company is considering an average-risk investment in a mineral water spring project that has a cost of €150 000. The project will
produce 1000 cases of mineral water per year indefinitely. The current sales price is
€138 per case, and the current cost per case is €105. The firm is taxed at a rate of 34
per cent. Both prices and costs are expected to rise at a rate of 6 per cent per year.
The firm uses only equity, and it has a cost of capital of 15 per cent. Assume that cash
flows consist only of after-tax profits, because the spring has an indefinite life and
will not be depreciated.
a. Should the firm accept the project? (Hint: The project is a growing perpetuity, so
you must use the constant growth formula to find its NPV.)
b. Suppose that total costs consisted of a fixed cost of €10 000 per year plus variable
costs of €95 per unit and only the variable costs were expected to increase with
inflation. Would this make the project better or worse? Continue to assume that
the sales price will rise with inflation.
( 11-24 )
( 11-2 5 )
( 11-2 6 )
Replacement analysis: The Gilbert Instrument Corporation is considering replacing
the wood steamer it currently uses to shape guitar sides. The steamer has six years of
remaining life. If kept, the steamer will have depreciation expenses of €650 for five
years and €325 for the sixth year. Its current book value is €3575, and it can be sold on
an Internet auction site for €4150 at this time. If the old steamer is not replaced, it can
be sold for €800 at the end of its useful life.
Gilbert is considering purchasing the Side Steamer 3000, a higher-end steamer, which
costs €12 000 and has an estimated useful life of six years with an estimated salvage
value of €1500. This steamer falls into the MACRS five-year class (see question 11-14),
so the applicable depreciation rates are 20.00 per cent, 32.00 per cent, 19.20 per cent,
11.52 per cent, 11.52 per cent and 5.76 per cent. The new steamer is faster and allows
for an output expansion, so sales would rise by €2000 per year; the new machine’s
much greater efficiency would reduce operating expenses by €1900 per year. To support the greater sales, the new machine would require that inventories increase by
€2900, but accounts payable would simultaneously increase by €700. Gilbert’s marginal federal-plus-state tax rate is 40 per cent, and its WACC is 15 per cent. Should it
replace the old steamer?
Replacement analysis: St John’s River Shipyard’s welding machine is 15 years old,
fully depreciated, obsolete, and has no salvage value. However, even though it is
obsolete, it is perfectly functional as originally designed and can be used for quite a
while longer. A new welder will cost €182 500 and have an estimated life of eight years
with no salvage value. The new welder will be much more efficient, however, and
this enhanced efficiency will increase earnings before depreciation from €27 000 to
€74 000 per year. The new machine will be depreciated over its five-year MACRS
recovery period (see question 11-14), so the applicable depreciation rates are 20.00 per
cent, 32.00 per cent, 19.20 per cent, 11.52 per cent, 11.52 per cent and 5.76 per cent.
The applicable corporate tax rate is 40 per cent, and the firm’s WACC is 12 per cent.
Should the old welder be replaced by the new one?
Scenario analysis: Shao Industries is considering a proposed project for its capital budget. The company estimates the project’s NPV is €12 million. This estimate
assumes that the economy and market conditions will be average over the next few
Chapter 11
Capital Budgeting: Evaluation of Cash Flows 307
years. The company’s CFO, however, forecasts there is only a 50 per cent chance that
the economy will be average. Recognizing this uncertainty, she has also performed
the following scenario analysis:
Economic scenario
(11-27 )
Probability of outcome
€270 million
Below average
225 million
12 million
Above average
20 million
30 million
What is the project’s expected NPV, its standard deviation, and its coefficient of
New-project analysis: Madison Manufacturing is considering a new machine that
costs €350 000 and would reduce pre-tax manufacturing costs by €110 000 annually.
Madison would use the three-year MACRS method (see question 11-14) to depreciate
the machine, and management thinks the machine would have a value of €33 000 at the
end of its five-year operating life. The applicable depreciation rates are 33.33 per cent,
44.45 per cent, 14.81 per cent and 7.42 per cent. Working capital would increase by
€35 000 initially, but it would be recovered at the end of the project’s five-year life.
Madison’s marginal tax rate is 40 per cent, and a 10 per cent WACC is appropriate for
the project.
a. Calculate the project’s NPV, IRR, MIRR and payback.
b. Assume management is unsure about the €110 000 cost savings—this figure could
deviate by as much as plus or minus 20 per cent. What would the NPV be under
each of these extremes?
c. Suppose the CFO wants you to do a scenario analysis with different values for the cost
savings, the machine’s salvage value, and the working capital (WC) requirement. She
asks you to use the following probabilities and values in the scenario analysis:
( 11-2 8 )
Cost savings Salvage value
Worst case 0.35
€88 000
€28 000
€40 000
Base case
110 000
33 000
35 000
Best case
132 000
38 000
30 000
Calculate the project’s expected NPV, its standard deviation, and its coefficient of
­variation. Would you recommend that the project be accepted?
Replacement analysis: The Everly Equipment Company’s flange-lipping machine was
purchased five years ago for €55 000. It had an expected life of ten years when it was
bought and its remaining depreciation is €5500 per year for each year of its remaining
life. As the older flange-lippers are robust and useful machines, it can be sold for €20 000
at the end of its useful life.
A new high-efficiency, digitally controlled flange-lipper can be purchased for €120 000,
including installation costs. During its five-year life, it will reduce cash operating
expenses by €30 000 per year, although it will not affect sales. At the end of its useful
life, the high-efficiency machine is estimated to be worthless. MACRS depreciation
will be used (see question 11-14), and the machine will be depreciated over its threeyear class life rather than its five-year economic life, so the applicable depreciation
rates are 33.33 per cent, 44.45 per cent, 14.81 per cent and 7.41 per cent.
308 Part 4
Projects and Their Valuation
The old machine can be sold today for €35 000. The firm’s tax rate is 35 per cent, and
the appropriate WACC is 16 per cent.
a. If the new flange-lipper is purchased, what is the amount of the initial cash flow at
year 0?
b. What are the incremental net cash flows that will occur at the end of years 1–5?
c. What is the NPV of this project? Should Everly replace the flange-lipper?
( 11-2 9)
Replacement analysis: DeYoung Entertainment Enterprises is considering replacing
the latex moulding machine it uses to fabricate rubber chickens with a newer, more
efficient model. The old machine has a book value of €450 000 and a remaining useful
life of five years. The current machine would be worn out and worthless in five years,
but DeYoung can sell it now to a Halloween mask manufacturer for €135 000. The old
machine is being depreciated by €90 000 per year for each year of its remaining life.
The new machine has a purchase price of €775 000, an estimated useful life and
MACRS class life of five years (see question 11-14), and an estimated salvage value of
€105 000. The applicable depreciation rates are 20.00 per cent, 32.00 per cent, 19.20
per cent, 11.52 per cent, 11.52 per cent and 5.76 per cent. Being highly efficient, it is
expected to economize on electric power usage, labour, and repair costs, and, most
importantly, to reduce the number of defective chickens. In total, an annual savings of
€185 000 will be realized if the new machine is installed. The company’s marginal tax
rate is 35 per cent, and it has a 12 per cent WACC.
a. What is the initial net cash flow if the new machine is purchased and the old one
is replaced?
b. Calculate the annual depreciation allowances for both machines, and compute the
change in the annual depreciation expense if the replacement is made.
c. What are the incremental net cash flows in years 1–5?
d. Should the firm purchase the new machine? Support your answer.
e. In general, how would each of the following factors affect the investment decision,
and how should each be treated?
(1) The expected life of the existing machine decreases.
(2) The WACC is not constant but is increasing as DeYoung adds more projects
into its capital budget for the year.
(11-3 0 )
Risky cash flows: The Bartram Pulley Company (BPC) must decide between two mutually exclusive investment projects. Each project costs €6750 and has an expected life of
three years. Annual net cash flows (annual NCF) from each project begin one year after
the initial investment is made and have the following probability distributions:
Net cash flows
Net cash flows
€6 750
€18 000
BPC has decided to evaluate the riskier project at a 12 per cent rate and the less risky
project at a 10 per cent rate.
a. What is the expected value of the annual net cash flows from each project?
b. What is the risk-adjusted NPV of each project?
c. If it were known that project B is negatively correlated with other cash flows of the
firm whereas project A is positively correlated, how would this affect the decision?
Chapter 11
Capital Budgeting: Evaluation of Cash Flows 309
If project B’s cash flows were negatively correlated with gross domestic product
(GDP), would that influence your assessment of its risk?
( 11-31)
Simulation: Singleton Supplies Corporation (SSC) manufactures medical products for
hospitals, clinics, and nursing homes. SSC may introduce a new type of X-ray scanner
designed to identify certain types of cancers in their early stages. There are a number
of uncertainties about the proposed project, but the following data are believed to be
reasonably accurate.
Random numbers
€2 000 000
4 000 000
6 000 000
Project life
Random numbers
3 years
8 years
13 years
Sales in units
Random numbers
Sales price
Random numbers
€13 000
13 500
14 000
Developmental costs
Cost per unit (excluding developmental
Random numbers
€5 000
6 000
7 000
SSC uses a cost of capital of 15 per cent to analyse average-risk projects, 12 per cent
for low-risk projects, and 18 per cent for high-risk projects. These risk adjustments
primarily reflect the uncertainly about each project’s NPV and IRR as measured by
their coefficients of variation. The firm is in the 40 per cent federal-plus-state income
tax bracket.
a. What is the expected IRR for the X-ray scanner project? Base your answer on the
expected values of the variables. Also, assume the after-tax ‘profits’ figure that
you develop is equal to annual cash flows. All facilities are leased, so depreciation
may be disregarded. Can you determine the value of IRR short of actual simulation or complex statistical analysis?
b. Assume that SSC uses a 15 per cent cost of capital for this project. What is the
project’s NPV? Could you estimate NPV without either simulation or a complex
statistical analysis?
310 Part 4
Projects and Their Valuation
c. Show the process by which a computer would perform a simulation analysis for
this project. Use the random numbers 44, 17, 16, 58, 1; 79, 83, 86; and 19, 62, 6 to
illustrate the process with the first computer run. Calculate the first-run NPV and
IRR. Assume that the cash flows for each year are independent of cash flows for
other years. Also, assume that the computer operates as follows:
(1) A developmental cost and a project life are estimated for the first run using
the first two random numbers.
(2) Next, sales volume, sales price, and cost per unit are estimated using the next
three random numbers and used to derive a cash flow for the first year.
(3) Then, the next three random numbers are used to estimate sales volume, sales
price, and cost per unit for the second year, hence the cash flow for the second year.
(4) Cash flows for other years are developed similarly, on out to the first run’s
estimated life.
(5) With the developmental cost and the cash flow stream established, NPV and
IRR for the first run are derived and stored in the computer’s memory.
(6) The process is repeated to generate perhaps 500 other NPVs and IRRs.
(7) Frequency distributions for NPV and IRR are plotted by the computer, and
the distributions’ means and standard deviations are calculated.
( 11-3 2)
Decision tree: The Yoran Yacht Company (YYC), a prominent sailboat builder in
Newport, may design a new 30-foot sailboat based on the ‘winged’ keels first introduced on the 12 m yachts that raced for the America’s Cup.
First, YYC would have to invest €10 000 at t 5 0 for the design and model tank testing
of the new boat. YYC’s managers believe there is a 60 per cent probability that this
phase will be successful and the project will continue. If stage 1 is not successful, the
project will be abandoned with zero salvage value.
The next stage, if undertaken, would consist of making the moulds and producing
two prototype boats. This would cost €500 000 at t 5 1. If the boats test well, YYC
would go into production. If they do not, the moulds and prototypes could be sold for
€100 000. The managers estimate the probability is 80 per cent that the boats will pass
testing and that stage 3 will be undertaken.
Stage 3 consists of converting an unused production line to produce the new design.
This would cost €1 million at t 5 2. If the economy is strong at this point, the net
value of sales would be €3 million; if the economy is weak, the net value would be
€1.5 million. Both net values occur at t 5 3, and each state of the economy has a
­probability of 0.5. YYC’s corporate cost of capital is 12 per cent.
a. Assume this project has average risk. Construct a decision tree and determine the
project’s expected NPV.
b. Find the project’s standard deviation of NPV and coefficient of variation of NPV.
If YYCs average project had a CV of between 1.0 and 2.0, would this project be of
high, low or average stand-alone risk?
( 11-3 3)
Use the option as described in Figure 11-4.
a. Confirm that the premium of a call option with a strike price of 100 is 17.3411.
b. Confirm that the premium of a put option with a strike price of 100 is 19.2141.
c. If you arranged to buy the underlying asset and a call option as in part a what
would be the maximum price you would have to pay (i.e. the asset plus the call
option) in cash flow terms, not discounting to the present?
d. To help finance the cost of the call option you decide to sell (or write) a put contract as in part b of this question for the same strike. What is going to be the net
Chapter 11
Capital Budgeting: Evaluation of Cash Flows 311
cost of the underlying asset and options, again in cash flow terms? Explain why
this is a guaranteed rate.
e. Instead of the put option in part d you decide to sell (or write) a put option for a
strike price of 96.5 on the same asset with a premium of 17.3059. What kind of
protection is being offered here, i.e. what is the possible range of the total cost of
the asset plus the options?
f. The contract in part e is known as a range forward or cylinder contract. Explain
why this might be attractive to firms.
g. It is said that all financial contracts can be modelled in terms of options. Consider
how you might make an offer to sell an underlying asset (currency, wheat, copper,
etc.) at some future date with an implied range forward, assume that 100 is the
current market price.
( 11-3 4 )
Take Table 11-4 as a representation of investment in a new use of the Internet. Change
the existing project values such that:
a. Firm A should not invest but Firm B invest.
b. Firm B should not invest but Firm A invest.
In each case describe circumstances where the outcome would be realistic.
Shrieves Casting Company is considering adding a new line to its product mix, and the capital budgeting
analysis is being conducted by Sidney Johnson, a recently graduated MBA. The production line would be set
up in unused space in Shrieves’ main plant. The machinery’s invoice price would be approximately €200 000,
another €10 000 in shipping charges would be required, and it would cost an additional €30 000 to install the
equipment. The machinery has an economic life of four years, and Shrieves has obtained a special tax ruling
that places the equipment in the MACRS three-year class (see question 11-14). The machinery is expected to
have a salvage value of €25 000 after four years of use.
The new line would generate incremental sales of 1250 units per year for four years at an incremental cost
of €100 per unit in the first year, excluding depreciation. Each unit can be sold for €200 in the first year. The
sales price and cost are both expected to increase by 3 per cent a year due to inflation. Further, to handle the
new line, the firm’s net working capital would have to increase by an amount equal to 12 per cent of sales revenues. The firm’s tax rate is 40 per cent, and its overall weighted average cost of capital is 10 per cent.
a. Define ‘incremental cash flow’.
(1) Should you subtract interest expense or dividends when calculating project cash flow?
(2)Suppose the firm spent €100 000 last year to rehabilitate the production line site. Should this be
included in the analysis? Explain.
(3)Now assume the plant space could be leased out to another firm at €25 000 per year. Should this be
included in the analysis? If so, how?
(4)Finally, assume that the new product line is expected to decrease sales of the firm’s other lines by
€50 000 per year. Should this be considered in the analysis? If so, how?
b. Disregard the assumptions in part a. What is Shrieves’ depreciable basis? What are the annual
depreciation expenses?
c. Calculate the annual sales revenues and costs (other than depreciation). Why is it important to include
inflation when estimating cash flows?
d. Construct annual incremental operating cash flow statements.
e. Estimate the required net working capital for each year and the cash flow due to investments in net
working capital.
f. Calculate the after-tax salvage cash flow.
312 Part 4
Projects and Their Valuation
g. Calculate the net cash flows for each year. Based on these cash flows, what are the project’s NPV, IRR,
MIRR, PI, payback and discounted payback? Do these indicators suggest that the project should be
h. What does the term ‘risk’ mean in the context of capital budgeting; to what extent can risk be quantified;
and, when risk is quantified, is the quantification based primarily on statistical analysis of historical
data or on subjective, judgmental estimates?
i. (1) What are the three types of risk that are relevant in capital budgeting?
(2) How is each of these risk types measured, and how do they relate to one another?
(3) How is each type of risk used in the capital budgeting process?
j. (1) What is sensitivity analysis?
(2)Perform a sensitivity analysis on the unit sales, salvage value, and cost of capital for the project.
Assume each of these variables can vary from its base case, or expected value by ±10 per cent, ±20
per cent and ±30 per cent. Include a sensitivity diagram, and discuss the results.
(3) What is the primary weakness of sensitivity analysis? What is its primary usefulness?
k. Assume that Sidney Johnson is confident in her estimates of all the variables that affect the project’s cash
flows except unit sales and sales price. If product acceptance is poor, unit sales would be only 900 units
a year and the unit price would only be €160; a strong consumer response would produce sales of 1600
units and a unit price of €240. Johnson believes there is a 25 per cent chance of poor acceptance, a 25 per
cent chance of excellent acceptance, and a 50 per cent chance of average acceptance (the base case).
(1) What is scenario analysis?
(2) What is the worst-case NPV? The best-case NPV?
(3)Use the worst-, base-, and best-case NPVs and probabilities of occurrence to find the project’s
expected NPV, as well as the NPVs standard deviation and coefficient of variation.
l. Are there problems with scenario analysis? Define simulation analysis, and discuss its principal advantages and disadvantages,
m. (1)Assume Shrieves’ average project has a coefficient of variation in the range of 0.2 to 0.4. Would the
new line be classified as high risk, average risk, or low risk? What type of risk is being measured
(2)Shrieves typically adds or subtracts three percentage points to the overall cost of capital to adjust for
risk. Should the new line be accepted?
(3) Are there any subjective risk factors that should be considered before the final decision is made?
n. What is a real option? What are some types of real options?