B1 FINANCIAL MANAGEMENT
FINANCIAL
MANAGEMENT
STUDY TEXT
B1
Intermediate level
THE NATIONAL BOARD OF
ACCOUNTANTS AND AUDITORS
TANZANIA (NBAA)
B1
B1
STUDY TEXT
STUDY TEXT
FINANCIAL MANAGEMENT
FINANCIAL MANAGEMENT
NBAA
NBAA
Edition 1, Version 1
ISBN No 978-9976-78-086-4
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FOREWORD.
FOREWORD.
The National Board of Accountants and Auditors is a professional body in Tanzania, established under the
Auditors and Accountancy Registration Act No 33 of 1972 (CAP 286 R.E.2002). The Board has been charged
The National
Boardthings,
of Accountants
and Auditors
is a professional
in Tanzania,
established
under the
with
among other
the responsibility
to promote,
develop andbody
regulate
the accountancy
profession
in
Auditors
and
Accountancy
Registration
Act
No
33
of
1972
(CAP
286
R.E.2002).
The
Board
has
been
charged
the country.
with among other things, the responsibility to promote, develop and regulate the accountancy profession in
the
country. its statutory obligations, NBAA prepares National Accountancy Examination Scheme for
In fulfilling
students aspiring to sit for Accounting Technician and Professional Examinations. F u r t h e r , f or effective
In fulfilling its of
statutory
obligations,
NBAA and
prepares
Accountancy
Examination
Scheme
for
implementation
improveNational
examination
results, the
Board provides
Study
the examination
scheme
aspiring
to
sit
for
Accounting
Technician
and
Professional
Examinations.
F
u
r
t
h
e
r
,
f
or
effective
students
Guides for all subjects to assist both examination candidates and trainers in the course of learning and
implementation
of the examination scheme and improve examination results, the Board provides Study
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CPA. Pius A. Maneno
EXECUTIVE DIRECTOR
CPA.
A. Maneno
JUNE,Pius
2019
EXECUTIVE DIRECTOR
JUNE, 2019
iv
Financial Management Function
B1 – Financial Management
B1 – Financial Management
i
i - viii
About
paper
About
thethe
paper
Section A
1.
Section A
1
2
1. Time value of money
2. Time
Risk and
return
value
of analysis
money
Principles of valuation
Principles of valuation
2. Complex investment appraisal
appraisal
Budgeting)
3. Investment
Investments in
securities(Capital
and portfolio
theory
investment
4. Complex
The security
market line appraisal
(SML) and the capital asset pricing model
(CAPM)
Investments
in securities and portfolio theory
Issues of new capital
Cost of capital
Dividend decision
Financial gearing and capital structure
Section E
1. Dividend policy
Section
F
Dividend policy
Section G
40
41
67
-
66 94
95
149
203
229
-
148
202
228
252
-
-
253
281
315
365
Working capital management
405
-
-
428
Working capital management
of effective management of working capital
1. Principles
Financial planning
429
2. Financial forecasting
Financial planning
Appendices
Financial forecasting
analysis
1. Financial
Present value
table and interpretation
Section H
Section
H
Appendices
3. Compound interest table
2. Annuity table
1.
2.
3.
-
-280
314
364
404
Financial planning and forecasting
Section
Financial planning and forecasting
3. FinancialG
analysis and interpretation
1.
2.
3.
--
Dividend decision
1. Principles of effective management of working capital
Section F
-
Financing decisions
3. Cost of capital
mediumandcapital
long-term
alternatives
4. Short,
Financial
gearing and
structure
Section E
1.
-
Section D
1. Short, medium- and long-term alternatives
1.
-
The security market line (SML) and the capital asset pricing model
(CAPM)
Financing decisions
Section
2. Issues ofD
new capital
1.
2.
3.
4.
-
Investment decisions
Section
Cappraisal (Capital Budgeting) Investment decisions
1. Investment
1.
2.
3.
4.
1
Financial management function
Risk and return analysis
Section C
vi
Financial management function
1. Introduction
Introduction toto
corporate
financial
decision
environment
corporate
financial
decision
environment
Section
Section
B B
-
Present value table
Index
Annuity table
Compound interest table
--
472
-
473
495
511
--
494
510
552
-
553
554
Total
555 Page Count: 464
Total Page Count: 562
Features of the book
‘The book covers the entire syllabus split into various chapters (referred to as Study Guides in the book). Each
chapter discusses the various Learning Outcomes as mentioned in the syllabus.
Contents of each Study Guide
‘Get Through Intro’: explains why the particular Study Guide is important through real life examples.
‘Learning Outcomes’: on completion of a Study Guide, students will be able to understand all the learning
outcomes which are listed under this icon in the Study Guide.
The Learning Outcomes include:
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EXAMINATION STRUCTURE
The syllabus is assessed by a three-hour paper-based examination. 5 conventional questions of 20 marks each
need to be solved.
The examination will consist of two sections.
Section A
Section B
One compulsory question
Four questions out of Six
A1
SECTION A
Introduction to Corporate Financial Decision Environment: 1
FINANCIAL MANAGEMENT
FUNCTION
STUDY GUIDE A1: INTRODUCTION TO
CORPORATE FINANCIAL DECISION
ENVIRONMENT
Financial management involves the effective management of the finances of an organisation in order to achieve
that organisation’s objectives. It requires financial planning and financial control. Financial planning ensures
that sufficient funds are available to meet the short, medium and long-term capital needs of the organisation. Once
these funds are raised the financial manager must ensure that they are used appropriately (control). This Study
Guide provides overview of the various responsibilities of the financial manager.
a) Define financial management, its scope and role(s) in corporate management.
b) Define the financial manager and the roles he/she plays in corporate decisions.
c) Identify the roles that financial markets and institutions play in facilitating investment, financing and
corporate development.
d) Identify the goals of the firm
e) Evaluate and explain the relationship between business objectives and financial management objectives
and the process of developing a strategy.
f) Discuss how agency theory can be used to analyse the relationship between various stakeholders in a
corporation and how the resulting agency problems may be overcome.
g) Describe the financial system and fund flow in an economy and its relevance to Tanzanian economy
h) Describe forms of market efficiency and its implication on determination of security prices
i) Describe the applicability of the efficiency market hypothesis (EMH) to corporate decision-making
process
2
Financial Management Function
2 : Financial Management Function
© GTG
1. Define financial management, its scope and role(s) in corporate management.
Define the financial manager and the roles he/she plays in corporate decisions.
[Learning Outcomes, a and b]
What is finance?
The word finance has been defined by the Oxford English Dictionary as “the management of large amounts of
money by governments or large organisations”.
What is financial management?
Financial management therefore means the efficient and effective management of money in such a manner as
to accomplish the objectives of the organisation.
Role of financial management
Money in a business organisation which needs to be managed flows between different sources and destinations.
Flow of finance in a business
Diagram 1: Flow of Finance
Introduction to Corporate Financial Decision Environment: 3
Introduction to Corporate Financial Decision Environment: 3
© GTG
As shown in the diagram above, there are different directions in which funds flow in a business.
The role of financial management is primarily to acquire funds needed by a firm and ensure that the funds so
pooled are utilised in a manner which would maximise the wealth of the shareholders of the firm. In order to
achieve this, the flow of funds should be harnessed and directed in the best possible manner by the finance
team of the firm.
Scope of Financial Management
Financial management is an integral part of an organisation’s management and provides a conceptual framework
for financial decision making. The function of finance is concerned with both acquisition and use of funds.
The scope of financial management can be presented as investment decisions, finance decisions, dividend
decisions and decisions regarding the management of working capital.
1.1 Investment decisions
A company invests in order to maintain or improve its profit-earning capacity. Investment decisions usually
relate to the acquisition of fixed or non-current assets (capital investments) e.g:
new equipment
automated or more advanced production technology
land and buildings
business units
Investments must be evaluated for financial viability before being selected or rejected. Factors to consider would
include the relevant cash inflows and outflows associated with each project, the projects’ risks and returns and
the company’s cost of capital.
It might be that more than one investment proposal is financially acceptable. In such a case, the capital budget
(i.e. the amount of funds available to spend on capital investments) needs to be considered. If sufficient funds
are available, it might be possible to take advantage of all financially viable projects, however, this is not usually
the case and capital rationing may have to be resorted to.
Enidan Ltd has Tshs 400 million available for investment purposes. The following information is available
regarding potential investments:
Project
A
B
C
D
Investment
Tshs’000
100,000
250,000
60,000
400,000
Net cash inflow
Tshs’000
50,000
82,000
20,000
100,000
Assuming that the company cannot proportionally invest, what will be the optimal investment policy?
It is not possible to invest in all four projects as the amount of funds are limited to Tshs400 million, but total
investments come to Tshs810 million. It is obvious in the example that the project earning the highest return in
absolute terms is project D, thus it could be considered first. Since project D requires Tshs400 million, the company
will be unable to undertake any further investments until more funds made available. The total cash inflow will be
Tshs 100 million, but is this the only option?
If the company wishes to maximise its cash inflow and spread its risks its optimal investment policy would be to
invest in projects A and B. The total investment would be Tshs 350 million and the net - cash inflow Tshs 132
million. Time value of money is required to be considered. Money in hand is worth more than the equal amount
of money receivable in future.
This is just a glimpse of what kind of issues are involved in the investment decisions. The function of investment
and the manner of taking these decisions are is covered in detail in latter part of this Study Text.
4 4 : Financial
FinancialManagement
ManagementFunction
Function
© GTG
1.2 Financing Decisions
Once the decision to invest has been made, the decision regarding how the investment is going to be funded,
needs to be considered. Companies in general have two major sources of finance:
Equity finance consisting of ordinary shares. Companies may wish to issue new shares or use reserves.
Debt finance consisting of fixed interest finance e.g. debentures, loans.
Before deciding the mix of funding, the company’s ability to tap certain sources needs to be looked into. For
example, utilising reserves may not be possible if the company has not been in existence long enough to have
built up its retained earnings, or loan finance may be denied in the absence of security. The cost of each source
must also be considered keeping in mind the need to maximise shareholders’ wealth.
A company earns 12% return on the funds invested and pays 8% on debt finance. Ignoring the effect of
taxation, the 4% saving (12 - 8) goes towards increasing shareholders’ wealth.
The above simple example illustrates the issues considered.
1. Dividend decisions
When shareholders invest in companies, they undertake the risk of the success or failure of the business, and
thus usually require a return commensurate with the level of risk. Their return can take two forms: dividends and/or
capital gains (where the share price increases).
Funds generated from operations can either be retained in the business for re-investment or distributed to the
shareholders as dividends. The proportion of dividends to net profits is called the dividend payout ratio, and it
is the financial manager who will advise the board on an acceptable ratio. The decision considers:


the required rate of return to the shareholders and
the future investment policy of the company.
2. Working capital management
Working capital is equal to current assets (stocks, debtors and cash) net of current liabilities; in effect, it is equal
to the amount of current assets funded through long term finance. The following needs to be decided upon:
 the optimal level of working capital
 the form the working capital should take
 how the working capital should be funded
A balance needs to be brought about between the conflicting objectives of profitability and liquidity when managing
working capital. The company needs to keep sufficient current assets to ensure liquidity i.e. the company’s ability
to pay off debts as and when they fall due. However, having too high a level of cash tied up in idle assets incurs
an opportunity cost of lost investment opportunities.
On 1 January 20X8 a business had a trade creditor of Tshs500 million payable on 1 March 20X8 and had a policy
of holding cash equal to short term debts. Thus, its cash balance on 1 January 20X8 was Tshs500 million. By 1
March 20X8 the company’s trade creditors increased to Tshs760 million, and so too its cash balance.
1. Will the company be able to pay off the debt on the first of March?
Yes. It has sufficient cash to cover all its debts.
2. Would this policy ensure profitability?
No. Cash on hand earns no interest; cash in a current account earns minimal interest. The sum of Tshs 500 million
would have been idle for two months i.e. January to March. The company would have been better off if it had
invested the money for two months and liquidated the investment when the payment was due. This would have
ensured maximum return on the money for the two-month period.
Introduction to Corporate Financial Decision Environment: 5
© GTG
Introduction to Corporate Financial Decision Environment: 5
Working Capital Management is covered in detail in latter part of this Study Text.
3. Interdependence of the decisions
All the decisions discussed so far are interdependent.




If a company decides to reinvest the profits earned, lower profits will be available for dividend distribution.
Similarly, there is less need for external financing.
If a company decides to pay a higher dividend, then lower internal resources will be available. The company
will have to look for outside sources. If the sources are not available, then investment proposals may have to
be cut down.
If finance obtained is at a higher cost, the investment proposals have to show high potential returns to justify
the investment. If sufficient attractive investment options are not available, then the company’s profits and
dividends in the future are likely to be lower.
SUMMARY
(a) Financial manager
A financial manager or Chief Financial Officer (CFO) is responsible for the overall financial health of an
organisation. He / she provide advice to various sections of an organisation in order to ensure that sound financial
decisions are taken across the organisation.
(b) Role of a financial manager
The financial manager has to make and implement decisions at different stages while managing the flow of
funds in an organisation. The functions of the financial manger relate to discharging the responsibilities mentioned
in the scope of financial management above.
Market research carried out recently by a company which manufactures and sells digital cameras has revealed
a scope to sell an additional 500,000 cameras per year. However, since the factory is currently operating at full
capacity, increasing production would only be possible if the company were to invest in an additional production
line. Alternatively, the company could buy cameras from another manufacturer at wholesale prices, and then
sell them in their stores. When the financial manager was asked to comment, his views were as follows:
Financial Manager: “Before a decision is made, the financial viability of each proposal must be evaluated; one
would have to look at the relevant cash flows and weigh up the cash inflows and outflows. If both proposals are
deemed to be financially viable, the proposal that would bring the company the most gain will be accepted; after
all, our aim is to maximise our shareholders’ return.”
“The next issue would be funding. We must consider the total amount of funding required, and the sources of
funds available to the firm: are we going to use reserves, issue shares, issue debentures or use loan finance?
Of course, the choice will depend on what is available to us, the costs associated with each option and our gearing
level among other things.”
Continued on the next page
6
Financial Management Function
6 : Financial Management Function
© GTG
“The working capital needs of the project must also be identified. We will have to decide on the levels of stocks,
debtors etc. and how they are going to be financed.”
Note: the financial manager has touched on three decisions: investment, funding and working capital. Once funds
are raised for the project the financial manager must ensure that they are used appropriately. Once the project
begins to yield returns a dividend decision will have to be made i.e. should these be distributed to shareholders or
re-invested in the business.
What are the main functions of a financial manager?
2. Identify the roles that financial markets and institutions play in facilitating investment,
financing and corporate development.
[Learning Outcome, c]
2.1 Financial markets
The knowledge of financial markets is critical as a finance manager needs to tap them for both long term and
short-term financing. Effective financial planning is not possible without sound knowledge of financial markets and
instruments. Money markets and capital markets enable organisations to obtain and invest funds. Money markets
deal with short term funds and capital markets deal with medium- and long-term funds.
The financial market in Tanzania consists of markets for money, bonds, equities, foreign exchange and collective
investment schemes. The Bank of Tanzania is involved in money, bonds and foreign exchange markets geared
towards:
 implementation of the monetary policy,
 ensuring that government financing needs are met and
 facilitating stability and efficiency of the markets.
Domestic financial markets are comparatively still at a nascent stage.
1. Money markets
A money market is a financial market for short-term borrowing and lending. In this context, short-term is
any period up to one year. It is a market in which the surplus short-term investible funds at the disposal of banks
and other financial institutions are lent to borrowers consisting of corporates, individuals and the government.
Money market investments are also known as cash investments as they involve short term investments. These
instruments are highly liquid in the sense that they can be bought or sold at will. However, some of the money
market instruments such as certificates of deposits may have a maturity date of up to 5 years.
These securities are of the nature of IOUs. They acknowledge that a certain amount will be paid at a certain
date to the order of a certain person. These securities are usually fixed interest securities.
Money market securities are dealt in high value lots. As a result, retail or individual investors may not find it easy
to access the market. Companies normally buy and sell securities in their own name.
Money market mutual funds pool together the financial resources of thousands of investors and invest in money
market securities on their behalf.
The following are the main kinds of transactions which are entered into in these markets.
(a) Discounting of bills
Short-term bills of the highest quality are discounted via the money markets. These instruments are bought and
sold at a discounted price.
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Introduction to Corporate Financial Decision Environment: 7
Introduction to Corporate Financial Decision Environment: 7
Kalmart Company holds bills which were issued by the central bank for Tshs 95 million and are due on 31
December 20X2 for redemption at a value of Tshs 100 million. The company requires cash immediately thus
cannot wait until the redemption date. It chooses to sell these bills at a discounted price on 1 November 20X2 for
Tshs 99 million to Talmart. Talmart pays Tshs 99 million and receives the full maturity value on 31 December
20X2. Both parties have benefited. Kalmart obtained the cash required and made a gain of Tshs 4 million while
Talmart made a gain of Tshs 1million.
(b) Inter-bank dealings
Financial institutions borrow and lend wholesale funds among themselves. They carry on this activity in order to
finance their regular lending and to meet temporary fluctuations in available funds.
(c) Other instruments
Other instruments such as certificates of deposit, commercial papers etc. are also dealt with at the money
market.
Role of money markets in facilitating investment and liquidity

Money markets play a crucial role in providing short term liquidity to the industry and the public sector. The
start point of implementation of a monetary policy is to change the money market rates which the central
bank can trigger through its control over money market conditions.

It is an important source of financing trade and industry through treasury bills or commercial paper. It
provides a channel through which suppliers of temporary cash surpluses meet users of funds with temporary
cash deficits.
Since holding cash has a cost associated with it, money market instruments provide an excellent opportunity
for parking excess cash for a limited period. This aids in efficient working capital management.
Role in management of foreign exchange rate and interest rate exposures - Organisations which seek to
achieve their commercial objectives approach the money market to hedge their foreign exchange (forex) risks
and interest rate exposures. The forex market helps companies to minimise the risks of foreign trade by
providing effective hedging mechanisms. The foreign exchange market facilitates the exchange of one
currency for another. Using money market hedge, a company can hedge its foreign currency
receivables/payables. If a company has diversified its commercial operations in different geographical
areas, it may reduce its interest risk exposure by borrowing short-term finance in different markets.


2. Capital markets
The capital market (securities markets) is the market where companies and the government can procure longterm securities. The stock market and the bond market are included in the capital market.
A stock market is a market in which company stock and their derivatives are traded. Both are traded privately
as well as being listed on a stock exchange.
Bonds are still traded in the bond market which is an informal market.
The distinguishing feature of a capital market is that it enables companies to raise medium or long-term finance.
The stock market deals with company shares, while the bond markets buy and sell loan securities such as
debentures.
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Capital markets are classified as follows.
(a) Primary and Secondary Capital Markets
Both the stock market and bond market are further classified into primary and secondary markets.
(i) Primary capital markets: they allow companies to raise new finance; new issues of equity and debt are
placed on the primary markets. These are over-the-counter markets and they have no physical location
or reporting system. The pricing of new issues is determined by the company after considering the market
conditions and the valuation of shares.
Mondberg Plc is considering investing in a new production line which requires a cash outlay of Tshs 500 million.
The company does not have sufficient security to obtain a loan thus decides to issue new shares via the stock
exchange.
(ii) Secondary markets: these are markets where the debt and equity instruments already issued by the
companies are traded. The secondary markets allow investors to liquidate their investments. These markets
have physical locations, such as the London stock exchange and the Tokyo stock exchange, however, due
to technological advances; the actual business of these stock exchanges is not physically conducted at the
exchanges but over telephones and the internet.
Clare, an investor, bought shares in Mondberg Plc two years ago for Tshs 2000 each. Due to expansion and
sustained growth over the two years, investor confidence has pushed up the market prices of the share to Tshs
11000. Clare now wishes to cash in on her investment and sells her holding on the secondary market via the
internet. She makes a capital gain of Tshs 9000 per share.
One of the major milestones for financial markets in Tanzania was the incorporation of the Dar es Salaam stock
exchange in September 1996. The Dar es Salaam Stock Exchange (DSE) was incorporated as a private company
limited by guarantee and not having a share capital under the Companies Ordinance. Trading activities at the
Dar-es-Salaam Stock Exchange commenced after two years of preparatory work under the stewardship of the
Government through the Capital Markets and Securities Authority. The equity market currently consists of thirteen
companies listed at DSE. Participation of non-residents in IPO is limited to 60 percent of the shares. The market
capitalisation of DSE exchange is Tshs 14,408.9 billion as on September 25,
2013.
Source – DSE market report
(b) Institutional Investors
Pension funds, provident funds, insurance companies, collective investment schemes and other institutions pool
together resources on a large scale and invest in large amounts. They are called institutional investors. They
hold a sizeable chunk of the total equity and are in a position to influence the management or even change the
directors. A recent study has shown that, on an average, institutional investors hold almost half of the share capital
of companies.
(c) Participants
The participants in the capital markets are individuals, the government and large institutions. Participation
by large institutions has brought influence on the regulators to stipulate fairer terms for the general public, including
lower brokerages.
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Introduction to Corporate Financial Decision Environment: 9
Introduction to Corporate Financial Decision Environment: 9
Role of capital markets / bond markets in facilitating investment and liquidity

Provide a source of finance to business units
Business organisations need finance for their operations or expansion. Stock markets and capital markets
enable them to raise finance for the medium and long-term.

Reduce risks to individual buyer and seller
Since the markets are regulated, sellers can rest assured that the payment against the securities sold will be
received on time. Similarly, buyers will have confidence that the securities purchased will be delivered to them
on time. Since the information about the rates and the rules is available to all and the process is transparent, there
is less chance of fraudulent dealings. This leads to easy access to markets in case additional funds are to be
raised through public issue.

Optimum allocation of financial resources
With the operation of market forces, the financial resources are directed to the most efficient firms. Non-efficient
firms will find it difficult to tap into the markets. This leads to an optimum allocation of resources.

Promote economic growth
Availability of finance and the facility to transfer the securities leads to efficient allocation of resources.
Elvis Ltd is a newly floated company. It makes a public issue of shares and bonds that are listed on the stock /
bond markets. It sets up a new factory, produces goods and provides employment to many people. This is
economic growth.

Encourage relevant, reliable and timely financial reporting system
Because of healthy procedures such as listing agreements, supervision by the market authorities and regulation
by the appropriate authorities, listed companies have to keep their financial reporting system in good shape i.e.
the reporting should be relevant, reliable and timely.

Act as a clearing house
These markets act as a clearing house, in the sense that they facilitate the settlement of accounts between the
buyers and sellers of securities.

Determine fair prices of stocks (shares)
The market forces of demand and supply of shares operating in the stock market determine the share price of a
company.

Reduce the burden of corporate lending on the banks
Companies requiring funds need not depend only on the commercial banks. They have an effective alternative
in the form of a bond market. Bonds are issued directly to the investors. They have an advantage over bank
finance in that they provide liquidity to investors or lenders. Investors can sell their bonds in the market and get
their money back any time. This is not normally possible with a bank.
2.2 Financial intermediaries
1. Meaning of Financial Intermediaries
Financial intermediaries are institutions which act as a mediator between two parties in a financial market. The
most common form of intermediation is that which occurs between borrowers and lenders, i.e. which links these
two parties. Intermediation may also take place between the central bank of the country and the commercial banks.
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Diagram 2: Flow of money from lender to borrower
Examples of financial intermediaries are:





banks
insurance companies
mutual funds
pension funds
governments’ savings department
2. Functions of financial intermediaries
(a) Aggregation
Relatively small sums of individual savings can be pooled and loaned to a single borrower. Financial intermediation
allows for the pooling of financial resources. For example, if ten individuals deposit Tshs 100,000 each, when
aggregated the bank could actually lend one borrower Tshs 1,000,000 i.e.10 x Tshs 100,000.
(b) Risk reduction
Lenders themselves do not run the risk of losing their investments as bad debts are borne by the financial
intermediary. In addition, financial intermediaries lend to a large number of individuals thus spreading their own
risk.
Continuing from the previous example under (a)
If the borrower defaults on any payments it is the bank that suffers the financial loss. The 10 investors who
deposited Tshs 100,000 each would lose nothing. This is because the bank owes money to them and the borrower
owes money to the bank. The intermediary bears all the risk.
(c) Maturity transformation
Intermediaries benefit from a continuous supply of finance through individual lenders. Because of this, it is
possible to allow lenders instant access to deposits and assure borrowers a fixed (but longer) repayment term.
(d) Convenience
Individuals are able to invest (or lend) without having to find an individual borrower. The investor merely decides
on the return required over a chosen period, approaches the relevant intermediary and makes a deposit. For
borrowers, it acts as a ready source of funds even when money is in short supply.
(e) Regulation
There is heavy regulation in place to protect investors against negligence or malpractice.
Introduction to Corporate Financial Decision Environment: 11
Introduction to Corporate Financial Decision Environment: 11
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Bank of Tanzania has prescribed certain guidelines to ensure adequate banking supervision. To ensure that
adequate capital is maintained by banks at all times, THE BANKING AND FINANCIAL INSTITUTIONS (CAPITAL
ADEQUACY) REGULATIONS, 2008 require that “ Every bank or financial institution shall maintain at all times
minimum core capital and total capital equivalent to ten percent and twelve percent respectively of its total riskweighted assets and off-balance sheet exposures”.
(f) Information
Intermediaries will be able to provide advice to borrowers and lenders on their options depending upon their
individual circumstances.
3. Credit Creation or money creation by banks
Banks can create money through the banking system via lending. For simplicity, in the following example, it will
be assumed that there is only one commercial bank and all customers wish to hold additional receipts of cash in
deposits.
1 January 20X3
John deposits Tshs 1,000,000 into the bank.
Assets of the bank
Tshs ’000
Cash
1,000
Liabilities of the bank
Tshs ’000
Deposit (John)
1,000
4 January 20X8
Mary approaches the bank for a loan. If the bank assumes that John will not withdraw any cash it would mean
that the maximum Mary could borrow would be Tshs 1,000,000.
Assets of the bank
Tshs ’000
Mary (loan)
1,000
Liabilities of the bank
Tshs ’000
Deposit (John)
1,000
8 January 20X8
Mary pays a supplier, Bill, Tshs 1,000,000 which he immediately deposits into the bank.
Assets of the bank
Tshs ’000
Mary (loan)
1,000
Cash
1,000
Liabilities of the bank
Tshs ’000
Deposit (John)
1,000
Deposit (Bill)
1,000
So far, the bank has created another Tshs 1,000,000 of credit.
It is unrealistic for banks to assume that customers will never withdraw cash from their deposits. It is also unrealistic
to assume that customers will withdraw all the cash held as deposits. In reality, banks keep cash amounting to at
least 10% of the value of deposits so as to be liquid enough to meet the cash needs of their customers. This
system is called fractional reserve banking.
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1 January 20X3
Harry deposits Tshs 1,000,000 into the bank.
Assets of the bank
Tshs ’000
Cash
1,000
Liabilities of the bank
Tshs ’000
Deposit
1,000
(Harry)
6 January 20X3
William approaches the bank for a loan. The policy of the bank is to retain 10% of deposits as cash therefore the
maximum amount that can be loaned to William is Tshs 900,000.
Assets of the bank
Tshs ’000
Cash
Loan (William)
100
900
Liabilities of the bank
Tshs ’000
Deposit
1,000
(Harry)
10 January 20X3
William pays Paul Tshs 900,000 for a car. Paul immediately deposits the cash into the bank.
Assets of the bank
Tshs ’000
Cash
Loan (William)
Cash
Liabilities of the bank
Tshs ’000
100
900
900
Deposit
(Harry)
Deposit
(Paul)
1,000
900
4. Benefits of intermediation to investors and companies
(a) To investors
(i) Diversification of portfolios: banks pool the funds together and invest them in a diversified portfolio. This
may not have been possible for an individual investor.
(ii) Reduced risks: as a result of diversified activities of the banks, the risks to the investors are reduced.
(iii) Access to bank’s expertise: bank’s experts assess the corporate risk and obtain the best possible return.
This benefit is passed on to the investors in a competitive market.
(iv) Most countries have a legislation providing protection to the people who invest in a bank, through a
guarantee or insurance schemes.
Collective investment schemes provide an opportunity for the majority of Tanzanian citizens to invest, acquire
a stake in privatization, further participate in the capital markets and obtain a return on their investments.
Moreover, they are structured to provide opportunities to both low and high income Tanzanian individuals as
well as registered organisations (whose beneficiaries are Tanzanians) to participate in it. These are Umoja
Fund, TCCIA Investment Company and National Investment Company (NICOL).
(b) To companies





Pooling of funds: companies have access to larger amount of resources.
Companies can benefit through transperancy in rates and competition among banks and institutions. They
can take advantage of economies of scale.
Bridging of the maturity gap: companies can access long term finance. Banks can do this even if individual
investors are changed.
Financial intermedaition can faciliitate financing of even high risk projects because a consortium of bankers
may be willing to fund the project, thereby mitigating individual risk, subject to compliance of norms on credit
and security.
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Introduction to Corporate Financial Decision Environment: 13
IntroductiontotoCorporate
CorporateFinancial
FinancialDecision
DecisionEnvironment:
Environment:1313
Introduction
What role do money markets play in facilitating investment and financing?
What role do money markets play in facilitating investment and financing?
3. Identify the goals of the firm
3. Identify the goals of the firm
[Learning Outcome d]
[Learning Outcome d]
From the point of view of financial management, a firm has two primary goals, namely, maximisation of profit
and
shareholders’
Frommaximisation
the point of of
view
of financialwealth.
management, a firm has two primary goals, namely, maximisation of profit
and maximisation of shareholders’ wealth.
Maximisation of profit: earning profit is the main aim of any economic activity. A firm, being an economic
entity,
should aim
at earning
profitprofit
in order
to main
not only
its economic
costs but activity.
also ensure
availability
of economic
funds for
Maximisation
of profit:
earning
is the
aimcover
of any
A firm,
being an
growth.
This
goal
can
also
be
studied
in
the
light
of
maximisation
of
earnings
per
share
of
a
firm.
entity, should aim at earning profit in order to not only cover its costs but also ensure availability of funds for
growth. This goal can also be studied in the light of maximisation of earnings per share of a firm.
The profit maximisation goal of a firm can be justified on the grounds of the following:
The profit maximisation goal of a firm can be justified on the grounds of the following:
 Efficiency of a firm would be measured in terms of its profit earning capacity. Moreover, only an efficient firm
survive
competitive
 can
Efficiency
ofina afirm
would be market.
measured in terms of its profit earning capacity. Moreover, only an efficient firm
 A
firm
is always
exposed to market.
adverse economic and business conditions like recession, severe competition,
can
survive
in a competitive
availability
of credit,tofall
in prices,
etc. Profits
a firm
to face like
such
risks.
 limited
A firm is
always exposed
adverse
economic
and enable
business
conditions
recession,
severe competition,
 Under
conditions,
the firm
earnahigh
willsuch
be able
to gain maximum market
limited imperfect
availabilitymarket
of credit,
fall in prices,
etc.which
Profitscan
enable
firmprofit
to face
risks.
 advantage.
Under imperfect market conditions, the firm which can earn high profit will be able to gain maximum market
 Profits
also enable a firm to meet its social goals.
advantage.
 Profits also enable a firm to meet its social goals.
However, profit maximisation as a goal of a firm has been criticised on the following grounds:
However, profit maximisation as a goal of a firm has been criticised on the following grounds:
 The profit maximisation goal is a short-term concept.
 The profit maximisation goal is
ignores
the time
value of money; earnings earned during different time periods
a short-term
concept.
as equal.
 are
Thetreated
profit maximisation
goal ignores the time value of money; earnings earned during different time periods
 The
risks associated
are treated
as equal. with the prospective stream of earnings and the effect of dividend policy on the market
of shares
are not
under stream
this goal.
 prices
The risks
associated
withconsidered
the prospective
of earnings and the effect of dividend policy on the market
prices of shares are not considered under this goal.
Maximisation of shareholders’ wealth: creation of value is considered to be the driving force behind financial
management.
a more appropriate
of a firm
wouldisbe
to create and
increase
wealth
of its
shareholders
Maximisation Thus,
of shareholders’
wealth:goal
creation
of value
considered
to be
the driving
force
behind
financial
by
increasing the
value
of their
investment.
Moreover,
maximising
a shareholder’s
wealth
(or economic
welfare),
management.
Thus,
a more
appropriate
goal
of a firmby
would
be to create
and increase
wealth
of its shareholders
a
is also the
able
to maximise
its consumption
utility
time. The
wealth maximisation
goal
is considered
to
byfirm
increasing
value
of their investment.
Moreover,
byover
maximising
a shareholder’s
wealth (or
economic
welfare),
be
the is
most
goal of a firm.
a firm
alsoimportant
able to maximise
its consumption utility over time. The wealth maximisation goal is considered to
be the most important goal of a firm.
A public limited company aims to achieve this goal by maximising its market value as reflected by the prices of
its
shareslimited
and securities
the long
run. this goal by maximising its market value as reflected by the prices of
A public
companyinaims
to achieve
its shares and securities in the long run.
Excerpts from the mission statements of some of the Fortune 500 companies:
Excerpts from the mission statements of some of the Fortune 500 companies:
American Financial Group, INC
American Financial Group, INC
“We build value for our investors through the strength of our customers' satisfaction and by consistently producing
superior
“We buildoperating
value for results.”
our investors through the strength of our customers' satisfaction and by consistently producing
superior operating results.”
Cooper Tire & Rubber Company
Cooper Tire & Rubber Company
“The purpose of the Cooper Tire & Rubber Company is to earn money for its shareholders and increase the value
of
their
investment.”
“The
purpose
of the Cooper Tire & Rubber Company is to earn money for its shareholders and increase the value
of their investment.”
Kerr-McGee Corporation
Kerr-McGee Corporation
“Create value for shareholders through the energy business.”
“Create value for shareholders through the energy business.”
Norfolk Southern
Norfolk Southern
“Norfolk Southern's mission is to enhance the value of our stockholders' investment over time by providing
quality
freight
transportation
services
and undertaking
related businesses
which
ourbyresources,
“Norfolk
Southern's
mission
is
to enhance
the value ofany
ourother
stockholders'
investment inover
time
providing
14
: Financial
Management
Function
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quality
freight
transportation
services
and
undertaking
any
other
related
businesses
in
which
our resources,
particularly our people, give the company an advantage.”
The market value of shares represents the perception of various market participants regarding the quality of a
14 : Financial Management Function
14particularly
Financial
ourManagement
people, giveFunction
the company an advantage.”
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The market value of shares represents the perception of various market participants regarding the quality of a
company’s financial decisions, and thus, serves as a company’s performance indicator. It also indicates how
well the management of a company is performing on behalf of the shareholders of the company.
The wealth maximisation approach takes into account the present and expected earnings per share and the timing,
duration and risk of the expected benefits. The primary functions of financial management, represented by the
functions of investing, financing and dividend decisions, need to be discharged in order to achieve shareholders’
wealth maximisation.
Market Value (MV) of a company can be calculated as:
Market Value of Equity (MVE) + Market Value of Debt (MVD)
Identify the main drawbacks of the profit maximisation objective of financial management.
4. Evaluate and explain the relationship between business objectives and financial
management objectives and the process of developing a strategy.
[Learning Outcome e]
At various levels of the organisation plans are made or objectives are set. Each employee seems to have his
own targets relating to his particular role. According to Peter Senge most people when asked what they do for a
living describe the tasks they perform and not the purpose which they fulfil. They see their responsibility as
being limited to the boundaries of their position but not in the context of the organisation as a whole. In reality each
employee, regardless of his position or role, is working towards objectives relating to the organisation’s ultimate
mission.
Within every organisation there is said to be a hierarchy of objectives as illustrated below:
Diagram 3: Hierarchy of objectives in an organisation
At each higher level in the hierarchy the aims are relevant to a greater proportion of the organisation’s activities.
The mission, as stated before, encompasses the activities of the entire organisation.
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Introduction to Corporate Financial Decision Environment: 15
Introduction to Corporate Financial Decision Environment: 15
5.1 Relationship between financial objectives, corporate objectives and strategy
As can be seen in the above diagram strategy formulation can only take place once the organisation’s objectives
have been clearly identified. These objectives relate directly to the organisation’s broad based goals and,
ultimately, to its mission. Objectives tell managers and employees precisely what they are supposed to achieve.
The origins of strategy and strategic thinking lie with the military. Strategy is usually associated with long-term
planning and thinking. Strategy can be defined as a course of action, including the specification of resources,
necessary to achieve an objective. In other words, it is a means to an end; it tells managers how to go about
achieving objectives.
Schwepsi Co, a world-wide food and drink manufacturer, produces an extremely varied range of products,
including more than just soft drinks. Aside from the Schwepsi brand, the company also owns Fruiticana, Crispy
and Shaker Oats and has a joint venture with Bigbuck’s Coffee. Schwepsi Co’s mission is to be the world’s leading
consumer Product Company, focussed on convenient foods and drinks.
The company’s goals, objectives and strategies are directly related to its mission. The goals include enabling
employees to build their future, enabling customers to build their business, and enabling shareholders to build
their wealth. In order to realise these goals, a primary objective of Schwepsi Co is growth and market penetration.
The company has shown consistent growth over the last four years and reported an increase in volume of 7.9%
in 20X8.
Despite these successes, Schwepsi Co recognises that changes in consumer preferences and tastes may reduce
demand for its products. To counteract this problem, a large part of their corporate strategy relates to marketing
and innovation. Schwepsi Co intends to continue to produce new products, while improving its marketing
programmes and advertising campaigns. Furthermore, in order to break into new markets and preserve its brand
loyalty, Schwepsi Co intends to maintain a good reputation world-wide.
Strategic decisions normally involve the following matters:





What should be the long-term direction of the organisation? What products should it sell and where should it
sell them (geographical areas)?
Achieving a competitive advantage: How should the company develop and retain unique features for its
products and services which competitors will find difficult to match?
What should the brands be and how should they be positioned?
How can the organisation use its resources and competencies in the best possible manner?
How can the values and expectations of the stakeholders be balanced?
1. Corporate Objectives
As mentioned before, objectives will relate directly to the organisation’s goals and indirectly to its mission.
Corporate objectives are more business or commercial oriented as opposed to financial.
AP is an organisation providing information technology solutions to other firms by developing softwares
as per their requirements.
The corporate objectives of AP include
(a) Customer Loyalty: to supply products, services and solutions of the highest quality and value to our
customers, in order to earn their respect and loyalty.
(b) Profit: to make sufficient profit to finance our company growth and other corporate objectives and increase
value for our shareholders.
Continued on the next page
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(c) Market Leadership: to grow by maintaining a supply of useful and significant products, services and
solutions to markets we already serve and to expand into new areas that build on our technologies, skills
and customer interests.
(d) Growth: to see change in the market as an opportunity for growth; to use our profits and our ability to develop
and produce innovative products, services and solutions that satisfy changing customer needs.
(e) Employee Commitment: to enable AP employees to benefit from the company's success; to reward good
performance with employment opportunities; to create a safe, dynamic and inclusive work environment that
values employees’ diversity as well as individual contributions; and to help them gain a sense of pride and
achievement from their work.
(f) Leadership Capability: to develop leaders at every level who are responsible for achieving business
results and exemplifying our values.
(g) Global Citizenship: to fulfil our responsibility to society by being an economic, intellectual and social asset
to each country and community in which we do business.
In practice, from the above, it can be seen that corporate objectives tend to be quite varied. This is coherent
with the views of Peter Drucker in that organisations do not pursue a single objective but in reality pursue
multiple objectives.
2. Financial objectives
Financial objectives mostly aim at the maximisation of shareholder wealth and are linked to measures of profit.
Examples of financial objectives include ROCE, ROI and EPS. Alternatively, financial objectives can refer to
objectives pursued by the financial manager. Other examples would therefore include maintaining optimal cash
balances, specific gearing ratios and stock turnover periods.
SUMMARY
Explain the relationship between corporate objectives and strategy.
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Introduction to Corporate Financial Decision Environment: 17
Introduction to Corporate Financial Decision Environment: 17
5. Evaluate and explain the roles , motivations and interests of different stakeholders in
financing decisions.
[Learning Outcome g]
5.1 Stakeholders
A stakeholder is a group or an individual who has vested interest in the organisation. They are affected by what a
company does, either positively or negatively. They want and expect different things from the organisation. It is
therefore said that they have a ‘stake’ in the business.
Stakeholders can be divided into two broad categories:
1. internal stakeholders
2. external stakeholders
Let us now understand the stakeholders in each of these groups and their objectives.
1. Internal stakeholders and their objectives
(a) Employees
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To have a cordial working environment.
To have ethical labour practices, e.g. reasonable working hours, safe working conditions etc.
To have opportunities for learning and advancement.
Direct, two-way communication between management and employees.
To receive a fair remuneration according to ability and performance.
To get satisfaction from doing meaningful and creative work.
(b) Managers
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To get satisfaction from doing meaningful and creative work.
To have opportunities for learning and advancement.
To have the freedom to take decisions for the work under their individual charge.
To have an input in decision-making.
To receive a fair remuneration according to ability and performance.
(c) Directors
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To have freedom to take decisions.
To have sufficient resources to implement the decisions.
To get technical support whenever required in taking various decisions.
To gain the support of the shareholders in the general meetings towards the well-intended decisions and
actions of the directors.
To receive a fair remuneration according to ability and performance.
To get notices of meetings well in advance, as laid down in the rules.
To have the full support of managers and employees in the fulfilment of corporate objectives e.g. work
discipline, team work etc.
To have the full support of suppliers and contractors in the fulfilment of corporate objectives e.g. social
responsibility, environment protection etc.
2. External stakeholders and their objectives
(a) Customers
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To get high quality and attractive products and services from the company.
To pay a reasonable (and not exorbitant) price for the goods / services.
Company should consider the opinion of the customers while designing the products.
To get good after sale service, e.g. warranty maintenance, supply of spares etc.
(b) Suppliers and contractors
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To get reasonable prices and other terms for the material or services supplied.
To receive payment on time.
To get the opportunity to grow alongside the company.
Regular interaction with the company to share each other’s viewpoints and act on them, if appropriate.
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(c) Shareholders
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To increase wealth through dividends or capital appreciation (i.e. increase in share values).
Ethical behaviour from the directors who should not benefit at the cost of shareholders.
To receive financial statements and other information from the board of directors.
Participation in the general meetings, asking questions, discussing the company’s performance and voting on
certain issues, for example, appointment of directors, auditors etc.
(d) Government and local community
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To behave as a responsible citizen
To protect the health, safety and environment.
To use the natural resource efficiently.
To pay all due taxes on time.
To work as tax collectors in the case of indirect taxes.
To follow good labour practices.
To have regular dialogue with government agencies.
To generate economic growth and job opportunities. The government may provide appropriate tax incentives and
grants for this purpose.
To have a wider spread of ownership.
To follow all applicable laws and regulations.
To practice corporate social responsibility.
(e) Financial community (banks etc.)
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To abide by the terms and conditions (warrants) agreed at the time of disbursement of finance.
To grow economically and provide further opportunities to the financial community for additional business.
To not compromise the assets provided as a security to the bank, and maintain its financial health, in order to
protect its creditors from losses.
5.2 Stakeholders and financing decisions
Financing decisions refer to the decisions regarding the capital structure of the firm. Debt and equity are the two
major sources of finance and each of them is associated with varied levels of risk, control and benefits.
Consequently, the financial investors in a company would be:
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debt holders who earn a pre-determined rate of return, exercise lower control and are protected by contractual
obligations with regard to the amount invested
shareholders who exercise control over the company, are the owners of the company and therefore absorb
greater risk
Firms deploy debt capital to avail tax advantages; however, debt brings with it financial distress, agency problems
and loss of financial flexibility. Every finance and business startegy is affected by relevant actions of key
stakeholders.
Similarly, financing decisions can affect the value of the firm according to the existence of a conflict of interest
between:
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Management
Financial stakeholders – shareholders and lenders
Non-financial stakeholders – suppliers, customers, government, competitors
1. Role, motivations and interests of management and financial stakeholders in financing decisions
(and related conflicts)
While implementing financing and investment decisions, the interactions among managers, shareholders and
financiers can impact the process of identifying and selecting investment projects and the process of value creation.
Conflicts among the financial stakeholders can lead to selection of sub-optimal strategies which benefit a particular
stakeholder rather than maximise overall firm value.
In the event of presence of debt which is considered risky, managers acting in the interest of equity shareholders
may reject investment ventures with positive return on investment since value created would be beneficial only to
the lenders of the firm. Furthermore, they may also encourage high risk investments that reduce value from
debt holders and increase value for equity shareholders.
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Introduction to Corporate Financial Decision Environment: 19
Introduction to Corporate Financial Decision Environment: 19
In firms with low level of debt, managers may undertake negative return projects for personal reasons such as
empire building. It is important to monitor the decision-making power of management. However, presence of
debt acts as a disciplinary force over the management since they have to meet their interest and repayment
obligations on time and therefore manage operations effectively. This prevents management from engaging in
projects for their own benefit.
2. Role, motivations and interests of non financial stakeholders in financing decisions (and related
conflicts)
Non financial stakeholders are the business associates who have no direct financial stake in the company but
are concerned with the financial status of the company. This is because any financial crisis would impact them
negatively and vice-versa. Therefore, capital structure decisions influence them and they also play a role in
financing decisions. It is important that these interests are kept in mind while making financing decisions.
The level of gearing has an influence on the perception which non-financial stakeholders have about a company.
For example:
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Employees may view a highly geared company negatively and the management may stand to lose good
talent due to this negative perception on employee growth prospects.
In the event of liquidation (due to non-payment of debt), customers may not be able to obtain the required
products and after-sales service.
Suppliers may go out of business in the event the company goes through financial crisis.
Therefore, the above stakeholders may demand compensation for increased risk while dealing with the firm.
ABV Ltd manufactures office equipment. It is highly geared, with long term debt to equity ratio of 4:1 based on the
latest financial statements.
Furthermore, the earnings have deteriorated significantly, leading to risk of financial crisis.Apart from significant
pressure on management from lenders, the non-financial stakeholders are also demanding increased payments
from the firm.
The suppliers have stopped credit terms and are demanding advance payment for supplies; key employees are
on the verge of resigning for fear of salary delays. Customers are shifting to competition for fear of nonfulfillment of delivery terms. They are also concerned about after-sales service in the event of liquidation of the
firm.
With regard to role of competition in financing decisions, we need to discuss the following:

The response of competing firms to a firm’s capital structure
In case a firm is heavily leveraged, and competition is aware of significant fixed obligations affecting the firm’s
cash flows, this may be viewed as an opportunity by competition to play aggressive pricing and marketing
strategies to capture market share. This is because competition is aware that the firm does not have the liquidity
to react to such strategies in the short to medium term.

A firm’s capital structure affecting its position in the industry
In the event of a recession, a firm with high debt in its capital structure is more prone to liquidation risk than a
debt-free company. Therefore, the latter is in a more favourable position to adopt measures to survive during a
recession. Such a firm can afford to absorb short-term losses in the absence of fixed repayment obligations.
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Match the following:
Stakeholder
(i) Employees
(ii) Customers
(iii) Suppliers
(iv) Shareholders
Stakeholder objectives
(a) To pay a reasonable price for the goods / services.
(b) To receive payment on time.
(c) To increase wealth through dividends or capital appreciation
(d) To receive a fair remuneration according to ability and performance
6. Discuss how agency theory can be used to analyse the relationship between various
stakeholders in a corporation and how the resulting agency problems may be overcome.
[Learning Outcome f]
“The directors can meet their legal duties to shareholders and can pursue the objective of long-term shareholder
value successfully, only by developing and sustaining stakeholder relationships”.
However, “…the directors as a board are responsible for relations with stakeholders; but they are accountable to
the shareholders. This is not simply a technical point. From a practical point of view, to redefine the directors’
responsibilities in terms of the stakeholders would mean identifying all the various stakeholder groups; and
deciding the nature and extent of the directors’ responsibility to each.
The result would be that the directors were not effectively accountable to anyone since there would be no clear
yardstick for judging their performance. This is a recipe neither for good governance nor for corporate success.”
(Source: Hampel committee report)
Management has to develop and sustain these stakeholder relationships while it tries to meet its overriding
objective of maximisation of shareholder wealth. This can, however, be difficult in view of the conflicting objectives
among stakeholder groups; it is possible to please some of the people some of the time but not all the people
all the time. The consensus theory recognises that each organisation is a coalition of shareholders, directors,
employees, customers etc. each having different and sometimes opposing goals.
Since it is virtually impossible to satisfy each group completely, political compromise results, whereby each
party settles for less than the ideal. In this instance shareholder wealth is not maximised, other stakeholder groups
will also settle for less.
6.1 Agency theory
A principal-agent relationship exists where one party appoints another to fulfill certain responsibilities on
their behalf. Generally, the agent should act in the best interests of the principal and should not aim to benefit
at the expense of the principal.
The most prominent among the agency relationships in a business is the relationship between the shareholders
and the managers. This occurs because of the divorce of ownership and control. Shareholders are the legal
owners of companies but because, many times, they are not in a position to run the company on a daily basis,
directors are appointed. The overriding goal of financial management is maximisation of shareholder wealth.
It is the duty of the directors (agents) to act in the best interests of the shareholders (principals), never aiming at
personal gain at the cost of the shareholders.
© GTG
Introduction to Corporate Financial Decision Environment: 21
Introduction to Corporate Financial Decision Environment: 21
Diagram 4: Agency relationships in the company
There are other agency relationships in the company as well, such as:
1. Directors/ shareholders and creditors
The directors and shareholders (acting through the directors) are responsible for safeguarding the money the
company owes to the creditors and repaying them on time.
2. Employees and management
The employees of the company, in the discharge of their duties, perform numerous acts on behalf of the company.
Therefore, they are the agents of the managers / shareholders as they are responsible for fulfilling the duties
allocated to them.
3. Directors / shareholders and customers
The customers expect certain standards to be fulfilled as regards quality and credibility. Directors need to
ensure that these expectations are met at all times to achieve customer loyalty.
6.2 The agency problem
1. Directors vs. shareholders
The agency problem arises when the directors, as agents, have different aims and objectives from the
shareholders, as principals; there is said to be a conflict of objectives. The directors may seek to further their
own interests rather than shareholder wealth, in the following ways:
(a) Directors may design remuneration packages which are beneficial to them, e.g. during a period of high
profits; they may keep the fixed element of remuneration packages relatively low, but award higher percentage
bonuses linked to profits. Alternatively, in times of low profits, fixed remuneration may be increased.
(b) Directors will want to ensure that they are seen to be ‘earning their keep’. They may therefore focus on short
term profitability, opting for projects with shorter payback periods and better short-term profits, ignoring the
projects which may give better long-term results and stability to the company.
(c) Some directors, in order to gain power and prestige, may engage in ‘empire building’. They may therefore
engage in unprofitable takeover bids.
(d) As a means of artificially boosting the results, directors may engage in creative accounting practices e.g. off
Statement of financial position financing.
(e) To achieve a wider public profile, managers may go for diversification, which may not be what shareholders
desire. It may result in a loss of focus on the core business activity.
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(f) The managers may push forward social projects where they have personal interests e.g. funding the
construction of a gym at the school of the finance director’s son. If the above is allowed to continue, the
personal objectives of the managers become a priority, thereby relegating the objectives of the shareholders.
2. Management (directors) vs. employees
As the earnings of the company improve, the employees may believe that they need to be rewarded adequately
on a consistent basis. They may look forward to additonal bonuses apart from regular salaries. Furthermore,
employee unions may exert force on the management if their demands are not fulfilled.
3. Creditors vs. management
Creditors to whom the company owes significant sums of money may wish to exercise greater control on the
company. They may require regular reports on operating revenue, financial status, project progress etc, which
management may resist.
4. Customers vs. management (shareholders)
Customers may have strict preferences and may exercise resistance to changes in products. Management may
sometimes be constrained between consumer interest vs. cost considerations. Furthermore, in all the above
conflicts, the additional conflict arising out of the effect of government / regulatory interventions cannot be ignored.
The Kelloggs Company is the world’s leading producer of cereals. Kelloggs has built its position as a market leader
through its committment to ethical practices. It was faced with a situation of conflicting stakeholders interests.
Kelloggs changed the formula of its product ‘Honey Loops’ to reduce the sugar content. This was done to
comply with government requirements for food content. However, this had a negative impact on consumer
perceptions about the brand.
6.3 Overcoming the agency problem
As seen earlier, there may be a conflict of interest between the objectives of different stakeholders. In the case
of a company where the shareholding is widely held, the shareholders may have little control / influence on
management. Since it is management that looks after the day-to-day operation of a company, it takes most of
the important decisions which affect the achievement of objectives. Therefore, the focus of the efforts to resolve
the conflicts is on the management. Similarly, as we discussed earlier, the main conflict of interest is likely to arise
in the relationship between shareholders and managers, although there may also be other conflicts of interest.
1. Market forces to reduce agency problems
There are certain market forces which may operate to reduce / eliminate agency problems.
(a) Certain large institutional shareholders / participants who hold significant shares in the company may act
together to resolve the agency problem. For example, in case the managment is incompetitive, they may act
to exercise voting rights jointly to replace the management.
(b) Weak management may face the pressure of takeovers by firms in the same industry who may wish to takeover
the company and improve its financial position through efficient management. The management would act in
shareholder interest due to the pressure of a hostile takeover.
2. Resolving the agency problem
Jensen and Meckling were the first to develop a comprehensive agency theory of the firm. They show that the
principals, i.e. the shareholders, can assure themselves that the agent (management) will make optimal decisions
only if appropriate incentives are given and only if the agent is monitored.
© GTG
Introduction to Corporate Financial Decision Environment: 23
Introduction to Corporate Financial Decision Environment: 23
The key is to achieve goal congruence, i.e. the goals of management and the goals of the shareholders should,
as far as possible, be the same or equivalent. When the objectives of the two are congruent, the conflicts of interest
will be eliminated. Goal congruence may be achieved by utilising managerial reward schemes such as share
options and performance related pay. In addition, corporate governance codes of best practice and stock
exchange listing regulations are all aimed at ensuring the activities of management are regulated, so as to avoid
the pursuit of self interest.
(a) Performance-related pay
The shareholders may choose to compensate management on the basis of its proven performance i.e.
compensation is linked to the achievement of specific objectives of the organisation. However, managers still
manage to manipulate these to their advantage.
(i) Profits
This may lead to short-termism. Managers will seek to maximise profits in the short term to boost their own income.
Projects which may benefit the company in the long term, but which may be unprofitable in its early days may
be rejected.
(ii) Sales
Sales growth can be achieved by increasing spending on marketing, promotions and advertising, by reducing
the selling price or a combination of both. If this is done, sales growth would be achieved, but at the expense of
profitability.
(iii) Return on capital employed (ROCE) / earnings per share (EPS)
ROCE expresses profits before interest and tax as a percentage of capital employed. Some performance
related pay schemes may reward managers for maintaining, achieving or exceeding a certain ROCE.
Paklan plc’s ROCE is currently 10%. In an attempt to improve this figure a decision has been made to link directors’
remuneration to ROCE. In the next financial year if the directors achieve a minimum ROCE of 18% on new
investments, they will receive a basic bonus of Tshs 12 million. For each percentage above 18%, managers will
receive an extra Tshs 1 million pro rata.
In division A, a proposal for an investment project has been put forward requiring an investment of Tshs 2,000
million which will generate profits of Tshs 340 million in the first three years, and Tshs 420 million thereafter. This
equates to a 17% return in years 1 to 3 and a 21% return for the future. Another proposal for a two-year project
has been put forward. The return in year one will be 25% and will fall to 16% in year two. No profit generation is
expected beyond year two.
The more favourable project from an ethical and long-term perspective would be proposal one. However, since
the director’s’ remuneration is linked to the ROCE for that period, it is easy to see how they might be tempted to
opt for proposal two. It is due to these limitations of performance related pay that offering share options to
managers is another potential method of achieving goal congruence.
(b) Employee stock option plans (ESOPs)
The share option scheme gives the manager the option to purchase a specified number of shares at a fixed
price, within a specified period. If the price of a company’s shares increases above this price, then the
managers gain by exercising their options. There is no obligation to exercise the options if the share prices are
lower. Share options can therefore act as an incentive for managers.
Med Co issues share options to the executives of the company, valid for 2 years, at a price of Tshs 2,500 per
share. At the end of the two years, the market price of the share was Tshs 4,000 per share. It is very likely that
the managers will exercise their option, since for Tshs 2,500; they get a share worth Tshs 4,000. On the contrary,
if the market price of the share is Tshs 2,000, the managers will not exercise the option.
24 Financial Management Function
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Although a useful method for achieving goal congruence, share option schemes are subject to limitations.
(i) As mentioned above, share option schemes act as an incentive for managers only during the period of
option. Therefore, shareholders should draw up an ESOP plan which provides stock options on a continuous
basis to maintian goal congruence.
(ii) The market price of the shares of a company depends on many external factors, alongside the company’s
performance. In a period of economic boom, the share price of most companies will generally rise, to the
extent that this rise is not related to the performance of the specific company. Managers get rewarded for
results that are not due to their good financial management, but due to external factors. However, this would
be corrected in the medium term, since market would reward only performing companies.
If managers choose to exercise their options to buy shares, in effect, the company must issue more shares. This
can dilute the degree of control for existing shareholders.
(c) Monitoring performance
The shareholders as principals may monitor the actions of their agents (the management) to ensure that they
act in the interest of shareholders. This is achieved through engagement of audit and control procedures. This
cost would have to be incurred to ensure that they act to achieve the objective of shareholder wealth maximisation.
3. Regulatory requirements
(a) Corporate governance codes of best practice
(b) Corporate governence legislation in Tanzania including stock exchange regulations
(a) Corporate governance codes of best practice
There is no formal definition as such, however, corporate governance can be summed up as ‘the systems by which
companies are directed and controlled’. The collapse of large companies such as Bank of Credit and Commerce
International, Maxwell Communications in the UK, Enron and Worldcom in the US and similar cases elsewhere,
have highlighted the need to monitor and regulate the activities of management.
In the UK, various committees such as the Cadbury Committee (1992), Greenbury Committee (1995), Hampel
Committee (1998) and Higgs Committee (2003) produced reports providing guidance to managers on matters
relating to company meetings, directors, directors’ remuneration, board meetings and internal audits. The Financial
Reporting Council (FRC) published the ‘combined code on corporate governance’ during 2003, incorporating the
suggestions made by these committees.
(i) OECD Principles of Corporate Governance
On the international level, the Organisation for Economic Cooperation and Development (OECD) published the
“OECD Principles of Corporate Governance” in 2004. The principles were endorsed by OECD Ministers in 1999
and have since become an international benchmark for policy makers, investors, corporations and other
stakeholders worldwide.
The principles provide guidelines on the following:
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ensuring the basis for an effective corporate governance framework.
the rights of shareholders and key ownership functions
Equitable treatment of shareholders.
the role of stakeholders in corporate governance e.g. their ability to freely communicate their concerns about
illegal or unethical practices without being victimised.
disclosure and transparency e.g. on material matters such as the financial and operating results and related
party transactions.
responsibilities of the board e.g. members should act in good faith, with due diligence and care and in the
best interest of the company and its shareholders.
(b) Corporate governance legislation in Tanzania including stock exchange regulations
The Companies Act and the Public Corporations Act, 1992 provide the regulatory framework for corporate
governance in both private and public companies. The Capital Market and Securities Authority in exercise of its
powers under The Capital Market and Securities Act, 1994 has issued guidelines for Corporate Governance
to be followed by public listed companies in Tanzania.
© GTG
Introduction to Corporate Financial Decision Environment: 25
Introduction to Corporate Financial Decision Environment: 25
These guidelines strengthen corporate governance practices and promote the standards of self-regulation to
bring the level of governance in line with international trends.
(i) Principles of good corporate governance practices
Every listed company should be headed by an effective board and be accountable to its shareholders.
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The board should establish relevant committees, including, specifically, the audit and nominating committee.
Director’s remuneration
o
It should be sufficient to attract and retain directors.
o
Executive director’s remuneration should be competitively structured and linked to performance.
o
Non-executive director’s remuneration should be competitive.
o
Companies should establish a formal and transparent procedure for it.

The board should disclose all remuneration policies, especially as laid down in the guidelines (including share
options, director’s loans etc.).
There should be a balance of executive directors and non-executive directors with diverse skills (including at
least one-third independent non-executive directors) on the board.
There should be a formal and transparent procedure in the appointment of directors to the board.
No person shall hold more than three directorships in any public listed company at any one time.
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There should be shareholder participation in all major decisions. The board shall provide information on matters
including but not limited to major disposal of company’s assets, restructuring, takeovers, mergers, acquisitions,
reorganisations.
The board shall ensure that the accounts are presented in line with Tanzania FAS issued by the NBAA. The Board
should maintain a sound internal control system to protect shareholder’s interests, including appointment of
independent auditors.
(ii) Recommended best practices in corporate governance by public listed companies
The best practices (based on international standards in corporate governance ) are recommended for listed
companies to achieve the objective of maximisation of shareholder value through effective and efficient
management of corporate resources. These best practices relate to the following:

Board of directors
o
Role and responsbilities of the board of directors
o
A balanced board constitution for an effective board
o
Appointment and qualification of directors
o
Remuneration of directors
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Position of Chairman and Chief Executive
Rights of the shareholders
Conduct of general meetings
Accountability and role of audit committees
SUMMARY
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7. Describe the financial system and its relevance to Tanzanian economy
[Learning outcome g]
The financial system shifts funds either directly or indirectly from savers (Surplus Spending Units – SSUs) to users
(Deficit Spending Units – DSUs). Borrowers or Lenders can be categorised as household, business firms,
government or foreigners. Both household, business firms, government or foreigners could be savers or borrowers
depending on whether they need fund or have extra fund to be invested.
Flow of fund in an economy can be categorised into direct, semi-direct and indirect. With the direct placements, there
is no financial intermediation process as the users (Deficit spending units) get there funds directly from the savers
(surplus spending units). On getting the funds, the DSUs pledge their securities directly to the SSUs which are then
returned when the DSUs repay the loan. While with a semi-direct flow, the linkage between SSUs and DSUs is made
possible through the use of broakers and dealers whose role is just to bring borrowers and lenders together.
With the indirect placements, the financial markets play the role of financial intermediation whereby they act as a link
between the users (Deficit spending units) and the savers (surplus spending units). There is no direct contact
between the savers and the users. The SSUs place their deposits with the different financial institutions in the
financial markets which then package them and provide different credit and other financing facilities to the DSUs.
On getting the funds, the DSUs pledge their securities to the financial institutions as opposed to the SSUs in the
direct placement. The repayments are also channeled through the financial institutions.
Diagram 1: A schematic representation of Tanzanian economy
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Introduction to Corporate Financial Decision Environment: 27
Introduction to Corporate Financial Decision Environment: 27
8. Describe forms of market efficiency and its implications on determination of
securty’s prices
[Learning objective h]
The Meaning of Efficiency Market: A market is efficient when security prices reflect all the available information.
Under ideal conditions, information is free, and investors have the opportunity to take advantage of available
information and make rational decisions about securities prices in the market. Under non-ideal conditions,
information is not free, and investors have to do cost benefit analysis in order to decide how much information they
acquire to make rational decisions.
The efficient markets hypothesis (EMH), popularly known as the Random Walk Theory, is the proposition that current
stock prices fully reflect available information about the value of the firm, and there is no way to earn excess profits,
(more than the market overall), by using this information. It deals with one of the most fundamental and exciting
issues in finance –why prices change in security markets and how those changes take place. It has very important
implications for investors as well as for financial managers.
The term "efficient market" implies that, on the average, competition will cause the full effects of new information on
intrinsic values to be reflected "instantaneously" in actual prices. Many investors try to identify securities that are
undervalued and are expected to increase in value in the future, and particularly those that will increase more than
others. Many investors, including investment managers, believe that they can select securities that will outperform
the market. They use a variety of forecasting and valuation techniques to aid them in their investment decisions.
Obviously, any edge that an investor possesses can be translated into substantial profits. The EMH asserts that
none of these techniques are effective (i.e., the advantage gained does not exceed the transaction and research
costs incurred), and therefore no one can predictably outperform the market. The efficient markets hypothesis (EMH)
suggests that profiting from predicting price movements is very difficult and unlikely. The main engine behind price
changes is the arrival of new information. A market is said to be “efficient” if prices adjust quickly and, on average,
without bias, to new information. As a result, the current prices of securities reflect all available information at any
given point in time. Consequently, there is no reason to believe that prices are too high or too low. Security prices
adjust before an investor has time to trade on and profit from a new a piece of information.
Reasons for Efficient Market Hypothesis
The key reason for the existence of an efficient market is the intense competition among investors to profit from any
new information. The ability to identify over-and under-priced stocks is very valuable (it would allow investors to buy
some stocks for less than their “true” value and sell others for more than they were worth). Consequently, many
people spend a significant amount of time and resources in an effort to detect "mis-priced" stocks. Naturally, as more
and more analysts compete against each other in their effort to take advantage of over-and under-valued securities,
the likelihood of being able to find and exploit such mis-priced securities becomes smaller and smaller. In equilibrium,
only a relatively small number of analysts will be able to profit from the detection of mis-priced securities, mostly by
chance. For the vast majority of investors, the information analysis payoff would likely not outweigh the transaction
costs.
Implication of Efficient Market Hypothesis
The most crucial implication of the EMH can be put in the form of a slogan: Trust market prices!
At any point in time, prices of securities in efficient markets reflect all known information available to investors. There
is no room for fooling investors, and as a result, all investments in efficient markets are fairly priced, i.e on average
investors get exactly what they pay for. Fair pricing of all securities does not mean that they will all perform similarly,
or that even the likelihood of rising or falling in price is the same for all securities. According to capital markets theory,
the expected return from a security is primarily a function of its risk. The price of the security reflects the present
value of its expected future cash flows, which incorporates many factors such as volatility, liquidity, and risk of
bankruptcy. However, while prices are rationally based, changes in prices are expected to be random and
unpredictable, because new information, by its very nature, is unpredictable. Therefore, stock prices are said to
follow a random walk.
Forms of Efficient Markets
There are three types of efficient markets: weak form, semi-strong form, and strong form.
Weak Form Efficiency: The weak form of the efficient markets hypothesis asserts that the current price fully
incorporates information contained in the past history of prices only. That is, nobody can detect mis-priced securities
and “beat” the market by analyzing past prices. The weak form of the hypothesis got its name for a reason –security
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prices are arguably the most public as well as the most easily available pieces of information. Thus, one should not
be able to profit from using something that “everybody else knows”. On the other hand, many financial analysts
attempt to generate profits by studying exactly what this hypothesis asserts is of no value -past stock price series
and trading volume data. This technique is called technical analysis. The empirical evidence for this form of market
efficiency, and therefore against the value of technical analysis, is pretty strong and quite consistent. After taking
into account transaction costs of analyzing and of trading securities it is very difficult to make money on publicly
available information such as the past sequence of stock prices.
Semi-strong Form Efficiency: The semi-strong-form of market efficiency hypothesis suggests that the current price
fully incorporates all publicly available information. Public information includes not only past prices, but also data
reported in a company’s financial statements (annual reports, income statements, filings for the Security Exchange
Markets, etc.), earnings and dividend announcements, announced merger plans, the financial situation of company’s
competitors, expectations regarding macroeconomic factors (such as inflation, unemployment), etc. In fact, the public
information does not even have to be of a strictly financial nature. For example, for the analysis of pharmaceutical
companies, the relevant public information may include the current (published) state of research in pain-relieving
drugs.
The assertion behind semi-strong market efficiency is still that one should not be able to profit using something that
“everybody else knows” (the information is public). Nevertheless, this assumption is far stronger than that of weakform efficiency. Semi-strong efficiency of markets requires the existence of market analysts who are not only financial
economists able to comprehend implications of vast financial information, but also macroeconomists, expert’s adept
at understanding processes in product and input markets. Arguably, acquisition of such skills must take a lot of time
and effort. In addition, the “public” information may be relatively difficult to gather and costly to process. It may not
be sufficient to gain the information from, say, major newspapers and company-produced publications. One may
have to follow wire reports, professional publications and databases, local papers, research journals etc. in order to
gather all information necessary to effectively analyze securities.
Strong Form Efficiency: The strong form of market efficiency hypothesis states that the current price fully
incorporates all existing information, both public and private (sometimes called inside information). The main
difference between the semi-strong and strong efficiency hypotheses is that in the latter case, nobody should be
able to systematically generate profits even if trading on information not publicly known at the time. In other words,
the strong form of EMH states that a company’s management (insiders) are not be able to systematically gain from
inside information by buying company’s shares ten minutes after they decided (but did not publicly announce) to
pursue what they perceive to be a very profitable acquisition. Similarly, the members of the company’s research
department are not able to profit from the information about the new revolutionary discovery they completed half an
hour ago. The rationale for strong-form market efficiency is that the market anticipates, in an unbiased manner,
future developments and therefore the stock price may have incorporated the information and evaluated in a much
more objective and informative way than the insiders. Not surprisingly, though, empirical research in finance has
found evidence that is inconsistent with the strong form of the EMH
9. Describe the applicability of the EMH to corporate decision-making process
[Learning outcome i]
Market Efficiency and Corporate Investors Decision Making
Much of the existing evidence indicates that the stock market is highly efficient, and consequently, investors have
little to gain from active management strategies. Such attempts to beat the market are not only fruitless, but they
can reduce returns due to the costs incurred (management, transaction, tax, etc).
I Investors should follow a passive investment strategy, which makes no attempt to beat the market. This does not
mean that there is no role for portfolio management. Returns can be optimized through diversification and asset
allocation, and by minimization of investment costs and taxes. In addition, the portfolio manager must choose a
portfolio that is geared toward the time horizon and risk profile of the investor. The appropriate mixture of securities
may vary according to the age, goals, tax bracket, employment, and risk aversion of the investor.
Decribe briefly what is meant by agency problem in relation to a firm.
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Introduction to Corporate Financial Decision Environment: 29
A company proposes to be listed on the Dar es Salaam stock exchange. What principles should the shareholders
be aware of regarding corporate governance?
Answers to Test Yourself
Answer to TY 1
The main purpose of the financial manager is to ensure that the short- and long-term financial resources are
effectively managed in order to achieve the organisation’s objectives. The financial manager would therefore be
responsible for decisions regarding investments and their funding, dividend payout ratios and working capital
management.
Answer to TY 2
Money markets play a vital role in providing various short-term financing and investment options.
Providing short term liquidity - Money markets provide short term liquidity to the industry and public sector.
The start point of implementation of monetary policy is to change the money market rates which the central
bank can trigger through its control over money market conditions.
Means of finance - It is an important source of financing trade and industry through treasury bill or commercial
paper. It provides a channel through which suppliers of temporary cash surpluses meet users if funds with
temporary cash deficits.
Aids in working capital management - Since holding cash has a cost associated with it, money market
instruments provide an excellent opportunity for parking excess cash for limited period. This aids in efficient
working capital management.
Hedging risk - Organisations which seek to achieve their commercial objectives approach the money market
to hedge their foreign exchange (forex) risks and interest rate exposures. The forex market helps companies
to minimise the risks of foreign trade by providing effective hedging mechanisms. The foreign exchange
market facilitates the exchange of one currency for another. Using money market hedge, a company can
hedge its foreign currency receivables/payables. If a company has diversified its commercial operations in
different geographical areas, it may reduce its interest risk exposure by borrowing short-term finance in
different markets.





Answer to TY 3
The main drawbacks of the profit maximisation objective of Financial Management can be summed up as
follows:



The profit maximisation goal is a short-term concept.
The profit maximisation goal ignores the time value of money, that is, earnings earned during
different time periods are treated as equal.
The risks associated with the prospective stream of earnings and the effect of dividend policy
on the market prices of shares are not considered under this goal.
Answer to TY 4
Objectives and strategy are both related to the mission of an organisation or its long term purpose. Objectives
tell managers and employees precisely what they must achieve while the strategy explains how to go about
achieving it.
Answer to TY 5
Stakeholder
(i) Employees
(ii) Customers
(iii) Suppliers
(iv) Shareholders
a)
b)
c)
d)
Stakeholder objectives
To receive a fair remuneration according to ability and performance.
To pay a reasonable price for the goods / services.
To receive payment on time.
To increase wealth through dividends or capital appreciation.
Answer to TY 6
The agency problem in relation to a firm arises when there are conflicts of interest between the different
stakeholders.
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1. Directors v/s. Shareholders
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The directors may seek to further their own interests rather than shareholder wealth. There are numerous areas
where the conduct of the directors to further their own interests, results in conflicts with shareholder interests.
Certain examples:
(a) Directors may design remuneration packages which are beneficial to them.
(b) Directors will want to ensure that they are seen to be ‘earning their keep’. They may therefore focus on short
term profitability, opting for projects with shorter payback periods and better short term profits, ignoring the
projects which may give better long-term results and stability to the company.
(c) Directors may engage in ‘empire building’. They may therefore engage in unprofitable takeover bids.
(d) They may inflate profits figures in financial statements to achieve personal objectives.
(e) They may engage in reckless diversification to gain public prominance. It may result in a loss of focus on the
core business activity.
2. Management (Directors) v/s. Employees
This group may have conflicting interests. With increased earnings employees may believe that they need to be
rewarded adequately on a consistent basis. They may look forward to additonal bonuses apart from regular
salaries. Further employee unions may exert force on the management if their demands are not fulfilled.
3. Creditors v/s. Management
Creditors may wish to exercise greater control on the company. There may require regular reports on operating
revenue, financial status, project progress etc, which management may resist.
4. Customers v/s. Management (shareholders)
Customers may exhibit resistance to any change in product characteristics and may have strict preferences.
This may come in the way of cost reduction initiatives by the management.
The regulator / government may also impose restricitons / policy changes which may impact each of the above
groups.
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Introduction to Corporate Financial Decision Environment: 31
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Answer to TY 7
A company listed on the Dar es Salaam stock exchange is governed by The Capital Market and Securities Act,
1994 and the guidelines that may be issued from time to time. The shareholders must ensure that the following
principles are followed with regard to good corporate governance practices.
1. The company should be headed by an effective board and be accountable to its shareholders.
(a) The Board should establish relevant committees including specifically audit and nominating committee
(b) Director’s remuneration
(i) It should be sufficient to attract and retain directors
(ii) Executive director’s remuneration should be competitively structured and linked to performance
(iii) Non-executive director’s remuneration should be competitive
(iv) Companies should establish a formal and transparent procedure for it.
(c) The Board should disclose all remuneration policies especially as laid down in the guidelines (including
share options, director’s loans.
(d) There should be a balance of executive directors and non-executive directors (including at least one-third
independent non-executive directors) on Board of diverse skills
(e) There should be a formal and transparent procedure in the appointment of directors to the Board.
(f) No person shall hold more than three directorships in any public listed company at any one time.
(g) There should be shareholder participation in all major decisions. The board shall provide information on
matters including but not limited to major disposal of company’s assets, restructuring, takeovers, mergers,
acquisitions, reorganisations.
(h) The Board shall ensure that the accounts are presented in line with Tanzania FAS issued by the NBAA. The
Board should maintain a sound internal control system to protect shareholder’s interests including appointment
of independent auditors.
Apart from the above, there are certain recommended best practices to achieve the objective of maximisation of
shareholder value through effective and efficient management of corporate resources. The shareholders should
ensure that the company adopts these while desigining its corporate governance policies.
Quick Quiz
1. What is financial management?
2. List the main functions of a financial manager.
3. Would a finance manager be involved in a merger or acquisition decision?
4. Can the board of directors make a decision regarding dividends, without consulting the financial manager?
5. What are the two aims of working capital management?
6. When does capital rationing arise?
7. Define the term financial intermediary and give three examples of financial intermediaries.
8. In financial management, what is assumed to be the main financial objective?
9. What is meant by the ‘principal-agent’ relationship that exists between managers and shareholders, and
how does this give rise to the ‘agency problem’?
10. What is meant by the term ‘goal congruence’?
11. Identify two methods for achieving goal congruence between shareholders and directors.
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Introduction to Corporate Financial Decision Environment: 33
12. What is meant by the term ‘corporate governance’?
13. State whether the following statements are true or false:
(a) The impact of an economic slowdown in one country is restricted to that region alone.
(b) Non-financial stakeholders have no role in financing decisions.
(c) Weak management may face the pressure of takeovers by firms in the same industry who may wish to
take over the company and improve its financial position through efficient management.
Answers to Quick Quiz
1. Financial management involves the efficient and effective management of the long and short term financial
resources of an organisation in order to achieve the organisation’s objectives.
2. The main functions of a financial manager are to make decisions on matters such as:
investment
financing

dividend

working capital

overall financial planning and control

3. Yes, the finance manager would advise on whether an investment is financially viable and how it should be
funded.
4. The financial manager should be consulted; however, the final decision lies with the board of directors.
5. The aims of working capital management are liquidity and profitability. The financial manager will advise on the
optimum level of working capital to ensure debts can be paid off as and when they fall due, and also to ensure
that investment opportunities are not lost because of cash being tied up in idle assets.
6. Capital rationing arises when an organisation’s potential to invest is limited because of restrictions on
funding. In such a case projects will have to be ranked according to profitability and invested in accordingly.
7. A financial intermediary is an institution that acts as a middleman between the borrower and the lender.
Examples of financial intermediaries are insurance companies, banks and mutual funds.
8. The maximisation of shareholder wealth is assumed to be the main financial objective.
9. A principal-agent relationship exists where one party appoints another to fulfill certain responsibilities on
their behalf. Such a relationship exists between shareholders and directors. The shareholders are the legal
owners of the business. However, many a time they are not in a position to run the company on a daily
basis. Therefore, directors are appointed to fulfill this responsibility on their behalf. As such the directors
(agents) should act in the best interest of the shareholders (principals), seeking to achieve the shareholders’
aim of wealth maximisation.
The ‘agency problem’ occurs as a result of the divorce of ownership and control. It is manifested where
directors’ priorities their personal goals at the expense of the shareholders.
10. ‘Goal congruence’ is any attempt made to equate the goals of one group to those of another e.g. equating
the goals of shareholders and directors.
11. Goal congruence between shareholders and directors may be achieved by:
(a) Performance related pay schemes where the remuneration of directors is linked to specific goals of
the organisation / shareholders e.g. profits, sales, certain levels of ROCE.
(b) Share options schemes which give managers the option to purchase shares at a specific price (relatively
low) within a certain period. Managers gain financially as they are allowed to purchase the shares at a
lower price and sell at the higher market price.
12. There is no definition as such for ‘corporate governance’, however, it can be summed up as ‘the systems
by which companies are directed and controlled’.
34 : Financial Management Function
13.
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(a) False
(b) False
(c) True
Self Examination Questions
Question 1
Whilst the financial plans of the business are based on a single objective, it faces a number of constraints that
put pressure on the company to address more than one objective simultaneously.
Required:
What types of constraints might the company face when assessing its long-term plans? In your answer, refer
specifically to:
(a) Responding to various stakeholder groups; and
(b) The difficulties associated with managing organisations with multiple objectives.
Question 2
It is said that failing to plan is planning to fail. Discuss this statement in the context of corporate and financial
objectives.
Question 3
It is said that remuneration schemes linked to performance encourage managers to focus on the achievement of
corporate objectives as opposed to their own personal objectives. Explain the operations and limitations of such
schemes as performance related pay.
Question 4
Source4u Ltd is an innovative IT services organisation that brings people, business and technologies together. It
has clients around the world in a variety of industries including automotive, oil and gas and manufacturing.
Source4u’s aim is to add value for clients by improving efficiency and productivity or reducing waste. It has been
on an earnings growth trajectory of 20-25% for the past few quarters. The management wants to ensure that the
growth rates are maintained.
As a finance manager of the organisation, discuss the external factors / scenarios that could impact business
and finance strategies and explain how the company could plan for it.
Answers to Self Examination Questions
Answer to SEQ 1
(a) Generally, when we look at the long-term goals of a company, we can say that there is no conflict of
interest. However, in the short run there is a possibility of a conflict between the various stakeholder
objectives.
Conflicts with the financial objective of stockholder wealth maximisation
In recent times, there has been a controversy regarding the primary goal of corporate governance i.e.
“Stockholders vs. Stakeholders”. If we look at the primary financial objective of shareholders’ wealth maximisation,
there are possible conflicts with the objectives of other stakeholders.
Employees, managers, suppliers, contractors and the financial community would like to get a higher income
from the company. However, paying higher amounts to these stakeholders means lower profits and hence
lower wealth creation for the shareholders. Similarly, charging lower amounts to customers or spending higher
amounts on the product reduces profits. Therefore, the two objectives conflict with each other, at least in the short
run.
We can generally say that the claims of the other stakeholders can be judiciously considered within the overall
long-term objective of shareholder wealth maximisation.
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Introduction to Corporate Financial Decision Environment: 35
Other possible conflicts
There may be other possible conflicts, for instance:

Customers may demand new high- t e c h products that have the latest features. The employees
may be afraid of the effects of new technology on their jobs. Shareholders may be concerned about the
possible effect on the return on their investments. Management may be worried about the huge capital
expenditure required.

The government may want the organisation to pay high direct and indirect taxes. The customer may
not be willing to share the burden of additional indirect taxes, nor may management be eager to bear the
additional direct taxes.

The CEO and other managers will want to have higher remuneration, but the shareholders may want to
put a cap on it.

The local community may want the entity to install environmentally friendly equipment, but the
shareholders and management may be opposed to this due to the exorbitant costs.

The financial community may want to raise the interest rates. However, management may wish to
repay the loans if the interest costs are raised, and opt for a share issue.

The financial community may want the company to invest in safe projects. However, management
may wish to invest in a risky but more profitable project.
(b) The following are the difficulties associated with managing organisations with multiple objectives:

Every organisation has a number of stakeholders such as shareholders, directors, employees etc.
The objectives of each stakeholder are different. Furthermore, the objectives of the various stakeholders
are not congruent. This can lead to opportunity cost, which in turn will lead to a reduction in profits.

Due to multiple objectives, each managerial decision will also face many limitations since the process
of goal congruence is complex.

High cost may be incurred by a company to satisfy the needs of various stakeholders other than
shareholders.

The objectives of stakeholders may conflict. For example, the shareholders objective is to maximise
profits whereas the employee’s objective is to increase their remuneration.

Therefore, stakeholders need to be ranked in order of
importance.

Sometimes, when new stakeholders emerge, it can create a difficulty of long-term strategic management
i.e. the demands of the stakeholders have to be taken into account.

When objectives are not clearly identified, the organisation will not be able to easily ascertain whether or
not they have met their objectives.
Answer to SEQ 2
The objectives of an entity relate directly to the organisation’s main goals and, ultimately, to its mission. The
objectives tell the managers and employees precisely what they are supposed to achieve. The objectives of an
entity can be broadly classified as corporate objectives and financial objectives.
(a) Corporate Objectives
Corporate objectives relate directly to the organisation’s goals and indirectly to its mission.
Some examples of corporate objectives are:
(i) Towards customers: to provide products, services and solutions of the best quality.
(ii) Market Leadership: to provide useful and significant products, services and solutions to markets and
expand into new areas that build on existing technologies, competencies and customer interests.
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(iii) Employees: to provide employees with employment opportunities based on performance; to ensure a safe
and comfortable work environment that values their diversity and recognises individual contributions; and to
help them gain a sense of satisfaction and accomplishment from their work.
It can be seen that corporate objectives tend to be quite varied.
(b) Financial objectives
Financial objectives are mostly linked to measures of profit and aim at the maximisation of shareholder wealth.
Examples of financial objectives include maximisation of ROCE, ROI and EPS. Alternatively, financial objectives
can refer to objectives pursued by the financial manager. Other examples would therefore include maintaining
optimal cash balances, specific gearing ratios and stock turnover periods.
Corporate objectives are more business or commercially-oriented, as opposed to financially-oriented. Once the
objectives of an organisation have been clearly defined the entity has to develop a strategy to achieve these
objectives. Strategies are usually associated with long-term planning and thinking. A strategy can be defined as
a course of action, including the specification of resources, necessary to achieve an objective. In other words, a
strategy tells managers how to go about achieving the objectives.
For example, if an entity has the corporate objective of market leadership as stated above, it will have to devise
strategies to retain the existing customers and expand the existing market.
Therefore, it will have to plan:



the number of employees, dealer and distributors required in each region to cater to the market
market research to analyse the customer needs so as to attract new customers, etc.
some attractive marketing schemes
Only if the company systematically plans each of the above aspects will it be able to meet its goals of market
leadership. On the other hand, if the company does not construct a plan to achieve its objectives, it will not be able
to meet the set goals. In other words, failing to plan is planning to fail.
Answer to SEQ 3
Performance related pay attempts to achieve goal congruence by equating the goals and objectives of the
organisation with those of the individual managers. Corporate objectives may relate to increases in profit levels,
sales turnover growth or achieving certain levels of ROCE on investments. Managers, however, may be
interested in enhancing their experience, prestige, status and wealth.
Good performance related pay schemes provide the above rewards to managers on the basis of achieving
corporate objectives. It is therefore imperative to link personal rewards with corporate objectives in order for
both parties (managers and shareholders) to win.
It therefore follows that the objectives of the company are to be clarified and made applicable to each manager,
e.g. if the organisation’s objective is to increase profits, this must be broken down into specific targets for each
director:

the marketing director must achieve an increase in the market share of, say, 7%.

the sales director should achieve a turnover with at least 20% rise in sales out of which 40% should be
contributed by the new product lines.

the finance director must ensure that new financing options are explored during the year, bringing the
weighted average cost of debt finance lower than the previous period by atleast 150 bps.
If objectives are specific and quantified as above, each manager will be completely aware of what they have to
achieve; this will avoid any confusion or ambiguity. The criteria for measuring the achievement of these
objectives should also be clear to managers.
The next step would be to link rewards to objectives e.g. the marketing manager may be awarded a bonus of Tshs
10 million if he meets his 7% target, and a further Tshs 1 million for each percentage above 7. This secures
commitment from the managers to achieve the objectives. However, in spite of the above, managers still
manage to manipulate such systems to their advantage e.g. if a manager’s remuneration is linked to profits this
may encourage short-termism, where managers favour projects yielding high profits in the short term, but which
may be costly as long term investments.
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Introduction to Corporate Financial Decision Environment: 37
Answer to SEQ 4
The organisation is involved in IT services and would be faced with constant challenges in each of the following
areas while evaluating its financial and business strategies:
(a) Political factors
(i) If the company is dependent significantly on outsourcing contracts, any changes in law by the foreign
country / any decision to roll back / reduce outsourcing would impact business strategies.
(ii) Any directive by the government in education needs to be evaluated. For example, if there is any drop in
admissions (on account of increased fees) leading to shortage of availability of skillled manpower, there would
be a direct impact on implementation of IT solutions and outsourcing contracts. In such a situation, the firm
can explore in-house technical training beyond basic university education to maintain quality of skilled
manpower.
(b) Economic factors
(i) Overall liquidity situation in the economy would impact interest rates and borrowing costs. The manager
should have complete knowledge of all money market and capital market products.
(ii) Willingness of financial intermediaries to support new ventures would impact financing decisions. This would
require significant efforts by management to explain business plan, growth prospects etc. to the financiers.
Also, the company needs to ensure that the market price is not impacted through increased usage of debt
finance.
(iii) The firm would be exposed to crrency risk. The extent of impact on revenue due to currency fluctuations
need to be evaluated. This would depend on the quantum of foreign exchange transactions and the
currency movement. The firm can tap financial markets to hedge against currency risks.
(c) Macro economic situation
(i) Any global recessionary trends would impact its revenue significantly since the firm is dependent on both
domestic and international clients. The firm should focus on cost cutting initiatives and discourage fixed
costs. However, since technology & outsourcing brings efficiency, it is possible that certain solutions
offered by the firm are sought by government and private firms during recession.
(ii) The macro economic parameters in terms of GDP, growth of various sectors, inflation, employment etc.
need to be reviewed constantly.
(iii) The impact on any economic or policy changes on the specific sector(s) which contribute to Source4u’s
revenue significantly need to be evaluated.
(d) Technological factors
The speed of technological advances means that existing electronic equipment, IT processes and systems will
quickly become outdated. To remain competitive, a business must ensure that its processes and systems support
innovation and creativity for itself and its customers. Financial and business strategies need to be reviewed and
changes adapted in quick response to changes in external environment and financial markets.
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/ŶĚŝĐĂƚŝǀĞdžĂŵŝŶĂƚŝŽŶYƵĞƐƚŝŽŶƐ
IEQ 1
At a recent board meeting of Co., a non-executive director suggested that the company’s remuneration committee
should consider scrapping the company’s share option scheme, since the executives could be rewarded by the
scheme even when they do not perform well. A second non-executive director had a view that, even when the
executives act in ways which decrease the agency problem, they might not be rewarded by the share option scheme
if the stock markets were in decline.
REQUIRED:
Explain the nature of the agency problem and discuss the use of share option schemes and performance-related
pay as methods of reducing the agency problem in a stock-market listed company.
IEQ 2
Is profit maximization an appropriate goal for financial managers? Should financial managers concentrate strictly on
cash flow and ignore the impact of their decisions on EPS?
IEQ 3
In relation to the efficient market hypothesis:
(i) Briefly discuss its significance to a financial manager.
(3 marks)
(ii) Explain the differences between the semi-strong form and the strong form of market efficiency and how each
can be tested.
(5 marks)
ŶƐǁĞƌƐƚŽ/ŶĚŝĐĂƚŝǀĞdžĂŵŝŶĂƚŝŽŶYƵĞƐƚŝŽŶƐ
Answer to IEQ 1
Agency problem
The problem arises when managers (agents) pursue their own interests (eg paying themselves high salary) instead
of pursuing shareholders (owners) interests i.e. Maximization of longterm shareholders wealth
The primary financial management objective of a company is usually taken to be the maximization of shareholder
wealth. In practice, the managers of a company acting as agents for the principals (the shareholders) may act in
ways which do not lead to shareholder wealth maximization. The failure of managers to maximize shareholder wealth
is referred to as the agency problem.
The agency problem refers to the fact that, in practice, actual total shareholder returns (TSR) are usually below the
theoretically possible TSR. The resulting loss in shareholder wealth is known as “agency costs” and is caused by
sub-optimal performance by management and the costs incurred in controlling the management.
Shareholder wealth increases through payment of dividends and through appreciation of share prices. Since share
prices reflect the value placed by buyers on the right to receive future dividends, analysis of changes in shareholder
wealth focuses on changes in share prices. The objective of maximizing share prices in commonly used as a
substitute objective for that of maximizing shareholder wealth.
Nature of the problem
This occurs due to the separation of ownership and control whereby shareholders who are the owners (Principals)
of a corporation are not the ones controlling affairs of the corporations rather the corporation is being controlled by
management (Agents). The agency problem arises because the objectives of managers differ from those of
shareholders, because there is a divorce or separation of ownership from control in modern companies; and because
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Introduction to Corporate Financial Decision Environment: 39
there is an asymmetry of information between shareholders and managers which prevents shareholders being aware
of most managerial decisions.
Methods of reducing agency costs
Share options/Linking management rewards to shareholders wealth improvement e.g employees share ownership
plans).
One way to encourage managers to act in ways that increase shareholder wealth is to offer them share options
These are rights to buy shares on a future date at a price which is fixed when the share options are issued. Share
options will encourage managers to make decisions that are likely to lead to share price increases (such as investing
in projects with positive net present values), since this will increase the rewards they receive from share options.
The higher the share price in the market when the share options are exercised, the greater will be the capital gain
that could be made by managers owning the options.
Share options therefore go some way towards reducing the differences between the objectives of shareholders and
managers. However, it is possible that managers may be rewarded for poor performance if share prices in general
are increasing. It is also possible that managers may not be rewarded for good performance if share prices in general
are falling. It is difficult to decide on a share option exercise price and a share option exercise date that will encourage
managers to focus on increasing shareholder wealth while still remaining challenging, rather than being easily
achievable.
Performance related pay
Due to the potential problems with share option schemes it may be advisable to consider performance related pay
as an alternative method of managing the agency problem. Performance-related pay is a financial reward system
for managers where some, or all, of their compensation is related to how their performance is assessed relative to
stated criteria. The criteria may include profitability targets and whilst profit maximization is not necessarily consistent
with shareholder wealth maximization at least management should feel a direct link between their performance and
profits, whereas the firm’s share price may be influenced more by overall stock market conditions.
Answer to IEQ 2
In arguing that managers should take steps to maximize the firm’s stock price, we have said nothing about the
traditional objective, profit maximization, or the maximization of earnings per share (EPS). However, while a growing
number of analysts rely on cash flow projections to assess performance, at least as much attention is still paid to
accounting measures, especially EPS. The traditional accounting performance measures are appealing because (1)
they are easy to use and understand; (2) they are calculated on the basis of more or less standardized accounting
practices, which reflect the accounting profession’s best efforts to measure financial performance on a consistent
basis both across firms and over time; and (3) net income is supposed to be reflective of the firm’s potential to
produce cash flows over time.
Generally, there is a high correlation between EPS, cash flow, and stock price, and all of them generally rise if a
firm’s sales rise. Nevertheless, as we will see in subsequent chapters, stock prices depend not just on today’s
earnings and cash flows—future cash flows and the riskiness of the future earnings stream also affect stock prices.
Some actions may increase earnings and yet reduce stock price, while other actions may boost stock price but
reduce earnings. For example, consider a company that undertakes large expenditures today that are designed to
improve future performance. These expenditures will likely reduce earnings per share, yet the stock market may
respond positively if it believes that these expenditures will significantly enhance future earnings. By contrast, a
company that undertakes actions today to enhance its earnings may see a drop in its stock price, if the market
believes that these actions compromise future earnings and/or dramatically increase the firm’s risk.
Even though the level and riskiness of current and future cash flows ultimately determine stockholder value, financial
managers cannot ignore the effects of their decisions on reported EPS, because earnings announcements send
messages to investors. Say, for example, a manager makes a decision that will ultimately enhance cash flows and
stock price, yet the short-run effect is to lower this year’s profitability and EPS. Such a decision might be a change
in inventory accounting policy that increases reported expenses but also increases cash flow because it reduces
Introduction to Corporate Financial Decision Environment: 39
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40 : Financial Management Function
current taxes. In this case, it makes sense for the manager to adopt the policy because it generates additional cash,
even though it reduces reported profits. Note, though, that management must communicate the reason for the
earnings decline, for otherwise the company’s stock price will probably decline after the lower earnings are reported.
Rewards - Senior managers might seek to ensure that they are highly rewarded, regardless of whether their company
is doing well or badly. shareholders are more likely to want directors to be paid well only if the company achieves a
good performance
Answer to IEQ 3
(i)
(ii)
Significance of EMH to financial managers.

If the EMH is correct and share prices are fair, there is no point in
financial managers seeking to
mislead the capital market, because such attempts will be unsuccessful. Window-dressing financial
statements, for example, in order to show a company’s performance and position in a favourable light,
will be seen through by financial analysts as the capital market digests the financial statement
information on pricing the company’s shares.

Another consequence of the EMH for financial managers is that there is no particular time which is best
for issuing new shares, as share prices on the stock market are always fair.

Because share prices are always fair, there are no bargains to be found on the stock market, i.e.
companies whose shares are undervalued. An acquisition strategy which seeks to identify and exploit
such stock market bargains is pointless if the EMH is correct.
Semi-strong form efficiency: This form of pricing efficiency arises when share prices fully and fairly reflect
all relevant and available public information, which includes all past information. Public information cannot
therefore be used to make an abnormal gain, since capital markets and share prices quickly and accurately
respond to new information. Well-developed capital markets are held to be semi-strong form efficient.
Strong form efficiency: this form of pricing efficiency arises when share prices fully and fairly reflect all private
information as well as public information. When capital markets are strong form efficient, no-one can make
abnormal returns, even investors who possess private or insider information. This level of pricing efficiency is
not found in the real world, which is why governments legislate against insider dealing.
Testing for both is based on the existence of abnormal return ARj = RrJ – Rej
Where
ARJ = Abnormal return of asset j
Rrj = realized return of asset j
Rej = expected return of asset j
If EMH holds then ARJ

 iid 0  2

For semi-strong it is about testing whether an event or information set leads to realizing AR.
For strong form it is about testing whether those considered as possessing inside or superior
information realize AR.
40
Financial Management Function
SECTION B
Time Value of Money: 41
PRINCIPLES OF VALUATION
B1
STUDY GUIDE B1: TIME VALUE OF MONEY
Financial decisions involve consideration of cash inflows and outflows which occur over different time periods.
When a person invests money, the person expects to receive returns in the future. A person may invest in various
avenues like bank fixed deposits, investment in shares and stocks, investment in a new business etc. A person
expects to receive returns on the investments made; there is an immediate cash outflow when a person invests
money whereas the inflow occurs after a certain period which may be a number of days, months, or even
years.
Similarly, when a person borrows money from a bank, there is an immediate cash inflow and there is a cash
outflow in the future in the form of interest payment and principal repayment. Value of money at the time returns
are received on the investment may be different from the value of money invested. Value of money at the time
the money is borrowed from the bank will be different from the value of money at the time of repayment. This is
called the time value of money.
Time value of money is a very important concept in financial management. It can be used to make decisions in
respect of investment alternatives or for calculations relating to interest on loan or in respect of leases etc. If
time value of money is not taken into account at the time of financial decision making, it may lead to wrong
decisions. Cash flows in absolute terms are not directly comparable until they are adjusted for timing differences.
This Study Guide discusses the meaning of time value of money, the techniques of measuring time value of
money, the role it plays in the financial management and its various applications.
a) Define the time value of money concept, its two main perspectives and explain the role it plays in
financial management.
b) Apply the time value of money concept to determine future and present values of different cash flow
patterns.
c) Apply the time value concept to evaluate different cash flow options and plan for various activities such
as sinking funds, deferred annuity, retirement plan and capital recovery plans.
d) Apply the time value of money to value real securities like ordinary shares, preferred shares and
debentures.
42 Principles of Valuation
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1. Define the time value of money concept, its two main perspectives and explain the role it
plays in financial management.
[Learning Outcome, a]
1.1 Time value of money
Time value of money means that the value of money is different at different points of time.
The value of a particular amount of money received today is more than its value if received in future. Also,
invested money earns income over time. This is referred to as time value of money. The worth of money that a
person has today is more than the expectation of receiving that money in the future. Money in hand today can
be invested and returns can be earned on that investment.
Arthur may have Tshs 1,000 in hand today, which he can invest @ 7% per year for one year. At the end of the
year, Arthur will receive an amount of Tshs 1,070. Hence, it can be said that the future value of Tshs 1,000 at an
interest rate of 7% for a year is Tshs 1,070.
Arthur will prefer the higher amount of Tshs 1,070 to the smaller amount of Tshs 1,000. The rate of interest of 7%
per annum is the time value of money. The cash flow received today has more value than the cash inflow in the
future due to the investment opportunity available.
Money has time value because of the following reasons:
1. Risk: there is no certainty about the future and involves risk; a business enterprise does not have much
control over future cash inflows as it depends on external factors like debtors etc. Therefore, a person prefers
receiving cash in the present rather than in the future.
2. Consumption: a person generally prefers current consumption to future consumption.
3. Investment opportunity: money received today can be invested by the person to earn a high rate of return in
the future.
4. Inflation: in an inflationary economy, money received today has more purchasing power than money
received in future.
1.2 Perspectives of time value of money
Any financial decision involves comparison of the cash inflows and outflows which accrue over a number of
years. For example, when investment is made in a project, the firm has to acquire assets which are used in –
say - production. The inflows from this activity will be accrued over a number of years. However, the firm will
have to invest in fixed assets at the time of inception for enabling production.
This means that there will be cash outflows at the time of setting up the plant which will have to be c ompared
with the inflows over a period once production starts. Thus, cash inflows and outflows accrue over different
periods of time. Comparing the inflows and outflows as they are generated will be incorrect as they accrue over
different periods of time. In order to enable a meaningful comparison, adjustment has to be made for the
difference in timing of the cash flows.
There are two perspectives to converting the cash flows to a common point in time:
1. Compounding Technique (Future Value)
2. Discounting Technique (Present Value)
Time Value of Money: 43
Time Value of Money: 41
© GTG
1. Compounding Technique
Compounding is the technique of calculating future value of cash flows when the present values are stated.
Future value represents the amount that an investment made today will grow to at some point of time in future if
invested at a specific rate of interest.
In compounding technique, interest is calculated on the total amount of principal + interest earned at the end of
each compounding period. Principal is the amount of money invested on which interest is received. For
example, a specific amount is invested at the beginning of the year for three years and if compounding of
interest happens at the end of every year, then interest will be calculated at the specified rate on the original
amount invested (principal) at the end of the first year.
The interest so calculated will be added to the original amount invested and interest for the second year will be
calculated on the original amount invested plus interest on it for the first year. For the third year, interest will be
calculated on the total of the principal invested plus interest for the first and second years. This is called
compounding technique.
Particulars
Amount invested ( Tshs )
Interest rate (%)
Interest amount ( Tshs )
Principal + Interest ( Tshs )
20X1
500,000
10.00
50,000
550,000
Year
20X2
550,000
10.00
55,000
605,000
20X3
605,000
10.00
60,500
665,500
In the above table, an amount of Tshs 500,000 invested in Year 1 earns an interest of Tshs 50,000 @ 10% yearly
rate compounded annually. This interest is added to the principal amount of Tshs 500,000; for Year 2, principal
becomes Tshs 550,000. Interest for Year 2 is calculated on Tshs 55,000 @ 10% which is then added to the
principal of Tshs 550,000. Principal for Year 3 is Tshs 605,000 and interest for Year 3 is calculated on Tshs
605,000.
In the above example, interest is earned @ 10% yearly rate compounded annually.
Formula for compounding
Formula for compounding of interest is given as follows:
𝐴𝐴 = 𝑃𝑃(1 + 𝑖𝑖)𝑛𝑛
In the above equation:
A= amount at the end of the period
P= principal at the beginning of the period
i= rate of interest
n= number of years
Continuing with the above example of compounding technique,
Amount of interest at the end of the third year can be calculated as follows:
𝐴𝐴 = 500,000(1 + 0.10)3 = 665,500
The above formula can be applied for arriving at the compounded interest value for an investment. However,
this calculation will be time- consuming if the number of years is high say 20 or 25 years. For this purpose,
compound interest tables are available which can be used for finding compound interest value.
44 Principles of Valuation
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There is a sample snapshot of compound value table at the end of this Study Text.
In the above example, we have considered annual compounding that means compounding is done once in a
year; interest can be compounded more than once a year also. Semi - annual compounding means compounding
of interest happens two times a year whereas quarterly compounding means that compounding will happen after
every 3 months in a year. Monthly compounding means that compounding will happen every month.
Formula to compute compound value for multiple compounding periods is given as follows:
𝑖𝑖 𝑚𝑚𝑚𝑚
𝐴𝐴 = 𝑃𝑃 (1 + )
𝑚𝑚
In the above equation:
A= amount at the end of the period
P= principal at the beginning of the period
i= rate of interest
n= number of years
m= number of times compounding is done in a year
Calculate the amount to be received by investors when they invest Tshs 100,000 for 2 years at an interest rate of
10% compounded quarterly.
Amount to be received will be:
𝑖𝑖 𝑚𝑚𝑚𝑚
𝐴𝐴 = 𝑃𝑃 (1 + )
𝑚𝑚
𝐴𝐴 = 100,000 (1 +
= Tshs 121,800
0.10 (4)(2)
)
4
2. Present Value or Discounting Technique
Present value is the current value of a future amount. Present value of money that will be received in the future
will be less than the value of money in hand today. Hence this technique is also called discounting techniq ue.
This technique determines the present value of a future amount assuming that the investor has an opportunity
of earning a return on his money. This return is known as the discount rate. Present value is the opposite of
compound value. In compound value, money invested increases because of compounding effect.
Formula for present value
Present value equation is given as follows
𝑃𝑃 =
𝐴𝐴
(1 + 𝑖𝑖)𝑛𝑛
P = present value of future sum to be received
A = sum to be received in future
I = interest rate
N = number of years
© GTG
Time Value of Money: 45
Time Value of Money: 43
We can calculate the present value with the help of annuity tables. These Annuity tables provide the present
value of a unit of currency for various combinations of interest rate and number of years. The present value of a
future amount can be calculated by multiplying the future amount with the appropriate present value factor
provided in the table.
Joe needs to receive Tshs 106,000 in one year. Present rate of interest is 6%. Joe wants to know what amount
he should invest today in order to receive Tshs 106,000 in one year.
If P is the amount to be invested today, then using the above formula Tshs 106,000= P(1+0.06)
𝑃𝑃 =
106,000
1.06
= Tshs 100,000
From the above, it is determined that Tshs 100,000 is required to be invested to earn Tshs 106,000. This means
that the present value of Tshs 106,000 received one year from now at an interest rate of 6% per annum is equal
to Tshs 100,000.
1.3 Role of time value of money in financial management
Time value of money is a very important concept in financial management. Its importance can be evidenced as
below:
1. Investment Decision
The concept of time value of money is very important for decisions pertaining to long-term capital investments.
A person intending to invest in a business project needs to understand the returns expected from the business.
Since returns from a business accrue over a number of years after the business is set up while investment has
to be made in the current period, the cash inflows and outflows occur in different periods and cannot be compared
with each other directly. Hence the investor computes the present value of future cash inflows and compares it
to the present cash outflows to arrive at the decision. The same principle is also used by an investor intending to
invest in shares and securities.
An investor first determines the inflows and outflows for the proposed project/ investment. The cash flows so
determined are converted to present value and difference between inflows and outflows is arrived at. If the
project’s net present value is greater than or equal to zero, the investment can be made. If the investor does not
calculate the present values of future cash flows using the time value of money concept, he may make wrong
decisions, especially in case of long- term projects.
2. Financing Decision
The time value of money concept is useful when comparing costs of different sources of financing to determine
the minimum cost source. In case of borrowings, cash inflow occurs immediately on disbursal of borrowings and
cash outflows occur over a number of years in the form of interest payment and principal repayment. Present
value of costs of various alternatives of financing are compared to decide the source of financing.
For example, when a company borrows funds from a bank or financial institution to be repaid in equal annual
instalments, it uses the present value technique to find out the size of the instalment.
For example, TRQ Plc borrows Tshs 2 million at an interest rate of 10% per annum and the repayment period of
5 years. The finance manager of TRQ Plc wants to know what would be the amount of equal annual instalments.
This means the finance manager needs to know what will be the future payments over the term of the loan whose
present value @ 10 per cent interest is Tshs 2 million. The finance manager will use the equation for present value
to determine the amount of instalment.
46 Principles of Valuation
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3. Other applications
The time value of money concept may be used to determine the amount to be contributed every year to
accumulate a fixed sum at the end of a certain period. Generally, companies create sinking funds to repay
debentures or bonds on maturity. A sinking fund is a fund which is created by contributing fixed amounts at
regular intervals so that a pre- decided sum is accumulated at the end of the specified period.
A fund may also be created to provide for replacement of an existing asset by a company or to provide for a
retirement corpus/ pension at the time of retirement by an individual. For retirement planning, it is necessary to
determine the sum of money that needs to be paid every year to provide adequately for retirement. This can be
determined using the present value technique (as explained in Learning Outcome 3 of this Study Guide).
An investor may use this concept to find the rate of growth in dividend paid by a company over a period of time
using the compounding technique.
Time value of money concept means:
A The value of money received today is more than the value of money expected to be received in future
B The value of money received today is less than the value of money expected to be received in future C
The value of money received today is equal to the value of money expected to be received in future
D None of the above
2. Apply the time value of money concept to determine future and present values of different
cash flow patterns.
[Learning Outcome b]
We need to know the following parameters to calculate the future value and present value of any investment:
1. Principal amount
2. Time period
3. Rate of interest
In simple terms, Future value = Principal + Interest and Present value = Future Value – Interest Earned
Tom invests Tshs 150,000 for 3 years @ 8% per annum compounded
annually: Future Value= Tshs 150,000 (principal) + Tshs 38,960 (Interest) =
Tshs 188,960
Present Value= Tshs 188,960 (Future Value) – Tshs 38,960 (Interest earned) = Tshs 150,000
The difference between future value and present value is the amount of interest earned during the period
2.1 Computing Future Values
Compounding relates to earning interest on previously earned interest. Money initially deposited at a certain
interest rate earns interest on that amount until the end of a compounding period. At that time the interest is
"credited" to the account, and future interest is earned on the sum of the original deposit plus the interest earned
in the first period. Interest earned in the second period is credited at its end, so interest earned in the third period
is based on the original deposit plus the first and second period's interest, and so on.
The more frequently (shorter compounding periods) the interest is compounded; the more interest is earned.
Interest rates are generally stated in annual terms (the nominal rate) and must be adjusted to reflect the
compounding periods in use.
Time Value of Money: 47
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Time Value of Money: 45
As we have already seen above, future value is determined by way of compounding technique and present value
by way of discounting technique. W e will now have a look at various scenarios to determine future and present
values covering different cash flow patterns.
Scenario 1
Semi-annual compounding for a single cash flow:
A wishes to invest Tshs 5,000,000 in a bank deposit for 2 years with interest @ 8% compounded semi- annually.
This means that interest will be paid to A @ 4% every six months compounded after every 6 months.
The table below gives the amount of interest that will be received by A at every interval:
Particulars
Principal
Interest rate
Interest amount
Amount= Principal + Interest
6 months
5,000,000
0.04
200,000
5,200,000
1 Year
5,200,000
0.04
208,000
5,408,000
18 months
5,408,000
0.04
216,320
5,624,320
2 years
5,624,320
0.04
224,972
5,849,292
We can see from the above table that future value of Tshs 5,000,000 invested by A after 2 years with 8% interest
rate compounded semi- annually is Tshs 5,849,292.
Scenario 2
Annual compounding for a series of payments:
In the above example, we had considered the future value of a single payment. We may also need to calculate
future value of a number of payments made at different points of time.
A deposits each year Tshs 50,000, Tshs 100,000, Tshs 150,000 and Tshs 200,000 in Fixed Deposit account
for 5 years with interest rate of 5%.
We need to determine the value of his deposits at the end of 5 years.
Year
1
1
2
3
4
Principal
( Tshs )
2
50,000
100,000
150,000
200,000
Number of
years
compoun
3
ded4
3
2
1
Compounded
interest factor
4
1.216
1.158
1.103
1.050
Future
Value
5 = 2x 4
60,800
115,800
165,500
210,000
Since deposits are placed at the end of the year, the first deposit will earn interest for four years, the second for
three years and so on.
3
We can also get the above amounts by using the formula given above: [50,000(1+0.05) ].
Scenario 3
Future Value of an Annuity:
Annuity means payment or receipt of a fixed amount every year for a specified number of years. For example,
equal annual instalments of a loan or rent payment for the rent -term etc. Future value of an annuity is given by
the following formula:
(1 + 𝑖𝑖)𝑛𝑛
𝐹𝐹 = 𝐴𝐴 × [
− 1]
𝑖𝑖
Where,
F = Future Value of Annuity
A = Annuity
i = rate of interest
n = number of years (period)
Continued on the next page
48 Principles of Valuation
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Katherine deposits Tshs 50,000 at the end of each year for 5 years at 6 percent rate of interest. Determine the
value of annuity at the end of the fourth year.
Future value of annuity according to the above formula will be as follows:
(1+0.06)5
F=5,000× [
-1]
0.06
© GTG
= Tshs 5,000 x Tshs 5.6371
Time Value of Money: 47
= Tshs 28,186
2.2 Computing Present Values
1. Single Cash Flow
B needs Tshs 5,000,000 after 5 years for certain expenditure which B has planned to incur after 5 years.
B wants to know how much amount he should invest now assuming interest rate of 10% per annum if they have
to receive Tshs 5,000,000 after 5 years.
As per the formula studied above, present value is calculated as follows:
𝑃𝑃 =
5,000,000
(1 + 0.10)5
Present Value = Tshs 3,105,000
From the above it can be concluded that B needs to invest Tshs 3,105,000 for 5 years @ 10% so that B gets
Tshs 5,000,000 at the end of 5 years.
2. Multiple cash flows
In the above example, we considered a single cash flow. W e will now look at an example for calculating the
present value for a number of cash flows.
Determine the present value of the cash flows given in the table below for the number of years specified in the
table discounted @ 10 per cent:
Year
Cash Flows
( Tshs )
2
500,000
1,000,000
1,500,000
2,000,000
Present
Present
Value
Value
F 3
1
4 = 2*3
a0
1
4,545,000
ct
2
0.
826,000
o
9
3
0.
1,126,500
r.
0
8
4
0
1,366,000
9.
2
7
5
6
3. Present Value of Annuity
1
8
3
As already explained above, annuity is payment
or receipt of a fixed amount every year for a specified number
of years. Suppose an investor wants to find out the present value of an annuity which they expect to receive on
investment made by them.
Present value of annuity is computed as follows:
1
1
P=A× [ ]
i i(1+i)n
Where,
P= Present value of annuity
A= annuity
investment made by them.
Present value of annuity is computed as follows:
1
1
P=A× [ ]
i i(1+i)n
Time Value of Money: 49
Where,
P= Present value of annuity
A= annuity
i= rate of interest
n= number of years
B invests an amount of Tshs 500,000 and receives annuity of Tshs 50,000 for four years @ 10%. Compute
the present value of annuity of Tshs 50,000.
48 : Principles of Valuation
1
1
P=50,000× [
]
0.10 0.10(1+0.10)4
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сϱϬ͕ϬϬϬdž΀ϭϬ–ϲ͘ϴϯϬ΁
сϭϱϴ͕ϱϬϬ
4. Present Value of Perpetuity
Perpetuity means the annuity that occurs indefinitely. For example, in case of irredeemable preference shares,
the company is required to pay dividend perpetually. In perpetuity, the time period is so large that mathematically
it reaches infinity; hence present value of perpetuity is given as follows:
Present value of perpetuity =
𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃
𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
If A expects to receive a perpetual sum of Tshs 100,000 annually from his investment with interest rate of 12
%per annum, what will be the present value of perpetuity:
As per above formula,
Present value of perpetuity =
100,000
= 800,333
0.12
A look at the diagram given below will help summarise what we learnt above:
Diagram 1: Time value of money
50
Principles of Valuation
© GTG
Time Value of Money: 49
A expects to receive Tshs 1 million after 5 years with a required rate of return of 10% per annum.
Required:
Calculate the present value of Tshs 1 million.
Nancy has placed Tshs 10,000 in bank fixed deposits for 3 years. The annual interest rate is 10% per annum.
Required:
How much amount will Nancy receive after 3 years if the interest is compounded?
(a) annually; and
(b) quarterly.
3. Apply the time value concept to evaluate different cash flow options and plan for various
activities such as sinking funds, deferred annuity, retirement plan and capital recovery plans.
[Learning Outcome c]
This Learning Outcome will apply the time value of money concept for evaluating cash flows under following
scenarios for better understanding of the practical applications of the concept.
1.
2.
3.
4.
Sinking Fund
Annuity
Retirement Planning
Capital Recovery Plans
3.1 Sinking Fund
A sinking fund is a fund which is created by contributing fixed amounts at regular fixed intervals so that a pre decided sum is accumulated at the end of the specified period.
Sinking fund is generally created by borrowers; e.g. companies create sinking fund to repay debentures or bonds
on maturity. Borrowers may pay interest at regular intervals during the life of the loan but may not have sufficient
provision to repay the principal on maturity of the loan. Hence, sinking funds are created to make provision for
repayment of loan on maturity.
Time value of money is taken into account to calculate the amount that needs to be contributed to the sinking
fund so that funds are available to repay loan on maturity. Funds contributed are so invested that amount is
available at the time of repayment of loan.
The factor that is used to calculate the equal annual contribution every year is called the Sinking Fund Factor
(SFF) and it ranges between 0 and 1.0.
PQR Plc intends to establish a sinking fund to repay Tshs 10 million 7% debentures 10 years from today. The
first payment will be made at the end of the current year. The company expects that the funds will earn 6%
interest per year.
Required:
What equal annual contributions should be made to accumulate Tshs 10 million after 10 years?
Continued on the next page
Time
ValueofofMoney:
Money:4951
Time
Value
© GTG
Answer
According to the annuity tables, annuity factor for 10 years @ 6% per annum is 13.181 which means that a unit
of Tanzanian Shilling invested at the end of each year for 10 years will accumulate to Tshs 13, 181 at the end of
th
the 10 year. In order to have Tshs 10 million, the required amount of annual contribution will be:
Tshs 10 million
=Tshs 13.181
758,669
If the company makes a contribution of Tshs 758,668 at the end of each year for 10 years, it will have Tshs
10 million in the account for retiring the debentures on maturity.
Formula for computing sinking fund can be given as follows:
A=
1
Compound value factor of annuity
A= Sinking Fund contribution
F= Future Value
In the above example, annual sinking fund contribution can be computed using the above formula:
A= Tshs 10
million
1
13.18079
A= Tshs 10 million x 0.07586
A= Tshs 758,680
3.2 Annuity
Annuity refers to equal annual contribution which means that a fixed sum is contributed or received at fixed
regular intervals.
1. Calculation of annuity
A plans to invest Tshs 1,000 in bank deposits every year @ 6% per annum for the next four years; amount is
deposited at the end of the year. This means that Tshs 1,000 deposited at the end of Year 1 will yield interest for
3 years, Tshs 1,000 deposited at the end of Year 2 will yield interest for 2 years, amount deposited at the end of
Year 3 will yield interest for 1 year and Tshs 1,000 at the end of the fourth year will not yield interest.
End of Year
1
1
2
3
4
Total
Amount
deposited
( Tshs )
2
1,000
1,000
1,000
1,000
Number of
years
Compound
ed3
3
2
1
0
Compounded interest
factor from compound
value table
4
1.191
1.124
1.060
1.000
Future
Value
5=2x4
1,191
1,124
1,060
1,000
4,375
Future value of annuity can be calculated using the below formula:
(1 + 𝑖𝑖)𝑛𝑛
F=A×
𝑖𝑖
F= Future value of annuity
A= Annuity
i= rate of interest
n= number of years
Continued on the next page
52 Principles of Valuation
50 : Principles of Valuation
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So future value of annuity
F=1,000× [
F=1,000× [
(1+0.06)4 -1
]
0.06
0.262477
0.06
=1,000 x 4.3746
]
= Tshs 4,375
Annuity tables are available for computing the compound value of an annuity at a specified rate over a given
period of time.
2. Deferred Annuity
Deferred annuity means that the equal annual payments begin after a specified number of periods and not from
the first period.
For example, an ordinary annuity of six instalments deferred for 3 years means that the first payment will occur
only at the beginning of the fourth year and that no payments will occur in the first three years.
(a) Future Value of a deferred annuity
The deferred period is not taken into account while calculating the future value of a deferred annuity just like in
case of an ordinary annuity which is not deferred.
(b) Present Value of Deferred Annuity
While computing present value of deferred annuity, we compute the present value of ordinary annuity as if the
cash flow has occurred for the entire period; deduct present value of cash flows not received/ paid during the
deferred period; balance is the present value of cash flows actually received/ paid subsequent to deferral period.
A has agreed to pay rent of Tshs 50,000 per month for 10 months beginning 5 months from today. Interest rate
is 8% per annum. What is the present value of the payments?
Present value of annuity is calculated as below:
Monthly rent: Tshs 50,000
Present value of ordinary annuity of 1 for total periods (10 months): 6.71
Less: Present Value of annuity of 1 for the deferred periods: 3.31213
Difference: 3.39795
Present value of six months’ rent: 50,000 x 3.39795
The present value of an annuity of 1 for the deferred periods is deducted from the present value of annuities for
the total period thereby eliminating the effect of non- contribution to cash flows during the deferred period.
3.3 Retirement Plans
Time value concept is very important in retirement planning. For retirement planning, it is necessary to
determine the sum of money that needs to be paid every year to provide adequately for retirement. An investor
needs to consider the following factors for the retirement planning:
1. Time frame available upto retirement
2. Return that will be earned on the investments till the retirement
3. Amount of funds that will be required at the time of retirement
© GTG
Time Value of Money: 53
Time Value of Money: 51
Tom earns Tshs 30,000 per month at the age of 25. Tom wishes to maintain the same standard of living after
retirement which will be at the age of 55. Average rate of inflation is assumed as 6%. Determine the amount that
will be required by Tom every month after retirement to maintain the same standard of living.
Please find below screenshot from excel for determining the future value of amount required every month:
Present value factor for 30 years @ 6% is: 0.174
Amount that will be required every month by Tom after retirement will be as follows:
FV=A×(1 + 𝑖𝑖)𝑛𝑛 FV=30,000×(1 + 0.06)30
= Tshs 172,304.74
The above calculation can be done using a spread sheet as follows:
Amount of Tshs 172, 305 per month will be required at the time of retirement to maintain the existing standard
of living.
54 Principles of Valuation
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3.4 Capital Recovery Plan
Capital recovery factor gives the amount of equal payments to be received at the end of the period of n years to
recover the investment made.
A capital investment decision needs to consider two factors- outflow for the capital investment occurs in the
current period whereas the cash inflows will occur over a number of years in the future. So, it is necessary to
convert the cash flows to a single point in time in order to enable meaningful comparison. Companies generally
use the present value to make this comparison rather than future value because the initial cost of investment is
already in the present value.
Anthony is contemplating starting a new business. He is considering two options for the new investment of
which he will evaluate and select one. One option is the production of television sets and other one is manufacture
of CD players. The cash outflow for both for purchase of machines with a five-year life and zero residual life will
be Tshs 10 million.
The cash inflows expected from both the businesses are as follows:
Year
1
2
3
4
5
Total
Television sets
( Tshs )
50,00,000
50,00,000
50,00,000
50,00,000
50,00,000
250,00,000
CD players
( Tshs )
60,00,000
55,00,000
55,00,000
45,00,000
20,00,000
235,00,000
It can be seen from the above table that Anthony will receive higher cash inflows in the earlier years from the
business of CD players but the total cash inflows will be more in case of television sets.
However, in order to arrive at the accurate decision, Anthony needs to find out the present value of all the cash
flows considered above. The current rate of interest considered for calculating present value is 14%.
Net Present Value for cash inflows of television sets using Present Value of Annuity Table with interest rate of
14% and period of 5 years is 3.433; cash inflows will be Tshs 5 million x 3.433 = Tshs 171,6,5,000.
Anthony will then deduct the cost of machines required from the above cash flow to arrive at the net present
value (NPV).
Hence, NPV= 171,65,000 less 100,00,000= Tshs 71,65,000
A positive NPV indicates that the investment earns more than the required rate of return.
Continued on the next page
TimeValue
ValueofofMoney:
Money:5355
Time
© GTG
NPV for the project of manufacture of CD players:
Year
1
1
2
3
4
5
Total
Present Value
Factor
2
0.877
0.769
0.675
0.592
0.519
Cash Inflow
( Tshs )
3
60,00,000
55,00,000
55,00,000
45,00,000
20,00,000
Present
Value ( Tshs )
4=2x3
52,62,000
42,29,500
37,12,500
26,64,000
10,38,000
169,06,000
Anthony will then reduce the cost of machines required from the above cash flow to arrive at the net present
value (NPV). Hence NPV= 169,06,000 less 100,00,000= Tshs 6906,000. It can be seen from the above workings
that business of manufacture of television sets is more profitable than that of CD players.
Kelley will be retiring from her job in the next month. Her employer has offered her two options for postretirement benefits:
(a) Tshs 3.5 million lump sum
(b) Tshs 0.4 million for 10 years. The rate of interest is 10%.
Required:
Which option should Kelley choose?
Monica borrowed Tshs 1 million from a bank to be repaid in five equal annual instalments with an interest rate
of16 per cent per annum.
Required:
Determine the amount of each instalment.
4. Apply the time value of money to value real securities like ordinary shares, preferred
shares and debentures.
[Learning Outcome d]
Securities like shares and bonds are called financial assets. Present value concept can be used to value the
securities so that an investor can take an informed decision to maximise the value of investment. The present
value concept as discussed above takes into consideration the time as well as risk factor while determining the
value of investment. Present value concept cannot measure the degree of risk; detailed risk and return analysis
is discussed in a separate study guide. For the purpose of this study guide, it is assumed that risk is known.
4.1 Valuation of debentures
A bond (also known as debenture) is a long- term debt instrument. Bonds are issued by government as well as
by private sector companies. In case of debentures or bonds, rate of interest is fixed and known to the investor.
Generally, the interest rate and maturity period of bonds is specified by the company issuing them. Bonds
involve payment of interest at fixed intervals over the term of debentures and maturity value at the end of the
period for which bonds are issued.
Since interest payments happen over a considerable period of time till the maturity of bonds, present value is
determined. Comparison of present value of bonds with its market value will enable the investor to know
whether the bond is undervalued or overvalued. Discount rate used for calculating present value of bonds is the
rate of interest that investors will earn on bonds with similar characteristics.
Lewis is considering purchase of five- year Tshs 50,000 value bond carrying interest of 7% p.a. Lewis’ required
rate of return is 8% p.a. Determine the amount that Lewis can pay now to purchase the bond if it matures at par.
56 Principles of Valuation
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Present value can be determined as follows:
Interest received every year: Tshs 3,500 and amount received on maturity Tshs 50,000
Present value will be calculated as follows:
𝑛𝑛
𝑃𝑃𝑃𝑃 = ∑
𝑡𝑡=1
𝑐𝑐
𝐴𝐴
+
𝑡𝑡
(1 + 𝑟𝑟)
(1 + 𝑟𝑟)𝑛𝑛
Where,
PV= Present Value
C = cash received
A= Maturity Value
r= rate of interest
n= number of years
5
𝑃𝑃𝑃𝑃 = ∑
𝑡𝑡=1
3,500
50,000
+
𝑡𝑡
(1 + 0.08)
(1 + 0.08)5
Using the values from the present value table, the present value of bonds will be:
PV= 3,500 x 3.993 + 50,000 x 0.681
PV= 13,975 + 34,050 = Tshs 48,025
The above indicates that a bond of Tshs 50,000 has a present value of Tshs 48,025 today with a required rate of
return of 8%. The investor will not pay more than Tshs 48,025 for the bonds today.
4.2 Valuation of preference shares
A company issues two types of shares: ordinary and preference shares. In case a company is wound up,
preference shares get a preference in terms of payment of dividend and repayment of capital.
The rate of dividend is fixed in case of preference shares. Like in case of bonds, generally the interest rate and
maturity period of preference shares is specified by the company issuing the preference shares. Preference
shares involve payment of dividend at fixed intervals and payment of maturity value at the end of the period for
which shares are issued. Since dividend payments happen over a considerable period of time till the maturity of
preference shares, present value of preference shares is determined.
Comparison of present value of preference shares with its market value will enable the investor to know whether
the preference shares are undervalued or overvalued. Discount rate used for arriving at the present value is the
rate of dividend that investors will earn on preference shares with similar characteristics.
Annie is considering purchase of preference shares with the following features:
10 year 10 per cent Tshs 10,000 par value preference shares. On maturity, the value of preference shares will
be Tshs 15,000. Annie’s required rate of return is 11%. What would be the price that Annie would be willing to
pay for the preference shares?
Annie would receive dividend of Tshs 1,000 for 10 years and Tshs 15,000 on maturity. To find out the price that
Annie would be willing to pay for the shares, we need to find out the present value of the dividends to be received
over 10 years and present value of the maturity amount to be received after 10 years. The present value annuity
factor will be used to find out the value of the equal annual amount of preference dividends and present value
factor to find out the value of the amount received on maturity.
Continued on the next page
Time Value of Money: 57
Time Value of Money: 55
© GTG
Value of preference share will be calculated by the below formula:
𝐴𝐴
1
1
PV= PD× [ −
]+[
]
𝑛𝑛
(1 + 𝑟𝑟)𝑛𝑛
𝑟𝑟 𝑟𝑟(1 + 𝑟𝑟)
P= Present Value
PD= Preference Dividend
R= required rate of return
A= Maturity value
In the above example, present value will be as follows:
PV= 1,000× [
1
15,000
1
−
]+[
]
10
(1 + 0.11)10
0.11 0.11(1 + 0.11)
= 1,000 x 6.206515 + 15,000 x 0.317
= 6,206 + 4755
= Tshs 10,961
The Tshs 100 preference share is worth Tshs 10,961 today at 11 per cent required rate of return. Annie can
purchase the share at Tshs 10,000 today.
4.3 Valuation of ordinary shares
Valuation of equity shares is difficult because the amount and timing of cash flows expected by equity share
holders is not fixed. This is because the rate of dividend is determined by the company every year and also it is
not mandatory for the company to pay dividend every year; the company may opt not to pay dividend in a
particular year due to low performance or low profitability or for any other reason.
An ordinary share consists of two cash flows- the dividends that the shareholder expects to receive during the
period that the shares are held, and the price expected to be received on sale of shares. However, when an
investor sells the shares to the buyer, the buyer will further sell the shares to another buyer after a certain period
of time. Thus, it is concluded that for equity shareholders, the expected cash inflow consists of only dividends
expected to be received in the future and therefore value of an ordinary share is the present value of future
expected dividends.
Bob intends to buy an equity share and hold it for 1 year. He expects to receive dividend of Tshs 500 in the next
year and he expects the selling price of the share to be 3,000 at the end of the year. The required rate of return
is 15 per cent. W hat amount should Bob pay today for acquiring the share?
The price that Bob should pay will be calculated as follows:
P = Dividend + Selling Price
1+ r (required rate of return)
P=
3
500 3,000
3,500
=
0
1.15
1 0.15
= Tshs 3,043
Bob will buy the share if the price of the share is less than Tshs 3,043.
In the above example, we considered the valuation of ordinary shares assuming that the shareholder will hold
the shares for one year only (single period) and will receive dividend for one year. In case shares ar e held for
more than one year, the valuation will depend upon the dividend expected to be received in subsequent years
and expected price of the share at the end of the subsequent years.
58 Principles of Valuation
56: Principles of Valuation
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If the price of a share today is Tshs 10,000 and it is expected to increase at an annual rate of 5%, the price in the
subsequent years will be as follows:
Year 2: Tshs
Year 3: Tshs
Year 4: Tshs
Year 5: Tshs
10,000 x 1.05= Tshs 10,500
10,500 x 1.05= Tshs 11,025
11,025 x 1.05= Tshs 11,576
11,576 x 1.05= Tshs 12,155
Similarly, if expected dividend is Tshs 1,000 per share and it is expected to grow at a rate of 5% per annum, the
expected dividend in subsequent years will be as follows:
Year 2: Tshs
Year 3: Tshs
Year 4: Tshs
Year 5: Tshs
1,000 x 1.05= Tshs 1,050
1,050 x 1.05= Tshs 1,102
1,102 x 1.05= Tshs 1,157
1,157 x 1.05= Tshs 1,215
If the required rate of return is 15%, determine the price of shares assuming it is held for 5 years:
Price of the share will be determined using the following formula:
𝑃𝑃 =
1,000
1,050
1,102
1,157
12,155
+
+
+
+
1
2
3
4
(1.15)
(1.15)
(1.15)
(1.15)
(1.15)5
© GTG
= 3,654 + 6,043
Time Value of Money: 57
= Tshs 9,697
A Tshs 1,000 bond will mature after 5 years. Interest rate is 14% and required rate of return is 13%.
Required:
What is the value of this bond?
Answers to Test Yourself
Answer to TY 1
Correct option is A. The value of money received today is more than the value of money expected to be
received in future.
Answer to TY 2
Present value of Tshs 1 million is calculated as follows:
𝐴𝐴
(1 + 𝑖𝑖)𝑛𝑛
1,000,000
𝑃𝑃 =
(1 + 0.10)5
𝑃𝑃 =
P=
1,000,000
1.61051
P= Tshs 620,921
Answer to TY 3
(a) Interest which will be received by Nancy in case of annual compounding is as follows:
P=
(1 + 0.10)
1,000,000
1.61051
Time Value of Money: 59
P= Tshs 620,921
Answer to TY 3
(a) Interest which will be received by Nancy in case of annual compounding is as follows:
𝐴𝐴 = 𝑃𝑃(1 + 𝑖𝑖)𝑛𝑛
𝐴𝐴 = 10,000(1 + 0.10)3
A= 10,000 x 1.331
A= Tshs 13,310
(b) Interest which will be received by Nancy in case of monthly compounding is as follows:
𝐴𝐴 = 𝑃𝑃 (1 +
𝑖𝑖 𝑚𝑚𝑚𝑚
)
𝑚𝑚
A= 10,000 (1+
0.10 4 * 3
)
4
12
A= 10,000 (1+0.025)
A=10,000 x 1.344889
A= Tshs 13,449
Answer to TY 4
In order to compare both the cash flows, it is necessary to bring them to a single point in time. We will calculate
58 : Principles of Valuation
present value of option b so that both cash flows are comparable.
10
PV= 400,000× ∑
𝑡𝑡=1
1
(1 + 0.10)10
P= 400,000 x 6.1446
P= Tshs 2,457840
Since the lumpsum amount of Tshs 3.5 million is higher today, Kelley should choose Option (a).
© GTG
60
Principles of Valuation
© GTG
Time Value of Money: 59
Answer to TY 5
5
PV= 1,000,000× ∑
𝑡𝑡=1
1
(1 + 0.16)5
Amount of instalment = 1,000,000 x 3.2743 = Tshs 3,274,300
Answer to TY 6
Interest paid on bond = 1000 x 14% = 140
Value of bond is:
5
PV= 140× ∑
𝑡𝑡=1
1
+ 1,000 × (1 + 0.13)5
(1 + 0.13)5
140 x 3.517 + 1,000 x 0.543 = Tshs 1,035.4
Quick Quiz
1. State whether the following statements are true or false:
(a) Time value of money concept states that the value of money is the same in different periods of time.
(b) Time value of money is different over different periods of time due to the opportunity to invest money
available to investors.
(c) Either compounding technique or discounting technique can be used to make cash flows comparable. (d)
To calculate the present value of cash flows, discounting rate used represents opportunity cost of funds.
2. Present value is the ----------------------- (opposite / equal) of future value.
Answers to Quick Quiz
1.
(a) This statement is false. Time value of money states that value of money is different in different periods
of time.
(b) This statement is true. Time value of money is different over different periods of time as money received
today can be invested by a person to earn returns in the future.
(c) This statement is true. Either discounting technique or compounding technique can be used to make
cash flows comparable.
(d) This statement is true. Discounting rate used for computing present value of cash flows represents
opportunity cost of funds.
2. Present value is the opposite of future value.
60 : Principles of Valuation
Time Value of Money: 61
© GTG
Self Examination Questions
Question 1
Explain the concept of time value of money and its role in financial management.
Question 2
Richard has a surplus amount of Tshs 2 million. The options available for investment are:
(a) Investment in real estate which is expected to fetch him Tshs 2.5 million in one year (Investment in shares of
XYZ Plc is expected to yield a dividend of 15%).
(b) Investment in bank fixed deposits at an interest rate of 10 per cent per annum compounded quarterly.
Required:
Distinguish between present value and future value and determine the amount that Richard will earn by
investing in real estate and in fixed deposits with the bank.
Question 3
ABC Plc has issued debentures which are to be repaid after 8 years and carry an interest of 10 per cent per
annum. The market is volatile, and the cash flows of the company vary significantly every year. Due to this, the
management of the company is worried that it may not have sufficient funds for repayment of principal on
maturity.
Required:
Suggest an appropriate method to the management to ensure that sufficient funds are available on a timely
basis for repayment of debentures on maturity.
Question 4
Frank has agreed to gift his daughter Nancy Tshs 1 million in cash 10 years from today for Nancy’s further
education. Frank has two options available for gifting the amount:
(a) Make annual payments into a fund after one year (fund carries an interest rate of 8 per cent per annum).
(b) Keep the funds in the bank after one year (bank pays compound interest compounded annually).
Required:
Explain the concept of annuity and determine what will be the amount of annuity for option (a) above and what
will be the amount of funds invested in the bank in case of option (b).
Answers to Self Examination Questions
Answer to SEQ 1
Time value of money means that the value of money is different at different points of time.
The value of a particular amount of money received today is more than its value if received in future. Also,
invested money earns income over time. This is referred to as time value of money. The worth of money that a
person has today is more than the expectation of receiving that money in the future. Money in hand today can
be invested and returns can be earned on that investment.
Money has time value because of the following reasons:
1. Risk: there is no certainty about the future and involves risk; a business enterprise does not have much
control over future cash inflows as it depends on external factors like debtors etc. As such a person prefers
receiving cash in the present rather than in the future.
2. Consumption: a person generally prefers current consumption to future consumption.
62
Principles of Valuation
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Time Value of Money: 61
3. Investment Opportunity: money received today can be invested by the person to earn high rate of return
in the future.
4. Inflation: in an inflationary economy, money received today has more purchasing power than money
received in future.
Time value of money is a very important concept in financial management. Its importance can be evidenced as
below:
1. Investment Decision
The concept of time value of money is very important for decisions pertaining to long-term capital investments.
In long- term investment, cash outflows occur at the time the business set up in the form of investment in fixed
assets etc and inflows occur over a period of time during the course of business.
Hence, it is not appropriate for an investor to compare the cash inflows and outflows directly. In order to conclude
whether the investment made is profitable, the investor computes the present value of future cash inflows and
compares it with the present cash outflows. The same logic is also used by an individual i nvestor intending to
invest in shares or securities. For an individual also, the outflow occurs at the time the amount is invested in
shares or securities and returns are received over a period till the shares are sold.
As per the above working by an investor, if the net present value of investment is greater than or equal to zero,
the investor concludes that the investment can be made. If the investor compares the cash flows directly without
calculating the present values, he may make wrong decisions especially in case of long- term investments.
2. Financing Decision
In case of borrowings, cash inflow occurs immediately on disbursal of borrowings and cash outflows occur over
a number of years in the form of interest payment and principal repayment. A borrower computes the present
value of interest payments and principal repayment to determine the equal annual instalment to be paid and
also cost of borrowing.
Companies or individuals may use the time value of money concept to determine the amount that needs to be
contributed every year to accumulate a fixed sum at the end of a certain period. Generally, companies create
sinking funds to repay bonds or debentures or to create a fund for replacement of an asset and individuals use
this concept to determine the amount of money needed to be contributed every year to provide adequately for
retirement.
An investor may use this concept to find the rate of growth in dividend paid by a company over a period of time
using compounding technique.
Answer to SEQ 2
Any financial decision involves comparison of the cash inflows and outflows which accrue over a number of
years. Comparing the inflows and outflows as they are generated will be incorrect as they accrue over different
periods of time. In order to enable a meaningful comparison, adjustment has to be made for the difference in
timing of the cash flows.
There are two perspectives to converting the cash flows to a common point in time:
1. Compounding Technique (Future Value)
2. Discounting Technique (Present Value)
In case of future value or compounding, money invested appreciates in value as interest is added with
compounding effect. Interest is calculated on the total amount of principal + interest earned at the end of each
compounding period. Principal is the amount of money invested on which interest is received.
Present value is the opposite of future value. In case of present value, money is received at some future date
and hence value of money will be less as money does not earn interest for that period.
In the given scenario, Richard has an option to invest Tshs 2 million in real estate, which is expected to fetch him
Tshs 2.5 million in one year. In order to decide whether to invest in real estate, Richard needs to find out the
present value of Tshs 2.5 million expected to be received after one year. Discounting rate used will be 15 per
cent which is the opportunity cost of capital (the rate at which Richard would have earned returns if money was
invested in shares of XYZ Plc.)
TimeValue
ValueofofMoney:
Money: 63
Time
6161
© GTG
Present Value =
=
2,500,000
(1 0
0.15)1
=
2,500,000
1.15
A
(1 i)
in
= 2,173,913
This indicates that the value of property today is Tshs 2,173,913 for which outflow required is only Tshs
2,000,000. Increase in wealth of Richard by this investment will be Tshs 2,173,913 less Tshs 2,000,000 = Tshs
173,913. Hence it can be concluded that Richard can go ahead with the decision of investing in the property.
Richard also has an option to invest the money in fixed deposits in banks at an interest rate of 10 per cent per
annum compounded quarterly.
So, interest that will be received by Richard will be as follows:
Particulars
Amount invested ( Tshs )
Interest rate (%) per annum
Interest amount for the quarter ( Tshs )
Principal + Interest ( Tshs )
Quarter 1
2,000,000
10%
50,000
2,050,000
Quarter 2
2,050,000
10%
51,250
2,101,250
Quarter 3
2,101,250
10%
52,531
2,153,781
Quarter 4
2,153,781
10%
53,845
2,207,625
Increase in wealth by investing in fixed deposits of bank will be
Tshs 2,207,625 less Tshs 2,000,000 = Tshs 207,625
Answer to SEQ 3
ABC Plc needs to create a sinking fund for the period from the issue of debentures to maturity in order to ensure
that sufficient and timely funds are available for repayment of debentures on maturity.
A sinking fund is a fund which is created by contributing fixed amounts at regular fixed intervals so that a predecided sum is accumulated at the end of the specified period.
Sinking fund is generally created by borrowers for eg companies create sinking fund to repay debentures or
bonds on maturity. Borrowers may pay interest at regular intervals during the life of the loan but may not have
sufficient provision to repay principal on maturity of the loan. As such sinking funds are created to make provision
for repayment of loan on maturity.
Time value of money is taken into account to calculate the amount that needs to be contributed to the sinking
fund so that funds are available to repay loan on maturity. Funds contributed to the fund are so invested that
amount is available at the time of repayment of loan.
The factor that is used to calculate the equal annual contribution every year is called the Sinking Fund Factor
(SFF) and it ranges between 0 and 1.0.
Answer to SEQ 4
Annuity refers to equal annual contribution which means that a fixed sum is contributed or received at fixed
regular intervals. Deferred annuity means that the equal annual payments begin after a specified number of
periods and not from the first period. For example, an ordinary annuity of six instalments deferred 3 years
means that the first payment will occur only at the beginning of the fourth year and that no payments will occur
in the first three years.
64 Principles of Valuation
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Value of deferred annuity is determined as follows:
Future Value of a deferred annuity: the deferred period is not taken into account while calculating the future
value of a deferred annuity just like in case of an ordinary annuity which is not deferred.
Present Value of Deferred Annuity: while computing present value of deferred annuity, we compute the
present value of ordinary annuity as if the cash flow has occurred for the entire period; Deduct present value
of cash flows not received/ paid during the deferred period; Balance is the present value of cash flows actually
received/ paid subsequent to deferral period.
For option a, amount of annuity will be calculated as follows:
(1 + 𝑖𝑖)𝑛𝑛 − 1
FV = A× [
]
𝑖𝑖
(1 + 0.08)9 − 1
FV = 1,000,000× [
]
0.08
1,000,000 = A x 14.48656
A=
1,000,000
12.48756
A= Tshs 80,080
Frank will have to contribute Tshs 80,080 annually to the fund.
For option b, amount to be invested in the bank will be:
Present value of annuity is:
F= P (1+i)
n
1,000,000= P (1+0.08)
9
1,000,000= P x 1.999
P=
1,000,000
1.999
= Tshs 500,250
Lump sum amount that will be invested is Tshs 500,250.
Refer compound value table which is given at the end of this Study Text.
Indicative Examination Questions
IEQ 1
You have just won the CPA-T Best graduate prize of TSHS 11,000,000 by the National Board of Accountants and
Auditors. Your winnings will be paid to you in 26 equals annual installments with the first payment made immediately.
If you had the money now, you could invest it in an account with a quoted annual interest rate of 9% with monthly
compounding of interest. What is the present value of the stream of payments you will receive?
TimeValue
ValueofofMoney:
Money: 65
Time
6363
© GTG
IEQ 2
You are planning to retire 15 years from now. You have estimated that you will have 25 years to live after your
retirement. Your objective is to set up an individual retirement fund that will provide shs. 800,000 each month to meet
your living costs after retirement. Your investigation has shown that it is possible to set up the fund by depositing a
fixed amount from your salary in a special retirement account that earn 4.8% p.a. You have also estimated that this
interest rate will remain constant for the first 15 years and then increase to 6% p.a. thereafter. How large does your
monthly deposit needs to be for you to achieve your objective assuming interest compounds monthly?
ŶƐǁĞƌƚŽ/ŶĚŝĐĂƚŝǀĞdžĂŵŝŶĂƚŝŽŶYƵĞƐƚŝŽŶƐ
Answer to IEQ 1
Using PVof an annuity due formular, establish PV given




PV
a= 11,000,000/26= 423,077
n=26 years
r = 9% p.a but compounds monthly, therefore EAR = 9.38% (note: EAR= (1+ip)p-1
PV=?
=
4,072,055.28
Answer to IEQ 2
1st Establish an amount needed at the time of retirement
This will be obtained as total present value for annuities due as at Y 15 (assuming that withdrawals occur at the
beginning since one has to have money prior spending it), now given




PV=
a
= 800,000 per month
n
= 25 years (i.e 25*12 months= 300 months)
r
= 4.8% p.a = 0.04% p.m
PVad as at end of Y15, time of retirement =?
139,616,796.07
2nd , establish an amount to be deposited each month such that the FV above of 139,616,796.07 will be obtained
after 15 years(since deposits are normally made at the end of months then it is ratiobal to assume that this is an
ordinary annuity problem). Given




FVoa
N
r
a
= 139,616,796.07
= 15 years (i.e 15* 12 months=180 months)
= 6.0 % p.a = 0.05% p.m
=?
a = 480,081.89
66
Principles of Valuation
B2
SECTION B
Risk and Return Analysis: 67
PRINCIPLES OF VALUATION
STUDY GUIDE B2: RISK AND RETURN
ANALYSIS
Any financial decision involves an element of risk. Whether it is selection of plant and machinery by a production
manager or selection of securities for investment by a finance manager, both decisions face the risk in terms of
the returns that will be achieved from the investment. It is important for a person/ company to assess the
financial impact of the risk before taking any decision. It is not possible to completely eliminate the risks
involved; however, a proper analysis will help the investor to take an informed decision.
In this Study Guide, we will understand the meaning and measurement of risks and returns in various scenarios.
a)
b)
c)
d)
e)
f)
Define and measure return and expected returns.
Define, measure and explain different types of risk.
Describe the relationship between risk and return.
Use market information to compute rate of return, variances and standard deviation of
returns. e) Define and measure risk and expected return in a portfolio context.
Analyse the power of diversification in achieving superior return for a given level of risk
or minimum risk for a given level of expected return.
Determine optimal portfolio weights.
68 Principles of Valuation
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1. Define and measure return and expected returns.
© GTG
[Learning Outcome, a]
1.1 Returns
Return on an asset/ investment is the actual income received plus any change in the market price of an asset/
investment. This is generally expressed as a percentage of the opening market price.
It is given by the following formula:
R=
𝐷𝐷𝑡𝑡 + (𝑃𝑃𝑡𝑡 − 𝑃𝑃𝑡𝑡−1 )
𝑃𝑃𝑡𝑡−1
Where,
R= Return on asset/ investment
𝐷𝐷𝑡𝑡 = annual income/ cash dividend at the end of the time period t
𝑃𝑃𝑡𝑡 = security price at time period t (closing security price)
𝑃𝑃𝑡𝑡−1 = security price at time period t-1 (opening security price)
Andrew has invested in the shares of Z Plc. The price of the shares on 1 January is Tshs 3000, dividend
declared for the year is Tshs 200 and the year- end price on 31 December is Tshs 3500. Calculate the rate of
return.
R=
𝐷𝐷𝑡𝑡 + (𝑃𝑃𝑡𝑡 − 𝑃𝑃𝑡𝑡−1 )
𝑃𝑃𝑡𝑡−1
R=
200 + (3,500 − 3,000)
3,000
R=
700
3000
R = 0.23 or 23%
Let us consider an example for computing the returns on an investment made by Michael in the securities of Strong
Cements Plc. Michael purchased 2000 shares of par value Tshs 100 at a market price of Tshs 2,500 per share.
During the year, Strong Cements Plc declared a dividend of 30 per cent, and the market price at the end of the
year of the company’s security was Tshs 3,200.
What will be the returns earned by Michael on the investment in the shares of Strong Cements Plc?
Answer
Total outflow at the time of purchase of securities: 2000 shares x Tshs 2,500= Tshs 50,00,000.
Dividend Income
Dividend per share x number of shares
= (30% of Tshs 100) x 2000 = 30 x 2000 = Tshs
60,000.
Continued on the next page
Risk and Return Analysis: 69
Risk and Return Analysis: 65
© GTG
Capital gain on sale of shares at the end of the year
(Selling Price- Purchase Price) x number of shares sold
= (3,200- 2,500) x 2000 = Tshs 1,400,000
Total returns = Dividend for the year + capital gain on sale of shares at the end of the year
Total Returns = 60,000 + 1,400,000 = Tshs 1,460,000
Returns calculated in percentage terms:
Returns in percentage =
=
Total Returns
Total Investment
1,460,000
5,000,000
= 29.20%
If returns are calculated on the basis of returns per share, the returns would be as follows:
𝐷𝐷
1
Dividend yield = 𝑃𝑃
0
Where,
𝐷𝐷1 = Dividend per share at the end of the year
𝑃𝑃0 = Share price at the beginning of the year
30
Dividend yield = 2,500 = 0.012 = 1.2%
Capital gain yield =
Where,
𝐷𝐷1 − 𝐷𝐷0
𝑃𝑃0
P 1 = Share price at the end of the year
P 0 = Share price at the beginning of the year
Capital gain yield =
700
= 28%
2,500
If Michael does not sell the shares at the end of the year, the difference between the share price at the end of
the year and at the beginning of the year is the unrealised capital gain or loss.
Average/ Mean Returns and Geometric Mean Returns
The average rate of return is the sum of rates of return for the periods under consideration divided by the
number of periods under consideration.
In the case of Geometric Mean Returns, it is assumed that dividend income received on investment at the end
of each period is reinvested. Annual compound rate is then determined for the return received at the end of the
periods under consideration and this compound rate of return is known as the Geometric Mean Return (we have
studied Compounding Technique in the Study Guide B1 ‘Time Value of Money’).
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1.2 Expected Returns
Since risk is associated with every financial decision and the returns are received in the future over a period of
time, it is difficult to accurately predict the expected returns. Returns can vary from say -10% to 10%, 15%, 50%
and so on. Also, the likelihood of these returns may vary. Hence an investor generally takes into consideration
the likelihood of the occurrence of the return. It is also called the probability. Probability represents the percentage
chance of the occurrence of an event. For example, if it is expected that a given outcome will occur six out of ten
times, then the probability is said to be 60%.
There is 60% chance that the outcome will occur. The probability of an event varies between 0 and 1. An event
that is not likely to occur at all is said to have zero probability whereas an event which is certain to occur has a
probability of 1. An event which is uncertain will have a probability between 0 and 1. The total of probabilities
assigned to the different possible outcomes of an event has to be 1.
Expected rate of return is the weighted average of all possible returns multiplied by their respective probabilities.
This can be expressed as follows in the form of a formula:
𝑛𝑛
𝑅𝑅̅ = ∑ 𝑃𝑃𝑖𝑖 𝑅𝑅𝑖𝑖 𝑖𝑖=1
Where,
R = expected return
R i = return for the ith possible outcome
P i = probability associated with R i
n= number of possible outcomes
Given in the table below are expected rates of returns and their probabilities for investment made in the
securities of City Corporation Plc:
Rate of Return
(%)
50
45
65
Probability of
Occurrence
0.5
0.3
0.2
Expected returns according to the above explained formula:
𝑅𝑅̅ = ∑𝑛𝑛𝑖𝑖=1 𝑃𝑃𝑖𝑖 𝑅𝑅𝑖𝑖 =(0.5) (50%) + (0.3) (45%) + (0.2)(65%)
R = 0.515 or 51.5%
A invests Tshs 100 in XYZ Plc’s shares for 5 years. Rates of return (dividend) for the five years are: 20%, 15%,
5%, 8% and -4%. Compute the geometric mean return for the shares held by A.
Risk and Return Analysis: 71
Risk and Return Analysis: 67
© GTG
2. Define and measure risk.
[Learning Outcome b]
Risk can be defined as the probability or chance of a negative outcome.
Risk can also be defined as the variability of actual returns from expected returns for a given asset, or in other
words, the uncertainty of outcomes.
From the above, it can be seen that risk has two main aspects: probability of occurrence of loss and amount of
potential loss.
2.1 Measuring Risk
The risk in relation to a single asset is measured with respect to behavioural and quantitative or statistical point
of view.
1. The two techniques for behavioural assessment of risk are
(a) Sensitivity analysis
(b) Probability analysis
(a) Sensitivity Analysis
This technique considers the various possible estimates of outcomes for assessing the risk. It takes into
consideration the worst (recession in economy), the most likely (normal conditions in the economy) and the
most optimistic outcome (boom) associated with the asset under consideration. The difference between the
worst outcome and the most optimistic outcome is referred to as the range. Range is the basic measure of risk
according to the sensitivity analysis technique. The higher the range, the higher is the risk to which the asset/
investment is exposed.
Given below are details of expected returns from two assets of a company:
Particulars
Expected Return under various
scenarios in percentages:
Pessimistic
Most likely
Optimistic
Range
Asset 1
15
19
23
12
Asset 2
23
25
29
6
Asset 1 has a higher range, which means that asset 1 is riskier than asset 2.
(b) Probability analysis
This technique is considered to be more accurate than Sensitivity Analysis. As already explained above,
probability is the likelihood or a chance of occurrence of an event.
2. Techniques for quantitative or statistical analysis of risk are
(a) Standard deviation
(b) Coefficient of variation
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(a) Standard Deviation
This commonly used measure of risk measures the standard deviation from the most likely/ expected value of
return. Standard deviation of returns is given by the following formula
𝑛𝑛
√∑(𝑅𝑅𝑖𝑖 − 𝑅𝑅̅ )2 × 𝑃𝑃𝑃𝑃𝑖𝑖
𝑖𝑖=1
Where,
R i = return for the ith possible outcome
R = Expected Return
P i = probability associated with R i
n= number of possible outcomes
The greater the standard deviation of returns, the greater is the risk for the asset/ investment.
(b) Coefficient of variation
This is the measure of risk per unit of expected return. This is useful for comparing risk of assets with different
expected returns. Co-efficient of variation is given as
CV =
Where
𝑟𝑟
𝑅𝑅̅
σ r = standard deviation
R = expected return
The greater the coefficient of variation, the greater is the risk for the asset/ investment.
Given below are details of expected returns and the probabilities for asset 1
I
Ri
1
2
3
15%
17%
20%
Pr i
0.20
0.50
0.20
Let us calculate the standard deviation.
i
𝑅𝑅𝑖𝑖
1
2
3
15%
17%
20%
𝑃𝑃𝑖𝑖
0.20
0.50
0.20
𝑅𝑅̅
15.5
15.5
15.5
𝑅𝑅𝑖𝑖 − 𝑅𝑅̅
(-0.50)
1.50
4.5
𝑛𝑛
𝑅𝑅̅ = ∑ 𝑃𝑃𝑖𝑖 𝑅𝑅𝑖𝑖 𝑖𝑖=1
𝑅𝑅̅ = ∑𝑛𝑛𝑖𝑖=1 𝑃𝑃𝑖𝑖 𝑅𝑅𝑖𝑖 = (15*0.20) + (17*0.50) + (20*0.20) = 15.5%
2
̅)
(𝑅𝑅𝑖𝑖 − 𝑅𝑅
0.25
2.25
20.25
̅ )2 × 𝑃𝑃𝑖𝑖
(𝑅𝑅𝑖𝑖 − 𝑅𝑅
0.05
1.125
4.05
5.225
Riskand
andReturn
ReturnAnalysis:
Analysis:6973
Risk
© GTG
𝑛𝑛
√∑(𝑅𝑅𝑖𝑖 − 𝑅𝑅̅ )2 × 𝑃𝑃𝑃𝑃𝑖𝑖 𝑖𝑖=1
𝑟𝑟 = √5.225
𝑟𝑟 = 2.29
Standard Deviation is 2.29
Coeffient of variation = CV
𝑟𝑟
2.29%
= 𝑅𝑅̅ = 15.5% = 0.15
When comparing two or more assets, the higher the coefficient of variation, the higher is the risk.
Following table gives information relating to rate of return and probability distribution of shares of Tasty Foods
Plc:
Rate of
Return (%)
15
26
(17)
(6)
Probability
0.25
0.55
0.10
0.10
Required:
Calculate variance and standard deviation of returns for Tasty Foods Plc.
3. Describe the relationship between risk and return.
[Learning Outcome c]
Any investment involves some amount of risk. In simple words, risk is the possibility that investment made may
not yield returns as expected and that the objectives of investment may not be fulfilled. Risks are generally
classified as market risk (economic changes, market conditions etc), liquidity risk (investments cannot be sold
easily), concentration risk (investing in only one investment or type of investment; no diversification), capital risk
(risk of losing the capital invested) etc. Returns are the amount earned on the investment. Returns may be in
the form of interest and dividend as well as in the form of capital gains. Returns are affected by inflation and the
tax regulations in the economy. Taxes reduce the amount of returns, whereas inflation reduces the value of returns.
Risks and returns are directly related to each other. The higher the risk an investment carries, the higher will be
the expected returns from the investment. Higher risk in an investment is compensated by a potential for higher
returns. For example, fixed deposits or government bonds have a lower rate of return as compared to mutual funds
and stocks. In the case of fixed deposits or government bonds, the returns are guaranteed; also the investor is
sure to get his principal back. In some cases, the returns are not guaranteed but the investor is certain of
getting the principle back. In the case of stocks or mutual funds, there is a possibility that an investor not only gets
lower returns but can also lose their principal amount invested.
Risk and return also depend upon the time period for which the investment is held. Returns from investments
carrying high risk tend to be higher if held for a long period of time. For short term investments, the more
conservative options yield higher returns.
Richard is investing in a fund to provide for his retirement which is 25 years after the current date. At the same
time, he also needs to invest money for buying a house next year. Richard can select investments with high risk
and high returns for his retirement fund as the time period of this investment is long whereas conservative
investments are recommended for the short period investment.
74 Principles of Valuation
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An investment may be classified in any of the following categories
(a) High Risk High Return: in this case, investment will yield high returns but the risk will also be high. For
example, shares, mutual funds etc.
(b) Low Risk Low Return: the investment will carry low risk and the return will also be low. For example,
money in fixed deposits, government bonds etc.
(c) High Risk Low Return: in this case, the investment carries a high risk and a high return up to a certain
point but after that the returns do not increase in proportion to the increase in risk.
A person purchases lottery tickets worth Tshs 500,000. The prize money is Tshs 1,000,000. So, the return is
50%. If the person purchases tickets worth Tshs 700,000, the return is only 30%. However, the risk is still high.
(d) Low Risk High Return: this is not a common phenomenon. This will be possible when say government needs
money in an emergency and issues bonds at a high rate of interest, then the investor will get high returns at a
low risk.
An investor makes investment decisions based on information available about the risks and returns of investment
options under consideration. The decision also depends upon the risk preference of the investor. Investors
generally show preference for investments with higher returns and lower risks. According to the economic principle
of diminishing marginal utility, when a person gets more wealth, his utility for additional wealth increases at
a declining rate.
Investors can be generally classified as follows:
Risk averse investor- in the case of equal rates of returns from various investment options, the investor will
choose the ones with the lowest standard deviation and vice versa.
Risk neutral investor- is the one who does not take risks into consideration and selects investments with
higher returns.
Risk seeking investor- is the one who shows preference towards investments with higher risk, irrespective of
the rate of return.
The relationship between risks and returns can be given by the following diagram:
Diagram 1: Relationship between risks and returns
© GTG
Risk and Return Analysis: 75
Risk and Return Analysis: 71
With reference to the diagram above
When a firm operates near the reference point, the risk and returns expectations are limited, and also the
perception is that resources of the firm are adequate. This is called the Relative Comfort Zone. Here the
assumption is that losses or gains are limited and hence managers are generally risk- averse. There will be a
positive relationship between risks and returns.
In the case of firms operating away from the relative comfort zone and below the failure reference point, it
means that the firms are in a very bad state and managers need to take immediate action. This may involve
decisions with a high amount of risk. Managers will try to reduce the risks and improve performance to move
towards the industry average. Managers will show risk seeking behaviour and hence there will be a negative
relationship between risk and returns.
In the case of firms operating above the success reference point, managers will be of the view that they have
already achieved the objectives of the organisation. Managers may be inclined to take higher risks like venturing
into new markets, development of new products etc. Thus, they display a negative relationship between risks
and returns and exhibit risk seeking behaviours.
Relationship between market risk and return
Sensitivity of a security to market risk is called beta ( β ). According to Capital Asset Pricing Model (discussed in
a separate chapter), relationship between risk and return is given as follows:
𝐸𝐸(𝑅𝑅𝑖𝑖 ) = 𝑅𝑅𝑓𝑓 + 𝛽𝛽𝑖𝑖 [𝐸𝐸(𝑅𝑅𝑚𝑚 ) − 𝑅𝑅𝑓𝑓 ]
Where,
𝐸𝐸(𝑅𝑅𝑖𝑖 )= Expected Return of security
𝑅𝑅𝑓𝑓 = Risk- free return
𝛽𝛽𝑖𝑖 = Beta of security
𝐸𝐸(𝑅𝑅𝑚𝑚 ) = Expected return on market portfolio
Expected return of security = Risk- free return + Risk Premium [𝐸𝐸(𝑅𝑅𝑚𝑚 ) − 𝑅𝑅𝑓𝑓 ]
Shares of Fair Cosmetics Plc have a beta of 1.5, risk- free rate of 10% and expected return on market portfolio
of 15%. Calculate the expected rate of return on the shares of Fair Cosmetics Plc.
4. Use market information to compute rate of return, variances and standard deviation of
returns.
[Learning Outcome d]
We have already studied in Learning Outcome 1 that return on investment is the sum of the dividend income
and the change in market price of the investment. Similarly, in Learning Outcome 2, we studied that variance
and standard deviation are measures of risk that an investment carries. We will now study some examples of
the working of returns, variances and standard deviation using market information and formulae as studied above.
The market price of the share of Star Plc is Tshs 5000. The company is expected to pay a dividend of Tshs 400
per share one year from now and the expected price one year from now is Tshs 6500. Calculate the rate of
return on investment in the shares of Star Plc.
76
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Answer
𝑅𝑅 =
𝑅𝑅 =
𝐷𝐷𝑡𝑡 + (𝑃𝑃𝑡𝑡 − 𝑃𝑃𝑡𝑡−1 )
𝑃𝑃𝑡𝑡−1
400 + 6,500 − 5,000)
5,000
R = 0.38 or 38%
Given below are the details of probability of occurrence and rate of return for Weatherfare Plc:
State of the
economy
Boom
Normal
Recession
pi
0.30
0.60
0.10
Ri
30
25
20
Compute the standard deviation.
Answer
State of the
economy
Boom
Normal
Recession
pi
0.30
0.60
0.10
Ri
30
25
20
pI Ri
9.00
15.00
2.00
RI –
R
4.00
-1.00
-6.00
𝑛𝑛
𝑅𝑅̅ = ∑ 𝑃𝑃𝑖𝑖 𝑅𝑅𝑖𝑖 = 9 + 15 + 2 = 26%
𝑖𝑖=1
𝑛𝑛
𝜎𝜎𝑟𝑟 = √∑(𝑅𝑅𝑖𝑖 − 𝑅𝑅̅ )2 × 𝑃𝑃𝑃𝑃𝑖𝑖 𝑖𝑖=1
𝜎𝜎𝑟𝑟 = √9 = 3%
Nancy holds shares of two companies in a portfolio in equal proportion:
Company 1- Expected return- 15% and standard deviation: 18%
Company 2- Expected return- 20% and standard deviation: 25%
Correlation between the shares of the two companies in the portfolio is 0.8.
Calculate the risk and return of the portfolio held by Nancy.
Answer
Return of the portfolio is given by the following formula:
𝐸𝐸(𝑟𝑟𝑝𝑝 ) = ∑ 𝑤𝑤𝑖𝑖 𝐸𝐸(𝑟𝑟𝑖𝑖 )
𝐸𝐸(𝑟𝑟𝑝𝑝 ) = (0.5 × 0.15) + (0.5 × 0.20)
𝐸𝐸(𝑟𝑟𝑝𝑝 ) = 0.075 + 0.10
(R I –
R )2
16.00
1.00
36.00
p I (R I –
R)2
4.80
0.60
3.60
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Risk and Return Analysis: 73
𝐸𝐸(𝑟𝑟𝑝𝑝 ) = 0.175 = 17.5
Risk of the portfolio is given by the following formula:
𝜎𝜎𝑝𝑝2 = (𝑤𝑤1 𝜎𝜎1 )2 + (𝑤𝑤2 𝜎𝜎2 )2 + 2𝑤𝑤1 𝑤𝑤2 (𝜎𝜎1 𝜎𝜎2 𝜌𝜌12 )
𝜎𝜎𝑝𝑝2 = (0.5 × 0.18)2 + (0.5 × 0.25)2 + 2 × (0.5 × 0.18)(0.5 × 0.25) × (0.8)
𝜎𝜎𝑝𝑝2 = 0.041725
𝜎𝜎𝑝𝑝 = 0.204267 = 20.43%
Mark has invested in the shares of ABC Plc. The current market price of the shares is Tshs 600 and market price
expected after one year is Tshs 750. Dividend is expected to be paid at a rate of Tshs 35 per share.
Determine the expected percentage of dividend income, capital gain or loss and total returns.
5. Define and measure risk and expected return in a portfolio context.
[Learning Outcome e]
A portfolio means a combination of two or more assets/ securities. Each portfolio will have different risks and
returns.
Investors generally prefer to invest in a portfolio of assets rather than a single asset or a few assets as the
investment is diversified in case of portfolio investment, and risk is therefore reduced. An investor is concerned
with the return and risk of the portfolio rather than with individual assets. Portfolio theory assumes that returns of
assets of a portfolio are normally distributed.
5.1 Portfolio Return
Expected return of a portfolio is the weighted average of the expected rates of return on assets comprising the
portfolio. There are two aspects of portfolio returns:

Expected rate of return on each asset in the portfolio

Relative share of each asset in the portfolio
The expected rate of return of a portfolio is given as:
𝐸𝐸(𝑟𝑟𝑝𝑝 ) = ∑ 𝑤𝑤𝑖𝑖 𝐸𝐸(𝑟𝑟𝑖𝑖 )
Where,
𝐸𝐸(𝑟𝑟𝑝𝑝 ) = Expected return from portfolio
𝑤𝑤𝑖𝑖 = Proportion invested in asset i
𝐸𝐸(𝑟𝑟𝑖𝑖 ) = Expected return for asset i
Expected returns on Asset 1 and Asset 2 are 15 and 20 percent respectively and the corresponding shares of
assets in the portfolio are 0.75 and 0.25 respectively. The expected portfolio return will be calculated as follows:
0.75 x 0.15 + 0.25 x 0.20 = 0.1625 or 16.25%
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5.2 Portfolio Risk
The portfolio risk is not measured as the weighted average of variance of returns on individual assets in the
portfolio. Portfolio risk is affected by three factors:



Standard deviation of each asset in the portfolio
Proportion/ share of each asset in the portfolio (this factor is within the control of the investor and can be
decided by them)
Correlation between returns of two assets measured by covariance of returns
What is Correlation?
Correlation is the measure of relationship between two variables.
Correlation is given by the following formula:
Correlation between Asset 1 and Asset 2 =
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 1 & 2
Standard Deviation of Asset 1 x Standard Deviation of Asset 2
Correlation between Asset 1 and Asset 2 =
𝐶𝐶𝐶𝐶𝐶𝐶 1 & 2
𝜎𝜎1 𝜎𝜎2
Value of correlation as derived from the above formula is called the correlation coefficient. The correlation
coefficient variation varies between -1 and 1. Zero correlation coefficient indicates that the variables are not related
to each other.
Given below is the formula for the total risk of a portfolio having two assets:
𝜎𝜎𝑝𝑝2 = (𝑤𝑤1 𝜎𝜎1 )2 + (𝑤𝑤2 𝜎𝜎2 )2 + 2𝑤𝑤1 𝑤𝑤2 (𝐶𝐶𝐶𝐶𝐶𝐶 1&2) or
𝜎𝜎𝑝𝑝2 = (𝑤𝑤1 𝜎𝜎1 )2 + (𝑤𝑤2 𝜎𝜎2 )2 + 2𝑤𝑤1 𝑤𝑤2 (𝜎𝜎1 𝜎𝜎2 𝜌𝜌12 )
Where,
𝜎𝜎𝑝𝑝 = Variance of returns of portfolio
w1 = Share of total portfolio invested in Asset 1
w2 = Share of total portfolio invested in Asset 2
σ 1 = Variance of asset 1
σ 2 = Variance of asset 2
σ 1 = Standard deviation of asset 1
σ 2 = Standard deviation of asset 2
𝐶𝐶𝐶𝐶𝐶𝐶 1&2 = Covariance between returns of two assets
ρ12 = Coefficient of correlation between the returns of two assets
Expected returns on Asset 1 and Asset 2 are 12 and 16 percent respectively and the corresponding shares of
assets in the portfolio are 0.75 and 0.25 respectively.
Standard deviation of Asset 1 and Asset 2 is 16 and 20 percent respectively and Coefficient of correlation
between their returns is 0.6.
Expected return on the portfolio is: (0.75 x 12%) + (0.25 x 16%) = 9% + 4% = 13%
Expected return of the portfolio of Asset 1 and Asset 2 is 13%.
Continued on the next page
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Risk and Return Analysis: 75
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2
2
Variance of the portfolio = (0.75 x 16) + (0.25 x 20) + 2x 0.75 x 0.25 x [0.6 x (16 x 20)]
= 144 + 25 + (0.375)(192)
= 144 +25 +72
= 241
𝜎𝜎𝑝𝑝 = √214 = 15.52 per cent
Tom holds shares of two companies in equal proportion and with the following characteristics:
Share 1: Expected return: 25% and Standard deviation: 30%;
Share 2: Expected return: 17% and Standard deviation: 22%;
Returns of these shares have a correlation of 0.5.
Calculate the portfolio return and risk.
If the investor wishes to reduce the portfolio risk to 15%, what will be the correlation coefficient?
6. Analyse the power of diversification in achieving superior return for a given level of risk or
minimum risk for a given level of expected return.
[Learning Outcome f]
Investors generally invest in more than two assets in a portfolio, which is called diversification. Diversification is
done in order to reduce the risks associated with the investment. It reduces the impact of any one security on
the overall performance of the portfolio and lowers the risk of the portfolio. It is necessary to check whether it is
possible to eliminate the risk completely by adding more assets to the portfolio.
The following points should be considered to ensure the best effects of diversification:



The portfolio must cover multiple investment options such as shares, mutual funds, bonds etc.
Investments with different risk types and risk levels should be selected.
Investments should be spread across a number of industries so that the portfolio is not affected by industry
specific risks.
There are two types of risks:

Systematic risk: this is also known as market risk. This risk arises due to the uncertainties in the economy
and cannot be reduced by diversification. Examples of systematic risk are increase in inflation rate, changes
in tax policies etc.

Unsystematic risk: this is also known as unique risk and arises from unique uncertainties of individual
securities. Uncertainties of individual securities in a portfolio cancel out each other and hence this risk can
be reduced through diversification. Examples of unsystematic risk are new competitors in the market, strike
in the company etc.
For the above purpose, it is necessary to study the various types of diversification:
1. Naive Diversification
This indicates random selection of securities in the portfolio. Ideally, as the number of securities in a portfolio
increases, the risk should reduce. However, it is not possible to reduce the risk to zero by increasing the number
of assets in the portfolio. It is not possible to eliminate systematic risk by adding the number of assets to the
portfolio. Systematic risk refers to the overall market risk that affects all securities and cannot be eliminated by way
of diversification. Non- systematic risk is a risk specific to the investment and can be avoided by diversification. It
is said that holding 10-15 securities in a portfolio can eliminate most of the non- systematic risk of a portfolio.
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2. Markowitz Diversification
In the above diversification, the number of securities in a portfolio is not important; covariance among the securities
is considered. In a portfolio of assets that have strong negative covariance, it is possible to reduce the portfolio
risk below the level of systematic risk. According to Markowitz diversification, an increase in the number of
securities in the portfolio leads to the portfolio risk approaching the level of systematic risk.
We have already studied earlier in this chapter that portfolio returns depend on the proportion of assets in the
portfolio whereas portfolio risks depend upon the proportion of assets as well as the correlation between return on
the assets in the portfolio. Correlation coefficient varies between 1 and -1.
Let us consider an example to see the effect of diversification on portfolio selection.
There are two assets in the portfolio:
Particulars
Expected Return (%)
Standard Deviation (%)
Asset 1
14
18
Asset 2
20
28
Table below gives risk and returns for different correlation coefficients:
Asset 1
Asset 2
1.00
0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
Expected
Return of
portfolio (%)
14.00
14.60
15.20
15.80
16.40
17.00
17.60
18.20
18.80
19.40
20.00
Standard deviation of portfolio (%)
Correlation
+1.00
18.00
19.00
20.00
21.00
22.00
23.00
24.00
25.00
26.00
27.00
28.00
Correlation
-1.00
18.00
13.40
8.80
4.20
0.00
5.00
9.60
14.20
18.80
23.40
28.00
Correlation
0.00
18.00
16.44
15.45
15.14
15.56
16.64
18.28
20.33
22.69
25.26
28.00
3. Perfect Positive Correlation
Perfect positive correlation between assets in a portfolio is not very common. It can be noticed from the table
above that for a correlation of 1, as an investor invests a higher proportion in Asset 2, the expected return and
standard deviation both increases. This means that there is a direct relation between risks and returns; the higher
the expected return, the higher will be the risk and vice versa. An investor can choose the portfolio depending
upon their risk preference. However, we can see from the above that diversification does not reduce risk when the
returns on assets have perfect positive correlation.
4. Perfect Negative Correlation
We can see from the above table (which gives the risks and returns for different correlation coefficients) that the
portfolio returns increase and portfolio risk declines when the proportion of the high-risk asset (Asset 2) is
increased. At the point where the proportion of Asset 1 is 60% and that of Asset 2 is 40%, portfolio risk is zero.
Thus, we can conclude that an investor gets maximum benefit of diversification when returns of two securities
have perfect negative correlation.
5. Zero Correlation
The above table which gives the risks and returns for different correlation coefficients) indicates that where both
assets are in equal proportion in the portfolio, the standard deviation of the portfolio is less than the standard
deviation of either of the assets in the portfolio. Hence, an investor can invest in high risk security and get higher
expected returns when there is zero correlation between the assets in the portfolio.
© GTG
Risk and Return Analysis: 81
Risk and Return Analysis: 77
All the above discussion was in respect of a portfolio having two assets. We now need to see what happens in
case there are more than two assets in the portfolio. In the case of a large number of securities in the portfolio,
the number of variances is equal to the number of securities whereas the number of covariance is much more.
The variance of securities reduces as the number of securities in a portfolio increase. As the number of
securities increases significantly, the variances of individual securities no longer remain and only the covariance
is relevant. Portfolio variance is equal to the average variance at this stage. Thus, we can see that risk is
reduced as number of securities in the portfolio increases, i.e. risk is reduced on account of diversification.
However, we have seen earlier that diversification can only reduce the unsystematic risk and not the systematic
risk.
A risk-averse investor prefers a portfolio with the highest expected return for a given level of risk or a portfolio with
the lowest level of risk for a given level of expected return. This is also referred to as the principle of dominance.
According to Markowitz portfolio analysis, the behaviour of investors in selecting the assets in a portfolio is based
on four assumptions:




Rate of return from the investment is the most important factor.
Risks are measured in terms of variability of expected returns.
Investors are generally averse to risk.
Decisions of investors are based on expected returns and standard deviation.
Explain the concept of diversification and the limits to diversification.
7. Determine optimal portfolio weights.
[Learning Outcome g]
The optimum portfolio theory assumes that an investor’s objective is to achieve maximum returns with minimum
risk from their investments. According to the theory of optimal portfolio, investors will make decisions aimed at
maximising returns for their accepted level of risk. An investor has to decide how much risk they are ready to
accept and then construct their portfolio.
According to the Harry Markowitz theory, there are two methods for selecting the Optimum Portfolio:
7.1 Two-step Optimisation (also known as Top-down approach)
According to this approach, there are three steps for selection of the portfolio:
1. Capital allocation decision where the total funds to be invested are divided between the risk- free asset
and the optimum portfolio of risky assets.
2. Asset allocation decision involves selecting the assets that will constitute the portfolio of risky assets, i.e.
allocating the funds between shares, bonds etc.
3. Security selection decision which involves selecting securities within each asset class.
The focus of the investor in this approach is on optimisation of the asset class i.e. shares, bonds etc. and then
on the securities within each class. Hence, this approach is known as two- step optimisation.
7.2 Efficient Portfolios
In this approach, an investor determines the risk- return opportunities available to them. This is also known as
determining the portfolio opportunity set or the minimum- variance portfolio opportunity set. Graphically, this is
represented by the minimum- variance frontier of risky assets.
The minimum variance represents the lowest possible variance for a given portfolio’s expected return whereas
the efficient portfolios have maximum return at each level of risk. Efficient portfolios dominate all other portfolios
and individual assets which lie below the efficient frontier. Dominant portfolios provide maximum return for a
given level of risk or minimum risk for the given rate of return.
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An investor intends to invest in two assets: Asset 1 and Asset 2. Let us consider the following portfolio
combinations for the assets for the purpose of our study:
Portfolio
P1
P2
P3
P4
P5
P6
Expected
Return (%)
10
12
13
15
18
20
Risk (%)
15
13
12
16
22
26
Graphically, the above table will be represented as follows:
As can be seen from the above diagram, Portfolio A is dominated by portfolios B and C whereas Portfolio B is
dominated by Portfolio C; thus they are inefficient portfolios. Portfolios C, D, E and F are efficient portfolios
hence Line CF is the efficient frontier. Segment AF is the minimum – variance portfolio opportunity set. Point C
represents global minimum variance portfolio (on the extreme left of the minimum variance frontier) and Point F
represents global maximum return portfolio.
1. Efficient Frontier with Margined Short Sales
A short sale is a sale by a person of an asset not owned by the seller but borrowed from another person
whereas a margin is a percentage of the market value of the transaction which the seller gives the person from
whom the security is borrowed. According to Edward Dyl, with margined short sales it is possible to have portfolios
that offer the same expected return with lower variance.
2. Efficient Frontier with One Risk Free Asset
A risk- free asset is an asset with zero variance and zero standard deviation. According to James Tobin,
portfolios that contain risky assets and one risk- free asset dominate portfolios formed of only risky assets.
For example, we have a risk- free portfolio A, a risky portfolio B and a total portfolio of A + B= C. The proportion
of total funds invested in B is given by w and the balance (1-w) is invested in A.
Risk and Return Analysis: 83
Risk and Return Analysis: 79
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Expected return of the total portfolio C is calculated as follows:
𝐸𝐸(𝑟𝑟𝑐𝑐 ) = 𝑟𝑟𝑓𝑓 + 𝑤𝑤[𝐸𝐸(𝑟𝑟𝑏𝑏 ) − 𝑟𝑟𝑓𝑓 ]
Where,
𝐸𝐸(𝑟𝑟𝑐𝑐 ) = Expected rate of return on complete portfolio
𝑟𝑟𝑓𝑓 = Risk- free rate of return
w= Proportion of total funds of portfolio C invested in portfolio B
𝐸𝐸(𝑟𝑟𝑏𝑏 ) = Expected return for risky portfolio B
𝐸𝐸(𝑟𝑟𝑏𝑏 ) − 𝑟𝑟𝑓𝑓 = Risk premium of the risky portfolio
Standard deviation of the complete portfolio is given by:
𝜎𝜎𝑐𝑐 = 𝑤𝑤𝜎𝜎𝑏𝑏
σ
c=
wσ
b
Where,
𝜎𝜎𝑐𝑐 = Standard deviation of complete portfolio C
w= Proportion of total funds of portfolio C invested in portfolio B
𝜎𝜎𝑏𝑏 = Standard deviation of risky portfolio b
Solving the above equations, we get the following:
𝐸𝐸(𝑟𝑟𝑐𝑐 ) = 𝑟𝑟𝑓𝑓 + 𝑤𝑤[𝐸𝐸(𝑟𝑟𝑏𝑏 ) − 𝑟𝑟𝑓𝑓 ]
Investors prefer to invest in efficient portfolios. A risk-averse investor prefers to invest in risk- free assets or in risky
assets with positive risk premium. (An investor considers the average return on government bonds over a number
of years in the past and compares it with the average return on the stock market. The excess return on the stock
market as compared to government bonds is the compensation for the higher risk of investment in the stock
market. This excess return is commonly known as risk premium).
7.3 Determining optimal portfolio weights
We have already studied in the earlier Learning Outcome in this Chapter that portfolio risk is not the weighted
average of the variance of returns of individual assets. The total risk of the portfolio depends upon the relation
between returns on assets in the portfolio i.e. the correlation coefficient between the assets. For a given correlation
coefficient, there is a minimum risk portfolio which has a standard deviation smaller than that of the individual
assets in the portfolio. The optimal weights that will give the minimum risk portfolio can be obtained by way of the
equation given below:
𝑤𝑤1 =
𝜎𝜎22 − (𝜌𝜌12 𝜎𝜎1 𝜎𝜎2 )
𝜎𝜎12 − 𝜎𝜎22 − 2(𝜌𝜌12 𝜎𝜎1 𝜎𝜎2 )
w 2 = 1- w 1
Where,
w 1 = Optimal weight of asset 1
w 2 = Optimal weight of asset 2
σ 12 = Variance of asset 1
σ 2 2 = Variance of asset 2
ρ12σ 1σ 2 = Covariance of returns
ρ12 = Coefficient of correlation between the returns on two assets
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Expected returns on Asset 1 and Asset 2 are 12 and 16 percent respectively. Standard deviation of Asset 1 and
Asset 2 is 16 and 20 percent respectively and the coefficient of correlation between their returns is 0. Determine
optimal portfolio weights of Asset 1 and Asset 2.
𝑤𝑤1 =
(20)2 − (0 × 16 × 20)
(16)2 − (20)2 − 2(0 × 16 × 20)
=
(400)
= 0.61 or 61 per cent
(256 + 400)
w 2 = 1-0.61 = 0.39 or 39 percent
Determine optimal weights of two assets: Asset 1 and Asset 2. Standard deviation of Asset 1 is 23 and that of
Asset 2 is 28. Correlation coefficient is 0.6.
Answers to Test Yourself
Answer to TY 1
In geometric mean return, it is assumed that dividend received at the end of each period is reinvested. Value of
investment after 5 years will be:
= (100 + 20) x (100 + 15) x (100 + 5) x (100 + 8) x (100 – 4)
= Tshs 15,023,232,000
Annual compound rate= P (1+i)
n
5
15,023,232,000= 1 (1+i)
i= 5 15,023,232,000 - 100
i= 108-100 = 8%
Geometric rate of return is 8%.
Answer to TY 2
Expected Return=
𝑛𝑛
𝑅𝑅̅ = ∑ 𝑃𝑃𝑖𝑖 𝑅𝑅𝑖𝑖 𝑖𝑖=1
= (15 x 0.25) + (26 x 0.55) + (-17 x 0.1) x (-6 x 0.1)
= 15.75
̅ 2
Variance = ∑𝑛𝑛
𝑖𝑖=1(𝑅𝑅𝑖𝑖 − 𝑅𝑅 ) 𝑃𝑃𝑖𝑖
2
2
2
2
= (15 – 15.75) x 0.25 + (26 - 15.75) x 0.55 + (-17 – 15.75) x 0.10 + (-6 – 15.75) x 0.10
= 212.49
𝑛𝑛
Standard deviation = √∑(𝑅𝑅𝑖𝑖 − 𝑅𝑅̅ )2 𝑃𝑃𝑖𝑖 =
𝑖𝑖=1
212.49
= 14.58
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Risk and Return Analysis: 83
© GTG
Answer to TY 3
Expected rate of return on shares of Fair Cosmetics Plc is calculated as follows:
𝐸𝐸(𝑅𝑅𝑖𝑖 ) = 𝑅𝑅𝑓𝑓 + 𝛽𝛽𝑖𝑖 [𝐸𝐸(𝑅𝑅𝑚𝑚 ) − 𝑅𝑅𝑓𝑓 ]
Expected rate of return= 10 + 1.5 (15-10)= 17.5%
Answer to TY 4
Dividend yield=
35
= 5.83%
600
Capital gain/ loss=
(750 − 600)
600
= 25%
Total Returns= 5.83% + 25%= 30.83%
Answer to TY 5
Portfolio Return = 25 x 0.5 + 17 x 0.5
= 21%
Portfolio risk:
𝜎𝜎𝑝𝑝2 = (0.5 × 30)2 + (0.5 × 22)2 + 2 × (0.5)(0.5) (30)(22)(0.5)
= 511
𝜎𝜎𝑝𝑝 = √511 = 22.61%
If standard deviation has to be reduced to 15%, then the required correlation coefficient will be calculated as
follows:
𝜎𝜎𝑝𝑝2 = (0.5 × 30)2 + (0.5 × 22)2 + 2 × (0.5)(0.5) (30)(22)(𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐)
σ2p =225+121+330×(correlation coeffient)
Correlation coefficient =
−121
330
= −0.367
Answer to TY 6
Investors generally invest in more than two assets in a portfolio, which is called diversification. Diversification is
done in order to reduce the risks associated with the investment. It is based on the principle that all the eggs
should not be kept in the same basket. If all the investible funds are invested in the same type of security or the
same industry, the risk will be very high. Diversification reduces the impact of any one security on the overall
performance of the portfolio and lowers the risk of the portfolio. For diversification, it is necessary to ensure that
the portfolio consists of various types of investments like shares, mutual funds etc. i.e. investments of different
types and risk levels and also spread across a number of industries.
However, diversification can only reduce the unsystematic risk. This is also known as unique risk and arises
from unique uncertainties of individual securities. Uncertainties of individual securities in a portfolio cancel out
each other and hence this risk can be reduced through diversification. Diversification cannot eliminate the
systematic risk or the market risk. This risk arises due to uncertainties in the economy like change in market
conditions, change in inflation rate etc. and cannot be reduced by diversification.
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Answer to TY 7
Optimal weight of Asset 1=
𝑤𝑤1 =
𝜎𝜎22 − (𝜌𝜌12 𝜎𝜎1 𝜎𝜎2 )
𝜎𝜎12 − 𝜎𝜎22 − 2(𝜌𝜌12 𝜎𝜎1 𝜎𝜎2 )
𝑤𝑤1 =
282 − (0.6 × 23 × 28)
232 − 282 − 2(0.6 × 23 × 28)
= 0.74 or 74%
Optimal weight of Asset 2: 1-0.74= 0.26 or 26%
Quick Quiz
1. What are the components of return on a single asset?
2. Define Expected Portfolio return.
3. A company losing a big contract or a company unable to buy the required raw materials are examples of
unsystematic risk. State whether the statement is true or false.
4. The minimum variance represents the ............. whereas the efficient portfolios ........- Complete the
statement.
5. What are the two main characteristics of risk?
6. Who is a risk- neutral investor?
7. Why do investors generally prefer to invest in a portfolio rather than in a single security?
8. What does the investor need to ensure in case of diversification of investment?
9. What is the optimum portfolio theory?
Answers to Quick Quiz
1. Return on a single asset comprises the dividend income (actual income) and capital gain/ loss (change in
market price of the asset).
2. Expected rate of return on a portfolio or the portfolio return is the weighted average of expected rates of return
on assets in the portfolio.
3. The statement is true. A company losing a big contract or being unable to buy the required raw materials
are examples of unsystematic risk. Unsystematic risk is the unique risk arising from unique uncertainties of
individual securities.
4. The minimum variance represents the lowest possible variance for a given portfolio’s expected return
whereas efficient portfolios have maximum return at each level of risk.
5. The two main characteristics of risk are probability of occurrence of loss and amount of potential loss.
6. A risk- neutral investor is the one who does not take risks into consideration and selects investments with
higher returns.
7. Investors generally prefer to invest in a portfolio rather than a single or few assets because investment is
diversified in case of investment in portfolio and hence risk is reduced. Diversification reduces the impact of
any one security on the overall performance of the portfolio.
Riskand
andReturn
ReturnAnalysis:
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8. While diversifying their investment portfolio, an investor has to ensure that the portfolio covers various types
of securities and securities with different risk levels like shares, mutual funds, bonds, fixed deposits etc. The
investor should also take care that investments in the portfolio are spread across a number of industries.
9. According to the optimum portfolio theory, investor’s objective is to achieve maximum returns with minimum
risk from their investments. An investor has to decide how much risk they are ready to accept and then
construct their portfolio.
Self Examination Questions
Question 1
What is the relationship between portfolio returns and risks of two securities in the following conditions?
(a) Perfect Positive Correlation
(b) Perfect Negative Correlation
(c) Zero correlation
Question 2
Explain the concepts of portfolio risk and return and how they are calculated.
Question 3
Explain the concepts of variance, standard deviation, covariance and correlation.
Question 4
Following is the information for securities of ABC Plc and XYZ Plc:
Particulars
Expected Returns
Standard Deviation
Beta
ABC Plc
25
42
0.85
XYZ Plc
26
40
1.25
Correlation coefficient between the returns of the two securities 0.70 and standard deviation of the market return
is 20%.
(a) Determine if it is better to invest in the securities of ABC Plc or XYZ Plc.
(b) If the proportion of investment in ABC Plc is 40% and that in XYZ Plc is 60%, determine the expected rate of
return and portfolio standard deviation.
(c) Determine the risk- free rate.
Question 5
Given below is the information pertaining to two assets: Asset A and Asset B:
Particulars
Expected Return (%)
Standard Deviation (%)
Asset A
14
12
Asset B
22
18
Covariance is 125.
(a) Determine the correlation between the two assets.
(b) Calculate the expected return and risk of the portfolio if the proportion of Asset A and Asset B in the portfolio
is 40% and 60% respectively.
Question 6
Following details are given for Assets X and Y:
Asset
X
Y
Expected
Returns (%)
15
20
Standard
Deviation (%)
17
25
Proportion of assets
in portfolio (%)
0.50
0.50
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(a) If required portfolio standard deviation is 20%, what will be the correlation coefficient that will give the
required level of risk?
(b) Determine the correlation if the required portfolio standard deviation is 18% and assets are invested in equal
proportion in the portfolio.
Answers to Self Examination Questions
Answer to SEQ 1
A portfolio means a combination of two or more assets/ securities. Investors generally prefer to invest in more
than two assets in a portfolio. This is called diversification. An investor generally diversifies the portfolio by selecting
securities of various types and risks, spread across different industries. This reduces the risk of the entire portfolio.
However, diversification can only reduce the unsystematic risk, i.e. the risk which arises from unique uncertainties
of individual securities. Uncertainties of individual securities in a portfolio cancel out each other and hence this
risk can be reduced through diversification. Systematic risk or market risk which arises due to uncertainties in the
economy cannot be reduced by diversification.
Portfolio returns depend on the proportion of assets in the portfolio whereas portfolio risks depend upon the
proportion of assets as well as the correlation between asset returns of the assets in the portfolio.
In case of perfect positive correlation, there is a direct relation between risks and returns; the higher the
expected return, the higher the risk and vice versa. An investor can choose the portfolio depending upon their risk
preference. However, diversification does not reduce risk when the returns on assets have perfect positive
correlation.
In case of perfect negative correlation, there is an inverse relation between risks and returns; investor gets
maximum benefit of diversification when returns of two securities have perfect negative correlation.
An investor can invest in high risk security and get higher expected returns when there is zero correlation between
the assets in the portfolio.
Answer to SEQ 2
A portfolio means a combination of two or more assets/ securities. For example, if an investor invests a portion
of their funds in the construction industry and the balance portion in say retail industry, it is likely that any downfall
in the construction industry is to an extent offset by the performance in the retail industry. It is unlikely that both
the industries will not perform well at the same time. So risk is reduced by investing in a portfolio rather than
in a single asset/ security. In a portfolio, the risk and return of the entire portfolio is considered and not of a
single asset/ security.
Expected return of a portfolio is the weighted average of the expected rates of return on assets comprising the
portfolio and consists of the expected rate of return on each asset in the portfolio and the relative share of each
asset in the portfolio.
The expected rate of return of a portfolio is calculated as follows:
E(r p )= w i E(r i )
Where,
E(r p )= Expected return from portfolio
w i = Proportion invested in asset i
E(r i )= Expected return for asset i
The portfolio risk is not measured as the weighted average of variance of returns on individual assets in the
portfolio. The factors taken into consideration for measurement of portfolio risk are the standard deviation of
each asset in the portfolio, the proportion of each asset in the portfolio and the correlation between returns of
two assets.
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Total risk of a portfolio having two assets is computed as follows:
σp
2
σp
2
2
=
w1 σ 1
=(
2
2
+
2
w2 σ 2 + 2w 1 w 2 ( σ 12 ) or
w1σ 1 ) 2 +( w2σ 2 ) 2 + 2w 1 w 2 ( σ 1σ 2 ρ12 )
Where,
σp
2
= Variance of returns of portfolio
w1 = Share of total portfolio invested in Asset 1
w2 = Share of total portfolio invested in Asset 2
2
σ 1 = Variance of asset 1
2
σ 2 = Variance of asset 2
σ 1 = Standard deviation of asset 1
σ 2 = Standard deviation of asset 2
σ 12 = Covariance between returns of two assets
ρ12 = Coefficient of correlation between the returns of two assets
Answer to SEQ 3
Risk of a portfolio is measured in terms of variance or standard deviation of its returns.
Variance means the variability from an average and is defined as the average of the squared differences from
the Mean. Standard deviation is square root of variance.
Variance is given by the following formula:
𝑛𝑛
∑(𝑅𝑅𝑖𝑖 − 𝑅𝑅̅ )2 𝑃𝑃𝑖𝑖
𝑖𝑖=1
Where,
𝑅𝑅𝑖𝑖 = return for the ith possible outcome
𝑅𝑅̅ = expected return
𝑃𝑃𝑖𝑖 = probability associated with 𝑅𝑅𝑖𝑖
n= number of possible outcomes
Standard deviation is the square root of the above.
Portfolio return is measured as the weighted average of returns on individual assets. However portfolio risk is
not measured as the weighted average of the variance or standard deviation of individual assets. Portfolio risk
also takes into consideration the covariance or the correlation between two assets. Covariance and correlation
measure the dependence or interaction between two variables. When two assets vary together, then we say
that there is covariance between the two assets.
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Covariance between two assets A and B is calculated as follows:
𝑛𝑛
𝐶𝐶𝐶𝐶𝐶𝐶(𝑎𝑎, 𝑏𝑏) = ∑[𝑅𝑅𝑎𝑎 − 𝐸𝐸(𝑅𝑅𝑎𝑎 )][𝑅𝑅𝑏𝑏 − 𝐸𝐸(𝑅𝑅𝑏𝑏 )] × 𝑃𝑃𝑖𝑖
𝑖𝑖=1
Where,
𝐶𝐶𝐶𝐶𝐶𝐶(𝑎𝑎, 𝑏𝑏) = Covariance between Assets A and B
Ra = Return on Asset A
E (Ra ) = Expected Return on Asset A
Rb = Return on Asset B
E (Rb ) = Expected Return on Asset B
P i = Probability
Covariance can be positive covariance, negative covariance or zero covariance. When both the assets in the
portfolio move in the same direction at the same time, they are said to be positively correlated. When they move
in opposite directions, they are said to be negatively correlated and when there is no pattern/ relationship between
the two assets, they are said to have zero correlation.
Covariance depends on the units of data, so it is difficult to compare covariance among data with different units.
Correlation coefficient eliminates this issue by dividing the covariance by the standard deviation of the variables.
When two assets correlate, change in one asset results in change in the other asset also; the two assets are
said to be correlated. Correlation is the measure of the linear relationship between two variables. Value of
correlation is called the correlation coefficient and it ranges between -1 and 1. A correlation coefficient of 1
indicates perfect positive correlation, -1 indicates perfect negative correlation and zero correlation coefficient
indicates no correlation between the two assets. Correlation is given by the following formula:
Cor (a,b) =
𝐶𝐶𝐶𝐶𝐶𝐶 (𝑎𝑎, 𝑏𝑏)
𝜎𝜎𝑎𝑎 𝜎𝜎𝑏𝑏
Answer to SEQ 4
(a) It can be seen from the information provided that securities of XYZ Plc have a higher return and lower risk;
hence it would be better to invest in the securities of XYZ Plc as compared to ABC Plc.
(b) Expected rate of return= 25 x 0.40 + 26 x 0.60= 25.6%
Portfolio standard deviation:
2
2
2
2
= (42) x (0.4) + (40) x (0.6)
= 858
Standard deviation =
858 = 29.29%
(c) Expected rates of return are given as follows:
r abc = 25= r
f
r xyz = 26= = r
abc c
+ (r c - r f )0.85
f
+ (r c - r f )1.25 r
r xyz = -1=(r c - r f )(-0.40) (r
- r f )= -1/-0.40= 2.5%
r abc = 25= r f + (2.5)(0.85)
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r f = 25 - 2.125= 22.875%
r xyz = 26= r f + (2.5)(1.25)
r f = 22.875%
Risk- free rate is 22.875%.
Answer to SEQ 5
Cor (1,2) =
Cor (1,2) =
𝐶𝐶𝐶𝐶𝐶𝐶 (1,2)
𝜎𝜎1 𝜎𝜎2
125
= 0.58
12 𝑥𝑥 18
(b) Expected Return= 0.4 x 14 + 0.6 x 22= 18.8%
Risk =
=
(0.4 * 12)2 + (0.6 * 18)2 + 2 * 125
23.04 + 116.64 + 250
=19.74%
Answer to SEQ 6
(a) Required correlation coefficient will be calculated as follows:
2
2
p = ( w1 1 )
2
+( w 2 2 )
2
+ 2w 1 w 2 ( 1 2 12 )
2
2
(20) = (0.50*17) +(0.50*25) +2(0.50)(0.50)(17*25* )
400= 72.25 + 156.25 + 212.5
= 0.81
ρ
(b) Required correlation coefficient will be calculated as follows:
2
2
p = ( w1 1 )
2
+( w 2 2 )
2
2
+ 2w 1 w 2 ( σ1σ2ρ12 )
2
(18) = (0.50*17) +(0.50*25) +2(0.50)(0.50)(17*25* )
324= 72.25+156.25+212.5
= 0.449
Indicative Examination Question
IEQ 1
a)
According to portfolio theory, a market estimate of investors reactions to risk cannot be measured precisely,
so it is impossible to set risk adjusted discount rates for various classes of investment with a high degree of
precision.
REQUIRED:
Discuss this statement. (6 marks)
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b) Jangala and Joseph are two famous security analysts at the local stock market. Recently the local stock
exchange has experienced market changes due to different economical and political factors which have affected
the price and return of the security traded in the market. As a result of the market changes, the two analysts
have selected different stocks with each claiming that the stock selected is highly performing than the other. The
expected return on the two stocks for two particular market returns are provided in the table below:
Jangala Selected stock
Joseph Selected Stock
Return
19%
16%
Beta
1.5
1.0
c)
REQUIRED:
i.
Can you tell which investor had a better performing stock aside from the issue of general movements in
the market? Explain. (4 marks)
ii.
If the government bond rate were 6% and the market return during the period were 14% which investor
would have a superior stock selection? (5 marks)
Assume that there are N Securities in the market. The expected return of every security is 10% and all
securities have the same variance of 0.0144. the covariance between any pair of the securities is 0.0064.
REQUIRED:
i.
Compute the expected return of an equally weighted portfolio. (3 marks)
ii.
Explain what will happen to the variance as N gets larger and outline the main determinant(s) of the
risk of a well-diversified portfolio. (2 marks) (Total: 20 marks)
IEQ 2
Mr. Waluwalu is a local entrepreneur doing business in Dar es Salaam. For long time, Waluwalu has been
considering investing his money in the stock market. He approaches a stockbroker about investing in stocks. The
stockbroker gave Waluwalu two stock options that he can invest in; Stock X and Stock Y. The stockbroker further
tells Waluwalu that the economy can either go in recession or it will boom. Upon further enquiry Mr. Waluwalu
established that the likelihood of observing an economic boom is two times as high as observing an economic
recession. He also learnt the following regarding the possible returns of the two stocks:
State of the Economy
Rx
Ry
Boom
10%
-2%
Recession
6%
40%
REQUIRED:
(i)
For each stock calculate the expected returns and total risk (variance and standard deviation).
(4 marks)
(ii)
Calculate the covariance of the returns of the two stocks.
(iii)
Mr. Waluwalu is considering creating two different portfolios. Portfolio I consist of 10% invested in X
and the reminder in Y, while Portfolio II has equal proportions in both stocks. Compute the expected
returns and risk of each portfolio and explain the risk-return characteristic of each portfolio.
(2 marks)
Answers to Indicative Examination Question
Answer to IEQ 1
(a)
This statement has considerable validity. It is impossible to precisely measure an individual’s attitude to risk,
and the problem is further compounded by the conceptual necessity of aggregating individual risk
indifference curves to form a market risk indifference curve further, even if it were possible to make the
required estimates at a given point in time, it would be difficult to use these estimates for long-run planning
purposes. Furthermore, investor attitudes to risk depend on psychological factors which vary over time.
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Risk and Return Analysis: 89
Risk and Return Analysis: 93
Despite these practical difficulties, the logic of the concept is appealing, and one must ask the question: is
it better to make subjective estimates and to construct an imperfect set of risk-adjusted discount rates for
use in evaluating assets with different degrees or risk, or is it preferable to use a constant discount rate for
all projects? It is often preferable to make an admittedly imprecise estimate of the appropriate risk-adjusted
discount rate rather than to assume that no differences exist. And finally, market estimates of investor
attitudes toward risk can be inferred for the firm as a whole base upon the values investors place on the
firm’s debt and equity securities. If the return offered bond and stockholders is too low given the level of risk
encountered, bond and stock prices will f all. If the return offered is high given investor risk expectations,
bond and stock prices will rise. (5 marks)
(b)(i)
(ii)
Which investor was better predictor
We know that: R1 = 19%, R2 = 16%, β1 = 1.5, and β1 = 1. To tell which investor was a better predictor of
individual stocks, we should look at their abnormal return, which is the ex-post alpha, that is, the abnormal
return is the difference between the actual return and that predicted by the SML. Without information about
the parameters of this equation (risk-free and the market rate of return) we cannot t ell which investor is
more accurate.
(4 marks)
Which Investor was superior stock selector
If Rf = 6% and Rm = 14%, then (using the notation of alpha for the abnormal return):
α1 = 19% - [6% +1.5(14% - 6%)] = 19% - 18% = 1%
α2 = 16% - [6% + 1(14% - 6%)] = 16% - 14% = 2%
here, the second investor has the larger abnormal return, and thus he appears to be a more accurate
predictor. By making better predictions, the second investor appears to have tilted his portfolio toward underpriced stocks.
(c)
(i)
Return = (1/N)(N*Ri)=N*0.1/N = 10%
(ii)
As N increases (approaching infinity), covariance approaches 0.0064 which is covariance between
any pair of the given security.
The covariance of the returns of the securities is the most important factor to consider when placing
security in a well-diversified portfolio.
(iii)
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SECTION C
Investment Appraisal (Capital Budgeting): 95
INVESTMENT DECISIONS
C1
STUDY GUIDE C1: INVESTMENT APPRAISAL
(CAPITAL BUDGETING)
Firstly, let us understand capital budgeting (investment) for a company as it is a key part of building up a business.
It can be defined as the planning process to identify, analyse and select long term investment of an asset or item
that is purchased with the hope that it will generate income or appreciate in value at some point in the future,
beyond one year.
The efficient use of an organisation’s funds for capital investment is of significant importance as it will involve
commitment of large funds over a long period and it tends to influence the value of the company due to impact
on growth, profitability and risk, thus impacting shareholder value.
One of the primary goals of capital budgeting / investments is to increase shareholder value, through increasing
the value of the company via expansion, acquisition, modernisation and replacement of long-term assets.
Investment is a monetary asset purchased with the idea that the asset will generate income in the future or
appreciate in value and be sold for a higher price.
For example, a large amount of cash is held in a savings account. A decision is made to invest the savings into
the purchase of a property at an extremely reasonable price for the size of the property and its location. The rental
income that is expected to be earned from the investment provides a larger return than the interest on the savings.
The investment in the property will now generate income in the future via rental as well as appreciation in value of
the property.
This Study Guide will help you to understand the nature and importance of long term investment appraisal and
certain techniques that are adopted by organisations to appraise investment projects
a) Discuss the nature of long-term investments and their roles in corporate development.
b) Explain the investment process and the framework for evaluating investment projects.
c) Identify, assess and explain appropriate investment appraisal techniques based on a given business, its
objectives and circumstances.
d) Compare various appraisal techniques.
e) Identify assess and explain appropriate discount factors or rates used to undertake an investment
appraisal based on a given business scenario, data and information.
f) Apply such appraisal techniques (discounted and non-discounted cash flow) and discount factors or
rates to appraise various investment project scenarios.
g) Identify, assess and explain appropriate data that may be used in cash flow calculations based on given
business scenario data and information.
h) Estimate cash flows for investment appraisal.
i) Perform investment appraisal under inflationary condition.
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1. Discuss the nature of long-term investments and their roles in corporate development.
[Learning Outcome, a]
1.1 Capital investment
It is the investment made to buy non-current assets or to improve the earning capacity of non-current assets
already held in the business. As a result of the capital investment, the non-current asset works more efficiently,
lasts longer or improves revenue generation. Hence, a capital investment increases the value of a non-current
asset and the value to shareholders.
Types of capital investment
1. Purchase of non-current assets: computers, vehicles, building, land, plant and machinery
2. Legal and professional fees paid for purchasing non-current assets: stamp duty, registration fees,
solicitor’s fees, architect’s fees, consultant’s fees
3. Improvement to existing non-current assets: fitting of air conditioner in vehicles, extension to a factory
site
Usually, capital investment decisions involve commitment of huge sums of money. In several cases the
organisation has to immediately make payments for making capital investments. The organisation earns the
benefit of a capital investment over a number of years. Hence, a capital investment made by an organisation
affects its business for a number of years and is therefore, a long-term investment.
The terms capital investment and capital expenditure can be used interchangeably.
1.2 Capital investment planning and control
Capital investment planning and control allows the management to assess the effectiveness of the capital
investment decision-making process that is used by it. It allows the management to refine its policies and
procedures for appraising and implementing capital investment projects. This ensures that the capital investments
made by an organisation:
(a) Are in line with its long-term goals / objectives.
(b) Support the business needs of the organisation.
(c) Minimise the risk and maximise the returns throughout the non-current asset’s life.
1.3 Role of of capital investment planning and control
1. Maximising shareholders’ wealth: the goal of a commercial organisation is to increase the wealth of its
shareholders. Appropriate capital investment planning and control ensures that a commercial organisation
successfully chooses and implements the capital investment that adds the maximum value to its net worth. An
increase in the net worth of an organisation increases the value of its shares. This results in an increase in
the wealth of its shareholders.
2. Taking strategic decisions: capital investments involve huge sums of money. An organisation receives the
benefit of capital investments for several years. Hence, capital investments have a huge effect on the profits
earned by an organisation. An opportune capital investment can yield spectacular results for an organisation.
On the other hand a wrong capital investment can force the organisation into bankruptcy.
3. Minimising the cost structure: an organisation commits itself to certain fixed costs while making capital
investments e.g. lease rental, wages, insurance charges etc. These fixed costs are not tied to the outcome
of the project. The organisation has to bear these fixed costs irrespective of the success / failure of the project.
These fixed costs have an effect on the sales, break-even point and profits of the organisation. Proper planning
ensures that the organisation considers the various fixed costs associated with the investment while accepting
/ rejecting a capital investment. Proper control over the implementation of capital investment ensures that the
organisation is able to minimise the fixed costs associated with the capital investment.
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4. Avoiding loss: a capital decision once made is not easily reversible. The organisation may be unable to
dispose of or find another use for the newly purchased asset such as a new plant and machinery. As a
result the organisation will have to write off the investment made in the non-current asset. Proper planning
ensures that the organisation avoids making imprudent capital investments. Proper control ensures that the
capital investment gets implemented and works according to the plan.
5. Avoiding fraud: usually huge sums of money are involved in capital investment decisions. A fraud may
result in heavy monetary loss to an organisation. In certain cases, it can even lead to irrecoverable injury to
the reputation of the organisation. An organisation can prevent the occurrence of fraud by implementing
strict capital investment control measures and ensuring the monitoring of such controls on a regular basis.
6. Growing through diversification: proper planning and control ensure that an organisation is successfully
able to implement various types of capital investment projects. This allows the organisation to diversify its risks
by investing in several types of capital investments.
7. Correcting discrepancy between planning and actual results: proper planning ensures that the
management foresees and prepares for the various challenges that a capital investment project may face.
Proper control ensures that any discrepancy between expected and actual results is quickly discovered and
rectified. This allows an organisation to achieve desired results.
SUMMARY
Outline the importance of capital investment planning and control.
2. Explain the investment process and the framework for evaluating investment projects.
[Learning Outcome b]
2.1 Capital budgeting process
1. Meaning
Capital budgeting process is the process through which an organisation generates, evaluates and selects
various capital investment proposals. It allows the organisation to assess the financial viability of a capital
investment proposal.
2. Issues considered and steps taken while preparing a capital expenditure budget
Investment appraisal is the most important part of the capital budgeting process. It is at this stage that a
decision is taken as to which projects are to be accepted and which are to be rejected. Investment proposals
are appraised to determine if they lead to the fulfilment of the overriding objective of shareholder wealth
maximisation.
Investments for the short-term as well as the long-term may be evaluated. However, only long-term investments
are the subject of capital budgeting.
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Step 1: Quantify the costs and benefits
The costs and benefits of an investment proposal are identified and quantified.
Step 2: Compare the costs and benefits with appropriate techniques
The costs and benefits should be compared to each other by using techniques such as the payback period,
Internal Rate of Return (IRR) or Net Present Value (NPV).
Step 3: Evaluate the risks involved and the sensitivity to changed situations
When we estimate the future cash flows, there is a risk that they may not actually materialise as the future is
uncertain; the actual outcome may be different. It is necessary to consider how this will affect the final outcome.
Step 4: Consider qualitative factors such as the environment or employment generation
The decision on the project will not depend only on the numerical calculations. We must also take into
consideration qualitative factors or non-financial factors. (This is covered in Paper C2 in more detail.)
A few factors considered at this stage are:

Legal issues: any legal action that the organisation may face due to the project.

Ethical issues: a project involving legal but unethical action will damage the image of the organisation.

Government regulations: various regulations that are applicable to the project e.g. employment laws,
environment laws, competition laws etc.

Political issues: whether any change in government will have an effect on the project.

Competition: the reaction of the competitors to the project.
Step 5: Take a decision
Management of the organisation will review all the investment proposals and make a decision of any one of the
following types:
(a) Accept/reject
This applies to independent projects. They do not compete with each other. You can either accept the
proposal or reject it. If a proposal meets the minimum standards required, it is accepted; otherwise it is rejected.
(b) Mutually exclusive choice
Sometimes projects may compete with each other in such a manner that acceptance of one signifies rejection
of the other. A criterion for the project is laid down. The best project is accepted, and the others are rejected.
This process assumes that all the competing projects are found acceptable by applying the ‘accept – reject’ test.
If all the projects are rejected by applying the test, then there are no projects left to compete!
A corrugated box manufacturer wants to purchase one new specialised corrugating machine. The criteria laid
down are that it should satisfy the technical specifications and the minimum accounting rate of return (ARR) should
be 15%.
There are four suppliers, Kat, Lat, Mat and Nat, who have submitted quotations. Kat’s quotation is rejected on
technical grounds. Nat’s machine gives an ARR of only 10%; hence it is rejected as it does not meet the criteria.
Only Lat and Mat are left in the competition since their machines satisfy the technical specifications. The machines
give an ARR of 16% and 20% respectively.
Mat’s machine is selected, and this means that Lat’s machine is rejected.
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Diagram 1: Issues considered, and steps taken while preparing a capital expenditure budget
3. Capital expenditure budget
The capital expenditure budget is an outline of an organisation’s decision to allocate funds amongst its various
existing and upcoming projects. The managers may overlook the risk of obsolescence while preparing their
short- t e r m capital expenditure plans. Hence, it is advisable that an organisation must prepare its capital
expenditure budget on the basis of the long-term capital expenditure plans of its managers.
A capital expenditure budget is decided on the basis of:


An individual manager’s request for issuing funds to the projects he handles.
The senior management’s decision to allocate funds amongst the various projects of the organisation.
The decision is made according to the long-term objectives of the organisation.
An organisation can decide the amount of its expected capital expenditure by:

Forecasting the capital investment projects that it is going to undertake. Usually the amount of expected
capital expenditure exceeds the amount of cash surplus that the organisation will have during the budgeted
period. In such a case the organisation has to make arrangements to borrow money from various sources
to finance the projects.

Obtaining the expected cash balance by preparing a long-term budget. The organisation chooses the capital
investments depending upon the expected cash surplus that it expects to have during the budgeted period.
2.2 Capital investment framework for evaluating investment projects
1. Appraisal of capital investment project
The stages involved in the project appraisal process of a capital investment project are as follows:
(a) Initial evaluation
Before actually starting a project, a decision evaluating the technical feasibility and commercial viability of the
project must be taken. In order to do this, the company should consider whether the project is in line with the
company’s long-term strategic objectives.
(b) Detailed assessment
Following the initial evaluation of the project, the company should consider whether the cash flows generated from
the project would add any economic value to the value and activities of the company. The organisation considers
the various costs and benefits that it will obtain by implementing the project. This stage also involves performing
sensitivity analysis and analysing the available sources of finance.
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(c) Management’s approval
Certain significant projects which have a material impact on the functioning and cash flows of the company should
be approved by the organisation’s senior management. For this approval to be obtained, the organisation’s senior
management should be satisfied that:



A detailed evaluation has been carried out.
The project conforms to the organisation’s long-term strategy.
The project will contribute to profitability of the organisation.
(d) Project implementation
During this stage, the project is assigned to a party who will assume responsibility for the project and oversee its
development. The resources will be made available for implementation and specific targets will be set. The project
team would then work towards meeting those targets.
(e) Monitoring the project
Projects involving capital expenditure take place over a significant period of time. It is necessary to monitor the
progress of a project by checking whether or not it is on schedule. Any delays in the implementation of a project
invariably increase the cost of the project. It is also necessary to check whether or not the cost of the project is
within the budget. In case any unforeseen events occur, all the costs and benefits associated with the project
should be re-assessed.
(f) Post-completion audit
This last and final stage involves conducting an enquiry into the benefits, costs, wastages and deviations from the
initial project plan. This investigation points whether or not the project is performing in line with expectations, and
what lessons can be drawn for future appraisals.
Diagram 2: Appraisal of a capital investment project
Build On Me Ltd is a construction company, which is looking to start a new project of building residential housing
on land that is already owned by the company.
(a) What are the 5 steps Build On Me Ltd needs to take while preparing a capital expenditure budget for the
new project?
(b) What are the stages of evaluation of the housing project that Build On Me Ltd should consider?
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3. Identify, assess and explain appropriate investment appraisal techniques based on a given
business, its objectives and circumstances.
[Learning Outcome c]
3.1 Investment appraisal techniques
Investment appraisals will feature an assessment of the expected return for the expenditure made and an
estimation of the future costs and benefits of the project(s) under consideration. When evaluating a capital budget,
the costs and benefits are required to be evaluated over the foreseeable future, which is usually the expected
useful economic life of the non-current asset that is to be purchased.
Typical capital projects include the purchase of a non-current asset immediately, which is then used for several
years to generate revenue or to attain operating cost savings. The asset will usually have running costs during
its use and maybe residual value at the end of its commercial life; for example: motor vehicles, machinery, printing
machines etc.
Capital projects go on for several years requiring estimations to be made for the revenues, costs and savings over
the life of the project, which can often lead to problems of inaccuracy in assumptions and calculations.
There are a number of investment appraisal techniques a company can use to assess the viability of capital
investment projects.
3.2 Return on Capital Employed
Any capital investment is made in order to earn a good return and maximise shareholders’ value. It is necessary
to check how this is achieved in practice. Return on capital employed (ROCE) is one of the ways of measuring the
return on an investment in terms of profitability.
ROCE measures the percentage of accounting profits (profits after depreciation) over the capital employed. A
widely used formula to calculate this is as follows:
ROCE =
Average annual accounting profits
Average investment
× 100
Accounting profits will be calculated after deducting depreciation from the cash profits.
As in other ratio calculations, slightly different formulae are sometimes used for ROCE. Hence, in place of average
investment, initial or final investment may be used. Note that the initial investment may include cost of new assets
bought, net book value (NBV) of existing assets to be used, investment in working capital and capitalised research
and development costs.
Average investment
The investment at the beginning of the project is the initial cost. The investment at the end of the project is the
disposable value or scrap value. If we want an average, we have to take the total of the two and divide it by two.
The formula will be:
Average investment =
(Initial investment + Scrap value)
2
Method of applying ROCE
A target or hurdle rate is decided beforehand. The projects that give an ROCE higher than the decided rate are
accepted. If there are two or more competing proposals out of which only one is to be selected, then the project
with the highest ROCE is selected.
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Spielberg Transport is considering purchasing a new transport vehicle. It has two offers.
The expected life of both the vehicles is 5 years. The following information is available
Original Cost
Scrap value at the end
Expected annual net cash inflows*
Offer A
(TSHS)
1,100,000
120,000
360,000
Offer B
(TSHS)
1,600,000
150,000
630,000
Assume the depreciation of the vehicle has already been
deducted from the expected annual net cash flows
Calculate the ROCE on both offers and state which offer will be accepted.
Offer A
ROCE =
360,000
×
610,000 (W1)
100 = 59%
Working 1
Average investment = 1,100,000 + 120,000 = 610,000
2
Offer B
ROCE =
630,000
×
875,000 (W2)
100 = 72%
Working 2
Average investment = 1,600,000 + 150,000 = 875,000
2
Based on the workings above, it can be seen that offer B provides the higher return and therefore, would be
accepted.
1. Advantages of ROCE
(a) It is reasonably simple to understand and use.
(b) It uses the familiar concept of percentage return: the percentage return can be compared with the
company's ROCE in order to decide whether it is in line with the company’s overall ROCE.
(c) It considers the cash flows for the entire life of the project: unlike the payback method, the ROCE
considers the cash flows for the entire life of the project.
(d) It can be used to compare mutually exclusive projects: a decision involving mutually exclusive projects
can be based on ROCE. The one with the higher ROCE is selected.
2. Disadvantages of ROCE
(a) It uses accounting profit which is subject to manipulations: if different estimates and accounting
policies are used in two otherwise identical situations, then the accounting profits will be different even though
the cash flows are the same. An example being differing depreciation rates applied to an asset will have an
impact on the accounting profits.
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(b) It ignores time value of money: this is indicated by the fact that this method as well as the payback
method does not discount the cash flows.
(c) It is a relative measure and ignores the size of the investment and the length of the project: the size
of the investment and the length of the project are relevant issues but are ignored. These factors determine
the risk and the volume of the profits.
The ROCE of two projects A and B are shown below:
Project A: ROCE = 50%
Project B: ROCE = 20%
If both projects were mutually exclusive, a rational manager would select Project A because its return is higher.
However, ROCE is merely a relative measure. It does not indicate an absolute return to the company. Additional
information regarding both the projects is as follows:
Project A
Initial investment = Tshs 100,000,000
Return = Tshs 50,000,000
Project B
Initial investment = Tshs 1,000,000,000
Return = Tshs 200,000,000
From an absolute perspective, project B would have been the preferred choice, as profits generated amount to
Tshs
200,000,000.
SUMMARY
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3.3 Payback
Payback period is a simple technique used for assessing the time it will take to pay back the money spent on
the project or asset. This technique is used for smaller businesses and focuses on cash flow and liquidity rather
than profits.
A widely used formula to calculate this is as follows:
Payback period =
initial investment
annual cash flow *
Used for when constant
annual cash flows
Where cash flows are uneven, payback is calculated by working out the cumulative cash flow over the duration
of the project. If an organisation is applying the payback period technique, they will need to set the target payback
period and then assess projects and select those that pay back within the target period. The company may select
projects on the basis of fastest payback period if timing of recovery of investment is of significant importance to
the investment decision.
If a project requires an investment of Tshs 1,000,000 and is expected to provide an annual cash flow of
Tshs 250,000, the payback period would be:
Payback period =
1,000,000
250,000
= 4 years
Similar calculations can be used to work out the payback period for a project with uneven annual cash flows.
A project is expected to have the following cash flows:
Year
0
1
2
3
4
5
Cash flow in
Tshs (000’s)
(19,000)
3,000
5,000
6,000
8,000
5,000
What is the expected payback period?
First, we need to calculate the cumulative cash flows over the 5-year period as follows:
Year
0
1
2
3
4
5
Cash flow in
Tshs (000’s)
(19,000)
3,000
5,000
6,000
8,000
5,000
Cumulative cash
flow Tshs (000’s)
(19,000)
(16,000)
(11,000)
(5,000)
3,000
8,000
Payback period is between year 3 and 4 as this is when the cumulative cash flow goes from negative to positive
cash flow. If we assume a constant rate of cash flow throughout the year, we could estimate that payback will be
three years plus ( Tshs 5,000/8,000) of Year 4. This is because the cumulative cash flow is Tshs 5,000 (negative)
at the start of the year and the year 4 cash flow would be Tshs 8,000. Therefore, payback will be after 3.625 years.
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1. Advantages of payback period
(a) It is easy to calculate and understand.
(b) It is useful under certain situations: the payback period method is useful for the rapidly changing technology
markets and for improving investment decisions.
(c) It favours quick return: the method favours projects with quick return which help company growth,
minimise risk and maximise liquidity.
(d) It considers the cash flows, not accounting profit: the payback method considers the cash flows rather
than accounting profits which are subject to manipulation.
2. Disadvantages of payback period
(a) It ignores any return after the payback period: this method does not consider the cash flow over the life of
the project, which the ROCE method does. For example, two projects could both have a payback period of
four years, but one might be expected to produce no further return after five years, while the other might
continue generating cash indefinitely.
(b) It ignores time value of money: this is indicated by the fact that this method as well as the ROCE method
does not discount the cash flows. For example, a Tshs 200 million investment that produced no cash flow
until the fourth year - and then a payback of Tshs 200 million - would have the same four-year payback period
as an investment that produced an annual cash flow of Tshs 50 million. In reality, the first is likely to be a
riskier and less attractive investment.
(c) It ignores the project profitability: the overall profitability of the project is an important factor that
determines the risk and volume of returns.
3.4 Discounting future cash flows
Money received today is worth more than the same money received in the future, i.e. money has a time value.
The time value of money occurs for three main reasons:
1. Potential for earning interest / cost of finance
2. Impact of inflation
3. Effect of risk
Discounted cash flow (DCF) techniques such as Net Present Value and Internal Rate of Return take the time value
of money into account. These apply a discount rate to work out the present-day equivalent of future cash flows.
For example, suppose you expect to receive Tshs 10,000 in one year's time, and use a discount rate of 10 per
cent. If you invest Tshs 9,091 at 10 per cent for one year, at the end of the year, you would have Tshs 10,000. In
other words, the present value of that Tshs 10,000 can be calculated as Tshs 9,091.
Similar calculations can be used to work out the present value of cash flows you expect to receive further into
the future. For example, suppose you expect to receive Tshs 10,000 in two years' time and use a discount rate
of 10 per cent. If you invest Tshs 8,264 for two years at 10 per cent, then at the end of two years, you would
have Tshs 10,000. In other words, the present value of that Tshs 10,000 is Tshs 8,264.
3.5 Net Present Value (NPV)
In the earlier section, we understood how the value of money depends upon the time of the cash flows. The
same amount of money received or paid at different times has different values. To make the cash flows at different
dates comparable, their present values are calculated.
The net present value (NPV) of an investment (project) is the difference between the present value of cash
inflow and the present value of cash outflow.
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The following steps are included to calculate the NPV of a project:
NPV = Present value of cash inflows - Present value of cash outflows
Diagram 3: Calculation of net present value (NPV)
Compute NPV by subtracting the
discounted cash inflows (step 4) from
the discounted cash outflows (step 2)
Compute the total discounted cash
inflow (cash inflow xx present
present value
value
factor)
Determine the total discounted cash
inflow of the project and the time periods
in which outflows & inflows occur
Compute the total discounted cash outflow
(cash outflow x present value factor)
Determine the total cash outflow of
the project & the time periods in
which outflows & inflows occur
2
4
3
5
5
4
3
2
1
The present value can be either positive (cash inflow greater than outflow), negative (cash outflow greater than
inflow) or zero (cash outflow and inflow exactly equal). The rule is to accept all the independent projects with
positive net present value or the competing projects with the highest NPV.
To obtain present value of a period:
calculate the relevant net cash flow of a period, and then apply the discount rate to the net cash flow.
to arrive at the net present value of the cash flows, add the present values calculated for each period.
An initial investment in a project is Tshs 100,000,000. The target or required rate of return is 12%.
The expected cash inflows are as follows:
Year
1
2
3
Tshs
60,000,000
50,000,000
45,000,000
Calculation of present value
Year
NPV
0
1
2
3
Cash flow
Tshs
(100,000,000)
60,000,000
50,000,000
45,000,000
Discount factor
1.000
0.893
0.797
0.712
Present value
Tshs
(100,000,000)
53,580,000
39,850,000
32,040,000
25,470,000
Since the project’s NPV is positive, it should be accepted. The positive NPV equates to a net cash inflow which
would add to shareholder wealth.
© GTG
Investment Appraisal (Capital Budgeting): 107
Investment Appraisal (Capital Budgeting): 101
Rate of return is also called ‘cost of capital’, ‘discount rate’ or ‘required return’, and therefore these terms can be
used interchangeably.
Timing assumptions made about cash flows when calculating NPV
The discounted value depends on the date of expected cash flows. Some assumptions relating to NPV
calculations include:
1. Initial cash outlay is incurred at the beginning of the first period, i.e. the year is taken as 0. The present
value of this initial investment is the same as the amount of investment; it is not required to be discounted
since the time is ‘now’. The discount factor for year 0 is 1.000.
2. Any transaction during a period is assumed to occur at the end of the period. E.g. receipts during year 2
are assumed to have taken place at the end of year 2.
3. Cash flows occurring at the beginning of a year will be assumed to have occurred in the previous year for
discounting purposes.
4. Cash flows generated during the life of the project will be reinvested at a rate equal to the cost of capital.
A cash payment of Tshs 600,000 on 1 January 20W8 will be assumed to have occurred in 20W7, for the
purposes of cash flow discounting.
3.6 Discounted payback method
Payback period has been discussed in detail earlier in this Study Guide.
Discounted payback method is similar to the payback method. It is the length of time that the discounted cash
flows require to recover the initial investment. Under this method, the cash flows are discounted at the
organisation’s cost of capital. After this, the present values of the cash flows are cumulated until they are equal
to the initial investment.
Payback period uses nominal cash flows.
Discounted payback period uses the discounted cash flows.
The organisation rejects the projects that have a discounted payback period of more than the discounted payback
period that is desired by the organisation. This ensures that all the projects that the organisation accepts
have positive net present value within the desired discounted payback period.
The advantages and disadvantages of the discounted payback period are similar to those of the payback
period. However, the discounted payback period overcomes the shortcoming of the payback period, which is
ignoring the time value of money.
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Let’s assume that cost of capital for a company is 10% and the following table shows the cash flows as well as
cumulative discounted cash flows for one of the company’s Project C:
Present value Cumulative
Discounting of cash flows discounted
Cash flow factor at 10%
at 10%
cash flows
Tshs
Year No.
Tshs 000's Tshs
000's
0
(300.00)
1.000
(300.00) 000's
(300.00)
1
80.00
0.909
72.73
(227.27)
2
150.00
0.826
123.97
(103.31)
3
140.00
0.751
105.18
1.88
4
80.00
0.683
54.64
56.52
5
70.00
0.621
43.46
99.98
Discounted payback period = 2 years + Tshs 103.31/ Tshs 105.18 x 12 months = 2 years and 11.79 months,
i.e. almost 3 years.
1. Advantages of Net present value method
(a) It assumes that cash flows are re-invested at the company’s cost of capital: the company’s cost of
capital represents the average opportunity cost of the company’s providers of finance.
(b) It is directly related to the objective of maximising shareholders’ wealth: if a project is accepted, its
NPV represents the change in the total market value of the company. Other investment appraisal methods
are not directly related to the objective of maximising shareholders’ wealth.
(c) It is not a relative measure of return: unlike IRR or ROCE, NPV is an absolute measure of return. It is
therefore able to reflect the amount of initial investment or the absolute increase in the corporate value.
(d) It considers the time value of money: money has a time value i.e. the same amount of money has a
different value at a different time. NPV considers the time value of money while appraising investment
projects.
(e) It does not consider the accounting profit: the NPV method considers the cash flows involved in a
project. Financial management, unlike accounting, considers cash flows to be more effective, as accounting
profits can be manipulated. However, cash inflows / outflows spread over a long period of time have no
common ground to be measured upon due to several factors.
(f) It considers all the cash flows over the life of a project.
(g) It can be used to appraise projects with non-conventional cash flows: a project has non-conventional
cash flow when negative cash flows occur during the life of the project.
2. Disadvantages of Net present value method
(a) It is more complex than ROCE, payback and IRR investment appraisal techniques.
(b) It fails to relate the return of the project to the size of the cash outlay.
(c) It requires detailed forecasts of long-term cash flows which can be difficult to explain to management:
NPV assumes that the management is accurately able to estimate long term cash flows.
Long term cash flows are affected by several factors such as cost of labour, material, interest rates, etc.
Due these factors the management usually overestimates or underestimates the long-term cash flows.
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(d) It requires knowledge of cost of capital.
(e) It is difficult to compare NPV with economic variables: NPV is an absolute measure of return. Hence,
unlike IRR or ROCE it cannot be compared with economic variables such as interest rates and inflation.
SUMMARY
3.7 Internal Rate of Return (IRR)
An investment project’s internal rate of return is the required rate of return or cost of capital which produces a
net present value of zero when used to discount the project’s cash flows.
In other words, when internal rate of return is used to discount the cash flows, the present value of
outflows and the present value of inflows will be equal.
Calculation of IRR
Two different methods can be used for calculation of IRR in the following two situations:
1. when the project cash inflows are identical
2. when the project cash inflows are not identical
1. When the project cash inflows are identical
Calculation of IRR for a project with identical cash inflows
The following table gives the particulars of a proposed project X of Strilco.
Period
0
1
2
3
4
5
6
Cash flow in
000's ( Tshs
(6,000)
1,450
1,450
1,450
1,450
1,450
1,450
)
In this case, the inflows are identical; therefore, we can use the cumulative present value factors table.
As we know, IRR represents the rate where NPV is Nil
Therefore,
( Tshs 1, 450,000 x CPVFr,6) – Tshs 6, 000,000 = 0
Where,
CPVFr,6 is the cumulative present value factor for 6 years, and r is IRR
CPVFr,6 = 6,000,000/1,450,000 = 4.137931
Continued on the next page
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If we look at the cumulative present value factor table and check the row of 6 years, we will find that the value of
4.111 (refer to the cumulative present value table below) which is the nearest to 4.137 appears in the 12%
column.
Therefore, we can conclude that the internal rate of return is approximately 12%.
This table of cumulative present value factors can be used in cases where the project cash inflows are
identical.
IRR obtained by the linear interpolation is only an approximation.
The actual NPV line is a curve rather than a linear as shown in the diagram below.
Diagram 4: Actual NPV Curve and estimation of IRR obtained by a single linear interpolation
The relationship between the discount rate and NPV can be seen in the above diagram. As the rate increases,
the NPV decreases.
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If we base our interpolation on points R, then we will get the IRR at L. Similarly, if we base our interpolation on
point S, we will get the IRR at M. However, the actual NPV is a curve and the actual IRR is at N where this
curve intersects the discount rate line.
2. When the project cash inflows are not identical
In this situation we use the interpolation method. The NPV at two discount rates will be required.
𝐼𝐼𝐼𝐼𝐼𝐼 = 𝑎𝑎 +
Where,
𝐴𝐴
× (𝑏𝑏 − 𝑎𝑎)%
𝐴𝐴 + 𝐵𝐵
a is lower of two rates of return used
b is higher of two rates used
A is NPV obtained using rate a
B is NPV obtained using rate b
Continuing from the previous example of Strilco,
The following table give the particulars of a proposed project Y:
Period
Cash flow in
000’s ( Tshs )
0
(6,000)
1
1,450
2
3,250
3
500
4
1,450
5
600
6
1,450
The internal rate of return of the above project can be calculated in the following way.
First, we take 10% as a PV factor. That gives us a positive NPV of Tshs 560
Next, since the NPV is positive, we increase the rate to 14%
0
(6,000)
1.000
(6,000)
1.000
Present
value in
000’s ( Tshs
)
(6,000)
1
1,450
0.909
1,318
0.877
1,272
2
3,250
0.826
2,685
0.769
2,499
3
500
0.751
376
0.675
338
4
1,450
0.683
990
0.592
858
5
600
0.621
373
0.519
311
6
1,450
0.564
818
0.456
661
Period
Cash flow in
000’s ( Tshs )
10% PV
factors
NPV
560
IRR = 10% +
× (14 - 10 )%
560 - (- 61)
= 10% + 3.61%
= 13.61%
Present value
in 000’s ( Tshs
)
560
14% PV
factors
(61)
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1. Advantages of IRR
(a) It is a percentage which is more easily understood.
(b) It considers the time value of money: money has a time value i.e. the same amount of money has a
different value at a different time. IRR considers the time value of money while appraising investment projects.
(c) It uses cash flow, not profits: the IRR method considers the cash flows involved in a project. Cash flow
consideration is deemed to be more effective, as accounting profits can be manipulated.
(d) It considers all the cash flows over the life of a project.
(e) It is directly related to the objective of maximising shareholders’ wealth: it means if a firm selects
projects where the IRR exceeds the cost of capital, it should increase shareholders’ wealth.
2. Disadvantages of IRR
(a) It is not a measure of absolute profitability.
(b) Interpolation only provides an estimate, and an accurate estimate requires the use of a spreadsheet
programme.
(c) It is fairly complicated to calculate.
(d) It cannot be used to appraise projects with non-conventional cash flows: projects that have nonconventional cash flows are those where negative cash flows occur during the life of the project. Nonconventional cash flows may give rise to multiple IRRs, which means the interpolation method cannot be used.
Decision Rule
Accept all independent projects where the IRR is greater than the company’s cost of capital or target rate of
return.
Diagram 5: NPV and IRR
SUMMARY
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Which of the following statements is true about Internal Rate of Return (IRR)?
A IRR is the rate at which an organisation attains the maximum net present value relating to an investment. B
If the IRR of an investment is greater than the company’s cost of capital, the investment can be accepted. C
IRR cannot be determined in case an investment has identical cash flows in all years of its life.
D IRR is the discount rate at which the net present value of an investment is negative.
4. Compare various appraisal techniques.
[Learning Outcome d]
Learning Outcome 3 above identifies and explains the advantages and disadvantages of the various investment
appraisal techniques such as return on capital employed, payback period, net present value and internal rate of
return.
Here, we will compare the discounted cash flow methods against the non-discounted cash flow methods.
4.1 Superiority of DCF methods over non DCF methods
Non-DCF methods, such as the payback method and the return on capital employed have already been discussed.
These methods suffer from certain drawbacks which are overcome by the DCF methods. In this sense, the DCF
methods are superior for the following reasons:
1. The timing of cash flows and the time value of money are taken into account through discounting
Tshs 1,000,000 to be received after one year is considered to be worth Tshs 1,000,000 today under non-DCF
methods. However, under DCF methods, if the discount rate is 10%, its present value will be treated as Tshs
909,000 (0.909 x 1,000,000 Tshs ) and not Tshs 1,000,000. This is more logical. If we invest Tshs 909,000 today,
and invest it at 10%, the amount will have increased to Tshs 1,000,000 by the end of the year.
2. Projects are considered over their entire lives; thus, a full evaluation is facilitated.
3. Only cash flows are incorporated into calculations as opposed to profits which are susceptible to
manipulation.
4. DCF techniques can indicate how undertaking investments can affect shareholders’ wealth.
SUMMARY
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Both NPV and IRR are methods of discounted cash flow. As seen in the earlier section, they are better than the
non-DCF techniques. However, when it comes to selecting between NPV and IRR, we need to know the relative
merits.
4.2 Selecting between NPV and IRR – General merits
1. Since the IRR method talks in percentage terms, it ignores the relative size of the project.
Compared to a large project with an IRR of 15%, a small project with an IRR of 16% will be selected.
In absolute terms, it may be more profitable for the company to pursue the large project.
2. IRR is easier to understand, especially for non-financial managers.
3. Reinvestment assumptions: in the NPV method, the assumption is that cash flows generated during the
life of a project can be reinvested elsewhere at a rate that is equal to the cost of capital. This is a logical
and practical assumption that can actually materialise.
In the IRR method, the assumption is that cash flows generated during the life of a project can be reinvested
elsewhere at a rate that is equal to IRR. If IRR exceeds the cost of capital this will not be a practical
assumption, hence it cannot actually materialise.
SUMMARY
4.3 Selecting between NPV and IRR - depending upon the kind of the projects
1. Single project with conventional cash flows
A conventional cash flow is where an initial cash outflow is followed by successive cash inflows. Both the NPV
and IRR methods can be used for this kind of project. Either method will give the correct decision.
2. Single / many project(s) with non-conventional cash flows
In a project with non-conventional cash flows, the cash outflows and inflows occur one after another.
Conventional and non-conventional cash flows
Project M
Year
0
1
2
3
4
Cash flows
Tshs (000’s)
(100,000)
20,000
27,000
37,000
45,000
Year
0
1
2
3
4
Project N
Cash flows
Tshs (000’s)
(200,000)
40,000
(13,000)
(8,000)
93,000
In project M, an initial cash outflow is followed with successive cash inflows. Hence, it is a project with
conventional cash flows.
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However, project N, does not have a conventional pattern of cash flow. Hence, it is a project with non- conventional
cash flows.
For project(s) with non-conventional cash flows, there are more than one IRR. In fact, there are as many IRRs
as there are changes in the signs (inflow to outflow and outflow to inflow). The following diagram depicts this.
Diagram 6: Non-conventional project with multiple rates of return
It can be seen that there are two IRRs: IRRA and IRRB. Let us assume that there are two possible costs of
capital: x and y. If the cost of capital is x, since it is below both the IRRs, the IRR method will recommend
acceptance of the project. However, the relevant point on the NPV curve, P, is in the negative area, which indicates
that the project should not be accepted. Following the IRR method would have resulted in taking the wrong
decision.
If the cost of capital is y, the IRR method may not be able to offer a decision, since the cost of capital falls between
the two IRRs. However, the relevant point on the NPV curve, Q, is in the positive area at this point, which indicates
that the project should be accepted.
It is evident from the above that for project(s) with non-conventional cash flows, NPV is more suitable.
3. Mutually exclusive projects
Mutually exclusive projects indicate that only one of them can be selected. The NPV and IRR methods may give
similar or conflicting results. Wherever a conflict occurs, NPV should be followed. This is because the NPV
method indicates the economic contribution or surplus of a project in absolute terms. The higher the NPV, the
better it is.
4. Projects where discount rates change during the life of a project
There may be changes in the cost of capital over the project life.
The IRR method cannot accommodate changes in the discount rates during the life of a project.
However, the NPV method can accommodate the changes. The following table illustrates them:
Year
Discount rates
PV factors
Cash flows Tshs (000’s) Present
values Tshs (000’s)
NPV Tshs (000’s)
0
(50,
000
)
(50,
000
)
1
15%
1 0.870
24,000
20,880
2
15%
0.756
23,000
17,388
3
10%
0.751
25,000
18,775
7,043
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Continuing the previous example of Strilco in the IRR section of Learning Outcome 3,
The following are the expected cash flows from project Z:
Period
0
1
2
3
4
5
6
Cash flow Tshs (000’s)
(10,000)
4,500
2,900
500
2,000
2,500
1,450
The internal rate of return for this project is 12.54% (calculations not given)
The cost of capital for the company is 8%.
If the management decides that one of the two projects (Project Y and Project Z) must be selected (assuming
that they are mutually exclusive) using the appropriate DCF technique.
1. Using IRR
The IRR of project Y is 13.61% and that of project Z is 12.54%. On this criterion, project Y is better.
2. Using NPV
Since the cost of capital is 8%, let us find out the NPV of both the projects, using this discounting rate.
Period
0
1
2
3
4
5
6
NPV
8% discount factor
1.000
0.926
0.857
0.794
0.735
0.681
0.630
Project Y
Cash flow Present value
(000’s)
(000’s)
Tshs
Tshs
(6,000)
(6,000)
1,450
1,343
3,250
2,785
500
397
1,450
1,066
600
409
1,450
914
914
Project Z
Cash flow Present value
(000’s)
(000’s)
Tshs
Tshs
(10,000)
(10,000)
4,500
4,167
2,900
2,485
500
397
2,000
1,470
2,500
1,703
1,450
914
1,136
Both projects are financially viable as both have produced positive NPVs. However, since the projects are mutually
exclusive, Project Z would be selected as its NPV is higher.
The logic behind giving preference to the NPV method is that it is consistent with the overriding goal of financial
management, i.e. maximisation of shareholder wealth; by selecting the project which gives higher NPV,
shareholder wealth will be maximised. NPV is superior to the IRR and Profitability Index approach as it is more
consistent with the shareholder wealth maximisation objective.
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SUMMARY
1. One element of superiority to the discounted cash flow method over the non-discounted cash flow method is
that the timing of cash flows and the time value of money are taken into account through discounting. True
or False.
2. Which of the following are types of methods of discounted cash flow?
A
B
C
D
Payback period
NPV and IRR
ROCE and payback period
d) NPV, IRR and ROCE
3. Internal rate of return takes the relative size of project into consideration. True or False.
4. For projects with non-conventional cash flows, there are more than one IRR. True or False.
5. For projects with non-conventional cash flows, IRR is more suitable than NPV. True or False.
6. NPV should be followed where a conflict occurs between mutually exclusive projects, as it demonstrates
contribution of project in absolute terms. True or False.
7. For projects where discount rates change during its life, IRR method should be used as it can accommodate
these changes. True or False.
5. Identify assess and explain appropriate discount factors or rates used to undertake an
investment appraisal based on a given business scenario, data and information.
[Learning Outcome e]
5.1 How is the rate of discount determined to calculate the present values?
An organisation’s overriding goal is to maximise the shareholder value. Therefore, normally it will target a rate
of return that is more than or equal to the cost of capital.
The cost of capital is the cost incurred by the organisation to use funds. An organisation will earn surplus cash if
its rate of return (cash inflows) is more than its cost of capital. The organisation can retain funds as long as it
can find projects that have cash inflows equivalent to the organisation’s cost of capital. Accepting a project that
has a rate of return that is less than the organisation’s cost of capital will result in cash outflow from the
organisation. Hence, an organisation must return funds to its shareholders if it is unable to invest in projects that
have a rate of return that is greater than or equal to the organisation’s cost of funds.
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The cost of capital f or Confounded Ltd is 10%. It has two proj ects , eac h requiring an investm ent of
TSHS10,000,000. The details of the project are:
Project name
Project Fathom
Project Bingo
Rate of return
8%
12%
If Confounded Ltd accepts Project Fathom, the company’s cost of capital will be Tshs 1,000,000 (10,000,000 x
10%). However, the return from the project will be Tshs 800,000 (10,000,000 x 8%). Hence, the organisation
will suffer a loss.
If Confounded Ltd accepts Project Bingo, the company’s cost of capital will be Tshs 1,000,000 (10,000,000 x
10%). However, the return from the project will be Tshs 1,200,000 (10,000,000 x 12%). Hence, the organisation
will have a surplus cash inflow.
The discount rate used should ideally include the following features:



Potential for earning interest/ cost of finance – what return is required for different providers of finance
Impact of inflation – whether ‘money’ rates or ‘real’ rates are required
Effect of risk – CAPM is one model that shows the link between risk and return
5.2 Weighted Average Cost of Capital (WACC)
The key idea is to identity the cost of capital that provides the background to specific calculations such as
identifying the cost of equity or cost of debt. Ideally, a discount rate that reflects the returns of all providers of
long-term finance is desired whilst assessing investment decisions.
Weighted average cost of capital is derived by obtaining the firm’s cost of equity and cost of debt and then
averaging them according to the market value of each source of finance.
1. Formula for WACC:
Or





Ve and Vd are the market values of equity and debt respectively.
ke and kd are the returns required by the equity holders and the debt holders respectively.
T is the corporation tax rate.
ke is the cost of equity.
kd(1-T) is the cost of debt.
WACC = (weight of equity x cost of equity) + (weight of debt x cost of debt)
Note: cost of equity is calculated using different models; for example, dividend growth model and capital asset
pricing model. The latter is deemed a more superior method.
Cost of debt is based on the yield to maturity of the relevant instruments. If no yield to maturity can be
calculated, we can base the estimate on the instrument's current yield.
The weights are based on the target market values of the relevant components. But if no market values are
available, we base the weights on book values.
When using book values, reserves such as share premium and retained profits are included in the book value of
equity, in addition to the nominal value of share capital. However, the value of shareholders' equity shown in a set
of accounts will often reflect historic asset values, and will not reflect the future prospects of an organisation.
Consequently, it is preferable to use market value weights for the equity.
When using market values, reserves such as share premium and retained profits are ignored as they are, in
effect, incorporated into the value of equity.
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Equally, we should also use the market value rather than the book value of the debt, although the discrepancy
between these is likely to be much smaller than the discrepancy between the market value and book values of
equity.
2. Capital Asset Pricing Model (CAPM)
As noted above, the CAPM is one model that can be used to calculate the cost of equity. It is deemed more
superior than the dividend growth model as it takes earnings into consideration, and it is a means to determine
the required return for a given level of risk.
The total return demanded by the investor is actually dependent on two specific factors:
the prevailing risk-free rate (Rf) of return

the reward investors demand for the risk they take in advancing funds to the firm

Formula:
Required return = Rf + × (Rm - Rf)
where:
Rf = risk-free rate
Rm = average return on the market
(Rm - Rf) = equity risk premium (sometimes referred to as average market risk premium)
= systematic risk of the investment compared to market and therefore amount of premium needed
To calculate the project return, the company would need to find a beta that reflects the systematic risk of the
project and then use the CAPM equation.
Strilco Company has 1 million shares of common stock currently trading at Tshs 300 per share. Current risk free
rate is 4%, market risk premium is 8% and the company has a beta of 1.2.
It also has 500,000 bonds of Tshs 1,000 paying a 10% return, currently trading at Tshs 950. The tax rate is
30%. Calculate the weighted average cost of capital.
Firstly, we need to calculate the weights of debt and equity.
Market Value of Equity = 1,000,000 × Tshs 300 = Tshs 300,000,000
Market Value of Debt = 500,000 × Tshs 950 = Tshs 475,000,000
Total Market Value of Debt and Equity = Tshs 775,000,000
Weight of Equity = Tshs 300,000,000 / Tshs 775,000,000 =
38.71% Weight of Debt = Tshs 475,000,000 / Tshs 775,000,000 =
61.29%
Weight of Debt can be calculated as 100% minus cost of equity = 100% 38.71% = 61.29%
Secondly, we need to calculate the cost of equity. With the given data we can use capital asset pricing model
(CAPM) to calculate cost of equity as follows:
Cost of Equity = Risk Free Rate + Beta × Market Risk Premium
Cost of equity = 4% + 1.2 × 8% = 13.6%
Thirdly, we need to find the cost of debt. Cost of debt is equal to the return yielded. With the given data, the
return is 10%. After tax cost of debt is hence 10% × (1 30%) = 7%
And finally, WACC = 38.71% × 13.6% + 61.29% × 7% = 9.5549%
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5.3 Using WACC as a discount rate
Weighted average cost of capital is used in discounting cash flows for calculation of NPV and other valuations
for investment analysis.
The WACC calculation is based upon the firm's current costs of equity and debt. It is therefore appropriate for
use provided:




the historic proportions of debt and equity are not to be changed
the operating risk of the firm will not be changed
the finance is not project-specific, i.e. projects are financed from a pool of funds.
the project is small in relation to the company, so any changes are insignificant.
If any of these criteria are not met, it will not be appropriate to appraise a project using the historic WACC. It's
important for a company to know its weighted average cost of capital as a way to measure the expense of funding
future projects. The lower a company's WACC, the cheaper it is for the company to fund new projects.
A company looking to lower its WACC may decide to increase its use of cheaper financing sources. For
instance, in the example above, the company may issue more bonds instead of stock because it can get the
financing more cheaply. This would increase the proportion of debt to equity, and because the debt is cheaper
than the equity, the company's weighted average cost of capital would decrease.
Note: the determination of discount rates using the method of CAPM and WACC are discussed in the further
study guides of this Study Text.
CAPM is denoted by the formula, Rf + × (Rm - Rf).
Which of the following options does Rm denote?
A
B
C
D
Rate of money
Average rate of return on money
Average rate of return on the market
Risk free rate prevailing in the market
6. Apply such appraisal techniques (discounted and non-discounted cash flow) and discount
factors or rates to appraise various investment project scenarios.
[Learning Outcome f]
The above two learning outcomes show the different investment appraisal techniques together with the relevant
advantages and disadvantage of each technique. Here, the techniques are to be applied and put into question
practice.
Project P
Project Q
Average Investment
Tshs
101,250,000
101,250,000
Both the projects have a total life of 4 years.
Expected cash inflows are as follows:
Year
1
2
3
4
Cash inflows
Project P
Project Q (
( Tshs )
Tshs )
24,750,000
38,812,500
27,562,500
38,812,500
27,562,500
37,687,500
72,000,000
36,562,500
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Required:
Calculate the ROCE and state which project is acceptable.
Answer
Depreciation 1/4, on straight line basis
Project P
Project Q
25,312,500 Tshs
25,312,500 Tshs
Year
Project P
Cash Flows
Depreciation
Accounting
Profit
Year
Project Q
Cash Flows
Depreciation
Accounting
Profit
Initial
Investment
1
TSHS
2
TSHS
3
TSHS
(101,250,000)
24,750,000
(25,312,500)
27,562,500
(25,312,500)
27,562,500
(25,312,500)
72,000,000
(25,312,500)
151,875,000
(101,250,000)
(562,500)
2,250,000
2,250,000
46,687,500
50,625,000
Initial
Investment
(101,250,000)
1
TSHS
2
TSHS
3
TSHS
4
TSHS
4
TSHS
Total
TSHS
Total
TSHS
38,812,500
38,812,500
37,687,500
36,562,500
151,875,000
(25,312,500)
(25,312,500)
(25,312,500)
(25,312,500)
(101,250,000)
13,500,000
13,500,000
12,375,000
11,250,000
50,625,000
Average investment = 101,250,000/2 = 50,625,000
Average profits
Project P = 50,625,000/4 = 12,656,250
Project Q = 50,625,000/4 = 12,656,250
𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 =
𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝
𝑥𝑥100
𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖
Project P
12,656,250
𝑥𝑥100 = 25.00%
50,625,000
Project Q
𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 =
𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 =
12,656,250
𝑥𝑥100 = 25.00%
50,625,000
Both the projects give the same ROCE. However, Project Q is preferable because of its consistency. Project P
shows heavy cash inflows at the end and little in the beginning, therefore it is risky.
The goal of financial management is to maximise the shareholders’ value. The projects that help in achieving
this objective are selected. The following techniques (NPV and IRR) are discounted cash flow techniques used
to evaluate investment proposals. These indicate whether projects will increase shareholder wealth.
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The following information relates to a proposed investment for a manufacturing organisation:
Year
Sales and production (units)
Selling price ( Tshs per unit)
1
337,500
25.00
2
157,500
24.00
3
135,000
23.00
4
135,000
22.00
Financial information for the first year of production is as follows:
Direct material cost (per product)
TSHS5.40
Other variable production cost (per product) TSHS6.00
Fixed overhead costs (per product)
TSHS4.00
The fixed overhead represents an apportionment of existing fixed costs. Total fixed costs are expected to
remain unchanged.
Advertising cost in the first year
Tshs 1,462,500
In the second year
Tshs 225,000
No advertisement costs are expected in third and fourth year
Cost of machine to be used for the production
Tshs 1,800,000
After tax discount rate used by the company for evaluating investment projects
10%
Required:
Ignoring taxation and capital allowances, calculate the net present value of the proposed investment.
The following table gives the expected relevant cash flows of a proposed project:
Period
0
1
2
3
Cash flow ( Tshs 000’s)
(30,000)
10,000
12,500
15,500
Required:
Calculate the internal rate of return (IRR).
The cash flows for Project A and B are as follows:
Period
0
1
2
3
4
5
Project A
Tshs (000’s)
(20,000)
2,200
3,630
5,324
7,320
9,666
Project B
Tshs (000’s)
(10,000)
1,110
1,848
2,736
3,795
5,055
The cost of capital for the company is 8%.
Required:
(a) Calculate the NPV of Project A and Project B.
(b) Calculate the IRR of Project A and Project B.
(c) Assume both the projects are mutually exclusive. Help the management to select one of the two projects
(using the appropriate DCF technique).
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7. Identify, assess and explain appropriate data that may be used in cash flow calculations
based on given business scenario data and information.
[Learning Outcome g]
7.1 Relevant cash flows
A cash flow will be relevant if it arises as a direct result of an investment, is incremental and will occur in the future.
These cash flows occur as a direct consequence of a particular investment decision. The relevant cash flows are
used for the decision-making process i.e. capital expenditure. Any cash flow which occurs whether a particular
project is undertaken or not, is irrelevant for the decision-making process.
The following should be taken into account when determining the relevant cash flows of a project or investment.
1. Check if the cash flows are the result of undertaking a project
The key issue to be considered is, whether the cash flows are resulting from the project. Cash flows which do
not result from the project are irrelevant and therefore excluded.
In a corner of a rented premise that has been used by Joline Co for the last few years, a new machine is to be
installed. Regardless of whether the new machine is installed or not, rent must be paid. Since rent is not a result
of the new machine, it should not be considered for the purpose of appraisal of investment in the machine.
2. Incremental cash flows
Only the increases in cash flows, i.e., the incremental cash flows, as a result of the project are considered. Any
savings or decreases in costs resulting from the project are also to be considered. The simplest examples of
incremental costs are the initial investment in the plant and building, cash receipts from sales generated by the
new plant and the direct costs related to sales.
(a) Sunk costs are not relevant
Sunk costs are the costs which are incurred before the start of the project. They are already ‘sunk’ or incurred
whether the project is undertaken or not. They do not increase or decrease as a result of the project.
Forman Remedies, a pharmaceutical company, spent Tshs 900,000 in market research. If any project is
undertaken as a result of the research, this amount is not relevant for the purpose of investment appraisal.
These costs are already sunk, whether a project is undertaken or not.
(b) Fixed costs are relevant to the extent they are incremental
Fixed costs, that do not change as a result of a project, are not relevant e.g. the rental payment of Joline Co.
Continuing the previous example of Joline,
However, if Joline rents a new place for the purpose of installing a new machine, the rent payment would be
relevant since it is an incremental cost.
(c) Incremental working capital investment is relevant
The turnover of a company may increase as a result of a new project. It may not be possible for the company to
function smoothly without increasing its investment in net current assets.
If the company has to increase the investment, it is a relevant cash flow.
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(d) Interest costs
For discounted cash flow methods which are covered in earlier in the Study Guide, interest costs are included in
the discount rate used for discounting cash flows. Therefore, they are not relevant costs.
However, for non-discounted cash flow methods, they are relevant cash flows.
3. Opportunity costs
An opportunity cost is the benefit that is abandoned when an asset is used for one purpose instead of another.
A company has an empty building for which it has received an offer of Tshs 20 million. A proposal has been put
forward to convert the empty building into a factory. If the company were to go ahead with the proposal it would
have to sacrifice the proceeds that would have been obtained, had the building been sold. The Tshs 20m foregone
is the relevant opportunity cost.
Opportunity costs are considered more relevant than historical costs for the purpose of decisions on
investment appraisal. Costs that are incurred in the past cannot be changed.
Component ‘X’ was purchased at Tshs 15 per piece for use in the existing plant, of which 20,000 pieces are in
inventory. A new plant is proposed for installation where 10,000 pieces of this component are to be used.


Ruling price for component ‘X’ is Tshs 17 per piece.
Resale price of the old stock in hand is Tshs 14 (in the second-hand market).
Which price should be used for the purpose of investment appraisal?
The historical price is Tshs 15, but it is not relevant for this purpose. Which of the other two is relevant?


If the material is not to be used for the existing plant, then the opportunity cost that is lost is the realisation
of the sales price, at the rate of Tshs 14.
If the material is to be used for the existing plant, then the incremental cost is the cost of the new
material that will have to be purchased for the existing plant at the rate of Tshs 17.
SUMMARY
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Investment Appraisal (Capital Budgeting): 125
Investment Appraisal (Capital Budgeting): 119
Baker Inc, a supplier of breads and cakes, is planning to start a new bakery. The management of Baker has
identified the following costs associated with the new bakery:
(a) The sales of the company will increase by Tshs 75,000.
(b) Two new employees will be recruited at a total annual cost of Tshs 30,000.
(c) One existing employee with a fixed salary of Tshs 2,500 per month will be moved to the new bakery.
(d) New equipment, with a total cost of Tshs 20,000 will be required.
(e) An idle piece of equipment, valued at Tshs 17,000 can be used by the new bakery.
Required:
Identify the relevant cash flows for the new bakery.
8. Estimate cash flows for investment appraisal.
[Learning Outcome h]
When any company is required to assess its investment decisions, it will need to make an estimation of the cash
flows. Therefore, the requirement of planning outcomes properly is an essential task of significant importance.
At the same time, the profits from the project should also be definite in order to arrange finances in a proper
way. This forecasting process is one of the most difficult steps involved in capital budgeting. Reasonably accurate
estimation of cash flows of projects is important because any kind of fault in the calculation could result in huge
problems.
The capital budgeting process is done through the co-ordination and input from a number of professionals or
departments of an organisation. For example, the engineering department may be responsible for the forecasting
of capital cash outflow, and then the production department may be responsible for the forecasting of operating
costs. The marketing department may be responsible for forecasting the revenues from the project as well as
timing of cash inflow. Following the circulation and information from the various departments, the finance
department is responsible for collecting the data and then assessing the information to then improve the
estimations made.
However, note that the estimation of the cash flow of a project comes as a separate calculation from the budget
projections. The latter serves as the baseline for the incremental effect of a venture on the cash position of the
business entity. This denotes that the projected cash inflows and cash outflows of the project are not at all
related to the ordinary course of the business operations.
Therefore, going forward, if the project is accepted, the normal expectation is that the net cash flow (inflow less
outflow) of a completed project will increase the budgeted net cash flow that will be added to the financial resources
of the business.
8.1 Basic principles
When companies are forecasting the cash inflows and outflows of a project, they need to take into account the
performance of certain principles in developing a set of cash projections. These principles provide guidance for
determining the relevant or irrelevant items to be included or discounted in order to come up with the best cash
flow estimation (CFE).
The most vital of these principles are as follows:
1. Consistency principle: this principle focuses on consistency between the flow of cash of a project and the
discount factor that is used to work out the cash flows.
2. Separation principle: according to this principle, the project cash flows can be split into two types; the cash
flow from financing side and the cash flow from investment side.
3. Post-tax principle: according to this principle, the forecast of cash flows for any project should be done
through the after-tax method.
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4. Incremental principle: according to this principle, the forecast of cash flows for any project should only
consider what cash flow will occur if the project is undertaken, which would not occur if it was left undone
and the business continued as before.
1. Consistency principle
This is one of four principles relating to the estimation of cash flows, which focuses on consistency in cash flows
as well as consistency in the relevant discount rate. The principle takes into account two important aspects that
can impact or be impacted by the quality of the estimations, being the investors’ expected income and inflation.
(a) Investors’ expected return
This principle suggests that as part of the estimation of the project’s cash flow, it is also important to consider
the investor's opinion or view. There are different types of investors in a firm like lenders or stockholders and so
on. In a situation where consideration for all investors' opinion is not possible, then only the stockholder's view
regarding the cash flow should be considered. This is due to some investors providing capital funds, usually in the
form of bonds.
Investors contribute funds with the expectation that the financial instrument will yield profits in the form of interests.
However, the rate of return should be consistently calculated as the net of all costs incurred to sustain the project.
Therefore, prior to presenting the feasibility of the project to the investors, offers of potential rates of return should
be net of the project’s estimated costs, including taxes. Therefore, there should be consistency in the discount rate
that is to be applied on the project cash flow.
(b) Inflation
In the context of the consistency principle, it means if an inflation rate is applied to increase the investors’ expected
income, the inflated costs incurred in generating the income should likewise be considered. Also, if interest is paid
on the borrowing cost, it should be calculated by using the inflated interest rates.
When taking inflation into account, there are two options for the estimation of the cash flows. One method is to
include the likely inflation into the project cash flow estimates, followed by a nominal discount rate being used
on the amount. Another method to resolve the inflation factor is to calculate the project cash flows of the future
in real terms and then apply real discount rates.
2. Separation principle
Prior to a new project commencing, it is essential that the estimation of cash inflows and cash outflows are
performed properly, and under this principle the cash flows of the project are required to be separated
appropriately.
This principle divides the project into two parts. The first part deals with the investment side and the latter part
is related to the financing side. In order to gain a more accurate picture of the project cash flow, the cash flow
is separated according to its relationship with the investment of financing side.
One feature of this principle is that the cash flow linked to the investment side of the project by no means considers
the cost of financing. However, the finance charges are considered while the cash flow calculations related to the
financing side are performed.
An important element of this principle is that interest on the debt securities is eliminated for the calculation of
profits and tax due. Based on this principle, while deriving the profit figure, if the related interest is subtracted,
the same amount should be added to the profit that remains after paying the relevant tax. On the other hand, if the
tax rate is applied directly to the profit (from which interest and taxes are not adjusted), the results are not going
to change.
3. Post-tax principle
This principle is more straightforward as it involves adjusting tax calculations in the project’s cash flows, making
it more relevant. Some companies are seen to forget to include the payment of tax while preparing cash flow
projections. Then they try to cover this up by using the discount rate. These discount rates are difficult to alter and
so the after-tax rate of discount and after-tax cash flows are used together.
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There are some significant matters within this principle and its application as discussed below.

Tax Rate
The average tax rate or differential tax rate is considered to be the entire tax as a proposal of the overall earning
from the business. However, the marginal tax rate represents those taxes that are imposed on the earnings, at a
margin. The tax rates tend to grow, and due to this, the average tax rates are always lower than the marginal rate.
The tax payable on projects is estimated through the marginal tax rate, as it is the most appropriate rate to apply.
This is due to the company running a project where the income from it is deemed marginal as it is in addition to
that generated from existing assets of the company which provide the main source of income.

Handling the Losses
This principle identifies that there is a chance of losses for the company and the particular project. There are
several ways of minimising these losses. In some instances, the tax saving is delayed until a point when the firm
or the particular project makes a profit.

Non-Cash Charges
This principle also notes that whenever the tax liabilities are affected by the non-cash charges, the project cash
flow estimation will also be impacted. E.g. Depreciation is one of these non-cash charges.
4. Incremental principle
This principle is used to calculate the profit potential of a project. All projects are considered in terms of their
individual potential to increase profits by generating additional cash inflows or by improving the present financial
condition of a business.
There are three main factors to consider as follows:
(a) Side effects or externalities
If a new product line is expected to increase the sales of another product line, any projected increase related to
the other product should be included within the cash flow estimation. Similarly, if the reverse is expected, whereby
the sales of the other project will decline due to the new project, the estimated decline will be included in the
projected cash outflow of the new project.
(b) Sunk costs
These are costs that are unrecoverable, which the company will incur as an expense no matter what, even if the
new project generates income or not.
An oil and gas company incur large amounts of expenditure which is deemed as sunk costs. When an oil
exploration project is successful, the investors of the project will expect a high rate of return. The costs incurred
at the beginning for the drilling expenses as a means to discover the oil well are deemed as sunk costs, as this
will not impact the investors’ return.
(c) Opportunity costs
If a project uses idle funds that could have earned interest if invested, then the amount that should have been
earned forms part of the cash flow estimation of the project. Foregoing this interest reduces the cash inflow of
the company and therefore, once the project is approved and goes ahead, it needs to be included as part of the
cash outflow in the estimation. A summary of the cash flow estimation allows management to understand and
visualise what impact the new project will have on the current financial resources and operations and whether
the expected outcome is worth the risks the company will be faced with.
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8.2 Biases in cash flow estimation
All projected cash flows are approximations, and for this reason, it is likely that there are some errors in the
calculations made. There can be overstatement and understatement biases on the profit related to a particular
project.
There are deemed to be several types of biases in cash flow estimation with overstatement and understatement
of profit being the most common.
1. Overestimation of profits
One of the main reasons for overestimation of profits is that the initial investment that has been calculated is too
low, whilst the operating cash inflow estimates are too high. There are a number of factors behind overestimation
of profit, one being the preparers lacking the knowledge and experience and another, where the firm intentionally
overestimates profits to obtain investors. In these instances, the costs are always estimated to be lower than what
is actually required.
2. Underestimation of profits
One of the main reasons for underestimation of a particular project is often due to an over-conscious attitude or
prudence of the preparers of the project. Underestimation can also occur due to neglect of important factors
such as future options from the estimation process or other potential cash inflows.
State what the four main principles relating to the estimation of cash flows are and provide a brief description to
explain the principle.
9. Perform investment appraisal under inflationary condition.
[Learning Outcome i]
Often, the cash flow for a particular investment project can span over a number of years, therefore, the inflation
during this period will impact profit considerably. As inflation increases, the rate of return expected by the investors
will also increase.
Inflation can be defined as the level at which the price of goods and services increases, therefore, leading to a
decrease in what can be purchased for the same monetary value. Most central banks will aim to reduce or stop
rigorous inflation, along with any severe deflation, in an attempt to keep the excessive growth of prices to a
minimum, ideally at a rate of 2-3%.
As inflation rises, every shilling will buy a smaller percentage of a good. For example, if the inflation rate is 7%
for a year, then a Tshs 3,000 carton of milk will cost Tshs 3,210 in a year’s time.
9.1 Nominal vs. Real Measure
1. Nominal cash flows: or money cash flows have been influenced by inflation. This is the actual shillings that
would change hands at the time the purchase is made.
2. Real cash flows: are cash flows that have not been subject to inflation. This is the shillings that would have
been exchanged to purchase something before the inflation took place, i.e. the inflation-free return is the
real rate.
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9.2 Impact of inflation on investment decisions
Inflation causes two main problems for investment project appraisals as follows:
1. the estimation of future cash flows becomes even more troublesome. Inflation adds a new dimension to the
problem of calculating net present values as more calculations are required and the level of uncertainty is
increased.
2. the rate of return required by the firm’s security holders such as the shareholders will rise with inflation.
9.3 Method of Adjusting Inflation
1. Method 1: estimate the cash flows in money terms and use a money discount rate.
2. Method 2: estimate the cash flows in real terms and use a real discount rate.
9.4 Converting the Nominal Return to Real Return
The discount rate used in assessing projects so far has been the real rate of return required by investors. This is
the rate which compensates investors for the risk of undertaking the activity and for not being able to use the
money. Since inflation erodes the purchasing power of money, investors will require compensation for this
additional factor. Therefore, the rate of return required for investments will increase.
The rate of interest which incorporates the real rate and the inflation rate is known as the nominal or money rate
of return. It can be calculated using the following formula:
(1 + Nominal rate or money rate) = (1+ Real rate) x (1+ Inflation rate)
Let as assume that Susan will receive Tshs 1,000,000 as cash in one year’s time. Inflation during the year is 6%.
The nominal value is therefore, Tshs 1,000,000, but the real value today (after deducting the impact of inflation)
will be Tshs 943,396 ( Tshs 1,000,000 / 1.06).
Now, if Susan’s real rate of return required is 10% and inflation is 6%, the effective nominal rate will be:
Nominal rate = (1+ 0.10) x (1+ 0.06) – 1
= 1.10 x 1.06 - 1
= 1.166 - 1
= 1.166 - 1
= 0.166
= 16.6%
9.5 Which discount rate is to be applied?
As noted above, the discount rate to be applied is dependent upon which types of cash flows are being applied.
If real cash flows are being used, then real cost of capital is required and if nominal cash flows (influenced by
inflation) are being used then nominal cost of capital should be used.
Continuing the previous example of Susan,
Nominal cash flow
Nominal cost of capital
cash flow = Tshs 100,000 / 1.166
Real cash flow
Real cost of capital
flow = Tshs 943,396 / 1.10
Tshs 1,000,000
16.6% Discounted value of the
Tshs 857,633
Tshs 943,396
10% Discounted value of the cash
Tshs 857,633
It can be seen from the above calculations that both the approaches give the same answer.
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You should never discount the nominal cash flow with the real discount rate as this will give an NPV much larger
than the true NPV, leading to incorrect decisions to accept investments which would not enhance shareholder
wealth.
Likewise, never discount real cash flow with the nominal discount rate as this will give an NPV lower than the
true NPV, leading to projects which would have enhanced shareholder wealth being incorrectly rejected.
SUMMARY
Roddex Ltd is in the process of evaluating Project A. The real cash flows (not subject to inflation) are as follows
(in millions):
Period
0
1
2
3
Project A
Tshs (million’s)
(2,000)
500
900
1,300
(a) If the real cost of capital is 10%, what is the NPV?
(b) If the real cost of capital is 10% and inflation is 5%, what is the NPV?
Answers to Test Yourself
Answer to TY 1
Proper capital investment planning and control allows an organisation to:
(a) Maximise shareholder wealth.
(b) Take strategic decisions that help the organisation to exploit opportune investment opportunities.
(c) Minimise the fixed costs associated with the capital investment project.
(d) Avoid financial losses caused due to the failure of a capital investment project.
(e) Minimise the risk by investing in various types of capital investment projects.
(f) Avoid occurrence of frauds.
(g) Discover and rectify any discrepancy between the planned and the actual results.
Answer to TY 2
(a) In relation to the new development, Build On Me Ltd is considering the following steps
(i) Quantify the cost and benefits: management will need to prepare a forecast of costs and revenue for the
new project.
(ii) Compare the cost and benefits with appropriate techniques: once a forecast has been prepared,
management will use techniques such as the payback period, net present values and return on capital
employed and compare the results of each.
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Investment Appraisal (Capital Budgeting): 131
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(iii) Evaluate the risks involved and the sensitivity to changed situations: when we estimate the future
cash flows for the construction project, there is a risk that they may not actually materialise as the future is
uncertain; the actual outcome may be different. It is necessary to consider how this will affect the final outcome,
by performing sensitivity analysis. For example, if cost of concrete becomes even higher than forecasted,
what would the net present value of the project be after adjusting the calculations for this?
(iv) Consider qualitative factors such as the environment or employment generation: non-financial factors
also need to be considered a part of this process such as legal issues on obtaining licences for building, ethical
and environmental factors such as the impact of building to the surrounding areas and destruction of
plantation, what competitors’ reaction would be if the project went ahead etc.
(v) Take a decision: if the result of the above steps is viable and conforms to the business requirements, the
project will be accepted by management. However, if the outcome of the above steps shows the project is not
a viable option, as the return is too low or the legal issues too high for example, the project will be rejected.
(b) For any capital investment project, the following stages of evaluation are usually followed
(i) Initial evaluation: before a project starts, the company needs to evaluate the technical feasibility and
commercial viability of the project by ensuring it is in line with the company’s long-term strategic objectives.
(ii) Detailed assessment: as noted in part a), the cash flows of the project need to be viewed in detail together
with sensitivity analysis performed to ensure the project adds value to the business.
(iii) Management approval: for such an important project for Build On Me Ltd, senior management approval is
required, so they can assess if the project is deemed in line with long term strategy of the firm as well as
ensuring the project adds to the profitability of the company.
(iv) Project implementation: this is when a team or person is assigned responsibility for overseeing the project
development with targets set as part of the process.
(v) Monitoring the project: given that the housing development is a long-term project, regular monitoring is
essential to ensure the progress is in line with the forecasts and expectations. Regular monitoring allows for
re-assessment at any stage of the project.
(vi) Post-completion audit: the final stage involves an enquiry into the cost and benefits of the project and
identifying any deviations from the initial plan. The final stage allows for lessons to be learnt for future projects
of the company.
Answer to TY 3
The correct option is B.
Answer to TY 4
1. True, one of the factors that make DCF method more superior to non-DCF is that the timing of cash flows
and time value of money are taken into account.
2. The correct option is C, as only NPV and IRR are types of methods of discounting cash flow.
3. False, one of the drawbacks of IRR is that it ignores the relative size of the project.
4. True, there are more than one IRR for non-conventional cash flow projects.
5. False, where there are non-conventional cash flows, NPV is more suitable method than IRR.
6. True, for mutually exclusive projects, the NPV method should be followed.
7. False, if there are varying discount rates over the life of a project, IRR method cannot accommodate for this,
but NPV can.
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Answer to TY 5
The correct option is C.
CAPM is denoted by: Rf + × (Rm - Rf)
where
Rf = risk-free rate
Rm = average return on the market
(Rm - Rf) = equity risk premium (sometimes referred to as average market risk premium)
= systematic risk of the investment compared to market and therefore amount of premium needed
Answer to TY 6
Calculation of NPV
Year
0
Tshs
’000
(1,800.00)
Initial cost
Sales Revenue
Direct materials
Variable production costs
Advertising
Net cash flow
Discount at 10%
(1,800.00)
1.000
Present values
(1,800.00)
NPV (sum of all years PV)
6,449.75
Initial investment
(1,800.00)
Net present value
4,649.75
1
Tshs
’000
2
Tshs
’000
8,437.50
(1,822.50)
(2,025.00)
(1,462.50)
3,127.50
0.909
(1/1.10)
2,842.90
3,780.00
(850.50)
(945.00)
(225.00)
1,759.50
0.826
(0.909/1.10)
1,453.35
3
Tshs
’000
4
Tshs
’000
3,105.00
(729.00)
(810.00)
2,970.00
(729.00)
(810.00)
1,566.00
0.751
0.826/1.10
1,176.10
1,431.00
0.683
(0.751/1.10)
977.40
Notes


Fixed costs are irrelevant as they represent an apportionment of overheads and are unaffected by
the investment decision. Only incremental costs are relevant.
Since the project’s NPV is positive it is financially viable and should be accepted.
Answer to TY 7
We can calculate NPV at 8% and 12%
Years
Cash flows
PV of
PV of
from
PV factor at Project A PV factor Project A
Project A
@ 8%
at 12%
@ 12%
8%
Tshs 000's
Tshs 000's
Tshs 000's
0
1
2
3
NPV
(30,000)
10,000
12,500
15,500
1
0.926
0.857
0.794
NPV @ 8% = Tshs 2,280,000
NPV @ 12% = Tshs (71,000)
2,280
IRR = 8% +
2,280 - (-71)
= 8% + 3.88%
= 11.88%
x (12 - 8)%
(30,000)
9,260
10,713
12,307
2,280
1
0.893
0.797
0.712
(30,000)
8,930
9,963
11,036
(71)
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Answer to TY 8
(i) Calculation of NPV
PV factor at
8%
Years
0
1
2
3
4
5
NPV
1.000
0.926
0.857
0.794
0.735
0.681
Cash flows
PV of Project A
from
Project A
Tshs
Tshs 000's
000's
(20,000.00)
(20,000.00)
2,200.00
2,037.20
3,630.00
3,110.91
5,324.00
4,227.26
7,320.00
5,380.20
9,666.00
6,582.55
1,338.12
Cash flows
PV of
from
Project B
Project B
Tshs
Tshs
000's
(10,000.00) 000's
(10,000.00)
1,110.00
1,027.86
1,848.00
1,583.74
2,736.00
2,172.38
3,795.00
2,789.33
5,055.00
3,442.46
1,015.77
(ii) Calculation of IRR
The Net Present Value for both the projects at the 8% rate of discount is positive.
We can discount the cash flows at 12% to obtain a negative net present value.
Project A
Years
0
1
2
3
4
5
NPV
PV of
PV of
Cash flows
PV factor at
PV factor
from
Project A @
Project A @
8%
at 12%
Project A
8%
12%
Tshs
Tshs
Tshs
000's
(20,000.00)
1.000 000's
(20,000.00)
1.000 000's
(20,000.00)
2,200.00
0.926
2,037.20
0.893
1,964.60
0.857
3,630.00
3,110.91
0.797
2,893.11
0.794
5,324.00
4,227.26
0.712
3,790.69
0.735
7,320.00
5,380.20
0.636
4,655.52
9,666.00
0.681
6,582.55
0.567
5,480.62
1,338.12
(1,215.46)
NPV @ 8% = Tshs 1,338,120
NPV @ 12% = Tshs (1,215,460)
IRR = a+
𝐴𝐴
× (𝑏𝑏 − 𝑎𝑎)
𝐴𝐴 − 𝐵𝐵
IRR = 8%+
1,338.12
× (12 − 8)%
1,338.12 − (−1,215.46)
= 8% + 0.524 x 4%
= 8% + 2.10= 10.10%
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Project B
Years
0
1
2
3
4
5
NPV
Cash flows
PV of
PV of
PV factor
PV factor at
from
Project A @
Project A @
at 12%
8%
Project A
8%
12%
Tshs
000's
(10,000.00)
1,110.00
1,848.00
2,736.00
3,795.00
5,055.00
Tshs
1.000 000's
(10,000.00)
0.926
1,027.86
0.857
1,583.74
0.794
2,172.38
0.735
2,789.33
0.681
3,442.46
1,015.77
Tshs
1.000 000's
(10,000.00)
0.893
991.23
0.797
1,472.86
0.712
1,948.03
0.636
2,413.62
0.567
2,866.19
(308.08)
NPV @ 8% = Tshs 1,015,770
NPV @ 12% = Tshs (308,080)
IRR = a+
𝐴𝐴
× (𝑏𝑏 − 𝑎𝑎)
𝐴𝐴 − 𝐵𝐵
IRR = 8%+
1,015.77
× (12 − 8)%
1,015.77 − (−308.08)
= 8% + 0.767 x 4%
= 8% + 3.07% = 11.07%
(iii) Mutually exclusive projects indicate that only one of them can be selected. If the NPV and IRR give
conflicting results, then the NPV must be considered. Hence, Project A must be selected.
Answer to TY 9
Relevant cash flows
(a) Increase in sales in an incremental cash inflow.
(b) Salary to new employees in an incremental cash outflow.
(c) Expenditure to purchase new equipment is directly related with the new bakery.
Irrelevant cash flows
(a) Moving an existing employee does not result in incremental cash outflow.
(b) An idle piece of equipment is a sunk cost.
Answer to TY 10
The four main principles in relation to cash flow estimation are as follows:
(a) Consistency principle: it focuses on cash flows and discount rates being consistent together with taking
into account the impact of quality of the estimations on the investors expected income and inflation.
(b) Separation principle: looks to separate out the cash flows into two parts, the investment side and finance
side.
(c) Post-tax principle: this principle is basic and involves applying post tax cash flows as part of the appraisal
process.
(d) Incremental principle: this focuses on identifying the individual profit potential of a project by taking into
account externalities, sunk cost and opportunity costs.
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Answer to TY 11
(a) Real cash flows with real cost of capital
Period
0
1
2
3
Project A
Tshs
(millions)
(2,000)
500
900
1,300
NPV
Calculation
500/1.10
900/(1.10)²
1,300/(1.10)³
NPV
Tshs
(millions)
(2,000)
455
744
977
176
(b) Nominal cash flow with nominal cost of capital
(1 + Nominal rate or money rate) = (1+ Real rate) x (1+ Inflation rate)
Nominal rate = (1 + 0.10) x (1 + 0.05) -1
= (1.10 x 1.05) – 1
= 1.155 – 1
= 0.155
= 15.5%
Period
Project A
Tshs
(millions)
Nominal cash
flow
calculation
(2,000)
500
900
1,300
500 x 1.05
900 x (1.05)²
1,300 x (1.05)³
0
1
2
3
Nominal
cash
flows
525
992
1,505
NPV
Calculation
525/1.155
992/(1.155)²
1,505/(1.155)³
NPV Tshs
(millions)
(2,000)
455
744
977
176
As seen from the above, both the calculations result in the same answer.
Quick Quiz
1. Average investment =
(Initial investment + Scrap value)
2
State whether the statement is true or false?
2. What is the effect of not discounting the cash flows?
3. Which profit does the ROCE consider in calculations?
4. Why do lenders want a higher interest rate during a period of high inflation?
5. “If the discount rate is increased, the NPV will also increase”. True or false?
6. What happens if a project is discounted using its IRR as the discount rate?
7. Which methods of investment appraisal are considered more superior: non-DCF or DCF?
8. Mutually exclusive projects A and B have IRR of 10% and 14% respectively, and NPV of Tshs 5,000,000
and Tshs 2,000,000 respectively. Which project should be preferred and why?
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Answers to Quick Quiz
1. True, Average investment =
(Initial investment + Scrap value)
2
2. The effect of not discounting the cash flows is that it ignores the time value of money.
3. ROCE considers the percentage of accounting profits (profits after depreciation) over the capital employed.
4. If there is inflation between the date of lending and the date of repayment, then the purchasing power of the
principal amount, which is repaid, is lower than the principal amount that was lent. To compensate for this
loss, lenders want higher interest rates.
5. False, if the discount rate is increased, the NPV will not increase; it will decrease.
6. If a project is discounted using the IRR as the discount rate, its NPV will be zero.
7. DCF models such as NPV and IRR are considered superior for the following reasons:





as they take into account the timing of cash flows,
they acknowledge that money has a time value via discounting,
they do not use profit, which can be susceptible to manipulation, they only use cash flow,
cash flows over the entire life of the project are considered. This is not the case with the nonDCF
technique like payback method and ROCE.
8. Mutually exclusive projects indicate that only one of them can be selected. NPV and IRR methods may give
similar or conflicting results. Wherever a conflict occurs, NPV should be followed. On this basis, project A
would be selected as its NPV is higher.
Self Examination Questions
Question 1
You have been appointed as a financial manager in Marksons Plc and are about to analyse a proposal to
market a drug, which claims to be able to cure a particular disease. You are given the forecasts shown in the
table. The project requires an investment of Tshs 25 million in plant and machinery (line 1). This machinery can
be dismantled and sold for net proceeds estimated at Tshs 4,873,000 in year 7.
This amount can be taken as the plant's salvage value.
The discount rate used by the company for evaluating projects is 20%.
Required:
Calculate the NPV and advise management on the acceptability of the project.
Years
1. Capital investment
2. Working capital
3. Sales
4. Cost of goods sold
5. Other costs
6. Depreciation
7. Profit (3-4-5-6)
0
25,000
10,000
(10,000)
1
1,375
1,308
2,093
5,500
3,958
(10,243)
2
3,222
32,218
19,323
3,025
3,958
5,913
3
8,153
81,525
48,880
3,328
3,958
25,360
4
12,225
122,253
73,363
3,660
3,958
41,273
5
8,957
89,585
53,730
4,028
3,958
27,870
Tshs ’000
7
(4,873)
5,005
49,293
29,575
4,430
3,958
11,330
6
Investment Appraisal (Capital Budgeting): 137
Investment Appraisal (Capital Budgeting): 131
© GTG
Question 2
A company has to decide whether to buy a machine for
Tshs 210,000,000
Saving for each of the 5 years
Tshs 55,000,000
Resale value at the end of 5 years
Tshs 22,500,000
Decide whether or not to take on this project using:
(a) Return on Capital employed (ROCE)
(b) Internal rate of return (IRR)
Question 3
Posterity Inc manufactures and distributes over-the-counter drugs. The company has formulated a new painkiller,
‘Anodyne’ which is expected to a have a life of four years. Posterity will launch the new painkiller within four
years. The company has paid TSHS15, 000,000 to a firm to conduct market research on ‘Anodyne’.
The following are the forecasts relating to ‘Anodyne’.
Year
Sales
( Tshs m)
Cost of
sales (
Tshs m)
Gross
profit (
Tshs m)
Variable
overheads
( Tshs m)
Fixed
overheads
( Tshs m)
Net profit
/ (loss) (
Tshs m)
1
90.00
(57.50)
32.50
(13.50)
(12.50)
6.50
2
100.00
(70.00)
30.00
(15.00)
(12.50)
2.50
3
80.00
(55.00)
25.00
(12.00)
(12.50)
0.50
4
60.00
(42.50)
17.50
(9.00)
(12.50)
(4.00)
Additional information:
1. Posterity’s cost of capital is 10%.
2. ‘Anodyne’ will be manufactured on idle equipment. The equipment has a written down value of Tshs 40,000,000
but its current realisable value is only Tshs 35,000,000. After four years, the piece of equipment will be sold
for Tshs 5,000,000.
3. Posterity will immediately require additional working capital of Tshs 10,000,000 to manufacture Anodyne.
The additional working capital will be released after four years.
4. The fixed overhead costs include:
(a) Tshs 7,500,000 per year on account of depreciation.
(b) Tshs 2,500,000 for re-allocating an existing business overhead.
Ignore inflation and taxation.
Required:
(a) Calculate the incremental cash flows arising out of ‘Anodyne’.
(b) Calculate the Net present value of ‘Anodyne’ for Posterity.
(c) Calculate the Internal rate of return of ‘Anodyne’ for Posterity.
(d) List the advantages and disadvantages of using the Net present value method for appraising investment
projects.
138 Investment Decisions
132 : Investment Decisions
© GTG
Question 4
Sisyphean Inc manufactures office stationery. It is planning to augment its production facility by purchasing new
equipment. It has received quotations from two suppliers.
The details of the equipment are given below.
Equipment 1
Cost of equipment
Net expected cash flows for six years
Salvage value
Tshs
150,000
40,000
0
The piece of equipment has a life of six years.
Equipment 2
Cost of equipment
Net expected cash flows for six years
Salvage value
Tshs
100,000
28,000
0
The piece of equipment has a life of six years.
The cost of capital for Sisyphean is 11%.
Ignore taxation and inflation.
Required:
(a) Calculate the Net present value (NPV) of both pieces of equipment.
(b) Calculate the Internal rate of return (IRR) of both pieces of equipment.
(c) Consider both the pieces of equipment as mutually exclusive. Which piece of equipment should Sisyphean
buy?
Answers to Self Examination Questions
Answer to SEQ 1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Years
Sales
Cost of goods sold
Other costs Cash
flow from
operations (1 - 2 3)
Change in working
capital
Capital investment
and disposal
Net cash flow
(4 + 5 + 6)
PV Factor @ 20%
Present value
Net present value
(sum of 9)
0
Tshs ’000
6
7
49,293
(29,575)
(4,430)
10,000
1
1,308
(2,093)
(5,500)
2
32,218
(19,323)
(3,025)
3
81,525
(48,880)
(3,328)
4
122,253
(73,363)
(3,660)
5
89,585
(53,730)
(4,028)
(10,000)
(6,285)
9,870
29,317
45,230
31,827
15,288
(1,375)
( 1,847)
(4,931)
(4,072)
3,268
3,952
5,005
4,873
(25,000)
(35,000)
(7,660)
8,023
24,386
41,158
35,095
19,240
9,878
1
(35,000)
0.833
(6,381)
0.694
5,568
0.579
14,119
0.482
19,838
0.402
14,108
0.335
6,445
0.279
2,756
21,453
Conclusion: the NPV is positive by a reasonable amount; hence the project should be accepted.
Net present value = Sum of 9 = Tshs 21,453, 000
Investment Appraisal (Capital Budgeting): 139
Investment Appraisal (Capital Budgeting): 133
© GTG
Answer to SEQ 2
(a) ROCE of the investment
Accounting profit = Tshs 55,000,000 – Tshs 37,500,000 (W1) = Tshs 17,500,000
Average investment 1/2 of ( Tshs 210,000,000 + Tshs 22,500,000) = Tshs 116,250,000
ROCE =
Tshs 17,500,000
× 100 = 15.05%
Tshs 116,250,000
Workings
W1 Calculation for depreciation
Value of machine
Less: Resale value
Amount to be recovered in 5 years
Depreciation charged every year (187,500,000/5)
Tshs
210,000,000
(22,500,000)
187,500,000
37,500,000
(b) IRR of the investment
Step 1: Discounting cash flows at 10%
NPV using 10% as the discount rate
Cash
Flows
Tshs
(000s)
(210,000)
55,000
22,500
Year
0
1 to 5
5
PV Factor
PV of Cash Flows
10%
Tshs (000’s)
1
3.791
0.621
NPV
(210,000.00)
208,505.00
13,972.50
12,477.50
Note: the cumulative discount rate table figures for 10% have been used for 1-5 years cash flow as it is
consistent.
Step 2: Calculate the second NPV using a higher rate (Since the NPV using 10% is positive a higher rate will be
used to obtain a negative NPV)
NPV using 14% as the discount rate
Year
Cash Flows
Tshs (000s)
(210,000)
55,000
22,500
0
1 to 5
5
PV Factor
14%
1
3.433
0.519
NPV
PV of Cash Flows
Tshs (000s)
(210,000.00)
188,815.00
11,677.50
(9507.50)
Step 3: Use the two NPV values to estimate IRR
The interpolation method assumes that the NPV rises in a linear fashion between the two NPVs close to 0. The
real rate of return is therefore assumed to be on a straight line between NPV = Tshs 12,477.5 at 10% and
NPV = Tshs (9,507,500) at 14%.
IRR = 10%+
Tshs 12,477.5
× (14 − 10)%
Tshs 12,477.5 − (−9,507.5)
= 10% + (0.5675 x 4)
= 10% + 2.27%
140 Investment Decisions
134: Investment Decisions
© GTG
= 12.27%
If the company policy is to undertake investments which are expected to yield 11% or more, this project would
be undertaken.
Answer to SEQ 3
1. Incremental cash flow
Years
Sales
Cost of sales
Variable overheads
Fixed overheads
Market value of equipment
Working capital
Incremental cash flows
0
Tshs
million
(35.00)
(10.00)
(45.00)
1
Tshs
million
90.00
(57.50)
(13.50)
(2.50)
2
Tshs
million
100.00
(70.00)
(15.00)
(2.50)
3
Tshs
million
80.00
(55.00)
(12.00)
(2.50)
16.50
12.50
10.50
4
Tshs
million
60.00
(42.50)
(9.00)
(2.50)
5.00
10.00
21.00
Workings
W1 Cost of market research is a sunk cost.
W2 Depreciation is a non-cash expense.
W3 The business overhead will be incurred irrespective of Posterity’s decision to manufacture Anodyne or not.
Hence, it is not a relevant cost. Only incremental fixed costs for the project are included.
2. Net present value
We can use the incremental cash flows calculated above to calculate the Net present value of the project.
Discount factor = 10%
Years
Incremental cash flows
Discount factor @ 10%
Present value
0
(45.00)
1.000
(45.00)
Net present value = Tshs 2.56 million
1
16.50
0.909
15.00
2
12.50
0.826
10.33
3
10.50
0.751
7.89
4
21.00
0.683
14.34
InvestmentAppraisal
Appraisal
(Capital
Budgeting):
141
Investment
(Capital
Budgeting):
135
© GTG
3. Internal rate of return
We can use 10% as the lower rate of return and 15% as the higher rate of return.
Year
0
1
2
3
4
NPV
IRR = a+
Cash
flow (
Discount
Tshs
factor @
million)
10%
(45.00)
1.000
16.50
0.909
12.50
0.826
10.50
0.751
21.00
0.683
Present
value @
10% (
Discount
Tshs
factor @
million)
15%
(45.00)
1.000
15.00
0.870
10.33
0.756
7.89
0.658
14.34
0.572
2.56
Present
value @
15% (
Tshs
million)
(45.00)
14.36
9.45
6.91
12.01
(2.27)
𝐴𝐴
× (𝑏𝑏 − 𝑎𝑎)
𝐴𝐴 − 𝐵𝐵
IRR = 10%+
2.56
× (15 − 10)%
2.56 − (−2.27)
= 10% + 0.53 x 5%
= 10% + 2.65%
= 12.65%
4. Advantages and disadvantages of using the Net present value method to appraise investment
projects.
Advantages
(i) It tries to maximise the shareholders wealth.
(ii) It considers the time value of money.
(iii) It is calculated on the basis of cash flows.
(iv) It considers the whole life of the project.
(v) It is an absolute measure of return.
(vi) It gives the correct ranking for mutually exclusive projects.
(vii) It can be used for appraising a project with non-conventional cash flows.
Disadvantages
(i) It is more complex than Return on capital employed and Payback period.
(ii) It is difficult to identify the correct discount rate.
(iii) It fails to relate the return of the project to the size of the cash outlay.
Answer to SEQ 4
(a) Net present value
Equipment 1
Year
0
1
2
3
4
5
6
NPV
Cash flow
Discount cash
Present
( Tshs
flow @ 11%
value ( Tshs
)
)
(150,000.00)
1 (150,000.00)
40,000.00
0.901
36,040.00
40,000.00
0.812
32,480.00
40,000.00
0.731
29,240.00
40,000.00
0.659
26,360.00
40,000.00
0.593
23,720.00
40,000.00
0.535
21,400.00
19,240.00
Net present value of Equipment 1 = Tshs 19,240.00
142
Investment Decisions
Decisions
136: Investment
© GTG
Equipment 2
Cash flow
Discount cash
Present
( Tshs
flow @ 11%
value ( Tshs
)
)
(100,000.00)
1 (100,000.00)
28,000.00
0.901
25,228.00
28,000.00
0.812
22,736.00
28,000.00
0.731
20,468.00
28,000.00
0.659
18,452.00
28,000.00
0.593
16,604.00
28,000.00
0.535
14,980.00
18,468.00
Year
0
1
2
3
4
5
6
NPV
Net present value of Equipment 2 = Tshs 18,468.00
(b) Internal rate of return
We can use 11% as the lower rate and 20% as the higher rate as both showing positive NPV at 11%.
Equipment 1
Cash flow
Discount factor
( Tshs
@ 11%
)
(150,000.00)
1.000
40,000.00
0.901
40,000.00
0.812
40,000.00
0.731
40,000.00
0.659
40,000.00
0.593
40,000.00
0.535
Year
0
1
2
3
4
5
6
NPV
IRR = a+
Present value
Discount
@ 11% ( Tshs factor @ 20%
) (150,000.00)
1.000
36,040.00
0.833
32,480.00
0.694
29,240.00
0.579
26,360.00
0.482
23,720.00
0.402
21,400.00
0.335
19,240.00
Present value
@ 20% ( Tshs
) (150,000.00)
33,320.00
27,760.00
23,160.00
19,280.00
16,080.00
13,400.00
(17,000.00)
𝐴𝐴
× (𝑏𝑏 − 𝑎𝑎)
𝐴𝐴 − 𝐵𝐵
IRR = 11%+
19,240
× (20 − 11)%
19,240 − (−17,000)
= 11% + 0.53 x 9%
= 11% + 4.77%
= 15.77%
Equipment 2
Year
0
1
2
3
4
5
6
NPV
IRR = 11%+
Cash flow Discount factor Present value Discount factor Present value @
( Tshs
@ 11%
@ 11% ( Tshs
@ 20%
20% ( Tshs
)
)
(100,000.00)
1.000 ) (100,000.00)
1.000
(100,000.00)
28,000.00
0.901
25,228.00
0.833
23,324.00
28,000.00
0.812
22,736.00
0.694
19,432.00
28,000.00
0.731
20,468.00
0.579
16,212.00
28,000.00
0.659
18,452.00
0.482
13,496.00
28,000.00
0.593
16,604.00
0.402
11,256.00
28,000.00
0.535
14,980.00
0.335
9,380.00
18,468.00
(6,900.00)
𝑇𝑇𝑇𝑇ℎ𝑠𝑠 18,468
× (20 − 11)%
𝑇𝑇𝑇𝑇ℎ𝑠𝑠 18,468 − (−6,900)
= 11% + 0.73 x 9%
= 11% + 6.55%
= 17.55%
(c) Choosing the equipment
Net present value is a better method than internal rate of return for appraising investment projects. Equipment 1
has a higher NPV than Equipment 2. Hence, Equipment 1 must be selected.
© GTG
Investment Appraisal (Capital Budgeting): 135
Investment Appraisal (Capital Budgeting): 143
Indicative Examination Questions
IEQ 1
Nzalu Co. Ltd is developing a new personal computer with an expected life of three years. The investment
has a total initial cost of TSHS 283 million. The projects after tax net operating cash flows are estimated
at TSHS 89 million, TSHS 198 million and TSHS 59 million for years. 1,2, and 3 respectively. To finance
the project TSHS 106, million will be from internally generated funds, TSHS 90 million from a rights issue
and the remainder from a fixed rate term loan at 12% per year. The proportion represented by the term
loan reflects the optimum debt capacity of the company. Issue costs are estimated at 3.5% for the rights
issue and 1% for the term loan.
Corporate taxes are payable at a rate of 40% on net operating cash flows in the year that the cash flows
occur. The Treasury bill is 9%, market return is 14% and an appropriate assets beta for the in for the
investment is believed to be 1.5
REQUIRED:
Explain why the adjusted present value technique is sometimes advocated as being a more appropriate
way of evaluating a project than Net Present Value.
IEQ 2
(a)
A company should invest in all projects with a positive net present value in order to maximize
shareholders’ wealth. In some cases, a company may have various attractive opportunities and
yet not be able to undertake them.
REQUIRED:
Discuss this in the context of investment finance.
(b)
(6 marks)
In the annual Board of Directors’ meeting of the Shengena International Hotels, it was decided that
the hotel expand it facilities by providing a gym and spa for the use of guests. The hotel’s Managing
Director noted that the move would result in an increase in the occupancy rate of the hotel and the
rates that can be charged for each room.
The cost of refurbishing the space, which is currently used as a library for guests, and installing
the gym and spa is estimated to be TSHS.100,000,000. The cost of the equipment is expected to
be TSHS.50,000,000. The gym and spa will need to be refurbished and the equipment replaced
every four years. The equipment will be sold for TSHS.15,000,000 cash at the end of year 4. This
amount includes the effect of inflation.
The hotel’s financial consultants have produced a feasibility report at a cost of TSHS.10,000,000.
The key finding from their report, regarding occupancy rates and room rates are as follows:



Current occupancy rate: 80%
Number of rooms available: 40
Current average room rate per night: TSHS.250,000
Occupancy rates, following the opening of the gym and spa, are expected to rise to 82% and the
average room rate by 5%, excluding the effect of inflation.
The hotel is open for 360 days per year.
Other relevant information is as listed below:
1. The gym will require four (4) full time employees each with an average salary of
TSHS.30,000,000 per annum.
2. The current budgeted overhead absorption rate for the hotel is TSHS.80,000 per square metre
per annum. The area required for the gym and spa is 400 square metres. The hotel’s
144 Investment Decisions
136: Investment Decisions
© GTG
overheads are expected to increase by TSHS.42,000,000 directly as a result of opening the
gym and spa.
3. Inflation is expected to be at a rate of 4% per annum and will apply to sales revenue, overhead
costs and staff costs. The rate of 4% will apply from Year 2 to each of the subsequent years of
the project.
4. The hotel’s financial consultants have provided the following taxation information:
 Tax depreciation is allowable on all costs of refurbishing, installation and equipment at 25%
reducing balance per annum.
 Taxation rate is 30% of taxable profits. Half of the tax is payable in the year in which it
arises, and the balance is paid the following year.
 Any losses resulting from this investment can be offset against taxable profits made by the
company’s other business activities.
The company uses a post-tax money cost of capital of 12% per annum to evaluate projects of
this type.
REQUIRED:
(i)
Calculate the Net Present Value (NPV) of the gym and spa project.
(ii)
Using linear interpolation estimate the post-tax money cost of capital at which the hotel would
be indifferent to accepting or rejecting the project.
(6 marks)
(8 marks)
Answer to Indicative Examination Questions
Answer to IEQ 1
(a) (i) APV = Base case NPV + Present Value of financing side effects
Base case NPV
This is the NPV that would be obtained if an all equity firm financed the project.
The cost of funds for an all equity firm;
=
βu =𝑅𝑅𝑓𝑓 + (𝑅𝑅𝑚𝑚 − 𝑅𝑅𝑓𝑓 )
=
0.9 + (0.14 – 0.9) 1.5 = 16.3%
NPV (TSHS. Million) = (283) +
=
TSHS.(5.7) million
89
198
+
1.165
(1.165)2
+
87
(1.165)3
Financing Side effects
To cover the shortfall sufficient funds must be raised to fund TSHS.87 million of the projects and
to cover the issue costs. In total then;
TSHS.87 million/0.99 = TSHS.87.879 million
Tax shield on loan
No detail is given on the repayment structure of the loan, but the simplest assumption is that all
principal is repayable in three years time.
Annual interest
=
TSHS.87.879 mil x 0.12 = TSHS.10.55 million
Annual tax saving
=
TSHS.10.55 mil x 0.4 = TSHS.4.22 million
© GTG
Investment Appraisal (Capital Budgeting): 135
Investment Appraisal (Capital Budgeting): 145
Assuming no lag in tax payments this has a present value of:
TSHS.4.22 mill x 3-year annuity factor at 12%
=
4.22 mil x 2.402 = TSHS.10.136 million
Issue Costs Funds required (million)
Rights issue
90
3.264
Debt
87
0.879
4.143
(Assumptions: the issue costs are not tax allowable)
Adjusted Present Value
TSHS(Million)
Base case NPV
(5.7)
Tax shield on interest
10.136
Issue costs
(4.143)
APV
0.293
Answer to IEQ 2
Model A
For Model A the net present value is worked out as below:
Cash inflow
Present value
First year
1,400,000,000
1,250,200,000
Second year
1,800,000,000
1,434,600,000
Present values of cash inflows
2,684,800,000
Less: Initial investment
2,250,000,000
Net Present Value
434,800,000
Model B
The cash flows along with respective probabilities are as given below:
Year 1
Probability
0.7
0.3
Year 2
Cash flow
1,500,000,000
1,800,000,000
Probability
Cash flow
0.3
1,500,000,000
0.4
1,800,000,000
0.3
2,200,000,000
0.5
2,200,000,000
0.3
2,300,000,000
0.2
2,500,000,000
Since the cash flows in the second year are sequentially dependent upon the cash flows of the
first year we examine the evaluation of Model B with a decision tree.
146 Investment Decisions
136: Investment Decisions
© GTG
The decision tree is as follows:
Year 1
1,500,000,000
Year 2
0.3
B
0.7
1,500,000,000
0.4
1,800,000,000
0.3
2,200,000,000
A
0.5
0.3
1,800,000,000
2,200,000,000
0.3
C
2,300,000,000
0.2
2,500,000,000
We examine Model B by finding the expected present values working backwards with the decision
tree. We first calculate the expected present values at Nodes B and C and then at Node A using
the probabilities given.
Present value of Year 2 cash flows at the end of Year 1
Expected cash flow at “B” = (0.3 x 1,500m) + (0.4 x 1,800m) + (0.3 x 2,200m) = 1,830,000,000.
Present value of expected cash flow at “B” = 1,830,000,000/(1+0.12) = 1,633,900,000.
Expected cash flow at “C” = (0.5 x 2,200m) + (0.3 x 2,300m) + (0.2,500m) = 2,290,000,000
Present value of expected cash flow at “C” = 2,900,000,000/(1+0.12)=2,044,600,000
Present value of Year 1 cash flows at the end of Year 0
Value of cash flow at
Node B
Note C
Cash flow of Year 1
1,500,000,000
1,800,000,000
PV of cash flow of Year 2
1,633,900,000
2,044,600,000
Total cash flow at Year 1
3,133,900,000
3,844,600,000
Expected cash flow at “A” = 3,133,900,000 x 0.7 + 3,844,600,000 x 0.3= 3,347,100,000
Present value of expected cash flow at “A” (Year 0) = 3,347,100,000/)1 + 0.12)
© GTG
Investment Appraisal (Capital Budgeting): 147
Investment Appraisal (Capital Budgeting): 135
= 2,988,500,000
Less: Capital expenditure
= 2,500,000,000
Expected NPV of the project
= 488,500,000
Decision
Since the expected NPV for Model B is higher (i.e. NPV for model A is Tshs .434,900,000 while
that of Model B is Tshs .488,500,000), the firm must develop Model B.
The project is therefore marginally acceptable
148
Investment Decisions
C2
SECTION C
Complex Investment Appraisal: 149
INVESTMENT DECISIONS
STUDY GUIDE C2: COMPLEX INVESTMENT
APPRAISAL
In the first Study Guide of this section, the basic methods of appraising investments together with the advantages
and disadvantages of each were discussed; being the payback period method, return on capital employed or
accounting rate of return, as well as discounting method of net present value (NPV) and internal rate of return
(IRR).
However, in Study Guide C1 it was assumed that the project’s cash flows and the discount rate applied to the
cash flows were already known, with the impact of risk and taxes as well as other factors not considered.
In the real world, the cash flows of a project and the cost of capital of a company are not always known with
certainty, but estimation is made together with the tax impact on the project’s cash flows.
As can be seen in the learning outcomes below, this Study Guide focuses on using the net present value
method in more detail together with factoring in risk and uncertainty within the estimated cash flows used. The
Study Guide also goes on to look at asset replacement and abandonment decisions that companies are faced
with, as well as techniques used to face the issue of limited resources of companies and identifying the optimum
investment plan. When making investment decisions, the financial aspect alone is not enough, as companies also
need to consider non-financial aspects as part of any investment appraisal decision.
a) Identify, assess and explain other factors that may need to be considered beyond basic investment
appraisal analysis including assessment of risk, subjective factors, intangible factors, and limitations in
data and information which may affect the advice given.
b) Incorporate risk and inflation into the investment appraisal using various techniques/models.
c) Perform investment appraisal (calculating optimal investment plan) under capital restrictions and limitations.
d) Perform investment appraisal under asset replacement and abandonment conditions.
e) Draft a straightforward investment plan with commentary based on a business scenario that requires an
investment appraisal to be undertaken or where information is given.
f) Identify, evaluate and explain the impact of non-financial factors such as economic, social and
environmental issues on making an appropriate investment decision.
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Decisions
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1. Identify, assess and explain other factors that may need to be considered beyond basic
investment appraisal analysis including assessment of risk, subjective factors, intangible
factors, and limitations in data and information which may affect the advice given.
[Learning Outcome, a]
1.1 Assessment of risk
The terms risk and uncertainty have different meanings though in practical life they are sometimes used
interchangeably.
Risk refers to quantifiable sets of circumstances, to which probabilities can be assigned.
Uncertainty refers to a situation where it is impossible to assign probabilities to sets of circumstances.
1. Risk
In the context of an investment project, risk has the following implications:






expected returns may vary in the future
different outcomes are possible
risk increases proportionately with the project life
risk also increases proportionately with the greater variability
companies show more concern for the ‘downside risk’ (i.e. possibility of receiving lower returns
than expected in comparison to a higher return than expected)
probabilities can be assigned, and the risks can be quantified
2. Uncertainty
In the context of an investment project, uncertainty has the following implications.


Different outcomes are possible.
Assignment of probabilities or quantification of costs and benefits is difficult mainly due to little past
experience.
For a given investment project, if it is possible to estimate the project’s returns at Tshs 500,000,000 with a
probability of 80%, then we are dealing with a risk.
If it is not possible to either assign probabilities or estimate the amounts, then we are faced with uncertainties.
This Learning Outcome shows the assessment of risk, but to understand the techniques of handling risk, refer to
Learning Outcome 2.
1.2 Subjective factors
The subjective factors that need to be considered beyond basic investment appraisal analysis are partly
covered in more detail in Learning Outcome 6 of this Study Guide. Other subjective factors are noted below.
1. Capital Structure
As already noted, one of the key aims of investment appraisals is to maximise shareholder wealth. The
company value is influenced by the way it is financed; therefore, the capital structure should be used to its full
potential. Beyond the basic investment appraisal analysis, management needs to also consider the way it decides
to finance a project. It needs to identify the optimum capital structure which involves external debt and internal
capital through shares, for example, and then choose the option that leads to the highest shareholder wealth.
This shows that the capital structure of a company is of significant importance when analysing potential projects.
© GTG
Complex Investment Appraisal: 151
Complex Investment Appraisal: 139
A company is looking to invest in a new project involving a new product range. Management are considering
whether internal capital should be used for the investment or whether a loan should be taken out to finance the
project.
Based on further analysis, it was identified that external financing will lead to lower shareholder value, so
management opted for using internal finance for the project as it was assessed as viable.
2. Inflation
Inflation is also a subjective factor as the impact of inflation on an investment appraisal is forward looking and
therefore, only an estimate can be made as to what the rate is anticipated to be.
See Learning Outcome 2 which focuses on the incorporation of risk and inflation into the calculation of net present
value of projects.
1.3 Intangible factors
Intangible factors are partly covered in Learning Outcome 6 which discusses the impact of non-financial factors
such as social, economic and environmental. Other intangible factors are noted below.
1. Management vs. Shareholders
There is often a difference between the interests and opinions of management compared to shareholders.
Therefore, within the investment appraisal analysis this intangible factor should also be taken into consideration.
This intangible factor takes into consideration incentives and information problems that occur due to the
information being interpreted by different people, with their own opinions and perspectives.
The interests or incentives of both parties make the information on the project sensitive to the available
resources of the company. Some research has shown that it can be the case that for companies with high level of
cash flow being available, they are more likely to invest in non profitable projects purely for the managers’ personal
benefits. The over investment in a project can increase the manager’s authority as they then have more
control over resources available and usually will lead to higher financial reward.
As a result of not having perfect information available and usually short- t e r m management goals to retain
control, long term investments tend to suffer. However, on the other side, there can be an interest to invest in more
long-term projects if the manager wants to ensure long term employment with the company, as it is important for
them to remain and control the project while it is going on.
Other research into this factor suggests that managers are influenced by the quality of the project as they will be
rewarded more for higher quality projects as compared to lower quality projects.
The way to reduce the impact of the misalignment between the two parties and for improvement in sharing of
information is to provide incentives to management to align their objectives with that of the company, by means of
a contract or by sharing the ownership through stock options (long term incentive plans).
2. Characteristics of those in charge of governance
Following on from the above intangible factor, another factor involves the characteristics of those charged with
governance. Certain research has shown that the characteristics of the Chief Executive Officer (CEO) of an
organisation can influence the investment policy implemented by the firm. Any misrepresentation in the policy can
lead to over confident management together with over estimation in the cash flow calculations of the
project’s return, mainly in cases with excess cash flow.
On the other hand, if the CEO is uncertain of its rewards as a result of investment decisions, the level of
investments undertaken by the company is expected to be low.
Similar to the point above, shareholders require an effective incentive scheme to encourage management to make
investment decisions that are in the best interests of the firm and be value enhancing.
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1.4 Limitations in data and information
Above and beyond the basic investment appraisal, there can be seen to be a number of factors to consider
consisting of both financial and non-financial aspects. Within these two categories, there are limitations in the data
and the available information that can impact any advice given.
1. Source of data and information
The information used in the calculations or assessment of non-financial factors has an impact on the advice given.
There are a number of sources of information, such as via television, newspapers, magazines, word of mouth etc.
There are limitations in this type of information, as it is dependent on where the data has come from.
You are looking to purchase a new mobile phone and have begun some research into which the best model for
your personal specifications is. The model you are leaning towards the most has been evaluated by a mobile
specific magazine (electronic gadget specific) and also in a leaflet you happen to have come across. The magazine
states that the model is of great quality, with minimal faults noted in its functionality. However, the leaflet suggests
the performance of the phone is no more than average. Which source of information would you rely on more in
making your decision?
Given that the magazine is specific to electronic products including mobile phones, the level of analysis and
research performed on the model is likely to be more substantial and therefore, would be deemed a more
reliable source of information than that contained within the leaflet.
2. Quality of information
Similar to the above point, the presentation and quality of the information impacts the decision made.
If information is presented in an easy to follow format, with assumptions noted and workings shown, together
with substantial research to support calculations performed, it is more reliable than information presented in a
draft, with no workings available and limited time spent on it.
3. IT limitations
In some instances, there can be limitations in information due to the limitations of IT functionality. The company
may not have the appropriate IT resource to perform a full estimation of a project and then perform sensitivity
analysis as an example.
4. Availability of experts
For certain projects, management may require the use of experts in the performance of evaluating a potential
project. The company may not have sufficient resources to perform the calculations themselves or the technical
knowledge, in which case external experts may be required. It is possible that management are unable to spend
the capital on experts or that the required level of experts for the particular project are not available, which has
an impact on the reliability of the information.
This Learning Outcome has demonstrated that due to limitations of investment appraisal techniques themselves,
it is important for a firm to also incorporate other factors such as the risk factors, subjective matters, intangible
factors and limitations in data and information as part of the evaluation prior to implementation of any project.
For a successful project, financial basis alone is not sufficient, as interests, opinions, behaviours and other
organisational factors are involved. As noted, non-financial factors have intangible aspects, which can be
difficult to quantify, which leads to the subjective analysis. A company will establish a tangible method to
evaluate the non-financial aspects of a project to allow for comparison of performance and aid the monitoring
process.
© GTG
ComplexInvestment
InvestmentAppraisal:
Appraisal:141
153
Complex
A company is in the process of evaluating project X. The management accountant, who has only two years
experience in finance, has been asked to prepare the cash flow estimations of the project by his manager. He has
been asked to use all resources available, such as the internet, magazines, newspapers etc. to prepare the
calculations for a 3-year project.
Required:
Can you identify three potential issues in this scenario?
2. Incorporate risk and inflation into the investment appraisal using various
techniques/models.
[Learning Outcome b]
This learning outcome incorporates the techniques of adjusting for risk and uncertainty into the investment
appraisal models and also includes the impact of inflation and tax on the appraisals.
Sensitivity analysis showed that, despite having a significantly lower Equivalent annual cash flow (EACF) value,
the financial certainty of the Club Mercury (CM) project made it superior to the Club Hawaiian (CH) project. The
variables for the CM project are far fewer than those for the CH project as the CM project only collects rent on
the property. Although, in the CH project, the estimated salaries are sunk costs, if any additional staff are employed
due to increased workload, the analysis must incorporate these extra costs.
When the costs of salaries exceed 3.56% of the CH project’s sales, the CM project becomes more profitable. In
addition, if the CH project’s sales revenue falls below 87.54% of expected sales, then the CH project’s EACF
would be lower than the CM projects. Furthermore, the CH project is more vulnerable to the effects of the cost
of capital as this project has a longer duration. The CH project would not be the preferred option if the COC
rises above 23.82%.
2.1 Techniques of adjusting for risk and uncertainty
This section will include the techniques used to embed risk and uncertainty into the appraisal models. The
techniques include sensitivity analysis, probability analysis and simulation.
2.2 Sensitivity analysis
Sensitivity analysis is a method used to estimate the risk of an investment project by evaluating how much
the NPV of the project changes when the variables from which it has been calculated change.
1. Relevant variables
The above definition refers to the variables from which NPV has been calculated. The following items can be
considered as relevant variables while calculating the net present value (NPV) of a project.
Diagram 1: Relevant variables for calculation of NPV
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2. Methods used for sensitivity analysis
(a) Quantifying the change in each key variable that will make the NPV zero.
(b) Changing each key variable by a set percentage and checking the impact on the NPV.
(c) Certainty equivalent approach.
3. Quantifying the change in each variable that will make the NPV zero
In this method, it is verified as to how much change in each key variable will cause the NPV to become zero.
These changes are converted into percentage terms. Then a conclusion is reached about which variables are
most important. It can be said that the project is more sensitive to those variables of which even a small percentage
change can cause the NPV to become zero. Management needs to keep a close watch on these variables if it
wants the project to succeed.
A 3% reduction in sales volume is sufficient to make the NPV of a project zero. As against this, it requires a 15%
increase in the initial investment to make the NPV of a project zero. This project is more sensitive to reduction in
sales volume. Management needs to take care that the sales volume does not dip.
4. Changing each variable by a set percentage and checking the impact on the NPV
Since we are more concerned with the downside risk, a percentage change that will reduce the NPV is considered.
The project is more sensitive to the variables that cause higher reduction.
A 5% reduction in the selling price reduces the NPV by Tshs 50,000,000; a 5% reduction in sales volume
reduces the NPV by Tshs 10,000,000. The project is more sensitive to changes in sales price than to changes in
sales volume.
5. Limitations of sensitivity analysis
(a) Only one variable can be changed at a time. This requires that the changes in each key variable must be
isolated. This may be unrealistic.
(b) This analysis only identifies key variables. It does not assess the risk in the real sense, since it does not
consider the probabilities or likelihood of variables actually changing.
(c) Management may not have control over the key factors, even if they are identified.
(d) Unless parameters are set, this analysis in itself does not provide a decision rule.
SUMMARY
Zest Plc is considering investment in a new machine costing Tshs 690,000,000 which is expected to have a
5- ye a r life. It is expected that the new machine will increase the capacity by 20,000 units per annum.
Selling price per unit is Tshs 32,000, and variable costs per unit are Tshs 20,000. If the new machine is
installed,
additional fixed costs of Tshs 38,000,000 will be incurred each year. The company’s cost of capital is 9%.
Required:
Ignoring taxes, evaluate the sensitivity of the project’s NPV to changes in the variables used to calculate the
NPV.
Complex Investment Appraisal: 155
© GTG
Complex Investment Appraisal: 143
2.3 Probability analysis
Instead of using single point estimates that have been used so far, a probability distribution of expected cash flows
can be prepared. It can be used to arrive at an expected NPV. This probability analysis can be used to find
out the possibility of achieving a negative NPV and the probability of the best- and worst-case scenario.
Simple probability distributions may just have a few probabilities.
Probability
0.3
0.6
0.1
Cash flow
Tshs 000’s
200,000
300,000
100,000
Expected net present value = (0.3 x Tshs 200,000,000) + (0.6 x Tshs 300,000,000) + (0.1 x Tshs 100,000,000) =
Tshs 250,000,000.
1. Probability distribution of expected cash flows
(a) Using different probabilities or joint probabilities, a probability distribution is prepared. This approach
recognises that there are several possible outcomes.
(b) Expected NPV is calculated.
(c) Risk is analysed from different angles.
The cost of capital for Supernova Inc is 14%. The initial investment for the project is Tshs 470,000,000. Estimate
the cash flows of the project under different economic circumstances. Their respective probabilities are as follows:
Net cash flows for Year 1
Economic Conditions
Probability
Cash Flow ( Tshs 000’s)
Weak
0.3
150,000
Moderate
0.5
300,000
Good
0.2
450,000
Net cash flows for Year 2
Economic Conditions
Probability
Cash Flow ( Tshs 000’s)
Moderate
0.7
375,000
Good
0.3
525,000
Find the expected value (EV) of the project’s NPV assuming that the economic conditions in Year 2 are not
dependant on Year 1. Also find out how much is the risk that NPV will become negative.
2. Standard deviation of NPV
When the project period increases (each year has many different probabilities), the calculation of the EV of NPV
will become awkward. There is a shorter way available to calculate the standard deviation of the NPV. This
gives a fair indication of the risk involved.
It can be calculated as:
S=√𝑃𝑃(𝑥𝑥 − 𝑥𝑥̅ )2
where,
S is the standard deviation
p is the probability
x is the EV of the NPV
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Two mutually exclusive projects P or Q are to be considered by Grill Plc. There is some uncertainty about the
running costs with each project. The probability distribution of the NPV for each project has been estimated as
follows:
NPV
Tshs
million
(10)
10
15
35
NPV
Tshs
million
5
10
20
30
Project P
probability
0.15
0.20
0.35
0.30
Project Q
probability
0.2
0.3
0.4
0.1
Which project should the company opt for?
Step 1: Calculation of the EV of the NPV for project P and Q
NPV
Tshs
million
(10)
10
15
35
Project P
probability
0.15
0.20
0.35
0.30
EV
Tshs
million
(1.5)
2.0
5.25
10.5
16.25
NPV
Tshs
million
5
10
20
30
Project Q
probability
0.2
0.3
0.4
0.1
EV
Tshs
million
1.0
3.0
8.0
3.0
15.0
Project P has higher EV of NPV, but we need to find out the risk of variation in the NPV above or below the EV;
this is to be measured by Standard Deviation of the NPV. It can be calculated as:
S=√𝑃𝑃(𝑥𝑥 − 𝑥𝑥̅ )2
Where, x is the EV of the NPV
Step 2: Calculation of Standard Deviation of a project’s NPV
Project P 𝑥𝑥̅ = 16.25
P
x
Tshs
million
(1.5)
0.15
2.0
0.20
5.25
0.35
10.5
0.30
𝑥𝑥 − 𝑥𝑥̅
Tshs
million
(17.75)
(14.25)
(11)
(5.75)
Project P
Project Q
S=√140.14
= 10.789
= 11.838
= Tshs 11.838m
𝑃𝑃(𝑥𝑥
− 𝑥𝑥̅ )2
Tshs
47.26
million
40.61
42.35
9.92
140.14
Project Q 𝑥𝑥̅ = 15
x
p
Tshs
million
1
0.2
3
0.3
8
0.4
3
0.1
𝑥𝑥 − 𝑥𝑥̅
Tshs
million
(14)
(12)
(7)
(12)
𝑃𝑃(𝑥𝑥
− 𝑥𝑥̅ )2
Tshs
39.2
million
43.2
19.6
14.4
116.4
S=√140.14
Tshs 10.789m
Project P has higher EV of NPV, it also has higher standard deviation of NPV and therefore has a higher risk
attached to it. Selection of a project depends on the management’s appetite to risk.
If the management is risk averse, it will select the less risky project, Project Q.
If the management is prepared to take a risk with a low NPV in the hope of a higher NPV, it will select
Project P.
Complex Investment Appraisal: 157
Complex Investment Appraisal: 145
© GTG
3. Evaluation of probability analysis
This method is growing in popularity. The fact that it is based on the subjective estimates of the managers does
not reduce their utility. These estimates are made by the managers on the basis of the information available. They
represent the assessments of the likelihood of future events. Such assessments are made by the managers
regularly in the normal course of business.
SUMMARY
The probability distribution of the NPV for a project has been estimated as follows:
Probability
0.10
0.15
0.20
0.25
0.30
Cash flow
Tshs 000’s
(75,000)
21,000
27,000
23,000
17,000
Required:
Calculate the expected net present value and standard deviation of the project’s NPV.
2.4 Simulation
One major limitation of sensitivity analysis is that it analyses the sensitivity of the project’s NPV to changes in
one variable at a time. In reality, a change in one variable may have knock-on effects on another.
Simulation models are useful to handle changes in more than one variable at a time. They determine by
repeated analysis, how simultaneous changes in these variables affect NPV. This method is also called Monte
Carlo method.
The following steps are included while using a simulation model for appraising a project:
1. For each project variable, a range of random numbers is assigned to the values at different probabilities.
2. A computer generates a set of random numbers and uses these numbers to randomly select a value for
each variable.
3. NPV of this set of variables is calculated.
4. This process is repeated and a frequency distribution of the NPVs is generated.
5. From the frequency distribution, the expected NPV and its standard deviation are calculated.
However, the variables are likely to be interdependent, e.g. an increase in prices may reduce sales volume. Simple
simulation models assume that these factors are unrelated to each other. Such interrelationships are frequently
complex to model.
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The Finance executive of J.W. Pillers Plc has drawn the following projections with probability distributions
Wages and salaries
Tshs million
8-10
10-12
12-14
Raw material
Tshs million
6-8
8-10
10-12
12-14
Probability
0.3
0.5
0.2
Probability
0.2
0.3
0.3
0.2
Sales revenue
Tshs million
28-32
32-36
36-40
40-44
Probability
0.1
0.2
0.5
0.2
Fixed costs are Tshs 12,000,000 and available cash balance is Tshs 52,000,000.
Students are required to simulate the cash flow projection and expected cash balance at the end of the sixth
month. Use the following random numbers:
Wages and salaries
Raw materials
Sales Revenue
3
4
0
8
5
5
9
1
6
3
0
8
9
3
0
7
4
2
1. Simulation of cash flow projection
(a) Random number allocation
Random numbers are allocated on the basis of cumulative probabilities of the lowest to the highest values e.g. if
the available random numbers for wages and salaries are taken as 10 (0 to 9) the random numbers range
based on the cumulative probability of 0.3 is (0-2). It covers three digits of 0, 1 and 2. Next cumulative figure is
0.8 (3-7) It covers next five digits 3,4,5,6 and 7.The next cumulative probability is 1.0. (8-9).It covers the next
two digits 8 and 9.
Wages and Salaries
Cum.
Midpoint
Random
Tshs
Prob.
Nos.
million
9
0.3
0-2
11
0.8
3-7
13
1.0
8-9
Raw Materials
Midpoint Cum. Random
Tshs
Prob.
Nos.
million
7
0.2
0-1
9
0.5
2-4
11
0.8
5-7
13
1.0
8-9
Sales Revenue
Midpoint Cum. Random
Tshs
Prob.
Nos.
million
30
0.1
0
34
0.3
1-2
38
0.8
3-7
42
1.0
8-9
(b) Simulation of cash flow
Actual random numbers for the respective months are given above. Depending upon the range under which the
number falls, the amount for that month is determined. For example, random numbers for wages and salaries for
6 months are 3, 8, 9, 3, 9 and 7. They fall under the classes having midpoints 11, 13, 13, 11, 13 and 11
respectively. These values are filled up in the table below.
Month
Sales
revenues
Tshs
million
1
2
3
4
5
6
30
38
38
42
30
34
Wages
and
salaries
Tshs
million
11
13
13
11
13
11
Raw
materials
Tshs
million
Fixed
costs
Tshs
million
Net Cash
Flow
Tshs
million
9
11
7
7
9
9
12
12
12
12
12
12
(2)
2
6
12
(4)
2
Cash balance
Opening balance
52 million
50
52
58
70
66
68
From the above simulation it will be observed that there are 4 months which have net cash inflows, the
probability of net cash inflows can therefore be estimated as 4/6 = 0.66. From the above table, the estimated cash
balance at the end of sixth month is Tshs 68,000,000.
Continued on the next page
Complex Investment Appraisal: 159
© GTG
Complex Investment Appraisal: 147
2. Expected Value (EV) Method of Cash Flow Projection
EV of salaries and wages
EV of raw materials
EV of sales revenue
Expected net cash inflow per month
Expected cash balance after six months
(9 x 0.3) + (11 x 0.5) + (13 x 0.2)
(7 x 0.2) + (9 x 0.3) + (11 x 0.3) + (13 x 0.2)
(30 x 0.1) + (34 x 0.2) + (38 x 0.5) + (42 x 0.2)
Tshs 37.2 – 10.8 – 10.0 – 12.0
Tshs 52.0 + (4.4 x 6)
Tshs
million
10.8
10.0
37.2
4.4
78.4
The difference between Tshs 68,000,000 and Tshs 78,400,000 is due to sample errors. If a number of simulation
iterations were carried out, then the mean of the balances predicted should approach the expected value more
closely as the number is increased.
Lozeggio expects to receive Tshs 200 million from a project (X) at the end of 3 years. The alternative project (Y)
gives Tshs 180 million after one year. The finance manager gave a report stating that, in view of inflation and
taxation effects, project Y is better. The recommendation was accepted, and project Y was approved.
2.5 Inflation incorporated into investment appraisal
The above case study shows that the factors of inflation and taxation affect the investment decisions. You may be
wondering how these are reviewed in investment decisions. In this Study Guide, we understand the techniques
used to do this. In our discussions on DCF methods so far, the effect of inflation was considered, but the impact
on investment decisions were not detailed. This Study Guide discusses how when inflation increases, the rate of
return expected by the investors also goes up.
1. Real vs. nominal cash flows (the effect of inflation on investment appraisal)
Real cash flows are cash flows that have not been subjected to inflation.
Nominal cash flows or money cash flows have been influenced by inflation.
Steve will receive Tshs 100,000,000 in cash next year. During the year, inflation of 3% is expected. Next year,
the nominal value will be Tshs 100,000,000 but the real value (after stripping away the effects of inflation) will be
Tshs 97,087,379 ( Tshs 100,000,000 / 1.03).
2. Real vs. nominal interest rates
The discount rate used in assessing projects so far, has been the real rate of return required by investors. This
is the rate which compensates investors for the risk of undertaking the activity and for not being able to use the
money. Since inflation erodes the purchasing power of money, investors will require compensation for this
additional factor. Therefore, the rate of return required for investments will increase.
The rate of interest which incorporates the real rate and the inflation rate is known as the nominal or money rate
of return. It can be calculated using the following formula:
(1 + Nominal rate or money rate) = (1+ Real rate) x (1+ Inflation rate)
If Steve’s real rate of return required is 10% and inflation is 3%, the effective nominal rate will be:
Nominal rate = (1+ 0.10) x (1+ 0.03) – 1
= 1.10 x 1.03 - 1
= 1.133 - 1
= 0.133
= 13.3%
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Complex Investment Appraisal: 149
3. Which rate is to be used for discounting?
The answer depends upon which cash flows are being discounted. If real cash flows are being discounted, the
real cost of capital should be used. If nominal cash flows are being discounted, the nominal cost of capital
should be used.
Continuing Steve’s example from above,
Nominal cash flow
Nominal cost of capital
cash flow = Tshs 100,000,000/1.133
Real cash flow
Real cost of capital
flow = Tshs 97,087,379/1.10
Tshs 100,000,000
13.3% Discounted value of the
Tshs 88,261,253
Tshs 97,087,379
10% Discounted value of the cash
Tshs 88,261,253
It can be seen from the above calculations, that both the approaches give the same answer.
1. When different costs and benefits are subject to different inflation rates: Each cash flow is inflated
individually according to the applicable rate of inflation. Thereafter, the nominal or money rate is applied to
discount the cash flows and the NPV is calculated.
2. When inflation rate changes during the life of a project: The same techniques as discussed in the previous
paragraph will be applied. The only difference is that the inflation rate for each year will be different.
SUMMARY
Fisher’s plans to make an investment in a production line which will facilitate the sale of a new product called XBX.
An initial investment of Tshs 396,000,000 in working capital would also be needed. Non-current assets costing
Tshs 840,000,000 would be needed, with Tshs 600,000,000 payable at once and the balance payable after one
year. Fisher’s expects that, after four years, the XBX will be obsolete and the disposal value of the non-current
assets will be zero.
The project would incur incremental total fixed costs of Tshs 660,000,000 per year at current prices, including
annual depreciation of Tshs 216,000,000. Expected sales are 130,000 units per year at a selling price of Tshs
25,000 per unit and a variable cost of Tshs 18,000 per unit, both in current price terms.
Fisher’s expects the following annual increases because of inflation:
General prices
Variable costs
Selling price
Fixed costs
Working capital
%
7.4
7
5
5
6
Assuming Fisher’s real cost of capital is 8 per cent, is the project viable? Ignore taxation for this question
2.6 Tax impact on investment appraisals
Variable costs
Selling price
Fixed costs
Working capital
7
5
5
6
Complex
Appraisal: 161
Assuming Fisher’s real cost of capital is 8 per cent, is the project viable? Ignore taxation
forInvestment
this question
2.6 Tax impact on investment appraisals
150 : Investment Decisions
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Businesses pay taxes on profits. If a business plans to invest in a new project e.g. a new factory, a new production
line etc., additional operating income and expenses will be incurred and therefore operating profit will be affected.
In addition, assets may be acquired and disposed of resulting in losses or gains on disposal which will, again,
have tax implications. The following section discusses, in detail, how these issues should be tackled.
1. Operating cash flows
Operating cash flows refers to revenue expenditure or income affecting operating profit. If an investment is
going to generate extra operating revenue, this will have the effect of increasing the level of operating profits. If
this occurs, the business will be required to pay tax on the additional profit. To take this into account, the
relevant tax to be paid on the additional revenue is deducted as a cash outflow in the NPV calculation.
Belco Ltd currently pays corporation tax at a rate of 28%. It is considering investment in a new production line
which it expects will generate additional sales revenue of Tshs 200,000,000 per annum.
Tax effect: the additional revenue will add to the company’s overall profits thereby increasing the amount of tax
to be paid. In calculating the NPV, this will be shown as a cash outflow. The amount of the outflow related to tax
will be Tshs 56,000,000 (0.28 x Tshs 200,000,000)
Alternatively, investment projects may incur additional operating expenses. These will have the effect of reducing
the overall profit levels of the business. If profits are lower, the tax paid will be lower. The adjustment required,
therefore, in the NPV would be a tax saving shown as a cash inflow or as a reduction of outflow.
Continuing the previous example of Belco Ltd,
Belco Ltd realises that it will also incur additional operating expenses of Tshs 40,000,000 per annum. This will
lower the company’s overall profit thereby reducing the amount of tax to be paid. The adjusted cash outflow on
account of taxation would be Tshs 44,800,000 i.e. ( Tshs 200,000,000 – Tshs 40,000,000) x 28%.
2. Capital cash flows
Often, money will be spent to obtain non-current assets for new investments e.g. buildings, equipment and
machinery. Generally, these are recorded in the Statement of Financial Position (SOFP) of a business and
depreciated over time through the Statement of Comprehensive Income (also called as Statement of profit or loss).
For this purpose, the taxation laws of each country may allow different allowances (known as tax- allowable
depreciations or capital allowances or writing down allowances) which have the effect of reducing profits,
resulting in tax savings. The tax effect of these allowances needs to be taken into consideration when calculating
NPVs. The tax effect of disposal gains or losses is also reflected in the NPV.
Capital allowances
Writing down allowances (WDA) on assets can be claimed at 20% on the written down value of assets. It is not
the writing down allowance that will be shown in the NPV but the resultant tax savings of 28% of the WDA. This
will be shown as a cash inflow in the NPV.
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Complex Investment Appraisal: 151
3. Disposal of assets
A balancing allowance or charge may arise upon the disposal of an asset. A balancing allowance arises if the
written down value of an asset is greater than its disposal value (loss on disposal). The company is allowed tax
relief on the loss. A balancing charge arises when the disposal value of an asset is greater than it’s written down
value (profit on disposal). The company will pay tax on the profit on disposal.
The balancing charge or allowance is calculated as follows:
$
X
(X)
X
(X)
X
X
Initial cost of asset
Cumulative capital allowances claimed
Written down value of asset
Disposal proceeds
Balancing (allowance)/charge
Tax saved / paid
4. Interest payments
Interest payments form a part of the cost of capital used to discount the projected cash flows. Therefore, they
should not be calculated separately for the appraisal of domestic capital investment projects. Instead, the aftertax discount rate should be calculated, as will be seen later in this Learning Outcome.
5. Timing of taxation items
Once it is decided that the tax cash flows are the relevant cash flows, the next question that arises is which
period do the tax cash flows relate to? The answer depends upon the following factors:
(a) the accounting policies and standards applicable in a country
(b) the timing of taxation items i.e., the period during which they are taxed
(c) the interest payment to discount the project cash flows
(d) the local tax laws
In many countries, tax is paid in the year following the financial year to which the profits relate. In other
countries, it is paid in the same year in which the profits arise.
Sometimes, information will be given in the exam. In the absence of this information, the assumption made
should be clearly mentioned
Realson Inc has estimated that a project will give net cash inflows of Tshs 100,000,000 during year 1 and
Tshs 150,000,000 during year 2. The corporate tax rate is 28%.
Assuming that the taxable profits are the same as cash inflows and there is a lag of one year in the tax
payments, the tax out flows will be as follows:
Cash inflow
year
1
2
Cash inflow
amount
( Tshs
000’s)
100,000
150,000
Tax outflow year
2
3
Cash (tax) outflow
amount 28%
( Tshs
000’s)28,000
42,000
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152 : Investment Decisions
SUMMARY
Spasco’s production manager put forward a proposal to purchase a machine worth Tshs 200,000,000
He says that it will result in annual cost savings of
Tshs 50,000,000
Expected life in years
5
Tax depreciation rate (reducing balance basis)
25% Salvage value of the
machine
Tshs 10,000,000
Advise the directors about the financial feasibility of the proposal, considering the following additional
information:
Rate of corporation tax
Tax is payable in the year subsequent to the year of the transactions
Cost of capital
28%
9%
2.7 Before-tax discount rate
If the tax effects are not taken into consideration while appraising a capital investment using a discounted cash
flow technique i.e. NPV or IRR, then the before-tax discount rate is used. The before-tax discount rate is calculated
by excluding the effects of tax on the rate of return.
The before-tax discount rate is used under the following conditions:

No taxes are charged: the capital investment is made in a tax- f r e e country or the government
offers incentives in respect of the capital investment in the form of tax exemption.

The project is exempt from tax for a few years: the government may offer sops for encouraging
investments in certain areas. The before-tax discount rate will be used if the capital investment is made in
an area that enjoys long term tax exemption.
The before-tax discount rate is calculated using following formula:
Discount rate (factor) =
where,
1
(1+ r )n
r = interest rate per period
n = term in periods
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Complex Investment Appraisal: 153
Therefore, with a target rate of return of 8%, the discount factor for 1 year is calculated.
1
Discount rate (factor) =
(1+ 0.08 )1
=
1
1.08
= 0.926
We also get these rates from the table of present value factors.
Since tax effect is not eliminated, these rates are before-tax discount rates.
2.8 After-tax discount rate
If the tax effect is to be considered while appraising a capital investment using a discounted cash flow
technique, then the after-tax discount rate is used. The after-tax rate is calculated by deducting the amount of tax.
The after-tax discount rate is used when the cash flows from the capital investment project are affected by the
rate of tax charged on the project.
The after-tax discount rate is calculated using the following formula:
After-tax rate = Before-tax rate x (1 - Tax rate)
Assuming a tax rate of 30% and a target rate of return of 8%, we get the after-tax rate as:
After-tax rate = Before-tax rate x (1 - Tax rate)
= 0.080 x (1 - 0.30)
= 0.080 x 0.70
= 0.056
= 5.6%
1
Discount factor =
1.056
= 0.947
For the purpose of the exam, when calculating NPVs the after-tax cost of capital will be used as the discount
rate.
SUMMARY
The relevant cash flow to be received after one year is Tshs 550,000,000 (before tax). The applicable tax rate is
35%. The target rate of return is 7%.
Required:
Calculate the present values using the ‘before-tax discount rate’ and the ‘after-tax discount rate’.
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2.9 Adjusted payback
1. Payback
The payback method has been discussed at length in the earlier Study Guide Learning Outcome. It represents
the expected period to recover the original investment from the net cash flows resulting from the project. A
target payback period is determined. A project that has a payback period lower than or equal to this period is
considered acceptable. Those beyond this are rejected.
2. Adjusted payback
In order to take care of the risks involved in a project, the payback period is shortened. The reason is that more
distant the cash flows into the future, the riskier and more uncertain they are.
A company first decided 5 years as a target payback period of a project. In order to adjust it for risk, it reduced
the target payback period to 4 years.
As the adjusted payback is a simple method, it is not usually recommended for use in the exam.
2.10 Risk adjusted discount rates
Risk free rate of return is normally relatively lower than other moderate or high risk investments. For example,
government securities are treated as almost risk free and the rate of return is lower. However, if we expect the
investors to put their money into a risky project, obviously, they will demand a higher rate of return.
A risk adjusted discount rate, therefore, has two components
1. Risk free rate of return representing liquidity preference or time preference of the investors. Investors want
a compensation for not being able to use their money now.
2. Risk preference: investors desire to obtain a risk premium or compensation for undertaking a riskier
project.
RADR = Risk free rate of return + Risk premium
However, determining a risk premium is not an easy task. The following alternatives can be applied to work it
out:

determine risk classes and assign appropriate discount rates to those classes. A project falling under
a particular risk class will be evaluated using the applicable discount rate.

assume that the risks of the projects will be similar to the company’s present average business risk.
This may be represented by a single overall rate such as weighted average cost of capital applicable to the
present business.
For Zeta Co, a risk-free rate of return is 8%. For a particular project, it wants to add a risk premium of 7%. The risk
adjusted rate of return will be 15% (8% +7%).
Risk adjusted discount rate assumes that with the project life, the risk constantly increases. If risk premium is
applied year after year, a cash flow after say five years will have a lower present value compared to that after four
years. That means we assume that the risk increases continuously. This is likely to be true in the majority of cases.
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Complex Investment Appraisal: 155
Unico Plc adjusts risk through discount rates by adding various risk premiums to the risk free rate. Depending
on the resultant rate, the proposed project is judged to be a low, medium or high-risk project.
Risk free rate (%)
(a)
8
8
8
Level of risk
Low
Medium
High
Risk premium (%)
(b)
4
7
10
Risk adjusted rate (%)
(a + b)
12
15
18
Suggest the acceptability of the project on the basis of Risk Adjusted rate.
The cash flows of the project considered are as following:
Point in time (yearly intervals )
Cash flow ( Tshs million)
0
(100)
1
45
2
80
If the project is judged to be Low risk
Years
0
PV ( Tshs
million)
(100)
1
𝟒𝟒𝟒𝟒
= 𝟒𝟒𝟒𝟒. 𝟏𝟏𝟏𝟏
𝟏𝟏 + 𝟎𝟎. 𝟏𝟏𝟏𝟏
NPV = 40.18 + 63.78 – 100 = Tshs 3.96m: Accept
2
𝟖𝟖𝟖𝟖
𝟏𝟏 + 𝟎𝟎. 𝟏𝟏𝟏𝟏𝟐𝟐
= 𝟔𝟔𝟔𝟔. 𝟕𝟕𝟕𝟕
If the project is judged to be Medium risk
Years
0
PV ( Tshs
million)
(100)
1
𝟒𝟒𝟒𝟒
= 𝟑𝟑𝟑𝟑. 𝟏𝟏𝟏𝟏
𝟏𝟏 + 𝟎𝟎. 𝟏𝟏𝟏𝟏
NPV = 39.13 + 60.49 - 100 = Tshs (0.38) m: Reject
2
𝟖𝟖𝟖𝟖
𝟏𝟏 + 𝟎𝟎. 𝟏𝟏𝟏𝟏𝟐𝟐
= 𝟔𝟔𝟔𝟔. 𝟒𝟒𝟒𝟒
If the project is judged to be High risk
Years
0
PV ( Tshs
million)
(100)
1
𝟒𝟒𝟒𝟒
= 𝟑𝟑𝟑𝟑. 𝟏𝟏𝟏𝟏
𝟏𝟏 + 𝟎𝟎. 𝟏𝟏𝟏𝟏
NPV = 38.14 + 57.45 – 100 = Tshs (4.41) m: Reject
2
𝟖𝟖𝟖𝟖
𝟏𝟏 + 𝟎𝟎. 𝟏𝟏𝟏𝟏𝟐𝟐
= 𝟓𝟓𝟓𝟓. 𝟒𝟒𝟒𝟒
2.11 Certainty equivalent approach
Of the predicted cash flows, the management may be sure that a specific proportion is guaranteed.
Management estimates that the total revenue over the next four years will be Tshs 5 billion. Of Tshs 5
billion, Tshs 2 billion is guaranteed as a result of the contractual obligations from customers. Tshs 2 billion is
certain.
Usually, a certainty percentage is determined for the cash flows and the cash flows are converted into certainty
equivalent. The NPV is then recalculated using the certainty equivalent values.
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156 : Investment Decisions
SUMMARY
3. Perform investment appraisal (calculating optimal investment plan) under capital
restrictions and limitations.
[Learning Outcome c]
Capital rationing arises when the amount of funds available for investments are restricted or limited. This restriction
on funds may apply to only one time period (single period capital rationing) or may extend indefinitely into the
future (multi-period capital rationing). In both cases, the finance manager must ensure that projects yielding the
greatest returns are prioritised. In this Study Guide the issues relating to single period capital rationing are
discussed. The F9 syllabus does not require knowledge of multi-period capital rationing.
3.1 Calculation of profitability indexes for divisible investment projects
1. Divisible investment projects
A divisible investment project is the one where any portion of the project may be undertaken. In other words, if
funds are insufficient, the company may partly invest in the project.
Along with being divisible, it is also assumed that the project is non deferrable (if not undertaken now, it cannot
be undertaken in the future) and non repeatable (it can be undertaken only once).
2. Need for profitability index (PI)
The PI is used to measure the relative ‘profitability’ of investments. The project’s NPV is taken as a proportion
of the initial investment. The following formula is usually used:
Profitability index =
Net Present value of future cash flows
Value of initial capital invested
Technically, if the above formula is used, it produces a profitability percentage. For a traditional index, the
following formula can be used:
PI =
Initial Investment + NPV
Initial Investment
3. Decision rule
Projects will be ranked according to their PI and invested in accordingly, starting with the project producing the
highest PI. This will be done until the available funds are exhausted. If this approach is adopted for divisible
projects, it will ensure that the company achieves the highest possible NPV. The PI approach to capital rationing
is more suitable for single-period capital rationing situations.
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Decisions
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Determine the optimal combination of products assuming that the projects are divisible. Total funds available
are Tshs 4,200,000.
Project
1 Initial investment ( Tshs 000’s)
2 Net present value ( Tshs 000’s)
3 Initial investment + NPV ( Tshs 000’s)
A
1,250
1,625
2,875
B
1,625
1,790
3,415
C
2,000
2,000
4,000
D
2,125
1,910
4,035
Project
Profitability index (3/1)
Ranking by profitability index
A
2.30
1
B
2.10
2
C
2.00
3
D
1.90
4
Profitability Index = PV of future cash flows / Initial Investment
Optimum investment schedule:
Tshs 1,250,000 invested in Project A
Tshs 1,625,000 invested in Project B
Tshs 1,325 invested in Project C ( Tshs
4,200,000 - 1,250,000 - 1,625,000)* Total
NPV for $4200 invested:
*
NPV (
Tshs 000’s)
1,625
1,790
1,325
4,740
Cumulative
investment
( Tshs 000’s)
1,250
2,875
4,200
(4,200 − 2,875) × 2,000 ( Tshs 000’s)
2,000
Therefore, the optimal combination of projects is project A, B and 2/3rd of project C.
3.2 Calculation of the NPV of combinations of non-divisible investment projects
If projects are non-divisible it is a case of ‘all or nothing’ i.e. the option to partly invest, as in the example above,
will not be available. In such a case, the PI approach will not apply. The finance manager will use a ‘trial and error’
approach to maximise the company’s NPV.
Continuing the example of the previous page,
Assuming that the projects are now indivisible, the combined investment schedule is as follows:
Projects A and B
Total NPV = 3,415
Projects A and C
Total NPV = 3,625
Projects A and D
Total NPV = 3,535
Projects B and C
Total NPV = 3,790
Projects B and D
Total NPV = 3,700
Projects C and D
Total NPV = 3,910
As project C and D have the highest NPV, so the optimum investment schedule is a combination of project C
and D.
Nature of project
Meaning
Indivisible (no
fractional investment)
Investment should be made in full.
Partial / proportional investment is
not possible.
Divisible (fractional
investment)
Partial investment is possible and
proportional NPV can be
generated
Approach to decision making
(a) Determine the combination of projects to
utilise the available amount
(b) Calculate the NPV of each combination
(c) Select the combination with the highest
NPV
(a) Compute the profitability indices (PI) of
various projects and rank them
(b) Select the projects based on maximum PI
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Complex Investment Appraisal: 157
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3.3 Reasons for capital rationing
Ideally, a company would prefer to implement all possible projects that will maximise the shareholder value if it
had unlimited capital. In theory, any project can be put to market so as to raise funds. However, in reality there
is a limit to the amount of capital that a company has or can raise from the capital market. This gives rise to the
need for capital rationing.
The reasons for capital rationing may arise due to external restrictions by the capital market, in which case it is
called ‘hard capital rationing’. Alternatively, they may arise due to internal limits imposed by the managers, in
which case it is called ‘soft capital rationing.
1. Hard capital rationing may be caused due to any of the following reasons:
(a) If capital markets are depressed, raising money may not be possible.
(b) Based on the credit appraisals, the financial institutions may consider lending to a company too risky.
(c) Cost of capital issue may be disproportionate, especially if the amount of capital requirement is small.
(d) Due to the credit policy of the government, there may be restrictions on lending.
In reality, hard capital rationing is less frequent. Most of the capital rationing is self imposed (soft).
2. Soft capital rationing may be caused by any of the following reasons:
(a) Management may refuse to raise additional funds through the issue of new shares to avoid dilution of
control for existing shareholders.
(b) To avoid commitment to large payments of interest or instalments of principal. This applies to debt finance. (c)
Small and Medium Enterprises (SMEs) may decide to rely only on internally generated funds for the
purpose of expansion.
(d) Managers may wish to create an internal market for funds, thereby ensuring that only the most financially
viable projects are selected.
(e) There may be a lack of managerial time or expertise to manage projects, therefore a limitation on the
amount of investments may be imposed.
SUMMARY
SUMMARY
170 Investment Decisions
158 : Investment Decisions
Project
P
Q
R
S
T
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Required initial investment
Tshs
(000’s)
50,000
150,000
25,000
100,000
50,000
NPV at appropriate cost of capital
Tshs
(000’s)
10,000
17,500
8,000
12,500
15,000
The amount available with the company is Tshs 150,000,000:
Determine the optimal combination of projects assuming that the projects are:
(a) Divisible
(b) Indivisible
4. Perform investment appraisal under asset replacement and abandonment conditions.
[Learning Outcome d]
Once an investment project is undertaken, it is not always continued to the end of its estimated life. A
performance review should be undertaken for existing projects together with a continuous search for new
investment opportunities. During the process of reviewing projects, a decision may be taken to abandon the project
or to replace the existing asset.
In this learning outcome, a distinction is made between asset replacement and abandonment decisions.

Abandonment: this involves a situation where an asset is used for some time, and then it is decided not
to continue the operation in which the equipment or asset is being used. The asset will be sold or
scrapped and not replaced.

Replacement: this involves a situation where a particular operation is intended to continue indefinitely.
This means the company’s need for the asset is expected to continue long after the present asset has been
sold or scrapped. In this case, a company is faced with a decision relating to when the existing asset should
be replaced.
4.1 Abandonment conditions
The decision to abandon or discontinue a project is just another investment decision and therefore, the net present
value method is still applicable in that a positive cash flow outcome is desired; and if NPV is less than zero, the
project should be rejected. The timing as to when to abandon a project is demonstrated in the example below.
A company owns a machine that is already 6 years old and the estimated physical life is no more than 2 further
years. Below are the net cash flows and residual value estimates for the machine:
End of year
6
7
8
Net cash flow
Tshs
000’s
8,000
5,000
Residual value
Tshs
000’s12,000
6,000
-
The cost of capital for the company is 10%.
Continued on the next page
Complex Investment Appraisal: 171
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First, we need to calculate the net present value of foregoing the Tshs 12,000,000 at its current residual value,
and running the machine for 1 more year as follows:
NPV = - Tshs 12,000,000 +
8,000,000 + 6,000,000
or – Tshs 12,000,000 + (14,000,000 x 0.909)
1.1
NPV = - Tshs 12,000,000 + 12,727,273
NPV = Tshs 727,273
The net present value is positive, showing that the machine should be retained for a further period of 1 year.
Management of the company may be interested in finding out what the net present value of retaining the
machine for 2 years may be to identify the optimum timing of abandonment. The company again will forego the
Tshs 12,000,000, its current residual value, but receive net cash flows in year 7 and 8 of Tshs 8,000,000 and Tshs
5,000,000, but no residual value at the end of year 8 as follows:
NPV = - Tshs 12,000,000 +
5,000,000
8,000,000
+
1.1
(1.1) x (1.1)
Or – Tshs 12,000,000 + (8,000,000 x 0.909) + (5,000,000 x
0.826) NPV = - Tshs 12,000,000 + 7,272,727 + 4,132,231
NPV = - Tshs 595,042
Unless there is some form of upward revision to the cash flow estimates for year 8, the machine should be
abandoned or retired at the end of year 7, as it generates a positive NPV.
4.2 Replacement conditions
As part of the replacement decisions for an asset, there are two cases to be discussed. The first decision is focused
on when to replace an existing project with an identical project. The second case is to replace an existing project
with a new one, involving different cash flows and therefore, these will be non-identical projects.
1. Identical replacement
Equivalent annual cost (EAC) is the average annual cost of owning and operating an asset over its entire
lifespan.
Most assets have a finite useful life and require maintenance while in operation. As the asset grows older,
maintenance as well as operating costs may increase because it may become less efficient. Similarly, assets’
residual values decrease as time goes by. In this case, it is not a question of whether or not to replace but, more
importantly, when to replace. Present value of future costs are an absolute measure and may not be sufficient
for comparison between alternative replacement cycles. Instead, management can calculate equivalent annual
costs for each possible replacement cycle and select the one giving the lowest EAC. The EAC is calculated as:
Equivalent annual cost (EAC) =
PV of cost for one replacemen t cycle
Cumulative PV factor for the no. of years in the cycle
172 Investment Decisions
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Malco provides the following details:
Cost of machinery Tshs 100,000,000
Discount rate 12%
Year
1
2
3
4
Cost of running and
maintenance
( Tshs
000’s) 10,000
20,000
35,000
65,000
Residual value
( Tshs
000’s)
30,000
25,000
20,000
15,000
You must use the equivalent annual cost method to determine the appropriate replacement policy of the
company.
Assumption: No maintenance costs in the year of disposal.
This is a common assumption for exam
purposes and should be followed unless the
question says otherwise.
(a) 1-year replacement cycle
Year
Cash flow
0
1
Machinery cost
Disposal proceeds
Tshs
000’s
(100,000)
30,000
DF (12%)
1.000
0.893
PV
Tshs
000’s
(100,000)
26,790
(73,210)
EAC = Tshs 73,210,000/0.893 = Tshs 81,982,083
(b) 2-year replacement cycle
Year
Cash flow
0
1
2
Machinery cost
Maintenance
Disposal proceeds
Tshs
000’s
(100,000)
(10,000)
25,000
DF (12%)
1.000
0.893
0.797
PV
Tshs
000’s
(100,000)
(8,930)
19,925
(89,005)
EAC = Tshs 89,005/1.690* = Tshs 52,665,680
*(0.893 + 0.797)
(c) 3-year replacement cycle
Year
Cash flow
0
1
2
3
Machinery cost
Maintenance
Maintenance
Disposal proceeds
Tshs
000’s
(100,000)
(10,000)
(20,000)
20,000
DF (12%)
1.000
0.893
0.797
0.712
PV
Tshs
000’s
(100,000)
(8,930)
(15,940)
14,240
(110,630)
EAC = Tshs 110,630,000/2.402* = Tshs 46,057,452
*(0.893 + 0.797+ 0.712)
Continued on the next page
Complex Investment Appraisal: 173
Complex Investment Appraisal: 161
© GTG
(d) 4-year replacement cycle
Year
0
1
2
3
4
Cash flow
Machinery cost
Maintenance
Maintenance
Maintenance
Disposal proceeds
Tshs
000’s
(100,000)
(10,000)
(20,000)
(35,000)
15,000
DF
(12%)
1.000
0.893
0.797
0.712
0.636
PV
Tshs
000’s
(100,000)
(8,930)
(15,940)
(24,920)
9,540
(140,250)
EAC = Tshs 140,250,000/3.038* = Tshs 46,165,240
* (0.893 + 0.797 + 0.712 + 0.636)
Note: cumulative discount factors obtained from annuity tables.
Conclusion: The three- ye ar replacement cycle produces the lowest EAC and should therefore be chosen as
the optimal replacement cycle.
It is also possible to calculate the Equivalent Annual Value (EAV) in the same format as any cash flow analysis
using NPV by factoring in any maintenance cost, cash inflow and the residual value as above, but this time the
year in which the NPV is highest is deemed the optimal replacement cycle period
2. Non-identical replacement
It can be the case that often, the machine may be operating fine, but it technically becomes outdated or
obsolete. This is the time when the machine is replaced, with the replacement being of a new design, which
may have the same capacity, but the operating costs are lower. Again, the question arises as to when the old
machine should be abandoned for the new one.
First, the optimum replacement frequency/year for the new machine is calculated by the method shown in the
example above for identical replacement. Following this, the equivalent annual value or equivalent annual cost
of the new machine at its optimum replacement frequency is compared to the net present value of continuing
operation under the old machine as shown in the example within the abandonment conditions above.
Decision rule
The changeover of the project should be made when the net present value of ‘continuing to operate the old
machine for one more year’ is less than the equivalent annual value of the new machine.
A company is looking to replace a current project with an identical one. The machine costs Tshs 20,000,000 and
has an estimated life of 3 years. The net cash flows are Tshs 12,000,000 in the first year, decreasing by 500,000
each year as a result of higher maintenance costs. The table below shows the estimated residual value at the end
of each year.
Year
1
2
3
Net cash flows
( Tshs
000’s) 12,000
11,500
11,000
Residual value
( Tshs
000’s)
16,000
14,000
12,000
The cost of capital for the company is 10%. Assume there are no taxes. Management would like to know when
the machine should be replaced, by considering the perpetuity of the net present value for each of the 3 years.
174 Investment Decisions
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5. Draft a straightforward investment plan with commentary based on a business scenario
that requires an investment appraisal to be undertaken or where information is given.
[Learning Outcome e]
In this Learning Outcome, let us take the example of a company to understand how an investment plan is
drafted along with a commentary.
Enjoy Life the Natural Way is a company who supplies organically grown produce. The company already runs 5
stores in the region and is looking to open a new store just a few miles from current location for a 3-year period.
As the management account, you have been asked to draft an investment plan with commentary. The research
department have supplied the following financial information, other information required to perform cash flow
calculation and draft a plan and asked you to conclude whether the project should be accepted or not.
The company requires initial cash outlay of Tshs 3 billion, which includes a machine required for Tshs 2 billion,
with capital allowance annually of 25% and tax rate of 28%. The machine is then to be sold for Tshs 1 billion.
The company has capital funds available of Tshs 3.5 billion.
The company is required to pay tax on cash inflows or gain tax relief on cash outflows for the year, in the
subsequent year.
The following table shows the inflation or increase in rates in general and for specific revenue and cost streams.
Inflation/increase
General prices
Sales
Cost of goods sold
Other costs
Working capital
%
4
20
18
30
6
The company requires initial working capital of Tshs 300 million and the cost of capital for the company is 9%.
The estimated revenue and cost for the first year of trading are shown below:
1.
2.
3.
Years
Sales
Cost of goods sold
Other costs
1 Tshs (m)
1,800
(350) (20)
Executive Summary
The investment project of opening a new store in a new location has been assessed in detail and appropriate
estimations have been made to the cash flows. Consideration of tax to be paid and projected inflation rates
have also been factored into the calculations of management and the conclusion on whether to accept or reject
this project has been demonstrated. Based on the calculations, the conclusion reached is that this project
should be accepted by senior management as it is deemed a viable project which will increase shareholders’
value.
The estimations have been made based on the performance of current stores, and therefore, the increases in
sales and costs for the 3-year period are deemed reasonable. Furthermore, the current inflation and tax rates
again appear reasonable under the current circumstances.
Main section of report
The information provided by the research department is inclusive of information obtained from the various
departments of the company, such as sales department, purchasing team, marketing team as well as other
sections of the finance team. Given the company has already in hand 5 stores in similar locations across the
region, the prior results and knowledge reduces the risk of this project further. The information obtained has
been used to calculate the net present value of the project for 3 years as shown below. For workings and
assumptions see appendix 1.
Continued on the next page
Complex Investment Appraisal: 175
Complex Investment Appraisal: 163
© GTG
Years
1.
2.
Sales (W1)
Cost of goods sold (W1)
0
Tshs
(m)
1
Tshs
(m)
-
1,800.00
-
2
Tshs
(m)
3
Tshs
(m)
4
Tshs
(m)
2,160.00
2,592.00
-
(350.00)
(413.00)
(487.34)
-
3.
Other costs (W1)
-
(20.00)
(26.00)
(33.80)
-
4.
Cash flow from operations
(Profits) (1, 2 and 3)
-
1,430.00
1,721.00
2,070.86
-
5.
Initial outlay on machine
(2,000.00)
-
-
-
-
6.
Initial outlay other
(1,000.00)
-
- (19.08)
-
-
7.
Working capital (W2)
(300.00)
(18.00)
(316.40)
337.08
-
8.
Tax charge on profits @28%
-
-
105.00
(381.08)
(458.89)
-
140.00
-
78.75
- (43.75)
-
-
1,490.52
-
(502.64)
(3,300.00)
1,552.00
0.778
2,105.61
0.606
1
0.882
(3,300.00)
1,368.86
9.
10.
11.
12.
13.
14.
Tax saved on capital
allowances (W3)
Tax paid on balancing
charge (W4)
Net cash flow
(4 + 5 + 6 + 7 + 8 + 9 + 10)
Discount rate @ 13.36%
(W5)
Present value
Net present value
(sum of 9)
1,159.62
0.686
(304.60)
1,444.45
368.33
Commentary
1. The cash flow estimations assume sales; cost of sales and other costs will increase at the same rate each
year. There may be an element of bias in the calculations as in reality the estimations may be considerably
different.
2. The general inflation rise of 4% is based on current levels, and it has been assumed it remains the same
over a three-year period. But in reality, this could vary significantly, which would lead to the discount factor
also requiring to be updated.
3. The working capital increase per year again remains consistent throughout the three-year period, which in
reality could change significantly, depending on the number of days it takes customers to pay and what the
payment terms for the company are to pay suppliers.
4. As noted in W5, the before tax rate has been used, as the impact of tax on earnings as well as capital gain
has already been factored into the cash flow estimation.
5. Sensitivity of revenue on NPV per W6 shows that a 7.30% drop in revenue will lead to zero NPV from this
project. There is an element of risk as 7.30 % can be seen as low in relation to the level of investment,
however, given the prior knowledge and experience, if management are comfortable with the revenue
figures as estimated to be reliable, then the project should still be accepted.
6. Sensitivity of cost of goods sold on NPV per W6 shows a 38.2% increase in costs; this will lead to zero NPV
from this project. This is deemed low risk as even if the cost of goods sold did increase over the three-year
period, such a large increase is deemed less likely.
7. The overall return on the project over three years as a percentage of the initial outlay is 11.2% ( Tshs
368.33/3,300.00 x 100) or 12.3% excluding working capital ( Tshs 368.33/3,000.00 x 100).
Continued on the next page
176 Investment Decisions
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8. The company has available capital resource which is sufficient for this project and therefore, can be used to
increase shareholder value, as it leads to additional income for the company.
9. From a non-financial perspective, organically grown produce is gaining more importance in society, with
people being more health conscious.
10. Another non-financial factor is that entry into a new location will allow the company brand to expand and be
known in more areas, which is good for the company image.
Appendix 1
W1 Increase in sales cost of sales and other costs over 3 years
Sales
Cost of goods
Other costs
Year 1
Tshs
million
(a)
1,800.00
(350.00)
(20.00)
Year 2
Tshs million
(a) x (b) = (c)
Year 3
Tshs million
(c) x (b)
1,800.00 x 1.20 = 2,160.00
(350.00) x 1.18 = (413.00)
(20.00) x 1.30 = (26.00)
2,160.00 x 1.20 = 2,592.00
(413.00) x 1.18 = (487.34)
(26.00) x 1.30 = (33.80)
Increase
year on year
(b)
20%
18%
30%
W2 Increase in working capital
Year
0
1
2
Working Capital
Tshs
(m) 300.00
300.00
318.00
Rate of
Increase
N/A
6%
6%
Increase
Tshs (m)
300.00
18.00
19.08
Cumulative WC
Tshs million
300.00
318.00
337.08
W3 Tax saved on capital allowances
Year
0
1
2
3
Written down Value
Tshs million
2,000.00
1,500.00
1,125.00
843.75
Capital allowance @ 25%
Tshs million
500.00
375.00
281.25
Tax saved @28%
Tshs million
140
105
78.75
Year of tax
savings
1
2
3
W4 Tax saved / paid on balancing allowance / charge
WDV year 3
Salvage value
Balancing charge
Tax charge @ 28% (received in
year 4)
Tshs million
843.75
1,000.00
156.25
(43.75)
W5 Nominal rate calculation for discount rate
The rate of interest required is the nominal rate, which incorporates the real rate and the inflation rate. It can be
calculated using the following formula:
(1 + Nominal rate or money rate) = (1+ Real rate) x (1+ Inflation rate)
Nominal rate = (1 + 0.09) x (1 + 0.04) -1
= 1.09 x 1.04 – 1
= 1.1336 – 1
= 0.1336
= 13.36%
Note, the cash flows already incorporate tax charges or allowances and therefore, the before tax discount rate is
required.
Continued on the next page
Complex Investment Appraisal: 177
Complex Investment Appraisal: 165
© GTG
1
Discount rate (factor) =(1 + 𝑟𝑟)𝑛𝑛
where,
r = interest rate per period
n = term in periods
Therefore, with a target rate of return of 13.36%, the discount factor for year 1 is calculated.
Discount rate (factor) =
1
(1 + 0.1336)1
= 0.0882
Year 2 =
1
(1 + 0.1336)2
1
= 1.285
= 0.778
Year 3 =
1
(1 + 0.1336)3
1
= 1.456
= 0.686
Year 4 =
1
(1 + 0.1336)4
1
= 1.651
= 0.606
W6 Sensitivity of sales and cost of sales on NPV
NPV/ revenue = Tshs 368.33 / (1,800.00 x 0.882) + (2,160.00 x 0.778) + (2,592.00 x 0.686)
= Tshs 368.33 / (1,587.60 + 1,680.48 + 1,778.11)
= Tshs 368.33 / 5,046.19
= 7.30%
NPV/ COS
= Tshs 368.33 / (350.00 x 0.882) + (413.00 x 0.778) + (487.34 x 0.686)
= Tshs 368.33 / (308.70 + 321.31 + 334.32)
= Tshs 368.33 / 964.33
= 38.20%
178
166 :Investment
InvestmentDecisions
Decisions
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6. Identify, evaluate and explain the impact of non-financial factors such as economic, social
and environmental issues on making an appropriate investment decision.
[Learning Outcome f]
6.1 Non-financial factors in the selection of projects
After the quantitative analysis is completed, management then need to make a decision on which project (s) to
implement or whether the project being reviewed should be accepted or not. However, management will not
automatically base this decision purely on whether the project has a positive NPV or whether one alternative
has a higher overall return than other projects. In this decision, they will need to take into account non-financial
factors that may affect the project (s).
A company has used the NPV method of appraisal on Project X, which has a positive NPV and therefore,
financially will increase the value of the company. However, the project involves some damage to the
environment, and this factor alone can change the decision to accept the project, due to the adverse impact it
will have on the company’s image.
Essentially, these qualitative or non-financial factors are those that management would ideally like to include in
the quantitative analysis but are unable to do so because they are difficult, if not impossible to measure in monetary
terms. For this reason, the non-financial factors are assessed separately, after the financial analysis of the
project or alternatives has been completed.
It should not be assumed that non-financial factors are less important than financial factors, as a non-financial
factor can play a vital role in the project selection process.
A company is looking to replace old trucks with a new model, whereby the NPV to replace in 2 years time is slightly
higher than the NPV of replacing trucks immediately. However, management chooses to replace the trucks
immediately because of non-financial factors such as wanting to maintain a modern image for the company, and
the improved satisfaction leading to improved productivity of the drivers.
There are many non-financial factors that impact an appropriate investment decision being made, which differs
from company to company as well as project to project, as it is influenced by the relevant strategies and policies
embedded into the company. Below is a list of some of these non-financial factors:
1. Legal issues: any legal issues the company may face as a result of undertaking the project, e.g. whether
the project will meet the requirements of current and future legislation etc.
2. Ethical issues: a project may be legal, but if the actions involved in the project are deemed unethical, this
can have severe adverse impact on the company’s image and reputation.
3. Industry issues: e.g. does the project conform to industry standards and good practice.
4. Government regulation: this can include various regulations such as employment laws, environmental law,
competition law and also planning permissions given by local governments etc.
5. Environmental issues: e.g. will the project have an adverse impact on the surrounding environment.
6. Strategy of company: consideration needs to be given as to whether the project is in-line with the aims
and objectives of the business.
7. Impact on various relationships: will the project lead to improved staff morale, better relations with
suppliers, customers and local community.
8. Developing the skills of the company: will the project lead to an increase in skills and experience in a
particular field, which overall leads to stronger capabilities.
Within this Study Guide, the focus will be on three significant non-financial factors of economic, social and
environmental issues. It is worth noting, that a number of factors are interrelated, as often issues impacting one
© GTG
will also impact another factor.
Complex Investment Appraisal: 179
Complex Investment Appraisal: 167
6.2 Economic issues in making appropriate investment decisions
Some of the economic factors that need to be taken into consideration in making appropriate investment decisions
include inflation, recession, interest rates, exchange rates if applicable, and wage rates. It can be seen that
in the last decade, the economy has shown great volatility and for this reason, these factors are to be considered
as part of any decision taken to accept and implement a project.
1. Inflation
As already noted in the earlier section of this Study Guide, cash flows and the discount rate need to be reflective
of the impact of inflation. Therefore, significant instability in inflation rate can lead to higher risk of a project. In
cases of recession, when inflation can vary significantly, management may deem the risk of change to the rate
too high to accept a project, even if a positive NPV is calculated.
A company has estimated cash flows for project X and the discount rate used is the nominal rate, being the real
rate and the inflation rate combined. The inflation rate applied is 4% and gives an NPV of Tshs 3.3 million; however,
the current economic environment is such that the inflation rate could change dramatically. Therefore,
management have decided not to accept the project as even small volatility in the inflation rate could lead to the
project giving negative net present value.
2. Interest rates
This has already been seen to impact the discount rate as it is part of the cost of capital calculation. Therefore,
this economic factor will also need to be taken into consideration prior to accepting or rejecting a project.
A company is looking to implement a new project which, based on NPV calculations, is profitable. The cost of
capital applied is based on the current rates; however, recent economic updates have shown that the interest
rates are expected to rise significantly. Management of the company have decided that the project will be rejected
as it does not want to take a risk that the cost of finance increases so much that it is unable to fulfil its debts and
that the project will no longer be financially viable.
3. Exchange rates
In certain circumstances, a company may be impacted by exchange rates, for example, if it is choosing to open
up a branch in another country. In these situations, the company will consider the fluctuation of the exchange for
the applicable currency, prior to making any investment decision. The NPV of a project may appear viable under
one rate, however, the smallest fluctuation could have significant impact on the cash flows, leading to the
project being unviable and not increasing shareholder value. Again, the uncertainty in the movement may lead
to a decision to reject a project.
4. Wage rates
A change in the wage rates can impact project appraisal. If a company has performed projections going forward
for current business or estimated cash flows for a new project, which is labour intensive, the change in
legislation over wages in its current economy can have a significant impact on the results. For example, legislation
announces a new minimum wage which is significantly higher than current wages paid to the employees - this will
reduce the profit levels of the company.
6.3 Social issues in making appropriate investment decisions
Social factors are those that influence or control people’s identity including personality, attitudes and lifestyle in
a given society. These can include education level, financial status, religion, locality, family etc. Social factors
that need to be taken into consideration as part of the decision-making process can be split into two categories:
1. Internal factors; such as the demographics and lifestyle
2. External factors; which include the social costs and benefits
180 Investment Decisions
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1. Internal social factors
Internal social factors need to be considered by companies as part of any investment decision as follows:
(a) Working population demographic
The general age range within the population is important to firms. For example, if a company was looking to
start a new project in the area, it will require a location where there are sufficient workers at the required skill level
being available.
(b) Population structure demographic
Depending on what market the company is targeting their products to, the structure of the population becomes
significant. For example, different age groups look to purchase different products; therefore, changes in the
structure of the population will impact the demand levels for the product or service.
(c) Lifestyle trends
Fashion and trends change constantly, so companies involved in this type of industry need to continuously remain
updated and react to change quickly.
In recent years, there has been a trend from eating take-away food to more healthy options. Many new brands
and stores have opened for organic food, as people wants to eat natural produce.
(d) Lifestyle beliefs and attitudes
These societal beliefs and attitudes are followed by those within the area, as it is the accepted behaviours. A
company looking to start a new project needs to be aware of the beliefs and attitudes of their consumer market.
Groups of people believe animal testing of products is morally wrong, and therefore, would only purchase products
that have not been tested on animals.
2. External social factors
External social factors need to be considered by companies as part of any investment decision, especially with
the rise in social media as follows:
Reputational factors
In recent years, for a company to be seen as acting in a socially responsible way has become of significant
relevance. If a company is known or shown in the media for not acting in a socially acceptable manner, this can
have a significant impact on the reputation and image of the company, leading to decrease in return to the
shareholders.
A construction company is looking to build a commercial building near a residential area. The local community is
not happy with the plans of having a large building for commercial use in their vicinity, mainly as it will change
the environment in the area. Moreover, during the construction stage, there will be significant noise pollution for
a substantial period of time. The decision to build a commercial building in a residential area would cause
disturbance, and hence, can hinder the company reputation.
© GTG
Complex Investment Appraisal: 181
Complex Investment Appraisal: 169
6.4 Environmental issues in making appropriate investment decisions
Social and environmental issues are often reviewed together, as some factors are similar such as reputational
impact. The impact on the environment has become a focal point for many organisations, with the need to state
products to be ‘environmentally friendly’ as this is what the consumers are looking for. If companies are seen to
be doing some good towards the environment, this is to their benefit, as it leads to stronger brand image and
reputation.
Below are some more common environmental factors and the impact they can have on making appropriate
investment decisions:
(a) Energy usage
If a company requires significant use of scarce resources for production, this has an impact on the environment
as scarce resources are being used up. Companies that fall under this category need to ensure they are making
optimum usage of the resources available, with minimum wastage and there should be some level of monitoring
over the quantity of energy being consumed.
(b) Water usage
Many organisations across the globe are faced with limited supply of water. The strain of these resources during
different times of the year can impact those businesses where this resource is required in substantial quantities.
A large water company supplying water to millions of residents has launched a new programme, where it works
with third parties, with the aim to reduce capital expenditure on water treatment plants by working with the local
environment, land owners and land users to improve the quality of water.
(c) Air pollution
There is now a huge focus on air pollution and monitoring of the level of emissions in the air, resulting in
improvement in the quality of air seen in many countries such as Japan, US and Europe. Carbon emissions
monitoring is an example of this, with companies emitting large quantities of polluting gases required to pay
large fines, which has the effect of encouraging companies to be more conscious of the air pollution they cause.
This non-financial factor will impact the investment decision, as a company looking to manufacture will need to
consider the additional environmental cost, and even if it is a non-manufacturing company, the use of vans, cars
etc. all have an impact.
An audit firm, which includes a number of employees who are required to travel daily to client sites, have introduced
a car share scheme. This scheme was introduced to reduce the level of carbon emissions from cars polluting the
air, as instead of two cars travelling to the same location, only one would be used.
The same audit firm is open to employees ‘working from home’, so long as they have the resources available, and
can be contacted as and when required. The audit firm encourages this style of working, as there are no emissions
because no travel is involved.
As highlighted above, social, economic and environmental factors are of great importance in the investment
appraisal decision making, as they should be assessed together with the financial information. The non-financial
factors can be considered by management and sometimes even quantified, but the assessment is not reliable,
which is why it cannot be included in the cash flow estimation. Some of these factors include intangible aspects,
such as impact on reputation and image of the company.
182 Investment Decisions
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The following are examples or statements relating to social, economic or environmental issues. State which
issue each of the following statement relates to:
(a) An employee has recently purchased a car with higher fuel consumption and uses it on a daily basis.
(b) A local government is looking to build a new road through a current green land area.
(c) Inflation rate has risen to its highest point in history.
(d) A woman has gone shopping and picks up an apple and asks herself ‘I wonder if this is organically grown?’
(e) A person is looking to get a loan to start a new business venture, but the uncertainty of interest rates is
causing concern.
Answers to Test Yourself
Answer to TY 1
The information in the scenario above is limited, but in general it is possible to identify at least three potential
limitations or issues that may arise in the evaluation process of this project:
1. Lack of experience of the management account
The management accountant has only two years of experience in finance, and therefore, the probability of error in
the estimation of cash flows becomes higher. Also, it is unknown whether he/she has much experience in using
the net present value method of calculation of the project’s viability.
2. Source of information
The quality and accuracy of calculations is based on the source of information. For example, to reflect the
impact of inflation on the projections and on the discount rate, depending on how the rate is calculated, it can vary
the results significantly, as can the fact that whether an average rate is applied or current rate.
3. Limitations of IT
The company may not have suitable IT packages that aid the estimation of the cash flow process, therefore, the
management accountant may only be able to use simple applications such as excel, which may restrict the
accuracy of the calculation.
Other suitable responses to the question:
1. Quality of information
When the management accountant prepares the cash flow estimations, it may not be of a good standard as
regards quality. The presentation of the information may be unclear, with details of assumptions made and sources
of information not noted.
2. Availability of sources of information
The source of information may be limited in relation to this project especially if the project is one that has never
been undertaken in the past.
3. Bias in opinions of management accountant
The management accountant may appraise the project in a manner that is to his own particular advantage, leading
to risk of bias in the information presented.
Complex Investment Appraisal: 183
Complex Investment Appraisal: 175
© GTG
Sensitivity Analysis
Analysis of NPV calculation
PV
Tshs
000’s
2,489,600
(1,556,000)
933,600
(147,820)
(690,000)
95,780
Sales revenue (20,000 x Tshs 32,000) x 3.890
Variable costs (20,000 x Tshs 20,000) x 3.890
Contribution
Fixed costs ( Tshs 38,000,000 x
3.890) Initial investment
NPV
Cumulative present value factor at 9% for 5 years is 3.890. The NPV is currently Tshs 95,780,000 (positive) hence
the decision to invest is justified from a financial perspective. If the decision is to change, the NPV must fall by at
least Tshs 95,780,000.
Sensitivity Analysis
1. Sales revenue
Sales revenue (PV) must fall by at least Tshs 95,780,000
% decrease = 95,780,000/2,489,600,000 = 3.8%
2. Selling price
If sales revenue must fall by 3.8%, selling price must fall by Tshs 1,216 (3.8% x Tshs 32,000).
3. Sales volume
Since sales volume affects the level of contribution, the change in contribution must be calculated first.
Required decrease in contribution = 95,780,000/933,600,000 = 10.26%
Required decrease in sales volume = 10.26% of 20,000 = 2,052
4. Variable costs
Required increase in variable cost = 95,780,000/1,556,000,000 = 6.15%
Increase per unit = 6.15% of Tshs 20,000 = Tshs 1,231
Answer to TY 3
Step 1: The present value of various cash flows
Year
1
1
1
2
2
Economic
Conditions
Weak
Moderate
Good
Moderate
Good
Cash Flow
Tshs 000’s
150,000
300,000
450,000
375,000
525,000
14% Disc Fact.
0.877
0.877
0.877
0.769
0.769
PV
Tshs
000’s
131,550
263,100
394,650
288,375
403,725
Step 2: Combined PV of cash flows for Year 1 and Year 2
Year 1
Economic
Conditions
Weak
Weak
Moderate
Moderate
Good
Good
PV of
cash flow
Tshs
000’s
131,550
131,550
263,100
263,100
394,650
394,650
Year 2
Economic
Conditions
Moderate
Good
Moderate
Good
Moderate
Good
PV of cash
flow Tshs
000’s
288,375
403,725
288,375
403,725
288,375
403,725
Total PV of
cash flow
Tshs 000’s
419,925
535,275
551,475
666,825
683,025
798,375
184
Investment Decisions
176: Investment Decisions
Step 3: Multiply the present value of both combinations by the Joint Probability
Total PV of
cash flow
Tshs 000’s
419,925
535,275
551,475
666,825
683,025
798,375
Year 1
Probability (a)
Year 2
Probability (b)
0.3
0.3
0.5
0.5
0.2
0.2
0.7
0.3
0.7
0.3
0.7
0.3
Expected present value of cash inflows
Less: Initial Investment
Expected value of NPV
Joint
Probability
(a x b)
0.21
0.09
0.35
0.15
0.14
0.06
© GTG
Expected PV
of cash flows
Tshs
000’s
88,184
48,175
193,016
100,024
95,624
47,903
572,926
Tshs
000’s
572,926
470,000
102,926
An indication that the project will have a negative NPV is that the total present value of cash flows is less than
Tshs 470,000,000. So, from the Total PV of cash flow column; select the values less than Tshs 470,000,000.
Therefore, the probability that the project will have a negative NPV is 0.21 or 21%.
Alternative calculation
Year 1 expected cash flow = (150,000,000 x 0.3) + (300,000,000 x 0.5) + (450,000,000 x 0.2) = Tshs
285,000,000
Year 2 expected cash flow = (375,000,000 x 0.7) + (525,000,000 x 0.3) = Tshs 420,000,000
NPV = ( Tshs 285,000,000 x 0.877) + ( Tshs 420,000,000 x 0.769) – Tshs 470,000,000 = Tshs 102,925,000
Answer to TY 4
Step 1: Calculate the expected net present value of the project
Probability
0.10
0.15
0.20
0.25
0.30
Cash flow
Tshs 000’s
(75,000)
21,000
27,000
23,000
17,000
Expected value
Tshs
000’s(7,500)
3,150
5,400
5,750
5,100
11,900
𝑥𝑥̅ = 11,900,000
EV of NPV (X)
Probability (p)
Tshs 000's
(7,500)
3,150
5,400
5,750
5,100
0.10
0.15
0.20
0.25
0.30
𝑥𝑥
− 𝑥𝑥̅
Tshs 000's
(19,400)
(8,750)
(6,500)
(6,150)
(6,800)
Standard deviation
S=√80,898,000 = 𝑇𝑇𝑇𝑇ℎ𝑠𝑠 8,994,332
Expected NPV = Tshs 11,900,000
Standard deviation = Tshs 8,994,332
𝑃𝑃(𝑥𝑥 − 𝑥𝑥̅ )2
Tshs 000's
37,636,000
11,484,375
8,450,000
9,455,625
13,872,000
80,898,000
Complex Investment Appraisal: 185
© GTG
Complex Investment Appraisal: 175
NPV calculation
Year
Capital ( Tshs 000’s)
Working capital ( Tshs 000’s)
(W2) Net operating cash flows (
Tshs 000’s) (W3)
Net cash flow ( Tshs 000’s)
16% discount factors
0
(600,000)
(396,000)
Present value ( Tshs 000’s)
(996,000)
(996,000)
1.000
1
(240,000)
(23,760)
2
3
4
(25,186)
(26,697)
471,642
442,500
413,990
381,714
344,315
178,740
0.862
(1/1.16)
154,074
388,804
0.743
(0.862/1.16)
288,881
355,017
0.641
(0.743/1.16)
227,566
815,957
0.552
(0.641/1.16)
450,408
NPV = Tshs 124,929,000
1.08 x 1.074 = 1.16. This gives the discount factor of 16%.
As the NPV is positive, the project can be selected on financial grounds. Since the NPV is not high, however,
we must take care to ensure the forecasts and estimates are as accurate as possible. In particular, an increase
in inflation during the life of the project might make the project uneconomical. Sensitivity analysis can be used to
determine the key project variables on which success may depend.
Workings
W1 Fixed costs
Depreciation is not a cash flow: we must deduct it from the total fixed costs to arrive at the cash fixed costs:
Cash fixed costs per year = Tshs 660,000,000 – Tshs 216,000,000 = Tshs 444,000,000
Year
1
2
3
4
Inflation
1.05
1.05
1.05
1.05
Fixed Costs
Tshs 000’s
444,000
466,200
489,510
513,986
Inflated Costs
Tshs
000’s
466,200
489,510
513,986
539,685
W2 Working Capital
Investment in working capital in Year 0 = Tshs 396,000,000
Year
0
1
2
3
Rate of
Increase
Working
Capital
Tshs 000’s
396,000
396,000
419,760
444,946
N/A
6%
6%
6%
Increase
Tshs
000’s
396,000
23,760
25,186
26,697
Cumulative
WC Tshs
000’s
396,000
419,760
444,946
471,642
Cumulative investment in working capital recovered at the end of Year 4 = Tshs 471,642,000
W3 Net operating cash flows
Year
A
B
C
D
E
Inflated Selling price per unit
Less: Inflated Variable cost per unit
Contribution per unit (a-b)
Total Contribution per year (130,000 units x con/unit)
Fixed costs per year (W1)
Net operating cash flow
1
Tshs
000’
s
26.25
(19.26)
6.99
908,700
(466,200)
442,500
2
Tshs
000’
s27.56
(20.61)
6.95
903,500
(489,510)
413,990
3
Tshs
000’
s28.94
(22.05)
6.89
895,700
(513,986)
381,714
4
Tshs
000’
s30.39
(23.59)
6.80
884,000
(539,685)
344,315
186 Investment Decisions
176: Investment Decisions
© GTG
NPV calculation
Year
0
Tshs
000’s
(200,000)
Initial cost
Tax saved on
capital
allowances (W1)
Tax paid on
balancing
charge
Annual savings
Tax paid on
savings @ 28%
Net cash flow
9% discount
factor
Present Values
1
Tshs
000’s
2
Tshs
000’s
14,000
10,500
3
Tshs
000’s
7,875
4
Tshs
000’s
5,906
5
Tshs
000’s
6
Tshs
000’s
4,430
10, 489
50,000
50,000
50,000
50,000
50,000
(14,000)
(14,000)
(14,000)
(14,000)
(14,000)
(200,000)
64,000
46,500
43,875
41,906
40,430
(3,511)
1.000
0.917
0.842
0.772
0.708
0.650
0.596
(200,000)
58,688
39,153
33,872
29,669
26,279
(2,093)
NPV = ( Tshs 14,432,000)
The NPV is negative; therefore, this proposal should not be accepted.
Workings
W1 Tax saved on capital allowances
Year
0
1
2
3
4
5
Written down Value
Tshs
000’s200,000
150,000
112,500
84,375
63,281
47,461
Capital allowance @ 25%
Tshs 000’s
50,000
37,500
28,125
21,094
15,820
Tax saved @28%
Tshs 000’s
14,000
10,500
7,875
5,906
4,430
Year of tax
savings
1
2
3
4
5
W2 Tax saved / paid on balancing allowance / charge
WDV year 5
Salvage value
Balancing allowance
Tax relief @ 28% (received in
year 6)
Tshs 000’s
47,461
(10,000)
37,461
10,489
Answer to TY 7
Gross cash flow
‘Before-tax discount factor' (W1)
‘After-tax discount factor’ (W2)
Present value using before tax discount factor ( Tshs 550,000,000 x 0.935)
(This is applicable only where a company has incurred losses and therefore does not have any
tax benefits from interest. In the exam, don’t use this unless specifically stated.)
Present value using after tax discount factor ( Tshs 550,000,000 x 0.956)
Workings
W1 Before-tax rate
1
Discount rate (factor) =(1 + 𝑟𝑟)𝑛𝑛
=
1
1+0.07
= 0.935
Tshs
000’s
550,000
0.935
0.956
514,250
525,800
Complex Investment Appraisal: 187
Complex Investment Appraisal: 175
© GTG
W2 After-tax rate
After-tax rate = Before-tax rate x (1 - Tax rate)
= 7% x (1 - 0.35)
= 7% x 0.65
= 4.55%
1
Discount rate (factor) =(1 + 𝑟𝑟)𝑛𝑛
176: Investment Decisions=
1
1+0.0455
© GTG
= 0.956
Answer to TY 8
1. Assumption: projects are divisible
Project
P
Q
R
S
T
Rank
1
2
3
4
Total
Required initial
investment
( Tshs 000’s)
(a) 50,000
150,000
25,000
100,000
50,000
NPV at appropriate cost
of capital ( Tshs 000’s)
(b)
10,000
17,500
8,000
12,500
15,000
Project
R
T
P
S
Profitability
index (b/a)
0.20
0.117
0.32
0.125
0.30
Ranking
3
5
1
4
2
Required Initial
( Tshs
000’s))
25,000
50,000
50,000
(1/4 of 100,000) 25,000
150,000
th
Therefore, the optimal combination of projects is R, T, P and 1/4 of S.
2. Assumption: projects are indivisible
Feasible
combinations
Q only
P,R
P,S
P,T
R,S
R,T
S,T
P,R,T
Aggregate of NPV's
( Tshs
000’s) 17,500
18,000
22,500
25,000
20,500
23,000
27,500
33,000
By inspection of the feasible combinations, we can say that the optimal project mix is P, R and T, as the
aggregate of their NPVs is the highest.
Answer to TY 9
The following shows the calculation and the NPV of the use of the machine as replacement for each of the 3
years. As the net present value of each year cannot be compared as they are based on different number of
years of expected lives, by assuming a constant chain of replacement, it is assumed that the machine is
replaced every year in perpetuity.
Year
1
2
Net present value of cash flows
calculation
(20,000) + (12,000 /1.1) + (16,000/1.1)
(20,000) + (12,000/1.1) + (11,500/1.1²) +
NPV (TSHS
000’s)
(a)
5,455
Calculation for
perpetuity
(b)
1.1 / (1.1) -1 = 11
NPV of
perpetuity
(a) x (b)
(TSHS000’s)
60,005
aggregate of their NPVs is the highest.
Answer to TY 9
The following shows the calculation and the NPV of the use of the machine as replacement for each of the 3
years.Investment
As the netDecisions
present value of each year cannot be compared as they are based on different number of
188
years of expected lives, by assuming a constant chain of replacement, it is assumed that the machine is
replaced every year in perpetuity.
Year
1
2
3
Net present value of cash flows
calculation
NPV (TSHS
000’s)
(a)
(20,000) + (12,000 /1.1) + (16,000/1.1)
(20,000) + (12,000/1.1) + (11,500/1.1²) +
(14,000/1.1²)
(20,000) + (12,000/1.1) + (11,500/1.1²) +
(11,000/1.1³) + (12,000/1.1³)
Calculation for
perpetuity
(b)
5,455
1.1 / (1.1) -1 = 11
NPV of
perpetuity
(a) x (b)
(TSHS000’s)
60,005
11,983
(1.1)²/ (1.1)² - 1 = 5.76
69,022
17,693
(1.1)³/ (1.1)³ -1 = 4.02
71,128
The results above show that the machine should be replaced after 3 years, which in this instance happens to be
its estimated
physical life, as this is when it maximises the project’s net present Complex
value forInvestment
a perpetual
chain of175
© GTG
Appraisal:
replacement or maximises its equivalent annual value.
Answer to TY 10
(a) Environmental issue:
The car consuming more fuel and also emitting harmful gases falls into the category of environmental factors.
(b) Environmental and/or social issue
Infrastructure will require trees being chopped down, and green land will no longer remain, which is an
environmental factor. However, the new road may also have a social impact, as it will cause disturbance to local
residents.
(c) Economic issue
Any news or impact to inflation rates relate to economic factors.
(d) Social issue
The recent trend is to be healthier and people look to purchase products that have been organically grown with
no pesticides etc, therefore, this is a lifestyle aspect falling into the social factor category.
(e) Economic issues
Any news or impact of interest rates relate to economic factors.
Quick Quiz
1. What is the difference between the real and nominal rate of return?
2. If we are discounting real cash flows, we should use the
cost of capital for discounting.
(a) real
(b) nominal
3. Are interest payments the relevant cash flows for discounting purposes?
4. How is the after-tax discount rate calculated?
5. What is the difference between risk and uncertainty?
6. Sensitivity analysis verifies the effect of changes in all the variables at a time. True or false?
7. What is a certainty equivalent approach?
Complex Investment Appraisal: 189
© GTG
178: Investment Decisions
8. Find the expected NPV from the following :
Probability
0.25
0.40
0.35
Cash flow
Tshs 000’s
200,000
300,000
100,000
9. Why is the risk adjusted discount rate higher than the normal rate?
Answers to Quick Quiz
1. Real rates of return do not compensate the lender for inflation. Nominal rates incorporate real rates and inflation.
2. If we are discounting real cash flows, we should use the real cost of capital for discounting.
3. No, interest payments are not relevant as they are taken into account when the cost of capital is applied in
discounting.
4. The after-tax rate is calculated after deducting the amount of tax.
Formula: After-tax rate = Before-tax rate x (1 – Tax rate)
5. Risk refers to sets of circumstances which can be quantified and to which probabilities can be assigned, while,
uncertainty implies those probabilities that cannot be assigned to sets of circumstances or outcomes.
6. False, it analyses the effect of changes in one variable at a time.
7. In certainty equivalent approach, a certainty percentage is determined for the cash flows which are guaranteed,
and the cash flows are converted into their certainty equivalents. The NPV is then re-calculated using the
certainty equivalent cash flows.
8. Expected net present value = (0.25 x Tshs 200,000,000) + (0.40 x Tshs 300,000,000) + (0.35 x
Tshs 100,000,000) = Tshs 205,000,000.
9. The risk adjusted discount rate considers risk factors in addition to the time value of money. A premium is
added on to account for risk, therefore the rate becomes higher.
Self Examination Questions
Question 1
Cubic Ltd has decided to acquire an asset worth Tshs 2,000,000,000. The following two options are available:
(a) Acquire the asset by taking a bank loan @ 15% p.a. repayable in five yearly instalments of
Tshs 400,000,000 each plus interest or
(b) Lease the asset at yearly rentals of Tshs 648,000,000 for five years starting from the end of year 1.
In both cases, the instalment is payable at the end of the year. The rate of capital allowances applicable to the
company is 15% using the reducing balance method. The corporate tax rate is 35% and tax is paid one year
after the end of the accounting year in which the transaction occurs. Use the cost of borrowing as the company’s
cost of capital.
Suggest which method would be more financially viable for Cubic Ltd.
190
Investment Decisions
© GTG
Complex Investment Appraisal: 177
Question 2
A company has Tshs 12,000,000 available for investment. After evaluation of its options it has found that only 4
investment projects given below have positive NPVs. All these investments are divisible. Advise the management
as to which investment(s) / project(s) it should select.
Project
P
Q
R
S
Initial Investment
Tshs million
10.00
6.00
8.50
3.00
NPV
Tshs
million
0.40
0.60
1.70
1.30
Profitability
Index
1.20
1.25
1.60
1.30
Question 3
Cardiff Ltd is currently experiencing a period of capital rationing which it expects will only last for one year. The
amount of funds available for investments is restricted to Tshs 3.35b. After evaluating many projects, it has
selected the projects listed below. All the proposals of investment are independent. The selected project list
provides Gross present value, NPV, Investment outlays, and present value index.
Project
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
Investment outlay
Tshs
000s600,000
1,155,000
675,000
750,000
622,500
420,000
237,500
287,500
212,500
216,000
196,000
184,000
132,500
127,500
91,000
NPV
Tshs
000s 475,000
935,000
107,500
137,500
790,000
212,500
310,000
195,000
305,000
238,750
147,500
152,500
53,750
102,500
150,000
4,312,500
Gross present value
Tshs
000s
1,075,000
2,090,000
782,500
887,500
1,412,500
632,500
547,500
482,500
517,500
454,750
343,500
336,500
186,250
230,000
241,000
10,219,500
Present value index
1.79
1.81
1.16
1.18
2.27
1.51
2.31
1.68
2.44
2.11
1.75
1.83
1.41
1.80
2.65
Recommend the optimal investment policy in view of the financial restrictions.
Question 4
Snowball Inc wants to invest in a project costing Tshs 75,000,000 on 1January 20X5. The time span for the project
is 4 years after which the salvage value will be nil. In the first year, the net cash flows expected from the project
are Tshs 18,750,000 and Tshs 37,500,000 for each of the next three years.
The discount rate is 16% and the corporate tax rate is 28%.
Required:
Should the project be accepted post tax cash flows?
Complex Investment Appraisal: 191
Complex Investment Appraisal: 179
© GTG
Question 5
A firm is planning to buy a piece of equipment. The piece of equipment costs Tshs 27,000,000 and is projected
to produce cash flows of Tshs 9,000,000, Tshs 15,000,000 and Tshs 10,500,000 respectively over the next three
years.
The expected rate of inflation is 5% and the firm’s cost of capital is 14.30%.
Assume the tax rate applicable to the firm is 30%.
Required:
(a) Forecast cash flows in money terms and discount them at the nominal after tax cost of capital.
(b) Forecast cash flows at real cost of capital.
Question 6
GTL Ltd is considering an investment of Tshs 5.5b in a new production line with an expected life of four years.
The new product to be produced is expected to have a selling price of Tshs 8,700 each and variable costs of Tshs
5,600 per unit. It is estimated that 650,000 such products will be sold every year. The company’s cost of capital
is 10%. Ignoring taxes and capital allowances, determine the change required in each variable to produce
a zero NPV.
Answers to Self Examination Questions
Answer to SEQ 1
Note: the cash flows relating to interest and capital repayment will not appear in the NPV calculation as they are
non-relevant cash flows.
Option 1: Borrow to buy
NPV calculation
Note: Cash flows must be discounted using the after-tax cost of capital i.e.
15% x (1 - 0.35) = 9.75%, say 10%
Year
Initial Cost
Tax saved on CAs (W1)
DF 10%
PV
0
Tshs
(m)
(2,000)
1.000
(2,000)
1
Tshs
(m)
105
0.909
95
2
Tshs
(m)
89
0.826
74
3
Tshs
(m)
76
0.751
57
4
Tshs
(m)
64
0.683
44
5
Tshs
(m)
365
0.621
227
NPV = Tshs (1,503,000,000)
Option 2: Lease
Note: the after-tax cost of capital is used, and tax is lagged by one year. NPV calculation
Year
1-5
2-6
Cash flow
Lease payment
Tax saved @35% on Tshs 648,000,000
Tshs (m)
(648.0)
226.8
DF (10%)
3.791
*3.446
* Cumulative present value discount factor for 6 years at 10% = 4.355
Present value discount factor for 1 year at 10% = 0.909
4.355 – 0.909 = 3.446
NPV = Tshs (1,675,015,200)
Conclusion: It would be cheaper to buy the asset.
PV Tshs (m)
(2,456.568)
781.553
(1,675.015)
192 Investment Decisions
180 : Investment Decisions
© GTG
Workings
W1 Tax saved on capital allowances
Note: the machine will be purchased immediately. Tax benefit is available in the next year.
Written
Down Value
Tshs (m)
2,000
1,700
1,445
1,228
1,044
Year
0
1
2
3
4
Writing Down
Allowances @
15%
300
255
217
184
Tax saved @
35%
Year of tax
effect
105
89
76
64
1
2
3
4
No capital allowance given in the year of disposal.
Tax saved on balancing allowance
Tshs
(m)1,044
1,044
365
WDV of asset in year 4
Disposal proceeds
Balancing allowance
Tax saved @ 35%
Answer to SEQ 2
Arranging the projects in descending order of present value index.
Project
R
S
Q
P
Projects
R
S
Q(W1)
Rank
1
2
Investment outlay
Tshs
(m)
8.50
3
4
Profitability Index
3.00
1.60
1.30
6.00
10.00
1.25
1.20
Total investment
Tshs
(m)
8.5
3.0
0.5
Total NPV
Tshs (m)
1.70
1.30
0.05
12.0
3.05
NPV
Tshs
(m) 1.70
1.30
0.60
0.40
Accept Project in R and S in full and Q in part ( Tshs 500,000) as it will maximise the NPV.
Workings
W1
Proportionate NPV of project Q for Tshs 50,000
= Tshs 500,000 / Tshs 6,000,000 X Tshs 600,000
= Tshs 50,000
Complex Investment Appraisal: 193
Complex Investment Appraisal: 181
© GTG
Answer to SEQ 3
Initially, the investment projects should be arranged in a descending order of Present Value Index. The optimum
investment portfolio will be one which yields the maximum NPV
Accordingly, the projects are listed below:
Investment
outlay
Tshs 000’s
Project
(1)
O
I
G
E
J
L
B
N
A (W1)
K
H
F
M
D
C
(2)
91,000
212,500
237,500
622,500
216,000
184,000
1,155,000
127,500
600,000
196,000
287,500
420,000
132,500
750,000
675,000
Cumulative
Tshs 000’s
(3)
91,000
303,500
541,000
1,163,500
1,379,500
1,563,500
2,718,500
2,846,000
3,042,000
3,329,500
NPV
Tshs
000’s
(4)
150,000
305,000
310,000
790,000
238,750
152,500
935,000
102,500
475,000
147,500
195,000
212,500
53,750
137,500
107,500
Cumulative
Tshs 000’s
(5)
150,000
455,000
765,000
1,555,000
1,793,750
1,946,250
2,881,250
2,983,750
3,131,250
3,326,250
4,312,500
Gross
present
value
Tshs
000’s
(6)
241,000
517,500
547,500
1,412,500
454,750
336,500
2,090,000
230,000
1,075,000
343,500
482,500
632,500
186,250
887,500
782,500
PI = Gross
present
value/Investment
outlay
(7)
2.65
2.44
2.31
2.27
2.11
1.83
1.81
1.80
1.79
1.75
1.68
1.51
1.41
1.18
1.16
10,219,500
If the project is to be selected on the basis of profitability index, then first eight projects (from O to N) plus
project K and H have to be considered.
However, to yield a high NPV and to have an optimal investment package, projects from O to B plus project A
should be considered. The firm generates a higher NPV form these projects. It is shown below:
Investment
outlay
Project
O to B
A
600,000
Cumulative
Tshs 000s
2,718,500
3,318,500
NPV
Tshs
000’s
475,000
Cumulative
Tshs 000’s
2,881,250
3,356,250
Workings
W1
The company has Tshs 3.35b to invest.
Tshs 3.35b – Tshs 2.846b is 0.504b which less than
0.6b. Hence project A is not selected
Answer to SEQ 4
Year
0
1
2
3
4
1
Pre-tax
Cash flows
Tshs 000’s
(75,000)
18,750
37,500
37,500
37,500
2
Tax
28% Tshs
000’s
5,250
10,500
10,500
10,500
3
After-tax cash
flows Tshs
000’s
(75,000)
13,500
27,000
27,000
27,000
4
Discount
Factor @16%
1.000
0.862
0.743
0.641
0.552
5
PV pre-tax
Column(1 x 4)
Tshs 000’s
(75,000)
16,163
27,863
24,038
20,700
13,764
6
PV post-tax
(3 x 4) Tshs
000’s
(75,000)
11,637
20,061
17,307
14,904
(11,091)
194 Investment Decisions
182 : Investment Decisions
© GTG
Notes:
1. If the company is paying tax (as it does not have losses), then the post-tax figures are relevant. The net PV
is negative Tshs (11,091,000). Therefore, we can say that it is not economically viable to accept the project
after considering the cash flows post tax payment.
2. If we assume that the company is making losses and will not pay tax, we can accept the project as there is a
positive cash inflow of Tshs 13,764,000.
Answer to SEQ 5
(a) The nominal cost of capital i.e. money terms approach
After tax cost of capital = Before tax cost of capital X (1 - Tax rate)
= 14.30 X (1 - 0.30)
= 14.30 X 0.70
= 10.01%
Cash Flow Inflation
Year
Tshs
000's
0
(27,000.00)
1.000
1
9,000.00
1.050
2
15,000.00
1.103
3
10,500.00
1.158
Net present value
Actual Money Prices
Tshs 000's
(27,000.00)
9,450.00
16,545.00
12,159.00
10% Discount
Rate
1.000
0.909
0.826
0.751
(b) The real cost of capital i.e. real terms approach
Calculating the real cost of capital
(1+ n) = (1+ R) x (1+ i)
where,
R = Real rate of discount
n = Money cost of capital
i = Rate of inflation
Therefore, R =
Therefore, R =
Year
0
1
2
3
1+ n
-1
1+ i
1.143
1.05
- 1 = 0.089 or 8.9%
Cash Flow
Tshs 000’s
(27,000)
9,000
15,000
10,500
Real Discount Rate at 8.9%
n
1/(1+r)
1.000
0.918
0.843
0.774
PV
Tshs
000’s
(27,000)
8,262
12,645
8,127
2,034
Present Value
Tshs 000's
(27,000.00)
8,590.05
13,666.17
9,131.41
4,387.63
© GTG
Complex Investment Appraisal: 195
Complex Investment Appraisal: 183
The net present value of the project in terms of the project variables is as follows:
NPV = ((S - VC) x N x CPVF10, 4) – I0
Where
S
= Selling price p/u VC
= Variable cost p/u N
= Sales volume
CPVF10, 4 = Cumulative present value factor for four years at 10 per cent
I0
= Initial Investment
The cumulative present value factor for 4 years is 3.17
Step 1
Inserting the above information, we have
NPV = ((8,700 – 5,600) x 650,000 x 3.17) – 5,500,000,000 = Tshs 887,550,000
Step 2 Calculation of change needed in each variable to make NPV zero
(a) Initial Investment = [(8,700 – 5,600) × 650,000×3.17] – I0 = 0
Therefore, I0 = ((8,700 – 5,600) × 650000×3.17) = Tshs 6,387,550,000
There is an increase of 887,550 (6,387,550 – 5,500,000) or 16.13% in the planned initial investment, then NPV
will be zero.
(b) Sales Price
The following equation will apply
[(S – 5,600) × (650,000 ×3.17)] – 5,500,000,000 = 0
(S – 5,600) x 2,060,500 = 5,500,000,000
S – 5,600 = 2,669
S = Tshs 8,270
There is decrease of (8,700 – 8,270) 430 shillings or (430/8,700 x 100) 4.9% on the planned sales price.
(c) Variable cost: as there is a decrease of 430 shillings in the sales price which makes the NPV zero, an
increase of 430 shillings or (430/5,600 x 100) 7.7% will have same effect in variable cost.
(d) Sales Volume
[(8,700 – 5,600) × N ×3.17] – 5,500,000,000 = 0
3,100 x N x 3.17 = 5,500,000,000
9,827N = 5,500,000,000
N = 559,683
There is a decrease of 90,317 units (650,000 – 559,683) or 13.9% (90,317/650,000 x 100) on the planned sales
volume.
(e) Project discount rate: the cumulative present value factor that will make the NPV zero is as follows:
((8,700 – 5,600) × 650,000 x CPVF) – 5,500,000,000 = 0
CPVF = [5,500,000,000/ (8,700-5,600) x 650,000] = 2.73
2.73 correspond to an IRR of 17% (approx.), an increase in 7% (17-10) in absolute terms and 70% (7/10 x 100)
in relative terms.
196 Investment Decisions
184 : Investment Decisions
© GTG
Sensitivity Analysis of the investment proposed by GTL Ltd
Variable
Initial Investment
Sales Price
Variable Cost
Sales Volume
Project Discount Rate
Change to make NPV zero
+ Tshs 887,550,000
+16.13%
-430 shillings
-4.90%
+430 shilling
+7.70%
-90,317 units
-13.90%
+7%
+70.00%
Sensitivity
Low
High
High
Low
Very Low
Note: if a small change in a variable causes NPV to be zero, the sensitivity is said to be high. Similarly, a big
change in a variable causes NPV to be zero, then sensitivity is said to be low.
Indicative Examination Questions
IEQ 1
A new polishing machine is required. The polishing machine forms a part of the production process and
most products manufactured require polishing at various stages in their production. A polishing facility is
expected to be required for as long as the factory remains in operation and no closure can be anticipated.
Details of the two machines under consideration are:
Machine
A
B
Initial cost
TSHS5,000,000
TSHS9,000,000
Life – years
4
7
Salvage value at end of:
Year
– machine A
4
TSHS500,000
Year
– machine B
7
Annual running costs
TSHS700,000
TSHS1,000,000
TSHS800,000
Both machines fulfill the same function and have equal capacities. The appropriate discount rate is 10%.
Taxation may be ignored.
Required:
Determine which machine should be purchased. Specify any assumption made. To what amount would
the initial cost of Machine A be required to alter in order that the two machines were then of equal financial
attractiveness? (10 marks)
IEQ 2
a) Describe capital rationing and indicate ways in which it may arise. Explain the extent to
which: (i) project selection techniques; and (ii) the discount rate require modification under
conditions of capital rationing.
b) Comment on the practical and theoretical merits and limitations of: (i) ranking by rate of
return, and (ii) linear programming when selecting projects under conditions of capital
rationing.
(12 marks)
ComplexInvestment
InvestmentAppraisal:
Appraisal:185
197
Complex
© GTG
IEQ 3
Mabruk Company is considering investing Tshs . 35 million in a new machine with an expected life of five
years. The machine will have no scrap value at the end of the five years. It is expected that 20,000 units
will be sold each year at a selling price of Tshs . 2,100 per unit. Variable production costs are expected to
be Tshs . 1,150 per unit, while incremental fixed costs, mainly the wages of a maintenance engineer, are
expected to be Tshs . 7,000,000 per year. Mabruk Company uses a discount rate of 12% for investment
appraisal purposes and expects investment projects to recover their initial investment within two years.
REQUIRED:
Calculate the Net Present Value (NPV) of the project and evaluate the sensitivity of the project’s NPV to
a change in the following project variables:
(i)
(ii)
(iii)
(iv)
Sales revenue
Sales price
Sales volume
Variable cost
SEQ 4
KOBELO Company owns an equipment that is already 5 years old and the remaining useful life is
estimated at not more than three years. It is now 3l December 2016 and the equipment can be sold now
at its residual value. The following are the net cash flows and residual value estimates for the equipment
over the next three years:
End of Year
Net Cash Flow (Millions of
Residual Value (Millions of
TSHS)
TSHS)
2016
-
14
2017
10
8
2018
2
1
2019
1
0
The cost of capital for the firm is 10%.
A decision is to be made whether to abandon the equipment at the end of year 2017, 2018 or 2019.
i.
REQUIRED:
Evaluate and comment on the appropriate timing of abandoning the equipment (6 marks)
ii.
Discuss the difference between a nominal (money terms) approach and a real terms approach to
calculating net present value. (6 marks)
ŶƐǁĞƌƐƚŽIndicative Examination Questions
Machine
A
B
Initial cost
TSHS9,000,000
Life – years
7
Salvage value at end of:
198 Investment Decisions
186 : Investment Decisions
© GTG
Answer to IEQ 1
Present value of life cycle of each machine (in TSHS)
Machine A
Discounting Factor (10%) Present Value
Year
0
1–4
TSHS
TSHS
Initial Purchase
(5,000,000)
1
(5,000,000)
Running costs
(1,000,000)
3.17
(3,170,000)
500,000
0.683
341,500
4
Scrap
Net Present Value
(7,828,500)
Machine B
Discounting Factor (10%) Present Value
Year
TSHS
TSHS
0
Initial Purchase
(9,000,000)
1
(9,000,000)
1–7
Running costs
(800,000)
4.868
(3,894,400)
700,000
0.513
359,100
7
Scrap
Net Present Value
(12,535,300)
The approach adopted is to express the two alternatives in equivalent annual cost terms.
Equivalent annual cost = NPV/Equivalent Annual Cost
Machine A: Equivalent Annual Cost = 7,828,500/3.17 = TSHS2, 469,558 Machine B:
Equivalent Annual Cost = 12,535,300/4.868 = TSHS2, 575,041 Machine A has the
lower annual cost and therefore should be the one purchased. Assumptions:
·
Exactly similar new machines will continue to be purchased when old ones are scrapped into the
indefinite future i.e. no technological changes.
·
No inflation.
For the two machines to be equally attractive, machine A’s annual equivalent cost would have to increase
e to TSHS2,575,041 and its NPV = TSHS8,162,879.97 Since initial cost is not discounted then the initial
cost would have to increase by TSHS334,379.97
Answer to IEQ 2
Capital rationing is used to describe a situation in which either financial and/or non-financial constraints
preclude the acceptance of all projects with a positive net present value. Capital rationing may be brought
into being by a number of situations. First, by unwillingness on the part of management to go over its selfimposed borrowing or investment limits.Second, by unwillingness of lenders to lend further funds. Finally,
capital rationing may arise when costs of issue are so great as to fail to justify the issue of more equity or
the acquisition of further debt.
© GTG
Complex
ComplexInvestment
InvestmentAppraisal:
Appraisal:187
199
GTG
Investment
Appraisal:
187
The ©conditions
of capital rationing require modification of project selection Complex
techniques
and the
discount
The conditions of capital rationing require modification of project selection techniques and the discount
rate in the following ways. First, although the objective of project selection remains unchanged by capital
rate in the following ways. First, although the objective of project selection remains unchanged by capital
rationing the means of achieving those objectives are changed.
rationing the means of achieving those objectives are changed.
In the absence of capital rationing the objective can be achieved by accepting all projects which have a
In the absence of capital rationing the objective can be achieved by accepting all projects which have a
positive net present value. Where there is capital rationing, however, there is a need to maximize NPV
positive net present value. Where there is capital rationing, however, there is a need to maximize NPV
whilst remaining within the spending limits, and therefore some projects which high NPV’s may be rejected
whilst remaining within the spending limits, and therefore some projects which high NPV’s may be rejected
in order to obtain a portfolio of projects which maximize NPV.
in order to obtain a portfolio of projects which maximize NPV.
A simple approach to project selection under capital rationing is that of ranking by rate of return. In practice
A simple approach to project selection under capital rationing is that of ranking by rate of return. In practice
this is only feasible when the capital rationing is for a single period and not a multi-period; and in theory it
this is only feasible when the capital rationing is for a single period and not a multi-period; and in theory it
is evident that the rate of ranking approach is deficient in that it considers rate of return and treats projects
is evident that the rate of ranking approach is deficient in that it considers rate of return and treats projects
individually. In theory, linear programming is more suitable, but its weakness lies in the assumption that
individually. In theory, linear programming is more suitable, but its weakness lies in the assumption that
partial projects can be undertaken.
partial projects can be undertaken.
Answer IEQ 3
Answer IEQ 3
Project NPV
Project NPV
End of Year
End of Year
Initial Cash Inv.
Initial Cash Inv.
Sales Revenue
Sales Revenue
Variable Costs
Variable Costs
Fixed Costs
Fixed Costs
Net Cash Flow
Net Cash Flow
Discount Factor (at 12%)
Discount Factor (at 12%)
Present Value
Present Value
0
0
(35)
(35)
(35)
(35)
1
1
(35)
(35)
1
1
42
42
(23)
(23)
(7)
(7)
12
12
0.893
0.893
10.7
10.7
2
2
42
42
(23)
(23)
(7)
(7)
12
12
0.797
0.797
9.6
9.6
3
3
42
42
(23)
(23)
(7)
(7)
12
12
0.712
0.712
8.5
8.5
4
4
42
42
(23)
(23)
(7)
(7)
12
12
0.636
0.636
7.6
7.6
5
5
42
42
(23)
(23)
(7)
(7)
12
12
0.567
0.567
6.8
6.8
NPV = TSHS [10.7 + 9.6 + 8.5 + 7.6 + 6.8] – 35
NPV = TSHS [10.7 + 9.6 + 8.5 + 7.6 + 6.8] – 35
=TSHS8.2 million
=TSHS8.2 million
Sensitivity of Project NPV
Sensitivity of Project NPV
(i) Sensitivity of Sales Revenue
(i) Sensitivity
of Sales
Revenue
For the NPV
to equal
zero sales revenue must fall by 5.4%, namely by:
For the NPV to equal zero sales revenue must fall by 5.4%, namely by:
NPV/PV of Sales Revenue = TSHS8.2 million/TSHS42(3.605). The project will cease to be
NPV/PV
of Sales
Revenue
= TSHS8.2
million/TSHS42(3.605).
The project will cease to be
economically
viable
if sales revenue
fall by
more than 5.4%.
economically viable if sales revenue fall by more than 5.4%.
(ii) Sensitivity to Sales Price
(ii) Sensitivity to Sales Price
If sales revenue must fall by 5.4%, selling price must fall by TSHS2,100 x 5.4% = TSHS113.40.
If
sales revenue
must
fallfall
byby
5.4%,
selling
must fallthe
by TSHS2,100
x 5.4%
= TSHS113.40.
Should
the selling
price
more
than price
TSHS113.40
project will stop
to be
economically
Should the selling price fall by more than TSHS113.40 the project will stop to be economically
viable.
viable.
(iii) Sensitivity to Sales Volume
(iii) Sensitivity to Sales Volume
200 Investment Decisions
188 : Investment Decisions
© GTG
Since sales volume affects the level of contribution, the change in the contribution must be
calculated first.
Required Decrease in Contribution
=NPV/PV of Contribution
=TSHS8.2m/(TSHS19)(3.605) = 11.97%
Thus the required decrease in sales volume will be 11.97% x 20,000 = 2,394 units
(iv) Sensitivity to Variable cost
For the NPV to equal zero variable cost must increase by 9.9%, namely by:
NPV/PV of Variable Cost = TSHS8.2 million/TSHS23(3.605) = 9.9%
Answer to IEQ 4
Establishing the Appropriate Timing of Equipment Abandonment
Operating the Equipment for One More Year (to Year 2017
We calculate the NPV of the project assuming the operations continue for one more year and the firm
foregoes the net salvage value receivable at the end of year 2016
End of Year
2016 (0)
Net Cash Flows (millions of (14)
TSHS)
1
Discount Factor (10%)
Present Value
(14)
2017 (1)
10
0.909
2018
2
0.909
9.09
7.272
NPV = TSHS[9.09 + 7.272]m – TSHS14m = TSHS2.362m
Operating the Equipment for Two More Years (to Year 2018)
We calculate the NPV of the project assuming the operations continue for two more years and the
firm foregoes the net salvage value receivable at the end of year 2016.
End of Year
2016 (0)
Net Cash Flows (millions of (14)
TSHS)
1
Discount Factor (10%)
Present Value
(14)
2017 (1)
10
0.909
2018(2)
2
0.909
2018(2)
1
0.826
9.09
7.652
0.826
NPV= TSHS[9.09 + 1.652 + 0.826]m – TSHS2,432m
Operating the Equipment for Three More Years (to Year 2019)
We calculate the NPV of the project assuming the operations continue for three more years and
the firm foregoes the net salvage value receivable at the end of year 2016.
End of Year
2016 (0)
Net Cash Flows (millions of (14)
TSHS)
1
Discount Factor (10%)
Present Value
(14)
2017 (1)
10
0.909
2018(2)
2
0.826
2018(3)
1
0.751
9.09
7.652
0.751
NPV= TSHS[9.09 + 1.652 + 0.751]m – TSHS14m = -TSHS2.507m
Comment: the NPV of the equipment if it is to be operated for one more year is positive. Thus, the
equipment should operate for one more year to 2017 and abandoned.
(b)
Nominal vs. Real Money Terms Approach
NPV= TSHS[9.09 + 1.652 + 0.751]m – TSHS14m = -TSHS2.507m
Comment: the NPV of the equipment if it is to be operated for one more year is positive. Thus, the
equipment should operate for one more year to 2017 and abandoned.Complex Investment Appraisal: 201
(b)
Nominal vs. Real Money Terms Approach
© GTG
Complex Investment Appraisal: 189
A nominal (money terms) approach to investment appraisal discounts nominal cash flows with a
nominal cost of capital. Nominal cash flows are found by inflating forecast values from current price
estimates, for example, using specific inflation. Applying specific inflation means that different
project cash flows are inflated by different inflation rates in order to generate nominal project cash
flows. A real terms approach to investment appraisal discounts real cash flows with a real cost of
capital. Real ash s flows are found by deflating nominal cash flows by the general rate of inflation.
The real cost of capital is found by deflating the nominal cost of capital by the general rate of
inflation, using the Fisher equation:
(1+ real discount rate) x (1 + inflation rate) = (1 + nominal discount rate)
The net present value for an investment project does not depend on whether a nominal terms
approach or a real terms approach is adopted, since nominal cash flows and the nominal discount
rate are both discounted by the general rate of inflation to give real cash flows and the real discount
rate, respectively. Both approaches give the same net present value.
202 Investment Decisions
C3
SECTION C
Investments in Securities and Portfolio Theory: 203
INVESTMENT DECISIONS
STUDY GUIDE C3: INVESTMENTS IN
SECURITIES AND PORTFOLIO THEORY
Investors aim to maximise returns by investing in a basket of securities. The securities could range from fixed
income instruments like deposits, bonds to market linked securities like equity, debentures to speculative
instruments like derivatives. Securities essentially comprise financial assets. Apart from this, the individual
would also hold real / physical assets like gold, real estate etc which is a separate asset class.
The investor can expect a certain rate of return from his portfolio of securities depending on his risk appetite and
time horizon. The risk appetite would depend on various factors, the most important being the investor’s stage in
the life cycle. Portfolio managers strive to achieve the investment objective by building, monitoring and rebalancing portfolios.
In this Study Guide, we shall discuss the portfolio management process, investor’s objectives, and asset allocation
strategies. We can also discuss portfolio theories on how to optimise risk and return.
a) Discuss the portfolio investment and management process, indifference curves and investor preferences,
investment policies and strategies.
b) Identify the objectives and constraints of individual investors.
c) Discuss the theory of portfolio allocation – asset allocation across risky and risk- free assets.
d) Discuss the principle of diversification – the Markowitz portfolio theory.
e) Determine the minimum variance portfolio and efficient frontier.
f) Describe the capital market line and the separation theory.
204
186 :Investment
InvestmentDecisions
Decisions
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1. Discuss the portfolio investment and management process, indifference curves and investor
preferences, investment policies and strategies.
[Learning Outcome, a]
1.1 Portfolio investment and management process
Portfolio management is the process of identifying, constructing, monitoring and re-balancing a basket of securities
woven together to achieve a stated investment objective.
Portfolio management involves balancing both risk and return. Each security belongs to a different
asset class. It is important for the portfolio manager to determine the allocation among different asset
classes.
Let’s discuss the steps involved in portfolio investment and management process:
1. Listing the investment objectives and constraints
The first step in the process of portfolio management is to clearly spell out the investment policy i.e. the investor’s
objectives along with the constraints. It is very important that a clear-cut outline is laid down of what the process
strives to achieve.
This is essential to:
(a) ensure that both the investor and the portfolio manager share a common understanding of what is expected
from the investment.
(b) provide a benchmark against which the portfolio can be evaluated in terms of both risk and return.
(c) remove any ambiguity that may exist and acts as a moral check on the portfolio manager to ensure that he
/she functions within the framework of the stated policy. It is a disciplinary tool to guide against any
deviations the portfolio might take against the stated objectives.
(d) Act as a planning aid as it helps the investor understand his needs better. The investor has to have a clear
understanding of financial markets and products as well as the risks associated with each class. This first step
ensures sufficient research and planning by both the investor and the portfolio manager to ensure that the
steps which follow are meaningful.
2. Market study and outlining of strategies
In this phase the manager has to do a detailed study of macroeconomic situation, financial background, policy
updates, financial markets / products etc. There is a constant change in each of these factors and it is critical for
the manager to have thorough knowledge of the macro parameters before going into the micro analysis of
securities and portfolio. The phase of the economy, the state of financial markets, the short term and mediumterm outlooks will determine the investment strategy.
3. Constructing the portfolio
This step involves the following:
(a) Portfolio allocation
Based on the investment strategy and macro analysis, the decision as regards allocation of funds across
different asset classes is made. The different asset classes would-be short-term instruments, equity, derivatives,
fixed income instruments.
Mr. X is a well placed professional aged 30 years. He may choose an aggressive strategy (with high return
expectation and high-risk appetite) and accordingly the portfolio manager may allocate up to 80-85% of the
portfolio to equity.
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(b) Analysis of securities
This process involves detailed analysis of securities in terms of both fundamental and technical factors. Security
analysis involves evaluating the risk-return features of individual securities and the correlation between
them.
(i) Fundamental analysis involves analysing the financial position of the company (in terms of EPS, dividend
payout, price-earnings ratio, growth rates in revenue and profits), market share, industry analysis,
management capabilities etc. Based on the above the valuation of each share is done and compared with the
current market value. If the current market value is less than the above determined price, the manager sees
value in the security and decides to shortlist the security.
(ii) Technical analysis involves studying the share price movements and calculating trends in the prices.
(c) Portfolio build up
Based on the above analysis, the securities are selected and aggregated to each asset class and further to form
the portfolio. The portfolio has its own risk and reward features which not a simple aggregation of the individual
securities. It is computed based on the risk return characteristics of individual securities and the pair-wise
correlations among them.
(d) Portfolio Monitoring
Since portfolio management is a continuous process there is need for constant monitoring in following areas:
(i) Changes to investor preferences based on changes in financial markets, investor needs.
(ii) Portfolio performance is to be measured against desired results (in terms of returns earned and risk borne)
(iii) Any shortcomings in the selection process / portfolio build up needs to be identified.
1.2 Investment strategies
Before formulating the investment strategy, a detailed study is required of the investor background in terms of:
Age .i.e. stage in the life cycle

Need for regular income

Short term and long-term financial commitments

Tax incidence

Other assets (real / physical assets) which the investor holds

Risk tolerance .i.e. risk-taking appetite

Health and dependencies

Further, as explained in Para 1.1 of this Study Guide, the macro economic and financial parameters are evaluated,
and an investment strategy is outlined. The strategy would direct the portfolio management process in terms of:
1. Value investing .i.e. investing in those stocks which is considered a value preposition based on detailed
fundamental analysis
2. Revenue generation .i.e. based on the investor objective, attach more weightage to fixed income securities as
an asset class and to dividend paying companies under equities.
3. Growth investing .i.e. investing in those stocks where a future growth potential is foreseen and would
provide capital appreciation to investors at a future date.
4. Timing the investments to ensure that investments are procured at a fair price and not when the intrinsic value
has been fully factored in the share price by the markets.
5. Striking the right balance among various asset classes as laid down in the investor objectives
6. Evaluating transaction cost to ensure that excessive churning is not done of the portfolio resulting in high
transaction costs.
7. Ensuring that reasonable liquidity is maintained to support any purchases that may be warranted on an
immediate basis due to a, c and d strategies mentioned above.
8. Forecasting of tax implications and tax planning.
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1.3 Indifference curves and investor preferences
Indifference curve symbolises the choice of an investor as regards risk and return. .As each investor has a
different level of risk aversion; the risk–return tradeoff is different. Indifference curves are used in deciding on
the most preferred portfolio. The indifference curve can be plotted on a graph, where the X axis represents the
risk denoted by the variance and the Y-axis stands for the expected return.
Thus,

All portfolios that lie on the same indifference curve are equally desirable to the investor. They are parallel
to each other and the indifference curves do not intersect.

For an investor, any portfolio on an indifference curve further towards the right (north west) is more
desirable than any portfolio lying on an indifference curve that is "not as far northwest."
As investors are generally risk averse, a rational investor will choose that portfolio with the lowest variance given
the same return. Moreover, risk averse investors will not take on a risk where the expected payoff is zero. These
two assumptions of “non-satiation” and “risk aversion” make the indifference curves to be positively sloped.
Diagram 1: Indifference curves
Describe in brief the portfolio management process.
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2. Identify the objectives and constraints of individual investors.
[Learning Outcome b]
2.1 Investor objectives
An individual investor simplistically stated looks at maximisation of return. However, return cannot be measured
without evaluating the risk attached to the portfolio. Therefore, an investor has to express his objectives in terms
of both risk and return. An investor needs to discuss and evaluate his risk appetite.
The objectives of individual investors can be one / more of the following:
1. Regular income: The investor looks at generating regular income from the portfolio to meet his financial
requirements rather than accumulate wealth.
Mr. Jacob has received his retirement proceeds aggregating Tshs 125 million. He wishes to invest this in such a
manner that he is ensured a monthly income of Tshs 1-1.5 million to supplement his household expenses.
Therefore, the primary objective in this case is regular income rather than aggressive growth.
2. Capital protection: Under this objective the investor seeks to protect his capital and is generally risk
averse. He is not looking at supernormal returns with high risk. So long as the capital stands protected with
a reasonable return adjusted for inflation he is satisfied.
3. Aggressive growth: An investor with this objective wants the portfolio to grow over a period of time and is
willing to stay invested to achieve a high capital appreciation. He is willing to take the required risk to
achieve the above objective. He is looks at a significant growth in portfolio through combination of securities.
4. Diversification: The investor wishes to diversify across different securities and different industries so that
his risk is mitigated through diversification.
5. Marketability of securities: The securities should be readily tradable and converted to cash when desired.
No investor would wish that funds get locked in illiquid securities.
2.2 Investor constraints
There are certain constraints that affect the portfolio strategy. They are listed below:
1. Time frame for investments
An individual’s time horizon to stay invested depends on his / her stage in the life cycle which in turn affects the
risk appetite. In general, an investor who is in the age bracket of 25-35 years is willing to allow his portfolio to grow
over a longer period of time. Investors with shorter time horizon prefer less risky and more liquid securities. It is
only those with a longer- te rm horizon who are willing to take higher risks and remain invested to witness their
securities grow.
2. Liquidity requirements
An individual investor may be constrained by liquidity needs that emerge to meet their short-term fund
requirements. Although an investor may have a reasonable time frame any urgent domestic needs / emergencies
may shorten his investment horizon. He may be constrained to liquidate securities (by converting them to cash)
and utilise the proceeds to meet the immediate financial requirements.
Mr. Andrew is a businessman aged 30 years. He has built a personal portfolio of equity and debt instruments
and is looking at maximising returns through long term equity investments.
His business has met with sudden cash crunch due to fierce competition requiring infusion of additional funds.
This has constrained Andrew to liquidate part of his securities immediately although he sees substantial growth
potential in most of the shares.
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3. Specific needs / preferences
There may be specific preferences which an investor / community may have to a particular asset class, industry,
corporate which may bias his opinion and act as a hindrance to value investing.
Further some individuals are unable to devote sufficient time to portfolio analysis. Others may not have the
necessary expertise to support the same. This may lead to incorrect investments in the absence of guidance /
professional advice.
4. Taxation
Taxation lowers the yield that the portfolio earns. In a slab-based taxation structure, different individuals have
different tax incidence depending on their applicable slab. Further capital gains arising on sale of securities
whether short term / long term, for shares listed on the DSE or otherwise would be different.
There are certain investment proceeds which are exempt from tax and the portfolio manager should consider
inclusion of these by comparing their yield with the after-tax yield of other securities.
The after-tax yield on a security is calculated as:
Yield on security X (1 – marginal tax rate)
5. Regulatory Framework
The investor has to comply with all legal and regulatory factors that may influence his investments. If there are any
restrictions on withdrawal in respect of any investment for a specified period, the same has to be complied with.
Match the following:
Sr. No.
1.
2.
3.
Investor profile
60-year old retiring within one year
28-year old salaried employee with no fixed obligations
35-year old working professional
Primary Investment Objective
(a) Capital appreciation
(b) Regular income
(c) Aggressive growth
3. Discuss the theory of portfolio allocation – asset allocation across risky and risk- free
assets.
[Learning Outcome c]
One of the key decisions governing portfolio management is the (a) portfolio allocation across asset classes (b)
asset allocation across risky and risk-free assets.
3.1 Portfolio allocation across asset classes
From an overall perspective, portfolio allocation involves various asset classes. An asset class is a group of
securities which have similar characteristics. Based on the overall investment policy, the portfolio is allocated
across:
1. Real Estate: this is a primary form of physical asset which every individual hold which acts as a capital
protection. It can also serve as a security for any future borrowing requirements.
2. Gold: investment in gold is governed by individual preferences. It is an idle asset and is not put to any
productive use. Gold investments have taken a new form of exchange traded funds (ETF) which does away
with the requirement of holding physical gold.
3. Cash and short-term bank deposits: this is held to meet any immediate contingencies. It can also be utilised
to purchase any securities available at reasonable price at short notice.
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4. Debt instruments: this comprise of bonds, commercial papers, money market instruments. These are by
nature fixed income securities and can provide pre-determined cash flows.
However, debt instruments are subject to the following risks.
Credit risk

Liquidity risk

Rating risk

Interest rate risk

Regulatory risk

5. Equity or common stock: equity investments by their very nature are considered risky because of the inherent
market risk. There is uncertainty associated with the return that the stock would generate. Individuals with high
risk high return expectations allocate significant assets to equity.
Apart from above, an investor ensures that he has taken adequate insurance to provide for his family in the
event of any contingencies.
Portfolio (financial assets) allocations by investors with different risk appetite(s) are illustrated below:
Investment policy
Conservative
Balanced
Growth
Aggressive
Very aggressive
Cash equivalents
30%
10%
5%
10%
10%
Debt instruments
50%
40%
30%
20%
10%
The above percentages would be within a range of
± 5%
Equity
20%
50%
55%
70%
80%
3.2 Asset allocation across risky and risk-free assets
1. Concept of risk aversion
Risk aversion is the nature of an investor to avoid, risky investments. Investors normally have a desire to maximise
their return while taking the least amount of risk. When faced with two or more investment opportunities with
similar returns, an investor will always choose the investment with the least risk as there is no additional benefit in
choosing a higher level of risk unless there is also a potential for a higher level of return.
Investors in general will take on a higher risk for a higher return. However, they differ in the quantum of risk they
are prepared to take for a given return. Investors who are risk averse require a greater return for a given
amount of risk. Although investors differ in their ability to bear risk, they are usually consistent in their selection
of any portfolio in terms of the risk-return trade-off.
2. Measurement of risk
(a) Risk associated with an asset can be measured based on behavioural aspects and statistical analysis.
Study of behavioural aspects involves:
(i) Sensitivity analysis: where all the possible outcomes are estimated. A possible approach is to estimate
the optimistic, pessimistic and most likely returns associated with each asset. The risk in this case is the range
between the optimistic and pessimistic values.
(ii) Probability distribution: Under this approach a probability is assigned to each possible outcome. Then the
expected value of the return is calculated by multiplying the possible returns with the respective probabilities.
The expected return is expressed as 𝑛𝑛
𝑅𝑅̅ = ∑ 𝑅𝑅𝑖𝑖 − 𝑃𝑃𝑃𝑃𝑖𝑖 𝑡𝑡=1
Where,
th
Ri is the return for the i possible outcome
Pri is the probability attached to its return
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Possible outcomes
Shares of A Ltd.
Recession
Normal
Boom
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Return (a)
Probability (b)
15%
18%
20%
Expected return (a)X (b)
0.30
0.50
0.20
4.5%
9.0%
4.0%
17.5%
(b) Statistical analysis involves measurement of standard deviation and coefficient of variation
(i) Standard deviation
The most common measure of risk is the standard deviation from the expected value of return. It is calculated
as follows
𝑛𝑛
𝜎𝜎 = √∑(𝑅𝑅𝑖𝑖 − 𝑅𝑅̅ ) × 𝑃𝑃𝑃𝑃𝑖𝑖 𝑖𝑖=𝑖𝑖
 = Standard deviation
Ri = expected return
R = mean of expected returns
Pri = probability of earning the return
Standard deviation of returns
Asset A
I
Ri
1
2
3
12%
14%
16%
Standard deviation =
Ri − R
R
14%
14%
14%
Ri − R
2
(2%)
0
2
Ri − R
Pri
4
0
4
2
X Pr
0.3
0.5
0.2
i
1.2
0
0.8
2.0
2 = 1.41%
Asset B
I
1
2
3
Ri
Ri − R
R
10%
15%
20%
15%
15%
15%
(5%)
0
5
Ri − R
2
Ri − R
Pri
25
0
25
0.3
0.4
0.3
2
X Pr
i
7.5
0
7.5
15.0
Standard deviation = 15 = 3.87%
Greater the standard deviation, greater is the risk of the asset. It is an absolute measure. Therefore it is not
suitable for evaluating the risk around varied assets if they differ in the size of expected returns.
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(ii) Coefficient of variation
Coefficient of variation converts standard deviation of expected returns into relative values to facilitate comparision
of risks among assets having different expected values. It is a relative measure of dispersion. It is computed as
follows:
σr
CV =
R
CV = coefficient of variation
= Standard deviation
R = mean of expected returns
In the above example CV for Assets A and B are 0.10(1.41/14) and 0.258 (3.87/15). The larger the coefficient of
variation, larger is the risk.
Compare the below two assets on their risk measure.
I
1
2
3
Asset X
Return
8
16
24
probability
0.3
0.4
0.3
Return
Asset Y
probability
10
0.2
20
0.6
15
0.2
4. Discuss the principle of diversification – the Markowitz portfolio theory.
[Learning Outcome d]
The modern portfolio theory was developed by Harry Markowitz in the early 1950s. This theory shows that portfolio
risk is not a simple aggregation of risks of individual assets. It depends on the contribution it makes to the investor’s
overall risk. This theory provides a platform to aid investors in optimising risk and return.
4.1 Portfolio return
The portfolio return is calculated as the weighted average of the returns of the individual assets constituting the
portfolio. Therefore, each asset return is multiplied by its proportion in the overall portfolio to arrive at the
portfolio return.
Mr. Jack has two assets in his portfolio, X and Y having expected returns of 12% and 15% respectively and their
weights in the portfolio are 0.70 and 0.3.
The expected return of the portfolio is 0.7 (0.12) + 0.3 (0.15) = 0.129 = 12.90%
4.2 Portfolio risk
The portfolio risk unlike the portfolio return is not the weighted average of the risk of the individual assets. This
is because of the correlation between the returns of the securities in the portfolio..
Covariance is a statistical measure that indicates how the expected returns of two entities behave relative to each
other. (whether between two assets or two portfolios).
COVxy =
(Rx − Rx)(Ry − Rb)
N
COVxy = covariance between x and y
Rx = return of security x
Ry = return of security y
Rx = mean return of security x
Ry = mean return of security y
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Coefficient of correlation is rxy =
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COVxy
σxσy
Correlation coefficients may vary between -1 to 1. If there is a perfect positive correlation between the two
assets the coefficient of correlation would be +1. Conversely -1 would indicate a perfect negative correlation
between them. Zero correlation implies the two are independent.
The variance of a portfolio with two securities can be calculated as follows:
2
2
2
2
2p = y1 σ 1 + y2 σ 2 + 2y1y2 ( ρ12σ1σ2)
Where,
2p = portfolio variance
y1 = proportion of amount invested in first security
y2 = proportion of amount invested in second security
2
1 = variance of first security
2
2 = variance of second security
1 = standard deviation of first security
2 = standard deviation of second security
st
nd
12 = correlation coefficient between the returns from 1 and 2 security
Let’s calculate the risk of the portfolio of two securities detailed below:
Return
Standard deviation
Weights
Coefficient of correlation between the returns
2
2
1 +
2p = y1
2
2
2
2
2
y2
2
X1
15%
16%
0.60
0.60
X2
18%
20%
0.40
+ 2y1y2 ( 12 1 2)
2
= (0.6) (16) + (0.4) (20) + 2 (0.6) (0.4) ((0.60)) (16 x 20))
= 92.16 +64 +0.48 (192)
= 92.16+64+92.16
= 248.32
Standard deviation =
248.32 = 15.76%
4.3 Principle of Diversification – the Markowitz portfolio theory (MPT)
The theory suggests that “putting all eggs in one basket” is not wise economically. Diversification implies investing
in a basket of securities to mitigate the concentration risk.
MPT enables the quantification of the benefits of diversification. Not putting all the money in one risky asset but
allocating the amount across a number of risky assets will significantly lower the downside risk without lowering
the expected return. An investor can maximise returns by holding a diversified portfolio. The movement of an asset
against the overall portfolio is more pertinent that the return from a single asset.
MPT emphasises on the correlation between investments. By looking at the statistical relationship between all the
assets in a portfolio, on a risk and return basis, the investor can optimise returns against a chosen level of
acceptable risk.
A portfolio is a basket of two or more securities. Through diversification an investor can reduce the total risk by
reducing or eliminating the unsystematic risk (explained under CAPM study guide D1). This is done without
affecting the portfolio return. In the above example, the portfolio standard deviation of 15.76% is lower than the
standard deviation of the two securities individually .i.e. 16% and 20%.
However, it is important to further understand the correlation between the assets in the portfolio to evaluate the
impact of diversification. We shall evaluate three scenarios with a portfolio of two securities:
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1. Perfect positive correlation
In case the securities are perfectly correlated, the correlation of coefficient would be +1. Then, the portfolio
standard deviation is the weighted average of the risks on individual assets.
p=
y1
1+
y2
2
p = standard deviation of the portfolio
y1 = proportion of amount invested in first security
y2 = proportion of amount invested in second security
1 = standard deviation of security 1
2 = standard deviation of security 2
Let’s assume in the above example that the assets are perfectly correlated,
p = y1 1 + y2 2
= 0.6(16) + 0.4 (20)
= 17.6%
The portfolio standard deviation lies between the standard deviation of the securities. It will change with change
in the proportion of amount invested in the securities.
Therefore, in case of perfect positive correlation, risk reduction is not possible as the risk cannot be decreased
below the individual security risk.
2. Perfect negative correlation
In case the securities are perfectly negatively correlated, the correlation coefficient between them is - 1 and the
returns move in opposite directions. In this case, the portfolio standard deviation would be
p=
y1
1-
y2
2
p = standard deviation of the portfolio
y1 = proportion of amount invested in first security
y2 = proportion of amount invested in second security
1 = standard deviation of security 1
2 = standard deviation of security 2
Continuing in the above example, when the assets are perfectly negatively correlated
p = y1 1 - y2 2
= 0.6(16) - 0.4 (20)
= 9.6 - 8%
= 1.6%
By modifying the proportion of investment in the two securities, it is possible to reduce the risk to zero.
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3. Uncorrelated returns
The coefficient of correlation for returns which do not show any dependency is 0. The portfolio standard
deviation in this case is:
2
2p = y1
2
1 +
2
2
y2
2
p = standard deviation of the portfolio
y1 = proportion of amount invested in first security
y2 = proportion of amount invested in second security
2
1 = variance of first security
2
2 = variance of second security
Continuing in the above example, when the assets are uncorrelated
2
2p = y1
2
2
1 +
2
2
2
y2
2
2
= (0.6) (16) + (0.4) (20)
2
= 92.16+64
= 156.16
p=
156.16
= 12.50%
Therefore, when the returns from the securities are not correlated, diversification can reduce risk. In the above
example, 12.50% is lower than both 16% and 20%.
From the above analysis, it is clear that diversification helps to decrease risk in all situations except when the
securities have perfect positive correlation.
Assumptions of the model
The model is based on the following assumptions:





The risk of the portfolio is estimated by the investor based on the variance of expected returns.
Investors prefer higher returns to lesser ones with equal or lower risk and vice versa.
Investment decisions are based on only two factors, the risk and the expected return.
Each investment option can be represented by a probability distribution of expected returns over a period
of time.
Investors as risk averse.
Mr. Peterson has invested in two securities and would like to understand whether the portfolio risk is lower than
the individual asset risks. The following details have been provided:
Return
Standard deviation
Weights
Coefficient of correlation between the returns
Shares of A Ltd.
10%
15%
0.45
0
Shares of B Ltd.
12%
18%
0.55
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5. Determine the minimum variance portfolio and efficient frontier.
[Learning Outcome e]
The selection of an optimal portfolio first involves determination of feasible set of portfolios.
Let us determine the minimum variance portfolio and efficient frontier for the below mentioned example.
Mr. Andy has invested his funds in two securities A and B. Security A has a risk measure (standard deviation) of
15% and expected return of 10%. Security B has a standard deviation of 26% and expected return of 20%.
These securities have low positive correlation and therefore it is possible to reduce portfolio risk through
diversification. We can alter their proportions and determine a number of portfolios with different levels of return
and risk. The below table shows the different types of portfolios that can be created:
Portfolio
X1
X2
X3
X4
X5
X6
Risk (%)
15
13
12
16
22
26
Expected return (%)
10
12
13
15
18
20
Efficient or not
No
No
Yes
Yes
Yes
Yes
The above is graphically depicted below:
Diagram 2: Minimum variance frontier and efficient frontier
We plot the standard deviations on the X-axis and the expected return on the Y-axis. The line segment X1 to X6
represents the minimum variance portfolio set. This is the set of feasible portfolio opportunities. The minimum
variance portfolio (MVP) basically plots the lowest possible risk for a given portfolio’s expected return.
There is an inflection at point X3. This is the extreme left point on the minimum variance frontier. This is also called
global minimum variance portfolio. This point indicates the lowest variance at the given level of expected return.
Point X6 is the global maximum return portfolio. This is the highest point along the MVP. The line segment x3-x6
is the efficient frontier .i.e. all portfolios along this line are more efficient than portfolios along x1-x3.
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Therefore the efficient frontier is the line segment between X3 and X6 i.e. between the global minimum variance
portfolio and the global maximum return portfolio. They dominate other portfolios below it. Dominant portfolios
are those which earn a maximum return for a given level of risk or minimum risk for a given rate of return. The
efficient frontier is always convex towards the Y axis. The efficient frontier line starts with lower expected risks and
returns, and it moves upward to higher expected risks and returns. Investors with different needs, depending upon
the time horizon, risk appetite and personal preference can identify an appropriate portfolio anywhere along the
efficient frontier line.
Explain the concept of efficient frontier.
6. Describe the capital market line and the separation theory.
[Learning Outcome f]
6.1 Capital market line
A risk-free security has zero standard deviation. James Tobin has analysed that (i) portfolios comprising risky
assets and one risk-free asset generate portfolio opportunity sets with linear relationship between expected risk
and return. (ii) one such portfolio opportunity set will dominate the portfolios formed by mixing only risky assets
(securities and / or portfolio of securities)
Consider a portfolio consisting of two assets: a risk-free asset that has a low rate of return but risk-free, and a risky
asset that has a higher expected return for a higher risk. Investment risk is measured by the standard deviation of
investment returns. This means that the greater the standard deviation, the greater will be the risk. By varying the
proportions between the two assets, the investor can earn a risk-free return by investing the entire capital
money in the risk-free asset, or potentially earning the maximum return by investing the entire amount in the risky
asset, or selecting a risk-return trade-off that lies between these two extremities by selecting varying proportions
of the two assets.
The investment quality of a two-asset portfolio is determined by the proportion of the risky asset to the risk-free
asset. If the portfolio consists of a risky asset with a proportion of w, then the proportion of the risk-free asset will
be 1 –w.
Portfolio Return = w X Expected return on risky asset + (1 – w) X Risk-free asset return
E (rc) = rf + x[E (rR) – rf]
Where rf is the risk-free return
w is the fraction of portfolio invested in risky asset R
E(rR) is the expected return for risky asset R
E(rR) – rf is the risk premium for the risky portfolio
The portfolio standard deviation is
σc = wσR
Where
c = standard deviation of portfolio
w is the fraction of portfolio invested in risky asset R
R = standard deviation of risky portfolio
c
Combining the above two, since w =
R
E(rc) = rf +
c
(E(rR) – rf)
R
E(rc) = rf + c{(E(rR) − rf)/ f)
This is equation of portfolio possibility lines with one risk-free asset. It is called capital market line. (CML). The
CML shows the increase in expected return per unit of additional standard deviation.
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Symbolically, Slope = (E(rc) – rf)/ R
Where E(rc) = expected return on portfolio
rf = risk free return
σR = standard deviation of portfolio
Diagram 3: Capital market line
There are three capital allocation lines starting from F and passing through M, Y and Z. F is the point of pure
risk-free portfolio where standard deviation is zero. Point Y is the lower end of the minimum variance frontier
and point Z is the upper end of the minimum variance frontier. The efficient frontier or risky assets and the highest
CAL are tangential at point M.
An investor can earn any combination of return with risk on the line segment FM by combining the risk- f r e e
asset F to the portfolio M.
6.2 Separation theory
The capital market line leads all investors to invest in the same risky asset portfolio M (as explained in above
example and diagram under 6.1. CML tangential to the efficient frontier of risky assets becomes the new
efficient frontier with one risk free asset. Individual investors would have their preferences regarding their
position on the capital market line. This depends on their willingness to take risk. In the diagram explained in
6.1, the portfolio was constructed with owned funds. Extending the line segment FM beyond point M shows further
opportunities for higher return. This is possible by creating a leveraged portfolio.
Therefore, an investor may either choose:

To lend a part of his portfolio at Rf by buying risk-free assets and invest the balance in the market
portfolio of risky assets.

To borrow funds at Rf and invest both his owned funds and borrowed capital to build a portfolio at a point
Cbeyond M. This point provides higher risk and return.
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Diagram 4: Capital market line and separation theory
Tobin called this separation of investment decision from financing decision as the separation theorem. An
investor may decide to invest in the market portfolio M, so that he would be on the CML efficient frontier. At a later
date, he may take a separate financing decision either to borrow or to lend to lie at a certain acceptable risk
position on the CML.
Select the answer from the choices below:
1. Capital market line is:
A
B
C
D
Capital allocation line of risk-free asset
capital allocation line of a market portfolio
capital allocation line of risk-free asset and market portfolio both
none.
2. Tobin’s separation theorem deals with:
A
B
C
D
The separation of financing decisions and financing decisions
The investor may decide to invest in the market portfolio so that he can be on the CML efficient frontier.
The investor may borrow beyond a point to build a portfolio with higher risk and return.
All of above
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Answers to Test Yourself
Answer to TY 1
Portfolio management process involves:
1. Listing the investment objectives and constraints
It is essential to draw up the investment policy i.e. the investor’s objectives along with the constraints. A clearcut outline has to be laid down of what the process strives to achieve. It ensures common understanding, acts
as a standard for performance and aids in planning.
2. Market study and outlining of strategies
Complete knowledge of the macroeconomic situation, financial background, policy updates, financial markets /
products etc is critical before going into the micro analysis of securities and portfolio. The phase of the
economy, the state of financial markets the short term and medium term outlooks will determine the investment
strategy.
3. Constructing the portfolio
This step involves the following:
(a) Portfolio allocation – allocation among different asset classes
(b) Analysis of securities – based on financial , promoter strength and technical analysis
(c) Portfolio build up
4. Portfolio Monitoring
Since portfolio management is a continuous process there is need for constant monitoring for changes to
investor preferences, risk-return analysis against benchmarks, any revisions / lacunae to be identified and
corrected.
Answer to TY 2
1. The correct option is (b), regular income.
2. The correct option is (c) aggressive growth.
3. The correct option is (a) capital appreciation.
Answer to TY 3
Asset X
I
Ri
1
2
3
Ri − R
R
8%
16%
24%
Standard deviation =
CV = 6.196/16 = 0.387
16%
16%
16%
38.4 = 6.196%
-8%
0
8
Ri − R
2
Ri − R
Pri
64
0
64
0.3
0.4
0.3
2
X Pr
i
19.2
0
19.2
38.4
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Asset B
Ri
I
1
2
3
Ri − R
R
10%
20%
15%
15%
15%
15%
-5%
5
0
Ri − R
2
Ri − R
Pri
25
25
0
2
X Pr
0.2
0.6
0.2
i
5.0
15.0
0
20.0
Standard deviation = 20 = 4.47%
CV = 4.47/15 = 0.298
Therefore, since larger the CV, larger the risk, Asset X is riskier than Y
Answer to TY 4
The portfolio risk when the two securities are uncorrelated .i.e. coefficient of correlation is 0 is
2
2p = y1
2
1 +
2
2
y2
2
2
2
2
= (0.45) (15) + (0.55) (18)
2
= 45.56+98.01
= 143.57
p=
143.57
= 11.98%
It has been advantageous for Mr. Peterson as diversification has helped to reduce risk to 11.98%.
Answer to TY 5
The efficient frontier is the basis of Modern Portfolio Theory. Investors and portfolio managers are concerned
with achieving the highest trade-off between risk and return. Portfolios that provide the highest return, given the
risk, or, alternatively, have the lowest risk for a given return, are called “optimal”. Optimal portfolios define a
line in the risk/return plane called the “efficient” frontier.
The best or optimal portfolio with more money in risky investments will be toward the top of the curve, or “frontier”.
The optimal portfolio for a less risky investor would be closer to the bottom of the curve. Any portfolio that lies on
the frontier will be expected to maximise return for that level of risk. The efficient frontier is the line segment
between the global minimum variance portfolio and the global maximum variance portfolio. They dominate
portfolios below it. It is always convex in shape towards the Y axis.
Answer to TY 6
1. The correct option is C.
2. The correct option is D.
Quick Quiz
1. List the constraints that affect portfolio strategy.
2. What is the use of an investment policy?
3. What does Markowitz portfolio theory primarily convey?
4. What is portfolio management?
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5. State True or False.
(a) Efficient frontier consists of all those portfolios that offer maximum risk for a given level of expected
returns.
(b) The point of tangency between the CML and the efficient frontier provides the optimal portfolio for the
investor concerned.
(c) The risk of the portfolio is the weighted average of risk of individual securities in the portfolio multiplied
by their weights in the portfolio.
(d) An aggressive growth fund is ideal for a working professional of 28-30 years of age.
Answers to Quick Quiz
1. The following are the constraints that affect portfolio strategy:
(a) Time horizon for investments
(b) Taxation
(c) Regulatory framework
(d) Specific needs/ preferences
(e) Need for liquidity
2. An investment policy is critical to guide the portfolio management process. It is a document containing the
investor’s objectives .i.e. is primarily desired to be achieved through the investment and the constraints. It also
ensures that there is clarity on evaluation benchmarks in case the portfolio is managed by professionals. The
process of developing the investment policy ensures that the investor studies the financial markets and
security choices available.
3. Markowitz portfolio theory quantifies the benefits of diversification. By allocating the investment across a
number of risky assets, an investor can significantly lower the downside risk without lowering the expected
return.
MPT emphasises on the correlation between investments. The return from a single asset is less important
than how that asset's value moves against overall portfolio values. By looking at the statistical relationship
between all the assets in a portfolio, on a risk and return basis, the investor can optimise returns against a
chosen level of acceptable risk.
4. Portfolio management is the process of identifying, constructing, monitoring and re-balancing a basket of
securities woven together to achieve a stated investment objective. It is a continuous process starting with the
drawing up of the investor objectives and preferences, conducting market study to constructing the portfolio.
The portfolio so built is subject to constant review and changes to ensure achievement of stated objectives.
5.
(a) False
(b) True
(c) False
(d) True
Self Examination Questions
Question 1
XYZ Ltd. has placed its short-term investments in two securities A and B detailed below:
Portfolio (%)
A (%)
B (%)
Expected return
12
16
Standard deviation
16
20
Proportion
0.5
0.5
Required:
(a) Determine the correlation coefficient to derive a portfolio standard deviation of 18%.
(b) If the weights of the two securities A and B is modified to 75:25, what would be portfolio risk be?
(c) What would the correlation be, if the desired portfolio standard deviation is 16% and the assets are
combined in equal proportion?
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Question 2
“Diversification of risk in the asset allocation process permits investor to combine risky assets in such a manner
that the risk of the overall portfolio is less than the risk of the individual assets.” Explain with an example.
Question 3
Mr. Danny wishes to measure the risk of his assets. He requires help to arrive at some statistical risk measure.
His assets are
Asset A
Return
Probability
10
0.4
15
0.3
20
0.3
I
1
2
3
Return
14
16
18
Asset B
Probability
0.3
0.2
0.5
Answers to Self Examination Questions
Answer to SEQ 1
2
(a) 2p = y 1
2
1 +
2
y2
2
2
+ 2y1y2 ( ρ12σ1σ2)
(182) = (0.5)2(16)2 + (0.5)2(20)2 + 2 (0.5) (0.5) ( 12) ) (16 x 20))
324 = 64 +100 +160 12
324 = 164+160 12
324-164 = 160 12
160 = 160 12
Coefficient of correlation is 1; therefore, the securities are perfectly
correlated. (b) Since the securities are perfectly correlated the portfolio risk is
calculated as
p = y1 1 + y2 2
= (0.75) (16) + (0.25) (20)
= 12 + 5
= 17%
(c) 2p = y
2
1
2
1 +
2
y2
2
2
+ 2y1y2 ( 12 1 2)
(162) = (0.5)2(16)2 + (0.5)2(20)2 + 2 (0.5) (0.5) ( 12) ) (16 x 20))
256 = 64 +100 +160 12
256 = 164+160 12
256-164 = 160 12
92 = 160 12
12 = 92/160 = 0.575
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Answer to SEQ 2
“Diversification of risk in the asset allocation process permits investor to combine risky assets in such a manner
that the risk of the overall portfolio is less than the risk of the individual assets.”
This statement emphasises the importance of diversification in portfolio management. A portfolio is a basket of
two or more securities. Through diversification an investor can reduce the total risk by reducing or eliminating
the unsystematic risk. This is done without affecting the portfolio return. This is the essence of the modern portfolio
theory.
Considering the following:
Mr. Trehan invested his annual savings in two securities shares of Mercury Ltd. (M) and shares of Venus Ltd.
(V). The expected return and risk parameters are detailed below:
Security M
15%
20%
0.4
Return
Standard deviation
Weights
Coefficient of correlation between the returns
Security V
20%
25%
0.60
0.55
Let’s calculate the overall portfolio risk denoted as 2p
2
2
1 +
2p = y1
2
2
y2
2
2
2
2
+ 2y1y2 ( ρ12σ1σ2)
2
= (0.4) (20) + (0.6) (25) + 2 (0.4) (0.6) ((0.55)) (20 x 25))
= 64 +225 +0.48 (275)
= 36+144+132
= 312
Standard deviation =
312 = 17.66%
The above portfolio standard deviation of 17.66% is lower than the individual risk measures of 20% and 25%
respectively for the individual securities. Therefore Mr. Trehan has benefited from diversification as the overall risk
has reduced. This diversification of risk in the asset allocation process has helped the investor in lowering the
risk below that of the individual securities. This is achieved without a compromise in the returns. The
portfolio return is calculated as the weighted average of the returns of the individual assets constituting the
portfolio.
In this case, Portfolio return = 15(0.4) + 20(0.6) = 6 + 12 = 18%
Answer to SEQ 3
To compare the two assets on their risk measure we first calculate the standard deviation from the expected
value of return. It is calculated as follows:
𝑛𝑛
𝜎𝜎 = √∑(𝑅𝑅𝑖𝑖 − 𝑅𝑅̅ ) × 𝑃𝑃𝑃𝑃𝑖𝑖 𝑖𝑖=𝑖𝑖
Asset A
I
Ri
1
2
3
Standard deviation =
R
10%
15%
20%
Ri 15%
15%
15%
17.5 = 4.18%
R
(5%)
0
5
(R − R )
2
25
0
25
Pri
i
(R − R ) X Pr
2
0.4
0.3
0.3
10.0
0
7.5
17.5
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Asset B
I
Ri
1
2
3
Standard deviation =
R
14%
16%
18%
Ri 16%
16%
16%
R
(R − R )
(2%)
0
2
(R − R ) X
Pri
2
4
0
4
2
0.3
0.2
0.5
Pri
1.2
0
2
3.2
3.2 = 1.79%
Higher the standard deviation higher is the risk. Therefore, Asset A is riskier than B. Standard deviation is an
absolute measure of risk. Let’s also further substantiate our findings. Coefficient of variation converts standard
deviation of expected returns into relative values to facilitate comparision of risks among assets having different
expected values. It is a relative measure of dispersion. It is computed as follows
σr
CV =
R
CV of Asset A = 4.18/15 = 0.279
CV of Asset B = 1.79/16 = 0.112
Therefore, since larger the CV, larger the risk, Asset A is riskier than B.
Indicative Examination Questions
IEQ 1
Assume that you are working as an assistant investment adviser at Finance 360 Ltd. You have been
approached by a client, Mr. Robert Mengison is planning to invest in a portfolio of shares for an investment
advice. He has identified two shares with the following details:
Share 1 – Mbuni Ltd, a company in the brewing industry whose expected annual returns are as follows:
Annual Investment Return
12%
24%
Probability of Occurrence
0.4
0.6
Share 2 – Samaki Limited, a company in the oil and gas extraction industry, whose expected annual
returns are as follows:
Annual Investment Return
10%
20%
Probability of Occurrence
0.3
0.7
You have calculated the co-efficient of correlation between the two shares which is +0.75.
Mr. Mengison plans to invest TSHS.600,000,000 in Mbuni Ltd shares and TSHS.400,000,000 in Samaki
Limited’s shares.
The following additional information is also known to you:


Return on government bonds is 4%
The Return expected from the market is 10% and the risk is 6%
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REQUIRED:
Prepare a brief note for Mr. Mengison which covers on the following issues to advise him on his proposed
investment:
(i) Explanation of the term’s portfolio theory, systematic and unsystematic risk. (6 marks)
(ii) The expected return and risk as measured by standard deviation for each share and the proposed
portfolio (8 marks)
(iii) The Capital Asset Pricing Model(CAPM) on the efficiency of the proposed portfolio considering that
its beta(s) is likely to be 0.843.
IEQ 2
Tangwi plc is considering investing in one of two proposed short-term portfolios of four short-term financial
investments. The correlation between the returns of the individual investments is believed to be negligible
in both options proposed. The market return is estimated to be 15%, and the risk-free rate 5%.
Portfolio 1
Investment Amounts invested Expected return Total risk Beta
Tshs . (million)
A
10
20%
8
0.7
B
40
22%
10
1.2
C
30
24%
11
1.3
D
20
26%
9
1.4
Portfolio 2
Investment Amounts invested Expected return Total risk Beta
Tshs . (million)
A
20
18%
7
0.8
B
40
20%
9
1.1
C
20
22%
12
1.2
D
20
16%
13
1.4
REQUIRED:
(i)
(ii)
Calculate the risk and return of the two portfolios using the principles of both portfolio theory
and the CAPM.
Which portfolio appears to be more efficient?
(8 marks)
Answers to Indicative Examination Questions
Answer to IEQ 1
(a) Portfolio Theory
(i)
A portfolio is a collection of different investments that comprise an investor’s total holding.
Such a portfolio may include different types of investments e.g. property, equities and
government bonds. Portfolio theory is concerned with setting guidelines for selecting a
portfolio of investments and the measurement of risk and return of a portfolio and,
understanding the impact that investment diversification will have on the risk and return of
a portfolio.
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Systematic and Unsystematic Risk
Systematic Risk- This is the risk of the market as a whole, caused by variable factors
affecting the whole of the market e.g. macro-economic. Systematic risk cannot be reduced
through portfolio diversification. Systematic risk must be accepted by the investor.
Unsystematic Risk – This is risk that is specific to a specific investment/industry. Some
investments are considered to be more risky than others. An example would be that the
property development industry would probably be considered more risky compared to the
retail industry. Unsystematic risk can be diversified away by investing in a portfolio of
investments in different industries.
Co-efficient of correlation
This measures the relationship between two (or more) investments in a portfolio. In this
case the property development and construction industries are closely related as the have
an ‘r’ score of +.75. This indicates that the financial fortunes of both industries are likely to
follow similar trends. To further reduce overall portfolio risk through diversification the
relationship between the new investments in the portfolio should be of an inverse (negative)
nature. Thus, the fortunes of one industry will be the opposite to the other.
Risk and return of proposed portfolio
MBUNI LTD
(ii)
The annual return expected from Investment in Mbuni Ltd. is 19.2% and
the risk attached thereto measured by standard deviation is 5.88% calculated as follows
Investment in Serengeti Ltd.
%
Return
Probability
Expectation
Deviation
x
12
24
p
0.4
0.6
Xp
4.8
14.4
19.2
x-EV
-7.2
4.8
(x-EV)2
51.84
23.04
Deviation
squared
p(x-EV)2
20.736
13.824
34.56
Std
deviation
5.88
Expected value (EV)
SAMAKI LTD.
The annual return expected from your investment in Samaki Limited is 17% and the risk
attaching thereto measured by standard deviation is 4.6%. They are calculated as follows:
Investment in SAMAKI LTD.
%
Return
Probability
x
10
20
P
0.3
0.7
Xp
3
14
17
Expectation Deviation Deviation Std
squired
deviation
X-EV
(x-EV)2
p(x-EV)2
-7
49
14.7
3
9
6.3
21
4.6
PORTFOLIO
The overall expected return from your proposed portfolio is 18.32%. This is a weighted
average of the expected return of both investments in the proposed portfolio, using the
proportion of the investment in each share as the respective weights.
EV = (0.192X60%) + (0.17X40) = 18.32%
The risk of the proposed portfolio (as measured by standard deviation) is 5.06% calculated
as follows: √(W1)2(12) + (W2)2(22) + (2)(W1)(W2)(r)(1)(2)□ = √(.6)2(.0588)2 + (.4)2(.046)2
+ (2)(.6)(.4)(.75)(.0588)(.46)▪ = √25.57 = 5.06
CAPM based return Risk free return (Rf)
4%
Plus: Risk Premium B(Rm-Rf) 0.843
Beta factor (note 1) *Rm-Rf = (10%-4%) = 6%
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CAPM Based Return = 9.06%
Expected Return = 18.32%
Note 1
Risk of Market Portfolio
Risk of Proposed Portfolio
Portfolio Beta Factor = 5.06/6
Portfolio Beta Factor = 0.843
6%
5.06%
The proposed portfolio is an efficient portfolio lies on the CAPM. However, this portfolio is worth
investing in since it has a return that is higher than what is required/predicted by CAPM. The
expected return there from exceeds by 9.26% (18.32%-9.06%) the return which would have been
expected using capital Asset Pricing Model (CAPM) principles to assess risk and return.
Answer to IEQ 2
TWIGA PLC
Portfolio 1 Solution
Investment
A
B
C
D
Investment
weightings
0.1
0.4
0.3
0.2
Expected return Portfolio expected
(%)
return (%)
20
2.00
22
8.80
24
7.20
26
5.20
23.20
Beta
0.7
1.2
1.3
1.4
Weighted
beta
.07
.48
.39
.28
1.22
The required return: 5 + (15 – 5) 1.22 = 17.20%
Portfolio 2 Solution
Investment
a
b
c
d
Investment
weightings
0.2
0.4
0.2
0.2
Expected return Portfolio expected
(%)
return (%)
18
3.60
20
8.00
22
4.40
16
3.20
19.20
Beta
0.8
1.1
1.2
1.4
weighted
beta
.16
.44
.24
.28
1.12
The required return: 5 + (15 – 5) 1.12 = 16.20%
Alpha table
Portfolio 1
Portfolio 2
Expected returns
23.20%
19.20%
Required returns
17.20%
16.20%
Alpha values
6.00%
3.00%
Portfolio 1 is chosen because it has the largest positive alpha.
Portfolio theory calculations
The formula for a multi-asset portfolio with no correlation between the returns is:
 port (A, B)   a  xa   b  xb   c  xc   d  xd 
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w12 a2  w22 b2  w32 c2  w42 d2
Portfolio 1
 port 1 
8  .1  10  .4  11  .3  9  2 
= 5.55%
Portfolio 2
 port 2 
7  .2  9  .4  12  .2  13  .2
= 5.24%
Summary table
Expected returns
portfolio risk
Portfolio 1
23.20%
5.55%
Portfolio 2
19.20%
5.24%
The portfolio with the highest return also has the highest level of risk. Therefore, neither portfolio can be
said to be more efficient than the other. An objective answer cannot be reached. As the company is making
decisions on behalf of its shareholders the correct way to evaluate the investments is by looking at the
effect, they have on a shareholder’s existing/enlarged portfolios.
C4
SECTION C
The Security Market Line (SML) and The Capital Asset Pricing Model (CAPM): 229
INVESTMENT DECISIONS
STUDY GUIDE C4: THE SECURITY MARKET
LINE (SML) AND THE CAPITAL ASSET
PRICING MODEL (CAPM)
In the previous Study Guide, we discussed how investors, being risk averse by nature, make portfolio decisions.
We also evaluated the effect of the existence of a risk-free asset on the decision making. This resulted in derivation
of the capital market line. The covariance of an asset with the market portfolio of risky assets was recognised as
a relevant measure.
It is important to understand whether an investor should select a security in his portfolio i.e. how to determine
whether the price of the security is favourable to invest in it. The answer to this question takes us to the Capital
Asset Pricing Model (CAPM) and creation of the Security Market Line (SML). This would help us to
compare the current market rate of return with the expected return on a risky asset. In this Study Guide, we
shall also understand how to evaluate a portfolio using risk adjusted benchmarks.
a) Derive the CAPM and SML; differentiate between SML and CML.
b) Illustrate the CAPM observing its assumptions and limitations.
c) Compute the beta factor and alpha values.
d) Compute the geared and ungeared betas.
e) Compare the CAPM and the Arbitrage Pricing theory (APT)
f) Assess performance of a portfolio using the risk adjusted benchmarks – The Treynor, Jensen and
Sharpe Measures.
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1. Derive the CAPM and SML; differentiate between SML and CML.
[Learning Outcome, a]
1.1 Capital Asset Pricing Model (CAPM)
The capital asset pricing model is a theory that explains how asset prices are derived in the market. It is an
extension of the portfolio theory, developed by Harry Markowitz. It was developed by William F. Sharpe (1964),
John Lintner (1965) and Jan Mossin (1967). In 1990, the Nobel Prize for economics was awarded to Sharpe
and Markowitz for their contribution to the field. This model used the results of capital market theory to arrive at
the relationship between systematic risk of an asset / security / portfolio and the expected return.
Sharpe introduced the Capital Asset Pricing Model (CAPM) for risky securities, comprising two components:

Risk free rate of return

Beta (systematic risk)
Risk free rate of return is the return earned on risk free assets e.g. government securities which earn a fixed return
and the repayment is guaranteed by the government.
While investing in securities, an individual is exposed to two types of risks – systematic and unsystematic risk
(explained in Study Guide D1). Unsystematic risk can be reduced / eliminated through diversification. Systematic
risk is the market related component of portfolio risk.
Beta is a measure of the systematic risk. It measures the volatility of the security. It describes the sensitivity of a
particular stock’s return on the market portfolio. The higher the risk involved (beta) in investing in a security, the
higher is the return expected by the investor. Using the beta and the risk free return, the CAPM helps to determine
the return from the security that an investor can expect if they choose to invest in the security. The CAPM relates
an asset’s risk premium to its beta.
Thus, for a given risk, CAPM helps the investor to calculate the return they should expect from the security for
taking exposure to the risk. In other words, for a given expected return from a security, CAPM helps the investor
to calculate the risk that they will be exposed to by investing in that security. Accordingly, based on their risk
appetite, the investor can decide whether to go ahead with the investment or not.
1.2 Derivation of CAPM and Security Market Line (SML)
The expected return of a security is dependent on the measure of systematic risk. The relevant risk measure of
a particular security is its covariance with the market portfolio. The return for the market portfolio should be in
line with its own risk which is the covariance with itself.
For a risky asset “i”, the expected return =Risk- free rate of return+ Risk premium specific to asset i
Or, E (return) = RF + (Market price of risk) x (Quantity of risk of asset “i”)
Risk-free rate of return is the rate of return earned on a security where the risk is negligible e.g. return earned
on government securities. This rate compensates the investor for inflation. Hence, it reflects the minimum rate of
return required by the investors.
CAPM helps to answer the questions


what is the price of risk?
what is the risk of asset i?
In the equation, the quantity of risk of any asset, however, is only part of the total risk (standard deviation) of the
asset:
Thus, the equation known as the Capital Asset Pricing Model
𝐸𝐸(𝑅𝑅𝑖𝑖 ) = 𝑅𝑅𝑓𝑓 + [𝐸𝐸(𝑅𝑅𝑖𝑖 ) − 𝑅𝑅𝑓𝑓 )] ×
Where
𝐶𝐶𝐶𝐶𝐶𝐶(𝑅𝑅𝑖𝑖 𝑅𝑅𝑚𝑚 )
𝑉𝑉𝑉𝑉𝑉𝑉(𝑅𝑅𝑚𝑚 )
1. Expected Return on asset i = 𝐸𝐸(𝑅𝑅𝑖𝑖 )
2. Equilibrium Risk-free rate of return = 𝑅𝑅𝑓𝑓
TheSecurity
SecurityMarket
MarketLine
Line(SML)
(SML)and
andthe
The
Capital
Asset
Pricing
Model
(CAPM):
231
The
Capital
Asset
Pricing
Model
(CAPM):
209
© GTG
3. Quantity of risk of asset i =
COV(Ri,Rm )
Var(Rm )
4. Market Price of risk = [E(Rm ) − Rf ]
Now,
COV(Ri,Rm )
Var(Rm )
is called the beta of the asset “ï”
E(Ri) = Rf + [E(Rm ) − Rf ]Xβi
Beta is a standardised measure of risk because it relates its covariance to the variance of the market portfolio.
The graphical representation of the CAPM is the security market line. By plotting the beta on the X-axis and the
expected return on the Y axis we get an upward moving line which is the risk premium measure [ E( )- ].
Therefore, the higher the beta of an asset, the higher is the risk premium it commands relative to the market.
Diagram 1: Security Market Line
The beta value for the market portfolio is 1. In case the security has a beta greater than 1 it indicates that it is
more volatile than the market portfolio and would command higher return moving rightward on the SML. The
reverse is true for a security with a point to the left of the market portfolio.
Securities that are correctly priced will remain on the fitted SML. Under-priced shares will lie above the SML and
over-priced shares will fall below the SML.
Investors will buy the under-priced shares. This will cause the price to go up and the rate of return to decrease.
This will bring it down on to the SML. Investors will then sell the over-priced shares, causing a fall in the price
and a rise in the rate of return. These movements are expected to be quick in capital markets which are
assumed to be perfect.
1.3 Differentiation between Capital market line (CML) and Security Market Line (SML)
We have discussed CML in detail in the previous study guide. The CML and SML differ as regards the following:
1. The CML portrays the relationship between expected return and risk for efficient portfolios. The SML applies
to individual securities. It also deals with all portfolios whether on the CML or below it.
2. The CML considers standard deviation of return on a portfolio as an appropriate measure of risk. The SML
on the other hand is considered with beta, which is a measure of systematic risk. The SML slope depicts the
risk premium for a given level of beta.
Explain the SML in brief and compare it with the CML.
232 Investment Decisions
210 : Investment Decisions
2. Illustrate the CAPM observing its assumptions and limitations.
© GTG
[Learning Outcome b]
2.1 Assumptions of the Capital Asset Pricing Model
The basic assumptions of CAPM are related to the efficiency of the capital market and investor preferences.
1. The investors are rational. Their objective is to maximise wealth. The try to achieve this through:
(a) following a long-term investment strategy
(b) no under or over reactions to various events e.g. sudden macroeconomic changes
(c) not holding on to a security because it was a strong performer in the past
2. All investors have homogenous expectations regarding the expected returns, variances and correlation of
returns among all securities.
3. Investors are allowed to borrow and lend funds at the risk-free rate of return. This is the assumption for the
portfolio theory, and CAPM has been developed from the portfolio theory. Risk-free return offers the minimum
level of return available to an investor. The investors may borrow or lend unlimited amounts of the risk free
asset at a constant, risk-free rate.
4. Investors hold diversified portfolios. Diversified portfolios allow an investor to eliminate unsystematic risk.
5. All investors have the same information about the securities.
6. There are no restrictions on investments.
7. There are no taxes or transaction costs.
8. No single investor can affect the market price significantly. The implication of the above explained investor
preferences is that all investors prefer security that provides the highest return for a given level of risk or the
lowest risk for a given level of return.
9. The model is a one period model. A return for three months cannot be compared with returns for five years.
Hence, it is assumed that the investments occur over a single standardised period. It allows comparison
among various securities on the basis of their returns. Usually, a period of one year is used.
10. CAPM is valid only under perfect capital market conditions. All the securities are correctly valued and their
returns can be plotted on the security market line (SML). There are no market imperfections such as taxes,
regulations, or restrictions on short selling. There are a large number of buyers and sellers. A single participant
cannot influence the market.
All investors are risk adverse individuals and have the same information at the same time. There is no cost
associated with the information i.e. it is freely available. As a result, investors have identical expectations
(beliefs) about asset returns.
11. The assets are perfectly divisible. There are a definite number of assets and their quantities are fixed within
the given period. These assets are perfectly divisible. Similarly, they are priced in a perfectly competitive
market. This implies that, for example, human capital does not exist. The returns of all assets are distributed
through normal distribution channels.
The Security Market Line (SML) and The Capital Asset Pricing Model (CAPM): 233
The Security Market Line (SML) and the Capital Asset Pricing Model (CAPM): 211
© GTG
SUMMARY
2.2 Illustrating the Capital Asset Pricing Model (CAPM)
The following equation lays down the relationship explained in the model:
()
(
E r i =R f + i E(r m ) - R f
)
Where,
E(rj) = the rate of return of security j, as projected by the model
βj = the beta coefficient of security j
Rf = the minimum risk-free rate of return
E(rm) = the return of the market
The components of the CAPM
From the above equation, the main components of the model can be identified as the:
beta coefficient of the security
minimum risk-free rate of return
premium expected for the risk . It is the difference between the market return and the risk free return.
The return on market portfolio is 12%. The return on government bonds (which is considered risk free) is 5%.
Therefore, the risk premium - (E(r m ) - R f ) = 12% - 5% = 7%.
Let’s assume the mix of portfolio between government bonds and market is 60:40. Compute the beta and
required returns.
Since beta for market is 1 and risk-free asset is zero i in this case is 0.6(0) + 0.4(1) = 0.4.
E(r i ) =R f + i (E(r m ) - R f )
= 5% + 0.4(7%)
= 5% + 2.8%
= 7.8%
234 Investment Decisions
212 : Investment Decisions
© GTG
CAPM derives the required rate of return for a security based on the risks involved. We can compare this with
the expected return based on market information. This helps us to decide whether to hold, buy or sell the security.
Condition
Expected market return > CAPM return
Expected market return < CAPM return
Expected market return = CAPM return
Result
Stock is undervalued
Stock is overvalued
Stock is properly valued
Strategy
Buy the security
Sell the security
Hold the security
Tom has picked two stocks based on his analysis on company fundamentals. The market information is as
follows:
Particulars
Beta
Expected return
Risk free rate
Market return
Shares of Planet Ltd
0.7
12%
8%
15%
Shares of Star Ltd
1.2
17.5%
Let’s compute the required rate of return in each case:
E(r i ) =R f + i (E(r m ) - R f )
For shares of Planet Ltd
8%+ 0.7(15%-8%) = 12.9%
Since expected return of 12% is less than the required return of 12.9%, the shares of Planet Ltd should not be
acquired.
For shares of Star Ltd
8%+ 1.2(15%-8%) = 16.4%
Since expected return of 17.5% is higher than the required return of 16.4%, the shares of Star Ltd can be
acquired.
For Mercury Co, the risk measurement service quoted a beta of 0.90 during September 20X3. Around the same
time, the yield on the three month treasury bills was 5%. Market risk premium is 5%. Calculate the required
return using CAPM.
The CAPM is easy to use and understand. It has varied applications as listed below:






Aids in deciding whether a stock is undervalued or overvalued which in turn would determine whether to
purchase the security from the market
Determines cost of equity capital
Analyses the risk return relationship for a particular security as well as for an efficient portfolio of assets
Determines the fair price for a security proposed to be listed on any stock exchange
Determines the impact of gearing on cost of equity.
Estimates the required rate of return on projects
2.3 Limitations of CAPM
CAPM is subject to certain limitations primarily because of its underlying assumptions.
1. The major limitation is that the beta is based on past performance. There is no certainty that the future will
replicate the past. The risk profile of the firm may change.
2. If a company’s shares are not traded publicly, historical data will not be available for the values needed in
the model.
The Security Market Line (SML) and The Capital Asset Pricing Model (CAPM): 235
The Security Market Line (SML) and the Capital Asset Pricing Model (CAPM): 213
© GTG
3. Estimating the model’s inputs (the risk-free rate, beta, and the market return) is a difficult task. It may be difficult
to estimate accurately.
4. The CAPM assumes than investors hold diversified portfolios and, therefore, the only relevant risk is market
risk. The investors may not be fully diversified. In such a situation, the CAPM may understate the required
return and the cost of equity.
5. The model assumes that returns are normally distributed random variables. However, it has been found that
returns in equity and other markets are not normally distributed. Instead, there are large swings. The CAPM
does not explain the variations in returns.
6. The above limitation leads to another one. The variance of returns is taken as a normal measurement of
risk. However, this can be true only for normally distributed returns.
7. The homogeneous expectation assumption states that everyone has the same information at the same
time. As a result, investors have identical expectations (beliefs) about asset returns. This assumption is not
valid in practice.
8. A perfect market is assumed to exist. However, there are several imperfections e.g. taxes, regulations,
restrictions on short selling, etc.
9. The following assumptions about market portfolio may not exist in practice:
(a) A market portfolio includes all assets in all markets. There is no preference between markets and assets for
an investor. Investors select assets only on the basis of the risk-return relationship.
(b) All assets are infinitely divisible.
(c) The market portfolio should theoretically include all types of assets. However, it is difficult to collect data on
them. The stock exchange index is used as a proxy. Richard Roll argued, in 1977, that this substitution is
not innocuous and therefore, CAPM may not be empirically testable.
Explain the disadvantages of the CAPM.
3. Compute the beta factor and alpha values.
[Learning Outcome c]
3.1 Beta coefficient of the security: measurement of risk (denoted by βj in the CAPM formula)
The beta of a security is an index indicating how the returns of the security change in response to a change in
the stock exchange or market portfolio. The beta of the market is taken as a benchmark and its value is 1.
The beta factor can be found by examining the securities’ historical return relative to the return of the market
portfolio.
𝒊𝒊 =
𝑪𝑪𝑪𝑪𝑪𝑪𝒋𝒋,𝒎𝒎 𝒊𝒊 × 𝒎𝒎 × 𝒋𝒋, 𝒎𝒎 𝒊𝒊 × 𝒋𝒋, 𝒎𝒎
=
=
𝒎𝒎𝟐𝟐
𝒎𝒎𝟐𝟐
𝒎𝒎
Where:
J
`
Cov j,m
I
M
Iam
= beta of the security i
= covariance of returns of the security I and the market
= standard return deviation of security i
= standard deviation of return of the market
= coefficient of correlation between the security i and the market
214 : Investment Decisions
214 : Investment Decisions
236 Investment Decisions
214 : Investment Decisions
© GTG
© GTG
© GTG
Beta of the security:
Beta of the security:
% return
% return of
Beta of the security:
Security A
Market
of%security
return
% market
return of
A
index
(A) A
Index
(I)
Security
Market
of security
market
% return
% return of
20X1
1500
1450(I)
23.33%
20.69%
A
index
(A)
Index
Security A
Market
of security
market
20X2
1850
1750
21.62%
17.14%
20X1
1500
1450
23.33%
20.69%
A
index
(A)
Index (I)
20X3
2250
2050
15.56%
7.32%
20X2
1850
1750
21.62%
17.14%
20X1
1500
1450
23.33%
20.69%
20X4
2600
2200
20.17%
15.05%
20X3
2250
2050
15.56%
7.32%
20X2
1850
1750
21.62%
17.14%
20X4
2600
2200
20.17%
15.05%
20X3
2250
2050
15.56%
7.32%
Covariance of security with market index = 56.56/3 = 18.85
20X4
2600
2200
20.17%
15.05%
Covariance
of security
market
index = 56.56/3 = 18.85
Standard deviation
= with
95.98
/ 3 = 5.656
A-A
A3.16
-A
1.45
3.16
A-A
(4.61)
1.45
3.16
(4.61)
1.45
(4.61)
I- I
I5.64
- I
2.09
5.64
I- I
(7.73)
2.09
5.64
(7.73)
2.09
(7.73)
(A - A )
(A - A
)
(I- I )
I)
(A
(17.84
I -- A
3.04
17.84
(I- I )
35.68
3.04
17.84
56.56
35.68
3.04
56.56
35.68
56.56
(I I(I )-2
I(I )-2
31.81
4.38
31.81
I )2
59.80
4.38
31.81
95.98
59.80
4.38
95.98
59.80
95.98
Standard deviation
= with
95.98
/ 3 = 5.656
Covariance
of security
market
index = 56.56/3 = 18.85
2=
2
Variance of the market index = (SD) (5.656) = 31.99
Standard deviation = 95.98 / 3 = 5.656
2=
2
Variance of the market index = (SD) (5.656) = 31.99
COV(security
index)
2 = A, market
2
Variance
ofA,the
market
(5.656) = 31.99
Beta (security
market
index) =index = (SD)
COV(security
A,
market
index)
variance (market index)
Beta (security A, market index) =
variance (market
index)
COV(security
A, market
index)
Beta (security A, market index) == 18.85/31.99
= 0.589
variance (market index)
18.85/31.99
= 0.589
= 18.85/31.99
= 0.589
Beta can also be calculated by plotting the returns of a security against the returns of the market, drawing a line
and
the slope
the line.
This
is shown
in the diagram
Betathen
can finding
also beout
calculated
byofplotting
the
returns
of a security
againstbelow:
the returns of the market, drawing a line
and then finding out the slope of the line. This is shown in the diagram below:
Beta
can also
be calculated
by plotting the returns of a security against the returns of the market, drawing a line
Diagram
2: Calculation
of Beta
and then finding out the slope of the line. This is shown in the diagram below:
Diagram 2: Calculation of Beta
Diagram 2: Calculation
of Beta
Security
return
Security
(%)
return
Security
(%)
return
(%)
Slope of
characteristic
Slope of line
(A/B)
gives the line
beta
characteristic
Slope
of
of the
security
(A/B)
gives
the beta
characteristic line
of the security
(A/B) gives the beta
of the security
A
A
A
B
B
B
Market return (%)
Market return (%)
Market return (%)
If the beta of a security is equal to 0.7, it indicates that when the market return changes by 10%, return on this
security
is likely
to change
by 7%to
(0.7
x 10%).
If the beta
of a security
is equal
0.7,
it indicates that when the market return changes by 10%, return on this
security is likely to change by 7% (0.7 x 10%).
If the beta of a security is equal to 0.7, it indicates that when the market return changes by 10%, return on this
security is likely to change by 7% (0.7 x 10%).
Implication of beta value
Implication of beta value
Beta value
Implication
Implication of beta value
More
than 1
Security
is known as an aggressive security. The share price is more volatile than the value
Beta value
Implication
of
the index.
Due to
the return offered
byThe
aggressive
securities
is volatile
more than
More than 1
Security
is known
asthis,
an aggressive
security.
share price
is more
thanthat
theoffered
value
Beta value
Implication
by
the index.
index during
the loss
is greater securities
than that sustained
by the
in
of the
Due to the
this,bull
theperiod
returnand
offered
by aggressive
is more than
thatindex
offered
More than 1
Security
is known as an aggressive security. The share price is more volatile than the value
the
bear
period.
by the
index
during the bull period and the loss is greater than that sustained by the index in
of the index. Due to this, the return offered by aggressive securities is more than that offered
Less
than 1
Security
known as defensive
security. The
share
price
less volatile
than the
value of the215
the bear is
period.
© GTG
Security
Line
(SML)
and
theisthan
Capital
Asset
Pricing
Model
by the index during theThe
bull
periodMarket
and the
loss
is greater
that
sustained
by the(CAPM):
index in
index.
Due
to
this
the
security
offers
less
gain
(as
compared
to
the
index)
during
the
Less than 1
Security
known as defensive security. The share price is less volatile than the value
of bull
the
the
bear is
period.
period
the bear
period.
index. and
Due vice-versa
to this thefor
security
offers
less gain (as compared to the index) during the bull
Less than 1
Security is known as defensive security. The share price is less volatile than the value of the
Equal to 1
Security
is known
as neutral
and follows the returns offered by the index.
period and
vice-versa
for the security
bear period.
index. Due to this the security offers less gain (as compared to the index) during the bull
Equal
to
1
Security
is
known
as
neutral
security
and follows
thestock
returns
offered by
the index.On the other
Defensive securities
will be
attractive
to investors
in aperiod.
period
when the
exchange
is declining.
period
and
vice-versa
for the bear
hand,
securities
be attractive
to investors
in afollows
period the
when
the stock
exchange
is rising.
Equalaggressive
to 1
Security iswill
known
as neutral
security and
returns
offered
by the index.
The Security Market Line (SML) and The Capital Asset Pricing Model (CAPM): 237
216 : Investment Decisions
© GTG
3.2 Alpha values
In analyzing risk adjusted returns it is necessary to compare them against a benchmark to access if there is
value in the security. This is done by computing the alpha of the security.
The difference between the estimated return and the required return is called the alpha value of the security.
Alpha value is therefore the excess return that the security generates over the benchmark. If the alpha is
positive, it indicates the stock is undervalued and if it is negative, it means the stock is overvalued.
The alpha is computed as:
Return on the security – (return on the benchmark X beta factor of the security)
Continuing from the previous example of calculation of beta of the security,
Let’s calculate the alpha value of Security A
Average return on security (as computed above) = 20.17%
Average return on market index (as computed above) = 15.05%
Beta factor = 0.589
Alpha = 20.17- (0.589 X 15.05)
= 20.17-8.86
= 11.31%
Therefore, the stock outperforms the index return; the investor should purchase the shares since they are
undervalued.
Compute the alpha factor from the following information and determine whether the shares are overvalued or
undervalued
Beta
Average return (last 5 yrs)
Market Index
1
15%
Shares of T Ltd
1.2
18%
4. Compute the geared and ungeared betas.
Shares of Z Ltd
0.60
12%
[Learning Outcome d]
4.1 Gearing
Gearing is the relationship between the relative proportions of debt and equity finance used by a firm. It is the ratio
of a company's long-term funds to its total capital. The ‘market gearing’ of a company is a measure of the
company’s gearing, based on its market value of debt and equity.
Market gearing can be calculated by using the following formula:
Market gearing ratio =
D
E +D
Where,
D is the market value of debt
E is the market value of equity
238 Investment Decisions
216 : Investment Decisions
© GTG
Let’s try to calculate the market gearing ratio of Spiral Inc assuming:
1. it has two million equity shares quoting Tshs 150 each; and
2. Tshs 350 million of debt with a market value of 80%.
To calculate the market gearing of Spiral Inc, we need the market value of equity and debt.
Market value of equity (E) = 2,000,000 x Tshs 150 = Tshs 300 million
Market value of debt (D) = Tshs 350 million x 0.80 = Tshs 280 million
Market gearing =
D
E +D
Using the above formula, market gearing can be calculated as:
=
Tshs 280 million
= 0.48
Tshs 280 million + Tshs 300 million
4.2 Asset beta
The beta of an investment project takes into account the risk arising from the nature of an investment project
(business risk) and the risk arising from the way in which the company finances the investment project (financial
risk). Hence for calculating a project-specific discount rate, it is necessary to remove the effect of the financial
risk or gearing from each of the proxy equity betas (betas of individual companies). The betas used for calculation
of project-specific risk must reflect only the business risk.
Asset beta can be calculated as:
𝑎𝑎 =
𝑉𝑉𝑒𝑒
𝑉𝑉𝑑𝑑
+
𝑉𝑉𝑒𝑒 + 𝑉𝑉𝑑𝑑 (1 − 𝑇𝑇) 𝑉𝑉𝑒𝑒 + 𝑉𝑉𝑑𝑑 (1 − 𝑇𝑇)
𝑎𝑎 = 𝑉𝑉𝑒𝑒 + 𝑉𝑉𝑑𝑑 Where,
a = asset beta
e = equity beta
d = debt beta
Ve = market value of company’s shares’
Vd = market value of company’s debt
((Ve + Vd(1 - t)) = after tax market value of company
T = company profit tax rate
4.3 Ungearing equity betas
Usually the market value of a company’s debt is very small compared to the market value of its shares. Moreover,
it has been observed that the value of debt beta is much lower as compared with the value of equity beta. While
calculating the asset beta, the value of debt beta reduces further due to the effects of tax-efficiency. Hence, it is a
common practice to assume debt beta as zero while calculating the asset beta.
Due to this assumption, the formula for asset beta is modified as:
𝑎𝑎 = 𝑒𝑒 ×
𝑉𝑉𝑒𝑒
𝑉𝑉𝑒𝑒 + 𝑉𝑉𝑑𝑑 (1 − 𝑡𝑡)
The Security Market Line (SML) and The Capital Asset Pricing Model (CAPM): 239
The Security Market Line (SML) and the Capital Asset Pricing Model (CAPM): 217
© GTG
Where,
a = asset beta
e = equity beta
Ve = market value of company’s shares’
Vd = market value of company’s debt
((Ve + Vd(1 - t)) = after tax market value of company
T = company profit tax rate
This calculation removes the effect of the financial risk or gearing of the proxy company from the proxy beta, hence
it is called ‘ungearing the equity beta’. Similarly, the amended asset beta formula is called the ‘ungearing formula’.
The asset beta for the investment project can be calculated by taking the average of the ungeared betas of
the proxy companies.
4.4 Equity beta
The systematic risk is represented by equity beta; therefore, it includes business risk as well as financial risk. If
a company has no gearing, and hence no financial risk, its equity beta and its asset beta are identical.
4.5 Regearing asset beta
The average betas of proxy companies will represent only the business risk faced by the company. Usually, an
investment project’s assets are financed by debt and equity. Therefore, the investment project’s asset beta must
be regeared to reflect business as well as the finance risk posed by the proposed investment project.
The asset beta can be regeared by rearranging the formula used for ungearing the beta.
𝑎𝑎 = 𝑒𝑒 ×
𝑉𝑉𝑒𝑒 + 𝑉𝑉𝑑𝑑 (1 − 𝑡𝑡)
𝑉𝑉𝑒𝑒
Calculating the project-specific discount rate
The regeared beta can be used in the CAPM formula to calculate the project-specific discount rate.
The following steps must be followed to calculate a project-specific discount rate:
Step 1: Identify proxy companies.
Step 2: Determine the following for the proxy companies:
(i) equity beta
(ii) finance risk i.e. gearing
(iii) applicable tax rate.
Step 3: Obtain asset betas by ungearing equity betas.
Step 4: Calculate the average asset beta.
Step 5: Regear the asset beta.
Step 6: Use CAPM to calculate the project-specific discount rate
The application of the capital asset pricing model to calculate a project-specific discount rate can be best
understood by the following example.
Home Decor Plc is a company that manufactures high-quality furniture and accessories. It has received a proposal
to diversify into the construction business from its business development manager. It needs to calculate an
appropriate discount rate for the new venture, which has an expected return of 14 per cent. Home Decor Plc will
use the Capital Asset Pricing Model to establish this discount rate, and has the following information about suitable
surrogate companies:
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Sweet Home Plc: This company has an equity beta of 1.89 and is wholly involved in construction. It is financed
by 30 per cent debt and 70 per cent equity.
Home Builder Plc: This company has an equity beta of 1.91 and is also wholly involved in construction. It is
financed by 35 per cent debt and 65 per cent equity.
Home Makers Plc: This company has an equity beta of 1.95 and is financed by 25 per cent debt and 75 per
cent equity. It is split into two divisions of equal size: one division constructs buildings and the other manufactures
paint. The risk involved in the paint division is 50 per cent higher than in the construction division.
Other information
 Home Decor Plc has traditionally adopted a financing mix of 40 per cent debt and 60 per cent
equity, although the project; if accepted will be financed entirely by equity finance.
 The current yield on treasury bills stands at 5 per cent, whereas the return on the stock exchange is 9
per cent.
 30 per cent corporation tax is applicable for all companies.
 It can be assumed that there is no risk involved in corporate debt.
We can use the information given above to calculate an appropriate discount rate to appraise the project.
Step 1: Calculate the appropriate asset betas by reducing the quantum of debt in the capital structure of the
surrogate companies’ equity betas using the following equation:
𝑎𝑎 = 𝑒𝑒 ×
𝑉𝑉𝑒𝑒
𝑉𝑉𝑒𝑒 + 𝑉𝑉𝑑𝑑 (1 − 𝑡𝑡)
Sweet Home Plc
𝛽𝛽𝑎𝑎 = 1.89 ×
70
70+30(1−0.3)
= 1.45
Home Builder Plc
𝛽𝛽𝑎𝑎 = 1.91 ×
65
65+35(1−0.3)
= 1.39
Home Makers Plc
𝛽𝛽𝑎𝑎 = 1.95 ×
75
75+25(1−0.3)
= 1.58
In the case of Home Makers Plc, the business risk of its paint division is partly reflected in Home Maker’s asset
beta which is irrelevant to the proposed project. Hence, we will have to calculate it further. Since the paint division
is 50 per cent more risky than the construction division, its asset beta is 1.5 times the asset beta of the construction
division. The asset beta of its construction division can be calculated as follows:
Home Makers asset beta = (0.5 x Paint asset beta) + (0.5 x Construction asset beta)
1.58 = (0.5 x 1.5 x βac) + (0.5 x βac)
Therefore:
Step 2:
Step 3:
𝛽𝛽𝑎𝑎 =
1.58
= 1.26
1.25
Take an average of the three asset betas:
Surrogate asset beta = (1.45+1.39+1.26)/3 = 1.37
Introduce further debt in the capital structure of Home Decor and accordingly assess its financial
risk:
Surrogate equity beta = a = 1.37 x [60+(40x(1-0.3))]/60 = 2
Continued on the next page
The Security Market Line (SML) and The Capital Asset Pricing Model (CAPM): 241
The Security Market Line (SML) and the Capital Asset Pricing Model (CAPM): 219
© GTG
Step 4: Insert the surrogate equity beta into the Capital Asset Pricing Model to calculate the hurdle rate:
Rj = 0.05 + 2 x (0.09 – 0.05) = 0.13, i.e. 13 per cent
The expected rate of return of the project (14 per cent) is greater than the discount rate (13 per cent) and hence
it is advisable to accept the project.
SKF Plc a company that manufactures ball bearings has received a proposal for diversifying into the automobile
manufacturing business from its business development manager. It needs to calculate an appropriate discount
rate for the new venture, which has an expected return of 19 per cent. SKF Plc will use the Capital Asset Pricing
Model to establish this discount rate, and has the following information about suitable surrogate companies:
Speed Automobiles Plc
This company has an equity beta of 1.89 and is wholly involved in automobile manufacturing. It is financed by
45 per cent debt and 55 per cent equity.
Wheels Automobiles Plc
This company has an equity beta of 1.91 and is also wholly involved in automobile manufacturing. It is financed
by 35 per cent debt and 65 per cent equity.
Other information




SKF Plc has traditionally adopted a financing mix of 50 per cent debt and 50 per cent equity, although the
project, if accepted, will be financed entirely by equity finance.
The current yield on treasury bills stands at 6 per cent, whereas the return on the stock exchange is 11 per
cent.
30 per cent corporation tax is applicable for all companies.
It can be assumed that there is no risk involved in corporate debt.
Required:
With the information given, calculate an appropriate discount rate for appraising the project and advise the
company whether or not to accept the proposal of diversification.
5. Compare the CAPM and the Arbitrage Pricing theory (APT).
[Learning Outcome e]
5.1 Arbitrage Pricing Theory (APT)
Another famous asset pricing theory is the arbitrage pricing theory developed by Stephen Ross in the 1970s. It
gained prominence because it is not subject to the restrictive CAPM assumptions.
The APT is a revolutionary model because it allows the user to adapt the model to any asset or security. It is based
on the concept of arbitrage. Arbitrage essentially is the purchase and sale of two securities that are similar
on a simultaneous basis to gain from the price differential. This concept in the subject of determining the asset
pricing, is concerned with finding two securities which have the same features, but different prices and returns.
The investor would then sell the expensive security. The assumption is that security prices adjust as investors
form portfolios while seeking to earn profits. The prices reach equilibrium when the arbitrage options end. Arbitrage
ensures that riskless assets provide the same returns in competitive markets.
The assumptions of the theory are:




An asset's return is dependent on various macroeconomic, market and security-specific factors. E.g. GDP
Growth, inflation, interest rate scenario, government regulations, competition, supplies constraints etc.
Capital markets are perfectly competitive.
Investors always prefer more wealth to less wealth.
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The APT is similar to extended CAPM and the formula is given as
Required return on asset
= R f + f1(rf1 – rf )+ f2 (rf2 – rf ) + f3 (rf3 – rf ) + f4 (rf4 – rf ) + ... + fk (rfk – rf )
Where,
f1, f2 are the asset sensitivities to the factors 1, 2 .. k,
‘rf1, rf2 are expected returns to factors 1, 2,K
‘k is the number of factors affecting security returns.
The shares of Tohan Ltd have a beta factor of 0.2 in relation to inflation, 0.45 in relation to GDP growth and 1.2
in relation to market portfolio. Assume the risk-free return to be 6% and the expected return on market portfolio
to be 12%. The expected growth in inflation is 3% and GDP is 7%.
Let’s determine the expected return using APT
= R f + f1(rf1 – rf )+ f2 (rf2 – rf ) + f3 (rf3 – rf ) + f4 (rf4 – rf ) + ... + fk (rfk – rf )
= 6% + 1.2(12%-6%) + 0.2 (3%-5%) + 0.45(7%-5%)
= 6% + 7.2% -0.4%+0.9%
= 13.7%
Although the APT takes into account multiple factors, its practical application is questionable. This is because it
is difficult to estimate the relevant factors and further determine their risk sensitivity. Therefore, while APT may
theoretically seem more convincing than CAPM, the fact cannot be concluded.
5.2 Compare CAPM and APT
Having discussed the Arbitrage Pricing theory, let’s compare it with the CAPM.
S No.
1
Capital Asset Pricing Model (CAPM)
CAPM is based on investors’ portfolio
demand and equilibrium
Arbitrage pricing theory (APT)
APT is based on the factor model of returns and
arbitrage
2
A stock's performance is evaluated on the APT, on the other hand, looks at the performance of a
amount of risk that the stock adds to the stock individually and not in the context of other stocks’
given portfolio. It looks at how the stock's performance within the portfolio.
expected risk interacts with the expected
risk of other stocks in the portfolio
3
CAPM suggests that returns are governed
by only one factor i.e. systematic risk.
APT considers multiple factors, both macroeconomic
and microeconomic
4
It is subject to numerous restrictive
assumptions pertaining to efficiency of the
capital market and investor preferences.
The APT is devoid of the CAPM assumptions. It makes
assumptions that capital markets are perfectly
competitive, investors always prefer more to less
wealth, the stochastic process generating asset returns
can be presented as a k- factor model.
5
CAPM considers only market risk and has
suggested a statistical method to measure
it.
Although APT is more customisable than CAPM, it is
more difficult to apply. This is because determining which
of the factors influence a stock or portfolio takes a
considerable amount of research. Furthermore, their
sensitivity needs to be estimated.
TheSecurity
SecurityMarket
MarketLine
Line(SML)
(SML)and
andthe
TheCapital
CapitalAsset
AssetPricing
Pricing
Model
(CAPM):
243
The
Model
(CAPM):
221
© GTG
List the advantages and limitations of APT.
6. Assess performance of a portfolio using the risk adjusted benchmarks – The Treynor,
Jensen and Sharpe Measures.
[Learning Outcome f]
6.1 Sharpe’s Ratio
Nobel Laureate William Sharpe developed this model. The Sharpe’s ratio measures what return the portfolio
earns per unit of risk. It is also called the reward to variability ratio.
S=
Return on portfolio - risk free return
Standard deviation of portfolio
The top half of the ratio looks at what a portfolio returned over a set period and subtracts what an investor could
have earned in a risk-free investment, typically such as three-month Treasury bills, over that same period. The
denominator is the portfolio's standard deviation, which measures the volatility of the portfolio. The higher the ratio,
the more an investor is compensated for the risk he takes on.
Diagram 3: Sharpe’s Ratio
In the graph given above, the intercept of the CAL (Capital Allocation Line) is at the risk-free rate. This capital
allocation line is the investment opportunity set of all possible combinations of the risk-free and risky assets. The
risk-free return can be subtracted from the portfolio return to obtain the proportion of the return due to the risky
asset.
An investor is contemplating investing funds amounting to Tshs 100 million in two capital assets. He wants to
invest Tshs 60 million in a risk-free return (6%T bill) and the balance in a risky return that will fetch 16%. The
standard deviation of his portfolio is 25%.
In this case, the Portfolio Return =
Sharpe’s ratio =
10% - 6%
60
100 − 60
X6% +
X 16% = 3.6% + 6.4% = 10%
100
100
= 0.16
25%
The advantage of Sharpe’s ratio as compared to other models is that it uses the standard deviation of the portfolio
i.e. the volatility of the portfolio rather than measuring the volatility against a benchmark. However, this ratio needs
careful consideration because it is based on standard deviation as a measure of risk which measures the
overall risk and does not consider upside and downside risk.
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Consider the following portfolios:
Portfolio X
Portfolio Y
Expected return
8%
14%
Risk free rate
4%
4%
10%
24%
(8%-4%) / 10% =0.40
(14%-4%)/24% = 0.4166
Standard deviation
Sharpe ratio
Portfolio Y according to Sharpe’s ratio produces slightly higher returns than portfolio X. However, it is questionable
whether an investor would be willing to take such higher risk (considering high volatility) for marginally higher
returns.
6.2 Treynor’s ratio
It calculates the fund’s average excess return to the fund’s beta. It is similar to the Sharpe ratio but uses beta
instead of standard deviation. Treynor ratio assumes that unsystematic risk or specific risk can be eliminated
through diversification. Hence only the systematic risk (beta) is considered to evaluate performance.
T=
Return on portfolio − risk free return
Beta of the portfolio
Both the above ratios measure risk adjusted returns. While the Sharpe ratio considers all elements of risk
(systematic and unsystematic), the Treynor ratio considers only systematic risk. Of the above ratios, which one
to deploy depends on the portfolio under consideration. For example, while evaluating diversified equity funds, the
Treynor ratio is more favourable.
This is because of the inherent nature of the fund; the portfolios are fully diversified which eliminates specific risks.
On the other hand, the Sharpe ratio is good to evaluate sector-specific funds since they would not be fully
diversified.
Let’s compare the two funds:
Portfolio
20X1
20X2
20X3
20X4
Fund A
18.0
28.0
0.5
-20
Average
return%
6.62%
Fund B
12
15
85
-55
14.25%
Risk free
rate %
4%
4%
Beta
0.60
Treynor
ratio
4.367
2.40
4.271
Although Fund B has a higher average annual return as compared to Fund A, its beta is very high at 2.4 as
compared to 0.60 for Fund A. Therefore, the Treynor ratio for Fund A is marginally higher at 4.37 as compared
to 4.27 for Fund B.
The Security Market Line (SML) and The Capital Asset Pricing Model (CAPM): 245
The Security Market Line (SML) and the Capital Asset Pricing Model (CAPM): 223
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6.3 Jensen’s Alpha
This is the difference between the return on the portfolio and the return on the benchmark portfolio with the
same risk. Jensen’s Alpha measures the ability of active fund management to increase returns above the level
that is purely sufficient to bear market risk. This can be used to compare portfolios having similar betas.
Return
Beta
Risk free rate 8%
Portfolio X
13
0.7
Market
12
1.0
Expected return = risk free rate + beta (return on market – risk free rate)
For fund X: 0.08 + 0.7(0.12-0.08) = 0.108
Alpha = return on portfolio – expected return
= 0.13-0.108 = 0.022
An investor has investments in stocks of two companies; High Return Ltd and Value Ltd High Return Ltd earned
an average of 14% per annum over the past 3 years and had a standard deviation of 30%. Value Ltd provided
an average return of 12% over the same period but had a standard deviation of 20%.
The short-term Treasury yields are 2%.
The investor is not very happy with the performance of Value Ltd and is contemplating selling the shares. What
is your advice?
Answers to Test Yourself
Answer to TY 1
The expected return for a security is derived using capital asset pricing model (CAPM), as follows:
()
(
E r i =R f + i E(r m ) - R f
)
Where,
E(rj) = The rate of return of security j, as projected by the model
βj = The beta coefficient of security j
Rf = The minimum risk-free rate of return
E(rm) = The return of the market
A graphic representation of the above can be made by plotting the beta on X-axis and the expected return on
the Y-axis. We obtain an upward slopping line which provides the market risk premium. This is the security market
line (SML). It demonstrates that the higher the beta, the higher is the risk premium required relative to the
market.
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On the other hand, the capital market line (CML) shows the increase in expected return per unit of additional
standard deviation.
Symbolically, Slope = (E(rc) – rf)/ σR
Where
E(rc) = expected return on portfolio
rf = risk free return
σR = standard deviation of portfolio
While CML considers standard deviation of the portfolio as an appropriate risk measure, SML is concerned only
with the measure of systematic risk i.e. beta.
The CML depicts the direct relationship between the expected return and risk for efficient portfolios. The SML
applies to individual securities as well as portfolios.
Answer to TY 2
E(rj) = 0.05 + 0.90 (0.05)
= 0.05 + 0.045
= 0.095
= 9.5%
Answer to TY 3
The disadvantages of CAPM are as follows:
(a) There is no certainty about the future, as the beta is based on past performance. So, the risk profile of the
firm may change.
(b) If a company’s shares are not traded publicly then historical date will not be available to calculate the values
needed in the model.
(c) Accurately estimating the model’s inputs is difficult, i.e. risk-free rate, beta and the market return, as its
variable are unobservable.
(d) Assumes that investors hold diversified portfolios and therefore the only relevant risk is systematic risk.
However, investors may not hold fully diversified portfolios. In this case, the CAPM method may understate
the required return and the cost of equity.
(e) It assumes that returns are normally distributed. The return in equity and other markets are not normally
distributed.
(f) Variance of return is taken as a normal measurement of risk; this is applicable only for normally distributed
returns.
(g) The assumption that the investors will prefer lower risk to higher risk and that at a certain level of risk
investors will prefer higher returns to lower one may not always hold true.
The Security Market Line (SML) and The Capital Asset Pricing Model (CAPM): 247
The Security Market Line (SML) and the Capital Asset Pricing Model (CAPM): 225
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(h) Assumes that investors have identical expectations about asset returns as the same information time is
available to everyone at the same. This assumption does not hold true in practice.
(i) In practice there are several imperfections i.e. taxes, regulations, restriction on short selling etc. the
assumption of a perfect market does not hold true.
Answer to TY 4
Return on the security – (return on the benchmark X beta factor of the security)
For shares of T Ltd
= 18% - (1.2 X 15%)
= 18%-18%
= 0%
For shares of Z Ltd
= 12% - (0.6 X 15%)
= 12% - 9%
= 3%
The shares of T Ltd. are correctly valued. The shares of Z Ltd are undervalued since the alpha factor is positive.
Answer to TY 5
Step 1: Calculate the appropriate asset betas by reducing the quantum of debt in the capital structure of the
surrogate companies’ equity betas using the equation:
𝑎𝑎 = 𝑒𝑒 ×
𝑉𝑉𝑒𝑒
𝑉𝑉𝑒𝑒 + 𝑉𝑉𝑑𝑑 (1 − 𝑡𝑡)
Speed Automobiles Plc
a = 1.89 ×
Wheels Automobiles Plc
a = 1.91×
55
55 + (45 × (1− 0.3))
65
65 + (35 × (1− 0.3))
= 1.20
= 1.39
Step 2: Take an average of the two asset betas:
Surrogate asset beta =
1.20 + 1.39
2
=1.30
Step 3: Introduce further debt in the capital structure of SKF, and accordingly assess its financial risk:
Surrogate equity beta = 1.30 ×
50 + (50 × (1− 0.3))
= 2.21
50
Step 4: Insert the surrogate equity beta into the Capital Asset Pricing Model to calculate the hurdle rate:
Rj = 0.06 + 2.21 x (0.11 – 0.06) = 0.17, i.e. 17%
The expected rate of return of the project (19 per cent) is greater than the discount rate (17 per cent) and hence
it is advisable to accept the project.
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Answer to TY 6
The APT has the following advantages:
It is not as restrictive as the CAPM in its requirement about individual portfolios.
It is also less restrictive with respect to the information structure it allows.
The APT is a world of arbitrageurs and vendors of information. It also allows multiple sources of risk; indeed,
these provide an explanation of what moves stock returns.
However, the limitations are:
The APT demands that investors perceive the risk sources which may be difficult in practice and
They can reasonably estimate factor sensitivities.
Answer to TY 7
Prima facie it appears that the return given by Value Ltd at 12% per annum on an average is lower than that of
High Return Ltd. We should, however, look at the Sharpe ratio of both the companies to determine whether the
decision to sell the shares of Value Ltd is correct.
The Sharpe ratio of:
High Return Ltd is
14 − 2
and for Value Ltd is
30
12 − 2
20
= 0.40
= 0.50
The Sharpe ratio for Value Ltd is higher at 0.5 compared to 0.4 of High Return Ltd. It means that Value Ltd yielded
higher returns per unit of risk which the investor took. The decision of the investor to sell the stock of Value Ltd
does not appear to be correct.
Quick Quiz
1. What is a beta of a security?
2. What is a risk-free return?
3. Equity premium for the period 20Y1 -20Y9 was 9.1%. What does this indicate?
4. Match the following:
(i) CAPM A Multiple factor (macroeconomic and micro factors) (ii) Sharpe’s ratio B Assumption of perfect capital
market (iii) Arbitrage pricing theory C Considers only systematic risk (iv) Treynor ratio D Return to variability ratio
5. Fill in the blanks:
(a) Sharpe’s ratio considers
the graphic representation of
as the measure of risk. (Beta / standard deviation) (b) SML is
. (CAPM / APT)
(c) The asset beta for the investment project can be calculated by taking the average of the
betas of the proxy companies. (geared / ungeared)
(d) The difference between the estimated return and the required return is called the
value of the security. (alpha / market)
6. State whether the following statements are True or False.
(a) SML considers the overall risk including market risk and security specific risk.
(b) The beta value for market portfolio is 1.
(c) Systematic risk can be reduced through diversification.
The Security Market Line (SML) and The Capital Asset Pricing Model (CAPM): 249
The Security Market Line (SML) and the Capital Asset Pricing Model (CAPM): 227
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Answers to Quick Quiz
1. The beta of a security is an index of responsiveness of the changes in returns of the security relative to change
in the market portfolio.
2. Return from securities which are considered to be risk –free i.e. when the default risk is negligible is called risk
free return. E.g. return on bonds issued by the government of a politically and economically stable country is
treated as being risk free.
3. Equity premium means the market risk premium. It is calculated as return of the market less risk-free rate of
return. Equity instruments are considered risky compared to risk-free investments, for example government
bonds. Investors expect higher returns on the equity instruments compared to the return on government bonds.
This difference is the equity premium, which averaged at 9.1% between 20Y1 and 20Y9.
4.
5.
6.
(i)
(ii)
(iii)
(iv)
B
D
A
C
(a) Standard deviation
(b) CAPM
(c) Ungeared
(d) Alpha
(a) False
(b) True
(c) False
Self Examination Questions
Question 1
A research house has recommended two stocks for investment and provided the following estimates for risk and
return:
Systematic risk
TBW Ltd
RWP Ltd
1.3
0.75
Expected return
17%
14%
The return on government bonds which is considered risk free is 4.5% and DSE index returns are 15%.
Required:
Guide the investor to make a decision on which stocks to acquire by using the SML graph.
Question 2
Compute the beta factor and alpha value for the following securities:
1. Standard deviation of P Ltd is 12%
Standard deviation of market portfolio is 9%, correlation of the security with market is +0.8
Return on security 15%, return on portfolio 12%.
2. Standard deviation of Q Ltd 5%
Correlation with market portfolio is +0.9, SD of market portfolio is 4%
Return on security 16%, return on portfolio 15%.
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Question 3
The historical data of returns of the market portfolio and the security under consideration X is provided below.
You are required to calculate the systematic and unsystematic risk of the security.
Year
20Y1
20Y2
20Y3
20Y4
20Y5
20Y6
Security (X)
10
13
9
1
8
(10)
Market
6
10
10
(3)
9
(3)
Answers to Self Examination Questions
Answer to SEQ 1
Step 1
Let’s compute the required return for the stocks using CAPM
(a) TBW Ltd
E(r i ) =R f + i (E(r m ) - R f )
= 4.5% + 1.3(15%-4.5%)
= 4.5% + 13.65%
= 18.15%
(b) RWP Ltd
E(r i ) =R f + i (E(r m ) - R f )
= 4.5% + 0.75(15%-4.5%)
= 4.5% + 7.875%
= 12.375%
Step 2
Let’s plot the above on an SML graph
The Security Market Line (SML) and The Capital Asset Pricing Model (CAPM): 251
The Security Market Line (SML) and the Capital Asset Pricing Model (CAPM): 229
© GTG
Step 3
Stock TBW Ltd has an expected return of 17% whereas the required return is 18.15% under CAPM. The stock
lies below the SML and is overvalued.
Stock RWP Ltd has an expected return of 14% against the required rate of 12.375%. The stock plots above the
SML and is undervalued.
Therefore, we advise the investor to acquire stock RWP Ltd
Answer to SEQ 2
𝒊𝒊 =
𝑪𝑪𝑪𝑪𝑪𝑪𝒋𝒋,𝒎𝒎 𝒊𝒊 × 𝒎𝒎 × 𝒋𝒋, 𝒎𝒎 𝒊𝒊 × 𝒋𝒋, 𝒎𝒎
=
=
𝒎𝒎𝟐𝟐
𝒎𝒎𝟐𝟐
𝒎𝒎
Where:
J
`
Cov j,m
I
M
Iam
= beta of the security i
= covariance of returns of the security I and the market
= standard return deviation of security i
= standard deviation of return of the market
= coefficient of correlation between the security i and the market
1. For P Ltd
i
=
12x 0.8
9
= 1.07
Alpha = Return on the security – (return on the benchmark X beta factor of the security)
= 15% - (12%x 1.07)
= 15% -12.84%
= 2.16%
2. For Q Ltd
i
=
5x 0.9
4
= 1.125
Alpha = Return on the security – (return on the benchmark X beta factor of the security)
= 16% - (15%x 1.125)
= 16% -16.875%
= -0.875%
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Answer to SEQ 3
Variance is a measure of total risk and beta factor is a measure of systematic risk. Let’s compute them as
follows:
Security
(X)
Market
(Y)
X- X
Y- Y
(X- X )2
(Y- Y )2
(X- X ) (Y- Y )
10
6
4.8
1.2
23.4
1.4
5.6
13
10
7.8
5.2
61.4
26.7
40.5
9
10
3.8
5.2
14.7
26.7
19.8
1
-3
(4.2)
(7.8)
17.4
61.4
8
9
2.8
4.2
8.0
17.4
32.6
11.8
-10
-3
(15.2)
(7.8)
230.0
61.4
31.0
5.2
29.0
4.8
354.8
59.1
194.8
32.5
Variance of security X = 354.8/6 = 59.1%
Variance of market = 194.8/6 = 32.5%
Systematic risk
Beta (security A, market index) =
COV(security A, market index)
variance (market index)
COV (security A, market) = 229.2/6 = 38.2
A = 38.2/32.5 = 1.175
Systematic risk
2
=(1.175) (32.5) = 44.87%
Unsystematic risk = Total risk – systematic risk
= 59.1% - 44.87%
= 14.23%
118.8
229.2
38.2
Sum
Average
D1
SECTION D
Short,Medium and Long Term Alternatives: 253
FINANCING DECISIONS
STUDY GUIDE D1: SHORT, MEDIUM AND
LONG TERM ALTERNATIVES
Working capital needs are generally financed through short-term sources of finance. In addition to routine day- today cash flow, short-term finance is also needed to manage unforeseen circumstances or seasonal factors that
cause a shortfall in the cash available to the business. There are different sources of short-term finance.
Each source of short- t e r m finance has its own unique features. A finance manager will have to select the
source of finance that is most suited to the given situation. In certain situations, trade credit may be suitable
while in others, an overdraft, short-term loans, factoring or lease finance may be preferred.
Medium and long-term finance is generally obtained to finance long-term assets. Its volume is likely to be higher
than the volume of short-term finance. The amount is locked up for a longer time hence the risks for the
investors are higher. As a result, it is relatively difficult, compared to short-term finance, to obtain medium and
long-term finance.
In this Study Guide, we try to understand the nature of the short- and medium-term sources.
a) Describe, compare and contrast short term sources of finance – overdraft, trade credit, factoring, bills of
exchange, and acceptance credit.
b) Describe, compare and contrast forms of medium-term sources of finance – term loan, hire purchase,
and leasing.
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1. Describe, compare and contrast short term sources of finance – overdraft, trade credit,
factoring, bills of exchange, and acceptance credit.
[Learning Outcome, a]
Total funding required
Initially, the management of Vista Ltd tried to source Tshs 100 billion through a medium-term loan. However, the
loan advisor at At Your Service Bank (AYSB) suggested that an overdraft facility should be included, in order to
provide Vista Ltd with a more appropriate and need based finance package. Together, the loan advisor and Vista’s
management agreed that a Tshs 85 billion medium term loan would cover the expansion project, and an overdraft
of Tshs 30 billion would be adequate for working capital needs.
Financial terms


After analysing the proposals and in- d e p t h negotiations, AYSB agreed to provide TSHS 80 billion medium
term loan at an interest rate of 10% per annum, payable quarterly. The loans are unsecured, for four years
The bank also offered an overdraft facility of TSHS30 billion. The interest rate was negotiated at 3% above
base rate, with an arrangement fee of TSHS200,000 for the use of the facility.
Key point
Although only a part of the short-term credit has been used, the overdraft facility provided Vista with the desired
safety net during a period of uncertainty.
Short term finance is usually needed for businesses to run their day-to-day operations. Finance needs could
involve ordering inventory and supplies, paying wages to employees, etc. Short term finance is generally arranged
quickly as opposed to long term finance. In addition to this, short term finance offers a great deal of flexibility
regarding the timing of the amount withdrawn.
Various sources of short-term finance and their characteristics are discussed below:
1.1 Overdraft
Overdraft (or cash credit) from a bank is one of the most popular methods of obtaining working capital finance. It
works as follows:
1. A limit or line of credit is sanctioned by the bank to the borrower.
2. This limit is not utilised all at one time i.e. in a lump sum.
3. The drawing power is determined based on the security and the margin stipulated. Security for this purpose
is normally by way of current assets such as inventories (that are paid for, i.e. after reducing the trade
payables) and trade receivables.
4. Sometimes, personal guarantees from the promoters are also requested.
5. Based on the day-to-day requirements, the borrower issues cheques drawn on the account to the suppliers
and deposits the cheques collected from customers.
6. The balance fluctuates from day to day; the bank passes the cheques issued by the borrower as long as the
balance stays within the sanctioned limit and the borrowing power.
7. The rate of interest is usually 2-3% above the prime rate.
8. Sources of this kind of credit are commercial banks.
Short,Medium
andLong
LongTerm
TermAlternatives:
Alternatives:323
255
Short,
Medium And
© GTG
The Dar es Salaam Bank sanctioned an overdraft limit worth Tshs 10 billion to Carefine Ltd, secured on its
inventory, with a 25% margin in the bank’s favour. The latest stock statement submitted by the bank shows the
availability of inventory:


Case 1: Tshs 10 billion
Case 2: Tshs 15 billion
Drawing power of Carefine is calculated as follows:
Case 1: 10billion x 75% = Tshs 7.5 billion
Case 2: 15billion x 75% = Tshs 11.25 billion
However, it cannot exceed the sanctioned limit i.e. Tshs 10 billion.
The bank officials will pass the cheques issued by Carefine so long as its fluctuating overdrawn balance
remains below Tshs 7.5 billion or Tshs 10 billion in case 1 and case 2 respectively.
9. Interest is calculated only on the balance actually used and not on the sanctioned limit. However, in some
countries, a small commitment charge is levied on the unutilised part of the limit.
10. These overdrafts are technically repayable on demand and normally sanctioned for a year at a time.
However, banks usually do not recall these advances. They are renewed year after year. In fact, if the
business is growing, the limits may be increased over a period of time.
Advantages and limitations of overdraft
Features that make the overdraft popular are:

Flexibility: usually, a maximum overdraft limit or facility is provided by banks. In the case of overdraft, the
borrower may not utilise the full facility immediately, but s/he may withdraw some funds from the availed limits
as and when required.

Limited documentation: for overdraft processing, the legal documentation is minimal. The prime documents
required by the banks are usually the maximum overdraft limit, the interest payable and the security required.

Speed: since the formalities to be completed and the assessment time required by the bank are quite low,
the overdraft facility can be obtained quickly by the borrower.

Interest: is only paid on the amount actually utilised, rather than on the full facility.
The main limitations of overdraft are:

Repayable on demand: the overdraft facility provided by the banks could be withdrawn at any time
by them. Generally speaking, this is only a technicality and not really an issue unless the firm is defaulting on
the interest payments or its performance has been unsatisfactory over a period.

Increase in limits: entities with few assets to offer as security will find it difficult to obtain an increase in
the limits.

Interest rate: the bank charges different interest rates to different customers depending on their
perceived credit risk. Moreover, if the interest is attached to a base rate, the rates will vary as the base rate
changes.
1.2 Trade credit
Quite often, businesses will extend credit facilities to their customers as a strategy for increasing sales. Customers
are allowed a certain amount of credit in goods and services and are informed of an authorized period within
which payment must be made. Credit available from suppliers is one of the easiest and cheapest sources of shortterm finance. If credit is obtained, it reduces the need for finance from other sources e.g. banks. The
advantage of trade credit is that interest is not usually charged unless the firm defaults on payment and is easily
sourced.
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Tanco currently has a one- m o n t h term of credit. The annual total credit purchases are estimated at Tshs
24 billion. This means that, on an average, 1/12 x 24 = Tshs 2 billion worth of creditors are outstanding. In
other words, Tshs 2 billion is financed by the creditors.
The creditors are ready to increase the credit terms to 2 months if prices are increased by 0.5%. Should the
company go ahead with this? Tanco’s bank charges 10% interest on overdrafts.
It should be remembered that the cost of trade credit beyond the agreed terms is very high in terms of the penal
interest charged, as well as in terms of straining relationships with suppliers.
1. Credit risk
There are two risks regarding trade credit, from a supplier’s point of view.
(a) The risk that customers will not pay on time (slow payment). If this occurs, the length of the cash operating
cycle increases, and the business is without cash for a longer period.
(b) The risk that customers will not pay at all. This will result in losses for the business as the debts will be
written off as an expense for bad debts or delinquent receivables.
2. Assessing credit worthiness
Credit worthiness refers to the dependability of the customers to meet their commitments regarding payment
and other terms of sale. Assessing credit worthiness of a new customer reduces the risk of bad debts and slow
payments. It is important to monitor continuously the payment history of the customers to ensure that the credit
terms are adhered to by them. If the customers regularly delay payments, there is a need to revise the credit terms,
which may include putting such customers on a “cash basis”.
The following methods are used to assess credit worthiness:
(a) Bank references: bank references provided by new customers give information about their financial standing.
However, as the reports from banks are very general in nature and often vague, not much reliance can be
placed on them.
(b) Trade references: trade references provide information about the satisfactory conduct of business dealings
between the potential customers and their suppliers. The problem with such references is that the customer
is free to choose the suppliers for reference. It is therefore, unlikely that the customer will provide the names
of suppliers with whom they have a poor trade relationship.
(c) Financial information analysis: the financial statements of a customer can provide valuable information
about the creditworthiness of the customer. Analysing the days payable and receivables, the cash flow and
the profitability of the customer’s business can provide a good insight into the liquidity and profitability position
of the customer.
(d) Credit rating: professional credit rating bureaus are available e.g. Dun and Bradstreet, Standards and
Poors. For a fee, they provide reports about customers such as their history, payment trends, financial
problems and other relevant information.
(e) Publicly available information: e.g. newspapers, trade journals
3. Using trade credit effectively
(a) Negotiating for best credit terms
The purchase department has to negotiate the best terms with the suppliers, considering the market conditions.
These terms will be a combination of factors such as price, credit period, and discounts.
(b) Good relations with suppliers
In order to use trade credit effectively, good relations with suppliers are essential. Such relations are built
through consistently complying with the suppliers’ terms. Delays in payment beyond the normal credit period affect
the company’s credit rating adversely and should be avoided. Understanding the market conditions and helping
suppliers to cope with them also helps.
Short,Medium and Long Term Alternatives: 257
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(c) Extending credit during difficult times
Short, Medium And Long Term Alternatives: 325
During difficult times, longer credit periods may be needed. A good relationship with suppliers will increase the
likelihood of the suppliers agreeing to this.
4. Early settlement and bulk discounts
When suppliers offer discounts, it is necessary to analyse the financial impact of accepting the discounts. A cost
benefit analysis will be required.
A supplier allows cash discount of 3% if payment is made within 10 days.
The terms stipulate that payment must be made within 40 days.
The company has a choice of paying Tshs 0 97 per Tshs 1 on day 10.
Or else, the company can pay the supplier Tshs 1 for every Tshs 1 it owes to the supplier on day 40.
Required:
Should the company accept the discount if alternative investments yield a 30% return?
5. Managing foreign accounts payable
The issues discussed in connection with foreign receivables are applicable for foreign payables as well, although
from the opposite side.
(a) Credit terms
Obtaining credit terms from the foreign supplier is more difficult than negotiating with a domestic supplier because
of the risks involved for the foreign supplier. However, using a letter of credit of a reputable bank is one of the best
and most popular ways of doing this. Normally, ordinary letters of credit are accepted. However, in some cases
the supplier may insist on a confirmed letter of credit where a letter of credit issued by a bank will be confirmed
by a foreign bank.
Usman Trading, a company in Dar es Salaam, places a purchase order worth $250,000 with Pranco Co of
Japan. Usman Trading gets its bank, NIC Bank Tanzania, to issue a letter of credit. Pranco wants this to be
confirmed by its bank, the Citi Bank. The LC issued by NIC Bank will be confirmed by Citi bank before Pranco
dispatches the material.
(b) Foreign currency
There is a risk that the amount to be paid in domestic currency will change due to variations in the foreign
currency rate. This risk is to be managed appropriately.
Continuing the above example of Usman
Suppose the rate at the time of the order placed by Usman Trading in the above example was 1$= Tshs 1600,
which changed to 1$= Tshs 1650 when the amount was actually paid. Al Othman pays Tshs 250,000 x (1650
1600) = Tshs 12.50million extra.
The company should have planned for this risk in advance and taken appropriate action to avoid this loss.
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The benefits and limitations of Trade credit
(a) Benefits of trade credit
(i) Increase in sales: from the perspective of the supplier, trade credit improves sales over time by enabling
customers to make purchases without having to pay cash immediately. This flexibility in purchasing methods
also encourages customers to make larger purchases when prices are right.
(ii) No cash: from the customer’s perspective, the availability of credit enables it to buy inventory even when
the firm is low on cash. Possessing liquidity to pay long-term debt and other more pressing obligations is
critical. Buyers may want to increase the volume of purchases when demand is higher, and the availability
of trade credit makes it more feasible to do so.
(iii) Collateral: there is no guarantee required to secure trade credit financing. The amount of credit will depend
on two major aspects; the relationship of a firm with the supplier and the repayment ability of the firm.
(iv) Continuous: trade credit is considered a continuous source of financing for most of the firms. This is
because firms are able to spread the payments over a certain period which in turn is helpful for suppliers.
(v) Interest free: this is the cheapest form of credit as interest is not usually charged on trade credit. Interest is
charged only if payments are outstanding.
(b) Limitations
As interest is not usually charged on trade credit, firms are tempted to maximise the use of trade credit by deferring
payment beyond the due dates. This is a misuse of the trade credit facility. The surpassing of the normal credit
terms can lead to a number of problems:
(a) When a firm is availing credit, the opportunity for obtaining cash discount is lost. This benefit may be
greater than the interest cost saved on the “free credit”.
(b) It is not always very easy and possible to obtain credit terms from new suppliers.
(c) If a key supplier is facing financial crisis or cash flow problems, it adversely affects the sustainability of
both the supplier and the customer organisations.
(d) Sometimes, regular suppliers may not be interested in extending further trade credit. It is also possible
that in order not to give trade credit, they may refuse to supply goods in the future.
(e) The constant exceeding of the normal credit terms can lead to negative goodwill and reputation in the
market.
(f) If firms are deferring payments on a regular basis, it results in reduced credit rating.
(g) Entities that suffer from late payment usually have to resort to additional overdraft finance while waiting for
their customers to pay.
1.3 Factoring
Factoring, an “off balance sheet” financing technique, is a credit transaction whereby a company holding a sale
invoice its bank or a specialised financial institution in exchange for the payment of the bill.
A factor is a financial institution that buys accounts receivable from a company at a discount. The factor takes
responsibility of collecting the accounts receivable of a business and pays an amount equal to an agreed proportion
of accounts receivable to the business.
The remaining balance of accounts receivable is paid to the business after collecting money from the accounts
receivable. The factor charges fees (for its services) and interest (on the money advanced to the business). The
transaction of collecting cash for accounts receivable before their due date allows a company to accelerate its
cash conversion cycle.
© GTG
Short,Medium
andLong
LongTerm
TermAlternatives:
Alternatives:327
259
Short,
Medium And
Diagram 1: Cash conversion
The services provided by a factor are
1. Finance provision
The factor pays an agreed proportion of the value of new invoices as soon as they are sent to customers. When
the debts are eventually collected, the factor is paid off. The factor usually charges interest on advances of
cash.
2. Administration of the sales ledger and debt collection
The factor takes over the whole of the company’s sales ledger i.e. issuing invoices and collecting debts. A fee is
charged for this service.
3. Credit protection / insurance
In some instances, the factor takes over responsibility for the company’s debts thereby protecting it from the risk
of bad debts. Factoring can be arranged ‘with recourse’ or ‘without recourse’.
Diagram 2: Factoring
4. Invoice discounting
Creditworthy invoices are sold to the factor at a discount; however, responsibility for debt collection is not
passed to the factor but is retained by the company. When the debts are eventually paid by the customers, the
factor is paid off. In effect, money is borrowed by firms from the factor using outstanding debts as security.
The service is completely confidential with the customer being unaware of the service provided. It is quite similar
to the financing service offered by factors except control of credit does not pass to the factor. Invoice discounting
is illustrated in the following diagram:
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Diagram 3: Invoice Discounting
Before deciding to use any of the above- mentioned services, a business will consider the cost and
benefit of doing so.
Advantages of factoring





Managers do not have to spend time chasing up defaulting customers.
Company does not have to incur the cost of running a receivables section.
Since cash becomes available immediately, the company can better manage its payables, and improve its
cash operating cycle and cash position.
It helps the company to grow.
It provides an alternative source of finance; sale invoices are used and other assets such as inventory,
plant, land, building etc. are still available to raise debt.
Disadvantages of factoring
 Interest charged on advances may be higher than that charged on alternative finance sources e.g.
overdrafts.
Customer may become annoyed by factors ‘pushing’ them for payment.

Factoring has a bad reputation as being associated with failing companies. The use of a factor may

suggest that the company is experiencing liquidity problems.
Once a company starts factoring it is difficult to revert to an internal system.

SUMMARY
© GTG
Short,Medium
and
Long
Term
Alternatives:
261
Short,
Medium And
Long
Term
Alternatives:
329
1.4 Bills of exchange
A bill of exchange is a negotiable instrument that a seller initiates and a buyer accepts. A bill of exchange is
discounted by the seller with a bank. After deducting a discount, the bank pays the billed amount to the
company. The bank then collects and keeps the full amount of the bill. This system is more prevalent in relation
to foreign trade.
By using a bill of exchange, the risk attached to the receivables is reduced for the following reasons:



A buyer’s bank can confirm a bill of exchange, thereby further reducing the risk and the discount.
A bill of exchange can be discounted or rediscounted and converted into cash; i.e. it is a liquid instrument.
A documentary letter of credit can be used with a bill of exchange, to reduce the risk even more.
Features of a bill of exchange
A bill of exchange has the following features:
(a) It is an instrument in writing.
(b) It must be signed by the maker or drawer.
(c) It contains an unconditional order. There is no condition attached to it e.g. A dispute about the quality or
quantity cannot be a reason to dishonour the bill. It has to be paid when due. The buyer will have other recourse
to pursue his grievances.
(d) The order must be to pay money and money only.
(e) The sum payable must be specific.
(f) The money must be payable to a definite person or to his order or to the bearer
Guaranteed Bills of Exchange
To provide greater payment security a seller may insist on having a bill of exchange guaranteed by the buyer's
bank. A guaranteed bill of exchange is one drawn on and accepted by the buyer and to which, the buyer's bank
adds its guarantee that the bill will be paid at maturity. The security to a seller comes from a bank giving an
undertaking to effect payment on a certain date regardless of the financial standing of the buyer on that date.
Advantages of bills of exchange
Organisations have used Bills of Exchange for a very long time. Their popularity is due to the advantages they
provide in a trading transaction.
(a) A bill of exchange aids the granting of trade credit legally by sanctioning payments on mutually-agreed
future dates.
(b) It provides a legal acknowledgement of the existence of debt. A bill of exchange is an official confirmation of
the demand for payment from a seller to a buyer.
(c) Through a bill of exchange, the seller can access finance by transferring debts to a bank or other financier
by just endorsing the bill of exchange to that bank or financier.
(d) A bill of exchange facilitates easy access to the legal systems in case of default. It allows the banker or
financier to hold a legal claim on both parties, i.e. The buyer and the seller. In specific situations, under a bill
of exchange, a bank or financier may have a more solid legal claim than the party who provided them the debt.
(e) A bill of exchange permits a bank to assure a drawee's acceptance (guarantee to pay on the due date) by
signing or endorsing the bill. This is how it allows a seller to get greater security over the payment.
(f) Foreign bills benefit in expanding foreign trade.
(g) The bill determines the date of payment, which cannot be delayed.
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The limitations of bills of exchange
(a) Unless a bill of exchange carries a bank guarantee, it does not eliminate the risks of non-payment, loss and
theft
(b) There is a long process involved in the receipt of a bill which consumes considerable amount of time. When a
bill is first submitted by the importer for acceptance, it is dispatched by post, and is intervene by many financial
establishments
(c) Sometimes, it is necessary to make enquiries about specific legal measures like price, language, etc. While
issuing a bill. This is because these measures are usually country-specific and may vary from country to
country
(d) Not only is there the interest (discount) payable, but also many other charges related to acceptance and
payment of the bill are to be paid. At the time of payment, transfer fees are also charged. Hence, a bill of
exchange is more expensive
On Jan 1 20X3, A draws a bill of exchange on B for 3 months for Tshs 10 million. A holds the bill without discounting
it with a bank. On March 4, 20X3, B pays the bill amount to A and avails a 12% discount.
What is the amount of discount B is entitled to?
1.5 Acceptance credit
Acceptance credit is one of the several means by which international trade is financed. Under this arrangement,
a bank or an acceptance house in the exporter's country sets up an acceptance credit facility. The exporter uses
the funds from this account up to its limit to execute export orders. This is also called acceptance financing.
A banker's acceptance is used in international trade. It is a time draft, drawn by the
seller of goods on a buyer and honoured by a bank. .An acceptance agreement
puts the acceptor under contractual obligation to pay, which strengthens a time
draft. As international trade involves banker's acceptances, they guarantee the
payment for goods.
The buyer is the
acceptor in trade
acceptance
1. Types of acceptance
There are broadly two different forms of acceptance financing which are:
(a) Trade acceptance: it is an acknowledgment of a debt and its execution is a reflection on the credit worthiness
of the buyer as well as the seller. It is a draft or a bill of exchange that is accepted or signed only by the
drawee (the buyer) and is not countersigned by the drawee's bank. Such bills are only as good as the
drawee's creditworthiness.
(b) Banker’s acceptance: it is generated when a time draft is co-signed or stamped “accepted” by the bank.
As seen earlier, a time draft is drawn on a bank to finance the shipment of goods. When the bank accepts
the draft, it makes an absolute assurance of paying the specific amount at a specified date to the holder of the
draft.
In cases where the bankers’ acceptance is a substitute to loan to finance an export, a time draft covering the
financing period is generated. The issuing bank signs and endorses the draft on the paying bank. The draft is then
accepted by the paying bank. It discounts the draft and uses the proceeds to make the obligatory payment.
On maturity of the bankers’ acceptance, it is settled by a debit to the account of the opener.
© GTG
Short,Medium
andLong
LongTerm
TermAlternatives:
Alternatives:331
263
Short,
Medium And
Prestige Engineering Products (PEP) wants to import some critical components for a new range of products it
has developed. PEP cannot pay for the components in advance and is a new customer who has yet to establish
a credit record with the German component manufacturer.
But PEP enjoys a very good credit record with its bank, First Tanzania Bank (FTB). PEP goes to its bank and
fills out the documents required for a draft to be made out to the German manufacturer. The payment date of
the draft is ten days after receipt of the components.
FTB has established a credit line for PEP and knows from experience that PEP is credit worthy. Therefore, FTM
accepts the draft on behalf of PEP and sends it on to the German manufacturer who is now assured that it will
be paid for the shipment of the components.
The German manufacturer goes to its bank and discounts FTB’s accepted draft and receives payment immediately.
On the due date, FTB will affect payment of the draft to the German manufacturer’s bank and debit the amount
to PEP’s account.
2. Pre-export financing
Acceptance financing is also used, by a borrower engaging in international or domestic shipments, to procure
material, process and pack finished goods for shipment. Under this type of arrangement, the borrower must
have a firm export sales order.
3. Working capital financing
Bankers’ acceptances are also available to finance inventories or for other working capital purposes not related
to any specific transaction
4. Characteristics of bankers’ acceptances
(a) Usually, a banker’s acceptance matures within six months or less. these are considered to be short-term
investment instruments
(b) Banker’s acceptances are actively transacted by:
(i) banks
(ii) brokers
(iii) other institutional investors
(c) Banks have the option of purchasing, discounting and selling the acceptances of other banks easily, as
funds are not tied up for longer periods
(d) Both the manner in which the bank attained the acceptance and the terms applicable to acceptance have an
influence on the creditworthiness of an acceptance. the creditworthiness for an accepting bank depends on
the creditworthiness of the customer whose transactions are financed by the accepting bank
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Similarities and differences among various short-term sources of finance
Bases
Involvement
of time,
procedures
and
formalities
Continuity
and
extension
Cost of
source of
finance
Domestic
and
international
sales
Requirement
of security
Overdraft
Trade credit
Factoring
Bills of
exchange
Involves many
procedures
Acceptance
credit
Involves
procedures
Separate for
each
transaction.
However, there
is an overall
limit set up by
the bank
providing the
acceptance
credit limit.
Generally fixed
for a period.
May change
over a period of
time. Interest
paid as
discounting
charges.
Involves time
and procedures
Easy access.
Few formalities.
Involves time
and formalities
There is
continuity. Can
extend
indefinitely,
subject to
compliance of a
few financial
performance and
legal parameters
There is
continuity and
can extend
indefinitely if
payments to
suppliers are
made on time.
There is
continuity. Can
extend for longer
periods if the
risks and the
collection
experience of
the factor is
satisfactory.
Although a
discounting limit
may be set up ,
each transaction
is separate and
not connected
with each other
Cost of overdraft
can vary from
time to time
depending on
several factors
such as financial
performance,
risk profile of the
company, state
of the economy
etc. Cost is paid
as interest
periodically
depending on
the utilisation of
the facilities.
Usually resorted
to for domestic
business funding
needs, but not
necessarily so.
Not directly
related to either
purchase or
sales.
Banks usually
demand some
security.
An inexpensive
form of credit.
Generally does
not vary.
No interest is
involved, except
in case of
delays.
May vary
depending upon
the risk and
collection
experience of
the factor and
the state of the
economy.
Interest is
charged in the
form of a
discount on the
total amount of
the bill amount
Generally fixed
for a period. May
change over a
period of time.
The interest
charged is called
discounting.
Trade credit can
be obtained from
both domestic
and international
suppliers.
Usually taken on
domestic sales
invoices. It also
involves bills of
exchange to be
accepted by the
customer.
Credit facilities
can be availed
both for
purchases and
sales.
Credit facilities
usually taken
on sales, but
can also in
some cases, be
used for
purchases.
No security
needed. Only
the credit
worthiness of the
customer is
checked.
Normally, no
separate
security is
needed to be
provided. The
receivable itself
is the security. In
the case of a
“with recourse”
sale, bad debts
are recovered
from the seller.
Usually,
separate
security is
needed to be
provided. In the
case of a “with
recourse” sale,
bad debts are
recovered from
the seller.
In the case of
purchases, the
buyer’s bank
pays the money
to the supplier
and recovers the
same from the
buyer.
Usually,
separate
security is
needed to be
provided. In the
case of a “with
recourse” sale,
bad debts are
recovered from
the seller.
In the case of
purchases, the
buyer’s bank
pays the
money to the
supplier and
recovers the
same from the
buyer.
© GTG
Short,Medium
andLong
LongTerm
TermAlternatives:
Alternatives:333
265
Short,
Medium And
2. Describe, compare and contrast forms of medium-term sources of finance – term loan, hire
purchase, and leasing.
[Learning Outcome b]
2.1 Medium term loans
With the aim of supporting the needs for capital for business projects, banks offer medium and long-term loans for
investment in non-current assets and business projects. This helps the firm to expand and grow its operations.
The availability of such loans enables firms to leverage its assets to finance its growth needs.
The loans often have fixed interest rates, with quarterly interest and repayment schedules and a set maturity date.
It is common to have a “moratorium “of one year or more after which the instalment repayment begins. This
allows time to the borrower to manage its cash flows.
There is no precise definition for the term “medium term”. The period can range from one year to around seven
years, although it usually does not exceed five years. Medium term loans are also called “intermediate” term loans
Terms beyond this are considered long term.
Medium term loans can be availed either in local currency or foreign currency.
1. Features of medium-term loans
Following are the features of term loans:
(a) Loans are debts and the lending institution is a creditor.
(b) The loan is repayable within a predetermined period.
(c) The loans may be either secured or unsecured. Usually, lenders seek a collateral to secure the loan.
(d) The borrower has to pay interest periodically, even in the absence of profits. The interest rate is set at the
time of the loan approval. The rate may vary according the riskiness of the project as perceived by the lender.
(e) As interest is tax deductible, the effective rate of interest is lower than the cost of equity.
(f) The rate of interest is usually lower than short term rates.
A firm negotiates with a bank for a medium-term loan of Tshs 250 million, repayable in three years in equal
half yearly instalments. The rate of interest is 12% per annum.
Determine the instalment which is payable. Also calculate the principal and the interest component in each
instalment
The instalments are payable in equal half yearly instalments. Hence the number of periods is 3 x 2= 6.
The interest for 6 months is 12/2 = 6%.
We need to find the present value of the future payments which will amount to Tshs 250,000 discounted at 6%
over 6 periods. As this is a case of an ordinary annuity, we use the PVOA table to find the applicable factor.
The PVOA factor =4.91732
The six-monthly instalments will therefore be 250,000,00 0 = Tshs 50,840,701.19
4.91732
We now have the instalment amount. In order to calculate the interest, we prepare an amortisation schedule.
Continued on the next page
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A simple way to calculate an amortisation schedule is to do the following:

For the first instalment, multiply the loan balance ( Tshs 250 million) by the periodic interest rate (6%). This
will give the interest part of the first instalment payment. Subtract that amount from the total instalment payment
( Tshs 50,840,701.19). This will yield the principal amount.

To calculate the next instalment interest and principal payments, subtract the principal payment made in the
first instalment ( Tshs 35,840,701.19) to arrive at the new loan balance, and then repeat the steps given above.
Period
0
1
2
3
4
5
6
Amortisation schedule
Instalment
Interest
50,840,701.19
50,840,701.19
50,840,701.19
50,840,701.19
50,840,701.19
50,840,701.19
15,000,000.00
12,849,557.93
10,570,089.33
8,153,852.62
5,592,641.71
2,877,758.14
Principal
35,840,701.19
37,991,143.26
40,270,611.86
42,686,848.57
45,248,059.48
47,962,943.05
250,000,307.41
Tshs
Loan balance
250,000,000.00
214,159,298.81
176,168,155.55
135,897,543.69
93,210,695.12
47,962,635.64
(307.41)
The small difference of Tshs 307.41 arises due to rounding off. This amount will be reduced from the final
instalment so that the principal amount repaid is Tshs 250 million.
2. The 5 Cs
Banks consider the following "five C's" when making decisions about term loans (medium and long):
(a) Character: how the firm has managed other loans and the business experience.
(b) Credit capacity: the bank will conduct a full credit analysis, including a detailed review of financial
statements to assess the feasibility of the project and the firm’s ability to repay.
(c) Collateral: the security offered by the borrower must be of a value higher than the loan amount to cover the
outstanding.
(d) Capital: in case of default, how easily can the assets of the firm have converted into cash. Sometimes,
personal guarantees and personal assets of promoters may also be sought if the loan is large.
(e) Comfort/confidence with the business plan: the reliability of the business plans are analysed in detail by
the bank before they take a decision.
3. Advantages of medium-term loans
(a) Flexible lending and repayment arrangements are possible and can be tailored to each firm
(b) A moratorium or grace period can be granted during project implementation phase to reduce cash flow
pressure.
(c) Flexible disbursement arrangements are possible, which allow single or multiple disbursements in line with
project progress. This can ease the problem of funds lying idle when not required and still having to pay
interest in them.
(d) Assets generated from the loan could be used as collateral
(e) Interest rate may be lower than short term loans.
4. Disadvantages of medium-term loans
(a) Fixed commitment: the lender expects to receive payment with the interest specified on the due dates.
There is usually a pressure on the cash flows until the project is completed and running. But the interest and
principal instalments have to be made irrespective of the cash pressures. It may be possible to obtain a
“moratorium” from paying the interest and principal for a short period.
(b) Additional charges: banks, in addition to the interest also charge types of fee such as commitment
charges, loan processing charges and so on. This itself may amount to around 4-5% of the loan amount.
Short,Medium
andLong
LongTerm
TermAlternatives:
Alternatives:335
267
Short,
Medium And
© GTG
(c) Disclosure of confidential information: banks may demand that they be provided with periodic
performance and financial reports. In addition, they may seek other details which are confidential in nature.
(d) Interest payable: interest is payable even if there are no profits, unlike in the case of equity shares.
(e) Lengthy process and documentation: the bank may take as much time to process the application as it
does in the case of a term loan. The documentation needed is also elaborate.
(f) Collateral and margin: often the banks insist on a security which is more than the loan amount.
2.2 Hire purchase
Hire purchase (HP) is a way of financing the purchase of a specified asset e.g. machinery, equipment, computers
and vehicles. The use of HP is common in businesses where expensive machinery is required, such as
construction, manufacturing, printing, road freight, transport, engineering and professional services. Smaller
businesses also make use of this to finance their capital requirements of the business.
The purchaser pays an initial deposit and the balance of the principal as well as the interest is paid over a
period of time. The firm possesses and controls the asset during the agreed term. Legally, under a hire
purchase contract, the ownership does not pass until the final instalment has been paid if the option to purchase
is exercised. However, the accounting treatment for such contracts requires that the asset be capitalised at the
outset at its cost and that the interest payments be charged to expense as it is a financing cost.
1. Nature of the HP agreement
A hire purchase (HP) agreement allows a hirer (user) to use capital goods by paying rentals (instalments) at regular
intervals e.g. monthly or quarterly. Hire purchase is similar to leasing except that usually, the hirer has an option
either to return the asset or to buy it at a predetermined price after paying the final instalment. The predetermined
price is a nominal sum. The instalment consists of the cost of the assets plus the interest charged by the
owner (financer of the asset). In case of an operating lease agreement, the lessee never becomes the owner of
the asset.
The hire purchase method is used to acquire asset where the hirer is unable make a lump sum payment but can
afford to pay a percentage of the cost of the asset as a deposit.
2. Features of the HP agreement
(a) It allows the hirer to use capital goods without making an initial lump sum payment. This helps the hirer to
use an asset without affecting its cash flows.
(b) At the time of payment of the last instalment, the hirer has an option to buy the asset.
(c) The owner of the assets can repossess the asset if the hirer fails to make timely payments of the instalments.
(d) Usually the cost of maintenance of the asset under hire purchase is borne by the hirer.
(e) The hirer can terminate the contract after giving valid reasons to do so.
(f) The hire purchaser generally makes a down payment and pays the agreed amount in periodical instalments.
(g) The vendor transfers only the possession of the goods (not the ownership) to the hire purchaser
immediately after the contract for hire purchase is made.
(h) Each instalment paid by the hire purchaser consists partly of a finance charge (i.e. interest) and partly of a
capital payment (i.e. cash price).
3. Calculation of interest on HP
Hire purchase interest can be calculated by three methods.
(a) Straight line method
(b) Actuarial Method
(c) Sum-of-digits Method
(a) Straight line method
Under this method, the amount of interest is allocated equally over the number of instalments decided upon.
HP interest per installment =
Total HP interest
Number of total installments
268
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Jubilee Inc has acquired machinery from Libra Ltd on the following terms:
Cash price
Down payment
HP Price
Nominal rate of interest
Four annual instalments
Tshs 10
million
Tshs 1
million
Tshs
13.6
million
10%
Tshs 3.4
million
Total HP interest
= HP Price – Cash price
= Tshs 13.6 - Tshs 10.0
= Tshs 3.6 million
HP interest payable per annum =
Tshs 3.6 million
= Tshs 900,000
4
An alternative way to calculate hire purchase interest is Tshs (10.0 - 1.0) million x 10% = Tshs 900,000
Each instalment therefore consists of
Interest
Add: principal ( Tshs 3.4million - 0.9 million)
Tshs 0.9
million
Tshs
2.50
million
(b) Actuarial Method
Under the actuarial method of hire purchase, the amount of interest is charged on the outstanding (unpaid)
balance of the cash price after deducting the down payment.
There can be two possibilities:
(i) Equal instalments
(ii) Unequal instalments
(i) Equal instalments
Equal installment =
HP price - Down payment
Number of l installments
Sahara Inc acquires an asset from Kingdom Inc on the following terms:
Cash price
Advance payment
HP price
Interest
Four annual instalments
Year
1
2
3
4
Total
Tshs 9.0 million
Tshs 1.0 million
Tshs 11.096 million
10% on outstanding balance
Tshs 2.524 million
HP interest
(9.0 -1.0)x 10%
(8.0+0.8-2.524)x 10%
(6.276 +0.628-2.524) x 10%
(4.38+0.438- 2.524) x10%
Tshs million
Capital
0.8000
0.6280
0.4380
0.2294
2.0954
1.7240
1.8960
2.0860
2.2946
8.0006
Instalments
2.5240
2.5240
2.5240
2.5240
10.10
Balance principal
8.0000
6.2760
4.3800
2.2940
-0.0006
Short,Medium
andLong
LongTerm
TermAlternatives:
Alternatives:337
269
Short,
Medium And
© GTG
(ii) Unequal instalments
Unequal installment =
Cash price - Down payment
+ Accrued interest
Number of l installments
An asset is acquired by Spark Co from Shine Co on the following terms:
Cash price
Down payment
HP price
Interest
Four annual instalments
Year
0
1
2
3
4
Tshs 10.000
million
Tshs 1.000
million
Tshs 9.000
million balance
10% on outstanding
Tshs 2.250 million +
interest
HP interest
9.000 x 10%=0.900
(8.000+0.900-3.150)*10%=0.575
(6.000+0.575-2.825)*10%=0.375
4.000+0.375-2.625)*10%=0.175
0.900
0.575
0.375
0.175
Capital
2.250
2.250
2.250
2.250
Tshs million
Instalments Principal balance
9.000
3.150
6.750
2.825
4.500
2.625
2.250
2.425
0.000
(c) Sum of digits method
Here, the hire purchase interest is allocated in accordance with the digits assigned (descending order). Under
this method, greater amount of interest is charged in the earlier periods which decreases as the period progress
.
n(n + 1)
Sum of digits =
2
Where n = number of instalments
HP interst per installment =
Total HP interest x Digit assigned to the installment
Sum of digits of total installments
Ruby Ltd purchases a machine from Sapphire Inc under a hire purchase agreement, with the following terms:
Cash price
Hire Purchase
Instalments
Date of sale
Tshs 11.00 million
Tshs 15.600 million
4 months
1 January 20X3
You are required to compute the interest chargeable for each year under the following situations:
(a) First instalment due at the beginning of month following the date of sale
(b) First instalment due at the date of sale.
Total HP interest = Tshs 15.600- Tshs 11.000= Tshs 4.600million
(a) As there are 4 periods, the sum of digits= 4 x (4+1)/2=10
Instalment
no.
1
2
3
4
Tshs million
4.6 x 4/10
4.6 x 3/10
4.6 x 2/10
4.6 x 1/10
Total
Interest
1.84
1.38
0.92
0.46
4.60
Continued on the next page
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(b) Total HP interest = Tshs 15.600- Tshs 11.000= Tshs 4.600 million
There are three periods and hence the sum of digits =
© GTG
Instalment
no.
1
2
3
Tshs million
4.6 x3/6
4.6 x2/6
4.6 x1/6
Total
3(3 + 1)
2
=
12
=6
2 Short, Medium And Long Term Alternatives: 339
Interest
2.30
1.53
0.77
4.60
Instalment 4 will not have any interest component
4. Calculating the cash price
At times, in the example, the cash price of goods purchased is not given, but only hire-purchase price is
available. In such a situation, the cash price can be calculated using the annuity method.
Cash Price = (Present Value annuity factor x Amount of one instalment) + Down payment (if any)
On 1st April, 20X5 a company buys on Hire-purchase a machine for Tshs 60.0 million, payable in three equal
annual instalments. The rate of interest is 12% per annum. Calculate the amount of cash price and interest. The
present value of an annuity of Tshs 1 for three years at 12% interest is Tshs 2.40183.
The annual instalment payment= Tshs 60million/3 = Tshs 20.0 million.
Calculation of Cash Price
The PV of an annuity of Tshs 20.0 million payable for 3 years
= Tshs 20.0 million x 2.40183
=
Tshs
48.0366
million
Total interest = Hire purchase price – Cash price
= Tshs 60.0 million – Tshs 48.0366 million
= Tshs 11.9634 million
5. Advantages of HP
(a) Businesses can control and use assets without putting its cash flow under pressure if they opt for a hire
purchase system.
(b) In a hire purchase system, the firm is aware of the exact timing of the cash flows and hence, through a
fixed-rate funding, complicated calculations for budgeting can be avoided.
(c) A flexible repayment structure can be made available such as annual repayments rather than monthly or
quarterly outflows. This is particularly useful for seasonal industries.
(d) Firms have an easier access to financing as the financier has the security of the asset because the
ownership rights vest in the financing company until the last instalment is paid.
(e) Under certain circumstances, maintenance is also included in the terms and conditions of the contract.
6. Disadvantages of HP
(a) Hire purchase price consists of cash price and interest. Hence, the total of the instalments paid is higher
than the full payment on the asset purchase.
(b) In a hire purchase agreement, if any specific clauses are included (such as updates on change of equipment
location), then administrative difficulty and costs are higher than other normal HP agreements.
(c) If the business changes its operations or functions, and in that situation, if the asset is no longer required,
the firm will lose possession of the asset even if it has paid a significant amount on HP.
2.3 Lease finance
Lease finance also serves the purpose of long-term financing. If a company wants to borrow in order to
(a) Hire purchase price consists of cash price and interest. Hence, the total of the instalments paid is higher
than the full payment on the asset purchase.
(b) In a hire purchase agreement, if any specific clauses are included (such as updates on change of equipment
location), then administrative difficulty and costs are higher than other normal HP agreements.
Short,Medium
Long
Term
Alternatives:
271
(c) If the business changes its operations or functions, and in that situation,
if the and
asset
is no
longer
required,
the firm will lose possession of the asset even if it has paid a significant amount on HP.
2.3 Lease finance
Lease finance also serves the purpose of long-term financing. If a company wants to borrow in order to
purchase an asset in its own name, it has to provide assets as a security for the borrowing. If it lacks good assets,
it may not be able to borrow.
title of the assets does not pass to the user in the case of leases. As a result, the asset can be repossessed
340The
: Financing
© GTG
by the lessor if there is a default in the payment from the lessee. In this way, the leased asset itself serves as a
security. Hence it is possible to acquire assets on lease even when there are no suitable assets to offer as a
security, other than leased assets. This factor has made lease financing popular, especially with smaller
companies.
1. Advantages of leasing
(a) The lessor earns a reasonable income by way of leases and gets capital allowances for the assets when
calculating tax, in the case of an operating lease.
(b) Since the total amount has been paid to the supplier in the beginning, he avoids the hassle of collection.
(c) The lessee can obtain an asset even when he lacks the security to obtain a bank loan. Finance leasing may
be cheaper than ordinary bank finance.
(d) In the case of an operating lease, the lessee does not bear the risk of obsolescence. The lessor will have to
sell the obsolete second-hand equipment.
2. Benefits of leasing
Leasing can be beneficial only if the financial benefits can be shared by both, the lessor as well as the lessee.
Financial benefits may accrue on account of one or more of the following:
(a) Different possibilities for availing capital allowances: some companies may be tax exhausted, in the
sense, they are not in a position to utilise capital allowances. In this case, it makes sense to let some other
party claim the allowance and share the benefits indirectly, for example, by reducing the lease premium.
(b) Different tax structures: large and small companies may have different tax structures.
(c) Different costs of capital: the cost of equity and debt funds for a large leasing company may be lower than
the cost of capital for a small company trying to raise finance from the market. Small companies may find
lease finance cheaper.
3. Leases are classified into two categories
(a) Financial leases and
(b) Operational leases
(a) Finance lease
A finance lease is a lease that transfers substantially all the risks and rewards incidental to ownership of an
asset. The title may or may not eventually be transferred.
IAS 17 Leases
Belco leases equipment to Nalco for 10 years, at a lease of Tshs 10 million per month. After 10 years, Nalco has
an option to continue the lease at the rate of Tshs 100,000 per month. Expected economic life of the asset is 10
years. This is a finance lease.
272 ©Financing
Decisions
GTG
Short, Medium And Long Term Alternatives: 341
An operating lease is a lease other than a finance lease.
IAS 17 Leases
In the case of operating leases:
The lessee treats operating lease payments as an expense.
The lessor presents the assets in its own SOFP according to the nature of the asset. Lease instalments are
treated as income.
Features of operating leases
The lessor supplies equipment to the lessee.
Responsibility for servicing and maintaining the equipment rests with the lessor.
The period of lease is normally shorter and lower than the economic life of an asset.
Bontec Co leases a car to Lesco for 1 year. Afterwards, Lesco returns the car to Bontec. This is an operating
lease.
What is the difference between an operating lease and a financial lease?
4. Accounting treatment of a lease
The lease payments can be claimed under expense from the tax viewpoint only if it is an operating lease. This is
because under operating lease, the lease expenses are treated as operating expense and the operating lease
does not show up as part of the capital of the firm.
Under a finance lease, the present value of the lease expenses is treated as debt, and interest is imputed on
this amount and shown as part of SOPL. However, as the asset is recognised in the SOPL, depreciation can be
claimed.
In accordance with IAS 17, a lease would normally be considered a finance lease under the following conditions:
(a) The lease transfers ownership of the asset to the lessee by the end of the lease term.
(b) The lessee has the option to purchase the asset at a price that is expected to be amply lower than the fair
value of the asset, at the date the option becomes exercisable.
(c) The lease term is for the major part of the economic life of the asset, even if the title is not transferred.
(d) At the inception of the lease, the present value of the minimum lease payments amounts to substantially all
of the fair value of the leased asset. The standard does not define the term ‘substantial’. However, if the
minimum lease payment is more than 90% of the fair value of the leased asset, it can be said to be substantial.
5. Lease Evaluation
Lease finance serves the purpose of medium/long-term financing. If a firm wants to borrow in order to purchase
an asset in its own name, it has to provide assets as a security for the borrowing. The title of the assets does
not pass to the user in the case of leases. Therefore, the asset can be taken back by the lessor if there is a default
in the payment from the lessee. Here, the leased asset itself serves as a security.
Hence it is possible to acquire assets on lease even when there are no suitable assets to offer as a security,
other than leased assets. This advantage has made lease financing popular, especially with smaller firms.
Short,Medium and Long Term Alternatives:
© GTG 273
342 : Financing
Leases can be evaluated from the perspective of both the lessee and the lessor. The lessee must determine
whether leasing is more beneficial than buying the equipment outright through a loan. The lessor must determine
the quantum of lease rentals to provide a rate of return consistent with the riskiness of the investment.
Caregiver Hospital requires a Colour Doppler Ultrasound system that costs Tshs 50 million. The equipment is
needed for two years. The hospital must choose between leasing and buying the equipment. If the machine is
purchased, the hospital could avail a loan from a bank at 10% interest per annum.
Thus, the hospital would have to pay the bank Tshs 5 million interest at the end of each year, and also pay back
the Tshs 50million in principal at the end of year 2.
Assume (for the sake of simplicity) that the hospital can depreciate the entire cost of the machine over two years
for tax purposes by the straight-line method. The tax rate is 40%. Also, for simplicity, assume the equipment's
residual value at the end of two years to be Tshs 0.
The hospital can lease the asset for two years for a payment of Tshs 27.50 million at the end of each year.
The analysis for the lease-versus-buy decision consists of (1) estimating the cash flows associated with borrowing
and buying the asset, (2) estimating the cash flows associated with leasing the asset, and (3) comparing the two
financing methods to determine which has the lower cost.
Option: Buy
Equipment cost
Loan amount
Interest expense
Tax savings on interest (tax shield)
Principal repayment
Depreciation*
Tax savings on depreciation (tax
shield)
Net cash flow
PV factor @6% discount rate
PV
* not considered for cash flow
Tshs million
Y1
Y2
Y0
(50)
50
0
(5)
2
25
(5)
2
(50)
25
10
7
0.943396
6.603774
10
(43)
0.889996
(38.2698)
Total
(31.67)
Discount rate is the effective rate on 10% after tax
Option: Lease
Tshs million
Y0
Y1
Y2
Lease payment
(27.5)
(27.5)
Tax shield on lease payment
11
11
Net cash flow
(16.5)
(16.5)
PV factor @6% discount rate
0.943396 0.889996
PV
(15.566) (14.6849)
Discount rate is the effective rate on 10% after tax
Total
(30.25)
As the PV of leasing is lower than the PV of buying, we should choose the leasing option.
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Similarities and differences among the various sources of medium term finance
Bases
Involvement of time,
procedures and
formalities
Repayment
Ownership of the
asset
Term loan
Takes some time to obtain
approval the funding limits
from banks.
Documentation is
elaborate. Periodic
performance reports have
to be provided to the
bank.
Funding is usually linked
to a project for buying new
equipment, expansion etc.
Repayment of the funds
borrowed is usually in
instalments over the
duration of the loan.
Interest is predetermined
and has to be paid
separately.
The asset is purchased by
the user who secures the
loan from the bank.
Claim of depreciation
The owner/user can claim
depreciation on the asset
Responsibility of the
maintenance of the
asset
Default in payment
The lender has no role in
the maintenance of the
equipment.
The lender can recall the
loan in the case of a
default. Usually the asset
is the security for the loan
and therefore, the lender
can take over the asset
and sell it to set off the
outstanding loan and
interest.
Hire purchase
Formalities and the time
involved are comparatively
limited. Essentially related
to the purchase of
equipment, motor car etc.
Leasing
Formalities and the time
involved are comparatively
limited. Funding is related
to the use of equipment or
other assets, including
land and buildings.
Repayment is in
instalments which includes
the principal and the
interest amount.
Repayment is in
instalments which includes
the principal and the
interest amount
The ownership of the asset
initially is in the name of
the financier. It later on
passes to the user at the
end of the hire purchase
term.
The hire purchaser can
claim depreciation on the
asset, even though in the
initial period the asset is
not transferred.
Hirer is responsible for the
maintenance of the asset
The user and the owner of
the asset are different. The
ownership does not get
transferred.
In the case of a default in
the payment of the
instalments, the financer
can repossess the asset.
Answers to Test Yourself
Answer to TY 1
Existing credit purchases
Existing average creditors
Existing credit terms- months
Proposed credit purchases ( Tshs 24billion x
1.005) Proposed credit terms- months
Proposed average creditors 2/12x24.12
Amount Tshs billion
24
2
1
24.12
2
4.02
Additional purchase cost (24.12 – 24)
Additional funds available from creditors ( Tshs
4.02 billion – Tshs 2 billion)
Interest saved @ 10%
Net saving (0.202 – 0.120)
0.120
2.02
0.202
0.082
The lessee can claim the
entire lease rent as an
expense.
The lessor is usually
responsible for the
maintenance of the asset.
In the case of a default in
the payment of the lease
charges, the lessor can
take back the asset.
Short,Medium
andLong
LongTerm
TermAlternatives:
Alternatives:343
275
Short,
Medium And
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Answer to TY 2
Annual benefit of accepting the discount
3
365
×
= 37.63%
100 − 3 40 − 10
Annual cost = Interest sacrificed on investment (opportunity cost) = 30%.
Alternative calculation
Suppose invoice from the supplier is for Tshs 100,000.
If the discount is
Payment to supplier
Return on investment of Tshs 97,000 @30% for 30 days:
97,000 x 30/365 x 30%
Net cost
Accepted ( Tshs
)
97,000
Refused ( Tshs
)
100,000
97,000
(2,392)
97,608
From the above table, it can be seen that it is cheaper to accept the discount.
Answer to TY 3
The bill is discounted 2 months after the bill was drawn. Hence the unexpired period of the due date is 1 month.
1
The amount of discount = Tshs 10 million x 12% x x = Tsh 100,000
12
Answer to TY 4
Leases are classified into two categories; operating leases and financial leases.
Time
period
Knowledg
e of the
asset
Risk
Cancellati
on of
lease
344 :Term
Financing
of
Operating lease
Finance lease
The lease period does not cover the whole It is a long- t e r m contract covering the whole
useful life of asset. The lessor earns profit by life of the asset. The asset will not have much
selling the asset or by leasing the asset again. useful life after the lease is over.
The lessor might be dealing / trading in the
leased asset and is expected to have a good
knowledge regarding the asset.
The lessor bears the risk associated with the
asset. Usually, the lessor is responsible for
maintenance and repair of the asset.
Normally, the lessor does not deal / trade in the
particular kind of asset that has been given on
lease.
The lessor transfers the risk and rewards
associated with the leased asset to the lessee.
In certain cases, the lease can be cancelled
by giving a short notice.
The lessee is liable for all the payments under
the lease. Hence, no cancellation of the lease
can take place.
finance
GTG
The lessee pays short-term rental on the asset. It can be said that the finance lease©allows
Hence, it is a short-term source of finance.
the lessee to finance the acquisition of the
asset by obtaining a loan from the lessor.
Hence, it is a long-term source of finance.
Tax
treatment
(a) Lessee shows the lease payments as a
tax deductible.
(a) Lessee
(i) considers lease payments tax
deductible expense
(ii) maintenance, insurance and other
running costs associated with the
asset are also tax allowable expenses
(b) Lessor:
(i) claims capital allowances
(ii) shows lease payments as income
(b) Lessor
(i) claims capital allowances
(ii) shows lease payments as income
276 ©Financing
Decisions
GTG
Short, Medium And Long Term Alternatives: 345
Quick Quiz
1. An overdraft is not recommended for acquiring long term assets. (True/False)
2. X draws a bill of exchange on Y for Tshs 750,000. X endorsed the bill to Z. On maturity, the payment will be
made by
to
3. Trade credit is not recommended for small organisations. (True/False)
4. A factor provides long term loans. (True/False)
5.
refers to the borrower's assets, which is also known as net worth:
A
B
C
D
Collateral
Capital
Capacity
Character
6. Dew Ltd negotiated a lease on the following terms: the term of the lease was 5 years; the estimated useful life
of the leased equipment was 10 years; the purchase price was Tshs 60million; and the annual lease payment
was Tshs 5 million
This lease should be classified as:
A Financial lease
B Operating lease
Answers to Quick Quiz
1. True; an overdraft is not recommended for acquiring long term assets
2. The payment will be made by Y to Z
3. False; trade credit is recommended for small organisations
4. False; a factor provides short-term loans
5. The correct option is B.
Capital refers to the borrower's assets, which is also known as net worth.
6. The correct option is B.
It is an operating lease.
Self Examination Questions
Question 1
Medicure Ltd considering an offer received from a factor to take over its account’s receivables on a non-recourse
basis at an annual fee of 3% of the credit turnover. The company incurs Tshs 30,000 per year in administration
costs and Tshs 105,000 per year in bad debts. The factoring agreement states that the factor will not change the
accounts receivables collection period and will advance 80% of the face value of accounts receivables at an annual
interest rate of 7%.
The company expects a turnover of Tshs 11,220,000 as credit sales. The company currently has Tshs 1,380,000
as accounts receivables and the average collection period is one month. The finance cost of accounts receivables
is 5%.
Required:
Advise the company on the offer made by the factor.
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Short,Medium
andLong
LongTerm
TermAlternatives:
Alternatives:345
277
Short,
Medium And
Question 2
Prado Ltd sells goods for a total value of Tshs 100,000 to its regular customers at the beginning of June.
However, it requires an earlier payment than the agreed 30-day credit period for these invoices. A discounter
agrees to finance 80% of their face value, i.e. Tshs 80,000. Interest is set at 12% p.a.
The invoices were due for payment in early July but were settled in mid-July, exactly 45 days after the initial
transactions. The service charge is set at 1%. A special account is set up with a bank into which all the
payments are made. Explain the transaction chronologically and find out the effective annual interest rate.
Question 3
Nelson Ltd is a newly incorporated company. It has estimated that its working capital requirements (investment
in inventory and trade receivables, net of trade payables) are to the tune of Tshs 5m. It has two options for
raising this finance: either to get an overdraft limit sanctioned or to obtain a loan for the amount.
Advise Nelson on which is the better option, explaining the reasons for your recommendation
Question 4
Explain “Acceptance credit”.
Question 5
Identify whether the following are finance or operating leases,
(a) A motor car is taken on lease, which costs Tshs 10 million. Three annual payments of Tshs 5 million
in arrears are payable. Interest is calculated at 10% pa.
(b) An equipment is leased the fair value of which is Tshs 20 million. Five annual payments of Tshs 5 million in
advance are payable. Interest is calculated at 14% pa.
(c) A warehouse is leased, current value of which is Ths200 million. Annual rental of Tshs 30 million in arrears
for a ten-year period has to be paid. Interest is calculated at 12% per annum.
Answers to Self Examination Questions
Answer to SEQ 1
Current accounts receivables = Tshs 1,380,000
Receivables under factor = Credit sales x Accounts receivables collection period/360
= Tshs 11,220,000 x 30/365 = Tshs 922,192
Reduction in accounts receivables = Tshs 1,380,000 - Tshs 922,192 = Tshs 457,808
Reduction in finance cost = Tshs 457,808 x 5% = Tshs 22,890
Administration cost savings = Tshs 30,000
Bad debts savings = Tshs 105,000
Factor’s annual fees = Tshs 11,220,000 x 3% = Tshs 336,600 per year
Extra interest cost on advance = Tshs 922,192 x 80% x (7% - 5%) = Tshs 14,755
Net cost of factoring
= Reduction in finance cost + Administration cost savings + Bad-debts savings – Factor’s annual saving – Extra
interest cost on advance
= Tshs 22,890 + Tshs 30,000 + Tshs 105,000 - Tshs 336,600 - Tshs 14,755
= ( Tshs 193,465)
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Answer to SEQ 2
In June, Prado receives an advance in cash of Tshs 80,000.
In mid-July, Prado’s customers pay Tshs 100,000.
The invoice discounter receives the full Tshs 100,000.
Prado receives the balance less charges, i.e.
Service fees 1% x Tshs 100,000
Tshs 1,000
Interest (12% x Tshs 80,000 x 45/365)
Tshs 1,184
Total charges
Tshs 2,184
Net receipts = (20% x Tshs 100,000) - Tshs 2,184 = Tshs 17,816
Total receipts by Prado = Tshs 80,000 + Tshs 17,816 = Tshs 97,816
In effect, Prado has settled for a discount of Tshs 2,184 / Tshs 100,000 = 2.184% over 45 days for early receipt
of 80% of accounts payable.
As there are eight 45-day periods in a year, this corresponds to an annual interest rate of:
(1.2184 – 1) x 8 = 0.2184 x 8 = 0.1747 or 17.47%.
Answer to SEQ 3
Nelson should consider the overdraft option as it has to finance its working capital requirements. Nelson can
use the facility as and when required to meet working capital requirements, also the rate of interest charged is
relatively low. In the case of the loan option, the full amount is taken at one time (whether it is needed or not)
and its interest payments start immediately. The interest charged is higher in the case of loans.
Answer to SEQ 4
Acceptance credit is a source of finance by which international trade is financed. Here, acceptance credit facility
is set up by either a bank or an acceptance house in the exporter's country. The funds are utilised by the
exporter from this account to fulfil export orders. This facility is also known as acceptance financing.
A banker's acceptance is used in international trade. It is a time draft, drawn by
the seller of goods on a buyer and honoured by a bank. An acceptance
agreement puts the acceptor under contractual obligation to pay, which
The buyer is the
acceptor in trade
acceptance
strengthens a time draft. As international trade is facilitated by banker's acceptances, they guarantee the
payment for goods.
Types of acceptance
There are broadly two different forms of acceptance financing which are:
1. Trade acceptance: it is an acknowledgment of a debt, and its execution is a reflection on the credit
worthiness of the buyer as well as the seller. It is a draft or a bill of exchange that is accepted or signed only
by the drawee (the buyer) and is not countersigned by the drawee's bank. Such bills are only as good as
the drawee's creditworthiness.
2. Banker’s acceptance: it is generated when a time draft is co-signed or stamped “accepted” by the bank.
As studied earlier, a time draft is drawn on a bank to finance the shipment of goods. When bank accepts the
draft, it makes an absolute assurance of paying the specific amount at a specified date to the holder of the
draft.
In cases where bankers’ acceptance is a substitute for a loan to finance an export, a time draft covering the
financing period is generated. The issuing bank signs and endorses the draft on the paying bank. The draft is then
accepted by the paying bank. It discounts the draft and uses the proceeds to make the obligatory payment.
On maturity of the bankers’ acceptance, it is settled by a debit to the account of the opener.
Short,Medium
andLong
LongTerm
TermAlternatives:
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279
Short,
Medium And
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Answer to SEQ 5
(a)
Year
0
1
2
3
PV
Payments
0
5
5
5
Tshs million
PV factor@ 10%
1
0.9091
0.8264
0.7513
Present Value
0
4.5455
4.132
3.7565
12.434
The present value of the lease payments of Tshs 12.434 million is higher than the cash price of Tshs 10 million.>
hence this is a financial lease under IAS 17
(b)
Year
0-4
Tshs million
Payments
P.V. 14%
5
3.9137
Present Value
19.56850
As the lease rental is payable in advance, we use the PV of an “annuity due” table.
The present value of the lease is Tshs 19.5685 million, although less than the fair value of Tshs 20 million is for
“substantially all” of the fair value. Therefore, this is considered a financial lease.
(c)
Year
0
01-Oct
Tshs million
P.V.
Payments
12%
Present
Value
0
1
0
30
5.65022
169.5066
The PV of the lease payment ( Tshs 169.5066 million) is significantly less than the fair value of the warehouse
( Tshs 200 million. Therefore, this is considered an operating lease.
280 Financing Decisions
SECTION D
Issues of New Capital: 281
FINANCING DECISIONS
D2
STUDY GUIDE D2: ISSUES OF NEW CAPITAL
A major function of the finance manager is to source funds to finance the operations of the business. The company
issues securities in the form of debt, equity and hybrid securities.
A debt security represents funds borrowed by the corporate that must be repaid, based on the stipulated terms
such as the amount borrowed, interest rate and maturity/renewal date. Debt securities include corporate bonds
or debentures, certificates of deposit (CDs).
Equities represent the owners interest held by shareholders in a company, through shares. Holders of debt
securities generally receive interest based on a contract and the repayment of the principal whereas, holders of
equity securities receive dividends (which may vary) and are able to increase their wealth through increases in the
share price. Hybrid securities as a source of financing have features of both simple debt and equity.
There are several types of securities available under each source and the finance manager has to decide on the
ideal mix of securities in a manner that takes into consideration the cost to the organisation and the risks involved.
This study guide discusses the different types of securities available to the organisation, their features, benefits,
drawbacks and costs. It also covers the procedures involved in the issue of securities.
a) Differentiate the various features of corporate securities – equity, debt and hybrid securities (both initial
public offerings and seasoned equity offerings).
b) Identify the advantages and disadvantages of each type of security as a method of raising the capital
required by the corporation.
c) Describe the processes involved in issuance of corporate securities and discuss the choice and roles of
investment advisers in the processes.
d) Estimate the cost of new issues.
e) Estimate the value of hybrid securities (convertible debentures and warrants).
f) Analyse the effects of issuing each of such securities on the share price and discuss the available
empirical evidence.
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1. Differentiate the various features of corporate securities – equity, debt and hybrid securities
(both initial public offerings and seasoned equity offerings).
[Learning Outcome a]
1.1 Equity
Equity shares or ordinary shares represent the real ownership of the company. Equity shareholders appoint the
board of directors and through them supervise and control the business. They have voting rights to decide on all
important matters of the company as enshrined in the memorandum and articles of association of the company.
Although they are the owners, they do not have an assured return on their investments. Each share has certain
face value which is also called nominal value. The market value would vary from time to time depending on the
intrinsic value of the shares and the market perception of growth.
Features of equity shares
1. Joint ownership: Equity shareholders are the joint owners of the firm. They collectively carry the ownership
risk of the company. In the event of liquidation of the company, the equity shareholders have only a residual
claim on the realized assets. This is after all external obligations to the government, creditors, lenders etc have
been met
2. Permanent capital: The equity capital represents the permanent capital of the company. It need not return
the capital except in the event of winding up. In the event of a winding up, they are the last to receive the
residual amount (if any) after all the other claimants have been paid
3. Changes in share value: Equity shares have a face or par value which is the amount which is payable on the
share. Shares can either be partly or fully paid up. The market value is the intrinsic value of the share, which
a potential investor is willing to pay to acquire one share. Therefore over a period of time, the intrinsic value
differs from the face value based on the performance of the company
4. Restricted obligation: Equity holders are the owners have a liability to the company only to the extent of
amounts remaining unpaid on the shares. Although they are the owners of the company, they are not
personally liable in the event of default by the company (due to the existence of the corporate veil)
5. Control on management: Equity shareholders exercise control on board of directors through voting rights
on several major matters related to the company management. This includes electing directors and proposals
for fundamental changes affecting the company such as mergers or liquidation, entitlement to dividends
Mr. Ben is an equity shareholder in Good management Ltd. The company is contemplating an increase in the
authorised capital of the company to enable it to access equity funds along with debts to finance its expansion
plans. The company has to convene a general meeting of the shareholders to approve this proposal. Mr. Ben
will receive a notice of the meeting and he can exercise his right either to approve or oppose the resolution.
6. Claim on residual earnings: The shareholder's fundamental right is to a share in the earnings of the
company. However these earnings are after payment of fixed contractual obligations in the form of interest
and preference dividend. Further the equity shareholders cannot demand a dividend. The decision of the board
of directors as regards dividend payout is binding on all shareholders.
7. Right of transfer: A shareholder may freely transfer shares by selling them, giving them away or bequeathing
them to heirs, except in the case of a private company, where certain restrictions apply.
8. Preferential rights in any new issues: When new or additional shares are issued, the existing shareholders
have a right to be offered these shares first.
1.2 Debt
Apart from equity, a corporate can use debt securities as a source of finance. In case of debt securities there is
a fixed contractual obligation.
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IssuesOfofNew
NewCapital:
Capital:351
283
Issues
1. Features of Debt securities
(a) Pre-determined contract
Unlike equity, in case of debt, the terms are pre-determined in terms of:
(i) Rate of interest
(ii) Time period
(iii) Repayment terms
(iv) Loan covenants
(b) Asset backed securities
Debt in most cases is backed by security (hypothecation / mortgage). In the event of default the security can be
utilised by the lender for the recovery of dues.
(c) Restrictive covenants
Loan agreements often contain restrictive covenants requiring a certain performance or restraint from the corporate
during the period of the loan. They may pertain to either the financial or operational aspects of business.
TWB Ltd. has availed of a term loan of Tshs 90 billion from BOITA which is a financial institution. The loan
agreement includes the following covenants.

Non payment of dividend during the tenancy of the loan
No expansion plans for the next 5 years

Any additional loans availed by TWB from other sources to require prior

approval by BOITA.
(d) Tax deductibility
The interest paid on debt securities is tax deductable and therefore debt securities enjoy tax arbitrage over
equity as a source of finance.
(e) Repayment obligation
Debt carries a fixed repayment obligation. The amount borrowed is amortised over the period of the loan. The
corporate could also avail of non-amortising loans which would be used to fund working capital etc. Loans requiring
a single bullet payment may also be availed depending on the terms of sanction by the bank / financial institution.
A corporate can tap both financial intermediaries and markets for issue of debt instruments.
2. The various forms of corporate debt are:
(a) Loans from banks / financial institutions
Corporates can avail of loans from banks for funding their expansion plans. Such loans are provided after
extensive analysis of both financial and non-financial aspects of the entity.
(i) Interest and fees
Interest rate may be fixed or flexible. Usually, the rate is tied up to the bank’s base lending rate. A loan processing
fee or an arrangement fee is charged at the time the loan is processed. A commitment charge is frequently levied
for the loan that is sanctioned but not utilised.
(ii) Securities
The loans are secured against the assets of the borrower. The charge may be fixed or floating. A fixed charge is
attached to specific assets that cannot be sold without the permission of the lender. A floating charge is a
charge on a class of assets that are allowed to be bought or sold individually, until the time there is no default on
the loan.
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(iii) Repayment
A borrower has to make a periodic payment towards the repayment of the principal and interest. The pattern is
mutually agreed depending upon the needs of the borrower and the policies of the lender. Often, a combined fixed
installment is worked out, consisting of the principal as well as the interest, e.g. equated monthly installments
(EMIs).
(b) Debentures / bonds
Debentures / bonds are used by corporate as a means of long-term finance. In this case a trustee is appointed
through a trust deed / indenture to protect the interest of the debenture holders. A credit rating would need to be
obtained from a rating agency as an assurance to the public as to the safety of their amounts invested. Further
any legal / accounting requirements/ guidelines as may be specified by law / capital market regulator would
need to be complied with. There are various innovative bond / debenture instruments that are issued by corporates.
The following concepts are commonly used in lending parlance
(i) Nominal or par value
Loan stock or debentures have a par value that signifies a debt owed by a company to the loan stock holder.
(ii) Market value
Loan stock or debentures can be bought or sold on the capital markets. The market value may be different from
the par value. This is because the market value depends upon market forces and interest rate expectations.
(iii) Interest or coupon rate
The interest or coupon rate is specified. Interest, at the specified rate, is paid every year or every six months
and is calculated on the par value. Usually the interest rate is fixed; however, it may also be floating related to
the current market interest rate. It may be linked to some benchmark rate such as TIBOR (Tanzanian interbank
offered rate). A floating rate is suitable for investors who want returns consistent with market conditions or investors
who want to be protected against unanticipated inflation. The expected inflation rate is built into the fixed nominal
interest rate.
(iv) Security
Although the words loan stock and debentures are used interchangeable, a debenture is usually taken to mean
a secured bond, and loan stock is taken to mean an unsecured bond. A debenture trust deed will usually
contain all the terms and conditions related to the securities and the procedures. Generally, investors would expect
higher returns on unsecured loan stock, compared to secured debentures because of the higher risk factor.
Debentures may have a fixed or floating charge on the assets. A fixed charge may be on specific assets such
as land and buildings. The specified assets cannot be sold while the loan is outstanding. A floating charge is a
charge on a class of assets, such as inventory, receivables, or machinery. Sale of some assets of the class is
permitted. When a default arises, such as a default in payment of interest, a floating charge crystallises into a fixed
charge on the specific class of asset.
(v) Ratings
Bond ratings are carried by credit rating agencies in each country. It measures the risk related to a bond regarding
the protection of interest payments and repayments of principal, in the present as well as in the future.
These rating agencies base their conclusions on a detailed analysis of the company’s financial position, the
expected conditions of the economy and the expected financial performance of the company. Institutional investors
invest only in the bonds with the minimum required rating such as investment grade. Each agency has a rating
methodology which the company has to comply with.
(vi) Redemption
The term redemption means repayment of a debenture or loan stock or any other security. Usually these securities
are redeemable after a certain period. Sometimes, the redemption terms allow a time span of a few years. This
allows flexibility to the company when planning cash flows. There may be irredeemable or undated debentures or
loan stock. Although the company is not under obligation to redeem these, it may elect to do so.
IssuesOfofNew
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285
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Arranging the money
Redemption calls for careful financial planning since it puts substantial demands on the cash flows of a
company. Some companies arrange for a sinking fund where a fixed amount is invested annually. This amount
along with cumulative interest generates money that will be sufficient to meet the redemption demands. A company
may also issue a fresh loan in order to raise money to redeem the earlier loan. This enables the company to
maintain the capital structure and the related ratios. If a debenture issue has a call option, the company has a right
(option) but not an obligation to redeem the debentures before maturity.
(vii)Restrictive terms and conditions
Terms of issue may contain some restrictive conditions where the investors can restrict the actions of the managers
of the issuing company that may increase the risk borne by the investors. Such restrictions may take the form of:
Restrictions on additional debt.
Target ratios such as current ratio, debt equity ratio, or gearing ratio.
Breach of any conditions may lead to disposal of assets. However, in practice this issue is usually resolved
through negotiations.
(c) Securitisation
In case of securitisation, financial assets having similar characteristics are pooled and converted into marketable
securities. They are then sold to investors by creating an ownership interest in the segregated asset or pool of
assets.
1. The bond indenture includes:






The basic terms of the bond issue
The total amount of bonds issued
A description of the security
Repayment arrangements
Call provisions
Details of the affirmative and negative covenants
2. The affirmative covenants explain what the borrower promises to do:




To pay interest and principal on a timely basis
To pay all taxes and other claims when due
To maintain all property and other assets in good condition and working order
To submit periodic reports to the trustee stating that the borrower is in compliance with the loan agreements
3. The negative (or restrictive) covenants identify certain restrictions on the borrower’s activities, which
include:



Not incurring future debt obligations without prior approval
Achieving certain financial parameters
Not disposing off assets without informing the trustee and/or lender
4. Maturity or term to maturity is the number of years the debt is outstanding or the number of years remaining
prior to the final principal payments.

The maturity date is the date on/by which the debt will be liquidated.
1 to 5-year maturity bonds – short-term

5 to 12 years – intermediate

Over 12 years – long-term

5. Par Value: The par value (principal, face value, redemption value, or maturity value) of a bond is the
amount that the borrower agrees to repay the bondholder at or by the maturity date. Bonds can have any
par value. Bond prices are quoted as a percentage of par value, with par value equal to 100.
6. Coupon rate (nominal rate) is the interest rate the borrower agrees to pay each year. Often the interest is
payable semi-annually. The annual amount of the interest payment made to the bondholders during the
term of the bond is called the coupon.
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Maturity: 1 December 20X9 Coupon rate: 10%. Par value: Tshs 10,000 Coupon =10% x 10,000 = Tshs 1000
3. Provisions for paying off bonds
(a) Bullet loan repayment
The borrower can agree to pay the entire amount in a lump sum at the maturity date. This is the most common
form of repayment.
(b) Amortising bonds
Mortgage and asset-backed bonds have a schedule of partial principal payments. These are called amortising
bonds. If a bond does not prohibit early call it is referred to as a currently callable issue. Most bonds provide for
some restrictions against early redemption. Generally, a bond restriction prevents the refunding of a bond for a
fixed number of years. In the case of an amortising bond, the borrower usually has the right to prepay the
outstanding principal balance in whole or in part prior to the scheduled principal payment dates (prepayment
option)
1.3 Hybrid securities
Hybrid securities have features of both debt and equity. The following securities which are issued by companies,
qualify as hybrid securities.
1. Preference shares
2. Convertible bonds / debentures
3. Warrants
1. Preference shares
Preference shares are a classic case of hybrid securities since they have features of both equity and debt. The
features akin to debt include:
(a) Fixed rate of return
(b) No control on company management
(c) Their claims rank above equity in the event of liquidation of the company
(d) Returns restricted to pre-determined dividend
The features akin to equity are:
(a) In case of irredeemable preference shares there is no repayment of capital
(b) Preference dividend is not tax deductible
2. Convertible bonds / debentures
Convertible bonds are fixed interest debt securities, which the holder can choose to convert into ordinary shares
of the company. This conversion takes place at a predetermined rate and on a predetermined date.
If conversion does not take place, the bonds will run their full life and be redeemed on maturity.
(a) Conversion rate
The conversion rate is expressed as a conversion ratio, i.e. the number of ordinary shares to be issued in
exchange for one bond, or a part of it. Alternatively, the conversion rate is also expressed as conversions
price i.e. the price of one ordinary share that will be appropriated from the nominal value of the convertible
bond. Conversion terms may vary over time.
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A company issues convertible bond of Tshs 1,000 each. The conversion rate may be specified as:
Five ordinary shares to be obtained from one bond; or
Each Tshs 200 of the face value of a bond will be converted into one ordinary share; or
If varying conversion terms are to be specified, five ordinary shares to be obtained from one bond on 1 april
20x8 and four ordinary shares to be obtained from one bond on 1 april 20y2.
(b) Conversion value
The conversion value is the market value of shares expected to be issued on conversion of one bond.
(c) Conversion premium
The conversion premium is the difference between the market price of the convertible bond and its conversion
value. In other words, it is the difference between the market price of the convertible bond and the market price
of the shares into which the bond is expected to be converted.
Conversion premium = Market price of the convertible bond - Its conversion value
The market value of a convertible bond is Tshs 1500. It is convertible into 3 ordinary shares. Market value of one
ordinary share is Tshs 400. Conversion premium = Tshs 1500 - (3 x Tshs 400) = Tshs 300
Features of conversion premium
(i) General
As the conversion date approaches, the market price of a convertible bond and its conversion value tend to
be equal. In other words, the conversion premium will be negligible.
Initially, the conversion value is lower than the market value of the bond.
The conversion premium is proportional to the time remaining before conversion. It is highest at the
beginning and decreases so that, just before conversion, it is negligible. It is expected that the price of ordinary
shares will increase over the period and gradually reduce the conversion premium.
(ii) Company
A company will look for the greatest possible conversion premium. This will enable it to stipulate the lowest
possible number of equity shares to be issued on conversion. Investors will accept this high premium only if
they believe in the growth potential of the company and its share price.
Due to the presence of a conversion right, the rate of interest on convertible debentures is lower than for
ordinary or straight debentures. This makes it attractive to companies.
(d) Rights premium
The difference between the market price of a convertible bond and the price of straight bonds with similar terms
excluding conversion is called a rights premium. Conversion into ordinary shares is a valuable right and causes
the value of convertible bonds to be higher than the value of ordinary bonds.
Consider an 11% convertible bond, redeemable at par in six years’ time that can be converted into 35 ordinary
shares at any time in the next three years. Currently the bond is trading ex-interest (buying the bond does not
confer the right to receive the next interest payment) at Tshs 14,520 and the current ordinary share price is Tshs
355. The ex-interest market value of ordinary bonds of a similar risk class and maturity is Tshs 12,970.
Required:
Calculate the current conversion value, current conversion premium and the current rights premium.
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3. Warrants
Warrants provide a right to buy equity shares in a company at a future date at an exercise price. The exercise
price is fixed and pre-determined. Usually warrants are issued along with loan stock, in order to make the loan
stock attractive.
(a) Advantages of warrants for the investor
(i) A potential for a higher percentage of profits due to the gearing effect discussed above.
(ii) Low initial investment. An investor requires lower funds to purchase the warrant.
(iii) Due to lower investment, the risk of loss of investment is also lower.
(b) Advantages of warrants for the company
(i) Lower interest rate on loan stock, due to the attraction of warrants.
(ii) Even when security for the loan stock is insufficient or not available, it may be possible to issue them
because of the warrants.
(iii) In the future, when the warrants are exercised, they will lead to an actual cash inflow. This is not the case
for convertible bonds.
1.4 Initial public offering (IPO)
There are various methods through which a company can raise securities. A private placement is possible
which involves a small issue size being made to a sponsor firm who in turn selects the institutional investors.
The second method where the issue size is large is to offer the shares for sale to the public. This is called and
initial public offering (IPO).
Different types of Public offers
1. Offer for sale at a fixed price
Shares are offered at a fixed price to the public. The price is determined by the company in consultation with the
sponsor and the broker who also helps to manage the issue. The issue price is decided in such a manner that it
is attractive to the shareholders, as it is lower than the market price. At the same time, it is not so low that it
increases the number of shares and dilutes the EPS by a high margin. The issue is underwritten so that the
company can be confident of the success of the issue. The underwriters subscribe to the shares that are not taken
up by the public.
2. Offer for sale by tender
A minimum price is decided. The public is invited to bid for the shares at a price that is equal to or above this level.
After the offers have been received, a ‘striking price’ is determined. A striking price is a price that ensures that all
the shares on offer are sold.
3. Intermediaries offer
Initially purchase all the shares. Subsequently, these intermediaries pass on the shares to their clients. This
ensures that the shares of the company are widely distributed. This method is quicker and cheaper compared to
offering the shares for sale at a fixed price. Offers for sale are generally for much larger amounts than the placing.
The shares / securities are then listed on a recognized stock exchange. There are certain requirements that a
company must comply with to obtain and keep a listing. The procedure for IPO has been elaborated in the
succeeding learning outcomes.
1.5 Seasoned equity offering (SEO)
A SEO is an issue of additional securities from an established company whose securities already trade in the
secondary market. A seasoned issue is also known as a "follow-on offering." The process of issuing SEOs is
substantially similar to the IPO. However, the price of the new shares is based on the current market price of the
outstanding shares. In case of SEO it is critical to decide on the issue timing, in terms of market potential.
Further the impact on share price post an SEO also needs to be evaluated.
Another feature of an SEO is that generally it focuses mainly on issuing new shares to existing shareholders.
.i.e. rights issue and private placement, instead of the general public offering. Pre-emptive rights (or a rights issue),
make the shares more illiquid as existing investors tend to hold on to them, whereas pure public offerings
substantially increase liquidity and thereby also unlocks value.
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Diagram 1: Corporate securities
Explain warrants as a form of hybrid security.
2. Identify the advantages and disadvantages of each type of security as a method of raising
the capital required by the corporation.
[Learning Outcome b]
2.1 Equity finance
Equity is the basic source of finance to start a business. In the preceding Learning Outcome, we have discussed
the distinguishing features of equity. Equity as a source of finance has numerous advantages
The main advantages of equity finance are:
 It is a permanent capital. The funding is committed to the business and need not be repaid. Equity forms the
basic source of finance for any business.
 There is no committed service cost. Debts have to be serviced, irrespective of the profitability. Equity shares
are not a burden on the resources of the company. Only if the company has sufficient profits and the directors
so recommend, dividend may be declared.
 Dividend Policy: A company may follow an elastic and rational dividend policy and may create huge
reserves for its developmental programmes.
 Creation of margin for debt financing: Equity finance acts a margin to enable the company to raise debt
capital. Further equity finance does not create any encumbrance on the assets of the company.
 The process of raising equity finance through an IPO brings in a lot of efficiencies and discipline into
business operations. Further institutional investors and private equity placements provide the company with
external knowledge and expertise which enhances the management skills. They aid in prudent decision
making.
 Existing investors can be tapped for any additional funding requirements through rights issue. This provides
the company with an investor base to cater to future requirements. Investors are often prepared to provide
follow-up funding as the business grows.

A strong equity base provides confidence to lenders about the stability of the company.
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The principal disadvantages of equity finance are:

Raising of equity shares (through an IPO, private placement etc.) would require proper planning and execution
by management. There are various regulatory requirements which need to be complied with. The guidelines specified
by the Capital Market and Securities Authority need to be met.

On-going reports and periodic information would need to be submitted to the shareholders and regulators.

Management needs to have the adequate systems in place to generate and provide these reports.

Reduction in controlling interest: When a company issues equity shares there is dilution of interest for
the equity shareholders. Significant dilution of control may result in change in the ownership and
management of the company.

Equity capital is the most expensive as a source of finance. Investors expect a high return as they
are compelled to take greater risks than the debt holders. In addition, the profit available to the shareholders
is an “after- tax” phenomenon, which makes it even more expensive when compared to debts, which have
the advantage of a “tax-shield”.
1. Raising equity finance through initial public offering (IPO)
(a) There are numerous advantages to getting a company’s shares listed on a stock exchange.
(i) Access to finance
Once a company is listed on the stock exchange, it is subject to the rules and regulations of the exchange and
is generally subject to a public scrutiny. There is more accountability and improved corporate governance. This
improves the image and credibility of the company.




Institutional investors are ready to put large amounts of money into the equity of a listed company on a long- term basis.
Since the company’s risk profile is lowered, it is possible for it to obtain debt at a lower cost of capital.
Listing enables the company to access the wider pool of finance from the general public.
Listing provides easy marketability and liquidity to the company’s shares. As a result, more investors, both institutional
as well as retail, are attracted to the company’s shares.
(ii) Better image
Generally, the image of the company improves. This is beneficial in its dealings with various parties. The
negotiating power of the company may increase in its dealings with suppliers.
(iii) Releasing capital for other uses
Promoters or venture capitalists may be interested in withdrawing their capital partially or fully. Listing provides
them with an opportunity of doing so.
(iv) Possibilities of acquisition and growth
Listed companies are better placed to make offers to the shareholders of a target company than unlisted
companies.
(b) Disadvantages of listing shares on the stock market
(i) Increased public scrutiny of the company
(ii) Possibility of dilution of control
(iii) Increased costs
2. Rights issue
Rights issue is an offer for sale of shares to the existing shareholders.
(a) Advantages of a rights issue
(i) A rights issue involves lower costs as compared to an issue to the general public.
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(ii) Existing shareholders are benefited in two ways:
Their shareholding proportion is protected, if they purchase the shares.
They get shares at a price lower than the market value.
(iii) Finance can be used to reduce gearing.
(b) Disadvantage of a rights issue
The amount that can be raised by a rights issue is limited, when compared to a public issue. This is because the
resources available with the existing shareholders are likely to be limited.
2.2 Debt financing
There are various forms of debt viz. term loans, debentures / bonds / securitisation etc.
1. The advantages of debt financing are:
(a) No loss of shareholder control as lenders / bondholders do not have any right to vote or participate in the
management. Autonomy is retained as there is no interference with the operating management. However
negative and positive covenants laid down in the loan document / trust deeds need to be complied with. Since
cost of debt is pre-determined it is possible to estimate with accuracy the cost of capital for any project.
(b) Interest paid on bonds/ loans is tax deductible. The effective rate of interest reduces considerably due to
this.
(c) The company can benefit through trading on equity. Since the cost of debt would be lower than the cost of
equity, the weighted average cost of firm can be reduced through deployment of debt.
(d) Debt can be repaid either at maturity or, if the terms so provide, even earlier, depending upon the cash
flows of the firm.
(e) It may be possible to make a refund and substitute a more expensive debt with a cheaper one. This
flexibility is not available in the equity shares.
(f) Debt provides greater flexibility in terms of:
(i) Period of loan .i.e. the time period can be decided by the company
(ii) Negotiations as regards the rate of interest since numerous debt options are available in the market.
(iii) The relationship is restricted to the particular debt instrument
2. The disadvantages of debt financing are:
(a) Debt servicing is mandatory. Irrespective of estimated cash flows the interest needs to be serviced as per
the contract, in the absence of which the lender can initiate legal action against the firm.
(b) Trading on equity has certain limitations. The firm cannot issue bonds at will. The higher the debt, the
greater the risk undertaken by the firm. Consequently, the expected return on equity also increases. The firm’s
cost of capital shifts upwards.
(c) At maturity, the bonds have to be paid. This has an effect on the cash flow of the firm. The firm has
therefore, to plan this eventuality well in advance and manage its cash flows.
(d) A charge has to be created on the firm’s assets in case of secured debt. Firms not having adequate assets
may not find issuing bonds convenient.
(e) Debt is also subject to fluctuations in market value depending on the movement in interest rates. This
makes bonds less attractive for investors.
(f) Agency costs and bankruptcy costs are associated with debt (as explained in Study Guide D2 of study text
B1).The firm needs to be aware of the impact on all aspects of business of any increase in debt beyond a
certain level. Debt has significant impact on the solvency and liquidity ratios of the company.
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What are the advantages of issuing a bond as compared to equity?
2.3 Hybrid securities
Hybrid securities contain features of both equity and debt securities.
1. The advantages of hybrid securities such as convertible bonds, preference shares are:
(a) Hybrid securities are a long-term source of finance available to a corporation as an alternative to issue of
equity. It does not dilute controlling interest. Example preference share holders do not have voting rights
except on matters that affect them.
(b) Improvement in gearing ratios: Hybrid securities in the form of instruments which have a significantly long
tenure or irredeemable preference shares are used by companies to improve their gearing ratios.
(c) Pre-determined returns: In case of hybrid securities it is possible to calculate the cost of finance in advance.
There are no dependencies in the calculations unlike the cost of equity which depends on the level of debt.
Further the rate of dividend / interest on hybrid securities can be decided by the management unlike mortgage
loans where banks decide the rate of interest.
(d) In the event of liquidation of the company, hybrid securities rank above equity shareholders providing
investors with the required assurance while subscribing to them.
(e) Since hybrid securities have conversion options, it is possible for management to convert debt to equity
after a certain time frame on fulfilment of certain conditions.
(f) The interest paid on hybrid securities like convertible bonds is tax deductible.
(g) Hybrid securities can function as an important source of unsecured finance for the company.
(h) Convertible bonds are expected to be self-liquidating. On account of their likely conversion to shares, cash
is not required to redeem them.
2. The disadvantages of hybrid securities
(a) Hybrid securities in the form of preference shares carry a higher rate of dividend compared to interest on
bonds / debentures. This is because it is a riskier asset – unsecured by nature as compared to debt.
(b) The company has to pay the pre-determined return on the hybrid security.
Trega Ltd has been reporting 10% growth in profits for the past two years. The company proposes to enhance
its existing line of business requiring additional investment of Tshs 10 billion. The finance manager proposes a
no-dividend policy for the next three years. However, the company has issued 12% preference shares two years
ago. The preference dividend would need to be paid irrespective of the proposed equity dividend policy.
(c) The issue of hybrid securities requires significant deliberation by the management to ensure easy marketability
of the instruments by providing investor confidence.
(d) The risks associated with high debt in terms of insolvency, agency costs and bankruptcy costs would have
to be dealt with in case of hybrid securities as well.
(e) On conversion of convertible bonds, there will be reduction in earnings per share and control of existing
equity shareholders.
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3. Describe the processes involved in issuance of corporate securities and discuss the
choice and roles of investment advisers in the processes.
[Learning Outcome c]
3.1 Every company needs funds for its business. To meet its long-term requirements, funds can be raised either
through debt or equity. Any major issue would involve offer for sale through a public issue of securities. .
Issuance of corporate bonds
1. A company applying for listing of debt securities must meet the following criteria:
(a) It must have already obtained a listing of its equities on the same stock exchange.
(b) It should offer at least Tshs 50 million of debt security of a class to be listed. Further issues of securities of
class already listed are not subject to these limits.
(c) It should have made profit in at least two of the last three years preceding application for issuance.
(d) Debt ratio including new issue should not exceed 400% of the company’s net worth and the average funds
from operation to total debt for the three years should be at least 40%.
(e) It should submit an offer document accompanied by an Accountant Report covering at least three years
audited financial statement preceding the issue.
(f) It should submit a cash flow projection covering at least 12 months.
(g) An applicant that does not meet the above conditions can seek a guarantor who complies with the specified
condition.
(h) It is required to enter into a contract with the Exchange on such terms as the Exchange may require for the
protection of stockholders.
2. Procedure (according to The Capital Markets and Securities
Authority (CMSA)
CMSA a Government Agency
established to promote and regulate
securities business in the country.
An issuer who has met the initial conditions must follow the following procedures.
(a) Preparation of an Information Memorandum (IM) for the purposes of listing as required by Capital Markets
and Securities (Prospectus Requirements) Regulations, 1997.
(b) The issuer must appoint a broker to sponsor its application for listing and inform the exchange of such
appointment.
(c) The issuer must submit to the Capital Market Securities Authority and the Dar es Salaam exchange, the
application through the sponsoring broker for approval of both institutions.
(d) The approval of the IM allows the issuer to start selling securities as mentioned above on investing during
primary markets.
The company would require professional advice to complete the above procedure. The issuer is required to appoint
a Lead Advisor/ Arranger to the issue.
The Lead Advisor coordinates the exercise including appointment of other service providers/professionals like
Sponsoring broker, Reporting Accountant, Auditor, Legal Advisers, Main receiving Bank, Receiving/ Placing
agents and Registrar of the securities.
The Lead adviser: this is a leader of the entire process who coordinates the activities needed to facilitate listing
of securities at the DSE. The lead adviser carries out the valuation of securities as well as preparation of the
offer document to be submitted to CMSA for approval of the public offer.
The Sponsoring Broker: this is the brokerage house which sponsors the company to the listing on the stock
exchange. The sponsoring broker will take the lead in marketing the issue, submit the application to CMSA and
DSE for consideration as well as play the role of receiving agent.
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3.2 Issue of equity
The CMSA has laid down certain conditions for listing shares under two segments at the DSE


Main Investments Market Segment (MIMS)
Entrepreneurship Growth Market (EGM)
Entrepreneurship Growth Market (EGM) is a new market segment which has been introduced in Tanzanian capital
markets following the completion of a study on appropriate capital markets structure in Tanzania. The market
segment is expected to facilitate mobilization of capital by companies which do not meet the eligibility criteria for
listing on the main investment market segment.
This market segment is also expected to help start up companies with good business plan but lacking capital, to
raise funds for their initialisation as well as implementation of their business plans.
1. Procedures
(a) An issuer who has met the initial listing conditions must follow the following procedures for listing
under MIMS.
(i) Obtain the shareholders consent to issue shares to the public.
(ii) Appointment of a team of consultants to prepare the company for public issue of securities and the listing of
these securities on the stock exchange.
(iii) Preparation of a prospectus by the lead adviser and other consultants as required by CMS Prospectus
Regulations.
(iv) The issuer must appoint a broker to sponsor its application for listing and inform the exchange of such
appointment.
(v) The issuer must submit to CMSA and DSE the application through the sponsoring broker for approval of
both institutions.
(vi) The approval of the prospectus allows the issuer to start selling securities on primary markets.
(b) An issuer who has met the initial listing conditions must follow the following procedures of listing
under EGM.
(i) Appointment of a team of consultants to prepare the company for public issuance of securities and the
listing of these securities on the stock exchange.
(ii) Appointment of a Nominated Advisor to nurse the company from the initial idea of raising capital via EGM until
de-listing from EGM (end of listing on EGM) (if any) or the company graduates to the Main Investment Market
Segment listing.
(iii) The issuer must submit to CMSA and DSE the application of a Nominated Adviser for approval of both
institutions.
(iv) Preparation of a prospectus for the purposes of public offer and listing as required by CMS Prospectus
Regulations.
(v) Provide a letter of undertaking that the company will comply with the DSE continuous listing obligations; and
The approval of the prospectus allows the issuer to start selling securities on primary markets.
3.3 Appointment of a lead adviser / investment adviser
The board appoints an independent investment adviser who has the required expertise to guide the company
regarding the proposed issue. The adviser is a regulated firm and is required to obtain a license from the Capital
Market and Securities Authority. The adviser’s duties include negotiating appropriate terms, conditions and
underwriting commitments with the company’s brokers or investment banks.
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The appointment of an investment adviser is very critical as the success of the issue hinges on the efforts of the
adviser.



Investment adviser is a person who carries on the business of advising others concerning securities;
as part of a regular business, issues or publishes analyses or reports concerning securities; or
pursuant to a contract or arrangement with a client, undertakes on behalf of the client, (whether on a
discretionary authority granted by the client or otherwise) the management of a portfolio of securities for the
purpose of investment”.
The approval by CMSA of an entity as a nominated advisor requires that the applicant shall be company duly
incorporated under Companies Act

Have Memorandum and Articles of Association which restricts the business of the company to only nominated
advisory services;

Have and maintain suitable facilities for carrying on business including offices space, operational system,
appropriate equipment and personnel.



Employ at least one person who shall be licensed as Nominated Advisor’s Representative;
Have capital of two billion shillings; and
Have acted at on at least three of the following transactions during the two years period preceding the
application
o
o
o
o
o
o
corporate advisory role involving financial planning services in analyzing the financial
circumstances of a company and providing a plan to meet that other company’s financial needs;
business creation and institutional building;
reorganizing and restructuring of company
the arrangement , takeover or merger of a corporation or any of its assets or liabilities;
examining the technical , managerial, commercial economics and finance aspects of the company,
establishing the necessary operational infrastructure and determining the price at which the price
of the company shall be offered to the public; and
the publication of an offer document and application for listing of shares on the stock exchange.



Pay application fees of Tshs 1,000,000.
The choice of advisor would depend on:
The prior experience of the adviser in providing specialised services such as handling public issues,
mergers and acquisitions, trading in capital markets, private placements etc.

Capable of conducting analysis of the company’s requirements, industry dynamics.

Has complied with all the requirements spelt out by CMSA in the past and has not received any negative
remarks.

Has the skill to provide strategic advice to the company on available alternative and evolve a realistic plan to
raise funds.

Experience in pricing shares so it will be attractive to the company but also reap a reasonable return for the
investor.

Experience in marketing, deal-making and co-ordination to create support for the stock after it is issued.

Market knowledge and understanding of investor psyche.

Has knowledge to ensure that the company complies with requirements before and after listing.
Describe the role of an investment adviser in the issue of securities.
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4. Estimate the cost of new issues.
[Learning Outcome d]
4.1 Cost of pubic issue of securities
Public issue of securities involves various intermediaries such as lead advisor / nominated advisor, legal
adviser, sponsoring broker, bankers, collecting agents etc. The cost of an issue is an aggregation of the fees
paid for advisory and other services to each of the above.
The costs of a new issue are summarised below:
1. Lead advisor / Nominated advisor fees – The lead adviser plays a crucial role in the success of the public issue
of securities. Lead advisers assist in organising public issues, private placements and syndication of loans
and flotation of both corporate and institutional bonds. The adviser is the binding force between the issuer
and the regulators / brokers / legal advisers / accountants.
A nominator advisor is required when the company is proposed to be listed under the EGM of the DSE. The
selected adviser should be capable of analysing the financial position of the company and play an advisory
role in providing a plan for the public issue. The lead advisor can also act as the sponsoring broker.
2. Legal advisor fees – A legal counsel would be engaged to guide the company to ensure compliance with all
regulatory requirements as laid down by the Capital Market Securities Authority (CMSA) with regard to The
Capital Markets and Securities (Prospectus Regulations Requirements) (Amendment) Regulations 2010
and The Capital Markets and Securities (Nominated Advisors) Regulations 2010.
3. CMSA prospectus evaluation fees – Prospectus evaluation and filing
4. Listing fees and processing fees– The fees with regard to listing on the Dar Es Salaam stock exchange in
the guidelines
5. Cost of marketing the issue, holding meetings, printing and other costs directly attributable to the issue.
Werely Ltd. is into manufacturing and marketing of cement and related products. The company plans a public
issue of 10,000,000 equity shares at Tshs 275 each representing 30% of its total authorised share capital.
The purpose of the issue is to finance the set up of a new factory which is estimated to enhance production
capacity by 30%. The company foresees sufficient demand to absorb the increased capacity.
The finance manager has provided the management an estimate of the costs to the issue to be 1.75% of issue
amount. The details are as follows:
Issue size
Particulars
Cost of issue
Lead advisor fees
Legal advisor fees
DSE processing and listing fees
CMSA fees
Cost of advertising / marketing / media / printing and other
expenses related to the issue
Total
The costs represent 1.89% of the issue size.
Tshs (‘000s)
2,750,000
15,000
9,000
3,200
6,500
18,000
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4.2 Cost of new equity
We have seen that the cost of equity ke is the rate at which investors discount the expected dividends to
determine the share value. The Gordon growth model and the CAPM are the two techniques used to find the
price of the share.
The Gordon growth model formula is:
𝑃𝑃0 =
𝐷𝐷1
𝐷𝐷1
𝑜𝑜𝑜𝑜 𝑘𝑘𝑒𝑒 =
+ 𝑔𝑔
𝑘𝑘𝑒𝑒 − 𝑔𝑔
𝑃𝑃0
While estimating the cost of new equity we have to consider the floatation costs and the effect of under-pricing.
Companies need to under price new offerings of shares mainly because:
1. In the scenario of market equilibrium, the offer price would need to be reduced to generate additional
demand.
2. There is dilution of ownership which acts as a trigger to a lower price.
3.
Investor perception that additional shares being offered by the company indicates that the shares are
overpriced, and the new offer would be at lower than the market price.
Let Nn represent the net proceeds from the sale of new equity share after deducting the under-pricing and
flotation costs. The cost of the new issue, k n, will be:
𝑘𝑘𝑛𝑛 =
𝐷𝐷1
+ 𝑔𝑔
𝑁𝑁𝑛𝑛
The cost of new issue would be greater than the existing cost of equity.
Newdeal Ltd is expected to pay dividend, D1, of Tshs 400; The current market price, P0, of Tshs 5000 and
an expected growth rate of dividends, g, of 5%.
The company is planning an issue of additional equity shares kn, at a price of Tshs 4700. The Tshs 300 per
share under-pricing is due to a highly competitive market. The costs of flotation associated with the new shares
are estimated to be Tshs 250 per share. Tshs 550.
The new price that is expected to prevail will be: current market price- under pricing- flotation cost
or Tshs 5000 – Tshs 550 = Tshs 4450.
Substituting the values in the Gordon growth model, we get
𝑘𝑘𝑛𝑛 =
400
+ 5% = 8.99% + 5% = say, 14%
4,450
The new cost of Newdeal’s equity will therefore be 14%.
While estimating the cost of bonds and preference shares, we need to consider the costs of issue and reduce
the same from the gross amount to arrive at the net proceeds.
The cost of each source of finance has been explained in study guide D1 of study text B1 and the effect of costs
related to new issue has to be factored in while calculating the net proceeds from the issue and the cost of capital.
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4.3 Cost of retained earnings
Dividends are paid out of a firm’s earnings. This payment reduces the firm’s retained earnings. In case a firm
decides to increase the number of shares, it can issue additional equity equivalent to that amount and
simultaneously pay dividends out of the retained earnings.
Alternatively, it can increase the equity shares by issuing bonus shares by a capitalisation of retained earnings,
without reducing its cash balance. Therefore, the cost of retained earnings, kr, to the firm is the same as the
cost of an equivalent fully subscribed issue of additional equity shares. Shareholders will accept retention
of the earnings only if it can earn at least the required return on the reinvested funds.
Thus, the cost of retained earnings will be the same as the cost of a company’s equity. Adjusting for flotation costs
is not necessary, because there is no actual issue of capital and no such costs are incurred. But, at the same time,
the firm is using the money belonging to the shareholders (and held in “trust” by the firm) as if it were an equity.
4.4 Cost of a preference issue
The dividend rate on preference shares may be stated either in value or as a percentage of the par (face) value.
Where the dividend is given as a percentage, it has to be converted into a value.
The process of calculating the cost of preference share is similar to the one adopted for the equity, except that the
growth percentage is not considered. This is due to the fact that preference shareholders are paid a fixed dividend.
The cost of preferred stock, kp, is the ratio of the preferred stock dividend to the firm’s net proceeds from the
sale of the preferred stock. The net proceeds are the amount of money to be received after deducting the flotation
costs.
𝑘𝑘𝑝𝑝 =
𝐷𝐷𝑝𝑝
𝑁𝑁𝑝𝑝
Where,
NP
DP
is the dividend receivable on the preference share, and
= the net proceeds per preference share after deducting the flotation costs.
Like the equity share, as preference shares are paid dividends from the after- tax profits of the firm, no
adjustments for tax is necessary.
Insta Communications Ltd is considering issuing 10% preference shares that is expected to sell for Tshs 950 per
share (face value Tshs 1000). The cost of issuing and selling the stock is expected to be Tshs 75 per share.
The amount of dividend is 10% of Tshs 1000 = Tshs 100.
The net proceeds per share from the proposed preference share sale = Tshs 950- Tshs 75 = Tshs 875
100
Therefore, the cost, 𝑘𝑘𝑝𝑝 = 875 = 11.43%
4.5 The cost of long-term debt
The cost of long-term debt, ki, is the after-tax cost today of raising long-term funds (bonds) through borrowing.
For convenience, we assume that the bonds pay annual (rather than semi-annual) interest.
The net proceeds from the sale of a bond, like we have seen for other securities, are the funds actually
received from the sale after reducing the costs of flotation.
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(a) Calculating the cost of debt using the IRR method
The before-tax cost of debt can be found out by calculating the internal rate of return (IRR) on the bond cash
flows. From the issuer’s point of view, this value is the cost to maturity of the cash flows associated with the
debt. The cost to maturity, when manually calculated, can be found out by using a trial-and-error technique. It
represents the annual before-tax percentage cost of the debt.
The IRR should be that rate at which:
The cash flow received initially from the sale proceeds of the bond = the PV of the interest payable on the bond
th
for “n” years + the principal repayment at maturity (at the end of the “n ” year)
The after-tax cost is found by using the formula: ki = kd x (1- t)
An important difference we should notice is that this is an exact reversal of the cash flows in a project
evaluation. In a bond or equity cost calculation, there is an inflow first and the outflow takes place
subsequently.
Sealand Ltd is planning an issue of Tshs 10 billion worth of 20-year, 9% coupon bonds, each with a par value of
Tshs 10,000. As bonds issued by firms with a similar risk fetch returns greater than 9%, the firm has to sell the
bonds for Tshs 9,800 to compensate for the lower coupon interest rate. The flotation costs are 2% of the par
value of the bond. The applicable tax rate for the company is 35%. Calculate the cost of the bond.
Annual interest = 9% x Tshs 10,000 = Tshs 900. The cost of flotation is 2% of the par value = 2% x Tshs 10,000
– Tshs 200.The net proceeds to the firm from the sale of each bond are Tshs 9,600 ( Tshs 9800- Tshs 200)
The before cost of the bond using the IRR method is found out as follows, by trial and error
As the rate of interest is 9%, we begin the iteration with this rate. The interest is receivable each year for 20 years.
Therefore, this is a case of an ordinary annuity. We therefore use the PVOA table to find the factor for
9%, 20 years. The principal amount is repayable only at maturity. Here, we use the PV table for 9%,20 years.
(Amounts in Tshs )
Cash flow
Inflow
Proceeds from Bond
sale
Outflow
Interest
Principal
PV outflow
Year
Amount
PVOA/PV
factor @ 9%
0
9600
1
1-20
20
900
10000
9.12855
0.17843
PV
9600.00
0.00
8215.70
1784.30
10,000.00
PVOA/PV
factor @ 10%
1
8.51356
0.14864
PV
9600.00
0.00
7662.20
1486.40
9,148.60
We find that at 9 %, the PV of outflow ( Tshs 10,000) is higher than the amount of inflow ( Tshs 9,600). The IRR
should therefore be over 9%. We now use a higher rate, 10%. At 10%, the PV of outflow is lower than the
inflow.
The IRR should lie between 9 and 10%. To exact rate is = 9% +
10,000 - 9,600
= 9% + 0.47% = 9.47%
10,000,- 9,148.60
The after-tax cost = 9.47x (1- 0.35) = 6.16%
(b) Calculating the cost of debt using the approximation method
A simpler and an approximate before-tax cost of debt, kd, for a bond can be found by found by using the
equation given below. This is fairly close to the actual calculation when the IRR is used:
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𝑘𝑘𝑑𝑑 =
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𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣 − 𝑁𝑁𝑑𝑑
𝑛𝑛
𝑁𝑁𝑑𝑑 + 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣
2
𝐼𝐼 +
Where,
I, annual interest in value
Nd, net proceeds from the sale of bond
n, number of years to the bond’s maturity
However, the effective cost of financing must be stated on an after-tax basis. As interest on debt is tax deductible,
it reduces the firm’s taxable income and consequently, the post tax cost (used to compare the cost of various
securities).
The after-tax cost is found by the formula, k i = kd x (1- t)
Continuing the example of Sealand example,
Here we will use the approximation method to calculate the cost.
Annual interest = 9% x Tshs 10,000 = Tshs 900. The cost of flotation is 2% of the par value = 2% x Tshs 10,000
– Tshs 200.The net proceeds to the firm from the sale of each bond are Tshs 9,600 ( Tshs 9800- Tshs 200)
𝑘𝑘𝑑𝑑 =
10,000 − 9,600
900 + 20
20
=
= 9.388%
9,600 + 10,000
9800
2
900 +
The after- tax cost of the new bond = 9.388 x (1-0.35) =6.10%. This rate is close to the rate of 6.16% derived
from the more complicated IRR method.
What are the costs involved in a new issue of shares?
5. Estimate the value of hybrid securities (convertible debentures and warrants).
[Learning Outcome e]
Valuation of hybrid securities
As discussed in the preceding learning outcomes hybrid securities have features of both debt and equity. The
valuation of hybrid securities would involve analysing the debt and equity components of the instrument.
5.1 Convertible debentures
Convertible bonds give bondholders the right but not the obligation to convert their bonds into a predetermined
number of shares at predetermined dates prior to the bond's maturity. This only applies to corporate bonds.
Convertible bonds are exchangeable into shares of common stock, at a fixed price, at the option of the bondholder.
A convertible bond may include a call option, in the sense that the company that issued the bond may have the
right to buy (call) it back. Likewise, a convertible bond may include a ‘put’ option; in this case the holder may
return (sell) the bond back to the company at a specified amount. Their value, like all bonds, depends on
the level of prevailing interest rates and the credit quality of the issuer. Entitlement of conversion is expressed in
a “conversion ratio”.
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Bondholders have the right to convert the Tshs 10,000 par amount (i.e. conversion value) of their convertible
bonds into common shares at Tshs 2500 per share. In this case, the conversion ratio is 4:1 (four to one).
A conversion premium is the difference in price between when a convertible security exceeds the market value
of the common stock into which it can be converted.
The difference between the market value of a convertible bond and its ordinary value as a straight debt is called
the rights premium.
A convertible bond, issued at a par value of Tshs 10,000, is convertible into 4 shares of a firm's stock, implying a
conversion price of Tshs 2,500 per share. If the current stock price is Tshs 2,000, the option to convert is not
profitable, and the bondholder will hold the bond and choose not to convert. If the stock price rises to Tshs 3,000,
it will become profitable for the bondholder to convert the bond into shares, since each bond can be converted
into Tshs 12,000 worth of stock, compared to the bond's face value of Tshs 10,000.
The straight bond value acts as a "floor price," since even if the stock price stays low throughout the holding period,
a bondholder can still retain the bond's value. Therefore, a convertible bond provides a safety net for investors.
From a valuation perspective, a convertible bond consists of two assets: a bond and a warrant. The actual market
value of a convertible bond depends on:



The current conversion values
The time of conversion
The expected conversion values
Conversion value
CV = P0 (1 + g) n R
Where,
CV
P0
g
n
R
= Conversion value
= Current ex-dividend ordinary share price
= Expected annual growth rate of ordinary share price
= Number of years to conversion
= Number of shares received on conversion
A convertible bond which is selling for Tshs 9500 per unit can be converted into 4 of XYZ shares. The current
market price of an XYZ share is Tshs 2000. The ex-interest market value of ordinary bonds of a similar risk class
and maturity is Tshs 9400.
Conversion ratio = 4 unit
CV = Current share price x CR
= Tshs 2,000 x 4 = Tshs 8,000
Conversion premium = Bond value – CV
= Tshs 9,500 - Tshs 8,000 = Tshs 1,500
Current rights premium = Tshs 9,500 - Tshs 9,400 = Tshs 100 i.e. Tshs 25 per share (100/4shares)
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A simple method of calculating the value of a convertible bond involves calculating the present value of future
interest and principal payments (usually at the cost of debt) and adding the present value of the warrant (usually
the conversion value).
Market value of convertible bond
𝑉𝑉0 =
(𝐼𝐼 + 𝐶𝐶𝐶𝐶)
𝐼𝐼
𝐼𝐼
+
+
(1 + 𝑘𝑘𝑑𝑑 ) (1 + 𝑘𝑘𝑑𝑑 )2 (1 + 𝑘𝑘𝑑𝑑 )𝑛𝑛
Where,
V0
I
Kd
n
CV
=
=
=
=
=
Ex-interest market value
Annual interest paid
Rate of return required by debt investors
Number of years to maturity
Conversion value at time t
What would the current market price of a 10% convertible bond of Tshs 10,000 be, if it can be converted, in 3
years’ time, into 2 ordinary shares or redeemed at par on the same date? The required rate of return is 12% and
the current market price of the underlying share is Tshs 4,500 and this is expected to grow by 6% every year.
Step 1: Find out the conversion value
n
CV= P0 (1+ g) R
3
CV=4,500(1+ 0.06) x 2 = Tshs 10719.14
Step 2: Check whether conversion is likely
Par value is Tshs 10,000 and conversion value is Tshs 10719.14 which means that the investor may choose
to convert.
Step 3: Calculate present value of expected cash flow
PVOA factor @12% for 3 years is 2.402 and the PV at the end of the third year it is 0.712
V0 = (1000 x 2.402) + (10719.14 x 0.712)
V0 = Tshs 10,034
SAO Ltd has an outstanding convertible bond. The bond can be converted into 2 equity shares (currently trading
at Tshs 5200/share). The bond has 5 years of remaining maturity, a Tshs 10,000 par value, and a 6% annual
coupon. SAO’s straight debt is currently trading to yield 5%. What is the minimum price of the bond?
5.2 Valuation of warrants
Warrants have been discussed in the preceding learning outcomes. Intrinsic or theoretical value of warrants is
calculated as:
(Current ordinary share price – Exercise price) x Number of shares obtained for each warrant
PQD Ltd. issues warrants that entitle a holder to purchase 3 ordinary shares at a price of Tshs 5,500. The price
of ordinary shares on the market is Tshs 6,000. The theoretical value of the warrants is:
(Current ordinary share price - Exercise price) x Number of shares obtained for each warrant
= ( Tshs 6,000 – Tshs 5,500) x 3 = Tshs 1500
The actual market price of the warrants may be equal to or higher or lower than the theoretical price, depending
upon the investors’ expectations about the future of the company. In the above example, if the actual warrant
price is Tshs 1,750, the warrant conversion premium is Tshs 250 ( Tshs 1,750 – Tshs 1,500).
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Warrant conversion premium or time value
The difference between the actual market price of a warrant and its intrinsic or theoretical value is known as
warrant conversion premium or time value.
Gearing effect of warrants
The effect of changes in the price of shares on the value of warrants is proportionately higher. This is known as
a gearing effect.
Continuing with the example of PQD Ltd
If the share price increases to Tshs 7,500, the increase in the share price is Tshs 7,500 – Tshs 6,000 = Tshs
1,500. In percentage terms, the increase is Tshs 1,500/ Tshs 6,000 x 100 = 25%. The revised warrant price is (
Tshs 7,500 – Tshs 5,500) x 3 = Tshs 6,000. The increase in the warrant price is Tshs 6,000 – Tshs 1,500 = Tshs
4,500. In percentage terms, the increase is ( Tshs 4,500/ Tshs 1,500) x 100 = 300%. Overall, the share price
increased by 25%, whereas the warrant price increased by 300%. This is called a gearing effect.
6. Analyse the effects of issuing each of such securities on the share price and discuss the
available empirical evidence.
[Learning Outcome f]
In making their capital structure decisions firms do not necessarily choose only equity to finance their growth
needs. Typically, a firm will have a mix of various equity and debt securities. Generally, there is an incentive to
use more debt as the interest expense is tax deductible and brings down the cost of debt. However, in doing so,
there is financial risk in taking on too much debt, so each company must find a balanced structure.
In order to finance any new project, the company can either approach the existing shareholders through a rights
issue, avail of loan from banks, issue debentures / bonds / hybrid securities. Each of these options will have an
impact on the share price of the company.
6.1 Impact of a rights or new issue on the share price
The issue of rights shares or a new equity issue increases the equity capital base. A rights issue is normally priced
at a discount (of approximately 15 to 20%) on the existing market price, in order to make the shares attractive to
shareholders. This is done to provide for the variations occurring in the market price of shares, until the time of
actual issue. Therefore there is a value attached to the rights.
The actual market price after a rights issue depends upon the expected rate of earnings on the new funds:
1. If the rate of earnings on new funds is expected to be the same as that on old funds, the actual market price
is likely to be the same as the theoretical ex rights price.
The current market value of one share of Fullerton Ltd is Tshs 1000. The current rate of earning is 15%. The
company decided to raise new funds through rights issue. The rate of earning expected on the new fund is 15%.
Hence, the actual market price of the share after the rights issue will be Tshs 1000.
2. If the rate of earnings on new funds is expected to be higher than that on old funds, the actual market price
is likely to be higher than the theoretical ex rights price.
Continuing the example of Fullerton Ltd
Assume that the rate of earning expected on the new fund is 20%. In such a case, the actual market price of the
share after rights issue will be more than Tshs 1000.
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3. If the rate of earnings on new funds is expected to be lower than on old funds, the actual market price is
likely to be lower than the theoretical ex rights price.
Continuing the example of Distribute Ltd
Assume that the rate of earning expected on the new fund is 10%. In such a case, the actual market price after
rights issue will be less than Tshs 1000.
Effect of the rights issue price on the EPS
Depending upon how the issue price or rights shares compares with the capital employed per share before the
issue, the EPS will be affected as follows:
1. If the rights issue price is the same as the capital employed per share before the issue, the EPS will not be
affected.
2. If the rights issue price is higher than the capital employed per share before the issue, the EPS will
increase.
3. If the rights issue price is lower than the capital employed per share before the issue, the EPS will be decreased
(diluted).
This can be illustrated by an example.
Diwa Inc has 10,000 outstanding shares. The capital employed by the company is Tshs 200 million. Hence, the
capital employed per share is Tshs 20,000 ( Tshs 200,000,000/10,000).
The company has decided to make a rights issue to raise Tshs 50 million. The rate of return on capital employed
is 10%. The current earning of the company is Tshs 20 million and the current EPS is Tshs 2,000( Tshs 20
million/10,000). The total earning of the company after the rights issue will be Tshs 25 million (( Tshs 200 m +
Tshs 50 m) x 10%).
(i) If the company issue shares at Tshs 20,000 then the company will have to issue 2,500 shares. In such a
case the total outstanding shares of the company would be 12,500 shares. The new EPS of the company would
be Tshs 2,000.
(ii) If the company issued shares at Tshs 25,000 then the company will have to issue 2,000 shares. In such a
case the total outstanding shares of the company would be 12,000 shares. The new EPS of the company would
be Tshs 2080.
(iii) If the company issued shares at Tshs 10,000 then the company will have to issue 5,000 shares. In such a
case the total outstanding shares of the company would be 15,000 shares. The new EPS of the company would
be Tshs 1670.
PPL Ltd can achieve a profit after tax of 22% on the capital employed. The present capital structure is as
follows:
275,000 ordinary shares of Tshs 1000 each
Retained earnings
Tshs million
275
125
It is proposed by the directors to raise an additional Tshs 155,000 m from a rights issue. The current market
price is Tshs 2200.
Required:
(a) Calculate the number of shares that must be issued if the rights price is Tshs 1900, Tshs 1800, Tshs
1600, and Tshs 1400.
(b) Calculate what the diluted EPS will be in each case.
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A company has 500,000 shares outstanding, with a market price of Tshs 1500. The market value of the firm is:
500,000 x 1500 = Tshs 750 million. It makes rights issue of 250,000 (1:2) at a price of Tshs 1200.
The value of the rights = 250,000 x 1200 = Tshs 300 million
The total value of the company will now be Tshs 1,050 million.
The theoretical ex rights market price will now be Tshs 1050million/750,000 shares = Tshs 1400.
The existing shareholders who have not opted for the rights stand to lose.
Allfine Company Ltd desires to expand its capacity to take advantage of a growing market. The company currently
has 1000,000 shares outstanding and no debt. The stock sells for Tshs 5000 per share, but the book value per
share is Tshs 4000. Net income for the company is currently Tshs 150 million. The new facility will cost Tshs 350
million, and it will increase net income by Tshs 5 million.
Required:
(a) Assuming a constant price-earnings ratio, what will be the effect of issuing new equity to finance the
investment?
(b) Calculate the new book value per share, the new total earnings, the new EPS, the new stock price, and the
new market to book ratio.
Answer
The number of shares outstanding after the stock offer will be the current shares outstanding plus the amount
raised divided by the current stock price, assuming the stock price doesn’t change. So:
Number of shares after the offering = (1000,000 + 350 million/ Tshs 5000/share) = 1,070,000
(we assume no flotation costs in the absence of information)
Number of shares after the offering = 1.07 million
Since the par value per share is Tshs 1000, the old book value of the shares is the current number of shares
outstanding.
New book value per share = (1.0 million x Tshs 4000 +0 .07 million x Tshs 5000)/1.07 million = Tshs 4065.42
The current EPS for the company is: Tshs 150 million / 1.0 million shares = Tshs 150
The current P/E is: Tshs 5000/150 = 33.33
If the net income increases by Tshs 5 million, the new EPS will be: Tshs 155 million / 1.07 million shares
= 144.86 per share i.e.., the transaction is dilutive
Assuming the P/E remains constant, the new share price will be: (P/E) x (New EPS) = 33.33 x Tshs 1.44.86
= Tshs 4828
The share price will decline from Tshs 5000 to Tshs 4828 as a result of the new issue. In their research study
have found that the issuance of new equity leads to a significantly negative stock price reaction.
6.2 Impact of a debt issue on the share price
Milestone Products Ltd. is into manufacturing of electrical components. The company has been in existence for
over 10 years and have a market share of over 50%. The company plans to diversify into manufacture of consumer
appliances. For this purpose, the company is planning to issue make a debenture issue of Tshs 10 billion which is
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80% of the project and the balance through internal accruals. The firm currently has a debt to equity of 2:1. This
project would increase the gearing to 4:1 which is expected to taper to 2.5:1 within 5 years following additional
cash flows from existing and new business segments.
The Board is contemplating whether this proposal would be accepted by the existing shareholders and the impact
that the bond issue would have on the share price.
The finance manager is of the view that the share price would decline on an immediate basis. The extent of impact
would depend on a couple of factors:
The size of the new offering
The quality (in terms of rating) of the debt being raised
The purpose for which the debt is being raised and viability of the project
The extent the share is overpriced.




This is because of the increased debt which would lead to increase in the risk borne by the shareholders. The
negative impact on the EPS would result in reduction in the share price. It is critical to conduct meetings with all
major shareholders and explain the intent of the proposed expansion with detailed cash flow projections. It is
essential that the shareholders be taken into confidence by providing complete information to prevent negative
perceptions.
We can take a look at Miller - Modigliani propositions in a world with taxes (where interest expense is taxdeductible). Firms which have a low leverage increase enterprise value by generating a tax shield when they
increase leverage. However, increase in debt beyond the indifference point results in the benefit of debt being
compensated by the risk of default. Issuing debt beyond that point would result in decline in share price and
erosion of shareholder value.
A summary of studies conducted in the United States to study the impact of securities offerings both straight
debt and convertible bonds in the past are provided below (not conclusive):
S No.
1.
2.
3.
Study
Dann and Mikkelson (1984)
Howton, Howton and Perfect (1998)
Mikkelson and Partch (1986)
Eckho (1986)
Hansen and Crutley (1990)
Shyam Sunder (1991)
Johnson (1985)
Findings
Negative average stock return of 0.37% in the announcement
period and issue date
Negative average stock return of 0.5%
Marginal impact on stock return
A summary of studies conducted in UK to study the impact of securities offerings in the past is provided below
(not conclusive):
S No.
1.
2.
Study
Simons (1999)
Abyankar and Dunnins (1999)
Findings
Significantly negative during the announcement period and
issue date
Further the impact of issue of convertible securities has been higher than the impact of straight debt. This is
because of risk of overpricing of the warrant and proposed dilution of control.
What is the impact of issuing new shares on the price of the existing equity shares?
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Answers to Test Yourself
Answer to TY 1
Current conversion value
= 35 x 355 = Tshs 12425
Current conversion premium = Tshs 14520 – Tshs 12425 = Tshs 2095 or Tshs 59.85 per
share. Current rights premium
= Tshs 14520 - Tshs 12970 = Tshs 1550 or Tshs 44 per
share. Answer to TY 2
Hybrid securities are akin to both equity and debt. Warrants are instruments that contain a right to buy equity
shares of a company at a future date at an exercise price. Warrants in combination with bonds / debentures attract
investors. Warrants provide an investor with an opportunity to earn higher income at a relatively lower investment.
The risk involved is therefore restricted.
Answer to TY 3
The advantages of issuing bonds:
1. No loss of shareholder control as bondholders do not have any right to vote or participate in the management.
Issuing equity shares dilutes the control as the holders of the new shares also become owners.
2. Bondholders are creditors and not owners.
3. Tax advantage: Interest paid on bonds is tax deductible. The effective rate of interest reduces considerably
due to this. The cost of equity is very high as dividends are not tax deductible.
4. Issuing bonds instead of shares will not decrease the earnings per share.
5. Temporary source of funds: These can be repaid either at maturity or, if the terms so provide, even earlier,
depending upon the cash flows of the firm. This affords great flexibility. Equity financing is a permanent source
and affords little flexibility.
6. It may be possible to make a refund and substitute a more expensive debt with a cheaper one. This
flexibility is not available in the equity shares.
7. Bonds are often liquid; it is often fairly easy for an institution to sell a large quantity of bonds without
affecting the price much. Share prices may be affected if a large chunk is offloaded into the market.
8. There are also a variety of bonds to fit different needs of investors. Such options are limited for equity
shareholders.
9. The volatility of bonds (especially short and medium dated bonds) is lower than that of equities (stocks).
Thus, bonds are generally viewed as safer investments than stocks.
Answer to TY 4
The lead adviser plays a crucial role in the success of the public issue of securities. Lead advisers assist in
organising public issues, private placements and syndication of loans and flotation of both corporate and
institutional bonds. The adviser is the binding force between the issuer and the regulators / brokers / legal
advisers / accountants.
His role includes:
1. Analysis of the purpose of the issue and assisting the company in financial planning.
2. Valuation of securities and advisory on pricing to ensure that the securities issue is successful.
3. Preparation of prospectus based on the requirements as laid down in the Capital Market and Securities
(Prospectus requirements).
4. Submission to the CMSA for approval.
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5. Co-ordinating with brokers for advertising and marketing the issue through road shows, media etc.
6. Co-ordination with legal advisors / accountants for fulfilment of regulatory requirements.
Answer to TY 5
A new issue of shares primarily involves the following costs:
1. Lead advisor / Nominated advisor fees: This consists of fees paid to the lead adviser who provides a variety
of services ranging from advisory on pricing, preparation of prospectus, liasioning with all parties to the issue.
Further a nominator advisor is required when the company is proposed to be listed under the EGM of the
DSE.
2. Legal advisor fees: A legal counsel would be engaged to guide the company to ensure compliance with all
regulatory requirements as laid down by the Capital Market Securities Authority (CMSA) with regard to The
Capital Markets and Securities (Prospectus Regulations Requirements) (Amendment) Regulations 2010
and The Capital Markets and Securities (Nominated Advisors) Regulations 2010.
3. CMSA prospectus evaluation fees: Prospectus evaluation and filing
4. Listing fees and processing fees: The fees with regard to listing on the Dar Es Salaam stock exchange in
the guidelines
5. Cost of marketing the issue, holding meetings, printing and other costs directly attributable to the issue.
In addition to the above, the effect of pricing also needs to be taken into account while arriving at the cost of
equity.
Answer to TY 6
The price must exceed the straight bond value or the value of conversion If converted, the debt is worth
Tshs 5200 x 2 = Tshs 10,400.
Annual coupon = Tshs 600
Number of years =5;
Maturity value payment = Tshs 10,000
Interest rate (yield) = 5 %
We compute the PV of the bond by using the PVOA table for annual coupon Tshs 600, 5 years @ 5% and the
PV table for Tshs 10,000, 5 years@ 5%
PVOA factor = 4.32948; PV factor =0.78353
Therefore, PV of the convertible bond = 600 x 4.32948 + 10,000 x 0.78353 = Tshs 10,432.99 or Tshs
10,433. The bond must be trading for at least 10,433.
Answer to TY 7
The earnings at present are 22% of Tshs 400 m = Tshs 88m. This gives an EPS of Tshs
320. The earnings after the rights issue will be 22% of Tshs 555m = Tshs 122.1 m
Rights
price
Tshs
1900
1800
1600
1400
No. of new shares (
Tshs 155 m /rights
price)
81,579
86,111
96,875
110,714
Total Shares
(275,000 + No. of
new shares)
356,579
361,111
371,875
385,714
EPS ( Tshs
122.1m/Total no.
of shares)
342
338
328
317
Dilution
(cents)
22
18
08
(3)
It is necessary to understand that, at a high rights price, the EPS increases, and does not get diluted.
The breakeven point or zero dilution occurs when the rights price is equal to the employed share capital i.e.
Tshs 400m/275,000 = Tshs 1,454
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Capital:377
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Answer to TY 8
The issue of rights shares or a new equity issue increases the equity capital base. There will not be an
immediate corresponding increase in the earnings of the company. Therefore, there is a dilution in the EPS.
Consequently, the market reacts negatively to the new issue resulting in a reduction in market price of the
share.
Quick Quiz
1. State True or False
(a) A hybrid security is a security that is neither debt nor equity.
(b) Underwriters to an issue buy the securities to add to their own portfolio.
(c) The prospectus is an advertisement for the issue and its contents are determined by the advertising
agency.
(d) Equity shareholders have liability in the event of liquidation of the company.
(e) Empirical studies suggest that debts can be issued for any amounts without affecting the share price.
2. Equity is more expensive than debt. Give reasons.
3. What are the pre conditions for a nominated advisor?
Answers to Quick Quiz
1.
(a) False
(b) False
(c) False
(d) True
(e) False
2. Equity is more expensive than debt because:
(a) the return is based on the earnings after tax, whereas debt is tax deductible.
(b) investors in the equity stock expect a higher return as the risks taken by them is much greater than
those of debt holders.
3. The nominated advisor should have acted on at least three of the following transactions during the two
years period preceding the application.
(a) Corporate advisory role involving financial planning services in analysing the financial circumstances of a
company and providing a plan to meet that other company’s financial needs;
(b) Business creation and institutional building;
(c) Reorganizing and restructuring of company
(d) The arrangement , takeover or merger of a corporation or any of its assets or liabilities;
(e) Examining the technical , managerial, commercial economics and finance aspects of the company,
establishing the necessary operational infrastructure and determining the price at which the price of the
company shall be offered to the public; and
(f) The publication of an offer document and application for listing of shares on the stock exchange.
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Self Examination Questions
Question 1
Why a preference share is considered a hybrid security? Evaluate preference shares as a source of finance.
Question 2
RIGA Ltd. is a newly incorporated company. It is engaged in the business of manufacture of soaps and detergents.
RIGA has sound business plans and plans to capture at least 10% market share in the next 3 years. However it
may not be a position to fulfil the capital requirements for listing on the stock exchange. The promoter
group has a sound background and has been successful in various business ventures undertaken earlier.
Question 3
The company wishes to approach the public through an initial public offering. Is it possible? Present a report
explaining the pros and cons of equity and debt financing.
(a) An investor has bought a 10-year convertible bond, with a 5% coupon rate trading at Tshs 5,400. The face
value of the bond is Tshs 5,000. The market interest rate of similar risk bonds are 8%. Determine the value
of the equity.
(b) Elaborate the advantages of convertible bonds
Question 4
A company proposes to issue debt securities of value Tshs 1000 million in the form of bonds through a public
issue. Advice the company on the following from a financial and regulatory perspective
(a) Types of bonds that can be issued
(b) Whether the company qualifies for issue
(c) Procedure for issue
Answers to Self Examination Questions
Answer to SEQ 1
A preference share is a hybrid security because it has the characteristics of both debt and equity. It is similar to
equity in that it:


Has no maturity date, and
Has payments which are considered dividends and are not tax deductible.
However, it is also similar to debt because:




It has a fixed rate for dividends,
It does not carry any voting rights, and
When the need for additional funds through an issuance of equity is foreseen, a proposal is made to the
board of directors. Discussions regarding the timing and structure take place and a formal approval of the
board is taken.
Has priority over equity shareholders in the event of bankruptcy.
The advantages of preference shares for a company are:

By issuing preference shares, there is no dilution of control. The existing shareholders can retain control
over the company as preference shareholders can vote only on matters that affect them.

Hybrid securities in the form of instruments which have a significantly long tenure or irredeemable preference
shares are used by companies to improve their gearing ratios.

Suitable to some investors: This is suitable for investors who do not like to take more risk and who like to
get fixed dividend.
Flexibility: The Company can choose among redeemable,convertible and participating preference shares to suit
their purpose. Such shares are also attractive to investors.
 No security is required to be offered for issue of preference shares
Issues of New Capital: 311
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Issues Of New Capital: 379

The cost of preference shares is lower than the cost of equity.

There is no annual repayment obligation unlike debt.

The company can decide the rate of dividend that is to be paid for the capital, as opposed to when borrowing
from the bank and a rate is forced upon them.
The disadvantages of preference shares:

The preference dividend is normally higher than the rate of interest on bonds.

Preference in claims: Preference shareholders enjoy similar situation like that of an equity shareholder but still
get a preference in both payment of their fixed dividend and claim on assets at the time of liquidation.
Answer to SEQ 2
th
28 November 20X3
The Board of Directors
RIGA Ltd.
Dar es Salaam, Tanzania
Report on the feasibility of equity issue and means of finance
RIGA Ltd. is a newly incorporated company. It is engaged in the business of manufacture of soaps and detergents.
RIGA has sound business plans and plans to capture at least 10% market share in the next 3 years. However it
may not be a position to fulfil the capital requirements for listing on the stock exchange.
In the light of the above a public issue may be floated for listing under the Entrepreneurship Growth Market (EGM)
of the DSE. This market facilitates mobilization of capital by companies which do not meet the eligibility criteria for
listing on the main investment market segment. This market segment is also expected to help start up companies
with good business plan but lacking capital, to raise funds for their initialisation as well as implementation of their
business plans.
An issuer who has met the initial listing conditions must follow the following procedures of listing
under EGM:
(a) Appointment of a team of consultants to prepare the company for public issuance of securities and the
listing of these securities on the stock exchange;
(b) Appointment of a Nominated Advisor to nurse the company from the initial idea of raising capital via EGM
until de-listing from EGM (end of listing on EGM) (if any) or the company graduates to the Main Investment
Market Segment listing;
(c) The issuer must submit to CMSA and DSE the application of a Nominated Adviser for approval of both
institutions;
(d) Preparation of a prospectus for the purposes of public offer and listing as required by CMS Prospectus
Regulations;
(e) Provide a letter of undertaking that the company will comply with the DSE continuous listing obligations; and
(f) The management can also tap debt in the form of bonds / loans from financial institutions. The company can
take advantage of the group credit standing for the same.
The advantages of equity are:
(i) Equity contributions do not have to be paid back even if the company goes bankrupt.
(ii) The business assets do not have to be pledged as collateral to obtain equity investments.
(iii) Businesses with sufficient equity will look better to lenders, investors and the IRS.
(iv) The business will have more cash available because it will not have to make debt payments.
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Disadvantages of equity financing:
(i) The company has to relinquish ownership and a share of the business’s profits to other equity investors.
(ii) Other owners may have different ideas on how the business should operate.
(iii) Dividend payments to investors in companies are not tax deductible.
On the other hand, as regards debt finance
Advantages of debt financing:
(i) There is no need for an owner to give up any ownership or future profits of his business. The lender has no
control in how the business is managed. They are only concerned with the repayment of the loan.
(ii) Borrowed money will help in obtaining business assets, it will allow us to keep the business profits in the
company or use the profits to pay a return to the owners of the company.
(iii) Interest paid on the loan is generally tax deductible.
Disadvantages of debt financing:
(i) The company must have sufficient cash flows to repay its loans.
(ii) Generally, cash profits are used to pay back the loans. If the business has a lot of debt, it may end up with a
profit but not have any cash to show for it.
(iii) Dealing with the lenders and their criteria to obtain the loan.
(iv) The riskier the loan, the higher the interest rate will be.
(v) Most lenders will require small business loans to be co-signed or guaranteed by the owner(s) of the
business.
(vi) Loans usually require collateral to secure them. If the loan cannot be repaid, the lender has a right to seize
collateral.
(vii) Too much debt may impair the ability to raise money in the future.
In the light of the above, the management should analyse the short term, medium term and long-term financing
requirements v/s. the company’s ability to fulfil the requirements under each method of financing to decide on
the best option.
Answer to SEQ 3
(a) The value of the straight bond and equity components can be estimated as follows:
The coupon value of the bond = Tshs 5,000 x 5% = Tshs 250.
Value of a straight bond is estimated as= coupon value of bond X PVOA(10 years, 8% + market valueX (PV 10
years ,8%) = Tshs 500 (PVOA, 10 years,8%) + 10,000,( PV10 years, 8%)
=250x6.71008 +5,000 x0.46319 = Tshs 3,993.47
Therefore, the value of the equity component = Tshs 5,000 – Tshs 3993.47 = Tshs 1,006.53
(b) The advantages of convertible bonds are:
(i) Raising low cost capital
One of the advantages of issuing convertible debentures is that they can provide immediate finance at lower costs
since the conversion option effectively reduces the interest rates payable. By raising finance from this source, a
company can use the lower cost of capital during the initial stage of investment when its effect is not fully reflected
in the earnings.
(ii) Represent attractive investment
The primary purpose of issuing convertible debentures is to make the issue attractive enough so that it is fully
subscribed. Convertibles represent attractive investments to investors since they are effectively debt risks for future
equity benefits. Hence, finance is raised relatively easily.
(iii) Deferred equity financing
By issuing a convertible debenture, the company can defer the equity financing i.e. the company sells ordinary
shares in the future.
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313
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(iv) Cash flow benefits
If the investors are ready to convert their debentures, the company can avoid cash flow problems associated
with the repayment of debentures, if any. If the company’s assumptions regarding the conversion of debentures
turn out to be true, then the company need not establish a large sinking fund to redeem the debentures.
(v) Higher gearing levels
Convertibles allow for higher gearing levels than would otherwise be the case with straight debt (interest costs
are potentially lower with convertibles).
Answer to SEQ 4
(a) Types of bonds that can be issued
There are broadly two types of bonds that can be issued
(i) Secured bonds
Secured bonds are straight debt which carry a coupon rate of interest and are repayable after a fixed period of
time. The annual outflow in the form of interest is pre-determined. The bonds can sold either through a private
placement or a public issue if the size is sufficient to warrant a public issue. Investors in bonds require an assurance
on the credit standing of the company.
(ii) Convertible bonds
Convertible bonds are fixed interest debt securities, which the holder can choose to convert into ordinary shares
of the company. This conversion takes place at a predetermined rate and on a predetermined date. They are
hybrid securities and benefit the company in managing the gearing ratios. There is no requirement for cash outflow
on redemption which is a distinct advantage.
(b) Whether the company qualifies for issue
The company has to meet the following criteria:



It must have already obtained a listing of its equities on the same stock exchange.
It should offer at least Tshs 50 million of debt security of a class to be listed. Further issues of securities
of class already listed are not subject to these limits.
It should have made profit in at least two of the last three years preceding application for issuance.

Debt ratio including new issue should not exceed 400% of the company’s net worth and the average funds
from operation to total debt for the three years should be at least 40%.

It should submit an offer document accompanied by an Accountant Report covering at least three years
audited financial statement preceding the issue.

It should submit a cash flow projection covering at least 12 months.

An applicant that does not meet the above conditions can seek a guarantor who complies with the specified
condition.

It is required to enter into a contract with the Exchange on such terms as the Exchange may require for the
protection of stockholders.
Since financial details are not provided, we cannot analyse further on the eligibility.
(c) Procedure for issue
An issuer who has met the initial conditions must follow the following procedures:


Preparation of an Information Memorandum (IM) for the purposes of listing as required by Capital Markets
and Securities (Prospectus Requirements) Regulations, 1997.
The issuer must appoint a broker to sponsor its application for listing and inform the exchange of
(c) Procedure for issue
An issuer who has met the initial conditions must follow the following procedures:
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 :Financing
Preparation
of an Information Memorandum (IM) for the purposes of listing as required by Capital Markets
314
Decisions
and Securities (Prospectus Requirements) Regulations, 1997.

The issuer must appoint a broker to sponsor its application for listing and inform the exchange of
such appointment.

The issuer must submit to CMSA and DSE the application through the sponsoring broker for approval
of both institutions.

The approval of the IM allows the issuer to start selling securities as mentioned above on investing during
primary markets.
The company would require professional advice to complete the above procedure. The issuer is required to appoint
a Lead Advisor/ Arranger to the issue. The Lead Advisor coordinates the exercise including appointment of other
service providers/professionals like Sponsoring broker, Reporting Accountant, Auditor, Legal Advisers, Main
receiving Bank, Receiving/ Placing agents and Registrar of the securities.
SECTION D
Cost of Capital: 315
FINANCING DECISIONS
D3
STUDY GUIDE D3: COST OF CAPITAL
Every finance manager is required to make decisions regarding an ideal capital structure which would maximise
the value of the firm. The capital structure of a company has a major influence on the financial health of the firm.
The cost of capital affects the profitability of the firm and has an impact on the decisions about future
investments.
Different sources of finance have different risks attached to them. The risk attached to a source determines the
return expected by investors. In order to take the right decision, it is necessary to understand the relative costs
of each source of finance. In this Study Guide, the cost of equity, debt and overall cost of capital is explained.
a) Define cost of capital.
b) Identify and assess appropriate options for financing an entity based on a given business scenario and
environment.
Calculate and evaluate giving suitable advice on the costs of different financing methods used by a
company both before and after tax.
d) Compute the company’s overall cost of capital and that of a project and identify the situations in which
each is used as a valuation and decision tool.
e) Discuss the roles of market and book values in computing cost of capital.
f) Discuss the determinants of the level of cost of capital.
g) Outline the different uses of cost of capital in finance.
c)
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1. Define cost of capital.
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[Learning Outcome, a]
Cost of capital is the bare minimum return that the firm must earn on the capital invested to keep the market
value of the firm unchanged.
Cost of capital is the minimum threshold rate used for discounting cash flows to determine the present value of
future cash flows and finally for deciding whether the project is worth taking up or not.
From another perspective, cost of capital is the cost of funds being used by the firm. It is basically the return which
the firm is required to pay for the various sources of finance. A firm has to pay:


Interest to the providers of loans and securities
Dividend to the shareholders (both equity and preference shareholders)
Furthermore, the retained earnings which are ploughed back into the business also have a cost. This is
basically the opportunity cost for the shareholders i.e. the minimum return which they would receive had they
deployed their funds elsewhere.
1.1 Assumptions in the theory of cost of capital
The basic assumption of the traditional theory of cost of capital is that the business risks and financial risks of
the firm remain unaffected by acceptance and financing of the projects.
Business risk is the uncertainty about the firm’s future operating earnings. It measures the change in operating
profits due to change in sales. If a firm adopts a project that is riskier, suppliers may demand a higher rate and
shareholders may demand higher returns. In analysing the cost of capital, it is assumed that there is no change in
business risk due to acceptance of an investment proposal.
Financial risk is the risk of not having the capacity to cover fixed obligations like interest, preference dividends
etc. In general, with an increase in long term debt, there is an increase in financial risk, because increased earnings
are required to take care of the interest outlay. All other things remaining constant, the risk of the firm being unable
to meet these obligations increases.
In the calculation of cost of capital, the financial structure is assumed to be static. This is required, as otherwise,
with the selection of one form of financing the cost of other forms of financing will change. In practice, this
assumption implies that the additional funds required to finance the project would be raised in the same proportion
as the firm’s existing financing structure.
1.2 Explicit and implicit costs
Explicit cost of capital: explicit cost of a particular source is the interest or dividend that the firm has to pay to
the financiers. There is an explicit flow of money from the entity to the supplier of funds.
Implicit cost of capital: in the case of certain sources of finance, there is no explicit flow of funds from the firm
e.g. in the case of retained earnings. The internal accruals are ploughed back into the business rather than
financing new projects / fixed costs with external debt. Although there is no explicit cost, there is an opportunity
cost for the shareholders. It is the rate of return that the shareholders would have earned had the profits been
distributed to them. This opportunity cost is the implicit cost of capital.
1.3 Relative risk-return relationship
The expected rate of return for every investment is affected by the financial relationship between risk and return.
A higher expectation of risk is compensated for by greater returns. A low risk generally means low returns. This
is the risk-return relationship that is characterised as “positive” or “direct”. Investors first quantify the risk and
then decide the price of that risk. The higher the risk, the higher the price expected by investors. When investors
demand or expect higher returns, the company’s cost of capital increases.
Cost of Capital: 317
Cost of Capital: 233
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When an investor provides a secured loan of Tsh1000million and he is satisfied with the quality of the security,
he may accept a lower return of 8%. However, if the loan is unsecured and is granted on the basis of only a
personal guarantee, the lender will demand a higher return to compensate for the higher risk, e.g. 12%.
Is there a direct correlation between risk and expected return?
2. Identify and assess appropriate options for financing an entity based on a given business
scenario and environment.
[Learning Outcome b]
Whenever funds are to be raised to finance investments, a capital structure decision is involved. In a given
business environment, for financing of any expansion / new project, a decision has to be arrived at regarding the
quantity and forms of financing.
XYZ Ltd is a manufacturer of automobile components. It is planning to expand its plant capacity by 30% and
requires additional capital of Tshs 2,500 million for this. The two broad options to raise additional funds are
shareholder’s funds and borrowed funds. However, before deciding on a particular financing option, the firm has
to evaluate the existing capital structure and the pay-out policy in terms of dividend pay-out / reinvestment of profit.
The company has to decide on the proportion of shareholder’s funds and borrowed funds for the proposed
investment. Based on their assessment of risk, the provider of each source of finance would require a minimum
rate of return. A combination of these would result in determination of the cost of capital which, in turn, would affect
the value of the firm. The process of financing or capital structure is depicted below:
Diagram 1: Process of financing of capital structure decision
There are various sources of finance available to a business organisation:
Shareholders’ Funds
Equity Share Capital
Reserves & surplus / retained earnings
Preference Share Capital
Borrowed Funds
Bonds
Debentures
Long term loans
1. Equity share capital
Equity share capital represents ownership capital. The equity shareholders are the owners of the firm. When a
company is formed, equity shares are issued to the promoters. As the company grows and demand for funds
increases, equity shares are issued to outsiders and may also be offered to the public through an initial public
offering (IPO). Equity shareholders bear the maximum risk as they are given the lowest priority in terms of cash
payouts and in the event of liquidation.
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Therefore, they expect the maximum returns. Among equity or ordinary shares, initial issues will have more risk
and therefore higher expected returns. Once the company stabilises in the business, the risk is reduced and the
expected return may be lower. As a result, the cost of capital is lower compared to the initial period. However,
compared to debt finance, equity finance generally involves a higher cost of capital.
2. Retained Earnings
Retained earnings are the undistributed profits ploughed back into the business. These funds belong to the equity
shareholders. As explained earlier, although these funds are available for financing of any new project, they involve
a cost which is expressed in terms of the opportunity cost foregone by the shareholders.
3. Preference share capital
As the name indicates, preference shares are given preference regarding payments of dividends and repayment
of capital, as against equity / ordinary shares, and carry a fixed percentage dividend. Therefore, the risk and the
cost of capital are lower compared to ordinary shares.
Preference shares may be cumulative or non-cumulative. In the case of cumulative preference shares, even where
there are insufficient profits, the dividends are carried forward to subsequent years. The risk of non- receipt of
dividends is lower. The return expected by investors, and therefore, the cost of capital, is slightly lower.
4. Debt finance
Other things being equal, the credit standing, and track record of the borrower affect the cost of borrowing or
debt. Furthermore, the longer the term, the higher is the uncertainty and risk and therefore, the higher will be the
interest cost. Usually, the cost of debt finance is likely to be lower than that of equity finance. However, within debt
finance, there are variations in the cost of debt, depending upon security, term and other factors determining the
risk profile.
Based on security, debt finance can be classified as:
(a) Unsecured debt
Interest on debt is to be paid whether there are sufficient profits or not. The risk of non-payment of interest and
the principal is lower compared to preference shares. Expected returns and costs of capital are, therefore,
lower. However, there is a higher risk of non-payment of the principal, compared to secured loans. Hence, the
expected returns may be comparatively higher than those on secured loans.
(b) Secured debt
Secured debt has a charge on certain assets e.g. a ‘fixed charge’ on one asset or a ‘floating charge’ over
several assets. In the case of default, those assets can be sold and the money may be realised. The risk of losing
the principal is lower than for an unsecured loan. However, all the assets are not of the same quality, therefore
the expected return may vary on the basis of the quality of the security.
A loan obtained using land and buildings as security is considered a secured loan. The interest on such a loan will
be relatively low, as in the event of the borrower being unable to pay, the lender will be able to realise the amount
owed to him through selling the land and buildings.
If, however, the loan were obtained using trade receivables as security, the rate would be slightly higher. This is
because there is a risk that the amounts outstanding from trade receivables may never be realised.
Estco is an established company with a good track record and a good business relationship with the bank. Nestco
is a new company, yet to prove itself. The bank may charge a higher interest rate to Nestco since the risk factor
is higher.
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Cost of Capital: 235
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Why are the costs of equity and debt different?

Risk: this is explained in paragraph 1.3 of this Study Guide.

Leverage: This indicates to what extent a company is dependent on borrowed capital. The higher the
gearing, the higher the risk for the company and the equity shareholders. The higher the risk, the higher the
expected return and hence the cost of equity capital.

Taxation: Higher debt will involve higher risks. However, higher interest costs will provide higher tax
benefits and therefore, an opportunity for equity holders to get a higher return. This benefit in corporate tax
assessment reduces the risk premium otherwise demanded by the equity holders of a highly geared or
leveraged firm.
SUMMARY
Explain why the cost of equity capital and retained earnings is not eligible.
3. Calculate and evaluate giving suitable advice on the costs of different financing methods
used by a company both before and after tax.
[Learning Outcome c]
3.1 Cost of debt
Debt capital refers to the capital borrowed by an entity, on which it pays a stipulated amount of interest periodically.
Repayment of the principal amount may be done periodically or at the end of the term. Debt may be in the form of
bank loans or debentures. To measure the explicit cost of debt, we need data regarding the following:


The net cash inflow (the issue of debentures / loan amount less floatation costs) from specific sources
of debt
Net cash outflows in terms of periodic interest and repayment of principal during the tenure of the debt /
at maturity.
Based on the terms of repayment, debt may be irredeemable / perpetual or redeemable. Debt that is repayable
is called redeemable debt. Debt that does not need to be repaid is known as irredeemable debt. Some debts
may be convertible into equity. All these are discussed in the subsequent sections.
1. Cost of irredeemable debt
Generally, the cost of debt capital is the internal rate of return (rate of interest) that equalises the discounted future
cash receipts with the current market price. Irredeemable debt is the debt that contains no stipulated date of
repayment and hence interest payments will be assumed to continue in perpetuity; and the cost of debt is
calculated accordingly.
Since there is no redemption, there is no capital gain, and we only need to consider the interest element. Moreover,
since interest on debt is tax deductible, cost of debt can be either before tax or after tax.
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Before tax cost of irredeemable debt (Kid)
This is calculated with the help of the following formula:
K
id
=
Interest rate payable
Market value of bond (ex interest)
Remember to take the ex-interest price. If the price given is cum interest (i.e. including interest) it should be
converted to ex-interest, by reducing the amount of interest.
An irredeemable bond offers an annual coupon rate of 9.5%. It is currently trading at Tshs 88.50 with the next
coupon due in one year.
Before tax cost of debt
K=
Interest rate payable
Market value of bond (ex interest)
9.5
K=
88.50
= 0.1073
= 10.73%
After tax cost of irredeemable debt
If the corporate tax rate is known and we assume it to be constant, we can derive the after- t a x cost
of irredeemable debt from the before tax cost as:
Kid (after tax) = Kid (Before tax) (1—CT)
Kid (after tax) = after tax cost of debt
Kid (before tax) = before tax cost of debt
CT = Corporate tax rate
The after-tax cost of debt can also be calculated as:
K
id
=
I(1 - t)
Market value of bond (ex interest)
Where ‘I’ is the rate of interest and t is the tax rate.
Continuing the above example
If the corporate tax rate is taken as 35%, then the after-tax cost of irredeemable debt is calculated as
Kid (after tax) = Kid (1—CT)
= 10.73 x (1 - 0.35)
= 6.98%
Cost
Capital:
321
Cost
of of
Capital:
237
© GTG
2. Cost of redeemable debt
As stated earlier , the cost of debt capital is the internal rate of return (rate of interest) that equalises the
discounted future cash receipts with the current market price. In the case of redeemable debt, the future cash
flows will be in the form of interest as well as proceeds at the time of redemption. To start this calculation, it is
preferable to start with the cost of capital as if the debt was irredeemable, and then add the annualised capital
profit that is expected to be earned on redemption.
Method 1:
i
I
i + MV
+ .... +
P0 =
+
n
(1+ k d) (1+ k ) 2
(1 + k d)
d
= i (CPVF
kd,n
) + MV (PVIF
kd,n
)
Where,
P0 = Priceof debenture/ bond i
= interestpaid
k d = cost of debt
MV = redemptionvalueof the debenture/ bond
n
= numberof years
CPVF = Cumulative present value factor
PVIF = Present value interest factor
After tax cost of debt
Interest on debt is a tax-deductible expenditure; therefore, the effective cost of debt changes if we consider the
tax aspect. As in the case of irredeemable debt, if the corporate tax rate is known, and we assume it to be constant,
we can derive the after-tax cost of redeemable debt from the before tax cost as:
Krd (after tax) = Krd (1—CT)
Krd (after tax) = after tax cost of debt
CT = Corporate tax rate
Diagram 2: Cost of redeemable debt
322 Financing Decisions
238 : Financing Decisions
© GTG
After tax cost of debt
Face value
Tshs 100
Coupon rate
9% Redemption
price
Tsh105
Cost (present market price)
Tshs 90
Profit for 15 years
Tshs 15
Annualised profit (Tsh15/15 years)
1
Tax rate
30%
Let us try to calculate the after-tax cost of debt in the following situations:
(i) if the debentures are irredeemable
(ii) if the debentures are redeemable
(i) If the debentures are irredeemable:
Interest payable = 9% of Tsh100
= Tsh9
Interest rate payable = Interest payable x (1 – Tax rate)
= Tshs 9 x (1- .30)
= Tshs 9 x 0.7
= 6.3
Cost of debt =
=
Interest rate payable
Market value of bond (ex interest)
6.3
90
= 0.07
= 7.00%
(ii) If the debentures are redeemable
To obtain a starting figure for the trial and error, we add the annualised profit (1.0) to the cost (as above), if the
debentures were irredeemable; i.e. 7+1.0 = 8.
Year
Particulars
0
1-15
1-15
15
Market value
Interest
Tax saved
Capital repayment
Cash flow
(90)
9
(2.7)
105
Discount
factor
@ 8%
1.000
8.559
8.559
0.315
Present
value
(90.0000)
77.0310
(23.1093)
33.0750
(3.0033)
Discount
factor
@ 7%
1.000
9.108
9.108
0.362
Present
value
(90.0000)
81.9720
(24.5916)
38.0100
5.3904
Since the NPV with 8% is a negative figure of 3.0033, we reduce the trial rate to 7% for the next calculation.
5.3904
x (8 - 7)%
IRR = 7% +
5.3904 - (-3.0033)
= 7% + 0.64
=7.64%
Cost of Capital: 323
Cost of Capital: 239
© GTG
Delay of tax
If it is assumed that there are no tax implications on capital profits and the tax benefit of the interest is available
in the year subsequent to the year of interest payment, the calculations would be as follows:
Year
0
1-15
2-16
15
Cash
flow
Particulars
Market value
Interest
Tax saved
Capital repayment
IRR = 7% +
6.9996
6.9996 - (-1.2915)
(90)
9
(2.7)
105
Discount factor @
8%
1.000
8.559
7.925
0.315
Present
value
(90.0000)
77.0310
(21.3975)
33.0750
(1.2915)
Discount
factor @
7%
1.000
9.108
8.512
0.362
Present
value
(90.0000)
81.9720
(22.9824)
38.0100
6.9996
x (8 - 7)%
=7.84%
Short cut method
The formula for calculating the cost of redeemable debt (approximately) is given as:
Krd =
I(1 − t) = (f + d + pr − pi) / N m
(RV + SV ) / 2
Where,
I = Annual interest
RV = Redeemable value of debentures / debt
SV = Net proceeds from issue of debt / debentures (face value less expenses)
Nm = Term of debt
F = Flotation cost
d = Discount on sale of debentures
pi = Premium on issue of debentures
pr = Premium on redemption of debentures
t = Tax rate
A company issues 10% debentures of Tshs 100 at 10% premium, redeemable at par after 5 years. The
company’s tax rate is 30%. Determine the cost of debt.
Answer
Krd =
I(1 − t) = (f + d + pr − pi) / N m
(RV + SV ) / 2
Krd =
10(1 − 0.3) − (10) / 5
(110 + 100) / 2
= 4.76%
324 Financing Decisions
240: Financing Decisions
© GTG
Prestole issued 9% debentures of Tshs 100 each. The market value of the debentures is Tshs 90, and the tax rate
applicable to Prestole is 35%.
(a) Calculate the before tax cost of capital in the following situations:
(i) If the debentures are irredeemable
(ii) If the debentures are redeemable at a premium of 5%, after 15 years
(b) Calculate the after-tax cost of capital in the following situations:
(i) If the debentures are irredeemable
(ii) If the debentures are redeemable at par, after 15 years
3. Convertible Debt
Convertible debt refers to the arrangement where a part or full amount of a debt is converted into equity at a given
time according to the agreed terms. The basic principle of calculating the cost of debt remains the same. It is the
IRR that equates the present value of future cash flows with the current market price of the security. In the case
of a convertible security, the nature of the cash flows may be slightly different. The value of the cash flow at the
time of conversion will be the value of the shares on conversion.
For this purpose, it is assumed that the conversion will take place. However, if the cost of capital by treating the
debt as non-convertible is higher than if the debt is treated as convertible, it indicates that the IRR (the effective
return) under the non-convertible option is higher for the investor. In such a case, he will opt not to convert the
debt into equity. Therefore, it should be assumed that the debt is not convertible. Sometimes information may
be given to enable students to compare the option of conversion and decide which one is better.
Information may be given about the possible value of shares on conversion, and the cash option. It should be
assumed that the investors, being rational, will select the option that gives them higher returns. The following steps
will enable us to find a solution:
Step 1 Find out the value of the conversion option
Step 2 Compare the conversion option with the redemption (cash payment) option. We assume that the
investors are rational and will choose the option with the higher value.
Step 3 Calculate the IRR of the cash flows for redeemable debentures using the value as determined in Step 2.
For a partly convertible bond, the part which is not convertible is a straight bond component and is valued just like
ordinary debt. For the convertible part, the steps described above are taken to find the cost of capital.
Diagram 3: Convertible debt
CostofofCapital:
Capital:
325
Cost
241
© GTG
A company has in issue 9% debentures, each with a nominal value of Tshs 100. Its market price ex interest is
Tshs 108. The debentures are convertible into 20 ordinary shares after four years. At the time of conversion, the
market value of shares is expected to be Tshs 6.25. The applicable tax rate is 30%. The debenture holders are
also given an option to receive Tshs 115 in cash per debenture.
Assume that tax savings occur in the same year as interest payment. Find out the cost of the convertible
debentures.
Answer
Step 1
Find out the value of the conversion option
Value of conversion option = No. of shares to be received x Expected market value
= 20 x 6.25
= Tshs 125
Step 2
Compare the conversion option with the redemption (cash payment) option. We assume that the investors are
rational and they choose the option with the higher value.
Shareholders have been given the option to receive Tshs 115 in cash. Since the conversion option has a
value of Tshs 125, it is assumed that the shareholders will opt for conversion.
Step 3
Calculate the IRR of the cash flows for redeemable debentures using the value as determined in Step 2.
(Conversion option)
We shall calculate IRR by trial and error method
Year
0
1-4
1-4
4
Details
Current MV
Interest
Tax on interest
(0.3 x 9)
Value of shares at
conversion date
IRR = 8% +
Cash flow
Tshs
Discount
factor @ 12%
Tshs
Present
value
Tshs
Discount
factor @ 8%
Tshs
Present
value
Tshs
(108)
9
1.000
3.037
(108.000)
27.333
1.000
3.312
(108.00)
29.81
(2.7)
3.037
(8.1999)
3.312
(8.9424)
125
0.636
79.500
(9.3669)
0.735
91.875
4.7406
4.7406
x (12 - 8)%
4.7406 - (-9.3669)
= 8% + 1.34%
= 9.34%
A company wants to issue 7% debentures of Tshs 100 nominal value at Tshs 105 each. The debentures are
convertible into 25 ordinary shares after ten years. At the time of conversion, the market value of shares is
expected to be Tshs 5.00. The applicable tax rate is 30%. The debenture holders are to be given an option to
receive Tshs 130 in cash per debenture. Assume that tax savings occur in the same year as interest payment.
Required:
Calculate the cost of the convertible debentures.
326 Financing Decisions
242: Financing Decisions
© GTG
4. Preference shares
Calculating the cost of preference shares is easier than calculating the cost of equity shares.
The calculation is similar to the calculation of the before tax cost of irredeemable debt.
The rate of dividend is normally constant. The tax factor, again, need not be considered since dividends are a
distribution of after-tax profits. However, in some countries, there is tax on dividends, for which no credit is available
to the recipients of dividends. In such a case, tax will be added to the cost of the preference shares. Preference
shares are usually irredeemable.
The cost of irredeemable preference shares is calculated as:
K=
Dividend per share
Market price per share
Corlend Co’s preferred stock is selling for Tshs 160 per share. It pays a dividend of 10% per share on par value
of Tshs 100.
The cost of preferred stock is:
K=
=
Dividend per share
Market price per share
10
x 100
160
= 6.25%
Cost of redeemable preference shares
They are calculated using the IRR method, just like redeemable debt, except that tax adjustment is not needed
since the dividend is not tax deductible.
Abnox Ltd issued 11% preference shares of Tshs 100 each. The shares are redeemable at par after 10 years.
The cost of issue of each share is Tshs 3.00. Determine the cost of the preference shares.
We will take the starting figure of 11% since it is the rate of dividend.
Year
0
1-10
10
Particulars
Market value
Dividend
Capital repayment
Cash
Flow
Tshs
(97)
11
100
Discount
factor @ 11%
1.000
5.889
0.352
Present
Value
Tshs
(97.0000)
64.7790
35.2000
2.9790
Discount
factor @ 12%
1.000
5.650
0.322
Present
value
Tshs
(97.0000)
62.1500
32.2000
(2.6500)
Since the NPV with 11% is a positive figure of 2.979, we will increase the trial rate to 12% for the next
calculation.
2.9790
IRR = 11% +
x (12 - 11)%
2.9790 - (-2.6500)
= 11% + 0.53%
= 11.53%
CostofofCapital:
Capital:
327
Cost
243
© GTG
5. Bank Debt
A distinguishing feature of bank finance as compared to the other forms of finance considered so far is that it does
not have a market value since it is not a tradable security. As a result, the ‘market value’ component found in the
earlier equations is not applicable in this case. The following steps are taken to calculate the cost of bank debt:
Step 1 Calculate the average interest rate.
Interest paid
Average interest rate (AR) =
Average bank borrowings for the year
x 100
Step 2 Since interest on bank debt is tax deductible, adjust the cost for the tax benefit.
Kbd (after tax) = AR (1—CT)
Where,
Kbd (after tax) = after tax cost of bank debt
CT = Corporate tax rate
Alternatively, the cost of debt or any bonds issued by the company may be taken as an approximation.
A company paid Tshs 210 million as interest on bank debt for the year. Balance of the debt was Tsh2000
million for the first nine months and Tshs 1800 million for the last 3 months. The tax rate for the company is
35%.
(2000 x 9) + (1,800 x 3)
12
= Tsh1950million
Average bank borrowings =
Average interest rate (AR) =
Tsh 210 million
Tsh 1,950 million
x 100
= 10.77%
After tax cost of bank debt
K bd (after tax) = AR (1- C T )
= 10.77 x (1- 0.35)
= 7%
3.2 C o s t of equity capital
The cost of equity shares is conceptually more difficult to calculate than the cost of debt. In the case of debt, the
coupon rate at which interest is to be paid on the funds is determined with certainty as the funds are contractual
obligations. Preference shares follow almost the same argument.
However, in the case of equity capital, the return varies from firm to firm as it depends on the management.
Furthermore, equity shareholders rank at the bottom as claimants in the event of liquidation of the firm. Due to
these reasons, it may appear that equity share capital has no cost.
However, non-payment of dividend / inadequate shareholder returns has an adverse effect on market price of
shares of the firm. Therefore, it is essential to provide net present value maximisation to equity shareholders. In
fact, cost of equity is the highest among the various sources of finance.
The cost of equity capital is the minimum rate of return that a firm must earn on the shareholder’s funds to maintain
the current market price.
328 Financing Decisions
244 : Financing Decisions
© GTG
There are two approaches to calculation of cost of equity capital
1. Dividend growth model
2. Capital asset pricing model (CAPM)
1. Dividend growth model
According to the Dividend Model (or the Gordon Growth model), cost of equity capital is calculated in terms of
the required rate of return relating to future dividends to be paid on the shares. The cost of equity capital Ke is
the discount rate that equates the present value of all expected future dividends per share with the current
market value of the shares.
Hence, it is calculated as:
𝑃𝑃0 =
𝐷𝐷1
𝐷𝐷1 (1 + 𝑔𝑔) 𝐷𝐷1 (1 + 𝑔𝑔)2
𝐷𝐷1 (1 + 𝑔𝑔)𝑛𝑛+1
+
+
+.
.
.
+
(1 + 𝑟𝑟𝑒𝑒 ) (1 + 𝑟𝑟𝑒𝑒 )2
(1 + 𝑟𝑟𝑒𝑒 )3
(1 + 𝑟𝑟𝑒𝑒 )𝑛𝑛
Where,
P = Current ex dividend market price of the share
0
D = Declared dividend at time t (first period or year in the future)
1
1
r e = Shareholders required rate of return
g = Expected future growth rate of dividends
n = Number of years for which the share is held
If shares are held for a very long time, ‘n’ tends towards infinity and, as a result, we have a simplified equation:
𝑃𝑃0 =
𝐷𝐷0 (1 + 𝑔𝑔)
𝐷𝐷1
=
(𝑟𝑟𝑒𝑒 − 𝑔𝑔)
(𝑟𝑟𝑒𝑒 − 𝑔𝑔)
This formula can be rearranged to obtain the cost of equity under the dividend growth model.
(a) Calculation of cost of equity using the dividend growth model
P0 =
D0 (1+g)
(re -g)
By rearranging this equation, we get
(re -g)=
re =
D0 (1+g)
P0
D0 (1+g)
+g
P0
r = shareholders required rate of return = cost of equity = Ke
Therefore,
D0 (1+g)
Ke =
+g
P0
Flotation costs are the costs incurred by the company for issuing new securities and significantly affect the cost
of equity. It includes the fees paid to the underwriters and expenses of the issuer e.g. printing costs, legal fees
and commission paid to the brokers.
© GTG
Cost of Capital: 329
Cost of Capital: 245
(a) Determination of dividend growth rate
The growth rate of a company is a function of the capital invested and the post tax return obtained by the
company.
Growth = capital invested x post tax rate of return
Let us try to calculate the growth rate of a company when
(i) Post tax rate of return is 10% and capital invested is Tshs 100m.
Growth = Capital invested x Post tax rate of return
= Tshs 100m x 10%
= Tshs 10m
(ii) Rate of return is 10% and capital invested in Tshs 200m.
Growth = Tshs 200m x 10%
= Tshs 20m
(iii) Rate of return is 15% and capital invested is Tshs 200m.
Growth = Tshs 200m x 15%
= Tshs 30m
From the above example we can conclude that the net earnings of a company depend upon the capital invested
and the post tax rate of return obtained by the company. Any increase in either of the capital invested or post
tax rate of return will increase the earnings of the company. Dividend is paid out of net earnings of the company.
Hence, we can assume that the dividend growth depends upon the post tax return on equity and the proportion
of profits reinvested i.e. retained earnings in the company.
Higher the retention ratio, higher will be the growth rate.
g = bre
Where,
g = growth rate of dividends
b = the proportion of profits re-invested
re = post tax return on equity
The rate of post-tax return on the equity of a company is 12%.
We can calculate the expected rate of growth in dividends using the ‘retention ratio’ or the proportion of profits
reinvested with
80%
50%
For the retention ratio of 80%
g = bre
= 0.12 x 0.80
= 0.096
= 9.6%
For the retention ratio of 50%
g = bre
= 0.12 x 0.50
= 0.06
= 6.0%
= 9.6%
For the retention ratio of 50%
g = bre
= 0.12 x 0.50
330
Financing Decisions
= 0.06
= 6.0%
246 : Financing Decisions
Malco provides the following information
© GTG
Tshs
Current ex dividend market price of the share 4652
Dividend paid currently
400
Expected future growth rate of dividends
3.50%
Calculate the cost of equity capital
Calculation of the cost of equity capital
Ke =
Ke =
Ke =
Ke =
D0 (1+g)
+g
P0
4(1+3.50%)
+3.50%
46.52
(400+1.035)
+0.035
4652
414
+0.035
4652
= 0.12399398
= 12.40%
The dividend per share of ABC Ltd is expected to be Tshs 200 per share next year and is expected to grow at
6% per year perpetually. Determine the cost of equity capital, assuming the market price is Tshs 2500.
This is a case of constant growth of expected dividends. Therefore,
Ke =
D0 (1+g)
+g
P0
200(1+6.0%)
+6.0%
2500
200(1.06)
+0.06
Ke =
2500
Ke =
Ke =
212
+0.06
2500
= 14.68%
Cost of Capital: 331
Cost of Capital: 247
© GTG
(b) Assumptions and weaknesses of dividend growth models
(i) The model assumes that a company pays dividend every year.
(ii) The market price depends on the expected dividends.
(iii) The model assumes that dividends will grow at a constant rate in perpetuity. Normally, a trend in past dividends
is used to estimate future dividends. However, there is no assurance that the companies will not skip dividends
or dividends will grow at the same rate in the future.
(iv) Other influences on the share prices are ignored e.g. inflation, political developments, and attempt to take
over the company.
(v) Certain companies e.g. companies in start up stage do not pay dividends as they prefer to reinvest their
profits. Hence, it is difficult to value new companies using this model.
(vi) It is assumed that D0 (current dividend) is greater than zero.
(vii) The growth model fails to consider capital gains.
(viii) However, it is contended that, even where shares are sold, the sale price will represent the present value
as on the date of sale of expected future dividends. Therefore, this model does not exclude capital gains.
(ix) Investors behave rationally
The objective of the investors is to maximise their wealth. The investors try to do so by following a long-term
investment strategy.
 not under or over reacting to various events e.g. rise in inflation, fall in fiscal deficit, death of prime
minister etc.
 not clinging to a security because it was a strong performer in the past.
In has been observed that most of the investors use a short-term investment strategy, under or over reacts
of various events and stay invested in a security because it was a strong performer in the past.
(x) Other assumptions, which may not hold true in practice are
Expected future growth rates of dividends can be estimated.
Investors’ expectations are predictable and they can be modelled into a discounted cash flow.
The company’s earnings will increase continuously to maintain dividend growth in the future.
SUMMARY
From the following details, calculate the cost of equity capital using the dividend growth model.
Dividend paid currently ( Tshs )
The company expects future growth rate of dividends to be
Current ex dividend market price of the share ( Tshs )
600
5.5%
4800
332 ©Financing
Decisions
GTG
248 : Financing
Decisions
Cost of Capital:
© GTG249
2. Portfolio Theory
We have seen how the dividend growth model can be used to calculate the cost of equity. But it has some
Thelimitations.
above limitations
necessitated the need for alternate models to calculate the cost of equity. Harry Markowitz
These include:
came up with the Portfolio Theory as an alternate model. The Portfolio Theory shows how unsystematic risk
The model
assumesbythat
a company
paysportfolio.
dividend every year. So, if a company skips dividend in
canbe reduced
or eliminated
building
a diversified
the current year then the solution to the equation will be zero.
©
GTGThe
model financial
ignores the
effect of inflation
and political developments on the share price. Cost of Capital: 249
(a) 
Risks
to which
instruments
are exposed

Start-up
companies
don’t
pay
dividends
in the initial years as they reinvest earnings forCost
future
growth.249
So,
© GTG
of Capital:
To
howbe
Portfolio
Theory
works,
we firsttoneed
understand the types of risks that financial instruments
it willTheory
not
possible
to apply
this model
suchtocompanies.
2. understand
Portfolio
are exposed to.
2. Portfolio Theory
The above limitations necessitated the need for alternate models to calculate the cost of equity. Harry Markowitz
Types
of with
risksthe Portfolio Theory as an alternate model. The Portfolio Theory shows how unsystematic risk
came up
The above limitations necessitated the need for alternate models to calculate the cost of equity. Harry Markowitz
can
be
reduced
or Portfolio
eliminatedTheory
by building
a diversified
portfolio.
came up with the
as an
alternate model.
The Portfolio Theory shows how unsystematic risk
While investing in a financial instrument, one needs to understand that there is a direct relationship between risk
can be reduced or eliminated by building a diversified portfolio.
and
returns.
Generally,
the higher
the risk involved
in investing in a financial instrument, the higher is the return
(a) Risks
to which
financial
instruments
are exposed
expected by the investor. An individual need to take into account two types of risks
(a) Risks to which financial instruments are exposed
To understand how Portfolio Theory works, we first need to understand the types of risks that financial instruments

systematic
risk; and
are
exposed
to.how Portfolio
To understand
Theory works, we first need to understand the types of risks that financial instruments

unsystematic risk.
are exposed to.
Types of risks
© GTG
Cost of Capital: 249
Total Risk = Systematic Risk + Unsystematic Risk
Types of risks
Portfolio Theory
While investing in a 2.financial
instrument, one needs to understand that there is a direct relationship between risk
The above
necessitated
the need forin
alternate
models in
to calculate
the costinstrument,
of equity. Harry Markowitz
andSystematic
returns. Generally,
the limitations
higher the
risk involved
investing
a financial
the higher is the return
(i)
risk
While investing in a came
financial
one as
needs
to understand
thatTheory
thereshows
is a how
direct
relationship
between risk
up withinstrument,
the Portfolio Theory
an alternate
model. The Portfolio
unsystematic
risk
expected
by
the
investor.
An
individual
need
to
take
into
account
two
types
of
risks
can
be
reduced
or
eliminated
by
building
a
diversified
portfolio.
and returns. Generally, the higher the risk involved in investing in a financial instrument, the higher is the return
expected by the investor.
individual
to take
into account two types of risks
(a) RisksAn
to which
financialneed
instruments
are exposed

systematic
risk; and

unsystematic
risk.
To understand
how Portfolio Theory works, we first need to understand the types of risks that financial instruments

risk;
and
Systematicsystematic
risk comprises
risk
are exposed
to. factors that are common to all securities within an asset class or among different
asset classes.
unsystematic risk.

Total Risk = Systematic
Risk + Unsystematic Risk
Types of risks
While investing
in a +
financial
instrument, one Risk
needs to understand that there is a direct relationship between risk
Total Risk = Systematic
Risk
Unsystematic
(i) Systematic riskand returns. Generally, the higher the risk involved in investing in a financial instrument, the higher is the return
expected by the investor. An individual need to take into account two types of risks
It
known as market
(i)isSystematic
risk risk and cannot be reduced or eliminated. It is also known as non-diversifiable risk as no

systematic
risk;
amount of diversification
can
reduce
orand
eliminate this risk.

unsystematic risk.
Total Risk = Systematic Risk + Unsystematic Risk
Systematic risk comprises
risk factors that are common to all securities within an asset class or among different
asset classes.
(i) Systematic risk
Systematic risk comprises
risk factors that are common to all securities within an asset class or among different
Inflation,
war, interest rates, recession, currency fluctuations, poor government policy actions etc. are common
asset
classes.
to all securities. They affect the entire market. It is to be noted that although the above factors affect the whole
Systematic
risk comprises
riskthan
factorsothers.
that are common to all securities within an asset class or among different
market, some sectors
get affected
more
asset
classes.
It is known as market
risk
and cannot be reduced or eliminated. It is also known as non-diversifiable risk as no
amount
of diversification
can
reduce
or be
eliminate
It is known
as market risk
and
cannot
reducedthis
or risk.
eliminated. It is also known as non-diversifiable risk as no
amount of diversification
canasreduce
orand
eliminate
this risk.
It is known
market risk
cannot be reduced
or eliminated. It is also known as non-diversifiable risk as no
Diagram 4: Systematic
amountrisk
of diversification can reduce or eliminate this risk.
Inflation, war, interest rates, recession, currency fluctuations, poor government policy actions etc. are common
Inflation,
war,the
interest
rates,market.
recession, currency
government
policythe
actions
etc. are
common affect the whole
to all securities.
They
affect
entire
It is
tofluctuations,
be notedpoor
that
although
above
factors
Inflation,
war, interest
recession,
currency
fluctuations,
government
policy
actions
etc. are common
to allrates,
securities.
They affect the
entire market.
It is to be notedpoor
that although
the above factors
affect
the whole
market, some sectors
get some
affected
than
others.
market,
sectorsmore
get affected
more
than others.
to all securities. They
affect the
entire
market.
It is to be noted that although the above factors affect the whole
market, some sectors get affected more than others.
Diagram 4: Systematic risk
Diagram 4: Systematic risk
Diagram 4: Systematic risk
Systematic risk remains
the risk
same
even
aftereven
constructing
a amarket
portfolio
containing
different
securities that are
Systematic
remains
the same
after constructing
market portfolio
containing
different securities
that are
not other.
correlated to each other.
not correlated to each
Cost of Capital:
© GTG 333
250 : Financing Decisions
(ii) Unsystematic risk
Unsystematic risk comprises risk factors that are specific to an individual security or securities within an asset
class or among different asset classes.
It is also known as specific risk, unique risk or diversifiable risk, and can be reduced or eliminated by diversification
into securities that don’t have direct correlation. Methods of reducing this type of risk are based on the old
saying - ‘Don’t put all your eggs in one basket’!
Poor company management, strikes, too much of debt, wrong acquisitions, increase in input costs, supply
disruptions, lawsuits, industrial accidents, frauds by employees or management etc. are all examples of risks
that individual companies are vulnerable to. If an investor has Tshs 100 million, he can overcome unsystematic
risk by spreading his investment among 10 different companies rather than investing the entire Tshs 100million
in one company.
Diagram 5: Unsystematic risk
As can be seen from the above diagram, unsystematic risk can be reduced or eliminated by building a
diversified portfolio of securities:
within the same assets of a class that are not correlated to each other; or
within assets of different classes that are not correlated to each other.
1
2
3
Systematic risk
Common to all
It is the extent of variability in the security’s
return on account of overall market factors
Cannot be reduced or eliminated through
diversification
Unsystematic risk
Specific to individual securities
It is the extent of variability in the security’s return
on account of factors unique to it
Can be reduced or eliminated through
diversification
As we have seen above, while investing, an individual has to factor in systematic and unsystematic risks. Financial
models help to measure the risk and accordingly arrive at a risk premium (i.e. expected return) that an
individual can expect to earn for bearing the risk. Investors have the option of investing their money either in
risk-free assets or in risky assets. Risk free assets (e.g. government securities) are those that pay a fixed return,
and the chances of losing money are extremely low or nil.
The risk premium is the extra return the investors demand for investing in risky assets rather than investing in riskfree assets. The higher the risk involved in investing in an asset, the higher is the risk premium demanded by
investors.
334 Financing Decisions
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Cost of Capital: 251
The biggest risk for an investor is the deviation from the expected return from the security. Before the Portfolio
Theory was introduced, investors looked at evaluating the risk-reward characteristics of individual securities before
considering them for inclusion in their investment portfolio. The Portfolio Theory was developed by Harry
Markowitz and published in the Journal of Finance in 1952.
The Portfolio Theory is about portfolio diversification by choosing the right combination of securities (not
perfectly correlated) that reduces or eliminates the overall unsystematic risk of the portfolio as compared to the
risk involved in an individual security.
Markowitz’s Portfolio Theory focuses on selecting multiple securities (having no direct co-relation) and building a
portfolio based on the overall risk-reward characteristics of the portfolio. While building a securities portfolio, an
investor should look beyond the risk and return of an individual security. Thus, a well-diversified portfolio can
help reduce or eliminate unsystematic risk from the portfolio.
The Portfolio Theory aims to identify and measure the acceptable level of risk tolerance and then build a riskefficient portfolio with the maximum expected return for that level of risk. It also helps to quantify the correlation
between securities. When a portfolio of securities not correlated to each other is built, it reduces the overall risk
of the portfolio.
3.3 Relation between Portfolio Theory and Capital Asset Pricing Model (CAPM)
CAPM is explained in the next para
Markowitz’s Portfolio Theory helped reduce or eliminate unsystematic risk from a portfolio through diversification;
however, the portfolio still remained exposed to systematic risk. The systematic risk cannot be reduced or
eliminated as it is common to the entire market. So Sharpe built on Markowitz’s Portfolio Theory and devised a
way of measuring the systematic risk. This measure of systematic risk is known as ‘beta’.
If an investor has Tshs 100,000, he can invest it either in risk free securities or in risky securities. If he chooses
to invest in risky securities, he will be exposed to both unsystematic risks and systematic risks. He can
overcome unsystematic risks using the Portfolio Theory by building a diversified portfolio of securities that are
not perfectly co-related to each other.
But this still leaves the portfolio exposed to systematic risks. It is here that Sharpe’s CAPM helps the investor
measure the systematic risks that he is exposed to, using beta. Once the investor knows the measure of systematic
risks that he is exposed to, they can arrive at the return on investment that can be expected by investing in those
securities.
3. Capital Asset Pricing Model (CAPM)
Sharpe introduced the Capital Asset Pricing Model (CAPM) for risky securities, comprising two components


Risk free rate of return
Beta (systematic risk)
Beta measures the volatility of the security. It describes the sensitivity of a particular stock’s return on the
market portfolio. Beta is a measure of the systematic risk. The higher the risk involved (beta) in investing in a
security, the higher is the return expected by the investor. Using the beta and the risk-free return, the CAPM helps
to determine the return from the security that an investor can expect if they choose to invest in the security.
The CAPM relates an asset’s risk premium (expected return) to its beta.
Thus, for a given risk, CAPM helps the investor to calculate the return they should expect from the security for
taking exposure to the risk. In other words, for a given expected return from a security, CAPM helps the investor
to calculate the risk that they will be exposed to by investing in that security. Accordingly, based on their risk
appetite, the investor can decide whether to go ahead with the investment or not.
The portfolio theory, developed by Harry Markowitz, was developed further by William F. Sharpe, a 26-year-old
researcher at the RAND Corporation. He produced a market equilibrium theory of asset prices under conditions
of risk, which he presented in a research paper. In 1990, the Nobel Prize for economics was awarded to Sharpe
and Markowitz for their contribution to the field. Sharpe’s model later came to be known as the capital asset
pricing model (CAPM).
Cost of Capital: 335
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252 : Financing Decisions
Different projects carry different level of risk. However, the dividend discount model does not differentiate between
the various types of risk. The alternative of dividend discount model for calculating the cost of equity is the capital
asset pricing model (CAPM). CAPM allows an investor to differentiate among various types of risk. It allows an
investor to assign the level of risk to an investment on the basis of the types of risk that is faced by the
investment.
(a) Assumptions of the Capital Asset Pricing Model
CAPM is only valid subject to a set of assumptions. The basic assumptions of CAPM are related to the
efficiency of the capital market and investor preferences.
(i) All investors have homogenous expectations regarding the expected returns, variances and correlation of
returns among all securities.
(ii) Investors are allowed to borrow and lend funds at the risk-free rate of return. This is the assumption for the
portfolio theory, and CAPM has been developed from the portfolio theory. Risk-free return offers the minimum
level of return available to an investor. The investors may borrow or lend unlimited amounts of the risk free
asset at a constant, risk-free rate.
(iii) Investors hold diversified portfolios. Diversified portfolios allow an investor to eliminate unsystematic risk.
Hence, the investor requires return only for the systematic risk of his portfolio.
(iv) All investors have the same information about the securities.
(v) There are no restrictions on investments.
(vi) There are no taxes or transaction costs.
(vii) No single investor can affect the market price significantly. The implication of the above explained investor
preferences is that all investors prefer security that provides the highest return for a given level of risk or the
lowest risk for a given level of return.
(viii) The model is a one period model. A return for three months cannot be compared with returns for five years.
Hence, it is assumed that the investments occur over a single standardised period. It allows comparison
among various securities on the basis of their returns. Usually, a period of one year is used.
(ix) Perfect capital market: All the securities are correctly valued and their returns can be plotted on the security
market line (SML). There is perfect competition in capital markets. There are no market imperfections such as
taxes, regulations, or restrictions on short selling. There are a large number of buyers and sellers. A
single participant cannot influence the market. All investors are risk adverse individuals and have the same
information at the same time. There is no cost associated with the information i.e. it is freely available. As a
result, investors have identical expectations (beliefs) about asset returns.
(x) The assets are perfectly divisible. There are a definite number of assets and their quantities are fixed within
the given period. These assets are perfectly divisible. Similarly, they are priced in a perfectly competitive
market. This implies that, for e.g., human capital does not exist. The returns of all assets are distributed through
normal distribution channels.
(xi) Many of the assumptions mentioned above may not be valid or fulfilled. Nevertheless, CAPM remains one
of the most widely-used investment models for determining risk and return.
(b) Capital Asset Pricing Model (CAPM) and its components
The following equation lays down the relationship explained in the model
This formula is given in the exam.
()
(
E r i =R f + i E(r m ) - R
f
)
Where,
E(rj) = The rate of return of security j, as projected by the model
βj = The beta coefficient of security j
Rf = The minimum risk-free rate of return
E(rm) = The return of the market
336 ©Financing
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GTG
Cost of Capital: 253
The components of the CAPM
From the above equation, the main components of the model can be identified as the
(i) beta coefficient of the security
(ii) minimum risk-free rate of return
(iii) premium expected for the risk the security. It is the difference between the market return and the risk free
return.
These are discussed in turn.
Market return of a security consists of the dividend yield and the capital gain received from the security.
Dividend yield is the amount paid as dividend by the company relative to its share price. Capital gain is the increase
in the price of the security.
(i) Beta coefficient of the security: measurement of risk (denoted by βj in the CAPM formula)
The beta of a security is an index indicating how the returns of the security change in response to a change in
the stock exchange or market. The beta of the market is taken as a benchmark and is always given the value of
1.
The beta factor can be found by examining the securities historical return relative to the return of the market
portfolio.
𝛽𝛽𝑖𝑖 =
𝐶𝐶ov𝑖𝑖,𝑚𝑚 𝜎𝜎𝑖𝑖 × 𝜎𝜎𝑚𝑚 × 𝜌𝜌𝑖𝑖,𝑚𝑚 𝜎𝜎𝑖𝑖 × 𝜌𝜌𝑖𝑖,𝑚𝑚
=
=
(𝜎𝜎𝑚𝑚 )2
(𝜎𝜎𝑚𝑚 )2
𝜎𝜎𝑚𝑚
Where,
𝛽𝛽 = Beta of the security i
Cov i,m = Covariance of returns of the security i and the market
𝜎𝜎𝑖𝑖 = Standard deviation
of
return of security i
𝜎𝜎𝑚𝑚 = Standard deviation
of
𝜌𝜌𝑖𝑖,𝑚𝑚 = Coefficicient of
return of the market
corelation between the security i and the market
Beta can also be calculated by plotting the returns of a security against the returns of the market, drawing a line
and then finding out the slope of the line. This is shown in the diagram below:
Diagram 6: Calculation of Beta
Security
return
(%)
Slope of
characteristic line
(A/B) gives the beta
of the security
A
B
Market return (%)
254 : Financing Decisions
Cost of Capital: 337
© GTG
If the beta of a security is equal to 0.7 this indicates that, when the market return changes by 10%, return on this
security is likely to change by 7% (0.7 x 10%).
Implication of beta value
Beta value
More than 1
Less than 1
Equal to 1
Implication
Security is known as an aggressive security. The share price is more volatile than the value
of the index. Due to this, the return offered by aggressive securities is more than that offered
by the index during the bull period and the loss is greater than that sustained by the index in
the bear period.
Security is known as defensive security. The share price is less volatile than the value of the
index. Due to this the security offers less gain (as compared to the index) during the bull
period and vice-versa for the bear period.
Security is known as neutral security and follows the returns offered by the index.
Defensive securities will be attractive to investors in a period when the stock exchange is declining. On the other
hand, aggressive securities will be attractive to investors in a period when the stock exchange is rising.
Types of beta




The equity beta risk reflects the risk borne by the shareholders of the company.
The asset beta reflects the business risk for a company.
The debt beta reflects the financial risk of a company.
In case the company has no debt, the asset beta reflects the risk borne by the shareholders of the
company. The asset beta is affected by changes in the company’s business operations and its business
risk.
(ii) Risk-free rate of return (denoted by Rf in the CAPM formula)
It is the rate of return demanded by investors to compensate them for foregoing investment in a risk-free
security (the return offered by a risk-free security). This rate compensates the investor for inflation. Hence, it
reflects the minimum rate of return required by the investors.
In practical terms, no investments are totally risk-free. However, short-term bonds issued by the government of
a politically and economically stable country are treated as being risk-free for this purpose.
(iii) Market rate of return (denoted by Rm in the CAPM formula)
Market return consists of two components. The first component is the capital gains for the chosen period; the
second component is the dividend yield over the same period. The sum of these two components is the market
rate of return.
Suitable stock exchange data is used for this purpose. The difference between the stock exchange indexes, for
example FTSE 100, on the two dates gives us the amount of capital gains. Dividend yield for the same index for
the same period gives us the dividend yield of the market. The return of the market is calculated as:
𝑅𝑅𝑚𝑚 =
𝑃𝑃1 − 𝑃𝑃0
𝑃𝑃0
Where,
RM = Return of market.
P1 = The stock exchange index at the end of the period.
P0 = The stock exchange index at the beginning of the period.
Div = Average dividend yield of the stock exchange index for the period.
Stock exchange prices are, at times, subject to abnormal variations. Therefore, it is desirable to use a timesmoothed average for this purpose. For example, if a monthly index is used, it is desirable to take an average
of, say, 3 years.
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Cost of Capital: 255
The last portion of the CAPM equation, i.e. (Rm – Rf) is calculated by deducting the risk-free rate of return from the
return of the market. In other words, it is the market risk or equity risk premium.
Diagram 7: Securities Market Line (SML)
A security market line (SML) represents a line on which a security is expected to lie. If the systematic risk is higher,
the required rate of return is also higher.
Securities that are correctly priced will remain on the fitted SML. Under-priced shares (P in this diagram) will lie
above the SML, correctly valued shares (S in this diagram) will lie in the SML and over-priced shares (Q in this
diagram) will fall below the SML
Investors will buy the under-priced shares. This will cause the price to go up and the rate of return to decrease.
This will bring it down on to the SML. Investors will then sell the over-priced shares, causing a fall in the price
and a rise in the rate of return. These movements are expected to be quick in capital markets which are
assumed to be perfect.
(c) Calculation of cost of capital or required rate of return using the Capital Asset Pricing Model
(CAPM)
The cost of capital of a security is equal to the rate of return demanded by the shareholders from that security.
The cost of capital of Zodiac can be calculated on the basis of the following data:
The beta coefficient of Zodiac’s ordinary shares
The rate of return on government securities, which are treated as risk-free
The stock exchange index at 31 December 20X9
The stock exchange index at 31 December 20X8:
Average dividend yield of the stock exchange index for 20X9:
1.25
5%
2000
1800
6%
Calculate the cost of the ordinary share capital for Zodiac.
First, we have to calculate return of market (RM )
𝑅𝑅𝑚𝑚 =
𝑅𝑅𝑚𝑚 =
𝑃𝑃1 − 𝑃𝑃0
𝑃𝑃0
2,000 − 1,800
1,800
= 0.11 + 0.06
= 17.11%
Continued on the next page
Cost of Capital:
© GTG 339
256 : Financing Decisions
Now, we can calculate the rate of return of ordinary shares of Zodiac (Rj ), as projected by the model
E(rj) = Rf + βj (E(rm) – Rf)
= 0.05 + 1.25 (0.17 - 0.05)
= 0.05 + 0.15
= 0.20
= 20%
The cost of ordinary share capital of Zodiac, therefore, is 20%
SUMMARY
For Metasphore Co, the risk measurement service quoted a beta of 0.95 during December 20X9. Around the
same time, the yield on the three- m o n t h treasury bills was 5%. Market risk premium is 4%. Calculate
the required return using CAPM.
(d) Advantages of the CAPM
(i) CAPM is easy to understand and use. The calculations are not complicated.
(ii) The model is founded on reasonable and standard behaviour patterns. It is a fact that with higher risk, investors
expect a higher return.
(iii) The implied ‘beta’ estimates normally lie fairly close to the market rate. Therefore, the market rate is given
due importance as a benchmark.
(iv) CAPM links the required return directly to the risk. When a business is looking to add to its activities and the
new activity has a different risk than the business’ existing activities, the CAPM concept is useful. The equity
cost of future activities will be different from the equity cost of present activities.
(v) CAPM is applicable to companies whether they pay dividends or not. This is not the case with the dividend
growth model.
(e) Disadvantages of the CAPM
(i) The major drawback is that the beta is based on past performance. There is no certainty that the future will be
like the past. The risk profile of the firm may change.
(ii) If a company’s shares are not traded publicly, historical data will not be available for the values needed in
the model.
(iii) Estimating the model’s inputs (the risk-free rate, beta, and the market return) is a difficult task. It may be difficult
to estimate accurately. It is said that these variables are unobservable.
(iv) The CAPM assumes than investors hold diversified portfolios and, therefore, the only relevant risk is market
risk. The investors may not be fully diversified. In such a situation, the CAPM may understate the required
return and the cost of equity.
(v) The model assumes that returns are normally distributed random variables. However, it has been found that
returns in equity and other markets are not normally distributed. Instead, there are large swings (sometimes
3 to 6 standard deviations from the mean). The CAPM does not explain the variations in returns.
340 Financing Decisions
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Cost of Capital: 257
(vi) The above limitation leads to another one. The variance of returns is taken as a normal measurement of
risk. However, this can be true only for normally distributed returns.
(vii) The homogeneous expectation assumption states that everyone has the same information at the same
time. As a result, investors have identical expectations (beliefs) about asset returns. This assumption is not
realised in practice.
(viii) A perfect market is assumed to exist. However, there are several imperfections e.g. taxes, regulations,
restrictions on short selling, etc.
(ix) The following assumptions about market portfolio may not exist in practice:



A market portfolio includes all assets in all markets. There is no preference between markets and assets
for an investor. Investors select assets only on the basis of the risk-return relationship.
All assets are infinitely divisible.
The market portfolio should theoretically include all types of assets. However, it is difficult to collect
data on them. The stock exchange index is used as a proxy. Richard Roll argued, in 1977, that this
substitution is not innocuous and therefore, CAPM may not be empirically testable.
SUMMARY
SUMMARY
Cost of Capital: 341
Cost of Capital: 257
© GTG
3.4 Cost of retained Earnings
It may appear that the retained earnings of the company do not involve any cost. This is because there is no formal
arrangement with the shareholders for using equity funds. However, it is clear that since retained earnings
are actually shareholders’ funds which are not distributed, they involve an implicit cost. This cost is equal to the
opportunity cost in terms of the dividend foregone by the equity shareholders. Therefore, the cost of retained
earnings (k r) evaluated from the perspective of external yield is equal to ke.. The cost of retained earnings
would be lower than the cost of equity due to flotation cost and dividend payment tax.
4. Compute the company’s overall cost of capital and that of a project and identify the
situations in which each is used as a valuation and decision tool.
[Learning Outcome d]
4.1 Calculation of weighted average cost of capital
We have covered the methods of estimating the cost of the different sources of finance, namely debt, equity,
preference shares and retained earnings. Let’s now measure the overall cost of capital. The overall cost of capital
comprises the cost of the various components of financing.
Weighted average cost of capital (WACC) is an average representing the expected return on all of a
company’s sources of capital.
Each source of capital, such as stocks, bonds and other debt is weighted in the calculation according to its
prominence in the company’s capital structure.
The computation of the overall cost of capital basically involves:
1. Assigning weights to the specific costs
2. Multiplying the cost of each source of finance by the appropriate weights
3. Dividing the total weighted cost by the total weights
The weighted average cost of capital (WACC) calculation for a company using ordinary shares, preference
shares and both redeemable and irredeemable bonds is represented by:
𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊 =
Where,
𝐾𝐾𝑝𝑝 × 𝑉𝑉𝑝𝑝
𝐾𝐾𝑑𝑑 (1 − 𝑇𝑇) × 𝑉𝑉𝑑𝑑
𝐾𝐾𝑟𝑟𝑟𝑟 (1 − 𝑇𝑇) × 𝑉𝑉𝑟𝑟𝑟𝑟
𝐾𝐾𝑒𝑒 × 𝑉𝑉𝑒𝑒
+
+
+
𝑉𝑉𝑒𝑒 + 𝑉𝑉𝑝𝑝 + 𝑉𝑉𝑑𝑑 + 𝑉𝑉𝑟𝑟𝑟𝑟 𝑉𝑉𝑒𝑒 + 𝑉𝑉𝑝𝑝 + 𝑉𝑉𝑑𝑑 + 𝑉𝑉𝑟𝑟𝑟𝑟 𝑉𝑉𝑒𝑒 + 𝑉𝑉𝑝𝑝 + 𝑉𝑉𝑑𝑑 + 𝑉𝑉𝑟𝑟𝑟𝑟 𝑉𝑉𝑒𝑒 + 𝑉𝑉𝑝𝑝 + 𝑉𝑉𝑑𝑑 + 𝑉𝑉𝑟𝑟𝑟𝑟
Ke = Cost of equity
Kp = Cost of preference share
Kd = Cost of irredeemable bonds
Krd = Cost of redeemable bonds
Ve = Value of equity share
Vp = Value of preference share
Vd = Value of irredeemable bonds
Vrd = Value of redeemable bonds
T = Corporate taxation
342 Financing Decisions
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© GTG
4.2 Identify the situations where each can be used as an investment and decision tool
The weighted average cost of capital (WACC) represents the overall compensation for the average risk of projects
which it may undertake in the near future. Therefore, if a firm is considering an investment project of
‘average risk’ and maintaining its target debt-equity mix, it can use WACC as the discount rate to determine the
project’s NPV.
It should be noted that the after-tax cash flows of the project should be estimated without any adjustment for
interest charges and repayment of principal, since WACC, as the discount rate, incorporates the tax shield impact
of debt.
In practice, firms undertake projects which have risk considerably different from the firm’s average risk. Hence,
the use of the firm’s WACC to evaluate individual projects with different risk characteristics is inappropriate. A
common practice in choosing a discount rate for a project is to apply a WACC that applies to the entire firm, but
a higher discount rate may be more appropriate when a project’s risk is higher than the risk of the firm as a whole.
Nevertheless, the WACC approach has some attractions


It relies predominantly on market data and therefore has less room for manipulation by managers.
It can be used as a benchmark for adjustment to reflect differentials between the project at hand
and‘average ’ co rpo rate ris k.
Firms, i n pr actice, may de velop gu idelines for r oughly i ncor porating th e pro ject risk differences. One approach
is to divide projects into broad risk classes and use different discount rates based on the decision maker’s
experience. For example, projects may be classified as:
1. Low risk projects: these include replacement and modernisation projects. The decision maker can estimate
the benefits (increase in revenue and/or reduction in costs) of replacement / modernisation projects with
relative accuracy.
2. Medium risk projects: these include investments for expansion of the current business. Although revenue
and cost estimates are relatively difficult to make, the decision maker is familiar with the nature of business.
Therefore, using his experience and judgement, he will have a reasonable idea of the variability of cash flows.
3. High risk projects: these projects include diversification into new business. As the decision maker has little
or no idea of the new business, he will have great difficulty in estimating cash flows. Cash flows could show
high variability. Within each category, projects could be further sub-divided.
SUMMARY
SUMMARY
Cost of Capital: 343
Cost of Capital: 259
© GTG
Diagram 8: Risk adjusted discounted rate (CAPM) and WACC
The diagram indicates that various projects’ have different risks, and the higher the project’s risk, the higher the
risk-adjusted discounted rate. Replacement and modernisation projects are discounted at a lower rate than
expansion or diversification projects since their risk is the lowest.
At the other extreme, diversification projects involve high risk. Therefore, their cash flows are discounted at a high
discount rate. It may be noted that WACC reflects average risk, and therefore, it is represented as a horizontal
line. It fails to distinguish between projects with different risk characteristics, and can be misleading when
deciding which projects to undertake. Due to this CAPM is used for calculating a project-specific discount rate.
Internal rates of return for projects X and Y are IRRx and IRRy. From the above diagram, it will be clear that if the
WACC criterion is used, Project X will be rejected (because IRRx < WACC) and Project Y will be accepted
(because IRRy > WACC). However, if risk-adjusted discount rates are used, then Project X should be accepted
whereas Project Y should be rejected.
SUMMARY
344 Financing Decisions
260 : Financing Decisions
© GTG
5. Discuss the roles of market and book values in computing cost of capital.
[Learning Outcome e]
The decision to be made in the selection of appropriate weights for calculation of WACC is depicted below:
Diagram 9: Selection of weights for calculation of WACC
1. Historical Weights
Historical weights essentially mean using weights that are the same as the weights of the various sources of the
existing capital structure of the firm. Example: if in the current capital structure, the debt equity mix is 2:1, the
same will be deployed for calculation of WACC using historical weights. The use of historical weights is based
on the assumption that the firm’s existing capital structure is ideal and should be maintained in future.
However, the above assumption is not valid in all situations since:


There could be constraints on the availability of the funds from these sources. For example, retained
earnings might fall short of its required share in financing new projects.
Raising funds from capital market depends on numerous factors like requirement of investors, economic
situation etc.
An important merit of this method is that it takes into account a long-term view. Although it may be true that the
firm actually raises funds from one or two sources instead of all the available sources, the use of historical weights
is more in line with the firm’s long-term goal of enhancing shareholder value.
As mentioned earlier, historical weights can be either book value or market value weights. Both of these have
distinct advantages:
(a) Book value weights
(i) The benefit of using book value weights is that they are readily available in the published accounts of the
company.
(ii) Analysis of capital structure in terms of debt equity ratio is based on book value.
(iii) Capital structure targets are fixed based on book value rather than market value.
(b) Market value weights
(iv) They reflect the actual amount to be received from their sale.
(v) The costs of the different sources of finance which comprise the capital structure are calculated using
prevailing market prices.
While the use of book value weights is convenient to deploy and compute,, the market value basis is
theoretically stable and sound and therefore, a better indicator of the actual capital structure of the firm.
Cost of Capital: 345
© GTG
Cost of Capital: 261
Britwick Ltd is currently trying to work out its weighted average cost of capital. The financial director of the
company has asked you to perform the necessary calculations, using both book values and market values. The
following information is given:
Non-current assets
Current assets
Current liabilities
12 per cent bonds (redeemable in 5 years)
11 per cent irredeemable bonds
Bank loans
Ordinary shares (250 par value)
10 per cent preference shares ( Tshs 1000 par
value) Reserves
Tshs million
668
277
(165)
(120)
(142)
(90)
428
135
75
218
428
1. The current dividend, to be paid shortly, is Tshs 300 per share. Dividends in the future are expected to grow
at a rate of 5 per cent per year.
2. Corporation tax currently stands at 30 per cent.
3. The interest rate on bank borrowings currently stands at 12 per cent.
4. Stock market price as at 31December (all ex-dividend or ex-interest):
Ordinary shares
Preference shares
12 per cent bond
11 per cent irredeemable bond
Tshs
2640
1010
90 per 100 block
80 per 100 block
The following steps allow us to obtain the required information.
Step1: Calculate the cost of the individual sources of finance
1. Cost of equity, using the dividend growth model:
Ke =
Ke =
D0 (1+g)
+g
P0
𝑇𝑇𝑇𝑇ℎ𝑠𝑠 300(1+0.05)
+0.05=16.93%
𝑇𝑇𝑇𝑇ℎ𝑠𝑠 2,640
2. Cost of preference shares
K=
𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 𝑝𝑝𝑝𝑝𝑝𝑝 𝑠𝑠ℎ𝑎𝑎𝑎𝑎𝑎𝑎
𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑝𝑝𝑝𝑝𝑝𝑝 𝑠𝑠ℎ𝑎𝑎𝑎𝑎𝑎𝑎
Ke=
𝑇𝑇𝑇𝑇ℎ𝑠𝑠 100
= 9.9%
𝑇𝑇𝑇𝑇ℎ𝑠𝑠 1,010
3. Cost of redeemable bonds (after tax):
Since issue and redemption rates are the same according to the problem, the cost of debt can be calculated as
if it were irredeemable debt. In other cases, an IRR calculation is required.
K rd =
𝑇𝑇𝑇𝑇ℎ𝑠𝑠 1,200(1-0.03)
=9.33%
𝑇𝑇𝑇𝑇ℎ𝑠𝑠 90,000
346
262 :Financing
FinancingDecisions
Decisions
© GTG
4. Cost of irredeemable debt
Interest rate payable
Market value of bond (ex interest)
K id =
K
id
=
Tshs 11000 × (1- 0.3 )
Tshs 80000
= 9.62%
5. Cost of bank loans (after tax)
Kbl (after tax) = AR (1—CT)
K bl = 12 x (1- 0.30) = 8.4%
Step 2: Calculate the book and market values of the individual sources of finance
Book value million
Tshs
135 + 218 = 353.00
75.00
120.00
142.00
90.00
780.00
Source of finance
Equity (Equity + reserve)
Preference shares
Redeemable bonds
Irredeemable bonds
Bank loans
Total
Market value million Tshs
540 x 2.64 = 1,425.60*
75 x 1.01 = 75.75
120 x 0.90 = 108.00
142 x 0.80 = 113.60
90.00
1,812.95
*( Tshs 135000000/ Tshs 250) x Tsh2640 = Tshs 1425.6 million
Step 3: Calculate the WACC using both book values and market values.
WACC (Book value weightings)
1
Source of finance
Equity (Equity + reserve)
Preference shares
Redeemable bonds
Irredeemable bonds
Bank loans
Total
2
3
4
5
Proportion Cost of Weighted cost
Amount
million Tsh
capital
(3 x 4)
353.00
0.4526
0.1693
0.0766
75.00
0.0962
0.0990
0.0095
120.00
0.1538
0.0933
0.0144
142.00
0.1821
0.0962
0.0175
90.00
0.1154
0.0840
0.0097
780.00
1.0000
0.1277
The weighted cost of capital using book value weights is 12.77%.
WACC (Market value weightings)
1
Source of finance
Equity (Equity + reserve)
Preference shares
Redeemable bonds
Irredeemable bonds
Bank loans
Total
2
3
Amount
Proportion
million Tshs
1,425.60
75.75
108.00
113.60
90.00
1,812.95
0.7863
0.0418
0.0596
0.0627
0.0496
1.0000
4
Cost of
capital
0.1693
0.0990
0.0933
0.0962
0.0840
The weighted cost of capital using market value weights is 15.30%.
5
Weighted cost
(3 x 4)
0.1331
0.0041
0.0056
0.0060
0.0042
0.1530
Cost of Capital: 347
Cost of Capital: 263
© GTG
Toady Inc has the following capital structure as at 31 December 20X8.
Source of finance
Equity shares (4,000,000 shares)
10% Irredeemable preference shares (2,000,000 shares)
14% irredeemable debentures (6,000,000 debentures)
Total
Book value
Tshs million
8,000
2,000
6,000
16,000
The current market price of one equity share of the company is Tshs 4,000. It is expected that the company will
pay a dividend of Tshs 400 per share this year, and continue to grow at 7% for the rest of its life. The debentures
and preference shares are trading at par value.
Assume a 30% tax rate.
Required:
Calculate the weighted average cost of capital using book value weights.
2. Marginal Weights
Marginal cost can be explained as the cost incurred in raising new funds. It represents the proportion of funds
which the firm intends to deploy. Marginal cost of capital is derived when the cost of capital is calculated using
marginal weights.
To calculate the marginal cost of capital, the intended financing proportion should be applied as weights to marginal
component costs. The marginal cost of capital should, therefore, be calculated in the composite sense. When a
firm raises funds in a composite manner and the component’s cost remains unchanged, there will be no difference
between average cost of funds (of the total funds) and the marginal cost of capital. The component costs may
remain constant up to a certain level of funds raised and then start increasing with the amount of funds raised.
The cost of debt may remain 10% (post tax) up to Tshs 25 million. Between Tshs 25 million to Tshs 35 million, the
cost may be 12%, and so on. Similarly, if the retained earnings are insufficient, and additional equity has to be
raised, the cost of equity will be higher due to floatation costs.
When the costs of the individual components of finance rises, the average cost of capital will increase and the
marginal cost of capital will also increase at a higher rate.
The following is the capital structure (including the relative cost of each type of capital) of Romantic Inc:
Debt
Preference stock
Equity
Market value
Tshs million
40
10
50
100
Proportion
%
40%
10%
50%
100%
After tax costs
%
8%
12%
14%
To finance a new project, Romantic Inc plans to raise capital in the following proportion:
Continued on the next page
348 Financing Decisions
264: Financing Decisions
Debt
Preference stock
Equity
© GTG
Source of finance
Tshs million
4
1
5
10
Proportion
%
40
10
50
100
After tax costs
%
8
12
14
The marginal cost of capital will be calculated as follows:
1
Source of finance
Debt
Preference stock
Equity
Total
2
Amount
Tshs million
3
Proportion
4.00
1.00
5.00
10.00
4
Cost of
capital
40%
10%
50%
100%
5
MACC
(3 x 4)
0.0800
0.1200
0.1400
0.0320
0.0120
0.0700
0.1140
The marginal cost of capital for Romantic Inc is 11.40%.
The effect of raising new capital on the weighted average cost of capital will be:
1
Sources of finance
Debt
Preference stock
Equity
Total
2
Amount
Tsh million
3
Proportion
44.00
11.00
55.00
110.00
4
Cost of
capital
40%
10%
50%
100%
5
MACC
(3 x 4)
0.0800
0.1200
0.1400
0.0320
0.0120
0.0700
0.1140
The weighted average cost of capital is 11.40%.
Now assume that Romantic Inc wishes to raise Tshs 10m for the new project only by way of equity and debt. It
plans to raise Tshs 4m as equity and Tshs 6m as debt. There is no change in the cost of debt or equity.
In such a case, the marginal cost of capital will be:
1
Sources of finance
Debt
Equity
Total
2
Amount
Tshs million
4.00
6.00
10.00
3
Proportion
4
Cost of
capital
40%
60%
100%
0.0800
0.1400
5
MACC
(3 x 4)
0.0320
0.0840
0.1160
The marginal cost of capital in now 11.60% for Romantic Inc.
The effect of additional capital on weighted average cost of capital will be:
1
Sources of finance
Debt
Preference stock
Equity
Total
2
Amount
Tshs million
44.00
10.00
56.00
110.00
3
Proportion
40%
9%
51%
100%
4
Cost of
capital
0.0800
0.1200
0.1400
5
MACC
(3 x 4)
0.0320
0.0108
0.0714
0.1142
Continued on the next page
Cost of Capital: 349
Cost of Capital: 265
© GTG
1
Sources of finance
Debt
Preference stock
Equity
Total
2
Amount
Tshs million
44.00
10.00
56.00
110.00
3
Proportion
40%
9%
51%
100%
4
Cost of
capital
0.0800
0.1200
0.1400
5
MACC
(3 x 4)
0.0320
0.0108
0.0714
0.1142
The new weighted average cost of capital for Romantic Inc is 11.42%.
6. Discuss the determinants of the level of cost of capital.
Outline the different uses of cost of capital in finance
[Learning Outcomes f and g]
6.1 Let’s us now discuss the determinants of the level of cost of capital of a firm i.e. the factors which
determine whether the cost of capital would be high or low:
Diagram 10: Determinants of cost of capital
1. Current macroeconomic scenario
The current macroeconomic scenario in terms of the demand- supply of capital as well as the level of inflation
has a bearing on the risk-free rate of return. This rate represents the rate of return on risk- free investments, such
as the interest rate on government securities. In principle, as the demand for money in the economy changes
relative to the supply, investors alter their required rate of return.
For example, if the demand for money increases without an equivalent increase in the supply, lenders will raise
their required interest rate. At the same time, if inflation is expected to deteriorate the purchasing power, investors
require a higher rate of return to compensate for this anticipated loss.
2. Liquidity and risk perception of firm’s securities
The expectation of return is dependent on the level of risk which the investor bears. In other words, as the risk
increases, the investor requires a higher rate of return. This increase is called a risk premium. When investors
increase their required rate of return, the cost of capital rises simultaneously.
Risk is a potential variability of returns. The expected rate of return also depends on how liquid the security is.
If there is significant demand for the security but there is a high price variance then again the investor requires
a high rate of return. In case of readily marketable, liquid and reasonably stable securities, investors would be
content with a slightly lower rate of return.
350 Financing Decisions
266 : Financing Decisions
© GTG
3. Internal structure of the firm
With a change in the firm’s internal structure and character, there might be a change in the business and
financial risks. For example, when the firm grows, its business risk may decline, resulting in a new structure and
cost of capital.
4. Changes in capital structure
There may be small changes in the capital structure of the firm on account of undistributed profits ploughed
back each year, unless the growth rate is sufficient to call for usage of debt on continuous basis.
5. Amount of financing
One major determinant of the cost of capital is the level of financing required. As the financing requirement
increases, there is an increase in the weighted average cost due to a variety of reasons:
(a) Additional floatation costs to raise additional securities will affect the percentage cost of funds.
(b) Investor’s required rate of return may increase with a requirement for larger amounts of capital comparative
to firm size.
(c) Larger issues cannot be placed with ease without a decrease in the price of the security.
(d) Company may face resistance from the suppliers of capital to grant higher amounts without evidence of
managerial competence.
6. Management decisions on finance and operating issues
The rate of return expected by the providers of finance depends on the risk perception. In case the management
takes aggressive decisions leading to high level of debt, the cost of capital would increase for the company.
7. Capital market conditions
There might be changes in the capital market conditions making either debt or equity more favourable than the
other.
6.2 The concept of cost of capital has extensive usage in the field of financial decision making. This is
outlined below:
1. Capital budgeting decision
Cost of capital is widely used in capital budgeting decisions to determine whether or not to undertake a project.
It is the hurdle rate and only if the project earns more than the cost of capital, the project is accepted. Thus,
selection of a particular project among various investment opportunities depends on the cost of capital.
2. Decision on the method of financing
A finance manager needs to have complete knowledge on the interest rate scenario, the capital market
situation, market expectations on dividend from time to time etc. In such situations, the manager would be better
equipped to select a source of finance which has the most competitive cost. Further factors pertaining to risk
and control have to be also kept in mind.
3. Designing the corporate financial structure
The cost of capital has a significant bearing in deciding the capital structure of the firm. A finance manager must
evaluate the various sources of finance and select a right mix to minimise the overall cost of capital and
maximise shareholder value.
4. Senior management performance
The cost of capital can be used to evaluate the performance of senior managers when the actual profit from a
project is evaluated with the overall cost of capital.
5. Other uses
This concept also finds application in varied areas of decision making such as dividend decisions, working capital
policy etc.
Cost of Capital: 351
Cost of Capital: 267
© GTG
What are the determinants of the level of cost of capital? How is cost of capital useful in finance?
Answers to Test Yourself
Answer to TY 1
Yes, there is a direct correlation between risk and return. The higher the risk, the higher is the return expected
since the return needs to compensate for the additional risk borne.
Answer to TY 2
Although it may prima facie appear that equity and retained earnings do not carry any cost, this is not true. The
market share price is dependent on the return that equity shareholders expect and get. In fact cost of equity capital
and retained earnings is the highest due to the risk associated with equity investments.
Answer to TY 3
(a)
(i) If the debentures are irredeemable
Cost of debt = Interest rate payable/Market value of bond (ex interest) = 9/90
= 0.10
= 10%
(ii) If the debentures are redeemable
Expected capital profit at the time of redemption
Redemption price
Cost (present market price)
Profit for 15 years
Annualised profit
105
90
15
1
To obtain a starting figure for the trial and error, we add this annualised profit (1.0) to the cost, if the debentures
were irredeemable (10); 10+1.0 = 11.0.
Years
0
1-15
15
Particulars
Market value
Interest
Capital repayment
Cash flow
Tshs
Discount
factor@ 11%
Present
value
(90)
9
105
1.000
7.191
0.209
(90.00)
64.72
21.95
(3.33)
Discount
Factor
@ 10%
1.000
7.606
0.239
Present
Value
Tshs
(90.00)
68.45
25.10
3.55
Since the NPV with 11% is a negative figure of Tshs 3.33, we will reduce the trial rate to 10% for the next
calculation.
10% +
𝑇𝑇𝑇𝑇ℎ𝑠𝑠 3.55
× (11 - 10)%
𝑇𝑇𝑇𝑇ℎ𝑠𝑠 3.55 − (−𝑇𝑇𝑇𝑇ℎ𝑠𝑠 3.33)
IRR = 10% +0.5
= 10.51%
Therefore, the before-tax cost of redeemable debt is 10.51%.
352 Financing Decisions
268 : Financing Decisions
© GTG
(b)
(i) If the debentures are irredeemable
Interest rate payable = Interest payable X (1 – Tax rate)
= 9 X (1- 0.35)
= Tshs 5.85
Cost of debt = Interest rate payable/Market value of bond (ex interest) = 5.85/90
= 0.065
= 6.50%
(ii) If the debentures are redeemable
To obtain a starting figure for the trial and error, we add the annualised profit (0.3333) to the cost as if the
debentures were irredeemable; 6.5 + 0.333 = 6.8333% i.e. 7% (approx)
Year
0
1-15
1-15
15
Particulars
Market Value
Interest
Tax saved(W 1)
Capital repayment
Cash flow
Tshs
(90.00)
9.00
(3.15)
100.00
Discount
Present value
Discout
Present value
factor @ 7%
factor @ 6%
Tshs
Tshs
1.00
(90.00)
1.00
(90.00)
9.108
81.97
9.712
87.41
(28.6902)
(30.59)
9.108
9.712
0.362
36.20
0.417
41.70
(0.52)
8.52
Since the NPV with 7% is a negative figure of 0.52, we will reduce the trial rate to 6% for the next calculation.
IRR =
Tshs 8.52
×(7 - 6)%
Tshs8.52-(-Tshs0.52)
= 6% + 0.94 x 1%
= 6.94%
Therefore, the after-tax cost of debt is 6.94%.
Workings
W1
Tax rate = 35%
Tax saved = Interest x Tax rate
= Tshs 9 x 0.35
= Tshs 3.15
Answer to TY 4
Step 1
Find out the value of the conversion option
Value of conversion option
= No. of shares to be received x expected market value
= 25 x 5 = Tshs 125
Step 2
Compare the conversion option with the redemption (cash payment) option. We assume that the investors are
rational, and they choose the option with the higher value.
Shareholders have been given the option to receive Tshs 130 in cash. Since the conversion option has a value
of Tshs 125, it is assumed that the investors will not select the conversion option but go for the cash redemption
offer.
Cost of Capital: 353
Cost of Capital: 269
© GTG
Step 3
Calculate the IRR of the cash flows for redeemable debentures using the value as determined in Step
2. (Conversion option)
We shall calculate IRR by trial and error. Since the capital profit for ten years is Tshs 25, the annualised amount
is 25/10 = 2. We add this to the rate of interest (7%) to find the initial rate for trial and error: 7 + 2.5 = 9.5. We
take a complete figure of 9.
Since the NPV with 9% is a negative figure of 5.214, we reduce the trial rate to 5% for the next calculation in the
table
Y
ear
0
Details
Current MV
1-10
Interest
1-10
Tax on interest (0.3 x 7)
Value of shares at
Conversion date
10
Cash
flow
Tshs
(105)
Discount
factor @ 9%
1.000
Present
value
Tshs
(105.000)
7
6.418
2.100
130
1.000
Present
value
Tshs
(105.000)
44.926
7.722
54.054
6.418
(13.478)
7.722
(16.216)
0.422
54.860
0.614
79.82
(18.692)
IRR = 5% +
12.658
x (9 - 5)%
12.658 - (-18.692)
= 5% + 1.6%
= 6.6%
Answer to TY 5
Calculation of cost of equity capital using the dividend growth model
Ke =
D0 (1+g)
+g
P0
600 × (1+5.50%)
+ 5.50%
4,800
600 × 1.055
+0.055
Ke =
4,800
Ke =
= 0.131875 + 0.055
= 0.186875
= 18.69%
Answer to TY 6
E(rj) = 0.05 + 0.95 (0.04)
= 0.05 + 0.038
= 0.088
= 8.8%
Discount
factor @ 5%
12.658
354 Financing Decisions
270 : Financing Decisions
© GTG
Answer to TY 7
Cost of individual sources of finance
Cost of equity shares
Ke =
Ke =
D 0 (1+ g)
P0
+g
Tsh400 (1 + 0.07 )
Tsh4000
+ 0.07
= 0.107 + 0.07
= 17.70%
Cost of preference shares
The preference shares are trading at par value.
Hence,
The market value of a preference share = the book value of a preference share.
Book value of one preference share =
Tshs 2,000,000,000
2,000,000
= Tshs 1,000
Dividend per share = 10% of Tshs 1,000 = Tsh100
Kp =
Dividend per share
Market price per share
Kp=
Tshs 100
= 10%
Tshs 1000
Cost of irredeemable debentures
Kd =
Tshs 140 (1 - 0.30 )
Tshs 1,000
Cost of irredeemable bond (Kd)
Cost of irredeemable debenture
= 9.8%
Calculation of weighted average cost of capital using book value weights
1
Source of finance
Equity shares (4,000,000 shares)
10% Irredeemable preference shares
(2,000,000 shares)
14% Irredeemable debentures
(6,000,000 debentures)
Total
2
3
Amount
Proportion
million Tshs
4
Cost of
capital
5
Weighted cost
(3 x 4)
8,000
0.5000
0.1770
0.0885
2,000
0.1250
0.1000
0.0125
6,000
16,000
0.3750
1.0000
0.0980
0.0368
0.1378
The weighted average cost of capital using book value weights is 13.78%.
© GTG
Cost of Capital: 355
Cost of Capital: 271
Answer to TY 8
The determinants of the level of cost of capital are:
1.
2.
3.
4.
5.
6.
7.
Current macroeconomic situation
Marketability of firm’s securities
Internal structure of the firm
Changes in capital structure
Amount of financing
Operating and financial decisions
Capital market conditions
The concept of cost of capital has extensive usage in the field of financial decision making. The same is outlined
below:
1. Capital budgeting decision: cost of capital is widely used in capital budgeting decisions to determine
whether or not to undertake a project. It is the hurdle rate and only if the project earns more than the cost of
capital, it is accepted. Thus, selection of a particular project among various investment opportunities depends
on the cost of capital.
2. Decision on the method of financing: a finance manager needs to have complete knowledge on the interest
rate scenario, the capital market situation, market expectations on dividend from time to time etc. In such
situations, the manager would be better equipped to select a source of finance which has the most competitive
cost. Further factors pertaining to risk and control have to be also kept in mind.
3. Designing the corporate financial structure: the cost of capital has a significant bearing in deciding the
capital structure of the firm. A finance manager must evaluate the various sources of finance and select a right
mix to minimise the overall cost of capital and maximise shareholder value.
4. Senior management performance: the cost of capital can be used to evaluate the performance of senior
managers when the actual profit from a project is evaluated with the overall cost of capital.
5. Other uses: this concept also finds application in varied areas of decision making such as dividend
decisions, working capital policy etc.
Quick Quiz
1. Is it true that a highly leveraged company is likely to have a higher cost of equity capital? If so, why?
2. What is the beta of a security?
3. An irredeemable debt of Tsh100 is quoted at Tsh90 on the market. It has a 10% rate of interest. The
corporate tax is 30%. Find out the after-tax cost of the debt.
4. “For preference shares, the tax element should be deducted before calculating the cost of capital”. Is this
statement true or false?
5. How can unsystematic risk be reduced?
6. What are the components of CAPM?
7. Give an example of implicit cost of capital.
8. State whether the following statements are true or false.
(a) It is preferable to use market value over book value weightage.
(b) The concept of cost of capital has no application in capital budgeting.
(c) Equity capital is cheaper than debt as a source of finance.
356 Financing Decisions
272 : Financing Decisions
© GTG
Answers to Quick Quiz
1. It is true that a highly leveraged company is likely to have a higher cost of equity capital. High gearing
increases the risk of returns to shareholders i.e. the risk that little or nothing will be left over after the
payment of debt interest. To compensate for this additional risk, shareholders require a higher return on
their investment.
2. The beta of a security is an index of responsiveness of the changes in returns of the security relative to a
change in the stock exchange or market.
3. Before tax cost =10/90 x 100 = 11.11% After
tax cost =11.11% x (1 - 0.30) = 7.78%
4. False, dividends are paid from post tax profits and hence they are not usually taxable. On the other hand, if
there is a dividend distribution tax for which the receiver of the dividend does not receive a credit, the tax
would be added to the cost of the preference shares.
5. Unsystematic risk can be reduced by diversification into securities that do not have a direct correlation. By
building a diversified portfolio of securities, either (a) within the same assets of a class that are not
correlated to each other or (b) within assets of different classes that are not correlated to each other.
6. The components of CAPM are:
(a) Beta coefficient of the security
(b) Minimum risk-free rate of return
(c) Risk premium
7. Cost of retained earnings is an example of implicit cost of capital.
8.
(a) True
(b) False
(c) False
Self Examination Questions
Question 1
A firm’s capital structure is as follows
Source of finance
Tshs (‘000s)
Bonds
Preference shares
Equity capital
Total
300,000
200,000
500,000
1,000,000
Cost of capital
(%)
8
14
17
It may be noted that the debt capital has been considered after tax, and that equity capital includes retained
earnings of Tshs 100,000,000.
Required:
(a) Calculate the weighted average cost of capital using book value weightings.
(b) Market value weight
Calculate the weighted average cost of capital, assuming that the market values of different sources of finance
are as follows:
Source of finance
Bond
Preference capital
Equity capital (including retained earnings)
Total
Market value
Tshs (‘000s)
270,000
230,000
750,000
1,250,000
Cost of Capital: 357
Cost of Capital: 273
© GTG
(c) The firm wishes to raise Tshs 500,000,000 for expansion of its plant. It estimates that Tshs 100,000,000 will
be available as retained earnings and the balance of the additional funds will be raised as follows:
Tshs
(‘000s)
300,000
100,000
Long-term debt
Preference shares
The estimated capital structure of the company is given in Part A.
Required:
Using marginal weightings, calculate the weighted average cost of capital (WACC).
Question 2
The following details of a market portfolio are provided
Initial price
Tsh
900
1100
700
5000
Textile Ltd
Chemicals Ltd
Metals Ltd
7% Government bonds
Year end price
Tsh
1250
1450
950
5040
Dividends
Tsh
30
40
20
350
Beta risk factor
0.70
0.80
0.60
0.99
Required:
(a) Calculate expected rate of return on market portfolio.
(b) Using the CAPM, calculate expected return of each security excluding government bonds.
Question 3
st
DCB Ltd has the following capital structure which is considered adequate as on 31 December 20X0
13% debentures
12% preference shares
Equity (100,000 shares)
(Amounts in Tshs )
2,500,000
1,000,000
16,500,000
20,000,000
The company has a share price of Tshs 250.0. The dividend per share is 50% ofthe year 2010 EPS.
The following trend of EPS is expected to continue in future
Year
20X1
20X2
20X3
20X4
20X5
20X6
EPS ( Tshs )
10
11
12.1
13.3
14.6
16.1
Year
20X7
20X8
20X9
20X0
EPS ( Tshs )
17.7
19.50
21.5
23.6
Preference shares at Tshs 92 (with an annual dividend of Tshs 11 per share) were also issued. The company
tax rate is 50%. Also, the company issued new debentures at 15% interest and the current price is Tshs 96.
Required:
(a) Calculate the after tax
(i) Cost of new debt
(ii) Cost of new preference shares
(iii) New equity share (consuming new equity from retained earnings)
(b) How much can be spent for capital investment before new shares must be sold? Assume retained earnings
for the next year are 50% of 2010.
358 Financing Decisions
274 : Financing Decisions
© GTG
(c) What is the marginal cost of capital when funds exceed the amount calculated in (B). Assume the new
equity share price as Tshs 200.
Question 4
TSIW Ltd wants to raise additional funds of Tshs 10 million for an investment proposal. It has Tshs 2 m in the
form of retained earnings.
Other details are as follows
Debt to equity 30:70.
Cost of debt up to Tshs 1.5 m: 11% and thereafter: 13%.
EPS Rs. 40, dividend pay-out 40% of earnings
Expected dividend growth 10%
Current market price 450; tax rate 30%.
Required:
Calculate
(a) Pattern for raising additional finance
(b) Cost of equity / retained earnings
(c) Cost of debt
(d) The overall weighted average after-tax cost of additional funds raised.
Answers to Self Examination Questions
Answer to SEQ 1
(a) Calculation of weighted average cost of capital (book value weights)
Source
(1)
Debt
Preference share
Equity capital
Total
(2)
Tshs (‘000s)
300,000
200,000
500,000
1,000,000
Cost
(3)
%
8
14
17
Total cost
(4 = (2 x 3))
Tshs (‘000s)
24,000
28,000
85,000
137,000
Weighted average cost of capital=137,000/1,000,000 x 100 = 13.7%
(b) On the basis of Gitman’s criterion, the sum of Tsh750,000 in question 2 is allocated between equity
capital and retained earnings as follows:
Source of finance
(1)
Equity shares
Retained earnings
Total
Book value %of Book value
(2)
(3)
Tshs (‘000s)
400,000
80
100,000
20
500,000
100
Market value
(4)
Tshs (‘000s)
600,000 (W1)
150,000 (W2)
750,000
Workings:
W1: Market value of equity shares= ( Tshs 750,000,000 x 80%)
W2: Market value of retained earnings = ( Tshs 750,000,000 x 20%)
(c) After determination of the market value, ko is calculated as follows:
Cost of Capital: 359
Cost of Capital: 275
© GTG
Calculation of weighted average cost of capital (market value method)
Source
(1)
Bond
Preference capital
Equity capital
Retained earnings
Total
Kp =
Tshs 181,300,000
Tsh1,250,000,000
Market value
(2)
Tshs (‘000s)
270,000
230,000
600,000
150,000
1,250,000
Cost
(3)
(%)
8
14
17
17
Total cost
((4) = (3 x2))
Tshs (‘000s)
21,600
32,200
102,000
25,500
181,300
× 100 =14.5%
One notable point that emerges from the weighted average cost of capital based on book value weightings and
market value weightings respectively is that the ko with market value is higher. This is mainly due to preference
shares and equity shares having market values considerably greater than their book values. Since these
sources of long-term funds have higher specific costs, the overall cost increases.
In operational terms, if book value weighted average cost of capital is used, some projects, which would be
accepted that would not have been acceptable based on the market value approach. The result given by the
market value based weightings are better as a decision criterion.
(d) Calculation of weighted average cost of capital (marginal weights)
Source
(1)
Debt
Preference capital
Retained earnings
Total
Market
value
(2)
Tshs
(‘000s)
300,000
100,000
100,000
500,000
Proportion
(3)
0.60
0.20
0.20
1.00
Cost
(4)
%
8
14
17
Total cost
(5=(2 x 4))
Tshs
(‘000s)
24,000
14,000
17,000
55,000
Weighted average cost of capital =55,000,000/500,000,000 x 100 =11%
Answer to SEQ 2
(a) Expected rate of return on market portfolio
Textile Ltd
Chemicals Ltd
Metals Ltd
7% Government bonds
Capital
appreciation*
A ( Tshs )
350
350
250
40
990
Dividends
B ( Tshs )
30
40
20
350
440
*Year-end price less initial price
Expected rate of return on market portfolio =
(b) Expected return on each security.
E(rj) = Rf + βj (E(rm) – Rf)
Textile Ltd (7% + 0.70 (18.57% - 7%))
Chemicals Ltd ((7% + 0.80 (18.57% - 7%))
Metals Ltd (7% + 0.60 (18.57% - 7%))
1,430
7,700
× 100 = 18.57%
15.10%
16.26%
13.94%
Total
returns
A+B
( Tshs
) 380
390
270
390
1430
Investment
Initial price
( Tshs )
900
1100
700
5,000
7,700
360 Financing Decisions
276 : Financing Decisions
© GTG
Answer to SEQ 3
(a)
(i) Cost of new debt
Kd =
𝐼𝐼 × (1 - t)
N
Kd =
15 × (1 - 0.5)
96
= 0.078
Cost of new preference shares
Kp =
Dividend
Market price
= 11/92 = 0.12.
Cost of new equity shares
D1
Ke = + G
P0
11.8
=
+ 0.10
250
=0.1472
D1 = 50% of 2010 EPS = 50% of 23.6 = 11.80
(b) Retained earnings = 0.50X23.6X100,000 = Tshs 118,000. Therefore, the company can spend this amount
before increasing the marginal cost of capital and without selling new shares.
Equity capital is 82.5% of total capital
Therefore, capital investment =
118,000
0.825
= Tshs 143,030.
(c) The cost of new issue
D1
Ke = + G
P0
11.8
=
+ 0.10
200
= 0.159
The marginal cost of capital will be:
Type of capital
Debt
Preference
Equity
0.14693 = 14.69%
Proportion
0.125
0.050
0.825
Cost
0.078
0.12
0.159
Product
0.00975
0.00600
0.13118
Cost of Capital: 361
Cost of Capital: 277
© GTG
Answer to SEQ 4
Pattern for raising additional finance:
Tshs 10 m will be raised in the same debt equity ratio of 30:70. The pattern is given below (in Tshs )
Retained earnings
Additional equity share capital
Debt funds
11% debt
13% debt
2,000,000
5,000,000
1,500,000
1,500,000
7,000,000
3,000,000
10,000,000
Cost of equity
Ke =
=
D1
P0
+G
40(0.50)(1+ 0.1)
+ 0.10
450
= 0.0488+0.1 = 0.1489
Cost of equity = cost of retained earnings = 14.89%.
Cost of debt
= ((1,65,000 + 1,95,000)*(1-0.3))/3,000,000
= 8.4%
The overall weighted average after tax cost of additional funds raised:
Source
Equity share capital
Retained earnings
Debt
Total
Amount
( Tshs )
5,000,000
2,000,000
3,000,000
10,000,000
Cost of
debt
0.1489
0.1489
0.084
Total
( Tshs )
744,500
297,800
252,000
1,294,300
The overall weighted average cost = 1,294,300/10,000,000 = 12.94%.
Indicative Examination Questions
IEQ 1
Angumiliki Ltd has in issue 8 million shares with an ex-dividend market value of TSHS.716 per share. A dividend of
TSHS.62 per share for 2015 has just been paid. The pattern of recent dividends is as follows:
Year
2012
2013
2014
2015
Dividends per share TSHS
55.1
57.9
59.1
62.0
Angumiliki Ltd also has in issue 8.5% bonds redeemable in five years’ time with a total nominal value of TSHS.500
million. The market value of each TSHS.10,000 bond is TSHS.10,342. Redemption will be at nominal value.
Angumiliki Ltd is planning to invest a significant amount of money into a joint venture in a new business area. It has
identified a proxy company with a similar business risk to the joint venture. The proxy company has an equity beta
of 1.038 and is financed 75% by equity and 25% by debt, on a market value basis.
The current risk-free rate of return is 4% and the average equity risk premium is 5%. Angumiliki Ltd pays profit tax
at a rate of 30% per year and has an equity beta of 1.6.
278 : Financing Decisions
362REQUIRED:
Financing Decisions
© GTG
278
Decisions
(a): Financing
Calculate
the cost of equity of Angumiliki Ltd using the dividend growth model.
(4 marks)© GTG
REQUIRED:
(b)
Discuss whether the dividend growth model or the Capital Asset Pricing Model (CAPM) should be used to
calculatethe
thecost
costofofequity
equity.
(5 marks)
(a)
Calculate
of Angumiliki Ltd using the dividend growth model.
(4 marks)
(b)
Discuss whether the dividend growth model or the Capital Asset Pricing Model (CAPM) should be used to
(c)
Calculate the weighted average after-tax cost of capital of Angumiliki Ltd using a cost of equity of 12%.
calculate the cost of equity.
(5 marks)
(6 marks)
(c)
IEQ 2
Calculate the weighted average after-tax cost of capital of Angumiliki Ltd using a cost of equity of 12%.
(6 marks)
IEQ 2
Safari Company wishes to calculate its Weighted Average Cost of Capital (WACC) and the following is the current
information relating to the company.
Safari Company wishes to calculate its Weighted Average Cost of Capital (WACC) and the following is the current
information relating to the company.
Number of ordinary shares
2 million
Number of 5%, Tshs .100 non-callable preferred stock
Number of ordinary shares
Book value of 10%, Tshs .1,000, irredeemable bonds
Number of 5%, Tshs .100 non-callable preferred stock
Market price of ordinary shares
Book value of 10%, Tshs .1,000, irredeemable bonds
Market price of 5%, Tshs .100 non-callable preferred stock
Market price of ordinary shares
Total dividend just paid
Market price of 5%, Tshs .100 non-callable preferred stock
Market price of 10% Tshs . 1,000, irredeemable debt
Total dividend just paid
Equity beta of Safari company
Market price of 10% Tshs . 1,000, irredeemable debt
Treasury bill rate
Equity beta of Safari company
Expected return on the market
Treasury bill rate
1 million
2 million
Tshs . 20 million
1 million
Tshs . 50 cum dividend
Tshs . 20 million
Tshs . 43 ex dividend
Tshs . 50 cum dividend
Tshs . 4 million
Tshs . 43 ex dividend
105 percent ex interest
Tshs . 4 million
1.5
105 percent ex interest
5%
1.5
12%
5%
Expected return on the market
12%
Additional information:
1.
The corporate tax rate applicable to Safari company is 35%.
Additional
2.
The information:
dividends of Safari Company are expected to grow at an average rate of 6%.
1.
2.
The corporate tax rate applicable to Safari company is 35%.
The dividends of Safari Company are expected to grow at an average rate of 6%.
REQUIRED:
(a)
Estimate the Safari Company’s equity risk premium and the cost of equity using the Capital Asset Pricing
REQUIRED:
Model (CAPM).
(3 marks)
(a)
(b)
(b)
(c)
Estimate the Safari Company’s equity risk premium and the cost of equity using the Capital Asset Pricing
Calculate the market value Weighted Average Cost of Capital of Safari Company using:
Model (CAPM).
(3 marks)
(i)
The dividend growth model
Calculate the market value Weighted Average Cost of Capital of Safari Company using:
(ii)
The Capital Asset Pricing Model
(12 marks)
(i)
The dividend growth model
Discuss whether the dividend growth model or the CAPM offers the better estimate of the cost of equity of
(ii)
The Capital Asset Pricing Model
(12 marks)
a company.
(3 marks)
(c)
(d)
Discuss whether the dividend growth model or the CAPM offers the better estimate of the cost of equity of
Discuss the circumstances under which the weighted average cost of capital can be used in investment
a company.
(3 marks)
appraisal.
(2 marks)
(d)
Discuss the circumstances under which the weighted average cost of capital can be used in investment
(Total: 20 marks)
appraisal.
(2 marks)
Answer to IEQ 2
(a)
Safari Company’s Equity risk Premium and the Cost of Equity using the CAPM.
Answer to IEQ 2
(a)
Safari Company’s Equity risk Premium and the Cost of Equity using the CAPM.
(Total: 20 marks)
© GTG
© GTG 



(b)
(b)
Equity risk Premium
Equity
Equity risk
RiskPremium
Premium =
Equity Risk Premium =
Cost of Equity
Cost
k of Equity
R 
e
ke
R
R
m
m
 R f  e
 R f  e
Cost of Capital: 363
Cost of Capital: 279
Cost of Capital: 279
= 12%  5%1.5  10.5%
= 12%  5%1.5  10.5%
Rm  R f  e
f
 R f  Rm  R f  e
= 5% + (12% - 5%)1.5 = 15.5%
= 5% + (12% - 5%)1.5 = 15.5%
The market value weighted average cost of capital of Safari Company.
The
value
weighted
average
cost
of capital
of Safari
Company.
(i) market
Market
Value
WACC
using the
dividend
growth
model
(i)
Market
Cost of Value
EquityWACC
(ke) using the dividend growth model
Cost of Equity (ke)
D 1  g 
k e  Do 1  g   g
k e  o Po
g
Po
Do = Total Dividend Paid/Number of Ordinary Shares in Issue
Do = Total Dividend Paid/Number of Ordinary Shares in Issue
+TSHS4,000,000/2,000,000 = TSHS2 per share
+TSHS4,000,000/2,000,000 = TSHS2 per share
Po = Market Price per Share cum dividend – Dividend per Share
Po = Market Price per Share cum dividend – Dividend per Share
= TSHS50 – TSHS2 = TSHS48
= TSHS50 – TSHS2 = TSHS48
g = 6%
g = 6%
Thus
Thus
D 1  g 
TZS 2(1.06)
k e  Do 1  g   g = ke = TZS 2(1.06)  0.06  10.4%
o P
ke 
 g = ke = TZS 48  0.06  10.4%
o
TZS 48
Po
Cost of Irredeemable Debt (ki)
Cost of Irredeemable Debt (ki)
Kd = I/Po = [10% x TSHS1,000]/(1.05 X TSHS1,000) = TSHS100/TSHS1050 = 9.52%
Kd = I/Po = [10% x TSHS1,000]/(1.05 X TSHS1,000) = TSHS100/TSHS1050 = 9.52%
Thus the after tax cost of debt, ki = kd(1 – T)
Thus the after tax cost of debt, ki = kd(1 – T)
=9.52% (1 – 0.35) = 6.2%
=9.52% (1 – 0.35) = 6.2%
Cost of Non-Callable Preferred Stock (k p)
Cost of Non-Callable Preferred Stock (k p)
Kp = Dp/Po = (5% x TSHS100)/TSHS43 = 5/43 = 11.6%
Kp = Dp/Po = (5% x TSHS100)/TSHS43 = 5/43 = 11.6%
The WACC
The WACC
Market Value of Equity
= TSHS48 x 2,000,000 shares = TSHS96 million
Market Value of Equity
= TSHS48 x 2,000,000 shares = TSHS96 million
Market Value of
=TSHS1,050 x 20,000 bonds = TSHS21 million
Market Value of
=TSHS1,050 x 20,000 bonds = TSHS21 million
Market Value of Preferred Stock =TSHS43 x 1,000,000 shares = TSHS43 million
Market Value of Preferred Stock =TSHS43 x 1,000,000 shares = TSHS43 million
Equity proportion = 96/160 = 0.6
Equity proportion = 96/160 = 0.6
Debt proportion = 21/160 = 0.13
Debt proportion = 21/160 = 0.13
Preferred stock proportion = 43/160 = 0.27
Preferred stock proportion = 43/160 = 0.27
WACC = (0.6)(10.4%) + (0.13)(6.2%) + (0.27)(11.6%) = 10.18%
WACC = (0.6)(10.4%) + (0.13)(6.2%) + (0.27)(11.6%) = 10.18%
(ii)
(ii)
Market Value WAC using the Capital Asset Pricing Model
Market
Value WAC using the Capital Asset Pricing Model
Cost
of Equity
Cost of Equity
ke
ke
 R f  Rm  R f  e
 R f  Rm  R f  e
WACC = (0.6)(10.4%) + (0.13)(6.2%) + (0.27)(11.6%) = 10.18%
364 Financing
Decisions
(ii)
Market Value WAC using the Capital Asset Pricing Model
Cost of Equity
ke
280 : Financing Decisions
 R f  Rm  R f  e
= 5% + (12% - 5%)1.5 = 15.5%
© GTG
After Tax of Debt
Ki = 11.6%
Thus the WACC = (0.6)(15.5%) + (0.13)(6.2%) + (0.27)(11.6%) = 13.23%
(c)
The Dividend Growth Model vs. CAPM
Dividend growth model
There are a number of problems with the dividend growth model. It uses a set of figures which assumes that
dividends grow smoothly. In reality, dividends change according to decisions made by managers who do
not necessarily repeat historical trends. It is therefore very difficult to accurately predict the future dividend
growth rate. The other main problem is how to incorporate risk. The dividend growth model does not explicitly
consider risk, particularly business risk. The company may change its area of business operations and the
economic environment is notoriously uncertain. The share price will however fall as risk increases, leading
to an increased cost of equity. The model also ignores the effects of taxation and assumes there are no
issue costs for new shares.
Capital asset pricing model
The main advantage that the CAPM has over the dividend valuation model is that it does explicit consider
risk. The CAPM is based on a comparison of the systematic risks of individual investments with the risks of
all shares in the market. Systematic risk is risk that cannot be diversified away and an investor will require
a higher return to compensate for higher risk. This higher return is the higher cost of equity that is calculated
using the CAPM formula. The formula does however require estimates to be made of excess return, the
risk-free rate and beta values. All of these can be difficult to estimate, but are more reliable than the dividend
growth rate used in the dividend valuation model.
Conclusion
The CAPM does explicitly consider risk and uses estimated values that are more reliable than those used
in the dividend valuation model. It can therefore be said that CAPM offers the better estimate of the cost of
equity of a company.
(d)
Circumstances under which WACC can be used in Investment Appraisal
The Weighted average cost of capital is the average cost of the company’s finance and represents the
average return required as compensation for the risks of the investment.
Business risk
The WACC can only be used if the business risk of the proposed investment is similar to the business risk
of existing operations. This would involve the expansion of existing business. If the proposed investment is
in a different type of business, a project-specific cost of capital should be used which reflects the changing
risk. The technique to use involves changing the beta in the capital asset pricing model.
Financial risk
The WACC can only be used where the existing capital structure will be maintained. This means that the
finance for the project will be raised in the same proportions as the existing finance.
Size of the project
The WACC can only be used if the project being appraised is small relative to the company. If the project is
large in scale, it is more likely to cause in risk and make the WACC inappropriate.
SECTION D
Financial Gearing and Capital Structure: 365
FINANCING DECISIONS
D4
STUDY GUIDE D2: FINANCIAL GEARING AND
CAPITAL STRUCTURE
The capital structure decision essentially involves deciding on the proportion of different sources of funds which
should be deployed. The twin objectives which a prudent finance manager tries to achieve are minimisation of
overall cost of capital and maximisation of firm value.
The use of debt finance is considered cost effective due to the tax advantage (discussed in the Study Guide D1
on cost of capital). However, financial gearing has to be increased carefully since an increase in debt leads to a
simultaneous increase in risk. Increase in financial gearing beyond a point can make the firm vulnerable if not
supported by a proportionate increase in earnings.
Therefore, a finance manager has to strike a balance between debt and equity to achieve the twin objectives
mentioned above. In this Study Guide, we shall discuss the impact of gearing, various capital structure theories
and other issues to be dealt with while deciding on a prudent capital structure.
a) Define financial gearing and capital structure.
b) Define and measure operational gearing and financial gearing.
c) Identify the relationship between financial gearing and operating gearing and between business risk and
financial risk.
d) State the basic capital structure theories (the traditional theories, the net operating theory, the
Modigliani and Miller theories, bankruptcy and agency costs, personal taxes).
e) Discuss critically whether or not a company by adopting a particular capital structure can influence its
value or its cost of capital.
f) Identify and explain the effect if capital gearing on investors perception of financial risk and return.
g) Determine the implications of debt financing on the return to shareholders under various financing
alternatives using both EBIT-EPS and ROI-ROE analyses.
h) Discuss the issues that must be kept in mind when determining optimal/target capital structure of a firm.
366 Financing Decisions
280 : Financing Decisions
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1. Define financial gearing and capital structure.
[Learning Outcome a]
1.1 Financial Gearing
1. Definition of financial Gearing
Before discussing the problems related to having high levels of gearing it is important to understand completely
what is meant by the term ‘gearing’.
In the world of finance, the term ‘gearing’ is usually used to describe the relationship between the relative
proportions of debt and equity finance used by a company. This is the more popular meaning for gearing and is
classified as ‘financial gearing’.
For financing of an investment proposal / expansion plan, there are broadly two sources of funds available:
(a) Debt comprising of long-term loans and debentures which involve a fixed contractual obligation in terms of
interest outflow. Preference shares are also included under this because they have to be repaid before any
payment is received by the equity shareholders.
(b) Equity, i.e. shareholders’ funds, where there is no fixed contractual obligation. However, the objective of the
firm is to maximise shareholder value.
Financial gearing is the result of the fixed financial obligations calculating the income of the firm. Financial gearing
measures the effect of changes in earnings before interest and tax (EBIT) on the shareholder’s profits.
Firms deploy debt with the objective of maximising shareholder return. Therefore, let’s define financial gearing
or financial leverage.
Financial gearing is the capacity of the firm to use fixed financial charges to enhance the effect of change in
EBIT on the earnings per share (EPS).
However, the maximisation of shareholder return is possible so long as the firm earns more than the fixed
interest obligations; else there would be erosion of wealth from a shareholder’s perspective. For a given level of
financial gearing, the impact of changes in EBIT on the company’s EPS is illustrated below:
ABC Ltd is expected to report a profit (EBIT) in the current year of Tshs 2,000 million. The firm has 12% loans of
Tshs 6,000 million and 10% preference share capital of Tshs 4,000 million. If the EBIT changes to either (i) Tshs
1,400 million, or (ii) Tshs 2,300 million, we need to calculate the impact on the EPS. Tax rate is 30%.
Number of shares outstanding are 1,000,000.
EPS for various levels of EBIT
Particulars
EBIT
Less: Interest on loans
Earnings before tax
Less: Taxes
Less: Preference dividend
Earnings available to equity shareholders(A)
Number of shares outstanding)(B)
EPS (A/B) (Tsh)
Change in EPS
Change in EBIT
(Amounts in Tshs million)
BASE
CASE 1
CASE 2
2,000
1,400
2,600
(720)
(720)
(720)
1,280
680
1,880
(384)
(204)
(564)
(400)
(400)
(400)
496
76
916
1,000,000 1,000,000 1,000,000
496
76
916
-85%
85%
-30%
30%
As seen above, for a 30% increase / decrease in EBIT, the EPS has increased/decreased by 85%.
Financial Gearing and Capital Structure: 367
Financial Gearing and Capital Structure: 281
© GTG
2. Gearing ratios / Capital structure ratios
Financial gearing can be calculated in a number of ways, as illustrated below. Some calculations will be based
on interest and income figures taken directly from the company’s SOPL, while others will be taken from the
company’s SOFP. SOFP gearing is therefore one measure of financial gearing.
(a) Equity Gearing
Preference share capital + Long term debt
Ordinary share capital and reserves
This is also commonly known as the debt/equity ratio and illustrates the company’s borrowings as a proportion
of its shareholders’ funds. If equity gearing is high, it implies a higher usage of borrowed funds and vice versa.
(b) Total Gearing
Preference share capital + Long term debt
Total long-term capital (Preference share capital + Long term debt + Ordinary share capital and reserves)
The total gearing ratio illustrates the proportion of the company’s total capital structure that comprises of debt. It
is an indicator of the company’s capital structure. The higher the ratio, the higher is the reliance on external capital
for finance.
(c) Income / interest gearing
Debt Interest
Operating profits before debt interest and tax
This ratio illustrates what proportion of the company’s operating profits will be paid out in the form of debt interest.
The operating profits after payment of interest and tax are available to equity shareholders. Therefore, a higher
interest gearing ratio would imply a lower proportion of funds remaining for equity shareholders.
The following information is available for Cell Inc:
Ordinary share capital
8% non-redeemable preference share capital
Debentures (12%)
Long-term borrowings
Bank overdraft
Reserves
PBIT
Tshs
million
450
100
100
400
500
125
220
The 8% non-redeemable preference share capital is to be classified as debt because, even though the preference
shares are non-redeemable, they carry a fixed percentage dividend. (The substance of the transaction is given
more importance than its form).
In the absence of other information, it is assumed that the bank overdraft is a short-term debt and is not to be
included in the long-term debt.
Continued on the next page
368 Financing Decisions
282 : Financing Decisions
© GTG
Long-term debt
Tshs million
100
100
400
600
8% non-redeemable preference share capital
Debentures
Long-term borrowings
Total long-term debt
Shareholders’ funds
Tshs million
450
125
575
Ordinary share capital
Reserves
Total shareholders’ funds
Debt/equity (equity gearing) =
Total gearing =
Tshs 600 m
Tshs575 m
Tshs 600 m
Tshs 600 m + Tshs575 m
Income/interest gearing
=
= 1.04
= 0.51
0.12 × Tshs 100 m
Tshs 220m
× 100 = 5.45%
However, no meaningful comments can be made in the absence of comparative data such as industry statistics
or past results.
(d) Interest coverage ratio
It indicates how many times the profit covers the interest charge. It is designed to show the financial risk in
terms of profit rather than equity and reserves. It is calculated as:
Interest coverage ratio =
Profit before interest and tax
Interest expense
Sometimes, companies use the reciprocal of this ratio i.e. interest to profit ratio.
The following information is available from Red Inc:
Profit before interest and tax
Interest
Profit before tax
Interest coverage =
Tshs (‘000s)
45,000
(18,000)
27,000
Profit before interest and tax
Interest expense
=
Tshs45,000
Tshs18,000
= 2.5 times
Rule of thumb for analysis purposes: the higher the interest coverage ratio, the better position is the
company in to pay the fixed charge of interest.
Interest coverage of less than 3 times is considered low, showing that the profitability is too low to cover the
interest cost.
Financial Gearing and Capital Structure: 369
Financial Gearing and Capital Structure: 283
© GTG
(e) Debt service coverage ratio
When we consider debt servicing, we cannot confine our discussions only to the ability to cover interest payments,
as debt invariably contains a requirement of repayment of the principal amount, in addition to interest payments.
It is necessary to check a company’s ability to pay the total of the principal repayment as well as the interest.
Debt service coverage ratio =
Profit After Tax + Interest + Depreciation + Other non - cash expenses
Interest + Principal repayments
Rule of thumb for analysis purposes: Financial institutions have their own guidelines on the desired ratio.
However, a ratio of 2:1 may generally be treated as a satisfactory ratio.
The logic is that, out of the cash generated, a maximum of half should be spent on debt servicing, leaving the
remaining half for dividend and reinvestment requirements.
Torres Industries Ltd has submitted the following projections. Work out the yearly debt service coverage ratio
(DSCR) and the average DSCR.
Year
1
2
3
4
5
6
7
8
Net profit for
the year
Tshs (‘000s)
21,000
34,000
36,000
17,000
19,000
20,000
17,500
16,500
Interest on term
loan during
Tshs (‘000s)
19,500
18,000
15,000
12,500
10,500
8,000
5,000
0
Repayment of term loan
during the year
Tshs (‘000s)
10,000
17,500
17,500
17,500
17,500
17,500
17,500
17,500
The net profit has been arrived after charging depreciation of Tshs 12,000,000 every year.
(f) Total cash flow coverage ratio
The ratios calculated from the SOPL suffer from the drawback that the figures in the SOPL do not represent
actual cash flows. To remove this limitation, a ratio based on cash flow is sometimes used.
Total cash flow coverage ratio
PBIT + Lease payments + Depreciation + Non - cash expenses
Lease payments + Interest + Principal repayments + Preference dividend
The logic and guidance for interpretation is similar to that related to the debt service coverage ratio.
370 Financing Decisions
284 : Financing Decisions
© GTG
Diagram 1: Summary of ratios
1.2 Capital structure
Capital structure is the structure of capital of the firm, i.e. the mix of shareholder’s funds and borrowed funds in
the sources of funds.
The capital structure decision is the decision to decide on the different forms of financing and their proportions in
the total capitalisation of the entity. The aim of a prudent finance manager is to develop an optimum capital
structure which minimises the overall cost of capital and maximises shareholder return. The value of the firm
depends on the capital structure and the costs of the relevant components.
For funding a new project / investment, a firm can use the following combinations of sources of finance
100% debt (comprising bank loans / debentures / bonds etc.)
X% debt and y% equity (additional issue of capital or retained earnings)
X% debt and y% preference capital
X% preference capital and y% equity
100% equity
100% preference capital.
There are certain important concepts which need to be understood in designing an optimal capital structure (like
operating leverage, EBIT-EPS analysis) which we shall discuss in the subsequent sections.
Financial
Gearing
and
Capital
Structure:
371
Financial
Gearing
and
Capital
Structure:
285
© GTG
In the current year, the earnings before interest and taxes of Royalwel Ltd are expected to amount to
Tshs 20,000 million. The firm has 10 percent bonds aggregating to Tshs 40,000 million, while the 10%
preference shares amount to Tshs 40,000 million.
Assuming an EBIT of (i) Tshs 12,000 m (ii) Tshs 28,000 m, how would the EPS be affected? The corporate
tax rate is 30%. The number of outstanding ordinary shares is 8,000,000.
Calculate the EPS after effecting the changes.
2. Define and measure operational gearing, and financial gearing.
Identify the relationship between financial gearing and operating gearing and between
business risk and financial risk.
[Learning Outcomes b and c]
Having explained financing gearing in Learning Outcome 1 above, let’s now understand what operational
gearing is.
2.1 Operational gearing
The operational costs of a firm can be classified into three types
 Fixed costs that do not change with a change in volume. They are constant and pre-determined based on
some contract.

Variable costs that vary with a change in the sales volume.

Semi-variable costs are those which are partly fixed and partly variable.
Operational gearing can be defined as the capacity of the firm to use the fixed costs to enlarge the result of
changes in sales on its earnings before interest and tax (EBIT).
Operational gearing is said to exist when the percentage change in EBIT divided by the percentage change in
sales is greater than 1.
1. Calculation of operational gearing
Operational gearing can be calculated in several ways. Companies with high fixed costs will show high
operational gearing and their earning will therefore be very sensitive to changes in sales.
Operational gearing =
Fixed operating costs
Variable operating costs
Shows fixed costs as a proportion of variable costs
Operational gearing =
Fixed operating costs
Total operating costs
Shows what proportion of total operating costs are represented by fixed costs.
Operational gearing=
Contributo
in
PBIT
Used to show the impact a percentage change in sales will have on Profit before Interest and Taxes (PBIT).
If this ratio is 1.5 it would mean a 1% increase in sales would lead to a 1.5% increase in PBIT.
Operational gearing=
% changein PBIT
% changein sales
372
286 :Financing
FinancingDecisions
Decisions
© GTG
Co A
Tshs
million
10,000
(6,000)
4,000
(2,000)
2,000
Sales revenue
Operating costs – (variable)
Contribution
Operating costs – (fixed)
Earnings before interest and tax (EBIT)
Co B
Tshs
million
10,000
(5,000)
5,000
(3,000)
2,000
Let us assume that there is an increase in activity by 10%. The revised calculations would be:
Sales revenue
Operating costs – (variable)
Contribution
Operating costs – (fixed)
Earnings before interest and tax
This can also be solved by using the following
formula: Contribution/PBIT
Increase in EBIT
% increase in EBIT
Operational gearing (proportion of fixed costs
to variable costs)
Tshs
million
11,000
(6,600)
4,400
(2,000)
2,400
Tshs
million
11,000
(5,500)
5,500
(3,000)
2,500
1.83
400
20.00%
2.20
500
25.00%
0.30
0.54
It can be seen that, due to an increase of 10% in revenue, A's EBIT increased by 20% whereas B's EBIT increased
by 25%. The reason for a higher increase in the case of B is that B’s operational gearing is higher as its fixed costs
are higher.
2.2 Calculation of financial gearing
As explained in Learning Outcome (a) above, financial gearing is the use of fixed costs to maximise the
earnings per share. The formula for calculation of financial gearing is expressed below
Financial Gearing =
% change in EPS
% change in EBIT
EBIT
= EBIT − INT
Relation between level of gearing and risks (business risk and financial risk)
If these two levels of gearing - namely operating gearing and financial gearing - are high, the risks for the
company and its shareholders increase. The types of risk are discussed below:
(a) Financial Risk
Also referred to as the gearing risk, financial risk will be high when a company is highly geared i.e. debt
accounts for a large proportion of the capital structure. For the company, this equates to high borrowing and
high interest payments. A company with a relatively higher proportion of debt has a proportionately higher
interest burden. Changes in the interest rates will cause large changes in interest expense, and therefore, the
profit available to equity holders. The risk is borne mainly by the shareholders. If committed interest payments are
high, there is a possibility that little or nothing will be left over for the ordinary shareholders.
Profit before Interest and Tax (PBIT) for the year Tshs
100,000,000. Interest cost Tshs 60,000,000 (8% on Tshs
750,000,000).
Profit before Tax (PBT) = 40,000,000 ( Tshs 100,000,000 - Tshs 60,000,000).
If profits are reduced by Tshs 40,000,000, there will be no profits left for the equity shareholders.
© GTG
Financial Gearing and Capital Structure: 373
Financial Gearing and Capital Structure: 287
In addition, if the company does not generate sufficient profits to cover interest payments, the threat of insolvency
becomes paramount. Debt holders, if secured, suffer no real risk. Shareholders, however, stand to lose the most
in such a situation as they are given the least priority.
If the profits available are reduced, the dividend will reduce. This makes equity returns volatile. With floating interest
rates, this problem increases. Even so-called fixed rates are sometimes subject to periodical changes.
(b) Risk of Bankruptcy
If capital gearing is too high, interest payments may become unsustainable, either due to a reduction in profits
before interest or an increase in interest payments. Similarly, due to a reduction in internal funds generation
through profits, the company may not be able to honour its repayment commitments. A competitive environment
may make it difficult for a company to maintain the sustained earnings required.
The dominant lenders could bring an action of liquidation against the company if any of the defaults mentioned
above take place. Bankruptcy may cause a loss to many stakeholders. Employees could lose their jobs and
creditors and shareholders may lose part or all of their money.
(c) Credibility risk
Financial information about listed companies is readily available to the public due to the stock exchange
requirements. Informed users analyse the information, evaluate the risks discussed in (a) and (b) above, and then
decide whether to invest in a company’s debt or equity. If they find that the risk is too high, they may be reluctant
to invest in the company.
The risk of short term-ism
If debt content in the company’s finances is high, then the management may have to focus on generating
enough cash flow to meet interest commitments to avoid the threat of insolvency. This is a short-term goal as
against the long-term goal of shareholder wealth maximisation.
Impact of high level gearing on the cost of capital
The cost of capital will increase since the lenders will expect a higher interest yield whenever there is a higher risk,
as indicated by higher gearing. Similarly, shareholders will also expect a higher return on their shares. These
factors lead to an increase in the cost of capital.
(d) Business risk
The operational gearing has a direct correlation with business risk. The higher the operating leverage, the
higher is the business risk. This is the possibility of a company experiencing proportional changes in the level of
its profit before interest as a result of changes in turnover or operating costs. This will concern those companies
operating in unstable markets where demand fluctuates widely.
Companies with high fixed costs are said to have high operational gearing. As operational gearing increases, a
business becomes more sensitive to changes in turnover and the general level of economic activity and profit
before interest becomes more volatile.
High levels of gearing can also have the following consequences

As a result of higher financial risk for shareholders, their required rate of return increases, thereby pushing
up the cost of capital.

Sourcing new finance may prove difficult. Debt holders, being aware of the high interest payment commitments
the firm already has, may refuse providing additional debt finance due to the fear that their interest payments
would not be met. Potential shareholders may see the company as being too high risk and opt not to take
up the shares.

If new debt finance is obtained, to compensate lenders for the high risk, the cost of debt would increase pushing up the company’s cost of capital.
In an attempt to continue to meet committed fixed costs and interest payments, managers may focus more on
averting the short term threat of insolvency and neglect the overall goal of shareholder wealth maximisation.
374 Financing Decisions
288: Financing Decisions
© GTG
XYZ Ltd. produces 10,000 units of auto parts. The selling price is Tshs 5,000 and variable cost is Tshs 2,000.
Fixed costs are Tshs 24,000,000. The sales have increased by 10%. Also, the company has borrowed Tshs 10
million @10% pa.
Let’s estimate the impact on EBIT. In the above case, we need to estimate the operating gearing first.
Particulars
Tshs
Sales
Less variable costs
50,000,000
(20,000,000)
Contribution
Less Fixed costs
(24,000,000)
EBIT
Less Interest
( 1,000,000)
30,000,000
6,000,000
EPS
5,000,000
Operational gearing=
% changein PBIT
% changein sales
= Contribution / EBIT
= Tshs 30m/ Tshs 6m
= 5 times
Therefore 10% change in sales, causes 50% change in profits.
Financial Gearing =
EBIT
EBIT − INT
= Tshs 6 million/ Tshs 5 million = 1.2 times
SOFP for X tools Ltd for the year ended 31 December 20X3:
Equity and Liabilities
Equity capital
(10,000 shares of Tshs 200 each)
15% debentures
Reserves and surplus
Current liabilities
Tshs
million
200
250
35
110,
595
Assets
Non-current assets (net)
Current assets
Additional Information given:
Fixed costs per annum (excluding interest) 100,000,000 Tshs
Variable operating cost ratio
75% Total asset
turnover
3.5
Income tax
30%
Calculate
(a) Earnings per share.
(b) Operating leverage and the impact on PBIT of a 10% decrease in sales.
(c) Financial leverage using a SOFP approach.
Tshs
million
350
245
595
Financial
Gearing
and
Capital
Structure:
375
Financial
Gearing
and
Capital
Structure:
289
© GTG
1. Effect on shareholder wealth
Modigliani and Miller put forward an argument (1958) that there exists an optimal capital structure that balances
the risk of bankruptcy with the benefit of tax savings. This capital structure will give higher returns to the equity
holders than they would receive from a company with only equity capital.
It is said that, due to globalisation of the economy, the rate of change in different industries has increased.
There is an immense pressure from competition. In this situation, excessive use of debt in order to increase the
returns to shareholders may endanger the long-term existence of a company. Management should not take a
short-term view and maximise the returns in the short run, at the cost of long-term survival.
If a company can generate returns on capital in excess of the interest payable, the financial gearing will raise
the earnings per share. However, gearing will also increase the variability of returns for the shareholders.
Capital structure swaps and shareholder wealth
Some analysts suggest that, in cases where a firm’s debt or equity has been mis valued, swapping debt for equity
or equity for debt, may lead to maximisation of shareholders’ wealth. Which tactic to adopt depends upon the
circumstances. For example, if a firm’s debt and equity are both undervalued, the optimal swap may be to issue
undervalued equity (which is an exception to the conventional rule).
2.3 Combined gearing
Combined gearing is a measure of total risk of the company. Combined leverage is a combination of operating
leverage and financial gearing. As explained earlier, operating gearing has an effect on business risk / operating
risk and financial gearing has an effect on financial risk.
Operational gearing=
Financial Gearing =
% changein EBIT
% changein sales
% change in EPS
% change in EBIT
Combined Gearing =
% changein EBIT
x
% changein sales
OR
Degree of combined gearing =
% change in EPS
% change in EBIT
Contribution
EBIT
x
=
EBIT
EBIT − Int
=
% change in EPS
% change in sales
Contribution
EBIT − Int
Futures Ltd has the following details:
Sales
Tshs 24,000 million Fixed
costs Tshs 10,000 million Variable
cost 50% of sales.
Borrowings comprise Tshs 10,000 million of term loans @10%.
The equity share capital is Tshs 10,000 million
Let’s calculate all the three gearing ratios.
Particulars
Sales
Less: variable costs
Contribution
Less: Fixed costs
EBIT
Less: Interest
EBT
Tshs million
24,000
(12,000)
12,000
(10,000)
2,000
(1,000)
1,000
Continued on the next page
376 Financing Decisions
290: Financing Decisions
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(i) Operating gearing
Operational gearing=
Contributo
in
PBIT
= 12000/2000 =6times
(ii) Financial gearing
EBIT
EBIT − INT
= 2000/1000 = 2 times
(iii) Combined gearing
Contribution
EBIT − Int
= 12000/1000 = 12 times
Combined gearing can also be computed as
= Operating gearing x Financial gearing
=6x2
= 12 times
3. State the basic capital structure theories (the traditional theories, the net operating theory,
the Modigliani and Miller theories, bankruptcy and agency costs, personal taxes).
Discuss critically whether or not a company, by adopting a particular capital structure, can
influence its value or its cost of capital.
[Learning Outcomes c and d]
Boris, the CMD of Sirob Plc, wants his company to have a capital structure which maximises its value. He
calculated that, with a certain degree of debt in the capital structure, the overall cost of capital of the company
goes down, but with increased risk perception, the cost of equity goes up, causing the overall cost of capital to
rise. Accordingly, the value of the firm goes down because of the increase in the cost of capital.
Being perplexed with the complex scenario, Boris contacted a management accountant who explained to him that
the capital structure has nothing to do with the value of the company, i.e. a company may have any capital
structure, but it will not affect the value of the company.
3.1 The traditional approach of capital structure
1. The traditional view
The traditional approach to valuation and leverage assumes that there is an optimal capital structure and that a
firm can increase its total value through the judicious use of leverage. The approach suggests that the firm can
initially lower its cost of capital and raise its total value through leverage. Although investors raise the expected
rate of return because of increased risk perception, the increase in the cost of equity (k e) does not offset
entirely, the benefit of using ‘cheaper’ debt funds.
With the increase in leverage, the investors start demanding a higher equity rate of return from the firm. The firm
keeps borrowing until the equity rate of return demanded by the investors offsets the benefit of ‘cheaper’ debt
funds.
Financial
Gearing
and
Capital
Structure:
377
Financial
Gearing
and
Capital
Structure:
293
© GTG
In one variation of the traditional approach, ke is assumed to rise at an increasing rate with leverage, whereas
the before-tax cost of debt (ki) is assumed to rise only after significant leverage has occurred. At first, the weighted
average cost of capital declines with leverage because the rise in ke does not offset entirely the benefit of use of
cheaper debt funds. As a result, the weighted average cost of capital (ko), declines with moderate use of leverage.
After a point, however, the increase in ke more than offsets the use of cheaper debt funds in the capital
structure, and ko begins to rise. The rise in ko is supported further, once ki begins to rise. The optimal capital
structure is the point at which ko is at its minimum. Hence, the traditional position implies that the cost of capital is
not independent of the capital structure of the firm and that there is an optimal capital structure.
The effect on cost of capital of a change in capital structure is depicted below:
SUMMARY
2. Implications of traditional approach
(a) To minimise its cost of capital, a company should raise debt finance until it achieves the optimal level of
gearing.
(b) After achieving the optimal level of gearing, it should maintain that level. It must raise additional capital in
part equity / part debt in order to keep the optimal level of gearing unchanged.
(c) Whilst gearing up, the company should appraise projects at the cost of the extra finance raised (the
marginal cost of capital).
(d) Since WACC remains unchanged, the cost of the extra finance will be equal to it.
Roberto Plc is expecting a net operating income of Tshs 25000million on a total investment of Tshs
2,00,000 million. The equity capitalisation rate is 11 per cent, the firm has no debt; but it would increase to
12 per cent when Tshs 50,000million is raised by issuing 5% debentures instead of equity.
13 per cent when Tshs 70,000million is raised by issuing 8% debentures instead of equity.
The market value of the firm, value of shares and the average cost of capital are shown below
Net operating income, X ,
Total cost of debt INT = KdVd
Net income, X – INT
Cost of equity, Ke
Market value of shares, Ve = X – INT/Ke
Market value of debt, Vd
No Debt
25,000
0
25,000
0.110
2,27,272
0
5% Debentures
25,000
(50,000 x 5%) 2,500
22,500
0.120
1,87,500
50,000
Tshs million
8% Debentures
25,000
(70,000 x 8%) 5,600
19,400
0.130
1,4,92,308
70,000
Total value of firm V = Ve + Vd
Average cost of capital Ko = X/V
2,27,272
0.110
2,37,500
0.105
2,19,230
0.114
This gives an idea of how the value of a company and overall cost of capital may move with a change in
leverage according to the traditional approach.
Value Adds Plc. has an EBIT of Tshs 400million. The firm has debt of Tshs 1,000 million @10% and the
current equity capitalisation rate is 16%. Calculate the current value of the firm and the overall cost of capital.
If the firm increases leverage by issuing additional Tshs 5,000million, wherein cost of debt will increase to 12%
and cost of equity will rise to 17%, what will be the impact on the firm’s value and cost of capital?
3. The underlying assumptions
378 Financing Decisions
292: Financing Decisions
The assumptions of the traditional approach to capital structure are as follows:
© GTG
(a) Tax does not exist, either at a personal or a corporate level and there is no bankruptcy cost.
(b) Firms have two choices of finance: either perpetual debt finance or ordinary equity shares.
(c) Firms can change their capital structure by issuing debt to repurchase shares, or issuing shares to pay off debt.
Accordingly, a change in the capital structure is effected immediately. It is considered that there are no
transaction costs in the issue or repurchase of capital.
(d) The business risk associated with a firm is constant over time.
(e) The firm has a policy of paying a hundred per cent of its earnings in dividends.
(f) The operating earnings of the firm are not expected to grow.
4. Criticism of the traditional approach
(a) The soundness of the traditional approach has been questioned on the grounds that the market value of the
firm depends upon its net operating income and the risk attached to it. The mode of finance can neither change
the net operating income nor the risk attached to it. It can simply change the way in which net operating
income and the risk involved in it are dispersed between equity and debt-holders. Therefore, firms with
identical net operating income and risk, but different modes of financing, should have the same total value.
(b) The traditional approach implies that the totality of risk incurred by all security-holders of a firm can be
altered by changing the way in which this totality of risk is dispersed among the various classes of
securities. However, the argument of the traditional theorists that an optimum capital structure exists can be
supported on two counts: the tax deductibility of interest charges and market imperfections.
SUMMARY
3.2 Net operating income (NOI) approach / theory
The net operating income theory suggested by Durand is that the capital structure decision of a firm is
irrelevant. Any change in leverage will not lead to a change in the total value of the firm and the market price of
the shares, as the overall cost of capital is independent of the degree of leverage.
According to this theory, the advantages of the use of debt are offset by an increase in the equity capitalisation
rate. This is because equity shareholders demand higher rate to compensate for the increased risk. The critical
assumption in this theory is that ko is constant regardless of the degree of leverage. The break down between debt
and equity is irrelevant as the market capitalises the firm as a whole. An increase in the use of debt is compensated
by an increase in the cost of equity ke . Since cost of capital cannot be changed with changes in capital structure,
there is no optimal capital structure.
The NOI theory is largely definitional and does not offer behavioural support which was provided by Modigliani
and Miller. They provided behavioural support to the independence of the firm value and cost of capital from its
capital structure.
Financial
Gearing
and
Capital
Structure:
379
Financial
Gearing
and
Capital
Structure:
295
© GTG
Diagram 2: Leverage and cost of capital (NOI approach)
Peter & Co. has operating income of Tsh 5,000 million. The firm employs Tshs 15,000 million of long term debt
@10%. The overall cost of capital is 15%.
By using the NOI theory, let’s determine the value of the firm and the cost of equity.
Net operating income / EBIT
Less: Interest on debt
Earning s available to equity shareholders
Cost of capital of the firm
Value of the firm
= EBIT/ Ko
=5000/0.15
Tshs million
5,000
(1,500)
3,500
15%
33,333.33
Cost of equity = Ke = Earnings available to equity shareholders / Value of equity
Market value of equity = Value of firm – market value of debt
= 33,333-5,000 = Tshs 18,333m
Cost of equity = Tshs 3,500 m/ Tshs 18,333 m = 19.09%
A firm has the following operating parameters: Operating income Tshs 8,000 million, outstanding debt
Tshs 25,000m and interest rate
12%.
Required:
(a) Calculate the firm’s value and equity capitalisation rate if the overall capitalisation rate is 12.5%.
(b) Determine the impact on the firm’s value and equity capitalisation rate if the firm increases the debt from
Tshs 25,000m to Tshs 35,000m and uses the proceeds to repurchase equity.
3.3 Modigliani and Miller on capital structure
1. The views of Miller and Modigliani on capital structure, considering that no corporate tax exists
Modigliani and Miller argue that, in the absence of corporate tax, a firm’s market value and cost of capital remains
indifferent with capital structure changes. In their 1958 articles, they provide analytically sound and logically
consistent behavioural justification in favour of their hypothesis, and reject any other capital structure theory.
380 Financing Decisions
294: Financing Decisions
© GTG
2. The assumptions that Modigliani and Miller made
The hypothesis of Modigliani and Miller is based on certain assumptions. These assumptions relate particularly
to the behaviour of investors, the capital market, the firm and the tax environment. The assumptions are as follows:
(a) Securities (shares and debt instruments) are traded in the perfect capital market situation. This specifically
means that investors are free to buy or sell securities; they can borrow without restriction at the same terms
that firms do; and they behave rationally. It is also presumed that there are no transaction costs for the
securities.
(b) Firms can be grouped into homogeneous risk classes. Firms are considered to be in a homogeneous risk
class if their expected earnings have identical risk characteristics. It is generally implied under the MM
hypothesis that firms within the same industry constitute the homogeneous class.
(c) The expected NOI is a random variable, with a constant mean probability distribution and a finite variance. (d)
Hence, the risk to investors depends on both the random fluctuations of the expected NOI, and the
possibility that the actual value of the variable may turn out to be different than their best estimates.
(e) Firms distribute all net earnings to the shareholders, which mean that there will be no retained earnings.
(f) There are no restrictions on lending and borrowing. All the market participants borrow at a single rate of
interest.
(g) In their initial hypothesis, Modigliani and Miller assume that no corporate income tax exists.
3. The hypothesis
The Modigliani-Miller hypothesis is based on the idea that no matter how we divide up the capital structure of a
firm among debt, equity, and other claims, the total investment value remains unaltered. This is because the
total investment value of a corporation depends upon its underlying profitability and risk; it is invariant with respect
to relative changes in the firm’s financial capitalisation.
Hence, the finance mix has no effect on the weighted average cost of capital or market value of the firm.
The support for this position rests on the idea that investors are able to substitute personal for corporate leverage,
thereby replicating any capital structure the firm might undertake. Since the firm is unable to do something for its
stockholders (leverage) that they cannot do for themselves, capital structure changes are not a thing of value in
the perfect capital market world that MM assumes.
Therefore, two firms alike in every respect except capital structure must have the same total value. If not, arbitrage
will be possible, and its occurrence will cause the two firms to sell in the market at the same total value.
Diagram 3: Overall cost of capital remains unaltered despite changes in Ke and Kd
Financial
Gearing
and
Capital
Structure:
381
Financial
Gearing
and
Capital
Structure:
295
© GTG
The following is data regarding two companies, Venus Ltd and Jupiter Ltd, belonging to the same risk class:
Tshs ’000s
Venus Ltd
Jupiter Ltd
Number of ordinary shares
1,80,000
3,00,000
Market price per share
Tsh1200
Tsh1000
6% Debentures
120,000
NIL
Profit before interest
36,000
36,000
All the earnings remaining after payment of debenture interest are distributed as dividends among the
shareholders.
Required:
Explain how, under the Modigliani and Miller approach, an investor, Mr. Mercury, holding 10 per cent shares in
Venus Ltd will be better off switching his holdings to Jupiter Ltd.
Answer
Arbitrage process
Step
1
Initial investment
Tshs ’000s
Particulars
Mr. Mercury's current position in Venus Ltd with 10 per cent equity holdings:
(i) Investments (18,000 shares x Tshs 1200)
(ii) Dividend income 0.10 x ( Tshs 36,000,000 - Tshs 7,200,000 (W1))
2
Funds available after selling initial investment
He sells his holdings of Venus Ltd for Tshs 21,600,000 and creates a personal
leverage by borrowing Tshs 12,000,000 (0.10 x Tshs 120,000,000). Therefore,
the total amount available to him is:
3
3,600
Calculation of Net income
Gross income
Less: Interest on personal borrowings (0.06 x Tshs 12,000,000)
Net income
5
33,600
Calculation of Gross income
Mercury purchases 10 per cent equity holdings of Jupiter Ltd for Tshs
30,000,000 (30,000 shares x Tshs 1,000); his dividend income is Tshs
3,600,000 ( Tshs 36,000,000 x 0.10).
Hence, Gross income is:
4
21,600
2,880
3,600
(720)
2,880
Conclusion
He breaks-even by investing in Jupiter Ltd. However, in the process, he
reduces his investment outlay by Tshs 3,600,000. Therefore, he is better off by
investing in Jupiter Ltd.
Alternatively, by investing Tshs 33,600,000, he could augment his income to
$3,312:
Dividend income from Jupiter Ltd Tshs 36,000,000 x
Less: Interest on personal borrowings
Net income
Working
W1 Interest on Debentures = Tshs 120,000,000 x 6% = 7,200,000.
Tshs 33,600,000
Tshs 300,000,000
4,032
(720)
3,312
382 Financing Decisions
296: Financing Decisions
© GTG
4. Calculation of the cost of equity
This formula can be derived from MM’s definition of the average cost of capital. The expected yield on equity or
the cost of equity is defined as follows:
𝐾𝐾𝑒𝑒 =
𝑋𝑋 − 𝐾𝐾𝑑𝑑 𝑉𝑉𝑑𝑑
Where,
𝑉𝑉𝑒𝑒
………………….. (1)
X is expected net operating income
Ke is cost of equity Ve
is value of equity Kd is
cost of debt and Vd is
value of debt
Again,
𝑋𝑋
𝐾𝐾𝑒𝑒 = 𝑉𝑉 ……………….. (2)
Where:
Ko is the overall cost of capital
V is the value of the firm
Since Ko and V are constant, according to Miller and Modigliani’s hypothesis,
therefore,
X = K0V = K0 (Ve + Vd) …….(3)
Substituting equation (3) in equation (1),
i.e.
i.e.
𝐾𝐾𝑒𝑒 =
𝐾𝐾𝑒𝑒 =
𝐾𝐾0 (𝑉𝑉𝑒𝑒 + 𝑉𝑉𝑑𝑑 ) − 𝐾𝐾𝑑𝑑 𝑉𝑉𝑑𝑑
𝑉𝑉𝑒𝑒
𝐾𝐾0 𝑉𝑉𝑒𝑒 + 𝐾𝐾0 𝑉𝑉𝑑𝑑 − 𝐾𝐾𝑑𝑑 𝑉𝑉𝑑𝑑
𝑉𝑉𝑒𝑒
𝐾𝐾𝑒𝑒 = 𝐾𝐾0 𝑉𝑉𝑒𝑒 +
( 𝐾𝐾0 − 𝐾𝐾𝑑𝑑 )𝑉𝑉𝑑𝑑
𝑉𝑉𝑒𝑒
5. The views of Miller and Modigliani on capital structure considering that corporate tax exists
Modigliani and Miller’s hypothesis that the value of the firm is independent of its leverage in capital structure is
based on the critical assumption that corporate income tax does not exist.
This is not a realistic assumption. In reality, corporate income tax does exist, and interest paid to debt holders is
treated as a deductible expense. Dividends paid to shareholders, on the other hand, are not tax deductible. Hence,
unlike dividends, the return to debt-holders is not subject to taxation at the corporate level. This makes debt
financing advantageous. In their 1963 article,
Modigliani and Miller show that the value of the firm will increase with debt due to the deductibility of interest
charges for tax calculation, and the value of the levered firm (i.e. the firm with debt in its capital structure) will be
higher than the un-levered firm (that is, the firm without debt in its capital structure).
Financial Gearing and Capital Structure: 383
Financial Gearing and Capital Structure: 297
© GTG
Valuation of levered and unlevered firm
Consider the following two firms
VI Inc is levered with debt of Tshs 2,000,000. The cost of debt for VI Inc is 8%.
Vee Inc is an unlevered firm. Its cost of equity is 10%.
Both the firms have Tshs 2,000,000 as net operating income.
The tax rate applicable is 40%.
The value of both the firms can be calculated by using the following method.
Calculation of net profit, after tax
Net operating income
Less: Interest (8% of Tsh2,000,000)
Net profit before tax
Less: Tax @ 40%
Net profit after tax
Value of Vee Inc =
=
Tshs ‘000
VI Inc
2,000
(160)
1,840
(736)
1,104
Vee Inc
2,000
2,000
(800)
1,200
Net profit after tax
cost of equity
Tshs 1,200,000
0.10
= Tshs 12,000,000
Amount available to the shareholders and debt holders of VI Inc = Interest + Net profit after tax
= Tshs 160,000 + Tshs 1,104,000
= Tshs 1,264,000
Amount available to the shareholders and debt holders of Vee Inc = Interest + Net profit after tax
= Tshs 0 + Tshs 1,200,000
= Tshs 1,200,000
Tax Shield available to VI Inc = Excess amount available to shareholders and debt holders of VI
= Tshs 1,264,0000 - Tshs 1,200,000
= Tshs 64,000
VI Inc can expect to enjoy this tax shield forever. Hence, it is perpetuity.
Present value of perpetuity =
Here,
A = Tax shield
r = cost of debt
A
r
Hence,
Present value of Tax shield
=
Tshs
64,000
0.08
384 Financing Decisions
298 : Financing Decisions
= Tshs 800,000
© GTG
Alternatively, the present value of the tax shied = T x Value of debt
= 0.4 x Tsh2,000,000
= Tshs 800,000
Hence VI Inc (levered firm) is worth Tsh800,000 more than Vee Inc (unlevered firm).
Value of VI Inc = Value of unlevered firm + (T x Value of debt)
= Tshs 12,000,000 + Tshs 800,000
= Tshs 12,800,000
3.4 Bankruptcy costs
Bankruptcy costs are an important imperfection that affects capital structure decisions. They involve liquidation
of assets at distress values when the company is about to become bankrupt. They also involve operational
inefficiencies and legal and administrative costs.
In a perfect capital market situation, it is assumed that there is no bankruptcy. However, in the event of bankruptcy,
creditors have to bear the load on account of shortfall of economic values of assets as well as administrative costs.
This makes a firm that is highly geared / leveraged less attractive than an unleveraged firm. Although creditors
bear the bankruptcy costs, they will pass it on to the equity shareholders in the form of higher cost (factored in
the interest rates). Therefore, bankruptcy costs have a direct (negative) effect on the value of the firm and the cost
of capital.
As the leverage increases, investors would penalise the price of the stock. With an increased probability of
bankruptcy, equity shareholders increase their required rate of return at an increasing rate beyond certain point.
Thus, in addition to the premium for business risk and financial risk, there is a need for increased return at a higher
rate to compensate for bankruptcy costs.
In case the effect of taxes are included, as the company increases its gearing, the present value of tax shield
will rise for some time. However, high leverage will be penalised by investors if the possibility of bankruptcy
rises at an alarming rate with increased leverage.
Initially, the tax shield on debt will exert a positive effect on the firm’s value. Over a period of time, the possibility
of bankruptcy and related costs will become pertinent. This in combination with the tax shield uncertainty and
will cause a firm’s value to increase at a lower rate - and decline later.
The effect of bankruptcy costs on the value of a firm is expressed below:
Value of firm = Value of unlevered firm + PV of net tax shield of debt - PV of bankruptcy costs
3.5 Agency costs
Jensen and Meckling have expounded a theory of agency costs. This theory shows that the monitoring costs
(costs associated with monitoring all aspects of business operations) have to be borne by the stakeholders
irrespective of who makes the monitoring expenditures.
Debt holders demand higher return anticipating monitoring costs. The higher the monitoring costs, the higher
will be the interest costs and the lower will be the firm value. The equity shareholders have an interest in seeing
that these costs are minimised.
There is a trade-off between high interest rates and agency costs. Debt holders may charge very high interest
rates if there is an absence of protectionist measures which would cost stakeholders more than the agency
costs associated with the existence of reasonable protectionist measures. A right balance has to be struck between
agency costs and interest rates charged on the debt utilised by the firm.
Some activities are expensive to monitor like production and investment decisions. Dividend and financing
decisions can be monitored at moderate cost. Furthermore, efficient monitoring should be done. Services of
experts like auditors can be used for the purpose.
Like bankruptcy costs, agency costs may restrict the use of debt beyond a point. With increased debt, creditors
might demand closer monitoring, leading to increased agency costs. Therefore, firm value would decrease due
to increased agency costs at gearing beyond a point.
Financial Gearing and Capital Structure: 385
© GTG
Financial Gearing and Capital Structure: 299
Diagram 4: Value of firm with taxes, bankruptcy costs and agency costs
The two companies, Rose Ltd and Marigold Ltd, belong to an equivalent risk class. They are identical, except
that Marigold Ltd. has a debt of Tshs 75,000,000 @10%. The other details are as follows:
Equtiy capitalisation rate
EBIT ( Tshs )
Rose Ltd
0.15
18,750,000
Marigold Ltd
0.20
18,750,000
An investor holds 10% in the leveraged company. Show the arbitrage process and the amount by which he
would reduce his outflow through the use of leverage. When will the arbitrage process end according to Modigliani
and Miller?
Explain how bankruptcy costs influence the value of a firm.
4. Identify and explain the effect of capital gearing on investors’ perception of financial risk
and return.
[Learning Outcome e]
In the previous Study Guide on cost of capital, we have discussed the return expected by an investor under
capital assets pricing model (CAPM). The following equation lays down the relationship explained in the model
()
(
E r i =R f + i E(r m ) - R f
)
Where,
E(rj) = The rate of return of security j, as projected by the model
βj = The beta coefficient of security j
Rf = The minimum risk-free rate of return
E(rm) = The return of the market
The main components of the model can be identified as
beta coefficient of the security
minimum risk-free rate of return
premium expected for the risk the security. It is the difference between the market return and the risk free
return.
386 Financing Decisions
300 : Financing Decisions
© GTG
4.1 Adjustment for gearing
In the above determination of risk adjusted return, there is no leverage which is considered. As discussed
earlier, capital gearing has a significant impact on investor perception of risk and return. Therefore, the beta and
required return will increase with an increase in the leverage of the firm.
In the case of an unlevered entity, the required return is adjusted for business risk premium. However, in the
case of a leveraged entity, the required return is to be adjusted for a premium for financial risk as well.
The tax advantages on leverage also need to be considered while adjusting the beta. Under these conditions,
Robert S Hamada and others have demonstrated that the required rate of return on stock is
Rj = Rf + (Rm − Rf) f) [1 + D/S(1 − t)]
Where
ju is the beta measuring the responsiveness of the excess return for the security in the absence of leverage to
the excess return for the market portfolio.
Thus, overall return is composed of risk-free rate Rf plus a premium for business risk (Rm – Rf)
for financial risk.
ju and
a premium
D/S is the debt to equity ratio in market value terms
T – corporate tax rate
Rearranging the variables, the beta for the stock in the absence of leverage is
𝐵𝐵𝑗𝑗𝑗𝑗 =
𝛽𝛽𝑗𝑗
𝐷𝐷(1 − 𝑡𝑡)
1+
𝑆𝑆
Let’s assume the measured beta for a security j is 1.5, debt equity ratio is 0.75 and tax rate is 30%. To calculate
the beta in the absence of leverage:
𝐵𝐵𝑗𝑗𝑗𝑗 =
1.5
1.5
=
= 0.983
0.75 × 0.7 1.525
1+
1
Therefore, we are able to arrive at the adjusted beta of the security for a different proportion of debt.
Calculate the beta for a security if the debt equity mixes changes to 0.60. Current details are: Debt equity
0.7, beta for the security: 1.20 and tax rate 30%.
FinancialGearing
Gearingand
andCapital
CapitalStructure:
Structure:301
387
Financial
© GTG
5. Determine the implications of debt financing on the return to shareholders under various
financing alternatives using both EBIT-EPS and ROI-ROE analyses.
[Learning Outcome g]
One of the key objectives in designing an optimal capital structure is to maximise the shareholder value i.e.
earnings per share (EPS) over the firm’s expected range of operating income (EBIT). EPS is an important measure
of investment value. This measures the return on shareholder investment. EBIT-EPS analysis is an important tool
in deciding the best financing alternative. The aim of EBIT-EPS analysis is to find the level of EBIT that will
equate to EPS, irrespective of the financing plan.
5.1 Financial break even
Financial break-even point is that level of EBIT which will cover the firm’s fixed financing charges i.e.
interest on all debt plus preference dividend.
At this level EPS will be zero and at a level below the financial break even point the fixed financing charges will
not be covered and EPS will be negative. Beyond this point, increase in EPS is more than the increase in EBIT.
Financial break even (FBR) can also be expressed as
I+
Dp
1− t
where I = interest charges,
Dp = preference dividend and t = tax rate
5.2 Indifference point
This is the level of EBIT at which EPS is the same among different financing options. Therefore, at this level of
EBIT, a finance manager is indifferent between various capital structures. Beyond this point, the benefits of
financial gearing begin to operate, i.e. it is beneficial to use debt as it would add value to shareholder wealth
through an increase in EPS. The reverse is true when the EBIT is less than the indifference point.
The indifference point is calculated mathematically as follows:
(EBIT − I1)(1 − t)
E1
=
(EBIT − I2)(1 − t)
E2
Where EBIT – Indifference point
E1 = Number of shares in first financing option
I1 = Interest charges in first financing option
E2 = Number of shares in second financing option
I2 = Interest charges in second financing option
T = tax rate
Trustwell Ltd has provided the following information:
(i) Investment proposal Tshs 5,000,000.
(ii) Financing options:
100% equity
50% debt 50% equity
50% preference shares 50% equity
(iii) Cost of debt is 10%, preference shares is 10%,
(iv) tax rate 30%
(v) Expected EBIT Tshs 2,000,000
(vi) Equity shares of Tshs 25 each issued at a premium of Tshs 25 per share
Continued on the next page
388 Financing Decisions
302 : Financing Decisions
© GTG
Let’s first determine the EPS under each plan and the financial break even, and then determine which plans are
preferable.
Tshs
Plan
1
2
3
EBIT
Less: Interest
2,000,000
2,000,000
EBT
2,000,000
1,750,000
2,000,000
Taxes @30%
(600,000)
(525,000)
(600,000)
EAT
1,400,000
1,225,000
1,400,000
(250,000)
Less: Preference dividend
Earnings for equity shareholders
2,000,000
(250,000)
1,400,000
1,225,000
1,150,000
100,000
50,000
50,000
14.0
24.5
23.0
No of equity shares
EPS (Tsh)
The financial break- e v e n point is the point at which fixed financing costs are met. In the above 3 plans,
the financial break-even point is as follows:
Plan 1 = 0
Plan 2 = Tshs 250000
Plan 3* = Tshs 833333 (Tsh250000/0.3)
* Since preference dividend has to be grossed up to the extent of tax (30%), to arrive at the minimum required
EBIT.
Now let’s measure the indifference point between the different financing plans:
(a) Indifference point between plan 1 and 2
(EBIT-0)(1-0.3)/1,00,000 = (EBIT-250000)(1-0.3)/50000
= 50000(0.7EBIT) = 100000(0.7EBIT-175000)
= 0.7EBIT = 2(0.7EBIT – 175000)
350000 = 0.7EBIT
EBIT = Tsh500,000
(b) Indifference point between plan 1 and 3
((EBIT-0)(1-0.3))/100000 = ((EBIT-0)(1-0.3)-250000)/50000
0.7EBIT/100000 = (0.7EBIT-250000)/50000
0.7EBIT = 2(0.7EBIT-250000)
500000 = 0.7EBIT
EBIT = 714286
(c) Indifference between plan 2 and 3
((EBIT-25000)(1-0.3))/50000 = ((EBIT-0)(1-0.3)-250000)/50000
0.7EBIT-17500 = 0.7EBIT-25000
This is absurd; therefore, there is no indifference point in the above case.
In case the financing plan includes preference shares, to calculate the financial breakeven point, preference
dividend has to be taken gross of tax.
© GTG
Financial Gearing and Capital Structure: 389
Financial Gearing and Capital Structure: 303
1. Graphic Representation
Another way of evaluating the impact of various financing alternatives is to prepare an EBIT graph. Under this, we
plot the EPS at each level of EBIT. EBIT is taken on the X-axis and EPS is plotted on the Y-axis. A straight line
representing the EPS at various EBIT levels is drawn. The point where the two lines intersect is the point of
indifference between two financing options. At this point, i.e. the level of EBIT, we are indifferent between the
financing options.
Diagram 5: EBIT – EPS Analysis
Let’s prepare a graphic representation of the above example of Trustwell
Diagram 6: EBIT- EPS graph
From the above graphic representation, it can be clearly seen that although plans 1 & 2 and plans 1 & 3 have an
indifference point, plans 2 and 3 does not have an indifference point. In the case of EBIT levels greater than the
indifference point, it is better to use debt capital. Moreover, in the case of EBIT levels being below the
indifference point, it is better to remain unlevered.
The finance manager of Smart Work Ltd. requires Tshs 100 m to finance a new venture. He can either finance the
entire cost by issuing equity shares @ Tshs 1000 face value or 50% debt can be deployed. The debt would be
in the form of 10% debentures. Tax rate applicable is 30%. Calculate the indifference point.
390 Financing Decisions
304 : Financing Decisions
© GTG
2. Indifference point using market value basis
Another way of measuring shareholder value is the maximisation of market value of the firm. Thus, the
indifference point is calculated on the basis of the level of EBIT, for which the market values are the same under
different financing options.
P/E1[
(EBIT)(1 − t) = P/E2[ (EBIT − I)(1− t) ]
]
E1
E2
Where
P/E 1 = P/E ratio of unlevered firm
P/E 2 = P/E ratio of levered firm
t = Tax rate
E1 = Number of shares in first financing option
E2 = Number of shares in second financing option
I = Interest charges in second financing option
Let’s determine the indifference point using market value basis and considering the following information
Existing capital structure 50,000 shares at Tsh 100 per share
Funds needed Tsh5,000,000
Existing leverage 10% debt Tsh 2,000,000
Required funds can either be raised by new debt @15% or equity issue of 20,000 shares @Tsh250
P/E ratio is 7 times in equity alternative and 6 times in debt alternative
Tax rate 30%
P / E1[
(EBIT − I1)(1 − t)
]
E1
= P / E2[
(EBIT − I2)(1 − t)
]
E2
(EBIT − 2,00,000)(1 − 0.30)
]
70000
= 6[
(EBIT − 9,50,000)(1 − 0.3)
]
50000
7[
(EBIT − 2,00,000)(0.7
]
70,000
= 6[
(EBIT − 9,50,000)(0.7)
]
50,000
7[
0.7EBIT − 140,000
]
70,000
= 6[
(0.7EBIT − 665,000)
]
50,000
7[
4.9EBIT − 980,000
7
=
4.2EBIT − 3,990,000 )
]
5
24.5EBIT-4,900,000 = 29.4EBIT – 27,930,000
4.9EBIT = 23030000
EBIT = Tshs 4,700,000
Financial Gearing and Capital Structure: 391
Financial Gearing and Capital Structure: 305
© GTG
6. Discuss the issues that must be kept in mind when determining optimal/target capital
structure of a firm.
[Learning Outcome g]
We have discussed in the earlier sections how the capital structure affects the cost of capital and the value of
the firm. While trying to achieve the basic objective of maximisation of shareholder wealth and firm value, the
finance manager is faced with a constant challenge of determining the optimal / target capital structure.
There are numerous factors/ issues which need to be dealt with before deciding on the level of gearing in the
capital structure. While the use of debt provides a tax shield and enhances the EPS, there is also a need to
evaluate the financial distress which can be caused by increased leverage. The ill effects of high gearing could be
in the form of short term liquidity crisis, danger of bankruptcy and erosion of firm value.
While the finance manager strives to build an optimal capital structure, in the real world, the task is extremely
challenging with complex parameters affecting both the industry in general and the company in particular.
Practically speaking, what the finance manager tries to build is a suitable capital structure in the back drop of
the market and operational restrictions. In this section, let’s discuss the issues which should be kept in mind
while determining the target capital structure.
1. EBIT-EPS analysis
This analysis calculates the impact of various financial plans on EPS at various levels of EBIT. As discussed
earlier, EBIT-EPS analysis calculates the point of indifference between two financing alternatives. At EBIT levels
greater than the indifference point, the debt alternative would be more beneficial and below that point equity
alternative would be preferred. At higher EBIT levels, assuming limited probability of it moving downward, it is
better to employ debt capital. The indifference point is computed as follows:
Equity Plan
Debt-equity plan
(EBIT)(1 − t)
E1
=
(EBIT − I2)(1− t)
E2
Another important aspect to be discussed is the ability of the firm to service debt, described as coverage ratios:
interest coverage ratio and debt service coverage ratio.
Interest coverage ratio =
Profit before interest and tax
Interest expense
Debt service coverage ratio =
Profit After Tax + Interest + Depreciation + Other non - cash expenses
Interest + Principal repayments
2. Requirement of management control
The capital structure also depends on the stand of management on dilution of control. Lenders do not have a direct
involvement in the operating management of the company. They exercise indirect control through covenants in
the agreement. In the absence of any default they do not interfere with the decisions taken by the Board. Same is
case with preference shareholders. The management control lies with the equity shareholders who are the owners
of the firm. Therefore, if the operating management wants to maintain control, it would opt for increasing financial
gearing to finance any new venture. However, this is possible only so long as there is no default.
Furthermore, in the case of closely held companies where the management wishes to retain control, they may
prefer to issue additional equity. However, in the case of a public limited company listed on a recognised stock
exchange where the shareholders’ interest is restricted to a reasonable return on investment, they may prefer
not to get involved in active management.
3. Cash flow analysis
This involves analysing the liquidity position of the company. It is very critical to go beyond EBIT-EPS analysis
and determine the actual cash position of the company to meet their fixed financing charges. Although ratios might
seem healthy, it is important to determine the actual cash position / composition of liquid assets representing the
EBIT.
392 Financing Decisions
306 : Financing Decisions
© GTG
Cash flow analysis involves
(a) Analysing the liquidity position of the company; while the EBIT-EPS analysis is concerned with leverage
analysis.
(b) Taking into account the changes in current assets and current liabilities and the net current asset position of
the company.
(c) A dynamic analysis extending over a period of time as compared to EBIT-EPS analysis which is static in
nature i.e. restricted to one year.
(d) Analysis of the risk of financial distress i.e. it measures the financial resources available during a downturn
On one hand, sources of finance have an impact on cash flow forecasts in various ways and on the other hand,
cash flow forecasts also influence how the finance is to be obtained from different sources. Cash flow forecasts
give management a picture of the expected cash flows and the extent and timing of problems, if any. This enables
management to respond to these problems appropriately.
(a) Debt finance entails commitments of interest payments as well as principal repayments on certain dates.
Cash flow forecasts have to provide for these. Defaults on payments may result in serious outcomes such
as lenders taking legal action against the company.
(b) For equity finance, usually there is no payment against the principal amount, unless management decides
on a buyback of shares. Buy back of shares cannot be planned without studying the cash flow forecasts.
(c) Dividends on equity finance depend on the dividend policy followed by management. Usually they have to
be paid within a certain period after dividends are declared. Cash flow forecasts will provide for these.
A company is experiencing a lean period. Projected sales growth of 25% may not materialise. Instead, a moderate
growth of 5% is more likely. A cash flow forecast enables the company to assess the impact of this shortfall.
Committed payments on account of debt interest and repayments are Tshs 500m.
However, the funds to be generated from operating activities according to the revised estimates are likely to be
only Tshs 400m. There is a risk of a shortfall of Tshs 100m in servicing the debt according to the cash flow forecast.
Management has to take timely action to avert a disaster on this front, for example, enhancing bank limits, resorting
to additional borrowings, or selling assets in order to generate extra cash.
4. Probability of cash insolvency
The important question here is not so much as to whether the coverage ratio will fall below 1, but what the
probability of insolvency is. According to Van Horne, cash budgets can be prepared for a range of possible
outcomes with probabilities attached to it. This will help in judging the firm’s ability to meet fixed obligations.
Apart from projected earnings, the purchase / sale of assets, dividend payout, liquidity position and other cash
flow determinants are taken into account. Given the probabilities of particular cash flow sequences, the finance
manager is able to determine the fixed financing obligation that the firm can still undertake, while remaining
within the insolvency limits tolerable to management.
Donaldson suggests that the ultimate concern of a company is whether cash balances during some future
period will be involuntarily reduced below zero. Therefore, cash flows are examined under adverse conditions. He
defines net cash balance in a recession as
CBr = CB0 + NCFr
CB0 = cash balance at start of recession
NCFr = net cash flows during recession
The probability distribution of expected cash flows is calculated, and the cash flow behaviour is analysed during
recession. By summing up, the cash balance at the beginning (CB0) with probability distribution of recession
cash flows NCFr CBr is prepared (i.e. probability distribution of cash balances in recession).
© GTG
Financial Gearing and Capital Structure: 393
Financial Gearing and Capital Structure: 307
5. Nature of industry
The capital structure is dependent on the nature of the industry in which the company operates. If the company
operates in an industry that is subject to extensive sales fluctuations (whether price variance or volume variance),
the level of gearing should be limited. In industries where the gestation period is high and the probability of not
meeting financial commitments in certain years exists, the possibility of financial distress is increased. In contrast,
industries with regular and inelastic demand can build an aggressive capital structure.
The level of maturity of the industry also has a bearing on the financial leverage. In a nascent industry, there
should be more deployment of own funds whereas with the passage of time, as the industry matures, the
deployment of debt capital can be increased as the earnings would then be sufficient to meet fixed obligations.
6. Industry benchmarks
It is important to draw a meaningful comparision between the financial gearing of the company and average
financial gearing of companies in the industry in which it operates. For example, if companies in the same industry
have significantly different capital structures as compared to that of the company in question, a detailed analysis
has to be done of the reasons for it. We need to determine whether the company is being over- aggressive or
others in the industry are being pessimistic.
7. Flexibility
The flexibility here refers to the ability of the firm to tamper with the sources of funds to meet a change in need
for funds. For example, if a company is operating at a significantly higher level of debt with no room for expansion,
and in case it requires additional capital, it has to be raised compulsorily through equity. In this case, equity
shareholders would demand a higher rate. Therefore, a company should raise debt up to a level that is a little
lower than the maximum debt level so that any debt capacity that is not used can be tapped for future expansion
plans. Finance managers can raise debt with call options; however, this flexibility would involve a cost which needs
to be kept in mind while designing capital structure.
8. Advice from professionals and investors
A finance manager can evaluate the opinions provided by professionals such as investment bankers, investment
analysts, institutional investors and company lenders. Market professionals have significant knowledge of the
current market scenario as well as best practices across the industry. This can help in evaluating different financing
options.
Also, the affected parties of any decision, namely the investors and lenders, can also help in arriving at a
prudent decision as the main aim of financial management is enhancing the value of the firm.
9. Tax implications
It is important to understand all tax advantages / disadvantages in deploying each source of finance. For example,
the provisions regarding deductibility of finance charges in calculation of income, provisions related to carry
forward of losses, dividend tax and other costs are relevant for decision making. Although use of debt capital
offers a tax advantage in the short term, thereby enhancing shareholder value, it is important to remember
that there is another angle of financial distress which needs to be checked for.
10. Features of the company
The features of the company in terms of its size and credit rating influence the quantum of debt and equity
which would be deployed. In the case of small companies, it is difficult to obtain debt finance at a reasonable
cost in the absence of rated papers. Therefore, they have to rely more on shareholder funds. On the other hand,
large-sized companies with good credit rating can raise capital from numerous sources at reasonable cost and
can utilise it to substitute equity.
11. Timing of raising capital
The market scenario in terms of inflationary trends, macroeconomic situations and investor sentiment has a
bearing on the issue of capital. For example, in a rising interest rate scenario, debentures can be raised at an
x% higher rate of interest only. This will push up the overall cost of capital and might make debt financing
unattractive. In some cases, the issuer may postpone the issue of debt instruments if a falling interest rate scenario
is foreseen.
394 Financing Decisions
308 : Financing Decisions
© GTG
What does cash flow analysis involve?
Answers to Test Yourself
Answer to TY 1
Determination of debt service coverage ratio
Year
a
1
2
3
4
5
6
7
8
Net
Profit
b
Tshs
(‘000s)
21,000
34,000
36,000
17,000
19,000
20,000
17,500
16,500
Depreciation
c
Tshs
(‘000s)
12,000
12,000
12,000
12,000
12,000
12,000
12,000
12,000
Interest
d
Tshs
(‘000s)
19,500
18,000
15,000
12,500
10,500
8,000
5,000
0
Cash Available
e (b + c + d)
Tsh s
(‘000s)
52,500
64,000
63,000
41,500
41,500
40,000
34,500
28,500
Principal
Instalment
f
Tshs
(‘000s)
10,000
17,500
17,500
17,500
17,500
17,500
17,500
17,500
Debt
Obligation
g (d + f)
Tshs
(‘000s)
29,500
35,500
32,500
30,000
28,000
25,500
22,500
17,500
Total
DSCR
h (e/g)
1.78
1.80
1.94
1.38
1.48
1.57
1.53
1.63
13.11
Therefore,
Average DSCR =
Total DSCR
Number of years
13.11
= 8 = 1.64
Answer to TY 2
EPS for different EBIT levels
Less
Less
Less
EBIT
Interest on bonds @10%
Earnings before taxes
Taxes @30%
Earnings after taxes
Preference dividend @10%
Earnings available for ordinary shareholders
Earnings per share: ( Tshs )
Earnings before tax and interest
Number of equity shares
Option 1
( Tshs
m) 12,000
(4,000)
8,000
(2,400)
5,600
(4,000)
1,600
BASE (
Tshs m)
20,000
(4,000)
16,000
(4,800)
11,200
(4,000)
7,200
Option 2
( Tshs
m) 28,000
(4,000)
24,000
(7,200)
16,800
(4,000)
12,800
200
900
1600
Interpretation: a 40% decrease in EBIT results in a 78% decrease in EPS (to 0.53). A 40% increase in EBIT
leads to a 78% increase in EPS (to 4.27).
Financial Gearing and Capital Structure: 395
Financial Gearing and Capital Structure: 309
© GTG
Answer to TY 3
Calculation of total sales
Tshs million
595
3.5
2,082.50
Total assets
Total asset turnover
Hence total sales (Tsh m 595 x 3.5)
Calculation of profit after tax
Sales
Variable cost (@75%)
Contribution
Less: Fixed costs
Net profit (PBIT)
Less: Interest on debentures (0.15 x Tsh 250 m)
Profit before tax (PBT)
Tax @ 30%
PAT
Tshs million
2,082.50
(1,561.88)
520.62
(100)
420.62
(37.50)
383.12
(114.93)
268.19
Therefore,
EPS =
Tshs 268,190,000
1,000,000
Operating leverage =
= Tshs 268.19
Contribution
PBIT
=
Tshs 520.62m
= 1.24
Tshs 420.62m
Therefore a 10% decrease in sales would result in a 12.4% (10 x 1.24) decrease in PBIT.
Financial gearing =
=
Debt
Equity
Tshs
250m
Tshs 200m + Tshs 35m
= 1.06
396 Financing Decisions
© GTG
Financial Gearing and Capital Structure: 311
Answer to TY 4
The increased gearing would have a negative impact on the firm’s value, as beyond the level of acceptable
leverage, debt would have a negative impact on overall cost of capital and value of the firm.
BASE
EBIT
Less: Interest on debt
Earnings available to equity shareholders
Equity capitalisation rate
Market value of equity (E)
Market value of debt (D)
Value of firm (D+E) Tshs m
Overall cost of capital = 400/2875 =
SCENARIO 1
EBIT
Less : Interest on debt
Earnings available to equity shareholders
Equity capitalisation rate
Market value of equity (E)
Market value of debt (D)
Tshs million
400
(100)
300
0.16
1,875
1,000
2,875
13.91%
Tshs million
400
(180)
220
0.17
1,294
1,500
Value of firm (D+E) Tshs m
Overall cost of capital (EBIT / value of firm)
2,794
14.32%
Answer to TY 5
(a) Firms value and equity capitalisation rate
Operating income (a)
Overall capitalisation rate (b)
Value of firm (a/b) --- 1
Market value of debt --- 2
Market value of equity --- (1-2)
Interest on debt (c)
Earnings available to equity shareholders (firm’s value) (a-c)
Equity capitalisation rate
(EBIT-I)/market value of equity
=5,250/39,000
Tshs million
8,000
12.50%
64,000
25,000
39,000
2,750
5,250
13.46%
(b) Impact on firms’ value and equity capitalisation rate, if the firm increases its debt
Impact of debt increase
Operating income (a)
Overall capitalisation rate (b)
Value of firm (a/b) --- 1
Market value of debt --- 2
Market value of equity – (1-2)
Interest on debt (c )
Earnings available to equity shareholders (a-c)
Equity capitalisation rate
(EBIT-I)/market value of equity
=4,150/29,000
Tshs million
8,000
12.50%
64,000
35,000
29,000
3,850
4,150
14.31%
312 : Financing Decisions
Answer to TY 6
Financial Gearing and Capital Structure: 397
© GTG
EBIT
Less: Int on debt
Earnings to equity shareholders
Equity capitalisation rate
Market value of equity (E)
Market value of debt(D)
Value of firm (E+D)
Rose Ltd
18,750,000
18,750,000
0.15
125,000,000
125,000,000
Investor's current position in Marigold Ltd.
Dividend income
Investment cost
He sells his holding in Marigold Ltd.
and borrows in personal capacity Tsh 7,500,000 (10% of Tsh75,000,000)
Sale value of holding
Total amount available
Cost of 10% equity in Rose Ltd.
Dividend income in Rose Ltd.
Less: Interest outlay
Net income
Reduction in outlay through use of personal leverage
Tshs
Marigold Ltd.
18,750,000
7,500,000
11,250,000
0.2
56,250,000
75000000
131,250,000
1,125,000
5,625,000
13,125,000
20,625,000
12,500,000
1,875,000
750,000
1,125,000
8,125,000
According to Modigliani and Miller, the arbitrage process will end when the value of both the companies is the
same.
Answer to TY 7
When a company is on the verge of bankruptcy, additional costs surface in the form of



Liquidation of assets at distress values
Operational inefficiencies
Legal and administrative costs
Creditors have to bear the load on account of shortfall of economic values of assets as well as administrative
costs. This has a directly influence on the ability of a leveraged firm to attract investors. The equity shareholders
have to bear the increased costs in the form of the highest cost (factored in the interest rates). Therefore,
bankruptcy costs have a direct (negative) effect on the value of the firm and the cost of capital.
As the leverage increases, investors would penalise the price of the stock. With an increased probability of
bankruptcy with increasing leverage equity shareholders increase their required rate of return at an increasing rate
beyond certain point. Thus, in addition to the premium for business risk and financial risk there is a need for
increased return at a higher rate to compensate for bankruptcy costs.
Although the tax advantages through deployment of leverage will cast a positive effect on the firm value,
bankruptcy costs will become important in the calculation of firm value over a period of time.
The effect of bankruptcy costs on value of firm is expressed below:
Value of firm = Value of unlevered firm + PV of net tax shield of debt - PV of bankruptcy costs
Answer to TY 8
𝛽𝛽𝑗𝑗𝑗𝑗 =
1.2
= 0.787
0.7 × 0.7
1+
1
Adjusted , = 0.787(1+0.6(0.3))= 0.787x1.18 = 0.929.
398 Financing Decisions
© GTG
Financial Gearing and Capital Structure: 313
Answer to TY 9
The formula for calculation of indifference point is
(EBIT − I1)(1 − t)
E1
=
(EBIT − 0)(1 − 0.3)
100000
0.7EBIT
=
(EBIT − I2)(1 − t)
E2
=
(EBIT − 5,000,000) (1 − 0.3)
50,000
0.7(EBIT − 5,000,000)
2
314 : Financing
Decisions 1
7,000,000=1.4EBIT -0.7EBIT
7,000,000 = 0.7EBIT
EBIT = Tshs 10,000,000
© GTG
Answer to TY 10
It is very important to carry out the actual cash flow analysis of the firm so as to determine its actual liquidity
position. It involves the following





Analysing the actual liquidity position of the company, while the EBIT-EPS analysis is concerned with
leverage analysis
Working out the changes in current assets and current liabilities and the net current asset position of the
company
A dynamic analysis extending over a period of time as compared to EBIT-EPS analysis which is static
in
nature (i.e. restricted to one year)
Analysing the financial resources that can be made use of during a decline / downturn.
Quick Quiz
1. What is financial ‘gearing’?
2. How is operational gearing computed?
3. What does the net operating income approach state?
4. What is combined gearing?
5. Company X has an interest coverage ratio of 1.5. The industry average is 2.5. Comment on the ability of the
company to meet its interest obligations.
6. State whether the following statements are true or false:
(a) An optimal capital structure exists because the cost of capital is not independent of the capital structure
of the firm.
(b) According to MM (tax exists), a firm with debt in the finance mix will have a higher value than an
unlevered firm.
(c) At any level of EBIT beyond the indifference point, equity capital is more preferable.
(d) Bankruptcy costs have limited effect in deciding capital structure.
(e) Operational gearing is said to exist when the percentage change in EBIT divided by the percentage
change in sales is greater than 1.
7. Fill in the blanks
(a) The market value of a firm depends upon its
and
.
(b) According to MM (no tax exists), a firm’s market value and cost of capital remain
changes to its
.
(c) At any level of
below the indifference point,
finance is preferable.
Answers to Quick Quiz
1. It is the amount of debt finance a company uses relative to its equity finance.
with
7. Fill in the blanks
(a) The market value of a firm depends upon its
and
.
(b) According to MM (no tax exists), a firm’s market value and cost of capital remain
with
Financial Gearing and Capital Structure: 399
changes to its
.
(c) At any level of
below the indifference point,
finance is preferable.
Answers to Quick Quiz
1. It is the amount of debt finance a company uses relative to its equity finance.
2. Operational gearing measures the change in operating income as a result of change in sales.
Operational gearing =
% changein PBIT
% changein sales
3. The net operating income theory suggested by Durand is that the capital structure decision of a firm is
irrelevant. Any change in leverage will not lead to a change in the total value of the firm and the market price
of the shares, as the overall cost of capital is independent of the degree of leverage.
4. Combined gearing is a measure of total risk of the company. Combined leverage is a combination of operating
leverage and financial gearing. As explained earlier, operating gearing has an effect on business risk /
operating risk and financial gearing has an effect on financial risk.
20X8
20X9
20,000
25,000
1,600
2,000
Required:
400 Financing Decisions
Estimate the operating leverage for Super Stores Ltd.
Question 3
There are two companies operating in the same industry: A Ltd. and B Ltd. These companies are similar, except
that A Ltd is unlevered and B Ltd. has a debt of Tshs 10,00,000 as 10% debentures. Both the companies have
an EBIT of Tshs 2,50,000 and a capitalisation rate of 10%.
Required:
Calculate the value of the firms according to the MM approach, assuming 30% as the tax rate.
Question 4
United Ltd. requires additional capital of Tshs 3,500m for a new investment proposal. The following options have
been worked out:
(i) Raise entire capital by issuing equity shares at face value of Tshs 100 per share
(ii) Raise Tshs 1750m through equity shares @ Tshs 100 and balance through 8% debentures
(iii) Issue 17.5m preference shares @ Tshs 100 and the balance through equity
shares. The EBIT of the companies are Tshs 70m, Tshs 140m, Tshs 280m and Tshs
700m. Required:
316 : Financing Decisions
(a) What is the EPS under each option? Assume a corporate tax of 30%.
(b) Which alternative is preferable?
(c) Determine the EBIT-EPS indifference point between plans a and b & a and c.
© GTG
Answers to Self Examination Questions
Answer to SEQ 1
There are two types of gearing, mainly financial gearing and operational gearing. If these two levels of gearing are
high, the risks for the company and its shareholders increase. The types of risk are:
(a) Financial risk
Also referred to as the gearing risk, financial risk will be high when a company is highly geared i.e. debt
accounts for a large proportion of the capital structure. For the company this equates to high borrowing and high
interest payments. A company with a relatively higher proportion of debt has a proportionately higher interest
burden. Changes in the interest rates will cause large changes in interest expense, and therefore, the profit
available to equity holders.
The risk is borne mainly by the shareholders. If committed interest payments are high there is a possibility that
little of nothing will be left over for the ordinary shareholders.

In addition, if the company does not generate sufficient profits to cover interest payments, the threat of
insolvency becomes paramount. Debt holders’, if secured, suffer no real risk. Shareholders, however, stand
to lose the most in such a situation as they are given the least priority.

If the profits available are reduced, the dividend will reduce. This makes equity returns volatile. With floating
interest rates, this problem increases. Even so-called fixed rates are sometimes subject to periodical
changes.
(b) Risk of Bankruptcy
 If capital gearing is too high, interest payments may become unsustainable, either due to a reduction in
profits before interest or an increase in interest payments. Similarly, due to a reduction in internal funds
generation through profits, the company may not be able to honour its repayment commitments. A
competitive environment may make it difficult for a company to maintain the sustained earnings required.
 The dominant lenders could bring an action of liquidation against the company if any of the defaults
mentioned above take place. Bankruptcy may cause a loss to many stakeholders. Employees could lose
their jobs, creditors and shareholders may lose part or all of their money.
(c) Credibility risk
 Financial information about listed companies is readily available to the public due to the stock exchange
requirements. Informed users analyse the information, evaluate the risks discussed in (a) and (b) above,
and then decide whether to put finance into the company’s debt or equity. If they find that the risk is
too high, they may be reluctant to finance the company.
competitive environment may make it difficult for a company to maintain the sustained earnings required.
 The dominant lenders could bring an action of liquidation against the company if any of the defaults
mentioned above take place. Bankruptcy may cause a loss to many stakeholders. Employees could lose
their jobs, creditors and shareholders may lose part or all of their Financial
money. Gearing and Capital Structure: 401
(c) Credibility risk
 Financial information about listed companies is readily available to the public due to the stock exchange
requirements. Informed users analyse the information, evaluate the risks discussed in (a) and (b) above,
and then decide whether to put finance into the company’s debt or equity. If they find that the risk is
too high, they may be reluctant to finance the company.
Risk of short termism:


If debt content in the company’s finances is high, then the management may have to focus on generating
enough cash flow to meet interest commitments to avoid the threat of insolvency. This is a short-term goal,
as against the long-term goal of shareholder wealth maximisation.
Impact of high-level gearing on the cost of capital:


The cost of capital will increase since the lenders will expect a higher interest yield whenever there is a
higher risk, as indicated by higher gearing. Similarly, shareholders will also expect a higher return on their
shares. These factors lead to an increase in the cost of capital.
(d) Business risk
This is the possibility of a company experiencing more proportional changes in the level of its profit before interest
as a result of changes in turnover or operating costs. This will concern those companies operating in unstable
markets where demand fluctuates widely.
Companies with high fixed costs are said to have high operational gearing. As operational gearing increases, a
business
level
of economic
activity,
and profit
© GTG becomes more sensitive to changes in turnover and the general
Financial
Gearing
and Capital
Structure:
317
before interest becomes more volatile.
A high level of gearing also affects the cost of capital
(g) As a result of higher financial risk for shareholders, their required rate of return increases thereby pushing
up the cost of capital.
If new debt finance is obtained, to compensate lenders for the high risk, the cost of debt would increase pushing
up the company’s cost of capital.
Answer to SEQ 2
Estimating operating leverage for Super Stores Ltd
Year
19W9
19W0
20X1
20X2
20X3
20X4
20X5
20X6
20X7
20X8
20X9
Net sales
( Tshs
million)
1,350
1,950
2,750
3,650
5,000
7,000
9,500
12,300
15,400
20,000
25,000
% Change
in
sales
(1,950 – 1,350/1,350) x 100
(2,750 – 1,950/1,950) x 100
(3,650 – 2,750/2,750) x 100
(5,000 – 3,650/3,650) x 100
(7,000 - 5,000/5,000) x 100
(9,500 - 7,000/7,000) x 100
(12,300 – 9,500/9,500) x100
(15,400 – 12,300/12,300) x 100
(20,000 – 15,400/15,400) x 100
(25,000 – 20,000/20,000) x 100
Therefore,
Operational gearing =
% change in PBIT
% change in sales
Operational gearing =
356.04
= 1.046
340.45
Answer to SEQ 3
Market value of A Ltd.
44.44
41.03
32.73
36.99
40.00
35.71
29.47
25.20
29.87
25.00
340.45
EBIT
(
Tshs
million)
100
130
190
250
400
600
750
1,100
1,250
1,600
2,000
% Change
in
EBIT
30.00
46.15
31.58
60.00
50.00
25.00
46.67
13.64
28.00
25.00
356.04
Operational gearing =
% change in PBIT
% change in sales
gearing =
402 Operational
Financing Decisions
356.04
= 1.046
340.45
Answer to SEQ 3
Market value of A Ltd.
EBIT (1-t)/Ke
= Tshs 2,50,000(1-0.3)/0.1 = Tshs 17,50,000
Market value of B Ltd.
Market value of A ltd. + tax shield
= Tshs 17,50,000+( Tshs 10,00,000*0.3)
= Tshs 17,50,000+3,00,000
318=: Tshs
Financing
Decisions
21,50,000
© GTG
Answer to SEQ 4
(a)
Plan A - Equity Financing
Tshs million
EBIT
70
140
280
700
0
0
0
0
EBT
70
140
280
700
Less: Tax @30%
21
42
84
210
PAT
49
98
196
490
No of equity shares (million)
35
35
35
35
EPS
1.4
2.8
5.6
14
Less: Interest
Plan A - Debt + Equity
Tsh million
EBIT
70
140
280
700
Less: Interest
140
140
140
140
EBT
-70
0
140
560
Less: Tax @30%
-21
0
42
168
PAT
-49
0
98
392
No of equity shares (million)
17.5
17.5
17.5
17.5
EPS
-2.8
0
5.6
22.4
Plan C - preference shares + Equity
Tshs million
EBIT
70
140
280
700
EBT
70
140
280
700
Less: Tax @30%
21
42
84
210
PAT
49
98
196
490
Less: preference div
140
140
140
140
PAT for equity shareholders
-91
-42
56
350
No of equity shares (million)
17.5
17.5
17.5
17.5
EPS
-5.2
-2.4
3.2
20
Less: Int
(b) The EPS is the maximum under plan B – i.e. debt equity mix. Thus, under increasing sales conditions, use
of debt capital offers a tax shield and enhances the EPS.
(c) As indicated above, the indifference point between plan A and plan B is at EBIT level of Tshs 280million.
EBIT-EPS indifference point for plans A and C is calculated below:
EPS
-5.2
-2.4
3.2
20
Financial
Gearingsales
and conditions,
Capital Structure:
(b) The EPS is the maximum under plan B – i.e. debt equity mix. Thus, under
increasing
use 403
of debt capital offers a tax shield and enhances the EPS.
(c) As indicated above, the indifference point between plan A and plan B is at EBIT level of Tshs 280million.
EBIT-EPS indifference point for plans A and C is calculated below:
(EBIT − I1)(1 − t)
E1
=
(EBIT − I2)(1 − t)
E2
(EBIT − 0)(1 − 0.3)
(EBIT − 0)(1 − 0.3) − 140
=
35
17.5
0.7EBIT = 2(0.7EBIT)-140
0.7EBIT = 1.4EBIT -280
280©=GTG
0.7 EBIT
Financial Gearing and Capital Structure: 319
ŶƐǁĞƌƐƚŽ/ŶĚŝĐĂƚŝǀĞdžĂŵŝŶĂƚŝŽŶYƵĞƐƚŝŽŶƐ
EBIT = 280/0.7 = Tshs 400 m
/ŶĚŝĐĂƚŝǀĞdžĂŵŝŶĂƚŝŽŶYƵĞƐƚŝŽŶƐ
IEQ 1
MTAKUJA Company is currently an unlevered firm. The Company anticipates a perpetual pretax earnings stream
of TSHS40,000,000 and faces a 35% percent corporate tax rate. Unlevered firms in the same industry have a cost
of equity capital of 20%. MTAKUJA is considering a capital restructuring to allow TSHS30,000,000 of debt.
Required: Use the Modigliani and Miller Model to determine the following:
(i) The Value of the all equity MTAKUJA Company
(ii) The Value of the levered MTAKUJA Company
(iii) The Value of the levered equity
(iv) The Cost of Equity of the levered MTAKUJA Company
(10 Marks)
IEQ 2
You’re a financial analyst for Kaaya Consulting Co. based in Dar es Salaam. Your managing director has asked you
to consider the following information on the operational and financial aspects of Kaaya Company, which is only one
year old in the DSE. It is now November 20X8:
Annual Sales Revenue
Total Variable Costs
Fixed Operating Costs
Corporate Tax Rate applicable to Kaaya Company
TSHS20,000,000
TSHS14,000,000
TSHS2,000,000
40%.
The cost of capital for the company is estimated at 12%. The company is authorized to issue 1,500,000 ordinary
shares and it has already issued 1,000,000 shares.
REQUIRED:
(i) Calculate the current market value of Kaaya Company
(ii) Assume that Kaaya Company introduce debt in its capital structure by issuing 10%, bonds valued at
TSHS5,000,000. Using the Modigliani and Miller framework determine the following for Kaaya Company:
The Market Value (3 marks)
The Market Value of Equity (3 marks)The DebtEquity Ratio (3 marks)
The Market Value per Share (3 marks)
(iii) Calculate the degree of operating leverage at sales of TSHS20,000,000 and the degree of financial leverage at
EBIT generated at the TSHS20,000,000 sales level. Interpret your results in each case. (4marks)
(ii) Assume that Kaaya Company introduce debt in its capital structure by issuing 10%, bonds valued at
TSHS5,000,000. Using the Modigliani and Miller framework determine the following for Kaaya Company:
404 Financing Decisions
The Market Value (3 marks)
The Market Value of Equity (3 marks)The DebtEquity Ratio (3 marks)
The Market Value per Share (3 marks)
(iii) Calculate the degree of operating leverage at sales of TSHS20,000,000 and the degree of financial leverage at
EBIT generated at the TSHS20,000,000 sales level. Interpret your results in each case. (4marks)
(iv) Based on your answers in (iii) above, determine the increase/decrease in percentage and shilling amount in
EBIT from a 10% increase in sales revenue from the current sales level. (2 Marks)
Answer to ESQ 1
i) Current Market Value of Kaaya Company (Vu)
Vu = [EBIT(1-T)] /ke = [TSHS4,000,000(1 – 0.4)]/0.12 = TSHS20,000,000 (2 marks)
320 : Financing
ii)Decisions
Introduction of Debt in Capital Structure
© GTG
Market Value of the Firm (VL) = Vu + BT = TSHS20,000,000 + 5,000,000(0.4) = TSHS22,000,000.
Market Value of Equity (S) = (VL – B) = TSHS22,000,0 00 – TSHS5,000,000 = TSHS17,000,000
Debt-Equity Ratio = B/S = TSHS5m/TSHS17m = 0.29
Market Value per Share = Market Value of Equity/No. of Shares Outstanding = TSHS17m/1m = TSHS17
iii) Degree of Operating Leverage and Degree of Financial Leverage
DOL at sales of TSHS20m = Contribution Margin/EBIT = TSHS6m/TSHS4m = 1.5. By DOL = 1.5 it means that a
one percent change in Sales revenue from the TSHS20m level will bring about a 1.5% change in EBIT. (2 marks)
DFL at EBIT of TSHS4m = EBIT/[EBIT-I] = TSHS4m/[TSHS4m-TSHS0.5m] = 1.14. By DFL = 1.14 it means that a
one percent change in EBIT from the current level of TSHS4m will bring about a 1.14 percentage change in EPS. (2
marks)
iv) Percentage Change in EBIT by 10% Increase in Sales
A 10% increase in sales will bring about 10% x 1.5 = 15% increase in EBIT i.e. the EBIT will increase to
TSHS4m(1.15) = TSHS4.6m. This represents an increase of TSHS0.6m. (4 marks)
Answer to ESQ 2
(i) Value of All Equity MTAKUJA Company [Vu]
Vu = EBIT (1 – T)/Keu = TSHS40,000,000 (1 – 0.35)/0. 15 = TSHS130,000,000(3 Marks)
(ii) The Value of the levered MTAKUJA Company [VL]
VL = Vu + BT = TSHS130,000,000 + TSHS30,000,000(0.35)
= TSHS130,000,000 + TSHS10,500,000 = TSHS140,500,000(3 Marks)
(iii) The Value of the levered equity
Because value of the levered firm (VL) is equal to the sum of the Value of the Debt (B) and Value of the Levered
Equity (S), the value of the levered equity is equal to:
S = VL – B = TSHS140,500,000 – TSHS30,000,000 = TSHS11 0,500,000(4 Marks)
SECTION E
Divided Policy: 405
DIVIDEND DECISION
E1
STUDY GUIDE E1: DIVIDEND POLICY
The earnings of the company after fulfilment of all fixed obligations and tax are available to equity shareholders.
The equity shareholders collectively own the firm. The management has two choices with regard to the earnings.
They can either be distributed as dividend or can be ploughed back into the business as retained earnings.
The earnings that are ploughed back into the business can be utilised for financing new projects / investments.
This is an internal source of finance which has gained significance in financial management. If it is distributed as
dividend then the management would need to tap external sources of finance. As the objective of a prudent finance
manager is to maximise firm value, the above decision of retention v/s dividend payout will depend on the effect
it would have on the value of the firm. Furthermore, the finance manager has to ensure efficient working capital
management so that funds are not blocked in current assets and put to productive use.
In this Study Guide, we shall evaluate the internal sources of finance and study the relevance of dividend and
dividend policies.
a) Describe the alternative dividend policies that companies can adopt and their significance.
b) Discuss the various arguments put forward by different schools about dividend policy – dividend
irrelevance, dividend relevance, mid-roaders schools as well as the role of market imperfections in the
debate.
c) Compute and interpret share price under the models representing each school of thought.
d) Examine the factors which determine a company’s dividend policy, with some reflections on the evidence
in Tanzanian market and beyond.
e) Discuss the alternatives to cash dividends such as share repurchases, and script dividend showing the
advantages and disadvantages of each alternative.
406 Divided Decision
318 : Dividend Decisions
© GTG
1. Describe the alternative dividend policies that companies can adopt and their significance.
[Learning Outcome, a]
1.1 The meaning of dividend and its relationship with financing
A dividend is a distribution of post-tax profits to shareholders, on a periodical basis. As in any other form of
business, the owners want to withdraw the profits earned by the business. It effectively rewards shareholders for
the risks undertaken by investing in the business and allows them to share the prosperity of the business.
The retained earnings of the firm that are kept in the business, rather than being distributed as a dividend, are
an internal source of finance, to the extent they are represented by cash. Consequently, a dividend policy that
encourages lower dividends will provide higher internal finance by way of retained earnings. The need for a
company to obtain finance from external sources is reduced.
Peterson Ltd earned profits of Tshs 1000 m during 20X9. The financial statements reveal total retained earnings
of Tshs 2000 m. Current assets include cash / bank balance of Tshs 400m and other liquid assets of Tshs 300 m.
If the company’s dividend policy enables it to omit paying a dividend if there are good investment opportunities
available, the company has internal resources to the tune of Tshs 700 m ( Tshs 400 m of cash / bank balance and
Tshs 300 m of liquid assets. However, if the company’s dividend policy requires it to increase the amount of
dividend to Tshs 300 m then the funds available from internal sources will only be Tshs 400 m ( Tshs 700 m –
Tshs 300 m).
On the other hand, if the company decides to invest Tshs 600 m , it can use the residual amount of money i.e.
Tshs 100 m ( Tshs 700m – Tshs 600m ) towards paying dividend.
Therefore, there is an inverse relationship between the dividend payout and the retained earnings available for
investment purpose. The higher the dividend, the lower is the residual balance of earnings available for
investment purposes, and vice versa. However, the two decisions (dividends and investments) may be subject
to separate considerations, as the earnings of the company may not be sufficient enough to cover both. It is
possible that a company decides the two independently, and then manages the shortfall through external
borrowings.
Experts argue that firms must adopt independent dividend and investment policies. Empirical evidence supports
this argument. Adequate debt finance is usually raised to satisfy the financial demands created by dividend and
investment decisions. As a result, it is possible to have independent dividend and investment policies.
1.2 Alternative dividend policies
Dividend policy is the policy that divides earnings attributable to equity shareholders into dividend payout and
retained earnings. The overall dividend policy is influenced by:

Financing decision: the decision on how much dividend is to be distributed to shareholders is a financing
decision as the retained earnings are an important internal source of finance. In case the firm has significant
investment opportunities and these investments are estimated to propel current growth rate, then the firm
would prefer to utilise the retained earnings for investment purpose. A dividend payout in such a case would
reduce the surplus available for long term financing. However, dividend may be paid when major investment
opportunities are not available.

Creating value for the shareholders: shareholders may want to receive early returns in terms of regular
dividends due to market uncertainties. A higher dividend pay-out may help in enhancing share value. In
contrast, a higher payout would reduce the surplus available for investment. This may affect the forecasted
EPS. On the other hand, usage of retained earnings as a source of long-term finance will enhance the
forecasted EPS. Therefore, management has to view all the effects and strike a balance between current
shareholder expectations and strategies to enhance future value.
© GTG
Divided Policy: 407
Dividend Policy: 319
The following are the main alternative policies regarding dividends.
1. Fixed percentage payout ratio
Dividend payout ratio is calculated as follows:
Total dividend paid to ordinary shareholders
× 100
Earnings after tax and preference dividends
This policy maintains a constant payout ratio. It is simple to operate and helps the company to send clear
signals to the shareholders about the company’s operating results.
If a firm has a dividend pay-out ratio of 30%, then 30% of every shilling earned is distributed as dividend.
Let’s assume the firm earned Tshs 100 per share. Then 30% of 100, i.e. Tshs 30 per share will be distributed as
dividend. If in year 2, the firm earns a profit of Tsh125 per share then dividend will increase to Tshs 37.5 per share.
Obviously, this policy is not suitable for a company with volatile profits, especially if the shareholders expect stable
dividends. Furthermore, this takes away from management the flexibility of retaining higher profits if they are
required for investment purposes. In a sense, this policy fixes the dividend that can be paid and is conservative in
approach.
2. Constant or increasing dividend
A dividend can be kept constant or increasing in:
(a) Money terms (without considering inflation) or
(b) Real terms (after removing the effect of inflation).
In the case of constant dividend policy, dividend is fixed irrespective of the level of earnings. The same level is
maintained year on year. If the company wishes to increase the threshold, it has to reach an increased level of
EPS and forecast to maintain that level. In case this policy is being followed, the company has to ensure sufficient
liquidity for dividend pay-outs.
If a company expects long-term sustainable growth in earnings, it may decide to follow a policy of increasing the
dividend. Management’s main aim is to avoid volatility. A reduction in dividend pay-outs may reduce the share
price, which is something that they would want to avoid. Accordingly, any increase in the dividend is planned in
a conservative manner.
A company achieved a 20% increase in profits in the current year and hopes to maintain the rate of growth.
However, it only increases dividends by 10%. Only when the company is confident that this earning is actually
sustained, will it raise dividends further.
If a dividend is kept constant or increasing in money terms, during a period of inflation, the dividend in real terms
may be decreased. During a period of deflation, the dividend in real terms may be increased.
One disadvantage of this policy is that shareholders expect the trend of increasing dividends to continue
indefinitely. When management wants to use the funds for profitable investments, they may want to reduce
dividend payments, but may not be able to do so.
3. Zero dividend
Zero dividend cannot be a long-term policy. A new company may wish to first stabilise by reinvesting substantial
profits over the initial years, and then start paying out dividends. The company can follow a zero-dividend policy
for a short period.
408 Divided Decision
320 : Dividend Decisions
© GTG
Although a small minority of shareholders may accept it as a policy for reasons such as tax benefits for capital
gains, the majority of shareholders would like to get some dividends. In fact, the large institutional investors who
control the bulk of shareholdings these days rely on dividend income. They are unlikely to be happy with a zerodividend policy.
In this case, the company does not have to incur administrative costs associated with the payment of dividends.
SUMMARY
TBM Ltd declared an interim dividend of Tshs 50 per share and a final dividend of Tshs 50 per share. Over the
same period, TBM Ltd reported net earnings of Tshs 400 per share.
Required
Calculate the dividend payout ratio and comment on it.
2. Discuss the various arguments put forward by different schools about dividend policy –
dividend irrelevance, dividend relevance, mid-roaders schools as well as the role of market
imperfections in the debate.
[Learning Outcome b]
2.1 Dividend irrelevance
The summary of the argument in favour of dividend irrelevance is that dividend is a passive residual since it is a
part of financing decision. Therefore, if the firm has certain investable opportunities, the retained earnings would
be utilised for them. In such case, no dividend will be paid.
Dividend irrelevance is based on the assumption that investors are indifferent between dividend and capital gains.
So long as the return from the business is greater than the cost of equity, they are willing to forego dividend for
higher growth, and consequently, the value of the firm will not decrease.
1. Modigliani and Miller (MM) Hypothesis
Miller and Modigliani are the proponents of a school of thought that dividends are irrelevant as far as share
prices are concerned. They contended that share prices depend on the level of corporate earnings which in turn
depend on the company’s investment decisions.
Investors are rational and they look to maximise their wealth. The extent and timing of dividend payouts is
irrelevant. What affects the value of the firm is the earnings potential and the risk associated with it. There may
even be no dividends if the retained earnings are consumed by investment projects. However, the expected future
earnings of the company will push the share prices up. In this manner, a shareholder gains in capital appreciation
even if he does not receive dividend payments.
DividedPolicy:
Policy:321
409
Dividend
© GTG
(a) Assumptions
This theory is based on the following assumptions:
(i) Capital markets are perfect.
No floatation and transaction costs
No single investor can influence the share price
Free flow of information
There are no taxes at the corporate or personal level.




(ii) There will be no change in business risk on account of financing investments through retained earnings.
(b) Arbitrage process
MM put forth the arbitrage argument to support their theory of dividend irrelevance. In the event of dividend payout
by the firm, an arbitrage process would involve payout of dividend to equity shareholders, and for the same
amount, raising additional capital through shares. The effect of dividend payout will be offset by the effect of raising
additional share capital. When dividends are paid, the market price will decrease and the gain from dividend will
be compensated by the decrease in share price.
Even if funds are raised through debt, there will be no difference due to the indifference between debt and
equity with respect to dividend. This is explained below:
(i) According to MM, the prevailing market price Po is determined as follows
Po =
1
(D1+ P1)
(1+ ke)
Where,
Po = current market price of share
D1 = dividend (to be received at end of year 1)
P1 = Share price at the end of year 1
Ke = cost of equity capital
(ii) If there is no external financing, the value of firm is equal to the number of times the price of the
share given by
nPo =
1
(nD1+ nP1)
(1+ ke)
(iii) If the firm were to finance all investment proposals, then the amount to be raised through new
shares is given by
nP1 = I-(E-nP1)
nP1 = I - E +nP1
Where,
nP1 = amount obtained through sale of new shares for investment
I = total investment requirement
E = earnings of the firm
nD1 = total dividend paid
(E-nD1) = retained earnings
(iv) Substituting the above values in the earlier equation, we get,
nPo =
(n + n)P1− I + E
(1+ ke)
As can be seen above, since dividend is not one of the variables in the above formula, MM concluded that
dividend is irrelevant in determination of share price and value of the firm.
410 Divided Decision
322 : Dividend Decisions
© GTG
(c) Critical evaluation
The theory of dividend irrelevance is based on critical assumptions stipulated earlier. However, in actual
practice, these conditions are untenable. Let’s critically evaluate the validity of the theory on account of two factors:
1. Imperfection of market
The assumptions include absence of flotation and transaction costs, taxation and no restrictions.
(i) Flotation costs
Flotation costs refer to the costs of raising funds through new issue of shares from the market. These include
advertising, underwriting commission, brokerage and related costs. It is assumed that the company is indifferent
between using internal financing and raising additional capital due to absence of flotation costs. However,
practically, since floatation costs would be involved, this would reduce the funds raised from a new issue. For
example, if the floatation cost is 5%, for every Tshs 1000 of funds raised, Tshs 950 only would be available for
investment purposes.
(ii) Transaction costs
Transaction costs refer to the costs of selling securities by the investors. Under the theory, MM assumes that there
are no transaction costs. Therefore, in case an investor requires liquidity, in the absence of dividend he can
sell the required shares and meet his cash flow requirements. Furthermore, the assumption of free tradability of
the shares is also questionable. If an investor is looking at regular income in the form of dividend flows, the
assumption of him being ready to use the alternate route of selling the required shares for liquidity would be
questionable.
(iii) Tax incidence
MM assumes that there are no taxes. Based on this, an investor is indifferent regarding the two options:
dividend payout v/s reinvestment. However, in actual practice, there are two tax incidences which have to be
taken care of:


Dividend is taxable in the hands of the investor
Capital gains arise only on sale of shares at a future date.
However, there is a difference on account of the timing of incurrence and quantum of tax. While capital gains
are required to be paid only in the event of sale of shares, dividend tax has to be incurred in the period of dividend
receipt. Furthermore, according to the applicable laws of each country, the taxability of dividend and capital gains
would be different.
Therefore, due to the effect of taxes which exist in practice, it is difficult to assume indifference between retained
earnings and dividend pay-out. As seen from the above analysis, due to imperfections in the market, there are
certain factors which would favour dividend payout (from both investor and firm perspective) and some which
would favour retained earnings. The theory of dividend irrelevance is diluted due to the impractical assumptions.
2. Conditions of uncertainty
MM assumes a condition of certainty, which is questionable. The conditions of uncertainty can be explained with
respect to:
(i) Near v/s distant dividend
In case dividends are paid regularly, there is a surety of income, as against stock appreciation at a future date
which is uncertain and unproven. According to Gordon, investors are not indifferent; they prefer near dividend to
distant dividend.
(ii) Preference for current income
Investors require funds to meet their regular needs. They cannot depend on future cash flows to fulfil their
consumption requirements.
Divided Policy: 411
Dividend Policy: 323
© GTG
(iii) Information obtained with dividend
At the time of announcement of dividend policy for the period, the management provides first hand information
on earnings, guidance etc. If the management recommends an increase in dividend from the current stable levels,
it is clear that there is a positive outlook. However, MM argues that this information again pertains to expectation
of future earnings - and dividend is irrelevant.
(iv) Pricing of new shares
The critics of the theory argue that the additional capital which needs to be raised for financing investments would
have to be offered at a lower price. The price will decline if shares are sold to replace dividends. Therefore,
a company will have to issue more shares to raise the same amount of capital and it would be better off using
retained earnings. Therefore, dividend indifference will not hold true.
2.2 Dividend relevance
This is an even earlier school of thought, which was prevalent before Miller and Modigliani published their
theory. The dividend relevance theory is exactly the opposite of the irrelevance theory. It argues that dividend
policies are relevant for share valuations.
Let’s discuss three theories which are based on dividend relevance:
1. Walter’s model
The model given by Prof James E. Walter is based on the relationship between the firm’s internal rate of return
or return on investments and the cost of capital. So long as the firm’s rate of return (r) is higher than the cost of
capital (k), the firm will retain the earnings. If r < k the investors are better off receiving dividend and investing it
in other avenues.
The model is based on the following assumptions:
(a) There is no change in business risk when new investments are undertaken.
(b) Key variables remain unchanged.
(c) Outside capital is not used for financing.
(d) The firm is a going concern.
The relationship between dividend and market value of a share according to Walter is given as
𝑃𝑃 =
𝐷𝐷 +
Where,
𝑟𝑟
(𝐸𝐸 − 𝐷𝐷)
𝑘𝑘𝑒𝑒
𝑘𝑘𝑒𝑒
P = market price of share
D = dividend per share
E = earnings per share
r = rate of return on firm’s investment
ke = cost of capital
The formula explains why the market price of companies which are on a growth trajectory is high even when
dividend is low. Similarly, it explains the reason why the share price of companies which pay high dividends is
also high.
2. Gordon growth model
Gordon’s growth model also supports the theory that dividend is relevant. The assumptions for this model are
similar to Walter’s model. This theory’s argument is that investors are risk averse, they put a premium on a definite
return and penalise uncertain returns. Therefore, investors would discount shares whose dividends are postponed.
Under Gordon’s model, the market price of a share is expressed as the present value of future streams of
dividends.
412
Decision
324 :Divided
Dividend
Decisions
© GTG
E(1 − b)
ke − br
Po =
Where,
P = price of share
E = earnings per share
b = retention ratio
ke= cost of capital
r = growth rate
3. Lintner’s model
In 1956, John Lintner conducted a research by discussing with business men how they made their dividend
decisions. He formed a model based on that as:
D1 = D0+ ((EPS X Target payout)-D0) X Af
Where, D1 = dividend in year 1, D0 = dividend in year 0,Af = adjustment factor
Based on the study, Lintner explained that firms fix the target payout ratios for a long term based on return
expectations. The dividend policy is changed only when there is surety that dividends are sustainable.
Is there a relationship between the internal rate of return of the firm and the cost of capital under Walter’s
model?
3. Compute and interpret share price under the models representing each school of thought.
[Learning Outcome c]
We have discussed the different theories in the previous Learning Outcome. Let’s now compute the share price
under each model.
3.1 Determination of share price under Modigliani & Miller Hypothesis (dividend irrelevance)
We have discussed the following formulae for determination of share price under MM hypothesis.
P0 =
1
(D1+ P1)
(1+ ke)
nPo =
(n + n)P1− I + E
(1+ ke)
A risk class to which the company belongs has an approximate capitalisation of 13%. The company has a
capital of Tshs 100 million shares of Tshs 100 each. The dividend proposed at the end of year 1 is Tshs 10
per share. The shares are currently quoted at par. Let’s calculate market price at the end of the year under
each of following scenarios:
1. Dividend is declared
1
(𝐷𝐷 + 𝑃𝑃1 )
(1 + 𝐾𝐾𝑒𝑒 ) 1
1
100 =
(10 + 𝑃𝑃1 )
(1 + 0.13)
113 = 10+P1
P1 = 103
𝑃𝑃0 =
Continued on the next page
Divided Policy: 413
Dividend Policy: 325
© GTG
2. Dividend is not paid
100 =
1
(𝑃𝑃 )
(1 + 0.13) 1
100 = P1/1.13
P1 = 113
3. Dividend is paid, earnings are Tshs 50 million and the company wishes to make new investments of
Tshs 100m
Let’s calculate how many shares must be issued under the MM model.
nP1 = I - (E-nD1)
= 100,000,000-(50.000.000-10,000,000)
= 60.000.000
= 60,000,000/103 = 5,82,524 shares.
3.2 Share price under Walter’s model
The relationship between dividend and market value of a share according to Walter is given as:
𝑃𝑃 =
𝐷𝐷 +
Where,
𝑟𝑟(𝐸𝐸 − 𝐷𝐷)
𝑘𝑘𝑒𝑒
𝑘𝑘𝑒𝑒
P = market price of share
D = dividend per share
E = earnings per share
r = rate of return on firm’s investment
LLM Ltd has the following details
EPS Tshs 100,
Dividend per share Tshs 60
Capitalisation rate 10%
Company IRR is 15%. Let’s estimate the market price per share.
𝑃𝑃 =
𝑃𝑃 =
𝐷𝐷 +
𝑟𝑟(𝐸𝐸 − 𝐷𝐷)
𝑘𝑘𝑒𝑒
𝑘𝑘𝑒𝑒
60 +
0.15(100 − 60)
0.10
0.10
= Tshs 1200
414 Divided Decision
326 : Dividend Decisions
© GTG
3.3 Share price under Gordon’s growth model
Under Gordon’s model, the market price of a share is expressed as the present value of future streams of
dividends.
Po =
E(1− b)
ke − br
Where,
P = present market price per share
E = earnings per share
b = retention ratio
ke= cost of capital
br = g = growth rate
Saturn Ltd has shared the following details:
Earnings per share Tshs 2000, IRR = 15%. Let’s calculate the value of a share when:
1. D/P ratio 10, retention is 90, cost of capital is 18%.
=
=
E(1− b)
ke − br
2000(1 − 0.9)
0.18 − 0.135
= 200/0.045
= Tsh4444.44
2. D/P ratio is 40, retention is 60, cost of capital is 15%.
=
2000(1 − 0.6)
0.15 − 0.09
= 2000(0.4)/0.06
= 800/0.06
= Tshs 13,333
st
PTC Ltd has 50,000 equity shares at Tshs 100 each outstanding on 1 April 20X0. The firm plans to declare
dividend of Tshs 20 per share. The shares are currently quoted at par. The approximate capitalisation rate is
15%. Under the MM model, calculate the price when:
(i) Dividend is declared
(ii) Dividend is not declared
(iii) How many additional equity shares need to be issued if the company needs Tshs 2,000,000, of which
earnings for the year are estimated at Tshs 1,200,000 and dividend payout will happen.
Divided
Policy:
415
Dividend
Policy:
327
© GTG
Determine the share price for Prime Retail Ltd using Gordon’s growth model.
Cost of capital
Rate of return
Earnings per share
Retention ratio
10%
8%
Tsh100
0.4
Information relating to James Plc:
Earnings of the company
Dividend payout
No. of shares outstanding
Equity capitalisation rate
Firm rate of return
= Tshs 1,000,000
=40%
=200,000
=12%
=16%
Calculate the market price per share. Also, determine the optimum dividend payout ratio for the firm and the
value of a share at that ratio.
4. Examine the factors which determine a company’s dividend policy, with some reflections
on the evidence in Tanzanian market and beyond.
[Learning Outcome d]
A company’s dividend policy has to take into account a number of factors ranging from shareholder expectations,
liquidity situations and investment opportunities to legal and regulatory framework.
4.1 Company’s financial requirements
One of the key factors influencing the dividend policy is the requirement of funds for investment. Since dividend
would reduce the profits ploughed back into business, it is critical to forecast the funds required for investment
over a sustained period before deciding on the quantum of dividend that can be distributed.
In the case of companies which are in their growth phase, it is preferable to retain the profits for investment as
there is a requirement for significant funds for business purposes. On the other hand, in the case of well established
companies with a proven track record, they can have a stable dividend policy and revise it whenever required,
based on future earnings potential.
4.2 Legal constraints
Laws of each land may prescribe certain constraints on declaring dividends with regard to accumulated profits.
Section 180(3) of the Companies Act, 2002 provides that a dividend can be paid out of (a) realised profits less
realised losses, or (b) realised revenue profits less ... revenue losses, whether realised or unrealised, provided
the directors reasonably believe that immediately after the dividend has been paid the company will be able to
discharge its liabilities as they fall due, and the realisable value of the company’s assets will not be less than the
amount of its liabilities.
4.3 Liquidity
Dividends are to be paid out of cash. However, retained earnings or a profit earned does not necessarily mean an
availability of cash. Profits earned from day-to-day operations are not kept separately in a cash box or bank
account. In fact, there is a continuous flow of working capital where one asset gets changed into another or is
used to pay off a liability. If you crystallise and compare the financial statements for two dates, you can trace
where the cash has gone. It might have been used to increase a bank balance, to increase an investment in
debtors or inventories, or to reduce the trade payables level.
416 Divided Decision
328 : Dividend Decisions
© GTG
It is clear from the discussions that management needs to check the availability of cash, i.e. liquidity, before
deciding upon the amount of dividends. If the cash available is less than the dividend the company wants to
distribute, then it has to decide how to source the amount represented by the shortfall.
Aqua has an ordinary share capital of Tshs 20m. It wants to distribute a dividend of 10%. Cash and liquid assets
are available to the tune of Tshs 1.5m. The cash requirement for the dividend pay-out is Tshs 2m. The company
will therefore have to raise additional finance of Tshs 0.5m, before it can distribute any dividends.
4.4 Shareholder’s expectation
Dividend policy of a company should be guided by the expectation of the shareholders as regards dividend income.
Certain class of shareholders invest in well established companies to receive a regular flow of income in the
form of interim and annual dividends. It provides them with assurance as to the return and liquidity of their
investment. Let’s discuss three aspects of shareholder expectations:
1. Taxation
The tax laws applicable to the dividend payout influence shareholder expectations. In the case of slab based
personal taxation, investors in the higher income bracket prefer capital appreciation of stock to dividend. This is
because tax on dividend income would have to be paid in the same year at the maximum marginal rate while
taxation on appreciation (capital gains) will have to be incurred only in the year of sale. Furthermore, in case tax
laws support retention of shares for increased tenure, taxation would be at a lower rate.
In Tanzania, when an individual receives dividends, the company that pays the dividend withholds tax by deducting
10% of the dividend (if the company is not listed in the Dar es Salaam stock exchange) or 5% (if the company is
listed in the Dar es Salaam stock exchange) and sends it to TRA. This satisfies the individual's tax liability for the
dividends.
As regards capital gains, when an individual sell shares or securities, he may be liable to individual capital
gains tax at a maximum rate of 10%. However, shares or securities listed on the Dar es Salaam stock exchange
are exempt. Therefore, in the case of shares listed on the exchange, there would be higher return if the shareholder
opts for appreciation instead of dividend.
2. Investment opportunities
Investors would expect higher dividend payout if there is an opportunity cost in terms of alternative investment
opportunities available in the market.
3. Ownership dilution
In case of higher dividend payouts, the management may need to issue additional equity shares for investment
purposes. If it is not subscribed by existing shareholders, there would be dilution of ownership and control.
What factors influence shareholder expectations with regards to dividend?
© GTG
Divided
Policy:
417
Dividend
Policy:
329
5. Discuss the alternatives to cash dividends such as share repurchases, and scrip dividend
showing the advantages and disadvantages of each alternative.
[Learning Outcome e]
Dividends are basically distribution of profits to the shareholders. They normally take the form of cash dividends.
However, dividend can also be distributed in the form of stock in form of scrip dividends or share repurchase.
5.1 Scrip dividends
Commonly referred to as bonus shares, scrip dividend implies distribution of shares in place of cash dividend.
When companies are in need of cash to finance new projects, they prefer this alternative. The scrip dividend is
paid by converting the reserves and surplus appearing in the company’s financials into equity share capital to
the extent of dividend i.e. capitalisation of profits. This is an accounting entry and there is no cash outflow from
the company.
1. The advantages of this alternative are:
(a ) From the company’s perspective
(i) Helps to retain liquidity to meet investment needs of the firm.
(ii) Allows the company to reduce its gearing ratio i.e. debt to equity.
(iii) Complies with any restrictions on payment of cash dividend to shareholders as may be imposed by any
loan covenants.
(b) From the shareholder’s perspective
(i) From a tax viewpoint, it is better as the shareholder need not incur tax on cash dividend
(ii) In case cash dividend is paid and the company needs to issue fresh capital to meet its investment needs, there
is a risk of dilution of control. This is avoided by payment of scrip dividend.
2. Disadvantages of this alternative are:
(a) Issue of stock dividend at frequent intervals creates administrative hassles for the company. It is difficult
to determine if all stock dividends are captured at the market value per share.
(b) There is no inflow of funds to the shareholder and this does not increase his income stream. It is a mere
capitalisation of profits, of funds which already belongs to shareholders. There is just a reassurance through
issue of additional shares.
(c) Companies have to pay dividend distribution tax.
Shennu Plc currently has a paid up capital of 4,00,000 shares of Tshs 100 each. It decided to pay dividend of
5%. This would amount to 20,000 shares and the fair market value is Tshs 750 per share. Therefore Tshs
15,000,000 is transferred from retained earnings and split as Tshs 2,000,000 under paid up capital and the balance
under share premium.
5.2 Share repurchase
Another alternative to cash dividends is to make share repurchases. Share repurchase is possible subject to the
regulations specified in the local laws with regard to buy back. Payments can be made only out of divisible
profits. Repurchases are strictly regulated to ensure that the share capital is not reduced so as to endanger the
security available to the creditors of the organisation. Michael J Brennan and Anjan Thakor have developed a
theory of corporate cash disbursement, stating that cash dividends are likely to be preferred for small distributions
and share repurchases dominate for large distributions.
There are three types of share repurchases
1. Fixed price tender offer: where the number of shares to be purchased and the price is pre-determined by the
company. In case the shareholders offer more shares than what was desired by the company, it may
repurchase the additional shares or refuse them. The disadvantage of the formal tender offer is high
transaction costs to the company.
418
Decision
330 :Divided
Dividend
Decisions
© GTG
2. Dutch auction tender offer: where the shareholders can submit to the company the quantum of shares
they are willing to sell. The minimum and maximum price is declared in advance by the company. The
minimum price is slightly above the current market price. Based on the offers received, the company calculates
the lowest price at which all the required shares would be repurchased.
3. Open market purchases: where repurchases are made through a broking house. This is subject to
regulations imposed by the relevant capital market regulator and is usually suitable for a large block of shares.
In the absence of significant investment opportunities, the excess earnings are distributed to the shareholders.
With repurchase of shares, there are fewer shares outstanding. Therefore, the earnings per share and dividend
per share go up. Consequently, the share price also increases. The share price under the tender offer has to be
fixed in such a manner that the shareholders who don’t subscribe are not worse off than the shareholders who
subscribe.
The equilibrium price is determined as follows
Price =
SXP
S−n
Where,
S is the number of shares outstanding prior to repurchase
P is the market price prior to repurchase
n is the number of shares to be repurchased
Rocket Ltd currently has 10 million shares outstanding at a market price of Tshs 400 per share. It wishes
to repurchase shares in lieu of dividend to the tune of 1 million shares. The equilibrium price would be:
P=
10,000,000 x 400
10,000,000 − 1,000,000
P = Tshs 444.44 per share
Advantages

There is a distinct tax advantage since the market price increase due to repurchase is subject to tax only
in the event of sale, while the tax on dividend is applicable in the year of payment. Furthermore, capital
gains in most countries are taxed lower than dividend. However, in the absence of tax differential, the
investors would be indifferent between repurchase and cash dividend.

In case of excess cash, the firm may choose to repurchase as a one-off alternative to dividend payout,
since payment of extra dividend might increase shareholder expectation, making it a regular feature.

Share repurchase has a signalling effect. In case the management believes that the shares are undervalued
and the repurchase is made at a premium, it reflects the management’s belief on the degree of
undervaluation.
Disadvantages

Cash dividends are a regular phenomenon which investors look forward to. Repurchase is viewed more as
a one-time affair.

Since there is cash outflow involved, accompanied with transaction costs, repurchase can be executed only
when there is sufficient liquidity.
What are the advantages of scrip dividend over cash dividend?
Divided Policy: 419
© GTG
Answer to Test Yourself
Dividend Policy: 331
Answer to TY 1
Dividend payout ratio =
Total dividend paid to ordinary shareholders
× 100
Earnings after tax and preference dividends
Using the formula, TBM Ltd’s dividend payout ratio is:
Tshs 100/ Tshs 400x 100 = 25%
In other words, TBM Ltd distributed 25% of its net income as dividends last year and ploughed back the balance
75%.
A ratio of 25% means that shareholders are only receiving a small amount for every shilling the company is
earning. The real question is whether 25% is good or bad, and that is subject to interpretation. Growing companies
will typically retain more profits to fund growth and pay lower or no dividends.
Answer to TY 2
The model given by Prof James E. Walter is based on the relationship between the firm’s internal rate of return
or return on investments and the cost of capital. So long as the firm’s rate of return (r) is higher than the cost of
capital (k), the firm will retain the earnings. If r < k, the investors are better off receiving dividends and investing
it in other avenues.
Answer to TY 3
(i) Dividend is declared
𝑃𝑃0 =
𝑃𝑃0 =
1
(𝐷𝐷 + 𝑃𝑃1 )
(1 + 𝑘𝑘𝑒𝑒 ) 1
1
(20 + 𝑃𝑃1 )
(1 + 0.15)
100 = (20+P1)/1.15
115 = 20+P1
P1 = 95
(ii) Dividend is not paid
𝑃𝑃0 =
1
(𝑃𝑃 )
(1 + 0.15) 1
100 = P1/1.15
P1 = 115
(iii)
nP1 = I-(E-nD1)
= 2,000,000-(1,200,000-1,000,000)
= 1,800,000
No. of shares to be issued = 1,800,000/95 = 18,947 shares.
420 Divided Decision
332 : Dividend Decisions
© GTG
Answer to TY 4
Po =
=
E(1− b)
ke − br
100(1 − 0.4)
0.10 − (0.4)(0.08)
=
100X0.6
0.10 − 0.032
= 60/0.068 = 882.35
Share price = Tshs 882.35
Answer to TY 5
EPS = 1,000,000/200,000 = 5
DPS = 1,000,000*0.4/200,000 = 2
𝑃𝑃 =
2+
0.16(5 − 2)
0.12
0.12
= (2+4)/0.12= 6/0.12 = Tshs 50
Answer to TY 6
The shareholder expectations on dividend depend on:
1. Taxation
The tax laws applicable on dividend pay-out influence shareholder expectations. In the case of slab based
personal taxation, investors in the higher income bracket prefer capital appreciation of stock to dividend. This is
because tax on dividend income would have to be paid in the same year at the maximum marginal rate while
taxation on appreciation (capital gains) will have to be incurred only in the year of sale. Furthermore, in case tax
laws support retention of shares for increased tenure, taxation would be at a lower rate.
2. Investment opportunities
Investors would expect higher dividend pay-out if there is an opportunity cost in terms of alternative investment
opportunities available in the market.
3. Ownership dilution
In the case of higher dividend pay-outs, the management may need to issue additional equity shares for
investment purposes. If they are not subscribed to by existing shareholders, there would be dilution of ownership
and control.
Answer to TY 7
1. From the company’s perspective
(a) Helps to retain liquidity to meet investment needs of the firm.
(b) Allows the company to reduce its gearing ratio i.e. debt to equity.
(c) Complies with any restrictions on payment of cash dividend to shareholders as may be imposed by any
loan covenants.
Divided Policy: 421
Dividend Policy: 333
© GTG
2. From the shareholder’s perspective
(a) From a tax viewpoint, it is better as the shareholder need not incur tax on cash dividend
(b) In case cash dividend is paid and the company needs to issue fresh capital to meet its investment needs,
there is a risk of dilution of control. This is avoided through scrip dividend.
Quick Quiz
1. There is a
_purpose.
relationship between the dividend payout and the retained earnings available for
2. Fixed dividend policy is not suitable for companies with
profits.
3. The scrip dividend is paid by converting the
appearing in the company’s financials into
equity share capital to the extent of
i.e. capitalisation of profits.
4. The model given by Prof James E. Walter is based on the relationship between the
and the
.
5. According to the MM hypothesis, the effect of
additional
.
_will be offset by the effect of raising
Answers to Quick Quiz
1. Direct, investment
2. Volatile
3. Reserves and surplus, dividend
4. Firm’s IRR , cost of capital
5. Dividend payout, capital.
Self Exami ation Questions
n
Question 1
Explain whether the dividend decision is relevant or irrelevant to the market price of the shares.
Question 2
How does share repurchase operate as an alternative to cash dividend?
Question 3
Brica Ltd has provided the following details:
Dividend per share
Tshs 30
Earnings per share
Tshs 100
Cost of capital
10%
Firm’s rate of return 12%
Calculate the market price per share using (i) Gordon’s model, (ii) Walter’s model.
422 Divided Decision
334 : Dividend Decisions
© GTG
Question 4
JFK Ltd has 1 million shares outstanding at the beginning of 20X0. The current market price is Tshs 1200 and
the Board has approved a dividend of Tshs 62 per share. The capitalisation rate suitable for the risk class to which
the company belongs is 9.8%. Calculate the following:
(a) Based on the MM approach, the market price when
(i) dividend is declared
(ii) dividend is not declared
(b) If the company proposes an investment of Tshs 372 m and the income for the year is Tshs 150m, how many
additional shares will it have to issue to finance the investment?
Answers to Self Examination Questions
Answer to SEQ 1
Miller and Modigliani are the proponents of a school of thought that dividends are irrelevant as far as share
prices are concerned. They contend that the share price depends on the level of corporate earnings, which in turn
depend on the company’s investment decisions.
Investors are rational and they look to maximise their wealth. The extent and timing of dividend payouts is
irrelevant. Since prime importance is given to investment decisions, dividends are determined as a residual
amount. There may even be no dividends if the retained earnings are consumed by investment projects. However,
the expected future earnings of the company will push the share price up. In this manner, a shareholder gains in
capital appreciation even if he does not get dividend payments.
Dividend relevance
This school of thought was prevalent before Miller and Modigliani published their theory. The dividend relevance
theory is exactly opposite to the irrelevance theory. This school of thought argues that dividend policies are
relevant for share valuations. There are three models of dividend relevance:
1. Walter’s model
The model given by Prof James E. Walter is based on the relationship between the firm’s internal rate of return
or return on investments and the cost of capital. So long as the firm’s rate of return (r) is higher than the cost of
capital (k), the firm will retain the earnings. If r < k the investors are better off receiving dividend and investing it
in other avenues.
2. Gordon’s growth
This model also supports the theory that dividend is relevant. The assumptions for this model are similar to Walter’s
model. This theory’s argument is that investors are risk averse, they put a premium on a definite return and
penalise uncertain returns. Therefore, investors would discount shares whose dividends are postponed.
3. Lintner’s model
Based on his study, Lintner explained that firms fix the target payout ratios for a long term based on return
expectations. The dividend policy is changed only when there is surety that dividends are sustainable.
Divided Policy: 423
Dividend Policy: 335
© GTG
Answer to SEQ 2
Share repurchases are an alternative to cash dividends. Share repurchase is possible subject to the regulations
specified in the local laws with regard to buy back. Payments can be made only out of divisible profits.
Repurchases are strictly regulated to ensure that the share capital is not reduced so as to endanger the security
available to the creditors of the organisation.
Michael J Brennan and Anjan Thakor advance a theory of corporate cash disbursement, stating that cash
dividends are likely to be preferred for small distributions and share repurchases dominate for large distributions.
There are three types of share repurchases:
1. Fixed price tender offer where the number of shares to be purchased and the price is pre-determined by
the company. In case the shareholders offer more shares than what was sort by the company, it may
repurchase the additional shares or refuse the same. The disadvantage of the formal tender offer is high
transaction costs to the company.
2. Dutch auction tender offer where the shareholders can submit to the company the quantum of shares,
they are willing to sell. The minimum and maximum price is declared in advance by the company. The
minimum price is slightly above the current market price. Based on the offers received the company calculates
the lowest price at which all required shares would be repurchased.
3. Open market purchases where repurchases are made through a broking house. This is subject to regulations
imposed by the relevant capital market regulator and usually suitable for large block of shares.
In the absence of significant investment opportunities, the excess earnings is distributed to the shareholders.
With repurchase of shares, there are fewer shares outstanding. Therefore, the earnings per
share
and
dividend per share goes up. Consequently, the share price also increases.
The share price under the tender offer has to be fixed in such a manner that the shareholders would don’t subscribe
are not worse off than the shareholders who subscribe. The equilibrium price is determined as follows
Price =
S XP
S −n
Where,
S is the number of shares outstanding prior to repurchase
P is the market price prior to repurchase
n is the number of shares to be repurchased
Advantages & Disadvantages

There is a distinct tax advantage since the market price increase due to repurchase is subject to tax only
in the event of sale, while the tax on dividend is applicable in the year of payment. Further capital gains
in most countries are taxed lowered than dividend. However, in the absence of tax differential, the investors
would be indifferent between repurchase and cash dividend.

In case of excess cash, the firm may choose to repurchase as a one-off alternative to dividend payout, since
payment of extra dividend might increase shareholder expectation to making it a regular feature.

Share repurchase has a signalling effect. In case the management believes that the shares are undervalued
and the repurchase is made at a premium, this reflects the management’s belief on the degree of
undervaluation.

However, cash dividends are a regular phenomenon which investors look forward to. Repurchase is viewed
more as a one-time affair.

Since there is cash outflow involved accompanied with transaction costs, repurchase can be executed only
when there is sufficient liquidity.
424 Divided Decision
336 : Dividend Decisions
Answer to SEQ 3
Dividend payout ratio = Dividend per share / Earnings per share
= 30/100
= 30%
Retention ratio = 1-dividend payout ratio = 1-0.3 = 0.7 = 70%
(i) Gordon’s formula
Po =
=
E(1− b)
ke − br
100(1− 0.7)
0.10 − (0.7)(0.12)
= (100 X 0.3) /(0.10-0.084)
= 30/0.016
= Tshs 1,875
(ii) Walter’s model
𝑃𝑃 =
𝑃𝑃 =
𝐷𝐷 +
𝑟𝑟
(𝐸𝐸 − 𝐷𝐷)
𝑘𝑘𝑒𝑒
𝑘𝑘𝑒𝑒
30 +
0.12
(100 − 30)
0.10
0.10
= (30 +84)/0.10 = 114/0.10
= Tshs 1140
Answer to SEQ 4
(a) Based on MM approach
(i) Market price when dividend is declared
P=
1
×(D1 + P1 )
1 +k e
1,200 =
1
×(62 + P1 )
1 + 0.098
1200 X 1.098 = 62 + P1
= 1317.6-62 = P1
Therefore P1 = 1255.60
© GTG
Divided Policy: 425
© GTG
Dividend Policy: 337
(ii) Market price when dividend is not declared
1
×(D1 + P1 )
1 +k e
1
1,200 =
×(0 + P1 )
1 + 0.098
P=
P1 = 1317.60
(b) Let’s calculate the number of shares to be issued under both the situations: when dividend is declared
and when dividend is not declared.
(Amounts in Tshs million)
Particulars
Investment required
Less: Earnings
Add: Dividend outflow
Total funds required(a)
Market price per share (b)
No. of shares to be issued
(a/b)
No. of shares to be issued (rounded up)
Dividend is
declared
372
(150)
62
Dividend is not
declared
372
(150)
-
284
222
1,256
1,318
226,186.68
168,488.16
226,187
168,488
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IEQ 1
(a)
Indicate whether the following events might cause the price of equities (stocks) in general to change and
whether they might cause a bank’s share price to change.
(i)
(ii)
(iii)
(b)
The government announces that inflation unexpectedly jumped by 2 per cent last month.
The bank’s earnings report, just released, generally fell in line with analysts’ expectations.
The government reports that economic growth last year was at 3 per cent, which generally agreed
with most economists’ forecasts.
(iv)
The Parliament approves changes to the tax laws that will increase the top marginal corporate tax
rate. The legislation had been debated for the previous six months.
(6 marks)
Amazon Company Ltd. and Zodiac Company Ltd, are in the same risk class. Shareholders expect Amazon
to pay a TSHS.400 per share dividend next year when the stock will sell for TSHS.2,000 per share. Zodiac
Co. has a no-dividends policy. Currently, Zodiac stock is selling for TSHS.2,000 per share. Zodiac
shareholders expect a TSHS.400 capital gain over the next year. Capital gains are not taxed, but dividends
are taxed at 25 percent.
REQUIRED:
(i)
(ii)
(iii)
(c)
The net income of GGM Corporation, which has 10,000 outstanding shares and a 100% dividend payout
policy, is TSHS.32,000. The expected value of the firm one year hence is TSHS.1,545,600. The appropriate
discount rate for Magita is 12 percent.
REQUIRED:
(i)
(ii)
IEQ 2
What is the current price of Amazon stock?
(4 marks)
If capital gains are also taxed at 25 percent, what is the price of Amazon stock?
(3 marks)
Explain the result you found in part (b) (ii) above.
(2 marks)
What is the current value of the firm?
(2 marks)
What is the ex-dividend price of Magita’s stock if the board follows its current policy?
(3 marks)
(Total: 20 marks)
426 Divided Decision
338 : Dividend
Decisions
© GTG
(a)
According
to Modigliani and Miller (M & M) theory, dividend policy is irrelevant in a world of frictionless
(a)
(b)
(b)
(c)
(c)
capital market. How did Miller and Modigliani arrive to this conclusion?
(6
marks)
According to Modigliani and Miller (M & M) theory, dividend policy is irrelevant in a world of frictionless
capital market. How did Miller and Modigliani arrive to this conclusion?
(6
marks)
Discuss, using appropriate theories, any three determinants of dividend policy and decisions in real world.
(9 marks)
Discuss, using appropriate theories, any three determinants of dividend policy and decisions in real world.
Crane Ltd. is listed in the local stock exchange. Currently, the company has 2 billion outstanding
(9 marks)shares
selling at market price of TSHS.100 per share. The company has no borrowing and has internal funds
available
capital
expenditure
of TSHS.30
billion. the
Thecompany
capital expenditure
is outstanding
expected to shares
yield a
Crane
Ltd.toismake
listeda in
the local
stock exchange.
Currently,
has 2 billion
positiveatnet
present
value
TSHS.20per
billion.
TheThe
firm company
also wantshas
to pay
a dividendand
per share
of TSHS.15.
selling
market
price
of of
TSHS.100
share.
no borrowing
has internal
funds
Given thetocompany’s
Capital
expenditure
and its
policyThe
of zero
borrowing,
the is
company
willtohave
available
make a capital
expenditure
of plan
TSHS.30
billion.
capital
expenditure
expected
yieldto
a
issue new
to value
finance
dividend
its also
shareholders.
positive
netshares
present
of payment
TSHS.20ofbillion.
Thetofirm
wants to pay a dividend per share of TSHS.15.
Given the company’s Capital expenditure plan and its policy of zero borrowing, the company will have to
issue new shares to finance payment of dividend to its shareholders.
REQUIRED:
With supporting computations, explain how Crane Ltd’s value will be affected.
REQUIRED:
(i) supporting
If it doescomputations,
not pay any dividend
(2 affected.
marks)
With
explain how Crane Ltd’s value will be
(ii)
(i)
If itit does
pays the
dividend
If
not TSHS.15
pay any dividend
(3 marks)
marks)
(2
(ii)
If it pays the TSHS.15 dividend
(3 marks)
(Total :20 marks)
(Total :20 marks)
Answers to Indicative Examination Questions
Answer
1
AnswerstotoIEQ
Indicative
Examination Questions
(a)
The government announces that inflation unexpectedly jumped by 2 per cent last month.
Answer to IEQ 1(i)

The change in systematic risk has occurred.
(a)
(i)
The
government
announces
inflation the
unexpectedly
jumped
2 per centnominal
last month.
An increase
in inflation
rate that
decreases
real rate of
return,byassuming
rates
remain
unchanged.

The
change
in systematic risk has occurred.
Therefore,
market
prices rate
in general
will most
decline.
Price of
the banknominal
will fall. rates

An
increase
in inflation
decreases
the likely
real rate
of return,
assuming
(ii)
Bank’s earnings
report, just issued, generally fell in line with analysts’ expectations.
remain unchanged.

Therefore, market prices in general will most likely decline. Price of the bank will fall.

No change
in unsystematic
risk (risk fell
factor)
(ii)
Bank’s
earnings
report,
just issued, generally
in line with analysts’ expectations.

The company stock price already reflects the market valuation of the company’s earnings
since
it is in line
with the analysts’
expectations.

No change
in unsystematic
risk (risk
factor)
of the
bankprice
stockalready
will mostly
likely
stay constant.

The price
company
stock
reflects
thetomarket
valuation of the company’s earnings
(iii)
The government
that the
economic
growth
last year was at 3 per cent, which generally agreed
since it isreports
in line with
analysts’
expectations.
economists’
with most
The
price of theforecasts.
bank stock will mostly likely to stay constant.
(iii)
The government reports that economic growth last year was at 3 per cent, which generally agreed

Noeconomists’
change in systematic
with
most
forecasts. risk (risk factor)

Market has already priced the stocks in expectation of economic growth.

No
change market
in systematic
(risk factor)
Therefore,
prices risk
in general
will stay constant and bank stock price will most likely
stay constant.

Market
has already priced the stocks in expectation o