Chapter 1
Gitman defines finance as “The art and science of managing money’’.
Financial management is therefore a subject that looks at the institutions,
markets and instruments that deal with the transfer of money among and
between individuals, businesses and governments. The following diagram
shows this arrangement.
Individuals
Corporations
Governments
Financial intermediaries
Parties with
Funds
Buy financial
Instruments
Thereby making
Finance available
To financial
Intermediaries
Individuals
Corporations
Governments
Parties in need of
Funds (demanders
of finance)
Create attractive
Financial instruments
that mobilize excess
Funds
Channel funds to individuals
Corporations and governments
In the form of loans and other
Instruments.
To appreciate the scope of financial management one has to look at the
functions performed by the financial manager in an organization. The
functions performed by the financial manager can be best understood by
focusing on the decisions that the financial manager makes in the
organization.
The financial manager makes a number of important decisions but these have
to be looked at in the context of the financial objectives that the firm would be
striving to achieve. It is therefore important to look at the possible financial
goals that can be pursued by an organization as this will help one to
understand why a particular alternative (decision) would have been chosen by
the decision maker.
Possible financial goals pursued by firms.
There are a number of financial goals that can be pursued by firms either
individually or collectively. These are summarized as follows:
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Survival
Sometimes severe economic or market shocks may necessitate survival to
become the overriding objective. Should this be the case management focus
on short-term issues to ensure survival of the concern, paying little attention to
long-term survival of the organization. Should this be the case management
can postpone the organization’s investment programme.
Maximizing sales
This is alternatively known as maximizing market share. A firm may want to
command a high market share. This is because a high market share can be
seen as rewarding. The rewards may be in the form of improved profitability or
increased survival chances. If this is the case decision like price reduction or
relaxation of credit terms can be made.
Growth
Growth, as an objective pursued by the firm is hardly admitted openly, but it is
a financial goal that is sometimes pursued. Size is seen as an end in itself.
This way managers can earn higher salaries, get huge expense accounts,
cars and other perks. Growth can be achieved either internally or externally.
Internal growth will generally take the form of expanded operations for a given
concern while external growth is achieved through merging or take-over.
Maximizing shareholder wealth
This is the financial goal, which is assumed in financial management. A proxy,
that is the firm’s current share price, can measure achievement of this goal. If
the firm’s current share price is maximized then it can be argued that the goal
of shareholder wealth maximization would have been achieved.
Maximization of profit
This is a much more popular financial objective that can be pursued by the
firm. The firm will try to maximize its reported profits. This is a much more
acceptable financial goal but others would want to argue that profit
maximization should not be the firm’s purpose.
Although profit maximization is a popular objective, it is not the preferred
financial objective from the financial management point of view. This is
because the financial objective has a number of problems.
Problems with profit maximization
The following problems associated with profit maximization should always be
borne in mind should an organization be pursuing this objective.
Basis of computation
Profit maximization is based on accrual or matching concepts unlike
shareholder wealth maximization, which is based on cash flows. Profits can
be padded through the use of cosmetic accounting. The following
arrangements indicate how profits can be manipulated to give a picture, which
may apparently be non-existent. An organization may under-provide for
depreciation, adopt misleading stock valuations or carry dangerous stock
levels, all in an attempt to manipulate reported profit.
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Objective’s orientation
Profit maximization leads to the adoption of short-term objectives as it has a
short-term orientation. The organization, in an attempt to improve reported
profit, may cut discretionary spending like Research and Development
expenditure. Wealth maximization favours long-term objectives, which is
consistent with the assumed goal of wealth maximization.
Time value concerns
Profit maximization places too much emphasis on the highest profit
irrespective of the time value of money aspect. Wealth maximization takes
into account the various times at which the benefits (cash flows) accrue and
the eventual effect of the benefits on the firm’s share price.
Risk
Wealth maximization, unlike profit maximization, carefully weighs and adjusts
for the risk inherent in projects since shareholders expect higher returns on
investments with larger inherent risks.
Maintaining a balance between dividends and retention of earnings
Wealth maximization strikes a balance between regular dividend distribution
and retained earnings since both decisions influence the share price, which in
turn reflects the shareholder’s wealth.
Having looked at the possible financial goals of the firm, the functions
performed by the financial manager can now be looked at. It is hoped that the
decisions that are eventually made by the financial manager can be
understood in their proper context if one has an appreciation of the financial
objective that the firm would be striving to achieve.
Functions performed by a financial manager
There are a number of important generic functions that are performed by the
financial manager and these are now discussed in the paragraphs that follow.
A. Financial analysis and planning
It is the responsibility of the financial manager to establish how well the
firm would have performed. He will therefore examine the organization’s
financial statements (Balance Sheet and Income Statement), to evaluate
the performance of the organization. Following this evaluation a number of
important planning decisions can then be made. These include the
addition or reduction in planned capacity and the determination of
additional funding or reduction of funding that may be necessary. The
financial manager primarily uses financial ratio analysis and trend analysis
to come up with an informed position on how well the firm would have
performed.
B. Making investment decisions
This particular function can also be looked at as managing the firm’s asset
structure. It is the responsibility of the financial manager to decide on the
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mix and type of assets to be acquired by the firm. These are real assets
like vehicles and plant or financial assets like shares. The financial
manager must also make decisions relating to modification, replacement
or liquidation of fixed assets. The financial manager uses appraisal
techniques like net present value analysis, payback method, internal rate
of return, accounting rate of return or profitability index to identify capital
projects that can best enhance shareholder value.
C. Making financing decisions
Financing decisions relate to the firm’s capital structure hence this
decision is often referred to as managing the firm’s capital structure or
financial structure. Having identified the assets to be acquired by the firm,
an appropriate mode of finance has to be established. The financial
manager must decide the best mix of financing that is both short-term and
long-term for assets to be acquired by the firm or the financing needed for
projects to be undertaken. There is a considerable body of knowledge that
the financial manager can draw from to establish an optimal mix of
financing that will maximize shareholder wealth. This will be looked at in
detail under the capital structure decision.
D. Working capital management
This is sometimes referred to as treasury management. All organizations
need working capital. Working capital refers to the firm’s current assets
and current liabilities. The financial manager must ensure that the firm has
sufficient working capital to continue operations so as to avoid costly
interruptions in the firm’s production operations.
E. Risk management
Risk is the probability that an outcome will not turn out as expected. Firms
are more concerned with adverse outcomes (downside risk). It is the
responsibility of the financial manager to manage or reduce the risk to
which the organization is exposed. A notable type of risk that is worrisome
to most organizations is exchange risk. This is a type of risk that
organizations engaged in external trade have to face. With exchange risk
the amount to be received in the home currency is not certain. It is the
financial manager’s function to manage and reduce this exchange risk.
The financial manager’s task is complicated if the organization he works
for deals in primary commodities. In this case the prices of the primary
commodities are not stable and in addition there will be exchange risk. All
this requires the skills of the financial manager.
To summarize, the following diagram can capture the primary role of the
financial manager:
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Capital Market
- Equity
- Debt
Searching for
Financing
Opportunities
Operating Assets
- Non current assets
- Current assets
Financial manager
Financial decisions
Money Market
Searching for
Investment
opportunities
Financial Assets
The primary role of the financial manager
When discussing the investment decision it is important to appreciate the
difference between Investment and speculation.
Investment
Investment is the purchase by an individual or institutional investor of a
financial or real asset that provides a return proportional to the risk assumed
over some future investment period.
Primary differences between investment and speculation
There are basically four different approaches that can be adopted to
differentiate investment from speculation.
1. Holding period
The holding period is the period over which the investor intends to hold the
investment. Usually speculation is for short periods of time for example one
week to a few months. An investment is continuous for a series of a number
of years for example 3 years over a long period of time. Emphasis in
speculation because of the shorter holding period is on capital gains rather
than dividend or interest income.
2. Expected return
Return represents the total annual income and capital gains as a percentage
of the beginning investment.
Return = P1 – P0 + D1 * 100
P0
1
Where P1 = Price at the end of period 1.
P0 = Price at the beginning of period 1.
D1 = Dividend received at end of period 1.
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The expected return from a single speculative security purchase is much
greater than the expected return from the purchase of an investment security.
Investors earn a much lower annual return over a longer period of time than
speculators.
3. Risk assumed
Speculators assume higher levels of risk than investors. This is because
speculators expect higher returns and higher returns can only be expected if
one is prepared to assume higher levels of risk.
4. Degree of information available
Speculators look for opportunities where information available for analysis
tends to be quite limited.
Investment approaches
There are three approaches that can be adopted when one is contemplating
an investment transaction.
The fundamental approach
This approach assumes that a rigorous analysis of each company will result in
the identification and selection of undervalued shares. These shares will be
identified after an economic analysis, industry and company analysis would
have been undertaken. The shares identified will be bought and held as long
as they promise a high return. They are sold if the investor believes they have
become overpriced. Usually the shares are held for relatively long periods of
time. This is a buy and hold approach that is followed by the majority of
institutional investors.
The technical approach
The approach emphasizes that the behaviour of the price of a share and the
volume of trading determines the future price of the share. It centers on the
plotting of the price movement of the share and drawing inferences from the
price movement. The technician then selects a few shares and trades in them.
The emphasis is on capital gains in the short term.
Modern portfolio theory (MPT)
The approach assumes that the market is efficient and information is available
about the market and individual shares. New information is quickly transferred
to the market place and a new price established. Since the market is efficient
and share prices of one moment are independent from prices in the next
moment, it is impossible to predict future prices. Information is known to all,
and no one on average can do much better than the market. Investors buy
and hold on to their shares.
The financial environment
The financial manager operates in an environment characterized by financial
institutions and financial markets.
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Financial institutions
Financial institutions are intermediaries that channel the savings of
individuals, businesses and governments into loans and investments.
Examples of financial institutions in Zimbabwe include commercial banks like
Kingdom bank, Standard Chartered or Barclays bank. There are also savings
banks like the People’s Own Savings Bank (POSB), credit unions like the
Zimta Co-operative Credit Union (ZCCU), life insurance companies like
Zimnat and pension funds like the NRZ pension fund or the mining industry
pension fund (MIFP).
Financial markets
Financial markets provide a forum in which suppliers of funds and those in
need of funds can transact business directly. Financial markets can take the
following forms:
A. Primary market
This is a financial market in which securities (shares) are initially issued. It
is a financial market for new issues.
B. Secondary market
This is a financial market in which pre-owned securities are subsequently
traded.
C. The money market
The money market is a financial market for short- term sources of finance
and financial instruments. Short -term financial instruments are
instruments having an original maturity of one year or less. The following
are examples of short-term financial instruments.
- Treasury bills: These are government of Zimbabwe 90 day
treasury bills. They are issued when the government wishes to
raise short-term financing.
-
Grain bills: These are issued on behalf of the Grain Marketing
Board to raise finance to pay for the produce delivered to the
GMB.
-
RBZ financial bills: These are short- term bill issued by the RBZ
to raise finance for central government or to achieve monetary
objectives of the central bank.
-
Agro bills: They are short-term financial instruments issued to
raise short-term financing for the new farmers. This financing is
used as seasonal finance to pay for land preparation, acquisition
of inputs and other working capital requirements.
-
Petrozim bills: These are issued on behalf of NOCZIM to raise
finance to procure fuel.
-
Megawatt bills: These are issued on behalf of the Zimbabwe
electricity supply authority either to raise financing for the rural
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electrification programme or to retire ZESA debt and pay for
electricity imports.
-
Tobacco bills: They are bill issued on behalf of the Tobacco
Marketing board to promote the production of tobacco.
-
NCDS: Negotiable certificate of deposits are short-term financial
instruments issued by banks. The certificates can be negotiated
to other investors.
It is important to note that financial institutions participate in both the money
market and the capital market as suppliers and demanders of finance.
Participants in the money market
There are a number of institutions that participate in the money market either
as suppliers or demanders of short-term finance. The following are examples
of institutions that participate in the money market:
-Commercial banks: These are institutions that accept demand (cheque) and
time (savings) deposits.
-Merchant banks: Merchant banks are bankers to corporations providing
investment and short to medium term loans to corporations.
-Discount houses: They are financial institutions involved in buying and
discounting money market instruments.
-Building societies: These are institutions involved in the mobilization of
savings deposits to provide mortgage finance.
Functions of the money market
The money market performs four main functions. These are explained in the
paragraphs that follow.
1. Provision of short-term capital
The money market provides short-term capital to companies, financial
institutions, governments and other organizations requiring short-term finance.
2. Provision of a market
The money market provides a market for short-term investors to invest funds
in short-term financial instruments that are low risk and highly liquid.
3. Acting as a barometer of liquidity
The money market acts as a barometer of liquidity within the economy. The
Reserve bank can increase or curb liquidity by adopting strategies that
operate via the money market for example open market operations (OMO).
4. Determining interest rates
The money market also acts as the main determinant of interest rates in the
economy. The demand and supply of funds in the money market determines
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the interest rates in the economy for example APDS for ZIMRA. Interest rates
firm because of excessive demand for cash. After the APDS the interest rates
ease.
D. The capital market
This is a financial market for long-term finance and financial instruments.
These will be financial instruments having an original maturity of more than
one year. Examples of these financial instruments include debentures,
preference shares, ordinary shares and agro-bonds (instruments to
provide finance for infrastructural development for the new farmers.
Functions of financial markets
Financial markets perform five broad functions. These are explained
below.
1. Allocation of financial resources
Financial markets provide a mechanism for transferring wealth between
periods in a way that increases the individual’s total level of utility.
2. Transfer of risks
Financial markets enable investors to reduce or even eliminate some risks
by shifting risk to those who are more willing to accept it (at a cost).
A invests in B`s debentures (a safe investment)
A
B
(Risk averse)
Offers Debentures
(Risk lover)
B buys equity in C
B shoulders risk
Inherent in C`s equity
Plus probability of financial
Distress (Debentures)
A has transferred risk to B
By virtue of holding relatively
Safe debentures.
C
It is important to note that there is a cost involved with this arrangement.
Equity pays more than debentures because of the risk element. The return
differential represents the cost of transferring risk to B.
3. Liquidity/Marketability
The availability of an active financial market provides the investor with
liquidity or marketability that facilitates changing the level of investment as
the situation dictates. If the investor requires cash he can readily sell part
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of his shareholding to get cash. If he has excess cash he can increase his
shareholding by buying additional units of shares from the market.
4. Increasing divisibility of real capital
The existence of financial markets reduces the effect of the indivisible
nature of real capital (assets). Subject to meeting the minimum numbers
required one can either increase or decrease his shareholding thereby
altering (dividing) upwards or downwards their real capital.
5. Provision of financial information
Financial markets provide information on the available returns of various
investment opportunities. Financial publications for example, disclose the
previous day or week’s price and give an indication of trading in given
shares on the market.
The Zimbabwe Stock Exchange
This is a physical market located in Harare. It provides two indices, the
industrial and the mining indices and price quotations on a daily basis
(Monday to Friday). The indices provide a measure of the overall
performance of financial instruments traded on the stock exchange.
Characteristics of a well-run stock exchange
A well-run stock exchange is one in which:
(a) Some investors and fundraisers are unable to benefit at the expense of
other participants.
(b) Is well regulated to avoid abuses, negligence and fraud. This is
necessary because investors need to be reassured that their hard
earned savings are safe.
(c) There are minimal transaction costs. It is desirable to transact cheaply.
(d) There are a large number of buyers and sellers to ensure efficient
share price setting.
(e) Investors can sell their shares at any time without materially altering
the share price.
Benefits accruing from a well-run stock exchange
Six benefits can be argued to accrue to any economy if the economy has wellrun stock exchange in operation.
1. Provision of funds to firms
Investors with quoted financial securities are assured that they can sell their
shares quickly and cheaply at a reasonably certain price. This induces them
to supply funds at a lower cost than would be the case if selling of shares was
slow and expensive or if the price was uncertain. Stock markets encourage
investment by mobilizing savings.
2. Allocation of capital
An efficient market assists in the direction or flow of investment capital. A
poorly regulated and operated stock market can mis-price financial securities
leading to the direction of scarce capital to sectors which are inappropriate
given the assumed objective of profit maximization.
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3. Provision of a secondary market for shareholders
Shareholders will benefit if there is a well-run stock market because they can
speedily and cheaply sell their shares should they want to do so. They may
also be able to establish the value of their investment even if they do not wish
to sell their securities.
4. Status and publicity
A stock exchange quotation enhances the public profile of a firm. Some firms
have been referred to as blue chips, a status only accorded to quoted firms.
The quotation also brings with it more confidence from banks and other
financial institutions leading to the provision of funds at a lower cost. The
detailed scrutiny of the firm brings about this confidence.
5. Facilitation of mergers
A public quotation can facilitate a merger where the mode of acquisition is a
share swap. Unquoted companies are difficult to value whereas quoted
shares have a value that is defined by the market.
6. Improvement in corporate behaviour
Directors of companies listed on the stock exchange are more inclined to
behave in a manner likely to enhance shareholder’s interest. For example a
quotation requires disclosure greater in range and depth than is required by
accounting standards and the companies act. Because the information is
disseminated widely it becomes the focus of the general public and press
comment.
Efficient Capital Markets
An efficient capital market is one in which security prices reflect available
information.
Types of efficiency
Three types of market efficiencies can be identified and these are now
explained.
(1) Operational efficiency: This refers to the cost of security transactions
to buyers and sellers on the exchange. It is desirable that the cost is as
low as possible and creating a lot of competition between market
makers and brokers can bring this about.
(2) Allocation efficiency: This refers to the ability of the stock market to
direct financial resources where they are most needed. Society’s
financial resources are scarce so it is important that this scarce
resource is allocated where it is most productive. Stock markets assist
in the allocation of the scarce financial resources between competing
real investments.
(3) Pricing efficiency: The market price of a share should reflect
available information so that no investors can earn returns above those
earned on average by the market. The ability of the market to correctly
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price a financial security is what is referred to as pricing efficiency. It is
the efficiency to focus on when dealing with the efficient market
hypothesis.
Importance of having an efficient market
It is desirable that the stock market operating in an economy is efficient. There
can be substantial benefits to be derived from this efficiency. These benefits
are now discussed.
1. An efficient market encourages share buying: Accurate security pricing
is important if investors are to invest in quoted companies. The investor wants
an assurance that securities are correctly priced. He would not want to lose
his hard earned financial resources. Inability to correctly price financial
securities can lead to a shortage of funds to organizations.
2. An efficient market provides correct signals to corporate
management: If companies are to pursue shareholder wealth maximization,
sound financial decision-making will require that the market correctly price
securities. The market will provide the necessary feedback on their efforts.
Unreliable security prices can distort the investment decision. Share prices
provide indication of the required rate of return. Projects can be wrongly
accepted or rejected.
3. An efficient market assists in the allocation of resources: Allocation
efficiency requires both operational and pricing efficiency. Assuming an
inefficient company has highly priced shares it would be able to attract capital
and the limited resources will be wasted.
Price behaviour in an efficient market
In an efficient market the price reflects what is known about a company’s
current operations, profitability and potential for future growth and profits.
Overreaction and correction
Price ($)
220
180
140
100
Efficient market reaction
Delayed reaction
-4
-3
-2
-1
0
+1 +2 +3
Time in days
+4
Fig. Reaction of share price to new information in efficient and inefficient
markets.
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Efficient market reaction: The share price instantaneously adjusts to and
fully reflects new information. There is no tendency for subsequent increases
and decreases to occur.
Delayed reaction: The share price partially adjusts to the new information. .
Four days elapse before the share price completely reflects the new
information.
Overreaction: The share price over-adjusts to the new information. It
overshoots the new price and subsequently corrects.
Efficient Market Hypothesis (EMH)
This is an investment theory that states that it is impossible to beat the market
because prices already incorporate and reflect all relevant information.
Proponents of this model believe that it is pointless to search for undervalued
stocks or try to predict trends in the market through any technique from
fundamental to technical analysis.
Eugene Farma formulated efficient market hypothesis in 1970. The
hypothesis suggests that at any given time, prices fully reflect all available
information on a particular stock and or market. No investor has an advantage
in predicting a return on a particular stock price since no one in particular has
access to information not already available to everyone else.
Degrees of market efficiency
The following are three classifications of market efficiency. They reflect the
degree to which efficiency can be applied to markets.
1. Strong efficiency
This is the strongest version which states that all information in the market,
whether public or private is accounted for in the stock price. Not even
insider information could give an investor an advantage.
2. Semi-strong efficiency
All PUBLIC information is calculated into a share’s current price. Neither
fundamental nor technical analysis can be used to achieve superior gains.
3. Weak efficiency
This type of efficient market hypothesis claims that all past prices of a
stock are reflected in today’s stock price. Technical analysis cannot be
used to predict and beat a market.
Challenges to Market efficiency
In the real world there are some investors who have beaten the market.
Warren Buffet’s investment strategy of focusing on undervalued stocks made
millions and set an example that is now being followed by many.
There are also consistent patterns that are present in the market. There is the
January effect, a pattern that shows that higher returns tend to be earned in
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the first four months of the year. There is also the “blue Monday on Wall
street”. This is a term that discourages buying stock on Friday afternoon and
Monday morning because of the “weekend effect”. This is a tendency for
stock prices to be higher than the rest of the week.
Studies in behavioural finance (a study into the effects of investor psychology
on stock prices) also reveal that there are some predictable patterns on the
stock market. Investors buy undervalued stocks and sell overvalued stocks.
Paul Krugman, MIT economics professor, suggests that because of mass
mentality of the trendy, short-term shareholder, investors pull in and out of the
latest and hottest stocks. This leads to stock price distortions and hence the
market becomes inefficient. Prices in this case would be manipulated by
profit-seekers.
Contributors to market efficiency
The following can be noted as significant contributors to the improvement of
market efficiency:
1. Investors must perceive that a market is inefficient and possible to
beat. Investment strategies intended to manipulate inefficiencies will
the actually be the fuel that keep a market efficient.
2. A market must be large and liquid.
3. Information must be widely available (in terms of accessibility and
cost). It should also be released to investors more or less at the same
time.
4. Transaction costs must be cheaper than the expected profits of an
investment strategy.
5. Investors should have enough funds to take advantage of the
inefficiencies until the inefficiencies disappear.
6. Investors must believe that they can outperform the market.
Conclusion
Efficient market hypothesis supporters argue that profit seekers will exploit
abnormalities that may exist until they disappear leaving the market to
eventually correct itself. Large transaction costs are likely to outweigh the
benefits of trying to take advantage of such a trend.
Markets cannot be absolutely efficient or wholly inefficient, they are a mixture
of both. Daily decisions by market players cannot be reflected immediately
into the market.
Electronic trading allows for prices to adjust more quickly to news entering the
market.
Information technology is leading to greater market efficiency. It allows for a
more effective, faster means to disseminate information widely. It however
restricts the time for the verification of information used to make the trade.
This may eventually result in less efficiency if the quality of the information no
longer allows investors to make profit-generating decisions.
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Implications of the EMH for investors
1. Public information cannot be used to earn abnormal profits.
Fundamental analysis is therefore a waste of money for as long as
efficiency is maintained. The best an average investor can do is to
select a diversified portfolio.
2. There is need for greater volume and timely information. Since semistrong efficiency depends on the quality and quantity of publicly
available information investors should pressure companies, accounting
bodies, governments and stock market regulators to produce as much
useful information as is possible without jeopardizing company
operations to competitors.
Implications of the EMH for companies
1. The timing of security issues does not have to be fine-tuned
2. Large quantities of new shares can be sold without materially moving
the share price.
Factors contributing to developing stock market inefficiencies
1. Lack of investment analysts. For the market to be efficient there must
be a large number of competing investment analysts. Competition
among investment analysts ensures that information is instantly
reflected in security prices. In emerging markets there are few analysts
and this reduces market efficiency.
2. Few buyers and sellers. There are relatively few buyers and sellers on
developing stock exchanges. Few institutional investors sometimes
have a very large impact on the performance of some shares. This
leads to less efficiency since price determination is only left to a few
investors.
3. The Government. Poor or unrealistic government policies have effects
on stock exchanges. In Zimbabwe for example, Socialist policies
adopted at independence impacted on investor confidence leading to a
slump in the operations of the exchange in the 1980s. This outside
influence leads to increased inefficiency of the exchange. The position
changed, however, following the adoption of more liberal policies and
this so the exchange being voted as one of the best performing
exchanges in the developing economies.
4. Limited number of traded firms (counters). In many developing states
the number of firms listed on the stock exchange are few compared to
the number of firms operating in those countries. This limited number
means that all industries will not be represented on the exchange
leading to problems in analyzing and incorporating information.
5. Limited information disclosure.
There is limited disclosure of
information by companies in developing economies. In Zimbabwe for
example, financial reports only show the minimum information
stipulated by legislation. This results in problems in the pricing of
securities, as information is the basis of security pricing.
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Insider Trading
Insider trading is the dealing in securities or financial instruments by a person
knowingly in possession of inside information, relating to the financial
instrument being dealt in.
Inside information is specific and precise information obtained by an insider,
which is price sensitive and has not been made public.
Price-sensitive information is information that has a material effect on the
price or value of an instrument if it is made public.
An insider is someone who has obtained inside information through being a
director, employee or shareholder of the issuer of the financial instrument, or
someone who has gained access to such information by virtue of his
employment, office or profession.
Insiders can either be primary or secondary. Primary insiders obtain
information directly. They include a director, employee, shareholder, legal
advisor, auditor, corporate advisor or sponsoring stockbroker of the company.
Secondary insiders are individuals who obtain inside information directly or
indirectly from a primary insider.
NB. Insider trading undermines confidence in the stock market.
Approaches to deal with insider trading
To avoid undermining the confidence in the stock market it is necessary to
deal with insider dealing. The following approaches have been suggested as
ways that could be used to deal with insider trading.
(a) Legislation and codes of conduct
(b) Increasing the level of information disclosure (price sensitive
information).
(c) Prohibiting certain individuals from dealing in the company’s shares at
crucial time periods. This is generally during the reporting season.
The Agency Problem
The agency problem is the possibility of conflict of interest between the
stockholders (owners) and management (agents of the stockholders) of the
firm. The problem is created by absentee ownership.
Absentee ownership creates a number of problems for the firm.
(1) Agents may consume excessive perquisites “Perks”. This is money or
goods given or regarded as a right in addition to one’s pay.
(2) Agents may shirk. This refers to avoiding doing one’s duty or not
expending one’s best efforts.
(3) Agents may act to their self-interest instead of that of the principal.
The problems highlighted above are of concern to shareholders. They would
therefore want the firm to minimize cases of divergence of interest between
16
shareholders and management. A number of possible solutions have been
suggested.
Possible solutions to the agency problem
1. Linking rewards to shareholder wealth improvement
It has been suggested that as motivation to management additional
rewards should be offered to discourage them from diverging far from what
is in the interest of shareholders. Those making this suggestion
recommend that additional financial rewards like bonuses if the firm’s
share price improves considerably can do the trick.
2. Share options
Directors and other senior managers are granted share options. These
permit them to buy shares at some future date at a price that is fixed now.
If the share price increases between the date of the option granting and
share acquisition, the manager makes a profit. This gives the managers an
interest in trying to improve the share price if they are to benefit. This
brings congruence, which reduces the agency problem.
3. Sackings
Companies can also threaten to sack non-performing managers. These
will be managers who will not be improving the firm’s share price. The
humiliation and financial loss following sacking may encourage managers
not to diverge too far from shareholder wealth maximization.
4. Selling shares and the take over threat
Financial institutions own the bulk of the shares quoted on the stock
exchange. These are not prepared to fund the cost of monitoring directors
in all firms in which they have shareholdings. If they perceive that directors
are not acting in the institution’s best interests, they sell the shares rather
than intervening. The downloading of a large volume of shares reduces
the price creating a real threat of a take-over at such depressed prices. At
such depressed prices the firm may also find it very difficult to raise
financing, creating even more problems for the firm.
5. Corporate governance regulations
Legislation (companies act) and other regulatory pressures like the stock
exchange guidelines are available and can be enforced to encourage
directors to act in shareholders interests.
6. Increasing information flow
The accounting profession and the stock exchange should encourage
firms to release accurate, timely and detailed information concerning their
operations. To the extend that this is adhered to, this may help to monitor
firms and identify wealth destroying actions of wayward managers early.
17
Chapter 2
Valuation is the process that links risk and return to determine an asset’s
worth. The value of an asset is the present value of all future cash flows
expected from the asset over the relevant time period. The value is
determined by discounting expected future cash flows to their present
value using the discount rate, which is commensurate with the asset’s
risk.
Determination of security prices
Security prices on the exchange are determined by supply and demand
and this supply and demand depends on the information that investors
have about the securities. This information can be obtained from the
press, the company and other publications like magazines. The
information obtained can be political, economic, industry or corporate
information.
Political factors
Political events affect stock market prices. Included in political events will
be things like political stability, government changes or statements by
politicians. These events can cause a positive or negative movement in
share prices.
Economic factors
Macro economic factors also affect security prices. Macro economic
factors include variables like economic growth, rate of inflation or
unemployment. These macro economic factors are influenced by
government policies like fiscal and monetary policies. Ultimately these
economic factors affect the financial performance of companies.
Interest rates
Interest rates play an important role in determining security prices in that
the equity market is in competition for funds with the debt market. If the
debt market has attractive interest rates debt instruments become
attractive and more funds are attracted to the debt market at the
expense of the equity market.
International factors
A recession in a country that is Zimbabwe’s major trading partner or
higher returns in markets competing for foreign investors affects security
prices as Foreign direct investment will be directed to those countries
that offer higher returns.
18
Corporate and industry information
The attractiveness of an individual company’s shares is largely
determined by the attractiveness of the industry in which the firm
operates and the performance of the company itself. If an industry is
attractive the shares of the companies in that industry will be priced
favourably. But the extend of the attractiveness of individual shares will
be a function of each firm’s performance in that industry.
Level of financial and business risk of the firm
For risk averse investors the higher the level of risk the less the price the
investors will be prepared to pay for the shares of such companies.
The valuation model
The following is the basic model that can be used to value financial
instruments.
V0 = CF1 + CF2 + ….CFn
(1+k)1 (1+k)2 (1+k)n
VALUATIONS
BONDS/
DEBENTURES
A.
ORDINARY SHARES/
EQUITY
Redeemable
Finite period
Perpetual
Perpetual
PREFERENCE
SHARES
Redeemable
Perpetual
VALUATION OF BONDS/DEBENTURES
A bond is a long-term debt instrument used by organizations and
governments to raise large sums of money. It carries a stated rate of
interest also known as a coupon rate. The coupon rate is expressed as a
percentage of the bond’s par value and it determines the periodic
interest payments. The interest can be paid annually or semiannually.
A redeemable bond has a maturity date. This is the date on which the
face value of the bond will be repaid. The last coupon payment is also
paid when the bond matures.
Bonds have original maturity periods. The period refers to the time
remaining until the bond matures from when the bond was issued.
Remaining maturity refers to the time currently remaining until maturity
date.
19
Bonds redeemable by the issuer prior to maturity are called callable
bonds. The call date is the date at which the bond can be called and the
call price is the amount that the issuer pays to call a callable bond.
The value of the bond is equal to the present value of interest payments
to be received over a defined period.
A1.Valuation of redeemable bonds/debentures
Consider the following example.
A Ltd. Issues a $50 000 10% 5 year bond. If the interest is paid annually
and the required rate of return on similar bonds is 10%, what is the value
of the bond if it is repayable at par?
Annual interest payment = 10/100*$50 000 = $5 000.
The following time line indicates the interest payments to be received by
a holder of such a bond.
0
$Nil
1
$5 000
2
$5 000
3
$5 000
4
$5 000
5
$5 000
+
$50 000
During year 5 there is the principal that has to be repaid as well.
The present value of the cash flows can now be presented.
0
$Nil
$4 545
4 130
3 755
3 415
34 155
50 000
1
$5 000
2
$5 000
3
$5 000
4
$5 000
5
$5 000
+
$50 000
= 0.909
= 0.826
= 0.751
= 0.683
= 0.621
3.790
A tabular format can also be used to show how the present value can be
arrived at. It is the method that will be used to illustrate the valuation of
all financial securities.
20
Present value computation
Time
Cash
Flow
Interest Principal
1
2
3
4
5
$5 000
5 000
5 000
5 000
5 000
$50 000
Discount
Factor
Present
Value
0.909
0.826
0.751
0.683
0.621
$4 545
4 130
3 755
3 415
34 155
$50 000
As the interest payment is an annuity a shorter approach (annuity
approach) can also be used to arrive at the same result.
Present value computation
Time
Cash Flow
Interest
principal
1-5
5
$5 000
-
Discount
factor
$50 000
3.790
0.621
Present
value
$18 950
31 050
$50 000
The above table is a representation of the approach given below which
is often indicated in the literature.
Bo = I (PVIFAkd,n) + RP (PVIFkd,n)
Where Bo = Value of bond at time zero
I = Interest in dollars
PVIFA = Present value interest factor for an annuity
PVIF = Present value interest factor
kd = required rate of return on similar bonds
n = number of years to maturity
RP = redemption payment
Bo = $5 000(3.790) + $50 000(0.621)
= $18 950 + $31 050
= $50 000
Whenever the required rate of return on similar bonds is EQUAL to the
coupon rate of interest, the value of the bond will be EQUAL to the face
value of the bond. The bond sells at par.
21
Variations to the required rate of return
Whenever the required rate of return on similar bonds differs from the
bond’s coupon rate, the value of the bond will differ from its par value.
The required rate of return on a bond can differ from the coupon interest
rate because of the following two reasons:
Economic conditions
Economic conditions change and this may result in a shift in the BASIC
cost of long-term funds. An increase in the basic cost of long-term debt
will increase the required rate of return on debt. A decrease in the basic
cost of debt will lower the required rate of return.
Changes in the firm’s risk posture
If the risk posture that the firm is facing changes, this may change the
rate of return required by suppliers of long-term debt finance. If risk
increases, the required return increases, if risk decreases, the required
rate of return decreases.
An increase in the required rate of return
The following example illustrates the effect of an increase in the required
rate of return on the value of a bond.
B Ltd. Has a $50 000 10% 5 year bond outstanding. Interest is paid
annually. Following an increase in the basic cost of long-term debt, the
required rate of return is now 12%. What is the value of the bond if it is
repayable at par?
Interest = 10/100 *$50 000 = $5 000, R P = $50 000
Present value computation
Time
Cash Flow
Interest Principal
1-5
5
$5 000
-
$50 000
Discount
factor
3.605
0.567
Present
value
$18 025
28 350
$46 375
When the required rate of return is greater than the coupon rate of
interest the value of a bond will be less than its par value. The bond is
said to sell at a discount. The discount is the amount by which the bond
sells at a value that is less than its par/face value.
The discount = $50 000 - $46 375
= $3 675
22
A decrease in the required rate of return
The example that follows shows the effect of a decrease in the required
rate of return on the value of a bond.
C Ltd. Has a $50 000 10% 5 year bond outstanding. Interest is paid
annually. The risk posture of the firm lowers reducing the required rate of
return to 8%. What is the value of the bond if it is repayable at par?
Time
(Year)
1-5
5
Cash Inflow
Discount
Interest Principal factor @8%
$5 000 0
3.993
0
50 000
0.681
Present
value
19 965
34 050
54 015
Whenever the required rate of return falls below the coupon rate of
interest, the bond value will be greater than the par value. The premium
is the amount by which a bond sells at a value that is greater than its par
or face value. The premium in the example just presented will amount to:
Premium = $54 015 - $50 000
= $4 015
Valuation of redeemable bonds, redeemable at a discount
The following example illustrates how the valuation of a redeemable
bond redeemable at a discount is valued. What is needed is to remove
the discount from the redemption proceeds and apply the valuation
model as already illustrated.
C Ltd. has a $100 000 10%, 5 year bond outstanding. Interest is paid
annually and the required rate of return is 10%. What is the value of the
bond if it is repayable at a discount of 10%?
The redemption payment = ($100 000 – (.10*$100 000))
= $90 000
Present value computation
Time
Cash inflow
(Years)
1 -5
$10 000 0
5
0
$90 000
Discount
Present
factor @10% value
3.791
$37 910
0.621
55 890
93 800
23
Valuation of redeemable bonds, redeemable at a premium
If a bond is redeemable at a premium, the premium should be
incorporated into the redemption payment. The following example will
illustrate how the bond that is redeemable at a premium will have to be
valued.
D Ltd. has a $200 000 10%, 5 year bond outstanding. Interest is paid
annually and the required rate of return is 10%. What is the value of the
bond if it is repayable at a premium of 10%?
Redemption payment = ($200 000 +(.10*$200 000))
=$220 000
Present value computation
Time
Cash inflow
(Years) Interest Principal
1 -5
$20 000 0
5
0
$220 000
Discount
factor @10%
3.791
0.621
Present
value
$75 820
$136 620
$212 440
B. VALUATION OF IRREDEEMABLE/PERPETUAL BONDS
Perpetual bonds pay interest perpetually. This means that interest will be
paid indefinitely.
Bo = I
Kd
Where BO = value of a bond at time zero.
I = annual interest in dollars.
Kd = required rate of return on similar bonds.
An example on how a perpetual bond is valued is now presented under
different scenarios.
E Ltd. has a $300 000 10% perpetual bond outstanding. Calculate the
value of the bond if the required rate of return is:
(a) 10%
(b) 15%
(c) 5%
(a) Bo = $30 000
0.10
= $300 000
(b) Bo = $30 000
0.15
= $200 000
24
(c) Bo = $30 000
0.05
= $600 000
YIELD TO MATURITY
Sometimes investors pursue a buy and hold philosophy. They buy a
financial asset and hold it until maturity. This type of investor is
interested in knowing the annual rate of return on a financial asset that
they hold until maturity. This return is what is known as yield to maturity.
Yield to maturity is a rate of return measuring the total performance of a
bond (coupon payments and capital gain or loss) from the time of
purchase until maturity. It is the market rate that equates a bond’s
present value of interest payments and principal repayment with its
price. It represents an annualized rate of return in percentage terms on a
fixed income instrument such as a bond or debenture.
Mathematically yield to maturity is found by using the following formula:
C (1+r)-1 + C (1+r)-2 + - - - + C (1+r)-n + B (1+r)-n =P
Where C = annual coupon payment in dollars not percent
n = number of years to maturity
B = Par value
P = Purchase price
Yield to maturity cannot be solved for directly and one has to use trial
and error or some iterative technique. It is however, fairly ease to get
yield to maturity if one uses a financial calculator.
An alternative would be to use some approximation using the
approximation formula. The results obtained by this method are quite
accurate for decision-making purposes. This approach is now presented.
YTM  Annual Interest Payment +
Par Value – Current Value
Years to Maturity
Par Value + Current Value
2
An illustration on how the approximation approach can be used to
approximate yield to maturity can now be presented.
25
F Ltd. has a $400 000 10%, 5 year bond outstanding. Interest is paid
annually. If the bond is redeemable at par, approximate its yield to
maturity if the required rate of return is:
(a) 10%
(b) 12%
(c) 8%
Before calculating the approximate yield to maturity, the bond current value
has to be calculated first. So one has to calculate current value as the first
step and then calculate approximate yield to maturity as the second step.
(a) Since the required rate of return is currently is 10%, the market value
of the bond is $400 000.
Approximate yield to maturity = $40 000 + ($400 000 -$400 000/5)
$400 000 + $400 000/2
= $40 000
$40 000
=0.10*100
= 10%
(b) When the required rate of return is 12% the value of the bond is as
indicated below:
Present value computation
Time
Cash inflow
(Years)
Interest
Principal
1-5
$40 000 0
5
0
$400 000
Discount
Factor @12%
3.605
0.567
Present
value
$144 200
$226 800
$371 000
Now that Bo is known the approximate yield to maturity can now be
calculated.
Approximate yield to maturity = $40 000 + ($400 000 - $371 000/5)
( $400 000 + $371 000)/2
= $45 800
$385500
= 0.1188067*100
=12%
(c) When the required rate of return is 8%, the value of the bond is
calculated as follows:
26
Present value computation
Time
Cash inflow
(Years)
Interest
Principal
1-5
$40 000
0
5
0
$400 000
Discount
factor @8%
3.993
0.681
Present
value
$159 720
$272 400
$432 120
The approximate yield to maturity can now be calculated.
Approximate yield to maturity = $40 000 +($400 000 - $432 120/5)
($400 000 + $432 120)/2
= $33 576
$416 060
= 0.0806998*100
= 8%
The above example has shown that the required rate of return is similar
to the yield to maturity. This means that when computing the value of a
bond one can use yield to maturity if the required rate of return is not
given.
OTHER COMPOUNDING PERIODS
Occasionally interest is paid more than once annually. The valuation
model has to be adjusted to incorporate the fact that interest is paid
more than once annually. The table presented below summarizes the
nature of the adjustments required to the variables in the valuation
model. The adjustment to be made is generally a function of the number
of times interest is paid annually.
Variable for model
Frequency of interest payment and nature of
adjustment to make
Semiannually
Quarterly
Monthly
Interest (I)
2/ (I/2)
4/ (I/4)
12/ (I/12)
Years to maturity (n) 2/ n*2
4/ n*4
12/ n*12
Required return (k)
2/ (kd/2)
4/ (kd/4)
12/ (kd/12)
27
VALUATION OF ORDINARY SHARES
Equity-holders expect to be rewarded in the form of periodic payments
(ordinary dividends) and an appreciation in the value of their shareholding.
Equity holders need to value their shareholding because they need to make
decisions l on whether to hold on to their investments or sell the equity. They
choose to purchase stock when they believe the stock to be undervalued (its
true value greater than the market value) and sell it when it is overvalued (its
market value being greater than its true value). True value in this case is the
intrinsic value. The summary below illustrates the positions just explained.
Share
A
B
C
Intrinsic value
$100.00
$100.00
$100.00
Market value
$100.00
$150.00
$80.00
Valuation status Investor decision
Correctly valued Hold share
Overvalued
Sell share
Undervalued
Buy share
Share A is correctly valued. It makes sense for an investor to hold on to this
share. Share B is overvalued. The sooner the investor sells the better. The
market self-corrects and the price will slide downwards to the intrinsic value
so the sooner he sells the better, as his returns will be fairly substantial. Share
C is undervalued. The market will self-correct and the market price will move
upwards. If he buys early his rewards will be greater.
The situations highlighted for share B and share C are temporary states of
disequilibria, which cannot be sustained. This is why one has to either buy or
sell. The situation for share A is an equilibrium situation, which can be
sustained so the investor need not do anything.
The valuation arrangements discussed in this chapter will show how one can
get the intrinsic value of a share using the dividend valuation model.
VALUATION OF EQUITY WITH A FINITE HOLDING PERIOD
Sometimes investors wish to have an investment over a finite period. The
valuation model to use should have a limited holding period. A limited holding
period assumes a sale of the share at the end of an assumed holding period.
The present value of the share in this case becomes the sum of the present
values associated with the dividends received during the holding period, plus
the present value of the sales price at the end of the holding period.
Valuation of equity with zero growth dividends over a finite holding
period
A Ltd’s ordinary shares are currently paying a dividend per share of $20.00
per annum. The dividends are not expected to grow over the next 5 years
because of stable economic activities obtaining. An investor currently holds 10
000 such shares. His intention is to sell them and earn a yield of 35% at the
end of the 5 years. If the required rate of return is currently 15% what is the
value of:
28
(i)
(ii)
each ordinary share
the shareholder’s total shareholding?
0
DO
1
D1
2
D2
3
D3
4
D4
5
D5
DO = $20.00, therefore if g is zero DO = D1 =D5 = $20.00
In addition to the dividend in the final year, there are the sale proceeds
of the share calculated using the yield approach.
Expected sale price computation
Yield = Dividendfinal year
Market pricefinal year
0.35 = $20.00
x
0.35x = $20.00
x = $20.00
0.35
= $57.14
Present value computation
End of
Cash Inflow
Period
Dividend Sale Price
1-5
$20.00 0
5
0
$57.14
Discount
factor@ 15%
3.352
0.497
Present
value
$67.04
$28.41
$95.45
Each ordinary share is worth $95.15
Value of shareholding = $95.45*10 000
= $954 500
Constant growth dividends over a finite period
Sometimes a shareholder may hold a share for a finite period but the
share will be receiving a growing dividend. The valuation of such a share
is illustrated by the following example.
29
EXAMPLE
B Ltd.`s ordinary shares are currently paying a dividend of $30.00 per
share per annum. The dividends are expected to grow at an annual rate of
8% over the next five years because of limited economic growth. An
investor currently holds 100 000 such shares. His intention is to sell them
to earn a yield of 40% at the end of 5 years. If the required rate of return
on such shares is currently 15%, what is the value of each ordinary share?
Solution
D0
D1
D2
D3
D4
D5
=$30.00
= 1.08($30.00) = $32.40
= 1.08($32.40) = $34.992
= 1.08($34.992) = $37.7914
= 1.08($37.7914) = $40.8147
= 1.08($40.8147) = $44.0798
Sale price = 0.40 = $44.0798
X
0.40x = $44.0798
x = $44.0798
0.40
= $110.20
Present value computation
End of
Cash Inflow
Period Dividend
Sale price
1
32.4
0
2
34.992
0
3
37.7914
0
4
40.8147
0
5
44.0798
100
Discount
factor@ 15%
0.87
0.756
0.658
0.572
0.497
Present
value
28.188
26.454
24.8667
23.346
76.6769
179.5315
The value of each share is $179.53
EARNINGS PER SHARE
Sometimes one is given earnings per share and no dividends. The model
being illustrated uses dividends and not earnings per share. It is necessary
to calculate how much of the earnings are paid as dividends and then use
the dividends as illustrated in the following illustration.
EXAMPLE
A share is bought at the end of year 0 at $95.00. Earnings per share at the
time of purchase were $9.50 and are expected to grow at a compound
annual rate of 6 per cent. The company pays out 55 per cent of earnings in
the form of dividends each year. The share will be sold at the end of the
30
third year and a price earnings ratio of 15 is expected to apply to the share
at the time of sale. If a rate of 8 per cent is available in alternative
investment opportunities felt to be of equivalent risk, what is the present
value of the share?
Solution
Year
0
1
2
3
EPS
$9.50
1.06($9.50) = $10.07
1.06($10.07) = $10.6742
1.06($10.6742)=$11.31465
DIVIDEND
0.55($10.07) = $5.53850
0.55($10.67420) = $5.87081
0.55($11.31465) = $6.22306
Computation of sale price
The sale price can be estimated by using the price earnings ratio that the
investor wishes to realize.
Price earnings ratio = Market priceend of period
EPSend of period
15 = X/$11.31465
= $169.7197
The following table shows the computation of the present value of the
share.
End of
Period
1
2
3
Cash Inflow
Discount
Dividend Sale price factor@8%
5.5385
0
0.926
5.8708
0
0.857
6.2231
169.71975 0.794
Present
value
5.12865
5.03128
139.69859
149.85852
Variable growth dividends over a finite period
The following example shows how an ordinary share that pays
dividends with variable growth will be valued.
EXAMPLE
C Ltd`s ordinary shares are currently paying an annual dividend per
share of $20.00. The dividends are expected to grow at a supernormal
growth rate of 15% for the next three years. Thereafter the growth rate
is expected to stabilize at 10% annually for the next two years. A
shareholder intends to sell her shareholding at the end of year 5. What
is the value of each share if her intention is to realize a yield of 25%
and the required rate of return is currently 20%?
31
Solution
D0 = $20.00
D1 = 1.15($20.00) = $23.00
D2 = 1.15($23.00) = $26.4500
D3 = 1.15($26.4500) = $30.41750
D4 = 1.10($30.41750) = $33.45925
D5 = 1.10($33.45925) = $36.80518
Sale price = $36.80518/x =0.25
= $147.22070
Present value computation
End of
Cash Inflow
Period
Dividend Sale price
1
23,0000
0
2
26.4500
0
3
30.4175
0
4
33.45925 0
5
36.80518 147.2207
Discount
factor @20%
0.833
0.694
0.579
0.482
0.402
Present
value
19.159
18.3563
17.61173
16.12736
73.9784
145.23279
The value of each share is $145.23
VALUATION OF PERPETUAL EQUITY
The value of perpetual equity is the present value of all future dividends
expected to be provided by the share over an infinite horizon.
Dividends vs. earnings
Earnings not paid out as dividends are retained. The retained earnings
invested in profitable projects add earnings to produce opportunities for
higher future dividends. The present value approach considers the
earnings potential that result from the reinvested earnings by taking
account of future dividends generated. It would be double counting to
discount both present earnings and future dividends that result from
earnings retention.
Zero growth dividends with infinite horizon
The approach assumes that a constant non-growing dividend stream
will be paid. Thus D0 = D1 = D2 = D
P0 = D1
ke
Where D1 = dividend expected at end of year 1.
Ke = required rate of return on equity.
P0 = price of share now.
32
EXAMPLE
D Ltd. Currently pay $20.00 per share as dividend annually. This
dividend is to remain at this level indefinitely. If the required rate of
return is currently 16%, calculate the value of the ordinary share.
Solution
D0 = $20.00
D1 = D0 = $20.00
P0 = $20.00/0.16
= $125.00
Constant growth rate model (Gordon model) with infinite holding
period
The model assumes that the dividends will grow at a constant rate
perpetually at a rate that is less than the required rate of return.
The value of such a share is obtained by using the following approach:
P0 = D1
Ke -g
EXAMPLE
E Ltd. has the following dividend history:
Year
2003
2002
2001
2000
1999
1998
DPS ($)
14.00
12.90
12.00
11.20
10.50
10.00
Calculate the value of E Ltd`s shares assuming that the required rate
of return on equity is currently 30%.
It is necessary to first of all calculate the growth rate of dividends (g).
g = $10.00(1+g)5 = $14.00
(1+g)5 = $14.00/$10.00
1 +g
= 5 $14.00/$10.00
1 + g = 1.0696104
33
g = 1.0696104 -1
= 0.0696*100
=  7%
Next D1 (D2004), next dividend must be calculated.
= 1.07($14.00)
=$14.98
By applying the constant growth model the value of the share can now be
found.
P0 = $14.9800
0.30 – 0.07
= $65.13
Variable growth rate with infinite holding period
This model allows for a change in the dividend growth rate. This appears to
be a more realistic assumption in that the arrangement allows for shifts in
growth rate due to changing expectations.
EXAMPLE
F Ltd. Has introduced a highly competitive and attractive electric gadget. It is
expected to experience a supernormal growth rate of 15% for the first 4 years.
This will then be followed by a fairly above normal growth rate of 10%…. For
the following 5 years. The anticipated new competition after the ninth year will
see a 2% decline in dividend for each of the following three years. After this
period a normal growth rate of dividends of 3% is expected to prevail
indefinitely. If the current annual dividend is $20.00 per share and the required
rate of return on equity is 25%, what is the value of each ordinary share?
Solution
D0
D1
D2
D3
D4
D5
D6
D7
D8
D9
= $20.00
=1.15($20.00) = $23.00
= 1.15($23.00) = $26.45
=1.15($26.45) = $30.41750
= 1.15($30.41750) = $34.98013
= 1.10($34.98013) = $38.47814
= 1.10($38.47814) = $42.32595
= 1.10($42.32595) = $46.55855
= 1.10($46.55855) = $51.21440
= 1.10($51.21440) = $56.33584
34
D10 = 1.08(456.33584) = $60.84271
D11 = 1.06($60.84271 = $64.49327
D12 = 1.04($64.49327) = $67.07300
D13 = 1.03($67.07300) = $69.08519
Priceend of year 12 = $69.08519/(0.25 – 0.03)
= $314.02359
Present value computation
End of
Cash Inflow
Period
Dividends
Sale price
1
23
0
2
26.45
0
3
30.4175
0
4
34.98013
0
5
38.47814
0
6
42.32595
0
7
46.55855
0
8
51.2144
0
9
56.33584
0
10
60.84271
0
11
64.49327
0
12
67.073
314.02359
Discount
Factor @25%
0.800
0.640
0.512
0.410
0.328
0.262
0.210
0.168
0.134
0.107
0.086
0.069
The value of each ordinary share is $153.24
35
Present
value
18.4
16.928
15.57376
14.34185
12.62083
11.0894
9.7773
8.60402
7.549
6.51017
5.54642
26.29566
153.2364
VALUATION OF PREFERENCE SHARES
The reward for holding preference shares is the preference dividend that
is paid after all the other expenses are paid. Unless otherwise stated a
preference share is cumulative and non-redeemable.
REDEEMABLE
DIVIDENDS
PREFERENCE
SHARES
WITH
NO
ARREAR
P Ltd. would like to sell 1 000 000, 15%, $100.00, 5 year redeemable
preference shares that it has as an investment. Similar shares available
on the stock exchange yield 20%. How much can P Ltd. expect to get
from the disposal of the investment? Assume that the preference shares
are redeemable at par.
Preference dividend per share = 15/100*$100.00 = $15.00
$15.00
$15.00
$15.00
Present value computation
End of
Cash
Inflow
Period
Dividend
Principal
1 -5
$15.00
0
5
0
$100.00
$15.00
$15.00
+
$100.00
Discount
factor @20%
2.991
0.402
Present
value
$44.865
$40.200
$85.065
Proceeds expected from disposal of investment = 1 000 000 *$85.065
= $85 065 000.00
REDEEMABLE CUMULATIVE
ARREAR DIVIDENDS
PREFERENCE
SHARES
WITH
Where the preference dividends are in arrears these have to be brought
into account in the valuation because the current dividend cannot be
paid before the arrears are cleared. An estimation of when the arrear
dividends will be paid is needed for valuation purposes.
EXAMPLE
A company in which Q owns 10 000 Preference shares of $100.00 each
has just made an announcement of financial difficulties ahead. It is
expected that the dividends for the next three years will be passed;
thereafter normal dividend payments will then be expected to resume. If
the preference dividend is 15% and the shares are redeemable at the
end of 5 years, what is the value of each preference share if the required
rate of return is currently 25%?
36
Preference dividend = 15/100*$100.00 = $15.00
0
1
$0
2
$0
Present value computation
End of
Cash
Inflow
Period Dividend
1
0
2
0
3
0
4
$60.00
5
$15.00
3
$0
Principal
0
0
0
0
$100.00
4
5
$15 +$45 $15 +$100
Discount
factor @25%
0.800
0.640
0.512
0.410
0.328
Present
value
0
0
0
$24.60
$37.72
$62.32
Each preference share is worth $62.32.
REDEEMABLE NON-CUMULATIVE PREFERENCE SHARES WITH
ARREAR DIVIDENDS
If dividends are passed, non-cumulative preference shareholders lose
out, as the passed dividends are lost. From a valuation point of view only
the current dividends will be relevant as these are the ones that will be
paid only.
The example just illustrated will now be re-visited with the assumption
that the preference shares are non-cumulative.
Present value computation
End of
Cash Inflow
Period
Dividend
Principal
1
0
0
2
0
0
3
0
0
4
$15.00
0
5
$15.00
$100.00
Discount
factor @25%
0.8
0.64
0.512
0.41
0.328
Present
value
0
0
0
$6.15
$37.72
$43.87
Each preference share is worth $43.87
PERPETUAL PREFERENCE SHARES
The value of a perpetual preference share is the present value of the
preference dividend received in perpetuity.
PO = Preference dividend
Required return (kp)
37
EXAMPLE
Find the value of perpetual preference shares that have a par value of
$5.00 each and carry a dividend of 10%. Similar shares available on the
stock exchange yield 20%.
Preference dividend = 10/100*$5.00 = $0.50
Po =$0.50
0.20
= $2.50
PERPETUAL CUMULATIVE PREFERENCE SHARES WITH ARREAR
DIVIDENDS
A Ltd. has in issue 100 000, 15% $100.00, cumulative perpetual
preference shares. It has made an announcement of financial difficulties
ahead. It expects that the dividends for the next four years will be
passed. Thereafter normal dividend payments will then be expected to
resume with no further passing of dividends. If the required rate of return
is 25% what is the value of each preference share?
Present value computation
End of
Cash
Inflow
Period Dividend
Share value
1
0
0
2
0
0
3
0
0
4
0
0
5
$75.00
$60.00
Pend of year
5
Discount
factor @ 25%
0.8
0.64
0.512
0.41
0.328
Present
value
$0
0
0
0
44.28
= $15.00
0.25
= $60.00
PERPETUAL NON-CUMULATIVE PREFERENCE SHARES WITH
ARREAR DIVIDENDS
It was indicated earlier on that if dividends are passed, then the arrear
dividends are lost. The example just illustrated will now be re-visited with
the assumption that the shares are non-cumulative.
38
Present value computation
End of
Cash Inflow
Period
Dividend
Share value
1
0
0
2
0
0
3
0
0
4
0
0
5
$15.00
$60.00
Discount
factor @25%
0.800
0.640
0.512
0.410
0.328
Present
value
0
0
0
0
$24.60
The value of each preference share is $24.60
LIMITATIONS OF THE DIVIDEND VALUATION MODEL
The model that was used to value ordinary shares and preference
shares, the dividend valuation model, has a number of limitations and
these are now highlighted.
Estimation of earnings and dividends
The tendency is to assume that earnings grow at a constant rate and
that dividends also grow at a constant rate or that the dividend payout
ratio is constant. Experience suggests that earnings growth rates can
vary markedly over time and that firms do change their dividends
policies.
Constant required rate of return
The discount rate is held constant for the time period covered by the
model. Required market rates change over time and the risk class of the
firm may also change. This invalidates the assumption of a constant
required rate of return.
Time horizon covered by the model
The model assumes earnings growth into perpetuity or a terminal value
representing the expected sales price of the stock at some predetermined time. The difficulty lies in imagining how accurate estimates
can be made over such long horizons. When a finite holding period is
assumed the question arises as to how one determines that holding
period in advance. Even if the holding period could be estimated
accurately, one still faces the difficult problem of estimating the market
value of the stock at the end of the holding period.
Taxation
After tax cash flows are estimated by assuming the tax bracket
applicable to the investment income for each annual holding period.
Estimating applicable rates into perpetuity or long holding periods is not
an easy task. Where a finite holding period is assumed the applicable
39
capital gains tax on the estimated market value of shares is also
required.
PRICE EARNINGS RATIO (PER) MODEL
The model estimates the intrinsic value of a share by multiplying
normalized earnings per share by an adjusted price earnings ratio, which
reflects the analyst’s subjective judgment about future growth prospects
for the firm and dividend policy.
The model is useful when a company’s share is not traded publicly and
no market price exists. The model is applied as follows:
a. Determine the P/E ratio for the industry.
b. Calculate the EPS of the company.
c. Multiply the P/E for the industry with the EPS of the company.
Price = Sustainable P/E ratio * EPS
40
PRACTICE PROBLEMS ON VALUATIONS
PROBLEM 1
Complex Systems has an issue of $1 000 par value bonds with a 12 percent
coupon interest rate outstanding. The issue pays interest annually and has 16
years remaining to its maturity date.
a. If bonds of similar risk are currently earning a 10 percent rate of return,
how much will the Complex Systems bond sell for today?
b. Describe the two possible reasons that similar-risk bonds are currently
earning a return below the coupon interest rate on the Complex
Systems bond?
c. If the required return were at 12 percent instead of 10 percent, what
would the current value of Complex Systems’ bond be? Contrast this
finding with (a) and discuss.
(b) Jones Designs wishes to estimate the value of its outstanding preferred
stock. The preferred issue has an $80 par value and pays an annual dividend
of $6,40 per share. Similar-risk preferred stocks are currently earning a 10
percent annual rate of return.
a. What is the market value of the outstanding preferred stock?
b. If an investor purchases the preferred stock at the value calculated in
a, how much would she gain or lose per share if she sells the stock
when the required rate of return on similar-risk preferred stock has
risen to 12 percent? Explain.
(c) Lawrence Industries’ most recent annual dividend was $1,80 per share,
and the firm’s required return is 10 percent. Find the market value of
Lawrence’s shares when:
a. Dividends are expected to grow at 8 percent annually for three
years followed by a 5 percent constant annual growth rate from
year 4 to infinity.
b. Dividends are expected to grow at 8 percent annually for each of
three years followed by zero percent annual growth in years 4 to
infinity.
c. Dividends are expected to grow at 8 percent annually for three
years followed by a 10 percent constant annual growth rate in years
4 to infinity.
PROBLEM 2
(a) B Limited has an outstanding issue of $100 par value debentures with
a 12% coupon interest rate. Interest on the debentures is paid annually
and 16 years still remain to their maturity. If debentures of similar risk
are currently earning a 10% rate of return, how much will the B Limited
debenture sell for today?
(b) Find the value of a debenture maturing in six years with a $100 par
value and a coupon interest rate of 10 percent per annum (interest paid
41
semi annually) if the required rate of return on similar risk debentures is
14 percent per annum (interest paid semi annually).
(c) You are requested to advise a potential investor who is considering
making an investment in a small business currently generating $85 000
of after tax cash flow. A review of similar risk investment opportunities
reveals that the fair rate of return for the proposed investment is 18
percent. You decide to estimate the firm’s value using several possible
cash flow growth rate assumptions.
i.
Estimate the value of the firm assuming that cash flows grow at
an annual rate of zero percent to infinity
ii.
Estimate the value of the firm assuming that cash flows are
expected to grow at a constant annual rate of 7 percent to
infinity
(d) TDA Limited has a better of 1,20. The risk – free rate of return is 10
percent and the required return on the market portfolio is 14 percent.
The company plans to pay a dividend of $5,20 per share in the next
year. The anticipated future dividend growth rate is expected to be
consistent with that experienced over the last 7 years.
Year
2004
2003
2002
2001
2000
1999
1998
Dividend per share ($)
4,90
4,56
4,20
3,80
3,64
3,60
3,46
You are required:
To determine the required return on TDA Limited’s equity using the
capital asset pricing model
Ii Estimate the value of TDA Limited using the Gordon constant
dividend valuation model
i.
ii.
PROBLEM 3
(a) Suppose a debenture has the following characteristics:




Face value of $1 000
Coupon rate of 20%
A yield to maturity of 20%
A maturity of 10 years
i.
ii.
iii.
What is the value of the debenture?
When the coupon rate is increased to 30%, everything else
remaining constant, what is the new value of the debenture?
Everything else remaining the same, when the coupon rate is
reduced to 10%, what is the value of the debenture?
42
(b) Identify from parts (i) to (iii) when the debenture is selling at a premium,
discount or par. Explain why?
(c) Given that the debenture with a nominal value of $1000, with a yield to
maturity of 20% a maturity of 10 years is now paying interest semiannually. The coupon rate is 10%, what is the value of the debenture?
(d) An irredeemable debenture has a face value of $1000, coupon rate of
20% and a yield to maturity of 30%, what is the value of the
debenture?
(e) Preference shares are to be issued with a nominal value of $1,00. The
coupon dividend rate is 25% per annum. Assuming the required rate of
return is 30%, what is the value of the Preference share?
A firm has just paid a preference stock dividend and it plans to pass the next
3-year dividend and resume regular dividend thereafter. Given that the par
value is $1,00, coupon dividend rate is 24% per annum and the required rate
of return is 30%, what is the value of the preference share if preference
shares are cumulative?
43
Chapter 3
RISK AND ITS MEASUREMENT
Risk is the probability that an outcome will not be as expected. The outcome
may be favourable in which case we talk of upside risk. The outcome may
turn out to be unfavourable. This is what is known as downside risk. Normally
when people talk of risk they focus more on downside risk largely because of
the negative effect it has on organizational operations. But this should not be
the case as the upside risk should be looked at as well.
TYPES OF RISK
Business risk. Business risk refers to the variability in organizational
earnings, which is function of the firm’s normal operations. It can be regarded
as risk that is intrinsic to the firm’s operations.
Investment risk. This variability in earnings due to variations in cash inflows
and outflows of capital investment projects undertaken. It is a function of the
ability of a decision maker to make accurate cash flow forecasts that are used
in the evaluation of potential investment projects.
Portfolio risk. This can be looked at as variability in earnings that is a
function of the degree of efficient diversification that the firm has achieved in
its operations and its overall portfolio of assets. If a firm identifies assets
whose returns are negatively correlated then its diversification can be argued
to be efficient and its variability of portfolio returns will be fairly minimal,
minimizing portfolio risk.
Cataclysmic risk. Cataclysmic risk refers to variability in earnings that is
function of events beyond managerial control and anticipation. Examples of
these events include expropriation, erratic changes to consumer preferences
or energy shortages. Management should not have anticipated the events and
management should not be in a position to control the events if they are to
qualify as events under cataclysmic risk.
Financial risk. This variability in earnings that is a function of the financial
structure of an organization and the need to meet obligations of fixed-income
securities. When an organization brings debt into its capital structure, it
creates a fixed obligation, which will have to be serviced whether the
organization makes a profit, or not. The variability in earnings that this
arrangement brings constitutes financial risk.
Political risk. Political risk is the probability of selective interference in a
company’s operations by host governments. This is a type of risk, which is
faced by transnational corporations.
44
CATEGORIES OF RISK
Risk can be categorized into two broad categories, diversifiable and nondiversifiable risk.
Diversifiable risk, unique risk, unsystematic risk, firm specific risk
This is that risk that can be diversified away through the selection of other
risky assets that are lowly or negatively correlated with the asset in question.
It is risk that is unique to a particular firm hence it can be diversified away.
Non-diversifiable risk, systematic risk, market risk
There will always be an element of risk, which cannot be diversified away
despite all efforts to diversify risk on the pert of a firm. This risk is what is
referred to as non-diversifiable risk. It is risk that obtains in the market that a
firm will have chose to operate.
The total risk of a project (j) = Systematic risk + Unsystematic risk.
The following diagram shows the two categories of risk just explained.
Risk
(standard
deviation)
Total risk
Unique, company specific, unsystematic, diversifiable
risk
Systematic risk, market risk, non – diversifiable risk
0
No of securities in portfolio
Fig. Diversifiable and non – diversifiable risk
MEASURES OF RISK
For the decision maker to make an informed decision, there is need to
quantify the level of risk that will be associated with the potential investment
being evaluated. There are statistical approaches that quantify the level of risk
associated with a potential investment. These are now going to be explained
and illustrated.
THE RANGE
This is a measure of an asset’s risk arrived at by subtracting the pessimistic
(worst) outcome from the optimistic (best) outcome. The greater the range for
the asset, the greater the variability (risk) associated with the asset.
45
The range (Rg) = Rh-Rl
Where Rg = range of the distribution
Rh = highest value in the distribution
Rl = lowest value in the distribution
EXAMPLE
The following information is given for assets A and B.
Asset A
Initial Investment
$10 000
Annual rate of return
Pessimistic
13%
Most likely
15
Optimist
17
Asset B
$10 000
7%
15
23
If the investor is risk averse, which asset will he select?
Solution
The range can be used to answer this question.
RangeA =17% - 13%
= 4%
RangeB = 23% - 7%
= 16%
A risk averse investor will select asset A because it offers the same most
likely return (15%) but with a lower risk (range) of 4%.
STANDARD DEVIATION
Although the range as explained above can be used to quantify the risk of an
asset, it is not very useful as outliers affect it. A much more useful measure of
risk is the standard deviation. The standard deviation (k) is a measure of the
dispersion of returns around the expected value (mean). Expected value of a
return (k) is the most likely return on a given asset. The basic idea is that the
standard deviation is a measure of volatility: the more a share’s returns vary
from the share’s average return, the more volatile the share.
STANDARD DEVIATION: NON-PROBABILISTIC DATA
When evaluating the risk of an asset given non-probabilistic data, the
following should be the procedure to adopt. Start by calculating the expected
value and then establish the dispersion around the expected value (mean).
Step 1. Expected value computation
This is the simple average of the return figures given. The following is the
applicable formula.
k =
n
k i
i 1
n
46
Where ki = return for the ith outcome
n = number of observations
Step 2. Standard deviation computation
Establish the dispersion around the expected value (mean) by using the
following formula:
k = 
n

(ki - k)2
i 1
n–1
The greater the standard deviation, the greater the risk.
EXAMPLE
The example earlier presented will now be re-visited to illustrate the
determination of standard deviation with non-probabilistic data.
Asset A
Computation of mean (expected value):
Expected return for asset: A = 13%+15%+17
3
= 15%
Computation of standard deviation: (Asset A)
Possible state
Pessimistic
Most likely
Optimistic
Potential Mean
return
return
13
15
15
15
17
15
Deviation
-2
0
2
ASSET B
Computation of expected value:
Expected return for asset: B = 7%+15%+23%
3
= 15%
47
Squared
deviation
4
0
4
8/(3-1)
= 4
=2%
Computation of standard deviation:
Possible state
Pessimistic
Most likely
Optimistic
Potential Mean
return
return
7
15
15
15
23
15
Deviation
-8
0
8
Squared
deviation
64
0
64
128/3-1
=64
= 8%
Asset B is more risky as it has a higher dispersion around the mean (a
higher standard deviation).
STANDARD DEVIATION: PROBABILISTIC DATA
The computation of the standard deviation of an investment whose probable
returns are given as a probability distribution also requires the two-step
approach already illustrated. First one has to calculate the expected value and
then establish the dispersion around the expected value (mean).
Expected value computation
For a probabilistic distribution, the expected value is the weighted value of
possible return multiplied by the probability of occurrence. It is obtained by
using the following formula:
k =
n

(ki = Pri)
i 1
Where ki = return for the Ith outcome
Pri = Probability of occurrence of the Ith outcome
Standard deviation computation
To get the standard deviation of a probabilistic distribution use the following
formula:
k = 
n

(ki - k)2 * Pri
i 1
EXAMPLE
The following information is given for two assets:
Possible outcome
Pessimistic
Most likely
Optimistic
Returns
Asset C
23%
25
27
Probability
0.25
0.50
0.25
Which asset is riskier and why?
48
Asset D
17
25
33
Step 1. Start by calculating the expected value for the asset. As indicated
earlier this is the weighted value of the possible returns. One can use one of
the following two approaches.
APPROACH ONE
Expected value computation: Asset C
Possible outcome Probability Return Weighted value
Pessimistic
0.25
23
5.7500
Most likely
0.5
25
12.5000
Optimistic
0.25
27
6.7500
25.0000%
APPROACH TWO
Expected value: Asset C =(0.25*23%)+(0.50*25%)+(0.25*27%)
=25.000%
After obtaining the expected value (mean) one must then calculate the
standard deviation of returns for the asset being evaluated.
Standard deviation
computation: Asset C
Possible
Potential Mean
outcome
return
return
Pessimistic
23
25
Most likely
25
25
Optimistic
27
25
Squared
Squared deviation*
Deviation deviation Probability probability
-2
4
0.25
1.000
0
0
0.50
0
2
4
0.25
1.000
2.000
=1.41%
Expected value computation: Asset D
Possible
Possible outcome Probability return
Pessimistic
0.25
17
Most likely
0.50
25
Optimistic
0.25
33
Weighted
value
4.25000
12.50000
8.25000
25.0000
Alternatively: Expected value: Asset D = (0.25*17%)+(0.50*25%)+(0.25*33%)
= 25.000%
49
Now the standard deviation of return for asset D can now be calculated.
Standard deviation computation:
Asset D
Possible Mean
Possible outcome return
return
Pessimistic
17
25
Most likely
25
25
Optimistic
33
25
Squared
Squared dev*
Deviation deviation Probability probability
-8.000
64.000
0.25
16.000
0
0
0.50
0
8.000
64.000
0.25
16.000
32.000
= 5.66%
Asset D is riskier as it has a higher standard deviation.
COEFFICIENT OF VARIATION (CV)
The coefficient of variation is a measure of relative dispersion used when
comparing assets with different expected returns. The following approach is
used to compute the coefficient of variation
CV = Standard deviation
Expected return
An example now follows to show how the coefficient of variation is used to
decide on an asset having a lower degree of relative risk.
EXAMPLE
M Ltd. has identified four alternatives that meet its need for increased
production capacity. The data gathered relative to each of these alternatives
is summarised in the following table.
Alternative
A
B
C
D
Expected
return (%)
20
22
19
16
Standard deviation
of returns (%)
7.00
9.50
6.00
5.50
(a) Calculate the coefficient of variation for each alternative.
(b) If the firm wishes to minimize risk, which alternative would you
recommend and why?
Solution
(a) CVA = 7.0
20
=0.35
CVB = 9.5
22
= 0.43
50
CVC = 6.0
19
=0.32
CVD = 5.5
16
=0.34
(c) Alternative C is chosen as it has the least risk as measured by
coefficient of variation.
TWO ASSET PORTFOLIO RISK ANALYSES
A portfolio is a group of assets from which returns are expected. Portfolios
are created because individuals do not usually want to hold shares in
isolation. They prefer instead to hold a portfolio of selected shares. The
motivation is the reduction in risk brought about by diversification.
Portfolio return
A portfolio’s return is the weighted average returns on the individual assets
constituting the portfolio. The weights reflect the proportion of the portfolio
invested in the shares.
PORTFOLIO ANALYSIS: NON-PROBABILISTIC DATA
The analysis of a given portfolio requires one to look at the expected
return from the portfolio in relation to the risk associated with the asset.
This section looks at how a portfolio expected return is calculated. It also
looks at the calculation of portfolio risk, which is then related to portfolio
expected return for decision-making purposes.
EXAMPLE
Portfolio AB comprises 50% of securities A and 50% securities B.
Expected returns for A and B for the next five years are as follows:
Year
1
2
3
4
5
Share A
12
16
20
24
28
Share B
28
24
20
16
12
Compute portfolio AB`s expected return and the portfolio’s standard
deviation of returns.
51
a) Expected return on portfolio AB computation.
Expected Return
Computation of Portfolio Expected
Return
Portfolio Return
Year Share A Share B
1
12
28
(0.50*12%)+(0.50*28%)
20
2
16
24
(0.50*16%)+(0.50*24%)
20
3
20
20
(0.50*20%)+(0.50*20%)
20
4
24
16
(0.50*24%)+(0.50*16%)
20
5
28
12
(0.50*28%)+(0.50*12%)
20
b) Mean value of portfolio returns (mean) = 20%+20%+20%+20%+20%
5
=20%
c) Computation of standard deviation of expected portfolio returns
Portfolio Mean
Squared
Year
Return Return Deviation Deviation
1
20
20
0
0
2
20
20
0
0
3
20
20
0
0
4
20
20
0
0
5
20
20
0
0
0/4
=0%
There is no variability in expected earnings from this portfolio. It is a
perfect portfolio.
DIRECT FORMULA FOR PORTFOLIO STANDARD DEVIATION
2
k = w 2 1  2 1 + w 22  2 + 2. w1 .w2. Covariance1, 2
The use of this method requires computation of covariance.
Covariance Covariance is a measure of association of two variables. It is
measured mathematically by finding the average of the products of the
deviations of each of the paired variables from the overall mean of the
relevant variable.
Covariance xy = Correlation xy * standard deviation x*standard deviation y
52
Computation of r – correlation coefficient
Year
1
2
3
4
5
A (x)
12
16
20
24
28
A = 100
A2 (x2)
144
256
400
576
784
2
A = 2160
B (y)
28
24
20
16
12
B =100
Correlation (r) = nxy -xy
nx2 – (x)2 * ny2 – (y)2
r =5(1840) – (100)(100)
5(2160) – (100)2 * 5(2160) – (100)2
= 9 200 –10 000
10 800 – 10 000 * 10 800 – 10 000
=
-800
800 * 800
= -800
28.28437 * 28.28427
= -800
799.99996
= -1.0000
Standard deviation of returns: Asset A
Mean return = 12% + 16% + 20% + 24% + 28%
5
= 20%
Actual
retuyrn
Year
1
2
3
4
5
Mean
return
12
16
20
24
28
20
20
20
20
20
Squred
Deviation deviation
-8
64
-4
16
0
0
4
16
8
64
160/(5-1)
=40
= 6.325%
53
B2(y2)
784
576
400
256
144
B2 = 2160
AB (xy)
336
384
400
384
336
AB =1840
Standard deviation for asset B = 6.325%
Covariance = --1.000 * 6.325 * 6.325
= -40.00563
AB = (0.50)2(6.325)2 + (0.50)2(6.325)2 + 2(0.50)(0.50)(-40.00563)
= (0.2500)(40.00563) + (0.2500)(40.00563) + 0.50(-40.00563)
= 10.00141 + 10.00141 +(-20.00280)
= 20.00282 – 20.00280
= 0%
PORTFOLIO ANALYSIS: PROBABILISTIC DATA
The following example will be used to illustrate how the risk – return
computations for a portfolio with probabilistic data is handled.
EXAMPLE
Probability
State of of state of Rate of return if state occurs
economy economy Share D
Share E
Recession
0.2
-0.15
0.2
Normal
0.5
0.2
0.3
Boom
0.3
0.6
0.4
There is an investor who has $20 000 to invest in total. He wishes to invest
$15 000 in share D and the remainder in share E. What is the expected
return and standard deviation on the portfolio?
ALTERNATIVE ONE
Computation of portfolio mean return
State of Expected return
economy Share D Share E
Recession
-0.15
0.2
Normal
0.2
0.3
Boom
0.6
0.4
Probability Portfolio
of state of expected
Portfolio return if state occurs
economy return
(0.75*-0.15) + (0.25*0.20) = -0.0625
0.2
-0.0125
(0.75*0.20) + (0.25*0.30) = 0.0050
0.5
0.1125
(0.75*0.60) + (0.25*0.40) = 0.5500
0.3
0.165
=0.2650
= 26.50%
54
Standard deviation of portfolio returns
State of
economy
Recession
Normal
Boom
Probability
Portfolio
Mean
Squared
* squared
return
return
Deviation deviation
Probability deviation
-0.0625
0.265
-0.3275
0.10726
0.2 0.02145
0.225
0.265
-0.04
0.0016
0.5
0.0008
0.55
0.265
0.285
0.08123
0.3 0.02437
= 0.04662
= 21.59%
ALTERNATIVE TWO (2)
Computation of expected portfolio return
Expected return Share D = (0.20*-0.15) + (0.50*0.20) + (0.30*0.60)
= 0.25 or 25%
Expected return Share E = (0.20*0.20) + (0.50*0.30) + (0.30*0.40)
= 0.31 or 31%
Proportions of investment: Share D = 15/20 =0.75
Share E = 5/20 = 0.25
Expected portfolio return = (0.75*25%) + (0.25*31%)
= 26.50%
Standard deviation of returns: Share D
State of
economy
Recession
Normal
Boom
Probability
Expected
Mean
Squared
* squared
return
return
Deviation deviation
Probability deviation
-0.15
0.25
-0.4
0.16
0.2
0.032
0.2
0.25
-0.05
0.0025
0.5 0.00125
0.6
0.25
0.35
0.1225
0.3 0.03675
= 0.070
= 26.46%
Standard deviation of returns: Share E
State of
economy
Recession
Normal
Boom
Expected
return
Mean
return
0.2
0.3
0.4
Probability
Squared
* squared
Deviation
deviation
Probability
deviation
0.31
-0.11
0.0121
0.2 0.00242
0.31
-0.01
0.0001
0.5 0.00005
0.31
0.09
0.0081
0.3 0.00243
= 0.0049
=7%
55
Covariance: DE
Pri
D
0.2
0.5
0.3
D
-0.15
0.2
0.6
(D -D) E
0.25
-0.4
0.25
-0.05
0.25
0.35
E
0.2
0.3
0.4
(E - E) Pri (D-D)(E-E)
0.31
-0.11
0.0088
0.31
-0.01
0.00025
0.31
0.09
0.00945
0.0185
Standard deviation computation
DE = (0.75)2(0.26458)2 + (0.25)2(0.070)2 = 2(0.75)(0.25)(0.01850)
= (0.56250)(0.070) + (0.06250)(0.00490) + 2(0.00347)
= 0.03938 + 0.00031 + 0.00694
= 0.04663
= 21.59%
Capital asset pricing model (CAPM)
Investors can eliminate diversifiable risk through diversification. The only
relevant risk, which the investor should be concerned about, is nondiversifiable risk. Measurement of non-diversifiable risk becomes important
in selecting assets to build up a portfolio. The capital asset pricing model
links together non-diversifiable risk and return for all assets (return on a
portfolio). CAPM can therefore be looked at as a measure of a security’s
systematic risk.
The CAPM provides an expression relating the expected return on an asset
to its systematic risk (Rock Mathis). This relationship is referred to as the
Security Market Line (SML). The measure of the systematic risk in the
CAPM is known as Beta ().
The security market line
The following is an expression of the SML equation:
E[Ri] = Rf + (E[Rm] – Rf)I
Where





E[Ri] = the expected return on asset I,
Rf = the risk-free rate,
E[Rm] = the expected return on the market portfolio,
I = the Beta on asset I,
[Rm] – Rf = the market risk premium.
56
The following graph shows the security market line (SML)
E[Ri]
SML
E[Rm]
Rf
i
1
The slope of the SML is equal to (E[Rm] – Rf) which is the market risk
premium. The SML intercepts the y-axis at the risk free rate. When the
capital market is in equilibrium, the required rate of return on an asset
should equal its expected return. This is why the SML equation can also
be used to determine an asset’s required rate of return if its Beta is
given.
The above SML equation, (CAPM) can be presented in a more simplified
arrangement as follows:
Re = Rf + Beta (Rm – Rf)
Risk free rate (Rf): This is the amount obtained from investing in
financial securities considered free fro credit risk such as government
bonds. The interest rate of interest on government treasury bill is
generally used as a proxy for the risk-free rate.
Beta (): This is a measure of how a company’s share price reacts
against the market as a whole. A beta of one indicates that the company
moves in line with the market. A beta in excess one indicates that the
share exaggerates the market’s movements and a beta less than one
means that the share is more stable. Occasionally a company may have
a negative beta meaning that the share price moves in the opposite
direction to the broader market.
There are basically two main approaches that can be used to compute
beta.
Approach one: The regression approach
EXAMPLE.
The following historical data on the return of security X and market
returns M has been collected for the past five years.
57
Year
1
2
3
4
5
Return X Return M Risk free rate
0.25
0.29
0.11
0.15
0.2
0.13
0.08
0.16
0.15
0.3
0.24
0.14
0.22
0.21
0.16
Computation of beta
Year X
M
Rf
Ex(x)
Ex(m)
Ex(x)Ex(m)
Ex(m)2
1
0.25
0.29 0.11
0.14
0.18
0.0252
0.0324
2
0.15
0.2 0.13
0.02
0.07
0.0014
0.0049
3
0.08
0.16 0.15
-0.07
0.01
-0.0007
0.0001
4
0.3
0.24 0.14
0.16
0.1
0.016
0.01
5
0.22
0.21 0.16
0.06
0.05
0.003
0.0025
Ex =1.00 Em =1.10
Ex(x)=0.31Ex(m)=0.41 Ex(x)Ex(m)=-0.0449 Ex(m)2=0.0499
The slope of the regression line, which defines beta, is given by:
 = x(X)x(M) - nx(X-)x(M-)
x(M)2 - nx(M-)
Where
 x(X) = excess of security returns over risk free rate of return,
 x(M) = excess of market returns over risk free rate of return,
 x(X-) = average of excess security returns over risk free
returns,
 x(M-) = average of excess of market returns over risk free
returns.
 = 0.0449 – 5(0.062)(0.082)
0.0499 – 5(0.082)2
= 0.0449 – 0.02542
0.0499 – 0.03362
= 0.01948
0.01628
=1.20
Approach two (2): Graphical approach
A graph is prepared with the x-axis (horizontal) axis measuring excess
market returns and the y-axis (vertical axis) measuring the excess individual
asset returns. Coordinates for the excess market returns and excess asset
returns at various points in time are plotted. A characteristic line or line of
best fit is developed. The slope of this line is the beta of a given asset.
A higher beta (steeper line of best fit) indicates that its return is more
responsive to changing market returns and is therefore more risky.
58
The following table summarizes the excess returns from the earlier
example. A graph is prepared from these excess returns.
X
Y
0.14
0.18
0.02
0.07
-0.07
0.01
0.16
0.1
0.06
0.05
Excess returns, Asset X
0.15
0.10
slope =
0.05
Excess returns, market portfolio
-0.06
-0.04 -0.02
-0.05 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18
-0.10
Equity market risk premium (Rm – Rf): This represents the returns
investers expect to compensate them for taking extra risk by investing in
the stock market and above the risk-free rate.
PRACTICE PROBLEMS ON RISK MEASUREMENT AND RETURN
PROBLEM 1
Two assets have the following returns:
Possible state
A
B
C
D
E
i.
ii.
iii.
Probability
0.18
0.22
0.31
0.08
0,21
X
10%
12%
15%
-8%
2%
Y
12%
15%
20%
25%
15%
What is the expected return for each of these assets?
Calculate the standard deviation of each of the two assets
Which asset is preferable if the investor is risk averse?
(b) You have collected the following information on security M and N. The
information is a reflection of your projections for a six-year period.
Year
1
2
3
4
5
6
M
18%
20%
22%
15%
10%
20%
59
N
20%
15%
21%
18%
15%
18%
i.
ii.
iii.
Calculate the expected rate of return for each security
Calculate the variance of each security
Calculate the standard deviation of each security
PROBLEM 2
Three F, G, and H assets are currently being considered by Perth Industries.
The following probability distributions of expected returns for these assets
have been developed.
i
1
2
3
4
5
Asset F
Pri
Return, ki
0.10
40%
0.20
10
0.40
0
0.20
-5
0.10
- 10
Asset G
Pri
Return, ki
0.40
35%
0.30
10
0.30
- 20
Asset H
Pri
Return, ki
0.10
40%
0.20
20
0.40
10
0.20
0
0.10
- 20
a. Calculate the expected value of return, for each of the three assets.
Which provides the largest expected return?
b. Calculate the standard deviation, for each of the three asset’s
returns. Which appears to have the greatest risk?
c. Calculate the coefficient of variation for each of the three assets.
Which appears to have the largest relative risk?
PROBLEM 3
a) Explain your understanding of the following types of risk:
i.
Business risk
ii.
Investment risk
iii.
Portfolio risk
iv.
Cataclysmic risk
v.
Financial risk
b) You are given the following expected return data on three assets:- X, Y
and Z over the period 2001 – 2004.
Year
2004
2003
2002
2001
Expected return %
Asset Y
17
16
15
14
Asset X
16
17
18
19
Asset Z
14
15
16
17
Using these assets you have isolated three Investment alternatives:
Alternative
1
2
3
Investment
100% of Asset X
50% of Assets X and 50% of assets Y
50% of Assets X and 50% of Asset Z
60
Required
a) Calculate the expected return over the four – year period for each of
the three alternatives
b) Calculate the standard deviation of returns over the four- year period
for each of the three alternatives
c) Use your findings in (a) and (b) to calculate the coefficient of variation
for each of the three alternatives
On the basis of your findings above which of the three alternatives would you
recommend? Why?
61
Chapter 4
Weighted average cost of capital
Cost of capital is the rate of return that a firm must earn on its project
investments to maintain its market value. It represents the investors`
opportunity cost of taking on the risk of putting money into a company.
Importance of weighted average cost of capital
It is important to correctly compute an organization’s weighted average cost of
capital since the weighted average cost of capital affects a number of
important decisions that will be made by the organization’s management.
1. Weighted average cost of capital and security valuation
Security analysts employ the weighted average cost of capital when
valuing financial securities. In the valuation of financial securities the
weighted average cost of capital is used as a discount rate, which is
applied to future cash flows to be generated by the financial instrument
being valued. In this case the weighted average cost of capital will be used
as a hurdle rate. If the weighted average cost of capital is wrongly
calculated then the intrinsic value of the financial instrument as calculated
will be wrong.
2. Weighted average cost of capital and the investment decision
Organizations also use the weighted average cost of capital when
evaluating capital projects. The weighted average cost of capital is used
as a hurdle rate when evaluating project cash flows using the net present
value analysis. If the weighted average cost of capital is wrongly
calculated then capital projects will either be wrongly accepted or rejected.
3. Weighted average cost of capital and economic value added
(EVA)
In financial management economic value added (EVA) is the
determination of value created for the shareholders of the company. The
approach used is as follows:
EVA = NPAT – (NOA * WACC)
Where NPAT = Net profit after taxes
NOA = Net operating assets
WACC = Weighted average cost of capital
Shareholders will receive a positive value added when the return from the
equity employed in the business operations is greater than the cost of
capital.
Schmalenbach, first introduced this concept, but the EVA as used today
has been developed by Stern Stewart and Company.
62
It can be noted that if the computation of weighted average cost of capital
were wrongly carried out then the value added would be wrong. Any
decisions that are eventually made on the basis of the economic value
added as calculated will be misleading.
4. Weighted average cost of capital and the individual investor
Weighted average cost of capital serves as a useful reality check for
investors. The average investor may not bother to calculate weighted
average cost of capital because it is a complicated measure that requires
much detailed information but it helps investors to know the meaning of
weighted average cost of capital when they encounter it in brokerage
analysts` reports.
Assumptions underlying the computation of weighted average cost
of capital
1. Business risk is assumed to remain constant.
2. Financial risk is also assumed to remain constant.
3. Component costs used in the computation of weighted average cost of
capital are after tax costs. This assumption is consistent with the
framework of making capital decisions.
Cost of capital is estimated at a given point in time and it represents the
expected average future cost of funds over the long run based on the best
information available.
Cost of capital is obtained by first obtaining the component costs of individual
sources of finance comprising the capital structure of the organization and
then multiplying this by the weight of each component. The weight of each
component is usually determined by the firm’s target capital structure. This is
the desired optimal mix of debt and equity financing the firm tries to achieve
and maintain.
Computation of component costs
A. Cost of debt: Investors who subscribe to debentures anticipate future
interest payments. This means that the present value of a debenture is
equal to the investor’s future expected receipts discounted at the
investors required rate of return.
Component cost of irredeemable debentures
These debentures give a return to the investor in the form of a constant
interest payment, which is paid in perpetuity. Debentures are usually
denominated in units of $1 000 or $100 nominal value and companies are
entitled to tax relief on the interest payable on debenture capital.
Cost of debt (ki) = Interest charge (1 – t)
Market value of debt (ex – interest)
Where ki = after tax cost of debt
T = marginal tax rate of corporation tax payable
63
EXAMPLE
A Ltd. has in issue 6% debentures quoted at $980 cum interest. Calculate
the cost of debt, assuming a tax rate of 35%.
Ki = $60 (1 – 0.35) * 100
$980 - $60
= $39 * 100
$920
= 4.24%
Assumption: Interest is payable annually.
Component cost of redeemable long- term debt
The starting point is to establish the before-tax cost of debt (kd) and then
provide the tax adjustment since interest payment is tax deductible.
Methods of obtaining before tax cost on debt (kd)
1. Quotations: A common method is to quote the coupon interest rate on
the bond as the before tax cost of debt if the bond is selling at par on a
net basis. A variation would be to quote YTM on similar risk bonds as
before tax cost on debt.
2. Approximating the cost of debt using YTM: This approach relies on
the use of the approximate yield to maturity on similar risk bonds. This
approximate YTM will then be used as the before tax cost of debt (kd).
For a bond with a $1 000 par value the approximate YTM (kd) is
obtained by the following equation:
Kd = I + ($1 000 – Nd)
n
Nd + $1 000
2
Where I = annual interest in dollars
Nd = net proceeds from the sale of bond
N = number of years to the bond’s maturity.
After tax cost of debt (ki): Since interest on debt is tax deductible a tax
adjustment is required because the real cost of debt should be lower.
Ki = kd (1 – t)
Where kd = before tax cost of debt
t = tax rate
64
SUMMARY ON COST OF DEBT
Computation of component cost of debt
Computation of component cost of perpetual debt
Begin by computing the before tax cost of debt. This is obtained by using the
following formula:
kd = I
SV
Where kd = before – tax cost of debt
I = Annual interest payment
SV = Sale proceeds of the bond/debenture
ki = I
SV
(1 – t)
Where ki = Tax – adjusted cost of debt
t = tax rate
Computation of component cost of redeemable debt
An accurate result can be obtained by trial and error.
EXAMPLE
A company issues new 15% debentures of $1 000 face value to be redeemed
after 10 years. The debenture is expected to be sold at 5% discount. It will
also involve floatation costs of 5%. The company’s tax rate is 50%. What
would the cost of debt be?
SOLUTION
The cash flow pattern of the debenture would be as follows:
Years
0
1 – 10
10
Cash flow
+ $900 ($1 000 - $100 i.e. par value less floatation cost
less discount.
- $150 (interest payment)
- $1 000 (repayment of principal at maturity)
10
Tax adjusted cost of debt, kd = $900 =  $75
+ $1 000
t 1
(1 + ki )t
(1 + ki )10
The value of kd is obtained by trial and error. But there is a short cut approach
that can be used to obtain the after tax cost of debt.
65
Short – cut Method for the Determination of After – tax Cost of Debt
The formula for approximating the effective cost of debt can, as a short – cut,
be shown as follows:
ki = I (1 – t) + ( f + d + pr – pi)/ Nm
(RV + SV)/2
Where I = Annual interest payment
RV = Redeemable value of debentures/debt
SV = Net sale proceeds from the issue of debenture/debt (face value
of debt minus expenses)
Nm = Term of debt
f = Floatation cost
d = Discount on issue of debentures
pi = Premium on issue of debentures
pr = Premium on redemption of debentures
t = Tax rate
Application of the short – cut method on the previous example
ki = $150 (1 – 0.50) + ($50 + $50)/10
($900 + $1 000)/2
= $75 + $10
$950
= 8.947%
 9%
Follow up problem
Nomzamo Holdings has debentures outstanding with 5 years left before
maturity. The debentures are currently selling for $90 (the face value is $100).
The debentures are to be redeemed at 5% premium. The interest is paid
annually at a rate of 12%. The firm tax rate is 50%. Calculate the after tax cost
of debt using the short – cut method.
B. Cost of preference shares
As with debentures, the cost of preference shares is calculated on the
assumption that the market value of the share is equal to all expected
future receipts (dividends) discounted at the investor’s required rate of
return.
66
Cost of irredeemable preference shares
Cost of preference shares (kps) = Preference dividend payable
Market value of share ex div
If floatation costs are incurred these have to be incorporated in the calculation
of cost of preference shares.
Kpn = Dp
Np
Where kpn = before tax cost of preference shares
Dp = annual preference dividend payable
Np = Net proceeds from sale of preference shares.
EXAMPLE
D Ltd. is considering issuing 10% preference shares that are expected to sell
for $87 per share par value. Floatation costs are expected to be $5.00 per
share. Calculate kpn.
Dp = 10/100 *$87 = $8.70
Np = $87 - $5 = $82
Kpn = $8.70 * 100
$82.00
= 10.61%
Tax adjustment
No tax adjustment to before tax cost of preference shares is necessary since
preferred share dividends are paid out from the firm’s after tax cash flows.
Cost of redeemable preference shares
The method is identical to that used for redeemable debentures ignoring
corporate tax.
C. Cost of equity
Cost of equity is the rate at which investors discount the expected
dividends of the share to determine its intrinsic value.
Determination of cost of equity depends with the assumption made
regarding the dividends to be paid by the equity being looked at.
Cost of equity with a constant dividend If the rate of ordinary dividend
is assumed to be fixed, cost of equity (ke) is obtained as follows:
Cost of equity (ke) = Ordinary dividend payable * 100
Market price ex dividend
67
EXAMPLE. A $1.00 share is quoted at $2.32 and is about to receive a
$0.20 dividend. Calculate the cost of equity.
Ke = $0.20 * 100
$2.32 -$0.20
= 9.43%
Cost of equity with constant growth dividends
The model assumes that the value of a share equals the present value of
all future dividends (assumed to grow at a constant rate) that it is expected
to provide over an infinite time horizon. The following equation is used:
Ke = D1
+g
Po ex dividend
Where Po = Value of equity now.
D1 = per share dividend expected at the end of year 1
Ke = required return on equity (cost of equity)
g = constant growth rate of ordinary dividends.
EXAMPLE. A $0.50 share is quoted at $1.80 and is about to receive a
$0.10 dividend. Dividends are expected to increase at the rate of 4% per
annum. Calculate the cost of equity.
Ke = $0.10(1.04)
+ 0.04
$1.80 - $0.10
= $0.104 + 0.04
$1.70
= 0.0612+0.04
= 0.1011764 * 100
= 10.12%
Limitations to computation of cost of equity
1. The computational assumption is that the dividend valuation model is
valid. This may not be the case.
2. The computational assumption is that dividends are payable at annual
intervals. In practice this is not usually the case as there are interim
dividends.
3. An accurate knowledge of the shareholder’s expected required rate of
return is also assumed. If what the shareholder requires, for some
reason changes, and this is unknown to the organization, then the
valuation becomes wrong. This problem is usually brought about by
growth in dividends.
68
Capital asset pricing model
The capital asset pricing model can also be used to approximate the cost
of equity.
The model calculates the risk-adjusted cost of equity capital. It describes
the relationship between the required rate of return (cost of equity) and the
non-diversifiable risk of the firm as measured by the beta coefficient, b.
Ke = Rf + [b * (Km – Rf)]
Advantage of the CAPM approach: While the constant growth model
does not look at risk and uses the market price to reflect the expected risk
– return preferences of investors the CAPM directly considers the firm’s
risk as reflected by beta.
Disadvantage of the CAPM approach: It is not easy to adjust for
floatation costs when using CAPM, as is the case with the Gordon model.
NB. The preferred approach is to use the Gordon model.
Cost of new ordinary shares
This is the cost of new ordinary shares being issued after considering the
amount of under pricing and floatation costs. Under pricing is the selling of
shares at a price below its current market price. It is necessary in order to
make an issue attractive.
Ken = D1 + g
Nn
Where ken = cost of new ordinary shares
D1 = dividend payable at the end of year 1
Nn = net proceeds from issue of new ordinary shares.
EXAMPLE: F Ltd. uses a constant growth model. Its expected dividend at the
end of the coming year is $4.00. Its current market price is $50.00 and the
expected growth rate of dividends is 5%. If a $3.00 under pricing is necessary
because of the competitive nature of the market and an underwriting fee of
$2,50 per share is required, what is the cost of new ordinary shares?
Nn = $50.00 – ($3.00 + $2.50)
=$50.00 - $5.50
= $44.50
ken = $4.00 + 0.05
$44.50
= 0.1398876 * 100 = 13.99%
69
Tax adjustment
No tax adjustment is necessary as ordinary dividends are paid out of after tax
cash flows.
Cost of retained earnings
Cost of retained earnings (kr) is the cost of an equivalent fully subscribed
issue of ordinary shares. Thus kr = ke.
Weighting schemes
Weights can be calculated as book value, market value or target weights.
Book value weights
Accounting book values are used to measure the proportion of each type of
capital in the financial structure when calculating the weighted average cost of
capital.
The advantage of this approach is that the accounting information is readily
available. The disadvantage is that book values do not usually indicate the
approximate value that could be realized on the sale of the assets.
Market value weights
The market values of each type of capital in the firm’s capital structure are
used to establish the weights to use when calculating the weighted average
cost of capital.
The advantage of using market values is that the market values closely
approximate actual dollar amounts to be realized should assets be sold. The
problem, however, is the fact that market values are generally not readily
available.
Target weights
Target weights can also be used. The target weights can either be book
values or market values based on desired capital structure proportions. These
will then be used when calculating weighted average cost of capital.
The preferred weighting scheme is to use target market values.
Calculating the weighted average cost of capital
Once the component cost is established and the appropriate weighting
scheme chosen, the weighted average cost of capital can then be calculated.
There are two computational approaches that can be used.
Method 1
The weighted average cost of capital can be obtained by using the following
approach:
WACC = (wi * ki) + (wp * kp) + (we * ke)
70
Where
 Wi = proportion of long-term debt in the capital structure,
 Ki = after tax component cost of debt,
 Wp = proportion of preference shares in the capital structure,
 Kp = component cost of preference shares,
 We = proportion of ordinary shares in the capital structure,
 Ke = component cost of ordinary shares.
Wi + wp + we = 1.0.
For computational convenience one can convert the weights to decimal form
and leave component costs in percentage terms.
Method 2
A tabular format can also be used to compute weighted average cost of
capital. The structure of the table to be used can now be presented.
Source of capital
Prefence shares
Ordinary shares
Long-term debt
Weight
-1
0.2
0.5
0.3
1
Cost
Weighted cost
1*2=3
xxxx
xxxx
xxxx
WACC = xxxx
-2
xxx
xxx
xxx
Weighted marginal cost of capital (WMCC)
This is the firm’s weighted average cost of capital associated with its next
dollar of total financing. WMCC is an increasing function of the level of total
new financing. As new financing increases, risk increases, increasing the cost
associated with the new financing. This ultimately increases weighted average
cost of capital. Computing weighted marginal cost of capital will require
knowledge of the breaking point for each type of financing. This is the point at
which the component cost of a particular type of financing increases.
Breaking point
This is the level of total new financing at which the cost of the financing
component increases creating an upward shift in the weighted marginal cost
of capital. The breaking point is obtained by using the following equation:
Breaking point = Amount of financing available from a given financing source
Capital structure weight stated in decimal form
Once the breaking points are established, the different weighted average cost
of capital at given levels of financing can be calculated. From this, the
marginal increments, which define the weighted marginal cost of capital, can
be deduced. It is also necessary to have knowledge of the investment
opportunities schedule. This can then be used in conjunction with the
weighted marginal cost of capital to indicate the various investments that will
be acceptable.
71
The investment opportunities schedule
This is the ranking of investment possibilities from the one with the highest
returns (best) to the one with the lowest returns (worst). As the cumulative
amount of money invested in a firm’s investment projects increases, the
returns from the projects as measured by IRR decreases. The return on
investments decreases as the firm accepts additional projects.
EXAMPLE.
Nice Time Ltd is a leading company with an optimal capital structure made
up of 30% debt, 20% preference shares and 50% equity. The cost of debt
is 20%, cost of preference shares is 18% and cost of equity is 24%. The
company can borrow up to $2.4 million in debentures and $3 million in
preference shares without a change in the cost of debt and preference
shares respectively. The expected retained earnings for the firm are $5
million after which the cost of equity would increase because of floatation
costs. If additional debt finance over $2.4 million is required the cost will
increase by 15%, additional preference shares over $3 million will increase
the cost of preference shares to 24% and a new issue of ordinary shares
will increase the cost of equity to 28%.
(a) What is the breaking point for each source of financing?
(b) What is the marginal cost of capital for each range of capital raised?
(c) Suppose that the firm had the following capital projects under
consideration?
Project
IRR
Initial Investment ($)
A
22%
2 000 000
B
25%
4 000 000
C
23%
6 000 000
D
24%
5 000 000
E
20%
7 000 000
F
18%
4 000 000
Construct a graph showing the marginal cost of capital and the
investment opportunity schedule and show which projects will be
implemented.
72
Solution
Breaking point (Equity) = $5 000 000
0.50
= $10 000 000
Breaking point (Debt)
= $2 400 000
0.30
= $8 000 000
Breaking point (Preference shares) = $3 000 000
0.20
= $15 000 000
Amount raised
Source of capital
Weight
Cost
Weighted cost
0 -<$8 000 000
Ordinary shares
0.50
24%
12%
Debt
0.30
20%
06%
Preference shares
0.20
18%
03.6%
1.00
$8m - <$10 000 000
21.60%
Ordinary shares
0.50
24%
12%
Debt
0.30
35%
10.50%
Preference shares
0.20
18%
03.60%
1.00
$10m - <$15 000 000
26.10%
Ordinary shares
0.50
28%
14%
Debt
0.30
35%
10.50%
Preference shares
0.20
18%
03.60%
1.00
$15m +
28.10%
Ordinary shares
0.50
28%
14%
Debt
0.30
35%
10.50%
Preference shares
0.20
24%
04.80%
1.00
73
29.30%
The weighted marginal cost of capital schedule can now be prepared from the
results obtained in the table above. This schedule will, however be, presented
in conjunction with the investment opportunity schedule. It is therefore
necessary to illustrate the preliminary requirements before one can prepare
the investment opportunity schedule.
The first step is to prepare a table of cumulative investments. The schedule
shows the ranking of the available opportunities starting with the most
preferred in terms of the internal rate of return to the lest preferred. The
schedule also shows the cumulative amount of investment financing needed
as each successive project is considered. The investment opportunity
schedule now follows.
Investment opportunity
B
D
C
A
E
F
IRR
25%
24%
23%
22%
20%
18%
Initial Investment
$4 000 000
5 000 000
6 000 000
2 000 000
7 000 000
4 000 000
Cummulative Investment
$4 000 000
9 000 000
15 000 000
17 000 000
24 000 000
28 000 000
From the above schedule it can be noted that the graph to be prepared
should be able to accommodate on one axis a 25% return and on the other
axis total new financing amounting to $28 000 000. From the weighted
marginal cost of capital table it can also be noted that the graph to be
prepared should be able to accommodate on one axis a maximum of 29.30%
cost while on the other axis the ceiling is not defined but it should be above
$15 000 000. Since the vertical axis will record both weighted average cost of
capital and the internal rate of return this axis should be able to accommodate
a highest rate of 29.30%, which is the highest weighted average cost of
capital. The horizontal axis will record new financing and investment so
provision should be made to accommodate a cumulative investment of $28
000 000.
The weighted marginal cost of capital and the investment opportunities
schedule can now be presented on a single graph to show which investment
opportunities are acceptable and those that are not acceptable.
74
IRR,
WACC%
30
25
29.30%
28.10%
26.10%
WMCC
B
D
21.60%
C
A
20
E
F
IOS
15
10
5
5
10
15
20
25
30
New financing or investment $m
Only those projects whose internal rate of return is above the weighted
marginal cost of capital are acceptable as they generate a positive return for
the shareholders.
From the previous graph it can be noted that project B is acceptable. Project
D can be problematic as part of it lies below the cost function. If it is a divisible
project then a substantial part of it can be implemented. If it is not divisible
then the whole project should not be considered at all.
75
PRACTICE PROBLEMS ON WEIGHTED AVERAGE COST OF CAPITAL
PROBLEM 1
Assuming the corporate tax rate of 55%, compute the after tax cost of capital
in the following situations:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
A perpetual 12% debenture of $1 000, sold at the premium of 10%
with no flotation costs.
A fifteen – year 10% debenture of $2 000, redeemable at par, with
3.75% floatation costs.
A ten – year 11% Preference share of $100, redeemable at a
premium of 5%, with 5% floatation costs.
An equity share selling at $50 and paying a dividend of $6 per
share, which is expected to be continued indefinitely.
The same equity share (in iv above), if dividends are expected to
grow at the rate of (a) 5%, (b) –5%.
An equity share, selling at $120 per share, of a company that
engages only in equity financing. The earnings per share amounts
to $20 of which 50% is paid in dividends. The shareholders expect
the company to earn a constant after – tax rate of 10% on its
investment of retained earnings.
The cost of equity capital of the company is 12%. The company
wishes to finance its new investment project by retained earnings.
PROBLEM 2
From the following information supplied, determine the appropriate weighted
average cost of capital, relevant for evaluating long – term investment projects
of the company:
Cost of equity
After – tax cost of long – term debt
After – tax cost of short – term loans
Source of capital
Equity
Long – term debt
Short – term debt
12%
7%
4%
Book value
$
500 000
400 000
100 000
1 000 000
Market value
$
750 000
375 000
100 000
1 225 000
PROBLEM 3
An electricity equipment manufacturing company wishes to determine the
weighted average cost of capital for evaluating capital projects. You have
been supplied with the following information to calculate the value of the
weighted average cost of capital:
76
Balance sheet at 31 March 2006
Assets
Sundry assets
$
3 900 000
Liabilities and equity
Equity shares
Preference shares
Retained earnings
Debentures
Current liabilities
1 200 000
450 000
450 000
900 000
900 000
3 900 000
Anticipated external financing information:
i.
ii.
iii.
20 year, 8% debentures of $2 500 face value, redeemable at 5%
premium sold at par, 2% floatation costs.
10% preference shares: sale price $100 per share, 2% floatation costs.
Equity shares: sale price $115 per share floatation costs would be $5
per share.
The corporate tax rate is 55% and expected equity dividend growth is 5% per
year. The expected dividend at the end of the current financial year is $11 per
share. Assume that the company is satisfied with its present capital structure
and intends to maintain it.
PROBLEM 4
Zamndela Investments is interested in measuring its cost of specific types of
capital as well as its overall capital cost. The finance department of the
company indicates that the following costs would be associated with the sale
of debentures, preference shares and equity shares. The corporate tax rate is
55%.
Debentures: The company can sell 15 – year 10% debentures of the face
value of $1 000 for $970. In addition, an underwriting fee of 1.5% of the face
value would be incurred in this process.
Preference shares: 12% preference shares having a face value of $100 can
be sold at a premium of 10%. An underwriting fee of $2 per share is to be paid
to the underwriters.
Equity shares: The Company’s equity shares are currently selling for $125
per share. The firm expects to pay $15 per share at the end of the coming
year. Its dividend payments over the past 6 years per share are given below:
Year
1
2
3
4
5
6
Dividend ($)
10.60
11.24
11.91
12.62
13.38
14.19
77
It is expected that the new equity shares can be sold at $123 per share. The
company must also pay $3 per share as underwriting fee.
Market and book values for each type of capital are as follows:
Book value ($)
1 800 000
450 000
6 000 000
1 500 000
9 750 000
Long – term debt
Preference shares
Equity shares
Retained earnings
Market value ($)
1 930 000
520 000
1 000 000
12 450 000
Requirement
(a) Calculate the specific cost of each source of financing.
(b) Determine the weighted average cost of capital using
(i)
book value weights and
(ii)
market value weights.
PROBLEM 5
A company has the following specific cost of capital along with the indicated
book and market value weights.
Type of capital
Long – term debt
Preference shares
Equity shares
Retained earnings
Cost
Book value
weights
%
30
20
40
10
100
%
5
10
12
12
Market value
weights
%
25
17
46
12
100
(a) Calculate the weighted average cost of capital using book value and
market value weights. Which of them do you consider better and why?
(b) Calculate the weighted average cost of capital using marginal weights
if the company intends to raise the needed funds using 50% long –
term debts, 35% preference shares and 15% retained earnings.
PROBLEM 5
Moroka Investments has compiled the following data relating to the current
costs of its sources of capital for various ranges of financing:
78
Source of capital
Long-term debt
Range of new financing
After- tax cost
$0 to $200 000
6%
$200 000 to $300 000
7%
$300 000 and above
9%
Preference shares
$0 to $100 000
17%
$100 000 and above
19%
Ordinary shares
$0 to $220 000
22%
$220 000 to $320 000
24%
$320 000 and above
26%
The company’s current earnings, of which 40 per cent will be retained,
amount to $200 000. The cost of retained earnings has been estimated to be
20 per cent. The company’s target capital structure is as follows:
Source of capital
Long-term debt
Preference shares
Ordinary shares
Target capital structures
40%
20%
40%
100%
1) Determine the breaking points and ranges of total new financing
associated with each source of capital.
2) Using the data developed in 1 above, determine the levels of total new
financing at which the company’s weighted average cost of capital will
change.
3) Calculate the weighted average cost of capital for each range of total
new financing found in 2 above.
4) Using the results obtained in 3 above along with the following
information on the investment opportunities of Moroka Investments,
determine the optimal capital budget of Moroka Investments.
Investment
opportunity
Project
A
B
C
D
E
F
G
H
I
Initial
investment
$
200 000
300 000
100 000
600 000
200 000
100 000
300 000
100 000
400 000
79
Internal rate of return
(IRR)
%
19
15
22
14
23
13
21
17
16
Chapter 5
The capital budgeting decision
Capital budgeting
Capital budgeting is the decision area in financial management that
establishes the decision area of financial management that establishes criteria
for investing resources in long-term projects (Clark, Hinderlang and Pritchard:
1989). This decision area is very important for the organization because of the
following reasons:
(a) The cost of assets to be acquired normally represents relatively
large expenditures.
(b) The funds will generally be committed for lengthy periods of
time. In addition, capital investment decisions are difficult or
very costly to reverse.
(c) The ability of the firm to attain most of its important financial
objectives is significantly impacted upon by its capital
investment decisions.
(d) The capital decision also determines the company’s future
course of development.
(e) The decision is also important because working capital
requirements closely relate to the size and utilization of fixed
assets.
Basic assumptions of capital budgeting
The following assumptions underlie the capital budgeting decision:
1. Management’s primary function is to increase the value of the firm as
reflected by the price of its ordinary shares.
2. Shareholders have a preference for current cash flows as opposed to
future cash flows. Investors must be compensated for postponing the
recovery of their investments and returns on investment. Since the
benefits of a capital asset acquisition are received over a future period,
the time value of money becomes the core of capital budgeting.
3. Shareholders are risk averse. Because of this risk aversion, present
dollars have greater value than future dollars. Should an investment
fail, the value of funds lost would be greater than the value of the funds
gained should the project have succeeded. For this reason rational
investors require higher returns for perceived higher risks.
4. When evaluating capital budgeting projects the analysis should be
based on after tax incremental cash flows directly attributable to the
project. These should be the cash flows that would otherwise not exist
if the project were rejected. Sunk costs are not relevant to the analysis.
MAKING THE CAPITAL BUDGETING DECISION IN A CERTAIN
ENVIRONMENT
Making a choice between a number of alternative capital projects should be
systematic. The following diagram illustrates the usual procedure to follow
when making such a decision.
80
A.
B.
C.
Compute relevant cash flows
Systematically evaluate the cash flows
Select the best project
CAPITAL BUDGETING UNDER CONDITIONS OF CERTAINTY
Computation of the initial investment
The initial investment is the relevant cash outflow that has to be paid now to
implement the selected capital project. The format presented below illustrates
how the initial investment is arrived at.
Cost of new asset
Add: Installation costs
Installed cost of new asst
Less Proceeds from sale of old asset
Plus or minus Tax adjustment on sale of old asset
After tax proceeds from sale of old asset
Plus or minus Change in net working capital
Initial investment
xxx
xxx
xxx
xxx
xxx
xxx
xxx
xxx
xxx
1. Cost of new asset: This is the total net cash outflow required to acquire
a new asset.
2. Installation cost: These are additional costs that will be incurred to
place the asset being acquired into production.
3. Installed cost of new asset: This is the combination of cost of new
asset and installation costs incurred. It is also known as the
depreciable cost of the asset as it is the amount to be used when
calculating depreciation on the new machine.
4. Proceeds from sale of old asset: The amount received from the sale of
the asset being replaced, net of removal or clean up costs, is the
proceed from sale of old asset.
5. Change in net working capital: This will represent the difference
between a change in current assets and a change in current liabilities
attributable to the new machine being evaluated.
Computation of change in net working capital
The following computation may prove to be very useful when there are a
number of changes to current assets and current liabilities associated with the
new capital asset.
81
Current account
Change in balance
Cash
xxx
Account receivable
xxx
Inventories
xxx
(1) Current assets
xxx
Accounts payable
xxx
Accruals
xxx
(2) Current liabilities
xxx
Change in net working capital [(1) - (2) ]
xxx
Computation of terminal cash flow
Terminal cash flow is the relevant cash flow attributable to the liquidation of a
long -term investment at the end of its useful life. It can be computed with the
aid of the following schematic diagram.
Proceed from sale of new asset
Plus or minus tax on sale of new asset
After tax proceeds from sale of new asset
Plus or minus cahnge in net working capital
Terminal cash flow
xxx
xxx
xxx
xxx
xxx
Incremental after tax operating cash flows
These are relevant cash inflows resulting from the use of a proposed longterm capital project. The after tax operating cash inflows are calculated using
the following format.
Computing incremental after tax operating cash inflows where
depreciation is involved and has an assumed tax shield effect
Revenue
Less expenses (excluding depreciation)
Income before depreciation and taxes
Less depreciation
Net income before taxes
Less Taxes @ x%
Net income after taxes
Add back depreciation
Operating after tax cash inflows
xxx
xxx
xxx
xxx
xxx
xxx
xxx
xxx
xxx
82
Computing after tax operating cash inflows where capital allowances are
available and are claimed
Revenue
Less expenses
Net income before capital allowances and taxation
Less Allowances claimed (SIA or W&T)
Net income before taxation
Taxation @ x%
Net income after taxation
Add back capital allowances claimed
After tax operating cash inflows
xxx
xxx
xxx
xxx
xxx
xxx
xxx
xxx
xxx
It is important to note that the relevant flow required for capital budgeting
purposes is after tax cash inflows rather than after tax net income. This is why
depreciation and the capital allowances are added back since their effect on
after tax cash flows would have been adjusted for.
When a replacement project is being evaluated an additional computation will
be required. The purpose of this computation would be to obtain differential
cash inflows. The following working arrangement can prove to be useful.
1. Compute the relevant cash flows on an after tax basis for the existing
project using the suggested format above.
2. Compute the relevant cash flows on an after tax basis for the new
project using the format already suggested above.
3. Compute incremental cash flows using the following format.
Year
Proposed
project
[1]
1
xxx
2
xxx
Present
project
[2]
xxx
xxx
Incremental
cash inflow
[(1) -(2)]
xxx
xxx
 After computing the relevant cash flows discount the cash flows when
the evaluation is done using discounted cash flow methods.
 Even when the evaluation is done using non discounted cash flow
techniques, the cash flows to be evaluated will still be the incremental
cash flows as calculated from the above schedules.
CAPITAL PROJECT APPRAISAL TECHNIQUES
An example now follows to illustrate how project cash flows are computed and
evaluated before one can recommend which project to invest in.
EXAMPLE
Musharukwa Investments Ltd. Currently uses an injection-moulding machine
that was purchased two years ago. This machine is being depreciated on a
straight-line basis towards a $500 000 salvage value, and it has six years of
remaining life. Its current book value is $2 600 000, and it can be sold at $3
000 000 at this point in time.
83
The company is offered a replacement machine which has a cost of $8 000
000, an estimated useful life of six years, and an estimated salvage value of
$800 000.The replacement machine would permit an output expansion, so
sales would rise by $1 000 000 per year. The new machine’s much greater
efficiency would cause operating expenses to decline by $1 500 000 per year.
The new machine would require that inventories be increased by $2 000 000,
but accounts payable would simultaneously increase by $500 000.
The company’s effective rate is 46 percent and its cost of capital is 15
percent.
Requirement
Using the net present value technique determine whether the company should
replace the old machine.
Solution
Computation of initial investment
Cost of new asset
Add Installation cost
Installed cost os new asset
Add Proceeds from sale of old asset
Tax on proceeds on sale of old asset (Note 1)
After tax proceeds on sale of old asset
($8 000 000)
Nil
($8 000 000)
$3 000 000
(184 000)
2 816 000
($5 184 000)
($1 500 000)
($6 684 000)
Change in net working capital (Note 2)
Initial investment
Note 1.
Current net book value of old asset
Amount realizable on sale of asset
Taxable gain
Tax payable at 46%
$2 600 000
3 000 000
400 000
$ 184 000
Note 2.
Current assets: Inventory
Current liability: Accounts payable
Change in net working capital
$2 000 000
500 000
$1 500 000
Computation of operating cash inflows
Revenue: Increase in sales
Decline in operating expenses
Incremental revenue
Incremental expenses
Income before depreciation and taxes
Depreciation
Net income before taxation
Taxatio at 46%
Net income after taxation
Add back depreciation
After tax operating cash inflow
84
$1 000 000
1 500 000
2 500 000
nil
2 500 000
(1 200 000)
1 300 000
(598 000)
702 000
1 200 000
$1 902 000
Computation of terminal cash flow
Book value of new asset on disposal
Realizable proceeds on disposal
Taxable difference
Tax payable on disposal
$ 800 000
800 000
Nil
Nil
Proceeds from sale of new asset
Recoupment of working capital
Terminal cash flow
800 000
1 500 000
$2 300 000
Summary of cash flows for the period
Year
0
1
2
3
4
5
6
Cash flow
($6 684 000)
1 902 000
1 902 000
1 902 000
1 902 000
1 902 000
1 902 000 + 2 300 000
THE NET PRESENT VALUE TECHNIQUE
The net present value criterion for evaluating proposed capital projects
involves summing the present values of cash outflows required to support an
investment with the present value of the cash inflows resulting from
operations of the project. The inflows and outflows are discounted to present
value using the firm’s required rate of return for the project. The NPV is the
difference in the resent value of the inflows and outflows.
Decision rules
1. If the NPV is positive, the project is expected to yield a return in excess
of the required rate of return. The project will be acceptable.
2. If the NPV is zero, the yield is expected to exactly equal the required
rate of return. The decision maker would be indifferent.
3. If the NPV is negative, the yield is expected to be less than the
required rate of return. Projects of this nature do not meet the criterion
for acceptance. They are only acceptable in unusual circumstances.
The example earlier presented can now be worked through using the net
present value method. Two methods of computation will be illustrated: the
annual discounting method and the annuity method (since the cash flows are
an annuity).
85
Method 1: The annual discounting approach
Cash flow
Discount factor@ 15% Present value
($6 684 000)
1
(6 684 000)
1 902 000
0.86957
1 653 922
1 902 000
0.75614
1 438 178
1 902 000
0.65752
1 250 603
1 902 000
0.57175
1 087 469
1 902 000
0.49718
945 636
4 202 000
0.43233
1 816 651
1 508 459
Method 2: Annuity method
Discount factor
Time
Cash flow
At 15%
0
(6 684 000)
1.00000
1–6
1 902 000
3.78449
6
2 300 000
0.43233
NPV
Present
Value
(6 684 000)
7 198 100
994 359
1 508 459
Since the NPV of the project is positive, the replacement project can be
undertaken.
Advantages of the NPV approach
a. The approach takes into account the time value of money. For
this reason it can be regarded as a sophisticated evaluation
technique.
b. The approach uses cash flows and cash flows are less
subjective than profits.
c. The NPV of a project reveals the amount by which the
productive value (present value of cash inflows) exceeds or is
less than the project cost.
d. The method also identifies those projects that meet the
minimum desired rate of return. These are projects having a
zero or positive NPV.
Disadvantages of the NPV approach
1. Uncertainty introduced
by cost
of
capital
computation To discount cash flows to their present
value, one has to calculate the weighted average cost of
capital. This is extremely difficult to calculate and
forecast. As a result, any decision made depends on the
accuracy of the calculations and forecasts.
2. Shareholders may not necessarily require high cash
flows The basic assumption in financial management is
shareholder wealth maximization. This is achieved by
dividends paid to shareholders from profits made. If this is
the case, then the objective should be to maximize profits
and not achieve high cash flows.
3. The concept is not easily understood Discounted cash
flow as a concept is difficult to grasp (for the layman). It
86
would be beneficial for the person on whose behalf the
calculations are performed (the layman investor) to have
a grasp of the basic concept underlying the technique.
4. Determination of the hurdle rate There are problems in
deciding the appropriate hurdle rate to use when
discounting the cash flows. The firm’s cost of capital is
sometimes used as the discount rate.
UNDISCOUNTED PAYBACK
The payback period is the time required to recover the investment in a project.
It is the period during which the cumulative net cash inflows generated by the
project just equal the net cash outflow necessary for the project.
PAYBACK WITH EQUAL ANNUAL CASH INFLOWS (ANNUITY)
The payback period is equal to the net cash outlay divided by the annual net
cash inflow.
Payback period = Net cash outlay
Annual net cash inflow
EXAMPLE A company is evaluating a project that requires $60 000 cash
outlay, and it is expected to generate annual net cash inflows of $8 000 over
its 15 year useful life. Determine the payback period for the project.
Payback period = $60 000
$8 000
= 7.5 years
This indicates that after 7.5 years the firm’s $60 000 cash outlay will have
been recovered.
PAYBACK WITH UNEQUAL ANNUAL CASH INFLOWSWhen net cash inflows are not equal from year to year, the payback period is
found by cumulating the cash inflows until they equal the net cash outlay.
EXAMPLE
B. Ltd. is evaluating a capital project that requires a $38 000 net cash outlay
and will generate net cash inflows of $10 000 for each of the first two years,
$8 000 each for years 3 and 4, and $6 000 for each of years 5 through 7.
Determine the payback period.
Solution
Table of annual and cumulative expected cash inflows
Year
Net Cash Inflow ($)
Cumulative Cash Inflow ($)
1
10 000
10 000
2
10 000
20 000
3
8 000
28 000
4
8 000
36 000
5
6 000
42 000
6
6 000
48 000
7
6 000
54 000
87
The payback period lies between year 4 and 5. The exact payback period can
be obtained as follows:
Either 4 + 2 000/6 000 = 41/3 years
Or 4 + [ 2 000/6 000 * 12 ] = 4 years and 4 months.
Decision rules
1. If calculated payback is less than the cut off payback period for the
firm, accept project.
2. If calculated payback is equal to the cut off payback period for the firm,
the decision maker can be indifferent.
3. If the calculated payback is greater than the cut off payback period for
the firm, the project is rejected.
Advantages of the Payback Period as a capital project evaluation
technique
1. Simplicity The payback period approach is simple in terms of
computation and comprehension.
2. Uncertainty Many managers have reservations about the estimates of
expected cash flows to be received in future and feel that if they were
to recover their investment early, they will make a profit. The payback
method assists them in identifying projects of this nature.
3. Liquidity Many firms have liquidity problems and are very concerned
about how rapidly invested funds will be recovered. The payback
method assists in identifying projects that rapidly repay invested funds.
4. Cost of external financing Some firms have high costs of external
financing and have to look for internally generated funds to support
their ventures. These firms become interested in the rate at which their
investment will be recovered. Again the payback method helps in
identifying projects with high capital recovery rates.
5. Compensation for risk It is simple to compensate for the differences
in risk associated with alternative projects. Projects that have higher
degrees of risk are evaluated using shorter payback periods compared
to the payback period associated with the projects usually undertaken
by the firm.
6. Technological changes and competition Some firms may be
involved in areas where the risk of obsolescence as a result of
technological changes and severe competition may be great so they
may be anxious to recover funds rapidly. The payback method assists
in cases like these.
7. Model changes There are firms that manufacture products that are
subject to model changes and therefore must recover their investment
within the model life. They need to use an evaluation technique that
can indicate a high rate of capital recovery. The payback method is
quite useful in this regard.
88
Disadvantages of the payback period
1. Limited period of consideration The period to be considered when
using the payback technique is limited to the payback period. Expected
cash flows beyond the payback period established by the firm are not
considered.
2. Time value of money The undiscounted payback period fails to
consider the time value of money. Because of this limitation it is
sometimes referred to as a naïve technique (an unsophisticated
technique) of appraising capital projects.
3. Magnitude of investment The payback method does not differentiate
between projects requiring different cash investments. If the decision
maker is not careful they may end up selecting fairly smaller projects at
the expense of larger capital projects.
4. Liquidity While the payback method does measure a project’s rate of
capital recovery (liquidity) it does not consider the firm’s liquidity
position as a whole which is a much more important consideration.
5. Cost of funds The undiscounted payback method ignores the cost of
funds used to support the investment even during the payback period.
By ignoring the coast of funds a very important cost is overlooked.
Recommended situations when to use the payback period
The payback period method of appraising capital projects can a be
recommended appraisal technique for the following cases:
1. As a measure of a project’s liquidity if such liquidity is of particular
importance to the firm.
2. For projects involving uncertain returns, especially when those returns
become increasingly more uncertain in future time periods.
3. During periods of very high external financing costs, which make
capital recovery very important.
4. For projects involving a high degree of cataclysmic risk.
5. For projects subject to model-year changes or obsolescence resulting
from technological changes or changing consumer preferences.
RETURN ON INVESTMENT (ROI) - ACCOUNTING RATE OF RETURN
(ARR)
The return on investment (ROI) method of appraising capital projects
compares the yearly after-tax (or pre-tax) income with the investment in the
asset. The underlying idea is to compare the return expected to be received
from a project with some pre-established requirement. The following are some
of the different methods that can be used.
EXAMPLE
The following information is provided concerning a potential capital project.
$
Investment
1 000
Estimated useful life (5 Years)
Income: Year 1 – Year 5
300
89
Compute the return on investment by various methods
Solution
Method 1: Average annual return on Investment
ROI = [Average annual income/ Original Investment * 100]
= [300/1 000 * 100]
= 30%
Method 2. Average annual return on average investment
ROI = [Average annual income/(Original Investment/2) * 100]
= [ 300/ (1000/2) * 100]
= 60%
Method 3: Average return on average investment
ROI = [(Total Income – Original Investment/ useful life)/(Original Investment/2]
= [(1 500 – 1 000/5)/ (1 000/2)] * 100
= 20%
Decision rules
If calculated ROI is greater than the established ROI the project is acceptable.
If calculated ROI is equal to the established ROI the decision maker is
indifferent and should the calculated ROI be less than the established ROI
then the project is unacceptable.
Return on investment calculations
A firm is evaluating a project which has an original investment of $24 000 and
a projected salvage value of $4 000 at the end of its 6-year life. The net
income before taxes generated by the project each year is as follows:
Year
1
2
3
4
5
6
Net income before tax ($)
2 000
3 500
4 000
2 400
2 000
1 000
The firm’s marginal tax rate is 40%. Determine:
a) ROI before tax on original Investment.
b) ROI before tax on average Investment
c) ROI after tax on original Investment.
d) ROI after tax on average Investment.
Solution
Average net income before tax
= $[(2 000 + 3 500 + 4 000 + 2 400 + 2 000 + 1 000)/6]
= $2 483.33
90
a) ROI before tax on original investment = $2 483.33/24 000 * 100
= 10.35%
b) ROI before tax on Average Investment
= $[(2 483.33/(24 000 + 4 000)/2] * 100
= 17.74%
If the firm’s marginal tax rate is assumed to remain at 40% over the six
years then the average annual net income after tax is computed as
follows:
Average net income after tax = (Average net income before tax)(1-tax rate)
= ($2 483.33)(1 –0.40)
= ($2 483.33)(0.60)
=$1 490.00
c) ROI after tax on original investment = $1 490.00/$24 000 * 100
= 6.21%
d) ROI after tax on average investment
= [$1 490.00/($24 000 + 4 000)/2] * 100
=10.64%
Advantages of Return on Investment
1. Simplicity The method gives a simple measure of anticipated
profitability from the project. It is also easy to understand.
2. Understandability The decision to undertake a project is made by
managers who have to convince shareholders on the gains to be
realized from such a project. Not all managers and shareholders are
skilled in financial management techniques and ROI is much easier to
understand.
3. Profitability If it is the maximization of profits that is hoped to be
achieved, then the ROI technique will ensure that profits are
maximized, by identifying a project with maximum profit.
4. The needed information is usually readily available.
Disadvantages of Return on Investment
1. Timing of the expected profits The ROI does not consider the timing
of the expected profits. Thus a project with a low initial profitability and
a high future profitability would have the same average rate of return as
a project with a higher initial profitability and a lower future profitability.
The former project would have much less value to the firm than the
latter. The following example illustrates the argument just presented.
Project 1
Year 1
2
3
4
5
Expected Profits ($) Project 2
5 000
Year 1
4 000
2
3 000
3
2 000
4
1 000
5
91
Expected Profits ($)
1 000
2 000
3 000
4 000
5 000
If both projects cost $20 000, then the ROI for both projects would be
identical creating a situation of indifference, which should clearly not be the
case for these two projects.
2. Problems associated with asset valuation The real value of an asset
to the firm is a function if management `s ability to employ the asset in
a productive manner. The firm’s balance sheet only lists the
investments that the firm has made and the sources of capital used to
obtain and maintain those investments. The listed amounts reflect
accounting values, which may differ substantially from the market and
productive values. Since the balance sheet values neither reflect the
value of the assets in terms of their earning ability nor their market
value, the return on investment method may be extremely misleading.
It is the fair market value or the productive value of the asset to the
firm, not the book value, which must be considered.
3. Time value of money The Return on Investment is a naïve appraisal
technique in that it ignores the time value of money.
4. Use of accounting profits The Return on Investment uses accounting
flows (profits) rather than cash flows. Accounting flows can be
manipulated (“doctored”) unlike cash flows.
5. Lack of benchmark for project selection Usually there is no
benchmark for project acceptance. Because of this the cost of capital is
sometimes used as a surrogate benchmark. The use of cost of capital
as a surrogate benchmark has inherent problems:
a. The cost of capital is based on the after-tax cost of funds used
for financing. Comparing pre-tax ROI with the cost of capital is
erroneous.
b. Even for cases where ROI is computed on an after-tax basis,
the fact that the time value of money is ignored renders the cost
of capital invalid as a benchmark.
PROFITABILITY INDEX (PI)
The profitability index is the ratio of the present value of the after-tax cash
inflows to the outflows. A ratio of 1 or greater indicates that the project has an
expected yield equal to or greater than the discount rate. The PI is a measure
of a project’s profitability per dollar of investment. Being a ratio it can be used
to rank projects of varying costs and expected economic lives in order of their
profitability.
Profitability Index = Present value of cash Inflows/ Present value of cash
Outflows
EXAMPLE
Three projects have been suggested to a company. The after-tax cash flows
for each are tabulated below. If the firm’s coast of capital is 12% rank the
projects in order of profitability.
92
Time
0
1
2
3
4
After tax cash flows
Project A
Project B
($10 000)
($30 000)
2 800
6 000
3 000
10 000
4 000
12 000
4 000
16 000
Project C
($18 000)
6 500
6 500
6 500
6 500
Step 1. Calculate the present value of cash inflows for each project
Present value of cash inflows: Project A
Time
Cash Flow ($)
Discount factor @ 12% Present value ($)
1
2 800
0.893
2 500
2
3 000
0.797
2 391
3
4 000
0.712
2 848
4
4 000
0.636
2 544
10 283
Present value of cash inflows: Project B.
Time
Cash Flow ($)
Discount factor @ 12%
1
6 000
0.893
2
10 000
0.797
3
12 000
0.712
4
16 000
0.636
Present value of cash inflows: Project C
Time
Cash Flow ($)
Discount factor @ 12%
1-4
6 500
3.037
Step 2. Compute the Profitability Indices
Project A
Present value of outflows ($)
($10 000)
Present value of inflows ($)
10 283
Present value ($)
5 358
7 970
8 544
10 176
32 048
Present value ($)
19 741
Project B
($30 000)
32 048
Project C
($18 000)
19 741
PIA = $(10 283/10 000)
= 1.028
PIB = $(32 048/30 000)
= 1.068
PIC = $(19 741/18 000)
= 1.097
Project ranking 1. C
2. B
3. A
The profitability index measures the return per dollar of investment. From the
above results it can be seen that while project B has the highest NPV it is not
the most profitable investment.
93
Advantages of Profitability Index
1. It takes into account the time value of money.
2. It is computed using cash flows
3. As it measures a project’s profitability per dollar of investment it can be
used to rank projects of varying outlays and expected economic lives.
Disadvantage of the Profitability Index
It ignores the size of a project. As a result an investment in a small project
might appear better than one in a huge project.
INTERNAL RATE OF RETURN (IRR)
The internal rate of return (IRR) is that rate of return, which exactly equates
the present value of expected after-tax cash inflows with the present value of
the after-tax cash outflows. It is that rate of return, which gives a zero NPV
zero.
The IRR of a project is arrived at by trial and error but the following approach
can be helpful to establish the rate at which trials can commence.
EXAMPLE
A new project has an after-tax cost of $10 000 and will result in after-tax cash
inflows of $3 000 in year 1, $5 000 in year 2 and $6 000 in year 3. Determine
the internal rate of return of the project.
Solution
Set up a solution table
Time
Cash flow ($)
0
($10 000)
1
3 000
2
5 000
3
6 000
Discount Factor @ ?%
1.000
Unknown
Unknown
Unknown
Present value ($)
($10 000)
Unknown
Unknown
Unknown
NIL
The present value of the three cash inflows is $10 000. Reconstruct the
problem using an average cash inflow each year rather than the exact
amount given.
[$(3 000 + 5 000 + 6 000)/3] = $4 667
After obtaining the average cash inflow reconstruct the solution table.
Time
Cash Flow ($)
Discount Factor @ ?% Present Value ($)
0
(10 000)
1.000
(10 000)
1–3
4 667
Unknown
10 000)
NIL
Since now only one unknown remains, it can be obtained as follows:
$4 667 * discount factor (x) = $10 000
discount factor = $10 000/ $4 667
= 2.143
94
The discount factor is 2.143. Determine the corresponding IRR from the
tables. The closest factor is 2.1399, which corresponds with 19%. 19% is the
estimate to be used to solve the problem. Refer to the original solution table
and replace the unknown discount factors with discount factors corresponding
to 19% to get the NPV.
Time
Cash Flow ($)
0
1
2
3
($10 000)
3 000
5 000
6 000
Discount Factor @
19%
1.000
0.840
0.706
0.593
NPV =
Present
Value ($)
($10 000)
2 565
3 655
3 744
($392)
The NPV is negative therefore the rate applied is too high. Trying a lower rate,
say 17%, the NPV is obtained as follows:
Time
Cash Flow ($)
0
1
2
3
($10 000)
3 000
5 000
6 000
Discount Factor @
17%
1.000
0.855
0.731
0.624
Present Value ($)
($10 000)
2 565
3 655
3 744
($36)
The NPV is close to zero but still positive so the rate is still high. Trying 16%
the NPV is going to be as follows:
Time
Cash Flow ($)
0
1
2
3
($10 000)
3 000
5 000
6 000
Discount Factor
@16%
1.000
0.862
0.743
0.641
NPV
Present Value ($)
($10 000)
2 586
3 715
3 846
$147
The IRR lies between 16% and 17%. By interpolation the exact IRR can now
be computed.
Interpolation
Decision rules
Once the IRR of a project has been determined, it is compared with the
required rate of return to decide whether or not a project is acceptable. If the
IRR equals or exceeds the required rate of return, the project is acceptable. If
the IRR is less than the required rate of return the project is not acceptable.
Advantages of the IRR
1. It takes into account the time value of money so it is a sophisticated
capital appraisal technique.
95
2. Understandability Although IRR is not truly a rate of return it provides
a basis for a decision that is readily acceptable by a layman with no
understanding of the NPV concept. To say a project has a positive
NPV at 10% has little meaning to the layman than to say while money
is costing 10% this project is generating a return of 15%.
3. Provision of margin of error If IRR is calculated and found to be say
15%, then it can be argued with certainty that as long as the cost of
money is less than 15% then the NPV of the project will be positive.
This cannot be the case with the NPV analysis. If the actual cost of
money exceeds the cost used to evaluate the project, then to check
whether the project is still acceptable one would have to recalculate the
NPV. With IRR this recalculation is not necessary.
Disadvantage of IRR
If a project has non-conventional cash flows, multiple IRRS will be arrived at. It
will therefore be problematic to indicate which of the rates would be the
correct IRR.
Superiority of the Net Present Value technique
DCF methods are more superior appraisal techniques to non- DCF
techniques because DCF methods take into account the time value of money.
Of the DCF methods the NPV method is the unique evaluation technique that
consistently helps firms to maximize ordinary shareholders` wealth positions.
Whenever mutually exclusive projects are being evaluated, only the NPV
model will consistently show the firm the project or set of projects that will
maximize the value of the firm. This is true for the following reasons:
1. The NPV model results in an absolute measure of the projects` worth,
while both PI and IRR are relative measures of project viability. The
NPV shows the dollar amount by which the project’s discounted cash
inflows (DCI) exceeds its discounted cash outflow (DCO). The PI
computes the ratio of DCI to DCO and the IRR determines a
percentage return figure. If three projects have NPV S OF $10 000, $14
000 and $16 000 these figures show the magnitude of the increase in
shareholders` wealth if the respective projects are accepted. On the
other hand if the same projects have IRRS OF 40%, 30% and 25% and
PIS of 1.68, 1.22 and 1.53 respectively, there is no indication which of
the three will lead to the greatest increase in shareholders` wealth by
looking at the IRRS and PIs.
2. The IRR expresses the return as a percentage and is therefore
inappropriate for evaluating projects of different sizes.
Concluding remark
Since firms try to maximize shareholders` wealth it is recommended that the
NPV criterion be used because it is the only model capable of helping the firm
achieve this goal.
96
CAPITAL BUDGETING UNDER CONDITIONS OF RISK
The nature of the environment in which firms operate is one, which can best
be described as risky or highly uncertain. It is important to highlight how firms
make the important decision of investing in long-term capital projects.
Project selection under conditions of risk
There are basically two methods of incorporating risk into the capital
budgeting process - The certainty equivalent method of risk adjustment and
the risk adjusted discount rate.
THE CERTAINTY EQUIVALENT METHOD
The method permits adjustment for risk by incorporating the manager’s utility
preference for risk versus return directly into the capital investment process.
The method is useful when management perceives different levels of risk
associated with the estimated annual cash flows over the life of the project.
Given the limitations of economic forecasting it is reasonable to assume that
the estimates of cash flows during early periods in a project’s life are likely to
be more accurate than those corresponding to the latter years.
When the certainty equivalent method is used, the estimated annual cash
flows (which represent the expected value of a probability distribution of
returns) are multiplied by a certainty equivalent coefficient (CEC) .
The CEC reflects management’s perception of the degree of risk associated
with the estimated cash distribution as well as management’s degree of
aversion to perceived risk. The product of the expected cash flow and the
CEC represents the amount that management would be willing to accept for
certain in each year of the project’s life as opposed to accepting the cash flow
distribution and its associated risk.
The CECS range in value from zero to 1. The higher values indicate a lower
penalty assigned by management to that cash flow distribution. A value of 1
indicates that management does not associate any risk with the estimated
cash flow and therefore is willing to accept the expected value of the cash
flow estimates as certain. The certainty equivalent adjusted cash flows are
then discounted at the risk free rate of return as opposed to the firm’s cost of
capital (to accommodate time value of money)
EXAMPLE
A firm is evaluating two projects – project A and project B. The following
details are provided:
Initial Investment
Cash Inflow – Year 1
2
3
4
5
PROJECT A
Cash Flow ($)
CEC
(42 000)
1.00
14 000
0.90
14 000
0.90
14 000
0.80
14 000
0.70
14 000
0.60
97
PROJECT B
Cash Flow ($)
CEC
(45 000)
1.00
28 000
1.00
12 000
0.90
10 000
0.90
10 000
0.80
10 000
0.70
Which project do you recommend using the certainty equivalent method
assuming a risk free rate of return of 6%.
Solution
PROJECT A
Cash
Inflow
Time
($)
0
(42 000)
1
14 000
2
14 000
3
14 000
4
14 000
5
14 000
Certainty
equivalent
Coefficient
1.00
0.90
0.90
0.80
0.70
0.60
Certain
Cash
Inflows ($)
(42 000)
12 600
12 600
11 200
9 800
8 400
Discount
Factor @
6%
1.000
0.943
0.890
0.840
0.792
0.747
PROJECT B
Cash
Inflow
Time
($)
0
(45 000)
1
28 000
2
12 000
3
10 000
4
10 000
5
10 000
Certainty
Equivalent
Coefficient
1.00
1.00
0.90
0.90
0.80
0.70
Certain
Cash
Inflow ($)
(45 000)
28 000
10 800
9 000
8 000
7 000
Discount
Factor @
6%
1.000
0.943
0.890
0.840
0.792
0.747
Present
Value ($)
(42 000)
11 882
11 214
9 408
7 762
6 275
4 541
Present
Value ($)
(45 000)
26 404
9 612
7 560
6 336
5 229
10 141
The project with a higher NPV is acceptable so in this case project B would be
recommended for acceptance.
Advantages of the certainty equivalent method
1. The method requires individual examination of projects in each time
period since the risk associated with a given project may change over
its life.
2. While the NPV methods lump together the discounting for time and the
adjustment for risk, the CE method disaggregates the two by adjusting
for risk with a CEC and discounting for time value of money at the risk
free-rate.
Disadvantage of the certainty equivalent method
The CECS used to convert uncertain cash flows to certain cash flows are
subjective estimates provided by managers.
THE RISK ADJUSTED DISCOUNT RATE (RADR) APPROACH
This is the rate of return that must be earned on a given project to
compensate the firm’s owners adequately, thereby resulting in the
maintenance or improvement of the share price.
98
The rationale underlying the use of the risk adjusted discount rate (RADR)
technique is that projects which have a greater variability in the probability
distributions of their returns should have these returns discounted at a higher
rate than projects having less variability or risk.
A project that has no risk associated with it would be discounted at the risk
free rate, since this is the appropriate rate just to account for the time value of
money. Any project that has risk associated with it has to be discounted at a
rate in excess of the risk free rate to discount both for futurity (the time value
of money) and for the risk associated with the project (risk premium).
r1 = i+ u + a
Where r1 = risk adjusted discount rate
i = risk free rate
u = adjustment for the firm’s normal risk
a = adjustment for above (or below) the firm’s normal risk.
EXAMPLE
M Ltd. is considering a replacement project. This type of project requires a
return of risk free rate plus 4%.
Cash Inflows
Original Cost
Years 1 - 5
Years 6 - 10
Probability
Amount
Probability
Amount
Probability
Amount
0.30
13 000
0.20
2 000
0.20
2 600
0.40
14 000
0.40
2 400
0.60
3 200
0.30
15 000
0.30
2 800
0.10
3 400
0.10
3 400
0.10
3 600
If the risk free rate is 10% determine the risk adjusted NPV.
Cost = (0.30 * 13 000) + (0.40 * 14 000) + (0.30 * 15 000)
= $3 900 + $5 600 + $4 500
= $14 000
Cash inflow Years 1-5
= (0.20 * 2 000) = (0.40 * 2 400) + (0.30 * 2 800) + (0.10 * 3 400)
= $400 + $960 + $40 + $340
= $2 540
Cash inflows Year 6 – 10
= (0.20 * 2 600) + (0.60 * 3 200) + (0.10 * 3 400) + (0.10 * 3 600)
= $520 + $1 920 + $340 + $360
= $3 140
Present value computation
Time
Cash Flow ($)
0
(14 000)
1–5
2 540
6 - 10
3 140
Discount Factor @14%
1.000
3.433
1.783
99
Present Value
(14 000)
8 720
5 599
319
Since the present value of this project is positive, the project is a candidate for
acceptance.
Advantages of Risk Adjusted Discount Rate
1. Project risk is dealt with explicitly through the determination of risk
premia (for a project’s cash flows).
2. Calculation of risk premia can be more straightforward than CE
analysis.
Disadvantages of Risk Adjusted Discount Rate
1. Decision on the risk premium for a given project class is problematic. It
is an intuitive analysis that is undertaken by the decision maker.
2. It is difficult to incorporate differences in risk for different periods as
compared the CE method.
3. It is based on risk – averse investors. This is not necessarily the case
with some investors.
SENSITIVITY ANALYSIS
This is a method of risk analysis. It is an analysis of the effect on a project
NPV of changes in the assumed values of key variables for example sales
level or labour costs. It is also known as “a what if” analysis foe example what
if raw material costs were to rise by 30%.
Advantages of the analysis
1. It is a practical method of risk analysis.
2. The results of a sensitivity analysis can be easily appreciated and used
in decision-making.
Disadvantages of the analysis
1. The method deals with one variable at a time while in capital budgeting
a change in one variable causes changes in other variables, for
example a change in unit sales changes both revenue and variable
costs.
2. Sensitivity analysis does not really measure risk but only looks at the
sensitivity of the expected NPV to different input factors.
General application of Risk Adjusted Discount Rate
Required
SML
Rate of
Return (%)
C
D
k
A
B
RF
Project risk
SML = Security Market Line. This is a graphic depiction of the CAPM
k = Single firm wide discount rate (SFDR)
100
It is generally not recommended to use a single hurdle rate (k) for all projects
as this fails to account for risk associated with the projects. If a single firm
wide discount rate is used the general assumption is that all the projects are
of equivalent risk. The graph shows the risk – return characteristics of the
projects. Using a single firm wide rate A and B would be rejected because
they fall below k. C and D will be accepted as they are above k.
If a simultaneous adjustment is made is made for risk and return using CAPM
projects C and A would now be acceptable while B and D would be rejected.
A, which was previously rejected is now acceptable. D, which was previously
acceptable is now rejected.
PRACTICE PROBLEMS ON THE INVESTMENT DECISION
PROBLEM 1
Moroka Investments has compiled the following data relating to the current
costs of its sources of capital for various ranges of financing:
Source of capital
Long-term debt
Preference shares
Ordinary shares
Range of new financing
$0 to $200 000
$200 000 to $300 000
$300 000 and above
$0 to $100 000
$100 000 and above
$0 to $220 000
$220 000 to $320 000
$320 000 and above
After- tax cost
6%
7%
9%
17%
19%
22%
24%
26%
The company’s current earnings, of which 40 per cent will be retained,
amount to $200 000. The cost of retained earnings has been estimated to be
20 per cent. The company’s target capital structure is as follows:
Source of capital
Long-term debt
Preference shares
Ordinary shares
Target capital structures
40%
20%
40%
100%
Determine the breaking points and ranges of total new financing associated
with each source of capital.
Using the data developed in 1 above, determine the levels of total new
financing at which the company’s weighted average cost of capital will
change.
Calculate the weighted average cost of capital for each range of total new
financing found in 2 above.
101
Using the results obtained in 3 above along with the following information on
the investment opportunities of Moroka Investments, determine the optimal
capital budget of Moroka Investments.
Investment
opportunity
Project
A
B
C
D
E
F
G
H
I
Initial
investment
$
200 000
300 000
100 000
600 000
200 000
100 000
300 000
100 000
400 000
Internal rate of return
(IRR)
%
19
15
22
14
23
13
21
17
16
PROBLEM 2
Chakalaka Investments (Pvt) Ltd employs the certainty – equivalent approach
in the evaluation of risky investments. The capital budgeting department of the
company has developed the following information regarding the new project.
Year
0
1
2
3
4
5
Certainty – equivalent
quotient
Expected CFAT
$
(200 000)
160 000
140 000
130 000
120 000
80 000
1.0
0.8
0.7
0.6
0.4
0.3
The firm’s cost of equity capital is 18%; its cost of debt is 9% and the risk less
Rate interest in the market on government securities is 6%. Should the project
be accepted?
PROBLEM 3
Changamukai Investments is considering a proposal to replace an automatic
press in one of its plants with a newer model that is expected to reduce labour
and raw material costs by $150 000 per year. Due to its greater capacity and
increased output, net income before taxes will increase by $50 000 per year.
The new press will cost $550 000 plus an additional $50 000 for installation. It
will be depreciated on a straight – line basis over its 5-year depreciable life to
a zero book value. However, at the end of five years it is still expected to have
a market value of $100 000, for which it is expected to be sold. The increased
102
output will require an immediate, one – time increase of $50 000 in net
working capital.
The old press can be sold today for $120 000. It was purchased 5 years ago
for $300 000, and is being depreciated over its 10 – year life to a book value
of zero.
Requirement
Given a tax rate of 40%, and a required rate of return of 12%, should the
company replace the old machine now? No initial or investment allowance
applies and inflation should be ignored.
103
Chapter 6
Leverage can be defined as the employment of an assets or sources of funds
for which the firm has to pay a fixed cost or return. The employment of an
asset resulting in the payment of a fixed cost creates operating leverage while
the employment of sources of funds for which the firm has to pay a fixed
return generates financial leverage. There are therefore two types of leverage,
operating leverage, which is a result of the investment decision of the firm and
financial leverage, which is a result of the financial decision of the firm.
The financing decision is concerned with financial leverage but a working
knowledge of operating leverage is necessary as the two types of leverage
are closely related. Operating leverage highlights the relationship between the
firm’s sales revenues and its earnings before interest and taxes (EBIT). These
earnings are also known as operating profits. Financial leverage on the other
hand highlights the relationship between the firm’s earnings available to
ordinary shareholders. It can be noted that EBIT is central in explaining both
operating and financial leverage.
Operating leverage
Operating leverage results from the existence of fixed operating expenses in
the firm’s income stream. It shows the firm’s ability to use fixed operating
expenses to magnify the effects of changes in sales on its earnings before
interest and taxes. Operating leverage occurs whenever a firm has fixed costs
that have to be met regardless of the volume of production. Firms employ
assets with fixed costs hoping that the volumes produced will generate sales
revenues that will cover all costs.
Degree of operating leverage (DOL)
This is a measure in quantitative terms, of the extent of operating leverage. It
exists when a proportionate change EBIT resulting from a change in sales is
more than a proportionate change in sales.
DOL = Percentage change in EBIT  1
Percentage change in Sales
EXAMPLE
A firm produces and sells a single product with the following revenue and cost
patterns: (Per unit)
Selling price
Variable cost
Contribution
$
200
100
100
Annual fixed costs $ 1 000 000,00.
Show comparative income statements for the following annual productions:
1. 10 000 units
2. 20 000 units and
3. 30 000 units
104
Solution
Income statements
Sales (units)
Sales revenue
Variable cost
Contribution margin
Fixed cost
EBIT
10 000
$
2 000 000
1 000 000
1 000 000
1 000 000
NIL
-100%
20 000
$
4 000 000
2 000 000
2 000 000
1 000 000
1 000 000
30 000
$
6 000 000
3 000 000
3 000 000
1 000 000
2 000 000
+100%
It can be argued that since the firm’s normal level of production is 20 000 units
then the point of reference is 20 000 units.
If production decreases to 10 000 units:
DOL1 = (1 000 000 – 0/1 000 000 * 100)
(4 000 000 – 2 000 000/2 000 000 * 100)
= 100
100
= 1
DOL2 = 100
100
=1
In both cases the quotient is 1 so there is no operating leverage.
Operating leverage can be favourable as well as unfavourable. The degree of
operating leverage depends on fixed operating costs. The higher the fixed
operating costs, the higher the firm’s operating leverage and operating risk
and vice versa. Operating risk refers to the firm’s inability to cover its fixed
operating costs. High operating leverage is a good working arrangement
when revenues are increasing but a disaster when revenues are falling.
In conclusion, the higher the firm’s fixed operating cost, the higher the degree
of operating cost, the higher the degree of operating leverage and the higher
the break-even volume and vice versa.
Financial leverage
Financial leverage is the ability of a firm to use fixed financial charges to
magnify the effects of changes in EBIT on the firm’s EPS. It involves the use
of funds obtained at a fixed cost in the hope of increasing the return to the
ordinary shareholders. Financial leverage results from the presence of fixed
financial charges in the firm’s income stream. The fixed charges do not vary
with the earnings before interest and taxes or operating profits. They have to
be paid regardless of the amount of EBIT available to pay them.
105
Financial leverage is also called trading on equity.
Degree of financial leverage
Financial leverage exists whenever a firm has fixed cost in its capital
structure. The greater the amount of fixed-interest sources of funds, (larger
financial cost), the higher the financial leverage. The degree of financial
leverage can be measured quantitatively as follows:
CAPITAL STRUCTURE AND VALUATION
Firms should strive to achieve an optimal capital structure. An optimal capital
structure is the combination of debt and equity that results in the maximization
of the value of the firm. Alternatively, capital structure can be argued to be the
combination of debt and equity that results in the minimization of the firm’s
cost of capital.
There is no consensus as to whether the capital structure decision affects
value. Some writers believe that the capital structure decision of a firm affects
the value of the firm while others argue that the capital structure decision does
not affect the value of the firm.
Four theories on capital structure decision will be looked at. They are:
a. The Net Income Approach (NI),
b. The Net Operating Income Approach (NOI),
c. The Modigliani-Miller Approach (MM) and
d. The Traditional Approach.
Before the capital structure theories can be looked at, it is important to look at
the assumptions that underlie these theories.
The following are the assumptions underlying the capital structure theories:
1. The organization has two sources of financing namely perpetual debt
(assumed to be risk less) and ordinary share capital.
2. The organization’s net income is not subject to corporate tax.
3. The firm has a 100% dividend payout ratio. This means that the
organization does not retain any earnings.
4. The organization’s total assets are given and will not change.
5. The operating profits of the firm are not expected to grow.
6. The firm’s business risk will be constant over time. The business risk
will be independent of the firm’s capital structure and financial risk.
7. The organization’s total financing will remain constant. If the firm’s
financial leverage increases, the proceeds are used to reduce equity. If
additional equity is issued, the proceeds will be used to retire debt.
8. The organization has perpetual life.
Formulae and symbols used in the evaluation
E = total market value of equity
B = total market value of debt
V = total market value of the firm i.e. V = (E + B)
I = interest payments.
106
Cost of debt (ki) = I/B
Value of debt = I/ki
Cost of equity capital = D1/P0 + g
OR ke = Net Income attributable to equity holders
Total market value of equity shares
Weighted average cost of capital (WACC) (ko) = (wi *ki) + (we *ke)
Or k0 = [B/(E + B)]*ki + [E/(E + B)]*ke
Or ko = EBIT/V
The Net Income (NI) Approach
Durand suggested the Net Income approach. Durand argues that the capital
structure decision of a firm is relevant to the valuation of the firm. A change in
financial leverage would affect the firm’s cost of capital and total value. An
increase in financial leverage, (as measured by the ratio of debt to equity),
reduces the weighted average cost of capital and increase the value of the
firm. A decrease in financial leverage increases the weighted average cost of
capital and reduces the value of the firm.
The argument behind the approach
An increase in financial leverage increases the proportion of inexpensive
financing in the organization’s capital structure and this reduces the weighted
average cost of capital, which results in an increase in the total value of the
concern. Since the cost of debt and equity would be constant, an increase in
financial leverage magnifies shareholders` earnings resulting in an increase in
the market value of equity.
Conclusion on the approach
According to the Net Income approach financial leverage is an important
variable in the firm’s capital structure decision. A judicious mix of debt and
equity financing, results in an optimal capital structure, which maximizes the
value of the firm. This optimal capital structure reduces the overall cost of
capital to its lowest possible position.
Illustration
A Ltd.`s expected annual net operating income (EBIT) is $500 000,00 and
these are not expected to grow. The company has $2 000 000,00 10%
debentures outstanding. The company also has 24 000 ordinary shares
outstanding. The equity capitalization rate of the company is 12.5%.
Using the Net Income Approach:
1. (a) Calculate the total value of the firm
(b) Calculate the cost of equity capital
(c) Calculate the value of each ordinary share
(d) Calculate the weighted average cost of capital.
2.Assume that A Ltd. raises its financial leverage by bringing in $1 000 000
more worth of debentures using the proceeds to retire equity.
a. Calculate the total value of the firm
b. Calculate the cost of equity capital
107
c. Calculate the value of each ordinary share
d. Calculate the weighted average cost of capital.
3.Assume that A Ltd. issues $1 000 000,00 worth of equity, using the
proceeds to retire debt:
a. Calculate the total value of the firm
b. Calculate the cost of equity capital
c. Calculate the value of each ordinary share
d. Calculate the weighted average cost of capital.
Solution
The basic approach to follow when calculating the total value of the firm when
using the Net Income approach is as follows:
1) Compute earnings attributable to equity holders.
2) Capitalize these earnings using the equity capitalization rate (ke). This
gives the total value of equity (E).
3) Bring in the market value of debt (B).
4) Add the market value of equity (E) and the market value of debt (B) to
get the total value of the firm.
1 (a) Value of the firm computation
EBIT
Debenture interest (0.10 * $2 000 000,00)
Income before tax
Taxation
Income after taxation
Preference dividend
Attributable earnings
Equity capitalization rate (ke)
Market value of equity (E)
Market value of debt (B)
Total value of the firm (V) = (E) + (B)
$
500 000
(200 000)
300 000
NIL
300 000
NIL
300 000
0.125
2 400 000
2 000 000
4 400 000
(b) Cost of equity capital (ke) = $300 000/$2 400 000,00 * 100 = 12.5%
(c) Cost of each ordinary share = $2 400 000,00/24 000 = $100,00.
(d) Computation of weighted average cost of capital (WACC)
= 12.5%($2 400 000,00/$4 400 000) + 10%($2 000 000/4 400 000)
= 0.0681818 + 0.0454545
= 11.36%
OR WACC = $500 000,00/$4 400 000,00 * 100
= 11.36%
108
2(a) Value of the firm computation
EBIT
Debenture interest (0.10 * $3 000 000,00)
Income before tax
Taxation
Income after tax
Preference dividend
Attributable earnings
Equity Capitalization rate (ke)
Market value of equity (E)
Market value of debt (B)
Total value of the firm (V) = (E) + (B)
$
500 000
(300 000)
200 000
NIL
200 000
NIL
200 000
0.125
1 600 000
3 000 000
4 600 000
(b) Cost of equity capital (ke) = $200 000/$1 600 000 * 100 = 12.5%
(c) Cost of each equity share
= $1 600 000/[$2 400 000 – ($1 000 000/$100)]
= $1 600 000/14 000
= $114.29
(e) Computation of weighted average cost of capital
= 12.5%($1 600 000/$4 600 000) + 10%($3 000 000/$4 600 000)
= 0.0434782 + 0.0652173
= 10.87%
OR weighted average cost of capital = $500 000/$4 600 000 * 100
= 10.87%
Evaluation
Increasing financial leverage to $3 000 000 increases the total value of the
firm to $4 600 000 ($114.29 on a per share basis), lowering the weighted
average cost of capital to 10.87% compared to the original position of $100,00
and 11.36% respectively. This is precisely what Durand indicated in his
argument. Increasing financial leverage increases the value of the firm
reducing the weighted average cost of capital for the firm.
3. (a) Value of the firm computation
EBIT
Debenture interest (0.10 * $1 000 000)
Income before tax
Taxation
Income after tax
Preference dividend
Attributable earnings
Equity capitalization rate (ke)
Market value of equity (E)
Market value of debt (B)
Total value of the firm (V) = (E) + (B)
109
$
500 000
(100 000)
400 000
NIL
400 000
NIL
400 000
0.125
3 200 000
1 000 000
4 200 000
(b) Cost of equity capital (ke) = $400 000/$3 200 000 *100 = 12.50%
(d) Cost of each ordinary share
= $3 200 000/[24 000 + ($1 000 000/$100,00)]
= $3 200 000/34 000
= $94,12
OR weighted average cost of capital = $500 000/$4 200 000 * 100
=11.90%
Evaluation
Reducing financial leverage to $1 000 000 reduces the total value of the firm
to $4 200 000 ($94.12 on a per share basis), increasing cost of capital to
11.90% compared to the original position of $100,00 and 11.36% respectively.
Again this is what Durand indicated would happen if financial leverage is
reduced. Reducing financial leverage reduces the value of the firm increasing
the weighted average cost of capital for the firm.
Diagrammatical presentation of the Net Income Approach
Ke, ki, ko (%)20
15
ke
ko
ki
10
5
0.5
Degree of leverage
1.00
Theoretically the above diagram shows that according to the Net Income
Approach, the firm can employ 100% debt to maximize its value. In practice
this is not possible.
NET OPERATING INCOME (NOI) APPROACH
Durand also suggests this theory. In this theory he presents an argument,
which is diametrically opposed to the argument he presented for the Net
Income Approach to capital structure.
The argument
In this theory Durand argues that the capital structure decision of the firm is
irrelevant to the valuation of the firm. Changing the degree of financial
leverage of the firm will not affect the total value of the firm as the weighted
110
average cost of capital is taken to be independent of the degree of financial
leverage.
The following arguments relating to the cost of equity and debt are worth
noting when discussing the Net Operating Income approach.
The cost of equity capital (equity capitalization rate) is an increasing function
of financial leverage. Increasing financial leverage increases financial risk to
equity holders who in turn require compensation for this higher financial risk in
the form of a higher required rate of return.
The cost of debt consists of two parts: an explicit cost and an implicit cost
(hidden cost). The explicit cost is represented by the interest rate. From the
assumptions it was indicated that the firm could borrow at a fixed rate of
interest as financial leverage is assumed not to affect financial risk. The
implicit cost (hidden cost), relates to the change to cost of equity capital. This
is the increase in the required rate of return by equity holders brought about
by increasing financial leverage.
The advantage of using debt (supposedly cheaper), in terms of explicit cost is
EXACTLY NEUTRALIZED by the implicit cost (the increase in the required
rate of return by equity holders).
Conclusion on Net Operating Income
The total value of the firm is not a function of the firm’s capital structure
decision. Regardless of the degree of financial leverage, the total value of the
firm remains constant. Since the market value of the shares will not change
with financial leverage, there cannot be an optimal capital structure.
Illustration
B Ltd.`s expected net operating income (EBIT) is $500 000 and these
earnings are not expected to change. The company has $2 000 000,00 10%
debentures outstanding. The company also has 20 000 ordinary shares
outstanding. The overall capitalization rate (overall cost of capital – weighted
average cost of capital) is 12.5%.
Using the Net Operating Income Approach:
1. (a) Calculate the total value of the firm
(b) Calculate the cost of equity capital
(c) Calculate the value of each ordinary share
(d) Calculate the weighted average cost of capital.
2.Assume that B Ltd. raises its financial leverage by bringing in $1 000 000,00
additional debentures, using the proceeds to retire equity shares.
a. Calculate the total value of the firm
b. Calculate the cost of equity capital
c. Calculate the value of each ordinary share
d. Calculate the weighted average cost of capital.
3. Now assume that B Ltd raises $1 000 000,00 additional equity the
proceeds to retire debt.
111
a.
b.
c.
d.
Calculate the total value of the firm
Calculate the cost of equity capital
Calculate the value of each ordinary share
Calculate the weighted average cost of capital.
Solution
The basic approach to follow when calculating the total value of the firm when
using the Net Operating Income approach is as follows:
i.
Since the overall capitalization rate of the firm remains the same for all
degrees of financial leverage, capitalize the given level of EBIT using
the overall capitalization rate (ko). This gives the total value of the firm
i.e. V = EBIT/ko.
ii.
Subtract the value of debt from the total value of the firm to get the
value of equity (which is a residual value) i.e. V – B = E.
1 (a) Value of the firm computation
EBIT
Overall capitalization rate (ko)
Total value of the firm (V)
Total value of debt (B)
Total market value of equity (E)
$
500 000
0.125
4 000 000
(2 000 000)
2 000 000
(b) Cost of equity = Attributable earnings
* 100
Total market value of equity
= ($500 000 - $200 000)/$2 000 000 * 100
= 15%
(c) Value of each ordinary share = $2 000 000/20 000
= $100,00
(d) Weighted average cost of capital
= 10%($2 000 000/$4 000 000) + 15%($2 000 000/$4 000 000)
= 0.05 + 0.075
= 12.5%
OR Weighted average cost of capital = ($500 000/$4 000 000) * 100
= 12.50%
2.Value of the firm computation
$
EBIT
500 000
Overall capitalization rate (ko)
0.125
Total value of the firm (V)
4 000 000
Total value of debt (B)
(3 000 000)
Total value of equity (E)
1 000 000
(b) Cost of equity capital =($500 000 - $300 000)/$1 000 000 * 100
=20%
112
(c) Value of each ordinary share
= $1 000 000/[20 000 – ($1 000 000/$100,00)
= $1 000 000/10 000
= $100,00
(d) Weighted average cost of capital
= 20%($1 000 000/$4 000 000) + 10%($3 000 000/$4 000 000)
= 0.05 + 0.075
= 12.50%
OR Weighted average cost of capital = $500 000/$4 000 000 * 100
= 12.50%
Evaluation
The above analysis shows that an increase in financial leverage has no effect
on the total value of the firm. The value of ordinary shares remains the same
and the cost of capital is also not affected by the increase in financial
leverage.
3. (a) Value of the firm computation
EBIT
Overall capitalization rate (ko)
Total value of the firm (V)
Total value of debt (B)
Total value of equity (E)
$
500 000
0.125
4 000 000
(3 000 000)
1 000 000
(b) Cost of equity capital = $500 000 - $100 000/$3 000 000 * 100
=13.33%
(c) Value of each ordinary share
= $3 000 000/[$2 000 000 + ($1 000 000/$100,00)]
= $3 000 000/30 000
= $100,00
(d) Weighted average cost of capital
= 13.33%($3 000 000/$4 000 000) + 10%($1 000 000/$4 000 000)
= 0.099975 + 0.025
= 12.50%
OR Weighted average cost of capital = $500 000/$4 000 000 * 100
=12.50%
Evaluation
This analysis shows that decreasing financial leverage does not affect the
total value of the firm. The value of the ordinary shares remains the same
113
and the cost of capital is also not affected by the reduction in the degree of
financial leverage.
Diagrammatical illustration of the net operating income approach
Ke, ki
Ko (%)
ke
20.0
15.0
ke
10.0
ki
5.5
0.5
Degree of leverage
1.0
The diagram shows that the cost of debt and overall cost of capital are
independent of the degree of financial leverage but the cost of equity is an
increasing function of the degree of financial leverage.
MODIGLIANI – MILLER (MM) APPROACH
Franco Modigliani and Morton Miller in their thesis relating to the relationship
between capital structure, cost of capital and valuation, presented a
proposition that is similar to the net operating income approach. They support
the argument put forward in the net operating income approach regarding the
independence of the cost of capital to the degree of financial leverage. Their
approach maintains that the weighted average cost of capital does not change
with the degree of financial leverage.
Ko(%)
V ($)
V
Ko
Degree of leverage (B/V)
Assumptions behind the approach
The proposition by MM is based on the following assumptions:
114
1. Perfect capital markets: This is a market in which:
a. Securities are infinitely divisible.
b. Investors are free to buy and sell securities
c. Investors can borrow without restrictions on the same terms and
conditions as firms.
d. There are no transaction costs.
e. There is perfect information i.e. each investor has the same information
which is readily available at no cost.
f. Investors are rational and behave accordingly.
2. Business risk is equal among firms operating in a similar environment. (The
firms are assumed to have the same risk characteristics).
3. The firm’s dividend payout ratio is 100%.
4. There are no taxes (assumption relaxed latter when proposition ii was
highlighted).
Proposition I
MM argue that the value of a firm remains constant regardless of the degree
of financial leverage. Since value does not change with financial leverage, the
weighted average cost of capital and the firm’s market price of shares remains
the same regardless of the degree of financial leverage.
Operational justification of proposition
MM provide an operational justification of their proposition by highlighting the
arbitrage process.
The Arbitrage process
This is the act of buying a financial asset in one market at a lower price and
selling it in another market at a higher price to bring about equilibrium in the
market price of the financial asset in different markets. Arbitragers take
advantage of temporary disequilibria and buy undervalued financial assets in
one market and sell overvalued financial assets in related markets. Arbitrage
is a balancing operation and implies that a financial security cannot sell at
different prices.
MM argue that firms similar in all respects except for leverage cannot
command different values. According to MM such firms are perfect
substitutes. Should differences in value occur, investors of the firm whose
value is higher would sell their shares and buy shares of the firm whose value
is lower. This way, MM argue, investors will be able to earn the same return at
a lower outlay with the same perceived risk or even lower risk. This leaves the
investors better off. This behaviour by investors will increase the share price
(value) of the firm whose shares would be purchased while lowering the share
price (value) of the firm whose shares would be sold. This will continue till the
market prices of the two identical firms become identical.
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MM also argue that investors are able to use “home-made” leverage or
“personal” leverage to substitute corporate leverage to finance the arbitrage
transaction.
Illustration of the arbitrage process
Assume that there are two firms, L Ltd. (Levered) and U Ltd. (Unlevered),
which are identical in all respects except that L Ltd. has 7.5% $4 million
debentures. The earnings before interest and taxes (EBIT) of both companies
are equal ($900 000). The equity capitalization rate for both companies is
10%.
L Ltd.
7.5% $4 million debentures
EBIT $900 000
Ke 10%
EBIT
Debenture interest (0.075 * $4m)
Attributable earnings
Equity capitalization rate
Market value of equity (E)
Market value of debt (B)(Note)
Total value of the firm (V)
U Ltd.
$
900 000
900 000
0.10
9 000 000
9 000 000
U Ltd.
All equity financed
EBIT $900 000
Ke 10%
L Ltd.
$
900 000
(300 000)
600 000
0.10
6 000 000
4 000 000
10 000 000
Note (B) = $300 000/0.075
= $4 000 000
According to MM an investor in L Ltd. can increase his return without incurring
any additional financial risk. He will achieve this through the arbitrage
process.
Assuming the investor in L Ltd. owns 10% total equity, he will have 10% of $6
000 000 i.e. $600 000 worth of shares in L Ltd. Assume that this investor
wishes to dispose of this 10% shareholding to purchase a 10% shareholding
in U Ltd.
This equity brings in $600 000. Assuming he can borrow an amount equal to
10% holding in L Ltd.`s debts, this brings in $400 000 (0.10 * $4m).
He then purchases 10% shareholding in U Ltd. for $900 000 (0.10 * $9 000
000). This leaves him with a surplus of $100 000 of uncommitted funs.
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The investor’s income position
Old income – Dividend (.10% of L Ltd.) (1.10 * $6 000 000)
New income – Dividend (10% of U ltd.) (0.10 * $9 000 000)
Debenture interest (0.075 * $4 m)
$
60 000
90 000
(30 000)
60 000
Real income remains the same although the cash flow position has changed
(+$100 000). If the investor can invest this $100 000, elsewhere, he can then
have a return on this investment on top of the shareholding in U Ltd.
According to MM homemade leverage is a perfect substitute for corporate
leverage and the arbitrage process operates because of this alleged
substitutability.
Limitation of the MM hypothesis
The MM hypothesis does not provide a valid framework to explain the
relationship between capital structure, weighted average cost of capital and
the total value of the firm.
Perfect substitutability of homemade and corporate leverage
MM argue that homemade leverage and corporate leverage are perfect
substitutes. This would imply that the risk perception of personal and
corporate leverage would be the same. If this were true then the risk to which
the investor is exposed to would be identical irrespective of whether it is the
firm that has borrowed (corporate leverage) or the investor himself has
borrowed (homemade leverage). The risk exposure to the investor is greater
with personal leverage (because of unlimited liability) than with corporate
leverage (corporations have limited liability). As a result, since homemade
leverage and corporate leverage are not perfect substitutes, the arbitrage
process cannot be effective.
Inconvenience
In addition to higher risk exposure, personal leverage can be very
inconvenient. This is because with personal leverage, the formalities and
procedures involved in borrowing will have to be done by the individual
himself whereas with corporate leverage these formalities and procedures are
undertaken by the corporation itself. Because of this inconvenience, some
investors may prefer that the borrowing be done by the firm, rather than by
investors themselves. This will, in turn constraint the arbitrage process.
High borrowing costs
Homemade leverage is more costly in that the cost of borrowing to an
individual is higher than the cost of borrowing by a firm. If homemade
leverage and corporate leverage are perfect substitutes as argued by MM,
then the cost of borrowing ought to be the same. Since it is more costly to
borrow personally (because of limited credit standing), the two cannot be
perfect substitutes and this limits the effectiveness of the arbitrage process.
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Institutional restrictions
Institutional restrictions could also limit the arbitrage process. Institutions
cannot engage in personal leverage. This means that the switching option
from the unlevered to the levered firm may not apply to all investors. To the
extent that this is the case, personal leverage and corporate leverage cannot
be argued to be perfect substitutes.
Double leverage
Some times homemade leverage does not work. A typical case is where an
investor has already borrowed to invest in the shares of the unlevered firm.
For an investor in this category arbitrage will entail double leverage, leverage
in the personal portfolio and leverage in the firm’s portfolio.
Transaction costs
Since transaction costs are inevitable, the investor will receive net proceeds
from the sale of shares, which will be lower than his investment holding. He
will have to invest a large amount in shares than his present investment to
earn the same return. This arrangement will limit the operation of the arbitrage
process.
Conclusion
The foregoing discussion showed that personal leverage and corporate
leverage are not perfect substitutes. The arbitrage process will therefore be
hampered and will not be effective. The MM argument cannot be valid. A firm
may increase its total value and lower its weighted average cost of capital with
an appropriate degree of financial leverage. The capital structure decision of
the firm is relevant to its valuation. Imperfections in the capital market retard
the perfect functioning of the arbitrage process. The MM approach does not
provide a valid framework for the theoretical relationship between capital
structure, weighted average cost of capital and the valuation of the firm.
THE TRADITIONAL APPROACH
The traditional view holds that through a judicious use of financial leverage, a
firm can increase its total value and reduce its weighted average cost of
capital. Using debt in its capital structure causes a decline in the weighted
average cost of capital (debt is a relatively cheaper source of funds). The
advantage of using modest levels of debt will outweigh the increased financial
risk to equity holders as reflected by a higher required rate of return (ke).
Going beyond modest levels of debt will however have the effect of raising the
weighted average cost of capital and adversely affecting the total value of the
firm. Thus, up to a point financial leverage favourably affects the value of the
firm, beyond that point financial leverage adversely affects the total value of
the firm. This is the optimal capital structure.
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Ke
Ko, ki
ko
Ke, (%)
ki
Degree of leverage (B/V)
A variation of the traditional approach suggests that there is no single capital
structure but a range of capital structures where the weighted average cost of
capital will be at its minimum and total value of the firm at its maximum.
Changes to financial leverage in this range will have little effect on the total
value of the firm.
FACTORS AFFECTING THE CAPITAL STRUCTURE DECISION
The combination of debt and equity that a firm chooses to use is affected by a
number of factors.
Control
The attitude of management towards control has a bearing on the capital
structure decision. Lenders are not directly involved in the management of a
company as long as there is no default in the payment of interest and
principal. If management wishes to maintain control on organizational
operations they will bring in more debt than equity. With this arrangement
management sacrifices little or no control. But this arrangement can be costly
if the company borrows more than it will have the ability to service, as
management will lose ALL control.
Industrial standards
Some firms wish to maintain capital structures that are in tandem with those
companies having similar risk complexions. The argument in this case will be
that what is good for the other companies would be good for the firm.
Adopting a capital structure not in line with the other players would make the
firm look conspicuous in the market place.
Nature of industry
If a firm is operating in an industry whose sales are subject to wide
fluctuations over the business cycle, it should adopt a low degree of financial
leverage. If a high degree of financial leverage is adopted the firm runs the
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risk of not being able to meet required payments during lean years and this
can lead to financial distress. On the other hand firms that deal in products
having inelastic demand can adopt modest levels debt if their capital
structures as the sales expected will generally not fluctuate much.
Stage of the life cycle of the industry
When the industry is in its infancy, the mortality rate would be high. Firms
cannot afford to adopt high levels of financial leverage. Emphasis will be on
the use of equity capital. When maturity is reached the firm should strive for
manoeuvrability to ensure that growth is financed and the needed funds are
obtained under acceptable terms. During the decline phase the firm should
aim to adopt financing strategies that allow for early contraction of financing
used.
Expert opinion
The opinion of investment analysts and institutional investors also influences
the capital structure decision of the firm. It is argued that these experts are in
a better position to assess a given financial plan. The recommendation would
be to seriously consider the experts` opinion.
Financial flexibility
It is necessary to maintain flexibility when creating an organization’s capital
structure. Flexibility is the firm’s ability to adjust its sources of funds either
upwards or downwards in response to changes in need for funds. If a firm
were to adopt an aggressive debt policy it may forced to issue equity on
unfavourable terms later on because of heavy indebtedness. It is therefore
important for the firm to maintain unused debt capacity for future needs if the
firm is to be able to maintain operating flexibility.
Timing
Sometimes the firm can make substantial savings by properly timing when to
issue financial securities. A public offering should be made when the state of
the economy and capital market is ideal to provide funds. When management
feels that debt finance will become costly or scarce they may chose to benefit
from financial leverage immediately. The organization will immediately use
high levels of financial leverage. If management expect interest rates to
decline, a choice may be made to postpone becoming highly financially
levered in order to remain flexible in order to take advantage of the lower
rates expected to prevail in the future.
Credit standing
Organizations that enjoy a high credit standing with investors or lenders in the
capital markets are usually in a better position to obtain funds from sources of
their choice. Those firms that have a poor credit standing usually find that
their choice of obtaining funds is limited.
Risk
Small firms have limited sources of financing and rely on the owner’s funds for
their financing. Providers of long-term debt see them as risky propositions.
Large companies on the other hand use funds from different sources as no
single source of financing can cater for their total financial requirements.
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PRACTICE PROBLEMS ON CAPITAL STRUCTURE
PROBLEM 1
Mojo Ltd has to make a choice between debt issue and equity issue for its
expansion programme. Its current position is as follows:
$
20 000
50 000
30 000
100 000
5% Debt
Equity capital ($10 per share)
Surpluses
Total capitalization
Sales
Total costs
Income before interest and taxes
Interest
300 000
(269 000)
31 000
(1 000)
30 000
(15 000)
15 000
Taxation at 50%
Income after taxation
The expansion programme is estimated to cost $50 000. If this is financed
through debt, the rate on new debt will be 7% and the price – earnings ratio
will be 6 times. If the expansion programme is financed through equity, new
shares can be sold netting $25 per share; and the price – earnings ratio will
be 7 times. The expansion will generate additional sales of $150 000 with a
return of 10% on sales before interest and taxes.
If the company is to follow a policy of maximizing the market value of its
shares, which form of financing should it choose?
PROBLEM 2
Mapepa Ltd is a plastic manufacturing company that is planning to expand its
assets by 50%. All financing for this expansion will come from external
sources. The expansion will generate additional sales of $300 000 with a
return of 25% on sales before interest and taxes. The finance department of
the company has submitted the following plans for the consideration of the
Board.
Plan 1: Issue 10% debentures
Plan 2: Issue 10% debentures of half the required amount and the
balance in equity shares to be issued at 25% premium.
Plan 3: Issue equity shares at 25% premium.
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Balance sheet of the company on 31 December
$
Assets
Total assets
1 200 000
Equity and liabilities
Equity capital ($10 per share)
8% debentures
Retained earnings
Current liabilities
400 000
300 000
200 000
300 000
1 200 000
Income statement for the year ending 31 December
$
1 900 000
(1 600 000)
300 000
(24 000)
276 000
(138 000)
138 000
3.45
Sales
Operating costs
EBIT
Interest
Earnings after interest
Taxation at 50%
EAT
EPS
(i)
(ii)
(iii)
Determine the number of equity shares that will be issued if
financial plan 3 is adopted?
Determine the indifference point between (a) plans 1 and 2, (b)
plans 1 and 3, and (c) plans 2 and 3.
Assume that the price – earnings ratio is expected to remain
unchanged at the figure of 8 if plan 3 is adopted, but is likely to drop
to 6 if either plan 1 or 2 is used to finance the expansion. Determine
the market price of the shares in each of the situations.
PROBLEM 3
Company X and company Y are in the same risk class, and are identical in
every fashion except that company X uses debt while company Y does not.
The levered firm has $900 000 debentures, carrying 10% rate of interest. Both
the firms earn 20% before interest and taxes on their total assets of $1 500
000. Assume perfect capital markets, rational investors and so on: a tax rate
of 50% and capitalization rate of 15% for an all – equity company.
(i)
(ii)
(iii)
(iv)
Compute the value of firms X and Y using the net income approach.
Compute the value of each firm using the net operating income
approach.
Using the NOI approach, calculate the over – all cost of capital for
firms X and Y.
Which of these two firms has an optimal capital structure according
to the NOI approach? Why?
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PROBLEM 4
The financial manager of Zamani (Pvt) Ltd. has formulated various financial
plans to finance $3 000 000 required to implement various capital budgeting
projects.
(a) Determine the indifference point for each financial plan assuming a 55%
corporate tax rate and a par value of equity shares as $100:
(i)
Either equity capital of $3 000 000 or $1 500 000 10% debentures
and $1 500 000 equity,
(ii)
Either equity capital of $3 000 000 or 12% preference shares of $1
000 000 and $2 000 000 equity,
(iii)
Either equity capital of $3 000 000 or 12% preference capital of $1
000 000, $1 000 000 10% debentures and $1 000 000 equity,
(iv)
Either equity share capital of $2 000 000 and 10% debentures of $1
000 000 or 12% preference share capital of $1 000 000, 10%
debentures of $800 000 and $1 200 000 equity.
(b) Indicate and briefly describe various considerations to be looked at before
a company comes up with an ideal capital structure.
PROBLEM 5
In considering the most desirable capital structure of a company, the following
estimates of the cost of debt and equity capital (after tax) have been made at
various levels of debt – equity mix:
Debt as percentage of total capital
employed
0
10
20
30
40
50
60
Cost of debt Cost of equity
%
%
5.0
12.0
5.0
12.0
5.0
12.5
5.5
13.0
6.0
14.0
6.5
16.0
7.0
20.0
Determine the optimal debt – equity mix for the company by calculating the
weighted average cost of capital.
- End of module Good luck with your studies
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