chapter 06 {final energy financial management}.doc

8/14/2019 Chapter 06 {Final Energy Financial Management}.Doc

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Chapter 6

Cost of capital

6.1 Introduction

The discussions in last chapter relating to Capital budgeting have shown therelevance of a certain required rate of return as a decision criteria. Such a rate is

the cost of capital of a firm. Apart from its usefulness as an operational criterion to

accept/accept an investment proposal, cost of capital is also an important factor in

designing capital structure.

The cost of capital for a firm is a weighted sum of the cost of equity and the cost ofdebt (see the financing decision). Firms finance their operations by threemechanisms: issuing stock (equity), issuing debt (borrowing from a bank isequivalent for this purpose) (those two are external financing), and reinvesting priorearnings (internal financing).

6.2 Important

As mentioned above, the cost of capital is an important element, as input

information, in capital investment decisions. In the present value methods of

discounted cash flow techniques, the cost of capital is used as the discount rate to

calculate the NPV. The profitability index or benefits cost ratio methods similarly

employed it to determine the present value of future cash inflows. When the internal

rate of return methods is used, the computed IRR is compared with the cost of

capital. The cost of capital, thus, constitutes an integral part of investment decisions.

It provides a yardstick to measure the worth of investment proposal and, thus,

performs the role of accept-reject criterion. This underlines the crucial significance

of cost of capital. It is also referred to as cut-off rate, target rate, burdle rate,

minimum required rate of return, standard return and so on.

The cost of capital, as an operational criterion, is related to the firms objective of

wealth maximization. The accept-reject rules require that a firm should avail of

only such investment opportunities as promise a rate of return higher than the cost

of capital. Conversely, the firm would be well advised to reject proposals whose

rates of return are less the cost of capital. If the firm accepts a proposal having a

rate of return higher than the cost of capital, it implies that the proposals yields

returns higher than the minimum required by the investors and the prices of shares

will increase and, thus, the shareholders wealth. By virtue of the same logic, the

shareholders wealth will decline on the acceptance of a proposal in which the actual

return is less than the cost of capital. The cost of capital, thus, provides a rational

mechanism for making optimum investment decisions. In brief, the cost of capital is


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important because of its practical utility as an acceptance rejection decision

criterion.

The considerable significance of cost of capital in terms of its practical utility

notwithstanding, it is probably the most controversial topic in financial

management. There are varying opinions as to how this can be computed. In view ofthe crucial operation signification of this concept, our focus is on the general

framework for the computation of cost of capital. We first define the term cost of

capital in general term. This is followed by a details account of the measurement of

cost of capital both specific as well as overall of different sources of financing.

6.3 Definition

In operational term, cost of capital refers to the discount rate that is used in

determining the present value of the estimated future cash proceeds and eventually

deciding whether the project is worth undertaking or not. In this sense, it is definedas the minimum rate of return that a firm must earn on its investment for the

market value of the firm to remain unchanged.

The cost of capital is visualized as being composed of several elements. These

elements are the cost of each component of capital. The term component means the

different sources from which funds are raised by a firm. Obviously, each sources

each sources of funds or each component of capital has of cost. For example, equity

capital has a cost, so also preference share capital and so on. The cost of each

sources or component is called specific cost of capital. When these specific costs are

combined to arrive at overall cost of capital, it is referred to as the weighted cost ofcapital. The terms, cost of capital, weighted cost of capital, composite cost of capital

and combined cost of capital are used interchangeably in this chapter. In other

words, the term, cost of capital, as the acceptance criterion for investment

proposals, is used in the sense of the combined cost of all sources of financing. This

is mainly because our focuses on the valuation of the firm as a whole.

6.4 Assumptions

The theory of cost of capital is based on certain assumptions. A basic assumption of

traditional cost of capital analysis is that the firms business and financial risks are

unaffected by the acceptance and financing of projects business risk measures the

variability in operating profits (earnings before interest and taxes EBIT) due to

change in sales. If a firm accepts a project that is considerably more risky than the

average, the suppliers of the funds or quite likely to increase the cost of funds as

there is an increased probability of committing default on the part of the firm in

making payments of their money. A debenture holder will charge higher rate of in


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interest to compensate for increased risk. There is similarly an increased

uncertainty from the point of equity holders of getting dividend from the firm.

There fore, they will also require a higher return as a composition for the increased

risk. In analyzing the cost of capital in this chapter, we assume that there would be

no change what so ever in the business risk complexion of the firm as result of

acceptance of new investment proposals.

The capital budgeting decision determines business risk complexion of the firm. The

financing decision determines its financial risk. In general, the greater the

proportion of long - term debt in the capital structure of the firm, the greater is the

financial risk because there is need for a larger amount of periodic interest payment

and principle repayment at the time of maturity. In such a situation, obviously, the

firm requires higher operating profits to cover these charges. If it fails to earn

adequate operating profits to cover such financial charges, it may be forced into

cash insolvency. Thus, with the increase in the proportion of debt commitments and

preference shares in its capital structure, fixed charges increase. All other things

being the same, the probability that the firm will unable to meet these fixed charges

also increases. As the firm continues to lever itself, the probability of cash

insolvency, which may lead to legal bankruptcy, increases. Clearly, there fore, as

firms financial structure shifts towards a more highly levered position, the

increased financial risk associated with the firm is recognized by the suppliers of

funds. They compensate for this increased risk higher by charging higher rate of

interest or requiring greater returns. In short, they react in much the same way as

they would in the case of increasing business risks. In the analysis of the cost of

capital in this chapter, however, the firms financial structure assumed to remainfixed. In the absences of such an assumption, it would be quite difficult to find its

cost of capital, as the selection of a particular source financing would the cost of

other sources of financing. In operational terms the assumption of a constant capital

structure implies that the additional funds required to finance the new project are

to be raised in the same proposition as the firm exists financing.

For the purpose of capital budgeting decisions, benefits from undertaking a

proposed project are evaluated on an after-tax basis. In fact, only the cost of capital

of debt requires tax adjustment as interest paid on debt is deductible expanse from

the point of view determine taxable income whereas dividend paid either topreference shareholders or to equity-holder are not eligible items as a sources of

deduction to determine taxable income.

To sum up, it may be said that cost of capital (k) consists of the following three

components.

I. The risk cost of the particular type of financing.rj;


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II. The business risk premium,b; andIII. The financial risk premium,f

Or jk r b f = + +

Since the business and financial risks are assumed to be constant, the changing

cost of each type of capital,j, over time should be affected by the change in thesupply of, and demand for, each type of funds.

6.5 Explicit and implicit costs

The cost of capital can be either explicit or implicit. The distinction between explicit

an implicit costs is important from the point of view computation of the cost of

capital.

The explicit cost of any sources of capital is the discount rate that equates the

present value of the cash inflows that are incremental to the taking of the financing

opportunity with the present values of its incremental cash outflows.

When firms raise funds from different sources, there is a series of cash flows.

Initially, there is cash inflow to the extent of the amount raised. This is followed by a

series of cash outflows in respect of interest payments, repayments of principal, or

payment of dividends. For example, a firm raises Rs. 5.00,000 through the sales of

10 per cent perpetual debentures. There will be a cash inflow of Rs. 5,00,000

followed by a inflows (Rs. 5,00,000) with the present value of cash outflows (Rs.

50,00,00) would be the explicit cost.

The determination of the explicit cost of capital is similar to the determination of theIRR, with one difference. While in the computation of the IRR, the cash outflows

(assuming conventional flows) are involved in the beginning, followed by the cash

inflows subsequently, it is exactly opposite with the explicit cost of the capital. Here,

as shown above, the cash flows take place only once and there is a series of cash

outflows subsequently.

The general formula for the explicit cost of capital of any sources of raising finance

would be as follows:

( )0

1 1

n t

tt

COCIC=

=

+

where CI0 = initial cash inflow, that is, net cash proceeds received

by the firm from the capital sources at time 0, CO1+CO2+ + COn = cash

outflows at times 1,2 n, that is, cash payment from the firm to the capital source.

If CI0 is received in instalmants, then, CI0


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( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

31 2

0 1 2 3

31 2

1 2 3

...1 1 1 1

...1 1 1 1

n

n

n

n

CI CI CI CI CI

C C C C

CO COCO CO

C C C C

+ + + + +

+ + + +

= + + + + +

+ + + +

It is evident from the above mathematical formulation that the explicit cost of

capital is the rate of return of the cash flows of the financing opportunity. In other

words, it is the internal rate of return that the firm pays to procedure financing. On

the basis of the above formula, we can easily find out that the explicit cost of an

interest free loan is zero per cent because the discount rate that equates the present

value of a future sum with an equivalent sum received today is zero. The explicit

cost of capital of a value bearing interest is that discount rate which equates the

present value of the future cash outflows with the net amount of funds initially

provided by the loan. The explicit cost of capital of a gift is minus 100 percent. The

explicit cost of capital derived from the sale of an asset is a discount rate that

equates the present value of the future cash flows foregone by the assets sale with

the net proceeds to the firm resulting from its liquidation. The explicit cost of funds

supplied by increases in certain liabilities such as accounts payable and accrued

taxes is zero percent unless, of course, penalties are incurred or discounts lost owing

to the increases in these liabilities.

The explicit cost of capital is concerned with the incremental cash flows that result

directly from raising funds. Retained earnings used in the firm involve no future

cash flows to, or from, the firm. Therefore, the explicit cost of retained earnings is

minus 100 percent. There are no future interests or principal payments imposed by

the retention of earning. There are no additional shares created and sold to

outsiders on which dividends will be paid. From this, it should, however, not be

concluded that retained earnings have no cost. (In fact, they also have costs like

other sources of raising finance have). The retained earnings are undistributed

profits of the company belonging to the shareholders. Given the ultimate objective

of the firm to maximize the wealth of shareholders, the cost of retained earning

would be equivalent to the opportunity cost of earning by investing elsewhere by the

shareholders themselves or by the company itself. Opportunity costs are technically

referred to as implicit cost of capital. The implicit cost of capital of funds raised andinvested by the firm may, therefore, be defined as as rate of return associated with

the best investment opportunity for the firm and its shareholders that would be

foregone, if the projects presently under consideration by the firm were accepted.

The cost of retained earnings is an opportunity cost or implicit capital cost, in the

sense that it is the rate of return at which the shareholders could have invested these

funds had they been distributed to them. However, other forms of financings also


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have implicit cost once they are invested. The explicit cost arises when funds are

raised, whereas the implicit costs arise when funds are used. Viewed in this

perspective, implicit costs are ubiquitous. They arise whenever funds are used no

matter what the source.

6.6 Opportunity cost of capital

Whenever we talk about money we also talk about its application. There can be

several alternative uses or several investment opportunities of a certain amount of

funds. The opportunity cost is the rate of return foregone on the next best

alternative investment opportunity of comparable risk.

Capital employed by the firm is obtained from various sources. To simplify our

discussion we have categorized capital employed by the firm into four categories

namely:

1. Long term debt (debentures, bonds, and term loans)2. Preference Capital3. Equity Capital4. Retaining Earning

Overall cost of capital of the firm is the overall, or average, required rate of return

on the total funds or capital used by the firm for carrying out its business

operations. Cost of different components of capital is different and is called

component cost. Now we will discuss cost each component of funds used by firms

and also learn to determine its related cost which occurs to the firm.

6.6.1 Cost of Debt

The cost of capital is the interest rate a company is paying on all of its debt, such as

loans and bonds. Debts are liabilities of firm. But we will focus upon long-term debt

(liabilities) of the firm, which includes term loans, debentures and bonds. Term

loans are loan taken from banks and financial institutions for a specified period of

time at a certain rate of interest having maturity period of more than 3 years.

Debentures and bonds debt instruments issued by the corporate to the public or

institutions at a specified interest rate for a specified period of time, creating

creditors to the company. A debenture or bond may be issued at par or at a discount

or premium.

The effective rate that a company pays on its current debt. This can be measured ineither before- or after-tax returns; however, because interest expense is deductible,the after-tax cost is seen most often. This is one part of the company's capitalstructure, which also includes the cost of equity.


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A company will use various bonds, loans and other forms of debt, so this measure isuseful for giving an idea as to the overall rate being paid by the company to use debtfinancing. The measure can also give investors an idea as to the riskiness of thecompany compared to others, because riskier companies generally have a highercost of debt.

Interest rate times 1 minus the marginal tax rate because interest is a tax deduction-symbolically, i(1 -t). Hence, an increase in the tax rate decreases the cost of debt.

To get the after-tax rate, you simply multiply the before-tax rate by one minus themarginal tax rate (before-tax rate x (1-marginal tax)). If a company's only debt werea single bond in which it paid 5%, the before-tax cost of debt would simply be 5%.If, however, the company's marginal tax rate were 40%, the company's after-taxcost of debt would be only 3% (5% x (1-40%)).

Note: - After-tax Cost of Debt

After-tax cost of debt = Interest rate x (1 - tax rate)

EXAMPLE:

0.08 = 10% x (1 - 0.2)

Where

Interest Rate: The rate at which you can borrow money to finance the equipment youwant to buy

Tax Rate: Combined federal and provincial business tax rate

The rate of interest at which the debt is issued is the basis of calculating the cost of

any type of debt. The explicit cost of debt i.e. Kb is the discount rate which equates

the present value of cash floes to the creditors (Suppliers of debt) with the current

market price of the new debt issue. . Kb can be solved by the help of the following

formula:

( )=

+

+=

n

t b

tt

tKPIP

1

01

Where

= Summation for period 1 through n


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It = Interest payment in period t on the principal

Pt = Payment of principal in period t( return of principal)

P0 = Current Market Price of debt

Kb = Cost of debt (Before tax)

After tax cost of debt, which is denoted by Kd can be determine by the equation:

( )tKKbd = 1 Where Kb is before tax cost of debt and Kd is after tax cost of debt.

But before further discussion, let us understand the concept of after tax and before

tax cost of debt. As already stated, cost of debt, has two dimensions of calculation,

before tax and after tax basis. Befors tax cost of debt i.e.

Kb can be determine by simply considering the interest payables as follows

incipal

InterestKb

Pr=

For example if a firm borrows Rs. 1, 00,000 for one year at 10%. The cost of debt is

Rs. 10,000/-

Which is the annual interest?

%10000,00,1

000,10==bK

After tax cost of debt i.e. Kd is calculated by adjusting before tax cost for the tax rate

(t) applicable. The formula for after tax cost of debt will be as follows:

( )tKK bd = 1

For example if before tax cost of debt is 12% and tax rate is 50% the after tax cost

of debt will be calculated as follows:

( ) ( ) %65.01121 === tKK bd

Debt may be two types

1. Perpetual debt2. Redeemable/Convertible debt

Perpetual Debt:-


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Perpetual debt is the debt which has no maturity value. Such debts do not have any

principal repayment as long as the company is operating. Cost of perpetual debt can

be calculated as follows:

( )SP

tIK

SP

IK

d

b

=

=

1

Where I = annual interest payments, SP = Net Sales Proceeds of debt, t = tax

rate.

Redeemable debt

Redeemable debt has a maturity value i.e. these debts are issued for specific time

period. Cost of redeemable debt can be calculated as follows:

( )

2

1

2

b

bt

b

b

bt

b

PMN

PMtI

K

PMN

PMI

K

+

+

=

+

+

=

Where

Kb = Before tax cost of debt

Kd= After tax cost of debt

It = Periodic Interest Payment

M= Par or maturity value of debt or Redemption value

Pb = Debts issue price or its purchase price or Net realized amount

M-Pb = Share Premium

N = Life of debt or no. of years to maturity

Illustration 1

A Ltd issues a non-convertible debt for Rs. 400 lac. Each debt has a face value of Rs

100 and carries a rate of interest of 14%. The interest is payable annually and the


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debenture is redeemable at a premium of 5% after 10 years. If A ltd realizes Rs 97

per debt and corporate tax rate is 50%, what is the cost of debt to the company.

( )%7.7

297105

10

975.105.0114

=

+

+

=dK

6.6.2 Cost of Preferences Shares

Preferred stocks are a hybrid security i.e. a hybrid between debt and

common/equity stock. Like debt preferred stock gets fixed, periodic payment (cash

inflows in form of fixed dividends) and during liquidation they get 1st claim over

those of common stockholders.

Unlike debt it is neither bound by legal provisions of debt nor has voting rights

(ownership privilege) of equity shares. To the firm preferred stock is more risky

than common stock but less risky than debts. To the investor preferred stock is less

risky than equity or common stock but more than debt. Cost of preference shares is

determined by the dividend paid to the preference stockholders i.e.

( )SP

P

P

D

Stockeferredofice

DividendeferredYieldeferredPY ==

PrPr

PrPr

A perpetuity selling for Rs. 80/- a share pays annual dividend of Rs.8. its yield is

PY = 8/80 = 10%

ThusP

PP

P

DK =

Where Dp = annual dividend of preference share

PP = market Price/Sales Price of preference share

If floatation costs are included then

fP

PP

P

DK

= Where f = floatation cost, (i.e. cost of selling the debt)

Redeemable Preference Shares: These are preference shares having maturity value.

They are held for a specified time period.


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2

b

bP

P PMN

PMD

K+

+

=

DP = Dividend

M = Redemption value

Pb = Purchased Price/ Net realized amount

N = Life of preference Capital

Excel Co. Ltd, each preference share has a face value of Rs. 100 and carries a rate of

dividend of 14% p.a. Shares is redeemable after 12 years at par. Net amount per

share is Rs. 95. what is the cost of Preference Capital?

%7.14

2

9510012

9510014

=+

+

=pK

6.6.3 Cost of equity

In finance, the cost of equity is the minimum rate of return a firm must offershareholders to compensate for waiting for their returns, and for bearing some risk.

The cost of equity capital for a particular company is the rate of return oninvestment that is required by the company's ordinary shareholders. The returnconsists both of dividend and capital gains, e.g. increases in the share price. Thereturns are expected future returns, not historical returns, and so the returns onequity can be expressed as the anticipated dividends on the shares every year inperpetuity. The cost of equity is then the cost of capital which will equate thecurrent market price of the share with the discounted value of all future dividendsin perpetuity.

The cost of equity reflects the opportunity cost of investment for individualshareholders. It will vary from company to company because of the differences in

the business risk and financial or gearing risk of different companies.

In financial theory, the return that stockholders require for a company. Thetraditional formula is the dividend capitalization model:

The cost of equity is calculated by the following formula:


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Ke=D1/Po+g

Po=D1/(Ke-g)s

Where D1=Do (1+g)

A firm's cost of equity represents the compensation that the market demands inexchange for owning the asset and bearing the risk of ownership.

Let's look at a very simple example: let's say you require a rate of return of 10% onan investment in TSJ Sports. The stock is currently trading at $10 and will pay adividend of $0.30. Through a combination of dividends and share appreciation yourequire a $1.00 return on your $10.00 investment. Therefore the stock will have to

appreciate by $0.70, which, combined with the $0.30 from dividends, gives you your10% cost of equity.

The capital asset pricing model (CAPM) is another method used to determine costof equity.

The formula above calculates the cost of equity based on a firm's current rate ofreturn. If one assumes a perfect market, industry-specific costs of equity reflect theriskiness of particular industries. A high cost of equity would then indicate a higher-risk industry that should command a higher return to compensate for the higherrisk.

Estimation of the cost of equity is based upon forecasting of future earnings ofequity shareholder in the form of dividends and capital gain and forecasting of stockvalue of equity shares. Among all the components of financing available to a firmthe cost of equity is most difficult and complex to ascertain. One can easily forecastthe expected interest payment of debt commensurate with its risk structure andpreferred dividend rate as specified by the firm. This simplicity is due to the factthat interest on debt and preferred dividends remain fixed and constant over aperiod of time. But unlike interest and preferred dividend, equity dividends areexpected to grow with time and hence do not remain constant. Further as alreadystated when it comes to estimating the cost of equity capital then one has to value the

future forecasted cash inflows (earning) associated with it. Due to the uncertainty offuture earning, the risk element of equity capital increases, thereby increasing thecost of equity capital.

There are two approaches involved with estimated of cost equity namely (a)dividend valuation approach and (b) Capital Asset Pricing Model (CAPM)approach.


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1. Dividend valuation approach or Constant Dividend Growth Model (GordonsModel)

It states that expected return to investors from equity stock comprises of 2components of benefits.

1. Dividend Receipts expected in each year till a particular time periods.2. Capital gain associated with the equity stock at the end of a particular time

period. In other words it is the value of stock (Selling price of Stock Purchase Price of Stock).

Thus

returnofratequired

tPeriodtimeatStockofValueExpectedStreamDividendExpectedP

Re10

+

+=

eK

PD

P +

+=

1

11

0

Where D1 = Dividend paid at the end of Period 1.

P1 = Market price of stock at the Period 1.

Ke = Required rate of return on equity shares (cost of equity)

Po = Current Market price of stock

In future cash inflows are expected to grow at a growth rate g then

( )

iceesent

iceinIncreaseExpected

iceesent

DividendExpectedKThus

gP

DK

gP

DK

gK

DP

K

gPDP

e

e

e

e

e

PrPr

Pr

PrPr

;

1

1

0

1

0

11

0

11

0

+=

+=

+=

=

+

++=

Cost of New Equity

If fresh or new equity is issued then floating cost is also considered whilecalculating cost of equity. Floating cost is the cost incurred in issuing theequity shares to the investors, by the company.


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( )g

fP

DKe +

=

10

1 Where f = floating costs.

From the given data calculated cost of equity shares of Co. X:

1. Current market price of shares = Rs. 1202. Cost of floatation/shares on new shares = Rs. 53. Dividend paid on outstanding share for the past three years:

Year 1 Rs. 10.5 per shares

Year 2 Rs. 12.5 per shares

Year 3 Rs 14.5 per shares

Expected dividend on the new shares at the end of the current year is Rs.

15.0 per shares.

Over the three years of dividends have increased from Rs. 10.5 to 14.5 givinga compound factor of 14.5/10.5 = 1.37. (We look for growth % in compoundfactor table at 3 years row for a value of 1.37. at 11% we get 1.38).

Thus the sum of Re.1 would amount to Rs. 1.37 in 3 years @ 11% interest

( )%04.2400.11

115

15%00.11

5120

15=+=+

=eK

2. Capital Assets Pricing Model approach (CAPM)

The Capital Asset Pricing Model (CAPM) is used in finance to determine atheoretically appropriate required rate of return (and thus the price if expected cashflows can be estimated) of an asset, if that asset is to be added to an already well-diversified portfolio, given that asset's non-diversifiable risk. The CAPM formulatakes into account the asset's sensitivity to non-diversifiable risk (also known assystematic risk or market risk), in a number often referred to as beta () in thefinancial industry, as well as the expected return of the market and the expectedreturn of a theoretical risk-free asset.

The capital asset pricing model (CAPM) is an equilibrium model which describes

the pricing of assets, as well as derivatives. The model concludes that the expected

return of an asset (or derivative) equals the riskless return plus a measure of the

assets non-diversiable risk ("beta") times the market-wide risk premium (excess

expected return of the market portfolio over the riskless return). That is:


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expected security return = riskless return + beta x (expected market risk premium)

It concludes that only the risk which cannot be diversified away by holding a well-

diversified portfolio (e.g. the market portfolio) will affect the market price of theasset. This risk is called systematic risk, while risk that can be diversified away is

called diversifiable risk (or "nonsystematic risk").

Unfortunately, The CAPM is more difficult to implement in practice than the

binomial option pricing model or the Black-Scholes formula because to price an

asset it requires measurement of the asset's expected return and its beta. But, on the

other hand, it also attempts to answer a more difficult question:

The binomial option pricing model or the Black-Scholes formula asks what is the

value of a derivative relative to the concurrent value of its underlying asset. The

CAPM asks what is the value of an asset (or derivative) relative to the return of the

market portfolio. Because of this, the option models are often referred to as

"relative" valuation models, while the CAPM is considered an "absolute" valuation

model.

The model was introduced by Jack Treynor, William Sharpe, John Lintner and JanMossin independently, building on the earlier work of Harry Markowitz ondiversification and modern portfolio theory. Sharpe received the Nobel MemorialPrize in Economics (jointly with Harry Markowitz and Merton Miller) for thiscontribution to the field of financial economics.

The Security Market Line, seen here in a graph, describes a relation between the

beta and the asset's expected rate of return.

A model that describes the relationship between risk and expected return and that is

used in the pricing of risky securities.


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The general idea behind CAPM is that investors need to be compensated in twoways: time value of money and risk. The time value of money is represented by therisk-free (rf) rate in the formula and compensates the investors for placing money inany investment over a period of time. The other half of the formula represents riskand calculates the amount of compensation the investor needs for takingon additional risk. This is calculated by taking a risk measure (beta) that comparesthe returns of the asset to the market over a period of time and to the marketpremium (Rm-rf).

The CAPM says that the expected return of a security or a portfolio equals the rateon a risk-free security plus a risk premium. If this expected return does not meet orbeat the required return, then the investment should not be undertaken. Thesecurity market line plots the results of the CAPM for all different risks (betas).

Using the CAPM model and the following assumptions, we can compute theexpected return of a stock: if the risk-free rate is 3%, the beta (risk measure) of thestock is 2 and the expected market return over the period is 10%, the stock isexpected to return 17% (3%+2(10%-3%)).

Assumption

All investors have rational expectations. There are no arbitrage opportunities. Returns are distributed normally. Fixed quantity of assets. Perfectly efficient capital markets. Separation of financial and production sectors. Thus, production plans are fixed. Risk-free rates exist with limitless borrowing capacity and universal access. The Risk-free borrowing and lending rates are equal.

No inflation and no change in the level of interest rate exist. Perfect information, hence all investors have the same expectations about

security returns for any given time period.

The CAPM calculates cost of capital of equity by considering risk free interest rateprevalent in the economy and the risk premium desired by the investor. It alsoconsiders to specify the relationship between the market and the equity. TheCAPM determine real value of equity in the market.


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fmfe RRRK +=

Where Ke = Cost of Equity

Kf= Risk free interest rate in the market

Km = Market Return/return

= coefficient or sensitivity of security or relationship of securitywith the market.

Rm,Rf= Risk premium

Assume that Rm = 18% and Rf= 9%. If a security has a bets factor of (a) 1.4 (b) 1.0and (c) 2.3. Find out the expected return of the security.

fmfe RRRK +=

Ke = 9 %+( 18%-9%) 1.4 = 21.6 %

Ke = 9 %+( 18%-9%) 1.0 = 18 %

Ke = 9 %+( 18%-9%) 2.3 = 29.7 %

Calculate market portfolio return and expected return on security using CAPM

Investment inequity shares

Initial Price(1)

Dividend (2) Year endMarket Price(3)

(4)

Cement Ltd 30 3 50 0.8Steel Ltd 45 3 60 0.7Liquor Ltd 55 3 135 0.5Govt. of IndiaBonds

1000 150 1015 0.99

Risk Return 14%

Solution

Dividend CapitalAppreciation (3-1)

Total Return Investment

Cement Ltd 3 20 23 30Steel Ltd 3 15 18 45Liquor Ltd 3 80 83 55


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Govt. of IndiaBonds

150 15 165 1000

Total 150 130 289 1130

Return on Mkt. Portfolio = 289/1130 = 25.57%

Return on

Cement = 14% + 0.8(25.57 14) = 23%

Steel = 14% + 0.7(25.57 14) = 22.1%

Liquor = 14% + 0.5(25.57 14) = 19.78%

Govt of India Bond = 14% + 0.99(25.57 14) = 23%

6.6.4. Cost of Retained Earning (profit the company makes, but does not giveto the shareholders in the form of dividends)

This is kind of weird to think about. It takes some time to understand so take itslowly. After a company makes money (earnings), who owns that money? Theshareholders, right? But when you retain earnings you are not giving the money tothe shareholders. You are keeping it. In a way, you are investing it for them in yourcompany. Well those shareholders want some return on that money you arekeeping.. How much return do they expect? They want the same amount as if theyhad gotten the retained earning in the form of dividends, and bought more stock inyour company with them. THAT is the cost of retained earnings. You as a financial

genius, have to ensure that if you are retaining earning, that the shareholders willget at least as good a return on the money as if they had re-invested the money backinto the company.

If you don't understand this, re-read it and re-think it until you do get it. There isreally no "cost" in the cost of retained earnings. I mean, no money is changinghands. You aren't paying anyone anything. But you are keeping the shareholdersmoney. You can't say it is "free" money. Frankly if you did, it would screw up yourcapital budgeting. So when you are doing your capital budgeting, to ensure that theshareholders are getting a decent rate of return, you "guess" a cost of retainedearnings. How?? One way is CAPM. Another way is the bond yield plus risk

premium approach, in which you take the interest rate on the company's own longterm debt and then add between 5% and 7%. Again, you are kind of guessing here.A third way is the discounted cash flow method, in which you divide the dividend bythe price of stock and add the growth rate. Again, a lot of guessing.

The cost of retained earning (internal actual) is usually taken to be the same as costof equity.


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Kr (Cost of Retained earning) = Ke

But when floatation costs are involved then

( )f

KK r

e

=

1

(f= Floatation cost)

For example say a company issues fresh share to raise its equity, equity investorsexpect a rate of return of 18%. The cost of issuing external equity is 6%. What is thecost of retained earning and cost of external equity?

Kr = Ke = 18%

Cost of external equity raised by the company.

( )fK

K

r

e

=

1 = 0.18/ (1-0.06) = 19%

6.7 Weighted average cost of capital (WACC)

The weighted average cost of capital (WACC) is used in finance to measure a firm'scost of capital. It has been used by many firms in the past as a discount rate forfinanced projects, since the cost of the financing seems like a logical price tag to puton it.

Corporations raise money from two main sources: equity and debt. Thus the capital

structure of a firm comprises three main components: preferred equity, commonequity and debt (typically bonds and notes). The WACC takes into account therelative weights of each component of the capital structure and presents theexpected cost of new capital for a firm.

A calculation of a firm's cost of capital in which each category of capital is

proportionately weighted. All capital sources - common stock, preferred stock,

bonds and any other long-term debt - are included in a WACC calculation.

WACC is calculated by multiplying the cost of each capital component by its

proportional weight and then summing:

Where:Re = cost of equityRd = cost of debtE = market value of the firm's equity


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D = market value of the firm's debtV = E + DE/V = percentage of financing that is equityD/V = percentage of financing that is debtTc = corporate tax rate

Broadly speaking, a companys assets are financed by either debt or equity. WACCis the average of the costs of these sources of financing, each of which is weighted byits respective use in the given situation. By taking a weighted average, we can seehow much interest the company has to pay for every dollar it finances.

A firm's WACC is the overall required return on the firm as a whole and, as such, itis often used internally by company directors to determine the economic feasibilityof expansionary opportunities and mergers. It is the appropriate discount rate touse for cash flows with risk that is similar to that of the overall firm.

This equation describes only the situation with homogeneous equity and debt. Ifpart of the capital consists, for example, of preferred stock (with different cost ofequity y), then the formula would include an additional term for each additionalsource of capital.

How it works

Since we are measuring expected cost of new capital, we should use the marketvalues of the components, rather than their book values (which can be significantlydifferent). In addition, other, more "exotic" sources of financing, such asconvertible/callable bonds, convertible preferred stock, etc., would normally be

included in the formula if they exist in any significant amounts - since the cost ofthose financing methods is usually different from the plain vanilla bonds and equitydue to their extra features.

Sources of information

How do we find out the values of the components in the formula for WACC? Firstlet us note that the "weight" of a source of financing is simply the market value ofthat piece divided by the sum of the values of all the pieces. For example, the weightof common equity in the above formula would be determined as follows:

Market value of common equity / (Market value of common equity + Market valueof debt + Market value of preferred equity)

So, let us proceed in finding the market values of each source of financing (namelythe debt, preferred stock, and common stock).


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The market value for equity for a publicly traded company is simply theprice per share multiplied by the number of shares outstanding, and tends tobe the easiest component to find.

The market value of the debt is easily found if the company has publicly

traded bonds. Frequently, companies also have a significant amount of bankloans, whose market value is not easily found. However, since the marketvalue of debt tends to be pretty close to the book value (for companies thathave not experienced significant changes in credit rating, at least), the bookvalue of debt is usually used in the WACC formula.

The market value of preferred stock is again usually easily found on themarket, and determined by multiplying the cost per share by number ofshares outstanding.

Now, let us take care of the costs.

Preferred equity is equivalent to perpetuity, where the holder is entitled tofixed payments forever. Thus the cost is determined by dividing the periodicpayment by the price of the preferred stock, in percentage terms.

The cost of common equity is usually determined using the capital assetpricing model.

The cost of debt is the yield to maturity on the publicly traded bonds of thecompany. Failing availability of that, the rates of interest charged by thebanks on recent loans to the company would also serve as a good cost of debt.

Since a corporation normally can write off taxes on the interest it pays on thedebt, however, the cost of debt is further reduced by the tax rate that thecorporation is subject to. Thus, the cost of debt for a company becomes(YTM on bonds or interest on loans) (1 tax rate). In fact, the taxdeduction is usually kept in the formula for WACC, rather than being rolledup into cost of debt, as such:

WACC = weight of preferred equity cost of preferred equity

+ weight of common equity cost of common equity

+ weight of debt cost of debt (1 tax rate)

And now we are ready to plug all our data into the WACC formula.

WACC. An average representing the expected return on all of a company'ssecurities. Each source of capital, such as stocks, bonds, and other debt, is weightedin the calculation according to its prominence in the company's capital structure.


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After assessing the cost of individual components of capital namely debt, equity(common equity and preference shares), we now ascertain the total or the overallcost of capital of the firm.

We already know that the entire capital of the firm consists of various components

as derived from various sources

1. Like debt which is the borrowed capital from outside like debenturesand bonds.

2. Like equity which is sum invested into the company for a long periodby the investor, know as shareholders etc.

Each sources of capital has distinct/characteristics cost related to its funds. Asdifferent sources of capital have distinct and different costs, one has to ascertain amethod to calculate the overall cost of capital.

Measurement of overall cost of capital (composite cost) requires following steps.

1. First determine various costs of different sources of funds. (Debt, equity,preferences capital etc.)

2. Assign weight to each cost of different sources of funds. The weight assignedto each cost of capital is equal to the proportion investment in the capitaldividend by Total Investment ot Total Capital of the firm.

3. Add all the weighted components of cost of capital and arrive at the firmsweighted average cost.

The overall cost of capital is also K/a weighted average cost of capital.

( )=

=

n

n

XX wkCCAW1

...

kx = After Tax cost of xth method of financing

wx = weight of this specified method of financing (x) % age of Total Capital offirm

= Summation of various financing methods 1 through n.

Amount (Rs) Proportion of (%) TotalFinancing

Equity Capital 3,50,000 21.9Preference Capital 2,00,000 12.5Retaining Earning 7,00,000 43.7Debt 3,50,000 21.9Total 16,00,000 100.0


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The firm computed the following after tax costs of different components offinancing.

Sources Weight Cost (%)Equity Capital 21.9 16

Preference Capital 12.5 15Retaining Earning 43.7 12Debt 21.9 10

How to assign Weights?

There are three types of weight systems that can be adopted for determining theweighted average cost of capital (WACC) of the firm.

1. Weights which are based upon, the book value of the different sourcesof finance used by the firm.

2. Weights based upon the current market value of the different sourcesof finance used by the firm.

3. Weights based upon the proportion of the financing of the differentsources used by the firm as compared to its total capital employed.

Factors affecting Cost of capital of a firm are:

1. Risk free rate of interest: the risk free rate of interest is the minimum cost ofcapital that any firm encounters in the market. It is a benchmark for allindustries to evaluate their individual cost of funds. When risk free rate ofinterest raises overall cost of funds increases in the economy. Vice verse when

risk free rate of interest decreases, cost of funds in the economy is loweredand liquidity increases in the market. Risk free rate of interest is governed bythe government. Thus we can state that cost of funds in any economy (whererisk free rate of interest is regulated by government) depends on governmentpolicies and principles.

2. Business risk: The business risk, to which a firm is explored to, also plays animportant role in designing its cost of capital. If the business risk is high, itscost of capital increases and vive versa.

3. Financial risk: Financial risk is the risk of debt finance. Higher theproportion of debt inn the firms capital structure, higher is its financial risk.As financial risk increases bankruptcy risk also increases for a given firm.

Higher the bankruptcy/insolvency risk of an enterprise higher is its cost ofcapital.4. Decisions of financing mix: Depending upon the decision of the management

about the proportion of different sources of funds, the overall cost of capitalof the firm is decided,

5. Attitude of management: If management of the company is aggressive, it willrequire less amount of liquid funds thereby decreasing its total cost. On the


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other hand conservative management keeps large amount of liquid fundsthereby increasing its total cost of capital.

6. Requirement of the firm: Firms requiring large amount of fundsconsequently bear a higher cost compared to those firms which require lessamount of funds, because large funds requirement leads to heavy external

borrowing of funds.7. Nature of Business: Firm that requires heavy investment in fixed assets bearsa high cost of funds in comparison with those firma which require lowinvestment in fixed assets. Long term maturity fund are more expensive thanshort term maturity funds, and fixed assets are financed by long term funds.

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