Cost of Capital and Capital Structure

Tax Shield Education Centre MAFA-1

Cost Of Capital And Capital Structure

Capital of a company consists of :

1. Equity ( equity share capital + reserves & surpluses )

2. Preference share capital

3. Loan capital i.e. Debenture

EBIT-EPS Chart

Falcon Limited plans to raise additional capital of Rs. 10 mln for financing an expansion project. In this context, it is evaluating two alternative financing plans: (i) issue of equity shares (1 mln equity shares at Rs. 10 per share), and (ii) issue of debentures carrying 14 per cent interest.

What will be the EPS under the two alternative financing plans for two levels of EBIT, say Rs. 4 mln and Rs. 2 mln? Following table shows the value of EPS for these two levels of EBIT under the alternative financing plans.

Calculate the indiference EBIT.

In general, the relationship between EBIT and EPS is as follows :

(EBIT - I) (1 – t)

EPS = ————————

n

The EBIT inifference point between two alternative plans can be obtained mathemetecally by solving the following equation

( EBIT – I1 ) ( 1 – t ) = ( EBIT – I2 ) ( 1 – t )

n1 n2

wereEPS= earnings per share

EBIT =earnings before interest and taxes

I=interest burden

t=tax rate

n=number of equity shares

whereEBIT* = indifference point between the two alternative financing plans

I1, I2 = interest expenses before taxes under financing plans 1 and 2

t = income-tax rate

n1, n2 = number of equity shares outstanding after adopting financing plans 1 and 2.

Risk Considerations

So far we looked at the impact of alternative financing plans on EPS. What is the effect of leverage on risk? A precise answer to this question is not possible with the help of EBIT-EPS analysis. However, a broad indication may be obtained with reference to it.

The finance manager may do two things : (i) compare the expected value of EBIT with its indifference value, and (ii) assess the probability of EBIT falling below its indifference value. If the most likely value of EBIT exceeds the indifference value of EBIT, the debt financing option, prima facie, may be advantageous. The larger the difference between the expected value of EBIT and its indifference value, the stronger the case for debt financing, other things being equal.

Given the variability of EBIT, arising out of the business risk of the company, the probability of EBIT falling below the indifference level of EBIT may be assessed. If such probability is negligible, the debt financing option is advantageous. On the other hand, if such probability is high, the debt financing alternative is risky.

The notion may be illustrated graphically as shown in where two probability distributions of EBIT (A and B) are superimposed on the EBIT-EPS chart. Distribution A is relatively safe, as there is hardly any probability that EBIT will fall below its indifference level. With such a distribution, the debt alternative appears to be advantageous. Distribution B, on the other hand, is clearly risky because there is a significant probability that EBIT will decline below its indifference value. In this case, the debt alternative may not be regarded as desirable.

ROI-ROE ANALYSIS

In the preceding section we looked at the relationship between EBIT and EPS under alternative financing plans. Pursuing a similar line of analysis, we may look at the relationship between the return on investment (ROI) and the return on equity (ROE) for different levels of financing leverage.

Suppose a firm, Korex Limited, which requires an investment outlay of Rs. 100 mln, is considering two capital structures.

Capital Structure ACapital Structure B

Equity 100Equity50

Debt0Debt50

While the average cost of debt is fixed at 12 per cent, the ROI (defined as EBIT divided by total assets) may vary widely. The tax rate of the firm is 50 per cent.

Based on the above information, the relationship between ROI and ROE (defined as equity earnings divided by net worth) under the two capital structures, A and B, would be as shown in Table 13.2. Graphically the relationship is shown as below

ROE

B A

ROI

Looking at the relationship between ROI and ROE it is observed that :

1.The ROE under capital structure A is higher than the ROE under capital structure B when ROI is less than the cost of debt.

2.The ROE under the two capital structures is the same when ROI is equal to the cost of debt. Hence the indifference (or breakeven) value of ROI is equal to the cost of debt.

3.The ROE under capital structure B is higher than the ROE under capital structure A when ROI is more than the cost of debt.

Mathematical Relationship

The influence of ROI and financial leverage on ROE is mathematically as follows :

ROE = [ROI + (ROI – r) D/E] (1 – t)

Where ROE= return on equity

ROI = return on investment

r=cost of debt

D/E= debt-equity ratio

t= tax rate

ASSESMENT OF DEBT CAPACITY

Employment of debt capital entails two kind of burden: interest payment and principal repayment. To assess a firm’s debt capacity we look at its ability to meet these committed payments. This may be judged in terms of:

Coverage ratios

Probability of cash insolvency

Inventory of resources

Coverage Ratios

A coverage ratio shows the relationship between a committed payment and the source for that payment. The coverage ratios commonly used are: interest coverage ratio, cash flow coverage ratio, and debt service coverage ratio.

This may be derived as follows:

PAT

ROE = ———

E

(EBIT – I) (1 – t)

ROE = ————————

E

(TA  ROI – I) (1 – t)

ROE = ———————————

E

[(E + D) ROI – rD] (1 – t)

ROE = ————————————

E

ROE = [ROI + (ROI – r) D/E] (1 – t)

Interest Coverage Ratio : The interest coverage ratio (also referred to as the times interest earned ratio) is simply defined as:

Earnings before interest and taxes

————————————————

Interest on debt

To illustrate, suppose the most recent earnings before interest and taxes (EBIT) for Vitrex Company were Rs. 120 million and the interest burden on all debt obligations were Rs. 20 million. The interest coverage ratio, therefore, would be 120/20 = 6. What does it imply? It means that even if EBIT drops by 831/3 percent, the earnings of Vitrex Company cover its interest payment.

Though somewhat commonly used, the interest coverage ratio has several deficiencies: (i) It concerns itself only with the interest burden, ignoring the principal repayment obligation. (ii) It is based on a measure of earnings, not a measure of cash flow. (iii) It is difficult to establish a norm for this ratio. How can we say that an interest coverage ratio of 2,3,4, or any other is adequate?

Cash Flow Coverage Ratio This may be defined as:

EBIT + Depreciation + Other non-cash charges

Loan repayment installment

Interest on debt + —————————————--

(1 – Tax rate)

To illustrate, consider a firm :

DepreciationRs. 20 mln

EBITRs. 120 mln

Interest on debtRs. 20 mln

Tax rate50%

Loan repayment installment Rs. 20 mln

Calculate the cash flow coverage ratio for this firm .

Debt Service Coverage Ratio Financial institutions which provide the bulk of long-term debt finance judge the debt capacity of a firm in terms of its debt service coverage ratio. This is defined as:

n PATi + DEPi + INTi

DSCR =  —————————— n

tINTi + LRIi

whereDSCR= debt service coverage ratio

PATi= profit after tax for year I

DEPi= depreciation for year I

INTi= interest on long-term loan for year I

LRIi= loan repayment instalment for year I

n= period of loan

In determination of best capital structure , share- holder prefers higher E.P.S. ( i.e. earning per share ) or
EPS volatility
EPS volatility refers to the magnitude or the extent of fluctuation of earnings per share of a company in various years as compared to the mean or average earnings per share. In other words, EPS volatility shows whether a company enjoys a stable income or not. It is obvious that higher the EPS volatility, greater would be the risk attached to the company. A major cause of EPS volatility would be the fluctuations in the sales volume and the operating levarage. It is obvious that the net profits of a company would greatly fluctuate with small fluctuations in the sales figures specially if the fixed cost content is very high. Hence, EPS will fluctuate in such a situation. This effect may be heightened by the financial leverage.
E.P.S. = Profits available to equity. Share holders  number of equity shares
= Earning per share or EPS = [ (PBIT - I ) (1-t) - Pref Dividend ]  No. of Equity Share.
Where, PBIT = Profit before tax. ; I = Interest.; t = Tax rate of the firm.
At point of Indifference : (EPS)1 = (EPS ) 2

Calculation of costs for each Elements

Costs of Capitals are of two types

1. One Time Cost Or Flotation Cost
2. Annual Costs e.g. Interest, Dividend

Cost of Debt (Cd)
a) When date of redemption is not given in the problem.
Cost of Debt. (after tax ) or Cd = ( 1-t ) x I
Where, i = Effective rate of Interest .
T = Tax rate .
Effective rate of interest = Interest amount p.a. x 100
Net Proceeds
Net proceeds = Face value – discount + premium –flotation cost . You can calculate on per debenture basis .
b) Cost of redeemable debt :
When Redemption is made at the end of its life or project .
Cost of debt (after tax ) I + RV - NP
Cd= , n , (1 - t )
RV + NP
0 2
Where, I = Fixed Interest charges p.a. or interest per debenture.
RV = Redeemable value i.e. face value + premium
NP = Net proceeds or Cash Inflow.
n = Life of the debt.
c) When DEBENTURES are redeemed during its life:
Apply the principle of EXPLICIT COST i.e. the rate of return at which the initial cash inflow equates the discounted future cash outflows . This method is opposite to I.R.R.
Cost of Preference Share Capital (Cp )
a) Cost of irredeemable preference Share .
Cp = Preference Dividend  100 NOTE : Tax on Dividend may be charged
Net Proceeds (NP ) or Market Value( MP )
b) Cost of redeemable preference Share
i.Redemption at the end
RV - NP
Cp = D + n , D= preference dividend
RV + NP
2
ii.Pref. sh. Redeemed intermittently -- Apply Explicit Cost principle as before.
Cost of Equity Share Capital (Ce)
a. Dividend Price Approach ( D/P ) with growth model
Ce = Dividend  100 + g

Net Proceeds or Market value.

Where, g = growth rate or expected growth in dividend from coming year.
b) Earning/ Price Approach ( E / P ):
Ce = Current Earning per Share  100

Current Market Price per share

c) Realised yield Approach :- It is that rate of return where investor’s initial investment = Total discounted cash
Inflow in form of dividend and sales realisation at the end of the period.
d) Earning growth Model
Ce = EPS x 100 + g

NP

e ) Estimating growth rate (g )
1) Dn = Do ( 1+ g ) n ; Dn = div / share in current year ; n = no of years
Do = div / share in first year ; g = growth rate
2) GORDON’S MODEL :
g = br ; g = growth rate ; b = constant proportion of net profit retained each year ;
r = average return of the firm .
where , b = Net profit - dividends THIS METHOD IS ONLY APPLICABLE
Net profit TO FIRMS WHICH HAVE
ALL EQUITY CAPITAL STRUCTURE
r = net profits
Book value of capital employed
Right share:

1. Theoretical Post Right Price = { market price no. of old share + no. of right share  subscription price }  total no. of shares
2. Theoretical value of rights = Post right price – subscription price

3. Bond Yield Plus Risk Premium Approach
According to this approach the rate of return required by the equity investors of a firm is equal to
Yield on the long-term bonds of the firm + Risk premium
The logic of this approach is simple. Equity investors bear a higher degree of risk than bond investors and, hence, their required rate of return should include a premium for this higher risk. The problem with this approach is how to determine the risk premium. Should it be 1 percent, 2 percent, or n percent ? There is no theoretical basis for estimating the risk premium. Most analysts look at the operating risk and financial risk characterising the business and arrive at a subjectively determined risk premium figure which varies normally between 2 percent and 6 percent. This is added to the yield on the firm’s long-term bonds to estimate the rate of return required by equity investors.
THE CAPITAL ASET PRICING MODEL (CAPM)
The previous chapter on portfolio theory dealt with how to measure the risk and expected return of a portfolio or collection of assets; so far we have not attempted to bring the two together, that is to specifically link risk with return.
In the chronological development of modern financial management, portfolio theory came first with Markowitz in 1952. It was not until 1964 that William Sharpe derived the capital Asset Pricing Model (CAPM)1 based on Markowitz’s portfolio theory. For example, a key assumption of the CAPM is that investors hold highly diversified portfolios and thus can eliminate a significant proportion of total risk.
The CAPM was a breakthrough in modern finance because for the first time a model became available which enable academic, financiers and investors to link the risk and return for an asset together, and which explained the underlying mechanism of asset pricing in capital markets.
TYPES OF INVESTMENT RISK
In the preceding chapter we have seen how the total risk (as represented by the standard deviation, ) of a two-security portfolio can be significantly reduced by combining securities whose returns are negatively correlated, or at least have low positive correlation – the principle of diversification.
According to the CAMP, the total risk of a security or portfolio of securities can be split into two specific types, systematic risk and unsystematic risk. This is sometimes referred to as risk partitioning, as follows :
Total risk = Systematic risk + Unsystematic risk
Systematic (or market) risk cannot be diversified away : it is the risk which arises from market factors and is also frequently referred to as undiversifiable risk. It is due to factors which systematically impact on most firms, such as general or macroeconomic conditions (e.g. balance of payments, inflation and interest rates). It may help you remember which type is which if you think of systematic risk as arising from risk factors associated with the general economic and financial system.
Unsystematic (or specific) risk can be diversified away by creating a large enough portfolio of securities : it is also often called diversifiable risk or company-unique risk. It is the risk which relates, or is unique, to a particular firm. Factors such as winning a new contract, an industrial dispute, or the discovery of a new technology or product would contribute to unsystematic risk.
The relationship btween total portfolio risk, p, and portfolio size can be bshon diagramatically as in Figure below . Notice that total risk diminshes as the number of assets or securities in the portfolio increases, but also observe that unsystematic risk does not disappear completely and that systematic risk remains unaffected by portfolio size.
Total risk
Portfolio risk Unsystematic risk
p
1 5 10 15 20
Number of securities in portfolio
THE CAPM MODEL
We have previously described the CAPM as a method of expressing the risk-return relationship for a security or portfolio of securities: it brings together systematic (undiversifiable) risk and return. After all, for any rational, risk-averse investor it is only systematic risk which is relevant, because if the investor creates a sufficiently large portfolio of securities, unsystematic or company-specific risk can be virtually eliminated through diversification.
It is therefore the measurement of systematic risk which is of primary importance for rational investors in identifying those securities which possess the most desired risk-return characteristics. It is the measurement of systematic risk which becomes critical in the CAPM because the model relies on the assumption that investors will only hold well diversified portfolios, so only systematic risk matters.
The CAPM is quite a complex concept so if you find it difficult to grasp at first do not become disillusioned, stick with it.
For reasons of presentation and ease of understanding we will approach our study of the CAPM by breaking it down into five key components as follows:
1.The beta coefficient, ();
2.The CAPM equation;
3.the CAPM graph—the security market line (SML);
4.Shifts in the SML—inflationary expectations and risk aversion;
5.Comments and criticisms of the CAPM.
Let us examine each component in turn, beginning with the key concept of beta, ,
The beta coefficient ()
Recall that the standard deviation, , is used to measure an asset or share’s total risk, while the beta coefficient, , in contrast is used to measure only part of a share or portfolio’s risk, namely the part that cannot be reduced by diversification, that is the systematic or market risk of an individual share or portfolio of shares.
Systematic risk can be further subdivided into business risk and financial risk. Business risk arises from the nature of the firm’s business environment and the particular characteristics of the type of business or industry in which it operates. For example the competitive structure of the industry, its sensitivity to changes in macroeconomic variables such as interest rates and inflation and the stability of industrial relations all combine to determine a firm’s business risk. The level of business risk in some industries, for example catering and construction, is higher than in others and is a variable which lies largely outside management’s control.
Categories of beta
Shares or securities can be broadly classified as aggressive, average or defensive according to their betas. Shares with a beta>1.0 are described as aggressive; they are more risky than the market average, although they will tend to perform well in a rising or bull market. Consequently investors would require a rate of return from the share which is greater than the market average.
Shares with a beta = 1.0 are described as average or neutral as their rate of return moves in exact harmony with movements in the stock market average return; they are of average risk and yield average returns. In contrast, shares with a beta < 1.0 are classed as defensive. A defensive share does not perform well in a bulk market but conversely it does not fall as much as the average share in a falling or bear market.
How are betas determined?
A share’s beta is determined from the historical values of the share’s return relative to market returns. It is important to appreciate therefore that beta is a relative, not an absolute, measure of risk. As each individual beta is derived from a common base, that is, the return on the market portfolio or a suitable stock index substitute, then beta is a standardised risk measure, i.e. this makes the beta of one share directly comparable with the beta of another.