Chapter 1: An Overview of Corporate Financing 1. Corporate Financing Pattern in India Broadly, the sources of finance for a company can be of two types

(1) Internal Sources

(2) External Sources

Internal Sources of finance can be in the form of reserve and surplus and depreciation

External sources can be:

(i) Equity Capital

(ii) Borrowings mostly from banks

(iii) Trade credit and other current liabilities

In Indian conditions, it can be seen that for most of the years between 1984-2007, companies

have depended more on external sources of finance to meet their investment requirement.

Also most of the money raised through external sources have been by borrowing and not by

issuing equity. And most of the borrowings are from banks and not by issuing debentures.

Two salient observations that enough from table 1 are:

(1) Primary (Capital) market is still to play a efficient role as an intermediary between

capital surplus units in the economy and the capital deficient units.

(2) Unlike US, UK, Germany & Japan, where corporate dependence on internal sources

is high (about two third of total finance requirement is met by internal sources) in

India, corporations, on an average, fund one third of their capital requirement from

internal sources.

2. Trends in Debt Corporate Financing The amount of debt in capital structure varied with (i) age of the firm (ii) domicile of the firm

(iii) type of firm and (iv) size of the firm. In a study by Love and Peria (2005) the following

salient features emerged:

(i) Young firms tended to have lower debts ratios than older firms. Since the study

did not find any clear difference in the repayment capacity of such firms, they

reasoned this phenomenon to the comparative lack of transparency among young

firms.

(ii) Foreign firms were seen to have lesser debt than both private & government

owned Indian firms. This may be because of the greater access to foreign equity

that such firms have.

(iii) Manufacturing firms tended to have more debt as compared to service. Firms

among other things, this may be because of the greater proportion of tangible

assets.

(iv) Smaller firms tended to have lower debt ratios as compared to large firms. Also,

relative to large firms, small firms seem to rely less on financing from formal

financial institutions and markets and mostly resort to borrowing from other

(mostly intra group) corporations of profitable growth opportunities to small &

medium firms.

3. Trends in Equity Financing

Despite reforms in the capital market, equity market is still not a dominant source of external

finance to meet the investment requirements of a company. On an average between 1984 to

1991 equity accounted for less than 7 per cent of external finance which increased, in the post

reform period (between 1991 to 2007), to 15 percent.

Most of the funds, raised from primary market, between 1994 to 2007 have been by banking

and financial institutions. Thus the increased activity in the post reforms primary market have

mainly benefited a industry (Banking/FI) that was forced primarily by regulatory

compulsions (and not growth concerns) to raise equity.

4. Costs Of Different Sources Of Finance

4.1 Cost of Debt

Two main sources of capital are equity and debt. A debt may be in the form of

secured/unsecured loans, debentures, bonds, etc. The debt carries a fixed rate of interest and

the payment of interest is mandatory irrespective of the profit earned or loss incurred by the

firm. By taking debt, the firm increases the total capital employed in the business and if it is

able to generate a high rate of return on capital employed, the return to shareholders increases

as debt carries a fixed rate of interest and the additional return earned belongs to

shareholders. However, debt is like a double-edged sword because if the firm is not able to

generate adequate returns on capital employed, the return to shareholders would decline, as

interest has to be paid. Another point about using debt in the capital structure is that the

interest payable on debt is tax deductible.

The cost of debt is defined as the discount rate which equates the net proceeds from the debt

to the expected cash outflows in the form of interest and principal repayment, i.e.,

1 (1 ) (1 )

n

t nt d d

I FPk k=

= ++ +∑ (1)

Where, dk = Pre-tax cost of debt

I = Annual interest payment

F = Redemption value of debt

P = Net amount realized

n = Maturity period

The dk so arrived at is then multiplied by the factor (1-t), for the purpose of calculating

weighted average cost of capital, because interest on debt is a tax-deductible expense.

However, it should be noted that this tax- shield is available only when the firm is profitable.

But such business losses can be carried forward to be written off against business income.

Solving equation (1) for Kd leads one to solve a complicated polynomial. An approximation

formula as given below can also be used.

2

d

F PInk F P

−+

=+

4.2 Cost of Preference Share Capital

Preferred stock shares some characteristics of debt and some of equity. Like debt, preferred

stock requires a fixed interest payment; if the firm does not have the cash to pay the dividend,

the dividend is cumulated and paid in a period when there are sufficient earnings. Like debt,

preferred stock does not confer a share of control in the firm, and voting privileges are

restricted to issues that might affect claims on the firm’s cash flows or assets. Like equity,

payments to preferred stock holders are not tax deductible and are paid from after-tax cash

flows. Also like equity, preferred stock does not have a maturity date when the face value is

due. In terms of priority, in the case of bankruptcy, preferred stockholders have to wait until

debt holders’ claims have been met before receiving any portion of the assets of the firm.

Thus, the cost of preference capital is more than the cost of debt but less than the cost of

equity capital. In India only redeemable preference shares up to a maximum time period of

20 years can be issued.

The cost of redeemable preference share ( pk ) is defined as the discount rate which equates

the proceeds from preference capital issue to the dividend payment and principal payments.

Symbolically,

∑= +

++

=n

tn

pt

p kF

kDP

1 )1()1(

Where, pk = cost of preference capital

D = Preference dividend per share payable annually

F = Redemption price

P = Net amount realized per share

N = Maturity period

As in the case of debt, an approximation formula as given below can also be used.

2PFn

PFDk p +

−+

=

Why Do Companies Issue Preferred Stock? In many ways, it is difficult to understand why

a firm would issue preferred stock if it can also issue straight debt. Preferred stock generally

costs more than debt (since it is riskier) and provides no tax benefits.

However for firms that are concerned about being viewed as being too levered, preference

share offer a way out since, most analysts and ratings agencies treat preferred stock as equity

for the purposes of calculating leverage. Also, preferred stock may offer a way of raising

money for companies that have no other options – debt or equity – available to them.

4.3 Cost of Equity Share Capital

The cost of equity capital is the most difficult cost to measure. This is so because of the

nature of equity share capital. As we know that the dividend payment on equity capital is not

compulsory and the capital is practically irredeemable. Hence, in the case of equity share

capital, the cost has to be viewed in the opportunity cost framework. The investor has

supplied funds to the firm with the expectation of some suitable return. The investment was

made, presumably on a logical basis, because the type of risk embodied in the firm

reasonably matched with the investor’s risk preference and because the expectations about

earnings, dividends and market appreciation were satisfactory. But at the same time, the

investor has foregone other investment opportunities when she selected this investment. So

we need to measure the opportunity cost of equity capital, i.e., the benefit foregone by the

investor when he chose to invest in a particular firm.

(a) Dividend Discount Model Approach

Dividend discount model is designed to compute the intrinsic value of an equity share.

According to the dividend discount approach, the intrinsic value of an equity stock is equal to

the sum of the present values of the expected dividends associated with it, i.e.

∑= +

=n

tt

e

te k

DP1 )1(

Where, eP = Price per equity share

tD = Expected dividend per share at the end of year one

ek = Rate of return required by the equity shareholders

If we know the current market price ( eP ) and can forecast the future stream of dividends, we

can determine the rate of return required by the equity shareholders ( ek ) using the above

equation which is nothing but the cost of equity capital.

In practice, the model suggested by the above equation cannot be used in the given form

because it is not possible to forecast the dividend stream accurately over the life of the firm.

Therefore, the growth in dividends can be categorized as nil or constant growth or

supernormal growth and the above equation can be modified accordingly.

(b) Security Market Line (SML) Approach

Security market line is the line that we get when we plot the relationship between the required

rate of return ( iR ) and non-diversifiable risk (beta). This line describes the relationship

between systematic risk and expected return in financial markets. As per capital assets pricing

model (CAPM) assumption, any individual security’s expected return and beta statistics

should lie on the SML. The SML intersects the vertical axis at the risk-free rate of return fR

and mR - fR is the slope of the SML.

According to this approach, the rate of return required on a security is given by the following

equation:

)( fmifi RRRk −+= β

Where, ik = Rate of return required on security i

fR = Risk-free rate of return

iβ = Beta of security i

mR = Rate of return on market portfolio

(c) Bond Yield Plus Risk Premium Approach

The logic behind this approach is that the return required by the investors is directly based on

risk profile of the security. The risk born by the equity investors is higher than that borne by

the bondholders or preference shareholders, therefore, the rate of return required by them

should also be higher. Hence, the required rate of return on equity capital can be calculated

as: Required rate of return = Yield on the long-term bonds of the company + Risk

premium

This risk premium is arrived at after considering the various operating and financial risk

faced by the firm.

4.4 Weighted Average Cost of Capital (WACC)

Weighted average cost of capital (WACC) is defined as the weighted average of the cost of

various sources of finance, weights being the market values of each source of finance

outstanding.

Assuming that there are only two sources of financed used by the firm, the WACC can be

calculated as follows:

WACC = Cost of equity x Proportion of equity in the financing mix + (Post – Tax) Cost of

debt x Proportion of debt in the financing mix

(1 )e e d dk w k t w= + −

(1 )e dE Dk k t

D E D E⎛ ⎞ ⎛ ⎞= + −⎜ ⎟ ⎜ ⎟+ +⎝ ⎠ ⎝ ⎠

4.5 Hybrid Securities

Equity represents a residual claim on the firm’s cash flows and assets and is generally

associated with management control. Debt, on the other hand, represents a fixed claim on the

firm’s cash flows and assets and is usually not associated with management control. There

are a number of financing choices that do not fall neatly into either of these two categories;

rather, they share some characteristics with equity and some with debt. These financing

choices, which we discuss next, are called hybrid securities.

Convertible Debt

A convertible bond is a bond that can be converted into a predetermined number of shares of

the common stock, at the discretion of the bondholder. Although it generally does not pay to

convert at the time of the bond issue, conversion becomes a more attractive option as stock

prices increase. Firms generally add conversion option to bonds to lower the interest rate they

pay on the bonds.

The Conversion Option: In a typical convertible bond, the bondholder is given the option to

convert the bond into a specified number of shares of stock. The conversion ratio is the

number of shares of stock for which each bond may be exchanged; the market conversion

value is the current value of the shares for which the bonds can be exchanged. The

conversion premium is the excess of the bond value over its conversion value.

Thus, a convertible bond with a face value of Rs. 1,000, which is convertible into 50 shares

of stock, has a conversion ratio of 1:50. The conversion ratio can also be used to compute a

conversion price – the face value of the convertible bond divided by the conversion ratio –

yielding a conversion price in this example of Rs. 20. Now, if the current stock price is Rs.

25, the market conversion value is 50*Rs. 25, or Rs. 1,250. If the convertible bond is trading

at Rs. 1,300, the conversion premium is Rs. 50. In other words, since the bond has the

sweetener of convertibility, it is being traded at a premium of Rs. 50.

Determinants of Value: The conversion option is a call option on the underlying stock; its

value is therefore determined by the variables that affect call option values: the underlying

stock price, the conversion ratio (which helps determine the strike price), the life of the

convertible bond, the variance in the stock price, and the level of interest rates. Like call

option, the value of the conversion option will increase with the price of the underlying stock,

the variance of the stock, and life of the conversion option; it will decrease with the exercise

price (determined by the conversion option).

When the riskiness of a firm increases, the value of the convertible bond is affected in two

ways. The higher risk will decrease the value of the straight bond portion, while increasing

the value of the conversion option. These offsetting effects mean that convertible bonds will

be less exposed to changes in the firm’s risk than are other types of securities.

The value of a convertible bond is also affected by a feature shared by most convertible

bonds, which allows for adjustment of the conversion ratio (and price) if the firm issued new

stock below the conversion price or has a stock split or dividend. In some cases, the

conversion price has to be lowered to the price at which new stock is issued. This is designed

to protect the convertible bondholder from misappropriation by the firm.

A Simple Approach to separating Debt and Equity: A convertible bond is a combination

of two securities. One security is a straight bond, with a stated face value, coupons, and

maturity; this option is debt. The other security is an option to buy equity in the firm; this

conversion option is equity. The value of each component is determined by different factors.

The value of the straight bond portion, like all debt, increases as interest rates and default risk

declines. The value of the conversion option, like all equity options, increases as the stock

price increases and becomes more volatile.

The value of a convertible debt can be separated into straight debt and equity components

using a simple approach. Because the price of a convertible bond is the sum of the straight

debt and the call option components, the value of the straight bond component in conjunction

with the market price should be sufficient to estimate the call option component, which is

also the equity components.

Value of the conversion option = price of convertible bond – value of straight bond

component.

The value of the straight bond component can be estimated using the promised coupon

payments on the convertible bond, the maturity of the bond, and the market interest rate the

company would have to pay on a straight debt issue. This last input can be estimated directly

if the company also has straight bonds outstanding, or it can be used on the bond rating, if

any, assigned to be company.

Why do we need to separate convertible debt into debt and equity components? By adding

the debt component to the other debt that the firm has, and the equity component to the

remaining equity, we can measure the firm’s debt ratio more precisely and estimate its cost of

capital.

Illustration 1.

As of today, i.e. 1st Jan 2002, ABC Ltd. has Rs. 2 crore worth of secured debt issued at 9 per

cent p.a., convertible debentures with face value of Rs. 1 crore issued at 8 per cent p.a. in Jan

2000 and would mature in Jan 2005 (between this it can be converted at any time). Each bond

has a face value of Rs. 1000 and is convertible into 20 shares when exercised. The instrument

is rated A+ and straight bonds with similar maturity yield 10 per cent p.a. Find the weighted

average cost of capital of ABC if its cost of equity is 18 per cent and it has 3 crore worth of

equity. The company falls in the 30 per cent tax bracket.

To find WACoC one will have to first find the bond and equity components.

To find the straight bond component:

The total straight bond value of the Rs. 1 crore in convertible bonds can then be estimated as

follows:

Total Straight Bond Value of Convertible Bonds = =Rs.95 lakhs

Since the convertible bond is a combination of the straight bond and the conversion option,

and the price of the convertible bond is known, the conversion option can be valued:

Conversion Option = Price of Convertible Bond – Value of Straight Bond

= Rs.1,250 – Rs. 950 = Rs. 300

The total value of the conversion option is then = = = Rs. 30 lakhs

Once the convertible bond has been broken up into straight bond and conversion option

components, their values can be used to calculate the debt and equity components of the

convertible bonds outstanding.

Thus, the WACoC is given by 2.95 3.30*9%*(1 .30) *18% 12.48%6.25 6.25

⎛ ⎞ ⎛ ⎞− + =⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

Why Do Companies Issue Convertible Debt? Some firms issue convertible bonds because

they believe it is cheaper for them to borrow using convertible debt than to issue straight

debt. If by cheaper, the implication is that the interest rate on the convertible debt will be

lower than the interest rate on straight debt, this is true. There is, however, a good reason why

the coupon rate on convertible debt is lower. The firm is packaging a valuable equity option

3

31

.80 .1,000PV of Bond = .950(1.1) (1.1)

t

tt

Rs Rs Rs=

=

+ =∑

100,00,0001,000

⎛ ⎞⎜ ⎟⎝ ⎠

*Rs. 950

100,00,0001,000

⎛ ⎞⎜ ⎟⎝ ⎠

*Rs. 300

with the straight debt to create the convertible debt, and it is the value of the option that is

pushing down the stated interest rate on the debt. If the conversion option is fairly priced,

there is no cost advantage to issuing convertible debt instead of straight debt.

There are some good reasons for firms to issue convertible bonds. First, convertible debt

provides an attractive alternative to straight debt for high-growth companies that do not

currently have high operating cash flows. The high growth and risk combine to increase the

value of the conversion option, which, in turn, pushes down the interest rate and reduces the

coupon payment and cash outflow for the firm. This is confirmed by studies. One study by

Jen, Choi, and Lee (1997) found that market react more positively to convertible issues by

highly levered and high-growth firms. Second, convertible debt is one way of reducing the

conflict between equity and debt holders in a firm. Equity investors, by taking on riskier

projects and new debt, can make existing bondholders worse off. If they do so with

convertible debt, debt holders can always exercise their conversion options and become

equity investors, thus removing themselves as a target for such actions.

Numericals 1. Neelkamal Ltd., a manufacturer of consumer plastic products, is evaluating its capital

structure. The balance sheet of the company is as follows (in millions):

Assets Liabilites

Fixed Assets Rs 4,000 Debt Rs. 2,500

Current Assets Rs.1,000 Equity Rs. 2,500

In addition, you have the following information:

• The debt is in the form of long-term bonds, with a coupon rate of 10 per cent. The

bonds are currently rated AA and are selling at a yield of 12 per cent (The market

value of the bonds is 80 per cent of the face value).

• The firm currently has 50 million shares outstanding, and the current market price is

Rs. 80 per share. The firm pays a dividend of Rs. 4 per share and has a

price/earnings ratio of 10.

• The stock currently has a bets of 1.2. The treasury bond rate is 8 per cent.

• The tax rate for this firm is 40 per cent.

a. What is the debt/equity ratio for this firm in book value terms? In market value

terms?

b. What is the firm’s after-tax cost of debt?

c. What is the firm’s cost of equity?

d. What is the firm’s current cost of capital?

2. Now assuming that Neelkamal is considering a project that requires an initial investment

of Rs. 100 million and has the following projected income statement:

EBIT Rs. 20 million

-Interest Rs. 4 million

EBT Rs.16 million

-Taxes Rs.6.40 million

Net Income Rs.9.60 million

(Depreciation for the project is expected to be Rs. 5 million a year forever.)

This project is going to be financed at the same debt/equity ratio as the overall firm and is

expected to last forever. Assume that there are no principal repayments on the debt. (it too is

perpetual)

a) Evaluate this project from the equity investors’ standpoint. Does it make sense?

b) Evaluate this project form the firm’s standpoint. Does it make sense?

c) In general, when would you use the cost of equity as your discount

rate/benchmark?

d) In general, when would you use the cost of capital as your benchmark?

e) Assume, for economies of scale, that this project is going to be financed entirely

with debt. What would you use as your cost of capital for evaluating this project?

3. You have been asked to calculate the debt ratio for a firm thaqt has the following

components to its financing mix:

a. The firm has 1 million shares outstanding trading at Rs. 50 per share.

b. The firm has Rs. 25 Million in straight debt, carrying a market interest rate of 8 per cent

for a period of 10 years.

c. The firm has 20,000 convertible bonds outstanding with a face value of Rs. 1,000 a market

value of Rs. 1,100 and a coupon rate of 5 per cent issued for 10 years.

4. A company is trying to estimate its debt ratio. It has 1 million shares outstanding trading at

Rs. 50 per share and it had Rs. 250 million in straight debt outstanding (with a market interest

rate of 9 per cent.) It also has two other securities outstanding:

(i) It has 200,000 warrants outstanding, conferring on its holders the right to buy stock in the

company at Rs. 65 per share. These warrants are trading at Rs. 12 each.

(ii) It also has 10,000 convertible bonds outstanding with a coupon rate of 6 per cent, Face

value of Rs. 1000 and 10 years to maturity.

Chapter 2: Capital Structure Theory

An Important goal of corporate finance is to help manager’s sources funds to undertake

investments. Even in the absence of new investment opportunities, firms can issue new

securities and use the funds to repay debt or reproduce shares. Capital structure theories seek

to explain how the financing mix is to be determined. The present chapter classifies these

theories in to three broad categories.

a) Early theories

b) Capital structure theories under perfect capital market conditions.

c) Capital structure theories in the present of taxes and transactions costs.

d) Capital structure theories under asymmetric information.

2.1 Early theories This chapter defines early theories as (i) The net income approach, (ii) net operating income

approach and (iii) the traditional approach to deciding on the optimal capital structure. The

three approaches differ as to their assumptions regarding what happens to the cost of debt and

equity as the firm levers.

2.1.1 The Net Income (NI) Approach The essence of the net income approaches is that the firm can lower its cost of capital by

using debt. The approach is based on the crucial assumption that neither creditors nor

stockholders perceive that increased borrowing adds to their risks, so the firm's cost of debt

and cost of equity remain constant regardless of its level of debt.

Consequently, the interest rate on debt (Kd) and the equity capitalization rate (Ke) remain

constant to debt. Therefore, the increased use of debt, lowers the overall cost of capital (Ka)

for the firm, which results in higher market value of shares. Ka can be measured as:

Ka=Ke-(Ke-Kd) D/V (1)

Where D is market value of debt and V is total market value of the firm. Thus, the NI

approach recognizes that there exists an optimum capital structure, which is reached when the

cost of capital is lowest. This optimal capital structure is reached when the firm is financed

100 per cent by debt as shown in figure 1.

Example: Company A is funded by Rs. 9000 worth of debt carrying a interest obligation of 5

per cent. With EBIT of Rs. 3000 and cost of equity of 10 per cent find the WACoC and the

market price per share for this company. Company B has the same capital requirement, but is

funded with Rs. 18,000 worth of debt and has issued 1650 shares of Rs. 10 each. Now find

the WACoC of this company too and also its Market price. Compare the two results.

2.1.2 The Net Operating Income Approach

The net operating income approach contends that capital structure does not matter, and that

the firm cannot affect its overall cost of capital through leverage. Like the net income

approach, this approach also assumes that creditors do not react to increased debt levels.

However, unlike Net Income approach, in the present approach, equity investors do react to

increased levels of debt. As a firm takes more debt, equity investors, in order to compensate

for the increased financial risk, increase their expected returns. This increase, in the absence

of taxes, cancels out any benefit derived from the use of debt, and the average cost remains

unchanged. For example, Ke can be defined as follows:

Ke=Ka+(Ka-Kd) D/E (2) Where D/E is debt-equity ratio at market values. Equation (2) indicates that, if Ka and Kd are

constant, Ke would increase linearly with debt-equity ratio, D/E . Thus, there is no single

point or range where the capital structure is optimum. The NOI approach is shown in Fig. 2.

Ka

D/V

Ke

kd

k

Example 2: A firm has a EBIT of Rs. 900,000. The firm is financed by debt to the tune of

Rs. 40,00,000 raised at 7.5 per cent p.a. The weighted average cost of capital is 10 per cent.

Find the present cost of equity and the cost of equity when the debt is increased to 50,00,000.

Example 3.: Calculate the cost of equity in the two alternatives given in example 1 following

net operating income approach.

2.1.3 The Traditional View This approach assumes that both creditors and stockholders perceive that increased

borrowing adds to their risks. As a firm increases its debt ratio, both its cost of debt and cost

of equity increase. As the leverage increases, initially, the cost of debt remains constant but

increased leverage leads to financial risk, the Ke will increase. However, during this phase,

the increase in Ke is lower than the decrease in Ka (debt being cheaper than equity). As the

firm levers further, a stage will come that the Kd will change. At this juncture, the Ka also

starts increasing. Thus the theory says that there does exist an optimal capital structure.

The actual location of the optimum leverage point or rang for any given firm will vary with

the amount of business uncertainty involved in its operations and with the attitude of the

capital markets towards this uncertainty. This in turn is made up of the composite of

expectation with regard to a company’s product markets and prices, the fixity of its costs, the

liquidity and marketability of its assets, and the opinion of market with respect to the firm’s

management. AS far as those elements of instability and uncertainty are concerned, a firm is

likely to resemble other firms in the same industry. But inter industry differences are likely to

be significant. Because of this each industry group can be expected to have a different

optimum range as far as leverage is concerned.

D/V

k Ke

kd

Ka

2.2 Capital Structure Theories under Perfect Capital

Market Conditions The following are the characteristics of a perfect capital market: (i) There are no costs

incurred in making transactions in any market. In particular, there are no information costs,

brokerage fees, distress costs or other costs associated with the purchase or sale of securities

or other assets. (ii) There is perfect information available to all market participants who share

the common objective of utility maximization.

Note that we assume not only that securities can be bought and sold costlessly but that the

firm’s real assets can also be purchased or sold with no transactions costs. The inclusion of

the market for real productive assets is important because in the event of a firm’s failure, its

assets can be sold without penalty in the secondary market.

2.2.1 The Modigliani & Miller (MM) Hypothesis

MM, supporting the net operating income approach, argue that under certain circumstances,

the total market value and the cost of capital of a firm remain invariant to changes in capital

Cos

t (pe

r cen

t)

O

Kd

L D/V

Ke

Ka

L̂

structure. Though MMs conclusion are the same as those of the Net operating income

approach, the way they reached their conclusion was very different.

Their theory is based on the following assumptions.

i) Perfect capital market conditions: (a) Investors are free to buy or sell securities,

(b) Individuals can borrow at the same terms as institutions from the capital

market; (c) Investors behave rationally and (d) Absence of transaction costs.

ii) Firms can be grouped into homogenous risk classes

iii) Firms distribute all their profit to shareholders

iv) Investors have homogenous expectations about the future operating performance

of the firms.

v) Absence of taxes.

vi) All cash flows are perpetuities

The MM hypothesis can best the expressed in terms of their two propositions.

Proposition 1: Financial leverage does not impact firm value

Given that the market for bonds and stocks yield annual returns of dr and er respectively,

individuals would try to maximize the returns of their investment and corporations would try

to maximize their market values.

Say there are many individuals who make savings in the current period is . Let their current

and future incomes & consumption be im and ioc , 1ic respectively.

Therefore, iioio smc −=

The individual must now decide how to allocate the is dollars between bond ( ib ) and stock

( ie ) investments. The choice is made by maximizing the utility of a given consumption

stream, which implies maximizing the end of period wealth iw , for a given savings decision:

Maximize 1 (1 ) (1 )i d i e iw r b r e= + + +

With the following constraints:

1. Savings must be allocated between bonds and equities

2. Equity cannot be short sold

3. If bonds are issued, they cannot exceed the present value of the individuals wealth

1

1i

i io iod

mb m wr

⎡ ⎤≤ + =⎢ ⎥+⎣ ⎦

∴ his next period consumption can be defined as

1 (1 ) (1 )io i d i e ic m r b r e= + + + +

Now if d er r> then the individual will save by buying only bonds, while if e dr r> the

individual will invest in equity only. Consequently the individual’s supply of funds to the

bond market can be depicted as

Where is denotes the individuals savings when d er r= Over the entire range where d er r= ,

the supply of funds.

Corporate financing decision and demand for funds in the market

Let jjL

j EBV += denote the value of securities issued by a (levered) corporation j, where

jB is the value of the firms debt and jE is the value of its equity.

Now, let jX depict the corporation’s earnings for the period. The value of the firm’s equity

can then be written as:

- 0 1

(1 )i i

e

m mr

⎡ ⎤+⎢ ⎥+⎣ ⎦

is ib

tr

dr

is

(1 )

(1 )J d j

JE

X r BE

r− +

=+

Thus, the value of the levered firms can be expressed as

(1 ) 11

1 (1 ) 1J d j j d

J j je e e

X r B X rV B Br r r

− + ⎡ ⎤+= + = + −⎢ ⎥+ + +⎣ ⎦

Thus, it can be seen that a corporation’s demand for funds via sale of bonds is perfectly

elastic so long as e dr r= . And when e dr r= the value of the levered firm is equal to the value

of the unlevered firm.

1

jL Uj j

e

XV V

r= =

+

If L uj jV V≠ , then there will be a arbitrage opportunity.

To illustrate the arbitrage process, assume there are 2 otherwise identical firms (i.e., with the

same total future each flows from assets) one unlevered ‘U’ and one levered ‘L’. Since the

expected returns from both firms are same their values LU VV & should also be the same. If

the market values of the two firms are not equal Lu VV ≠ , the arbitrageur would sell the

overvalued firm, borrow additional funds on personal account and invest in the undervalued

firm in order to obtain the same return.

Say uL VV > and the arbitrageur hold α proportion of the levered firm’s equity LS . She could

sell his stake in the levered firm and borrow equivalent to α proportion of the levered firm’s

debt LD at the same rate as the firm, say and acquire α proportion of stake in the

unlevered firm.

The value of the new investment ∴is ( )u L u LV D V Dα α α− = − and the returns are

( )L Lx D x Dα α α− −

− = − which is what she would have got if she had stayed put with his α

proportion investment in the levered firm.

In the process she makes arbitrage gain of )( jL VV −α .As a result of such actions the price of

the levered firm decreased but note this actions will not increase the price of the unlevered

firm.

Now say Lu VV > , then the arbitrage would work in the opposite direction. Say an investor

holds α proportion of stocks in the unlevered firm. If Lu VV > the investor would sell the

stocks and acquire α proportion of the levered firms debt and equity.

Therefore his investment is LVα & his returns −

=+− xDDx LL ααα )(_

which is what she

used to get in his earlier investment in the unlevered company’s stocks and in the process she

makes a arbitrage profit of )( Lu VV −α . The said proof, is sometimes also called “home

made” leverage where investors use leverage in their own portfolios to adjust the leverage

choice made by the firm.

Illustration: Homemade Leverage

MM showed that the firm’s value is not affected by its choice of capital structure. But

suppose investors would prefer an alternative capital structure to the one the firm has chosen.

MM demonstrated that in such a case, investors can borrow or lend on their own and achieve

the same result. For example, an investor who would like more leverage than the firm has

chosen can borrow and add leverage to his or her own portfolio. When investors use leverage

in their own portfolios to adjust the leverage choice made by the firm, we say that they are

using homemade leverage. As long as investors can borrow or lend at the same interest rate

as the firm1 homemade leverage is a perfect substitute for the use of leverage by the firm.

To illustrate, suppose the entrepreneur uses no leverage and creates an all-equity firm. An

investor who would prefer to hold levered equity can do so by using leverage in his own

portfolio- that is, she can buy the stock on margin, as illustrated in Table 2.1.

1 This assumption is implied by perfect capital markets because the interest rate on a loan should depend only on its risk.

Table 2.1: Replicating Levered Equity Using Homemade Leverage

Date 0: Cash Flows

(in Rs.)

Date 1: Cash Flows

(in Rs.)

Initial Cost Strong Economy Weak Economy

Unlevered equity 1000 1400 900

Margin loan - 500 - 525 - 525

Levered equity 500 875 375

If the cash flows of the unlevered equity serve as collateral for the margin loan, then the loan

is risk-free and the investor should be able to borrow at the 5 per cent rate. Although the firm

is unlevered, by using homemade leverage, the investor has replicated the payoffs to the

levered equity illustrated in Table 2.2, for a cost of Rs. 500. Again, by the Law of One Price,

the value of levered equity must also be Rs. 500.

Now suppose the entrepreneur uses debt, but the investor would prefer to hold unlevered

equity. The investor can recreate the payoffs of unlevered equity by buying both the debt and

the equity of the firm. Combining the cash flows of the two securities produces cash flows

identical to unlevered equity, for a total cost of Rs 1000, as we see in Table 2.2.

Table 2.2: Replicating Unlevered Equity by Holding Debt and Equity

Date 0: Cash Flows

(in Rs.)

Date 1: Cash Flows

(in Rs.)

Initial Cost Strong Economy Weak Economy

Debt 500 525 525

Levered equity 500 875 375

Unlevered equity 1000 1400 900

In each case, the entrepreneur’s choice of capital structure does not affect the opportunities

available to investors. Investors can alter the leverage choice of the firm to suit their personal

tastes either by borrowing and adding more leverage or by holding bonds and reducing

leverage. With perfect capital markets, because different choices of capital structure offer no

benefit to investors, they do not affect the value of the firm.

Homemade Leverage and Arbitrage

Problem

Suppose there are two firms, each with date 1 cash flows of Rs. 1400 or Rs. 900 (as in Table

2.1). The firms are identical except for their capital structure. One firm is unlevered, and its

equity has a market value of Rs. 990. The other firm has borrowed Rs. 500, and its equity has

a market value of Rs. 510. Does MM Proposition I hold? What arbitrage opportunity is

available using homemade leverage?

Solution

MM Proposition I states that the total value of each firm should equal the value of its assets.

Because these firms hold identical assets, their total values should be the same. However, the

problem assumes the unlevered firm has a total market value of 990, whereas the levered

firms has a total market value of 510 (equity) + 500 (debt) = 1010. Therefore, these prices

violate MM Proposition I.

Because these two identical firms are trading for different total prices, the Law of One Price

is violated and an arbitrage opportunity exists. To exploit it, we can borrow Rs. 500 and buy

the equity of the unlevered firm for Rs. 990, re-creating the equity of the levered firm by

using homemade leverage for a cost of only 990 – 500 = 490. We can then sell the equity of

the levered firm for 510 and enjoy an arbitrage profit of 20.

Date 0 Date 1: Cash Flows

Cash Flow Strong Economy Weak Economy

Borrow 500 - 525 -525

Buy unlevered equity - 990 1400 900

Sell levered equity 510 - 875 - 375

Total cash flow 20 0 0

Note that the actions of arbitrageurs buying the unlevered firm and selling the levered firm

will cause the price of the levered firm’s stock to fall until the firm’s values are equal and

MM Proposition I holds.

2.3 Modigliani & Miller Corporate Tax Corrected Model

Earlier we saw that according to MM in the absence of taxes and under certain conditions the

value of a firm is independent of the way it is financed and the value of its equity is

(1 )

(1 )j d j

je

x r BE

r− +

=+

Now, say the corporations are taxed at a rate tc and the interest on debt is tax deductible. The

corporation’s taxable income now becomes ( )j d jx r B− and the value of its equity will be

(1 ) ( )

(1 )j d j j d j c

je

x r B x r B tE

r− + − −

=+

(1 ) (1 (1 ))

(1 ) (1 )j c j d c

e e

x t B r tr r− + −

= −+ +

And the value of the levered firms is jjj EBV +=

Hence,

(1 ) 1 (1 )11 1j c d c

j je d

x t r tV Br r− ⎡ ⎤+ −

= + −⎢ ⎥+ +⎣ ⎦

In the above equation when d er r=

(1 )

1 1j d c j

je d

x tc r t BV

r r−⎡ ⎤

= +⎢ ⎥+ +⎣ ⎦

Value of the unlevered Value of interest tax shield Firm

Note that above model is a single period version of Modigliani and Miller (1963) tax

corrected model when d er r= . What we can see is that there does exist tax benefit due to

leverage and hence the optimal capital structure for most firms in such as economy would

gravitate towards 100 per cent debt. Consequently the demand for debt in the market will

increase and with constant supply (because there is no treatment so far for personal taxes) the

interest rates must rise. As shown in the figure below, the equilibrium interest rate will be

achieved when 1

ed

c

rrt

=−

Substituting (1 )d e cr r t= − is

(1 ) 1 (1 )11 1j cL d c

j je e

x t r tV Br r− ⎡ ⎤+ −

= + −⎢ ⎥+ +⎣ ⎦ we get

(1 )1j cL u

j je

x tV V

r−

= =+

Thus, under conditions of market equilibrium the tax saving advantage of debt financing is

driven to zero. Hence, MM show that even in the presence of corporate taxes, capital

structure is irrelevant.

/(1 )e cr t−

er

dr

S

D

2.4 Personal taxes and the Miller Model (1977)

Say bond interest income is taxed at the rate tp and equity income is not taxed. According to

Miller (1971) even in such a market where you have corporate tax (tc) and personal tax on

interest income from debt investment (tp), capital structure does not affect firm value.

We saw earlier that in the absence of taxes the equilibrium interest rate is d er r= . Further, in

the presence of corporate taxes, the demand for debt would increase and so would the cost of

debt. As a result the equilibrium rate of interest now becomes /(1 )e cr t− .

Now, in the presence of personal tax on debt income, corporations would have to compensate

investors for their tax liability. Hence, to compensate investors the rate of return offered now

must be /(1 )e pr t− . Since different investors would fall in different tax brackets, the

corporation would first issue debt to investors whose interest income is not taxed (tp=0) and

then it will increase the rate of interest depending upon the tax bracket in which the investor

will fall.

Since the corporate demand for bond funds is the same as that already derived for the case

with corporate taxes, we can now consider the bond market equilibrium under both personal

Br

S

D

b, B

/(1 )e pr t−

/(1 )e cr t−

and corporate taxes. The equilibrium rate of interest is again /(1 )d e cr r t= − . Hence, it can be

said that a firm can attract debt investors till tp<tc; if tp>tc investors would prefer to invest in

equities.

Earlier we saw that the gain from leverage is

*(1 ) 1 (1 )1

1 1j cL d c

j je e

x t r tV Br r− ⎡ ⎤+ −

= + −⎢ ⎥+ +⎣ ⎦

If we substitute at equilibrium bond rate

* /(1 ) /(1 )d e p e cr r t r t= − = − , we get

uj

Lj VV =

Thus, market equilibrium conditions in the bond market (even in the presence of personal &

corporate taxes) produces conditions under which the firm’s capital structure choice is a

matter of indifferences to its owners.

Including Personal taxes in valuation of Interest tax shield

Say tpd & tpe denote the personal tax on debt and equity income respectively. And tc denote

corporate tax rate. Therefore, the after tax cash flows for every Re.1 of pretax cash flow to

debt holders and equity holders is given by (1-tpd) and (1-tc) (1-tpe) respectively.

Under these circumstances, through there may be a tax advantage due to issuing debt, it may

not be the same as when there was only corporate tax.

Say tc = 35 per cent tpd=35 per cent and tpe=15 per cent. In this case the equity holders receive

less after tax cash flows as compared to debt holders.

* (1 ) (1 )(1 ) (1 )(1 )1

(1 ) (1 )pd c pe c pe

pd pd

t t t t tt

t t− − − − − −

= = −− −

= %1565.0

525.065.0=

−

When there are no personal taxes t*=tc. But when equity income is taxed LESS HEAVILY

(td>tpe) then T* is less than Tc. However, as long as T*>0, then despite any tax disadvantage of

debt at personal level, the value of the firm with leverage becomes:

*L uV V t D= +

Because of the personal tax disadvantage of debt, WACoC will decline more slowly with

leverage than it would otherwise would.

2.5 Asset Pricing under Asymmetric Information

2.5.1 Privately-known-Prospects Model A borrower/entrepreneur has no funds (A=0) to finance a project costing I. The project yields

a return of R in the case of success and 0 in the case of failure. The borrower and the lenders

are risk neutral, and the borrower is protected by limited liability. The interest rate in the

economy is normalized at 0.

The borrower can be one of two types. A good borrower has a probability of success equal to

p. A bad borrower has a probability of success q. Assume that p > q and that pR > I ( at least

the good type is creditworthy). There are two subcases, which we will treat separately:

Either pR > I > qR

(only the good type is creditworthy).

Or pR > qR > I

(both types are creditworthy).

The borrower has private information about her type. The capital market, which is

competitive and demands an expected rate of return equal to 0, puts probabilities α and 1 - α

on the borrower being a good or bad type, respectively. Under asymmetric information, the

capital market does not know whether it faces a “p-borrower” (a good borrower) or a “q-

borrower” (a bad borrower). Let m = αp + (1-α) q denote the investors prior probability of

success.

Market Breakdown and Cross-Subsidization

1. Symmetric Information

To set a benchmark, first consider financing when the investors know the project’s

prospects. The good entrepreneur obtains financing. One optimal arrangement for her is

to secure the highest level of compensation, GbR in the case of success, consistent with

investors’ breaking even on average:

IRRp Gb =− )(

If qR < I, the bad borrower does not want to invest because, under symmetric

information, she would receive the NPV, qR – I < 0 if she could secure funding. Besides,

she cannot obtain financing anyway because the pledgeable income, qR, is smaller than

the investor’s outlay, I.

If qR > I, then the bad borrower received funding and secure compensation BbR in the

case of success, where

.)( IRRq Bb =−

Clearly,

.Gb

Bb RR <

2. Asymmetric Information

The symmetric information outcome, however, is not robust to asymmetric information, as

the bad borrower can, by mimicking the good borrower, derive utility GbqR that is greater

than that (either 0 or BbqR ) she obtains by revealing her type.

Let us assume that the only feasible financial contracts are contracts that give the borrower a

compensation 0≥bR in the case of success and 0 in the case of failure. Such contracts

necessarily pool the two types of borrower as each prefers receiving financing to not being

funded, and conditional on being funded, prefers contracts with a higher compensation. The

investor’s profit for such a contract is therefore on average:

IRRmIRRqp bb −−=−−−+ )()]()1([ αα

No lending: mR < I. This case can arise only if the bad borrower is not creditworthy. It then

arises whenever the probability that the borrower is a bad borrower is large enough, or

,*αα <

Where, 0))(1()( ** =−−+− IqRIpR αα

Because the borrower cannot receive a negative compensation ( 0≥bR ), investors lose

money if they choose to finance the project. Accordingly they do not and the market breaks

down. The good borrower is therefore hurt by the suspicion that she might be a bad one.

There is under investment.

Lending: 1≥mR . This case corresponds either to the situation in which both types are

creditworthy or to that in which the bad borrower is not creditworthy but .*αα ≥ The

borrower’s compensation bR is then set so that the investors break even on average.

.)( IRRm b =−

This implies that, ex post, investors make money on the good type ))(( IRRp b >− and lose

money on the bad type ))(( IRRq b <− : there is cross-subsidization.

Note also that

Gbb RR <

(and Bbb RR > if the bad borrower is creditworthy). The good borrower is still hurt by the

presence of bad ones, although to a lesser extent than when the market breaks down. The

good borrower must content herself with a lower compensation (i.e., a higher cost of capital)

in the case of success than under symmetric information. Put differently, and interpreting the

investor’s share as a risky loan with nominal interest rate r such that ,)1( IrRR b +=− then

,Grr > where Gr is the rate of interest that the good borrower could obtain under symmetric

information: IrRR GGb )1( +=− .

How much discount is suffered by the good borrower?

ImR ≥

Can be rewritten as

IpRp

qp≥⎥

⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛ −−− )1(1 α

We can thus define an index of adverse selection:

(1 ) .p qp

χ α⎛ ⎞−

≡ − ⎜ ⎟⎝ ⎠

In the absence of signaling possibility, the good borrower’s pledgeable income, pR, is

discounted by the presence of bad borrowers. The discount is measured by the product of the

probability of bad types, 1-α, times the likelihood ratio, (p-q)/p.

2.5.2 Pecking-Order Hypothesis

An important theme in corporate finance is that adverse selection calls for the issuance of

debt claims. As we discussed in the introduction, Myers (1984) and Myers and Majluf (1984)

have formulated a pecking-order hypothesis that places debt as the preferred source of

external financing. Recall that these authors argue that sources of financing can be ranked

according to their information intensity, from low to high information intensity: (1) Internal

finance (entrepreneur’s cash, retained earnings), (2) debt, (3) junior debt, convertibles, and

(4) equity.

The pecking-order hypothesis is based on the investor’s concern about the value of the claim

they acquire. It is clear, for example, that default-free debt creates no concern for investors as

to the value of their claim. We first provide conditions under which debt is indeed the

preferred source of financing under asymmetric information about the firm’s prospects, and

then discuss the robustness of the pecking-order hypothesis.

There is no distinction between debt and equity claims when the profit is either R or 0. Let us

therefore add a salvage value of the assets RF : the profit in the case of failure is RF > 0 and

that in the case of success is Rs = RF + R, where R still denotes the profit increment. Except

for the introduction of a salvage value, the model is otherwise that of section 2.5.1: there are

no assets in place. The investment cost I must be entirely defrayed by the investors. The

probability of success is p for a good borrower (probability α) and q for a bad one

(probability 1- α). The prior mean probability of success is m≡αp + (1-α)q

Let us assume that

IRmmR Fs >−+ )1(

and so there is enough pledgeable income to secure funding even when the bad borrower

pools with the good one.

Let { }Fb

Sb RR , denote the (nonnegative) rewards of the borrower in the cases of success and

failure. Assuming that the borrower receives funding, the investor’s breakeven condition is

.))(1()( IRRmRRm Fb

FSb

s ≥−−+−

The good borrower maximized her expected payoff.

Fb

Sb RppR )1( −+

subject to the breakeven constraint. At the optimum, the investor’s breakeven condition is

satisfied with equality. It can be rewritten as

.))]()(1(1[))]()(1([ IRRqppRRqpp Fb

FSb

S =−−−+−+−−−− αα

The good borrower’s utility is then equal to Fb

Sb RppR )1( −+ )]())[)(1(])1([ F

bFS

bSFS RRRRqpIRppR −−−−−−−−+= α

On the right-hand side of this equality, the first term in brackets represents the NPV of the

good borrower, namely, what she would receive under symmetric information. The second

term as usual refers to the adverse-selection discount.

The good borrower wants to minimize this discount while satisfying the investor’s breakeven

constraint. Because the discount increases with FbR and decreases with ,S

bR the good

borrower sets

0=FbR

Then, ,SbR is determined by the investor’s breakeven constraint:

IRmRRm FSb

S =−+− )1()(

To sum up this analysis, the borrower commits the entire salvage value as safe debt issued to

investors. The borrower further issues risky equity with stake Sb

S RR − in the case of success

( and 0 in the case of failure) so as to make up for the shortfall in pledgeable income:

.)( FSb

S RIRRm −=−

Thus, the firm first issues safe debt with a debt obligation D given by

,FRD =

and, second, supplements the capital thus raised through an equity issue entitling shareholders

to a fraction R1/R of profits in excess of RF, where

DImR −=1 ,

Note that the borrower must issue more equity, the more acute the adverse-selection problem

(the lower m is) or the higher the investment cost.

Intuitively, the borrower starts by issuing the claim that is least exposed to adverse selection,

here the safe-debt claim. Doing so allows the good borrower to minimize the cross-

subsidization with the bad borrower. The more sensitive the investors’ claim to the

borrower’s private information, the higher the return that the investors demand from a good

borrower to make up for the money they lose on the bad one.

Alternative Ways to Signal i) Certification

As we have seen, adverse selection in general leads to cross-subsidization or market

breakdown, which are costly to good borrowers or issuers. Therefore, good issuers

have an incentive to try to mitigate the investor’s informational disadvantage. The

asymmetry of information can be reduced through disclosure to investors of

information about the firm’s prospects.

Lending by an informed party (whether a bank, a peer, or a trade creditor) is a signal

that the informed party is confident about the possibility of repayment. Such

“informed lending” is therefore likely to bring along less well-informed investors.

More generally, issuers can reduce informational asymmetries by borrowing from

well-informed investors or by asking them to certify the quality of the issue. There is

a large variety of certifying agents: underwriters, rating agencies, auditors, venture

capitalists. Of course, it must be the case that the certifying agent has an incentive to

become well-informed about the firm’s prospects and to take actions that properly

convey their information to the prospective investors. The “actions” can be a rating, a

report, or a subscription to the issue (or, in the case of a venture capitalist, the action

of keeping a non-negligible stake in the firm). And, in all cases, reputation is the only

such incentive for a rating agency, which does not take a stake in the firm.

ii) Costly Collateral Pledging

Signaling by pledging collateral. The collateral is valued less risky by the lender than

by the borrower. Therefore, a good borrower would signal his quality by pledging a

costly collateral which is to be seized by the lender in case of failure. In doing so the

good borrower is offering terms that do not appeal to the bad borrower.

Signaling can occur live because it is more costly for a bad borrower to pledge

collateral than for a good one.

iii) Raise less resource for the future than would be efficient under symmetric

information. Consequently a good borrower is trying to convey that she is not afraid

of going back to the capital market at an intermediate stage.

iv) Payout Policy: Dividend payout has generally been used by firm’s insiders to signal

information beyond that contained in earnings announcements. A firms stock price

substantially increases (decreases) upon announcement of an increase (decrease) in

payout. Thus, suggesting that dividends convey information held by the firms

insiders, but not by the stock market. Dividends may demonstrate the existence/realty

of cash to investors. Dividends may also be a signal that the company does not need a

large financial cushion in the future.

v) Diversification and incomplete insurance.

A borrower may want to issue claims not only because there exists a risk averse

entrepreneur who has a substantial stake in her firm and now wants to diversify her

portfolio. In such a situation, the entrepreneur decision to issue equity claims is not so

as to undertake a new project or to expand an existing one. Rather, gains from trade

result from risk sharing with investors who are less exposed to firm’s specific risk.

Under symmetric information and in the absence of moral hazard the entrepreneur

optimally obtains full insurance and the risk attacked to firm’s income is fully borne

by the investors. However, under symmetric information this is not the case since the

investor is concerned about purchasing a “lemon”.

Thus, under such circumstances, the good borrower is willing to bear risk in order to

demonstrate that she is confident about the firm’s prospects. Although, imperfect

diversification has a cost, it allows a good borrower to obtain a better price for the

claims she issues. In doing so, the borrower has to signal good prospects to probable

investors, by increasing the sensibility of her own returns to the firms profits.

vi) Under pricing: Under symmetric information conditions when the investors being

wary about ‘adverse selection’ are not willing give money to the firm the good

borrower may under price the issue in-order to signal to the investors that they are

buying in to a high quality asset. However, under pricing is a very primitive signaling

device used only when the good borrower does not have any other cheaper mean of

setting herself export from the bad ones.

2.5.3 Trade off theory

According to this theory, the optimal proportion of debt financing will be determined

by the trade off between the positive and negative effects of borrowing. Debt provides

two significant advantages to firms relative to equity. It provides a tax benefit because

interest expenses are tax deductible and for some firms, it can force managers to be

more disciplined in their investment choices. However, along with these advantages

debt also comes with some costs. Debt increase the risk that a firm will be unable to

meet its fixed payments and go bankrupt. As firms borrow money they increase the

potential for conflicts between lenders and equity investors, and firms that borrow

money lose some flexibility with regard to future financing. It is this tradeoff that tells

us how much a firm should borrow.

Benefits of debt Two benefits of debt as citred in literature are” (i) Interest tax shield and (ii)

Disciplining effect of debt.

Interest Tax shield

Tax laws allow firms to deduct interest payments on debt from taxable income but do

not provide a similar deduction for cash flows from equity. The tax benefit from debt

can be calculated in one of the two ways:

(i) Compute the present value of tax savings from interest payments.

(ii) Measure the savings from the tax deduction as the difference between the pre

tax and after tax rate of borrowing.

Tax savings from interest payments: Consider a firm that borrows Rs. B to finance

its operations on which it pays and interest rate of r per cent and assume that its

marginal tax rate is t per cent of its income. The annual tax savings from the interest

tax deduction can be calculated as:

• Annual interest expense arising from the debt = rB

• Annual tax savings arising from the interest payment=trB

However, when it comes to valuation of interest tax shields across a period of time, then one

needs to think of the rate at which the tax shields needs to be discounted. The most frequently

suggested discount factor is the interest rate of debt itself, assuming that the tax shield is as

risky as the debt servicing. For example, say the debt for a firm is perpetual, the present value

of tax shield for the entire life of the company can be calculated as (trB/r)=tB

However, the above simplification of treating the interest tax shield to be as risky as interest

payment, overlooks the following points:

(i) The interest tax shields may be more uncertain than interest payments because to

make use of tax shields, there needs to be some taxable profit. What if the

company is not currently making profits.

(ii) Also, the government takes two bites out of the corporate income: The corporate

tax and the tax on the bondholders’ and stockholders’ personal income. While

corporate tax favours debt, personal taxes favour equity holders. Hence, one

should consider the effective interest tax shield.

(iii) The debt capacity of a firm depends on how well it performs. Hence, more often

than not companies tie their borrowings to their performance (future project/firm

value), hence the interest amount and the tax shields so generated are not constant.

As for the first point stated above, it can be said that the company may be able to carry

forward the loss to be set off against next years business income. The solution to the second

point can be reached by using effective tax shields that accounts for the personal tax

disadvantage to debt holders vis a vis equity holders. Finally, the valuation of interest tax

shields would depend on the financing policy of the company.

(i) If the firm borrows a fraction of the initial value of the project and no more and

also make any debt repayments on a predetermined schedule, then the interest tax

shields can be considered to be as risky as the interest payments and hence

discounted at Kd.

(ii) If the firm borrows a constant fraction of the future value of the project and adjust

its borrowing as the future value changes, then interest tax shields pick up the

projects business risk. Hence, they need to be discounted at the project’s

opportunity cost of capital (its WaCoC).

Discipline of Debt

In the 1980s, in the midst of the leveraged buyout boom, a group of practitioners and

academics, led by Michael Jensen at Harvard proposed a new rationale for borrowing,

based on their perception that some managers make wasteful investments with what

they called a firm’s free cash flows. Free cash flows, as they defined them, represent

cash flows from operations over which managers have discretionary spending power.

Cost of Debt Two costs of debt as cited in literature are: (i) Expected cost of bankruptcy and (ii)

Agency cost of debt.

Cost of Bankruptcy

A firm is bankrupt when it is unable to meet its contractual commitment. To ascertain the

cost of bankruptcy, it is necessary to measure the probability of bankruptcy, which, inturn is

determined by the following:

1. Size of operating cash flows relative to size of cash flows on debt obligation.

2. Variance in operating cash flows.

The direct cost of bankruptcy is the cost incurred in terms of cash outflows at the time of

bankruptcy. These costs include legal and administrative costs as well as the cost of distress

sale. Generally, researchers have found that the direct costs of bankruptcy for large firms are

likely to be fairly small.

Indirect costs of bankruptcy are due to the following:

(i) Loss in revenue that may occur due to the customer’s perception that the firm is in

trouble. Customers may stop buying the product or service out of fear that the

company will go out of business.

(ii) Suppliers may demand stricter credit terms in order to protect themselves against the

possibility of default.

(iii)The firm may experience difficulty in raising new capital.

Shapiro (1989) and Titman (1984) point out that the indirect costs of bankruptcy are likely to

be higher for some firms than for others. The difference depends on the type of products the

firm produces and sell. They argue that indirect bankruptcy costs are higher for the following

groups of firms:

(i) Firms that sell durable products with long lives that require replacement parts and

service.

(ii) Firms that provide goods or services for which quality is an important attribute that is

difficult to determine in advance.

(iii) Firms producing products whose value to customers depends on the services and

complementary products supplied by independent companies.

(iv) Firms that sell products requiring continuous service and support from the

manufacturer.

Agency Costs

Agency theory refers to the incentives of different parties to pursue their own interest ahead

of the shareholder organisation’s interest. This theory attempts to reduce the potential for

conflicts among the firm’s capital providers by recognizing the circumstances in which

managers’, shareholders’, and debt-holders’ interests are most likely to diverge. In corporate

finance, agency problems are mostly encountered in the context of establishing a firm’s

optimal financial policy. Existing literature classifies these agency problems under the

following two broad categories:

(i) The agency costs of equity and

(ii) The agency costs of debt.

Agency costs of equity

Agency costs of equity arise when there is a conflict between the decisions made by

managers and the interest of the shareholders. For instance, suppose a entrepreneur owns 100

percent of equity of a firm. Suppose that she is considering the purchase of a fleet of Toyota

Corolla for his top management team. Consequently, the value of the company as well as the

entrepreneur would drop by Rs. 1 crore. Now, suppose instead that the entrepreneur’s stake

had been 50 per cent. Consequently, though the value of the company would reduce by Rs. 1

crore, the entrepreneur only stands to loose Rs. 50 lacs. In other words, she gains resources to

the tune of Rs. 1 crore with a personal investment of only Rs. 50 lacs. Accordingly, it can be

said that as the management’s share of equity falls, there is lesser incentive to refrain from

value destroying investments.

Several courses of actions have been suggested to align the interest of the managers and the

share holders:

(i) Increase the entrepreneur/manager’s stake

(ii) Board of directors and other external investors may monitor the investment decisions

of the managers.

(iii) A high level of leverage, since it enforces discipline on managers by reducing the free

cash flows available to them and it also increases the percentage of the manager’s

equity holding thus mitigating possible conflict between managers and shareholders.

Agency costs of debt

One way to overcome the agency costs to equity, suggested above, is by relying more on

debt. However, greater usage of debt may create conflict of interest between debt holders and

equity holders. Because, greater usage of debt gives equity holders an incentive to invest sub

optimally. There are two ways in which greater reliance on debt can result in suboptimal

investment:

(i) Asset substitution problem and

(ii) Debt overhang problem

Asset substitution problem

Debt holders have limited upside potential and any further gain is passed on to the equity

investor. But if the investment fails, debt holders also have to bear the consequences. Hence

debt holders and equity holders have different incentives to bear risk, which affects their

preferences for the type of investment firms should make. The potential for conflict is

greatest when the firm is near or in financial distress. Under these circumstances, equity

holders may favour investing in very risk projects that have a negative NPV. This is so

because, they feel that the negative NPV is because of the higher expectations arising due to

the enhanced risk perception. However, in a distress kind of a situation, any ways the equity

holders may have only residual claim and hence, they may be tempted to undertake the risky

investment with the hope that if the risk pays off, they may stand to gain. This view point is

in direct contradiction with how a debt holder may think under similar circumstances. The

debt holder would try to secure his investment since she has the primary claim under

liquidation. Thus, this agency conflict results in an incentive to overinvest in excessively

risky projects.

Consequently, debt holders would increase their lending rates to cover for agency costs or

they would impose restrictive covenants on decisions that have economic impact beyond a

specified limit.

Debt overhang problem

When a firm has excessive debt as compared to its assets, even if it has profitable investment

opportunities, it would not normally find debt or equity providers of capital. For instance, say

the firm has assets worth Rs. 100 crore and debt outstanding of Rs. 125 crore. Currently the

firm has a project that could be undertaken with an investment of Rs. 20 crore and would

yield a definite NPV of Rs. 15 crore. If the firm could fund this project, its asset value will

rise to Rs. 135 crore. But how will the company raise the necessary funds?

Suppose a debt provider agrees to lend Rs. 20 crore and if the company goes into liquidation,

the existing debt holders will be paid first a worth of Rs. 125 crore and hence the new debt

provider will get only Rs. 10 crore in return for the Rs. 20 crore that she has provided. Hence,

no sane debt provider would fund this project. Equity, funding is even less plausible since

they have claim only on the residual wealth. As in the case of asset substitution, the debt

overhang problem also is acute if the company is in financial distress, when the firm’s value

is predominantly based on future growth opportunities or has few tangible assets. Hence, both

the existing debt providers (Rs. 25 crore loss) as well as the new debt providers (an

opportunity to make definite positive NPV) end up loosing. An equilibrium solution would be

then to negotiate with the existing lenders to accept a small loss (lesser than Rs. 25 crore; say

10 crore). Now if the company has to go into liquidation after making the new investment,

then the old lenders need to be provided Rs. 115 crore and the new lenders will get Rs. 20

crore for their investment of Rs. 15 crore. Thus, everyone is better off. However, in reality it

is very difficult to renegotiate the terms of the debt contracts. Thus, the best way is to avoid

such a situation by not levering beyond what your tangible assets allow for.

Other agency costs

Both the instances cited above deal with agency problem between managers/entrepreneurs

and investors. But going further there also could be agency costs between different firms and

with customers. For instance, say firms whose products have long lives and which involve

extensive maintenance and/or repair service requirement during its effective life. Hence, the

customer’s decision to buy today will depend on his confidence that the firm will provide

those services even in the future. If the customer expects the company to go bankrupt or be in

financial distress, she may not purchase the same. This would further hurt the firm’s sales and

operating performance. Thus, the type of product one manufactures as well as the kind of

post sales support that would be needed for such a product may also be important factors

while deciding on the amount of debt that a firm should take.

Numericals

1. The Bharat Co. and Charat Co. belong to the same risk class – these companies are

identical in all respects except that the Chart Company has no debt in its capital structure,

whereas Bharat Company employs debt in its capital structure. Relevant financial particulars

of the two companies are given below:

Particulars Bharat Charat

Net Operating Income Rs. 500,000 Rs. 500,000

Debt Interest - Rs. 200,000

Equity Earnings Rs. 500,000 Rs. 300,000

Equity Capitalisation rate 12% 14%

Market Value of Equity Rs. 41,66,667 Rs. 21,42,857

Market Value of Debt (Debt Capitalisation rate is 8%) - Rs. 25,00,000

Total Market Value of the Firm Rs. 41,66,667 Rs. 46,42,857

Average cost of capital 12% 10.77%

(a) You own Rs. 10,000 worth of Bharat’s equity. Show what arbitrage you would resort to.

(b) When will, according to Modigliani and Miller, this arbitrage ease?

2. Amalsons Ltd. had debt outstanding of Rs. 1.7 billion (it will be kept constant

throughout) and a market value of equity of Rs. 1.5 billion; the corporate marginal tax

rate was 36 per cent. The T Bill rate is 5.8 per cent and the T Bond rate is 6.4 per cent.

a. Assuming that the current beta of 0.95 for the stock is a reasonable one,

estimate the unlevered beta for the company.

b. How much of the risk in the company can be attributed to business risk and

how much to financial leverage risk?

3. You have just done a regression of monthly stock returns of Hiy Tech Ltd., a

manufacturer of heavy machinery, on monthly market returns over the last five years

and come up with the following regression:

Hiy Tech 0.5% 1.2 MR R= +

The variance of the stock is 50%, and the variance of the market is 20 per cent. The

current T. bill rate is 3 per cent. (It was 5 per cent one year ago.) The stock is currently

selling for Rs.50, down Rs. 4 over the last year, and has paid a dividend of Rs. 2.50 over

the next year. The National Stock Exchange (NSE) Nifty has gone down 8 per cent over

the last year, with a dividend of 3 per cent. Hiy Tech Ltd. has a tax rate of 40 per cent.

The market risk premium over T Bond rate is 5.5 per cent and over T Bill rate is 8.76

per cent.

a. What is the expected return on Hiy Tech over the next year?

b. What would you expect Hiy Tech’s price to be one year from today?

c. What would you have expected Hiy Tech’s stock returns to be over the last year?

d. What were the actual returns on Hiy Tech over the last year?

e. Heavy Tech has Rs. 100 million in equity and Rs. 50 million in debt. It plans to issue

Rs.50 million in new equity and retire Rs.50 million in debt. Estimate the new beta.

4. OVL, which had a market value of equity of Rs. 2 billion and a beta of 1.50, announced

that it was acquiring RPL, which had a market value of equity of Rs.1 billion and a beta

of 1.30. Neither firm had any debt in the financial structure at the time of the acquisition,

and the corporate tax rate was 40 per cent.

a. Estimate the beta for OVL after the acquisition, assuming that the entire

acquisition was financed with equity.

b. Assume that OVL had to borrow the Rs. 1 billion to acquire RPL. Estimate the

beta after the acquisition.

5. You run a regression of monthly returns of OIL Ltd., an oil-and gas-producing firm, on

the S&P CNX Nifty and come up with the following output for the period 2003-2008.

The market risk premium over T Bond rate is 5.5 per cent.

Intercept of the regression = 0.06 per cent

Slope of the regression = 0.46

Standard error of X-coefficient =0.20

R squared = 5 per cent

There are 20 million shares outstanding, and the current market price is Rs. 2 per share.

The firm has Rs. 20 million in debt outstanding. (ignore tax effects)

a. What will an investor in OIL’s stock require as a return if the T. bond rate is 6

per cent?

b. What proportion of this firm’s risk is diversifiable?

c. Assume now that OIL has three divisions of equal size (in market value

terms). It plans to divest itself of one of the divisions for Rs. 20 million in cash

and acquire another for Rs. 50 million. (it will borrow Rs. 30 million to

complete this acquisition.) The division it is divesting is in a business line

where the average unlevered beta is 0.20, and the division it is acquiring is in a

business line where the average unlevered beta is 0.80. What will the beta of

OIL be after this acquisition?

6. You have just run a regression of monthly returns of Jet Airways against the S&P CNX

Nifty over the last five years. You have misplaced some of the output and are trying to

derive it from what you have.

a. You know the R squared of the regression is 0.36, and that your stock has a

variance of 67 per cent. The market variance is 12 per cent. What is the beta of

Jet?

b. Your are comparing Jet to another firm that also has an R squared of 0.48.

Will the two firms have the same beta? If not, why not?

7. ZEES TV., the entertainment conglomerate, has a beta of 1.61. Part of the reason for the

high beta is the debt left over from ZEES’s leveraged buyout of ATN in 1999, which

amounted to Rs. 10 billion in 2005. The market value of equity at ZEES in 2005 was

also Rs. 10 billion. The marginal tax rate was 40 per cent.

a. Estimate the unlevered beta for ZEES TV.

b. Estimate the effect of reducing the debt ratio by 10 per cent each year for the

next two years on the beta of the stock.

7. You are advising a phone company that is planning to invest in projects related to

multimedia. The beta for the telephone company is 0.75 and has a debt/equity ratio of

1.00; the after-tax cost of borrowing is 4.25 per cent. The multimedia business is

considered to be much riskier than the phone business; the average beta for comparable

firms is 1.30, and the average debt/equity ratio is 50 per cent. Assuming that the tax rate

is 40 per cent (The risk less rate is 7 per cent and the market risk premium above T Bond

rate is 5.5 per cent).

a. Estimate the unlevered bets of being in the multimedia business.

b. Estimate the beta and cost of equity if the phone company finances its multimedia

projects with the same debt/equity ratio as the rest of its business.

c. Assume that a multimedia division is created to develop these projects, with a

debt/equity ratio of 40 per cent. Estimate the beta and cost of equity for the projects

with this arrangement.

8. Intel is exploring a joint venture with Ford to develop computer chips to use in

automobiles. Although Intel has traditionally used a cost of equity based on its bets of

1.50 and a cost of capital based on its debt ratio of 5 per cent, it is examining whether

it should use a different approach for this project. It has collected the following

information.

• The average beta for automobile component firm is 0.90 per cent, and the

average debt/equity ratio across these firm is 40 per cent.

• The joint venture will be financed 70 per cent with equity form Ford and Intel,

and 30 per cent with new debt raised at a market interest rate of 7.5 per cent.

a. Estimate the beta that Intel should use for this project.

b. Estimate the cost of capital and Intel should use for this project

c. What would be the consequences of Intel using its current cost of equity and

capital on this project.

9. IPC Ltd. is reexamining the costs of equity and capital it uses to decide on

investments in its two primary businesses – food and tobacco. It has collected the

following information on each business.

• The average beta of publicly traded firms in the tobacco business is 1.10, and the

average debt/equity ratio of such firms is 20 per cent.

• The average bets of publicly traded firms in the food business is 0.80, and the

average debt/equity ratio of such firms is 40 per cent.

IPC has a beta of 0.95 and a debt ratio of 25 per cent, the pre-tax cost of debt is 8 per

cent. The treasury bond rate is 7 per cent, and the corporate tax rate is 40 per cent.

a. Estimate the cost of capital for the tobacco business.

b. Estimate the cost of capital for the food business.

c. Estimate the cost of capital for IPC, as a firm.

10. Assume that IPC Ltd. is considering separating into two companies – one holding the

tobacco business and the other the food business.

b) Assuming that the debt is allocated to both companies in proportion to the market

values of the divisions, estimate the cost of capital for each of the companies. Will

it be the same as the costs of capital calculated for the divisions? Why or why not?

c) Assuming that the tobacco firm is assigned all the debt and that both firms are of

equal market value, estimate the cost of capital for each company. (Assume that

the pre-tax cost of debt will increase to 10 per cent, if this allocation is made.)

Chapter 3: Deciding on the Optimal Financing Mix

3.1 Operating Income Approach

The operating income approach is the simplest and one of the most intuitive ways of

determining how much a firm can afford to borrow. We determine the firm’s maximum

acceptable probability of default. Based on the distribution of operating income, we then

determine how much debt the firm can carry.

Steps in Applying the Operating Income Approach

We begin with an analysis of a firm’s operating income and cash flows, and we consider how

much debt it can afford to carry based on its cash flows. The steps in the operating income

approach are as follows:

1. Assess the firm’s capacity to generate operating income based on both current conditions

and past history. The history is a distribution for expected operating income, with

probabilities attached to different levels of income.

2. For any given level of debt, estimate the interest and principal payments that have to be

made over time.

3. Given the probability distribution of operating cash flows and the debt payments, estimate

the probability that the firm will be unable to make those payments.

4. Set a limit on the probability of its being unable to meet debt payments. The more

conservative the management of the firm, the lower this probability constraint will be.

5. Compare the estimated probability of default at a given level of debt to the probability

constraint. If the probability of default is higher than the constraint, the firm chooses a

lower level of debt; if it is lower than the constraint, the firm chooses a higher level of

debt.

Limitations of the Operating Income Approach

Although this approach may be intuitive and simple, it has some drawbacks

• Estimate a distribution for operating income is not as easy as it sounds, especially

for firms in businesses that are changing and volatile.

• Second, even when we can estimate a distribution, the distribution may not fit the

parameters of a normal distribution, and the annual changes in operating income

may not reflect the risk of consecutive bad years

• Finally, the probability constraint set by management is subjective and may reflect

management concerns more than stockholder interests. For instance, management

may decide that it wants no chance of default and will refuse to borrow money as

a consequence.

3.2 Cost of Capital Approach

Weighted average of the costs of the different components of financing – including debt,

equity, and hybrid securities – used by a firm to fund its financial requirements determine its

cost of capital. By altering the weights of the different components, firms might be able to

change their cost. In this approach, we estimate the costs of debt and equity at different debt

ratios, use these costs to compute the costs of capital, and look for the mix of debt and equity

that yields the lowest cost of capital for the firm. At this cost of capital, we will argue that

firm value is maximized.

Cost of Capital and Firm Value

In chapter 1 we examined the approaches available for estimating the costs of debt, preferred

stock and equity, and the appropriate weights to use in computing the cost of capital.

Summarizing,

• The cost of equity should reflect the riskiness of an equity investment in the

company. The standard models for risk and return – the capital asset pricing

model and the arbitrage pricing model - measure risk in terms of market risk and

convert the risk measure into an expected return.

• The cost of debt should reflect the default risk of the firm: the higher the default

risk, the greater the cost of debt. The cost of debt also reflects the tax advantage

associated with debt, since interest is tax deductible and cash flows to equity are

not.

Cost of Debt=Pre-tax Interest Rate on Borrowing (1-tax rate)

• The cost of preferred stock should reflect the preferred dividend and the absence

of tax deductibility.

or as stated in chapter 1, as YTM. However, unlike debt preference dividend does

not offer tax shield.

• The weights used for the individual components should be market value weights

rather than book value weights.

In order to understand the relationship between the cost of capital and optimal capital

structure, we rely on the relationship between firm value and the cost of capital. We know

that the value of the entire firm can be estimated by discounting the expected cash flows to

the firm at the firm’s cost of capital. The cash flows to the firm can be estimated as cash

flows after operating expenses, taxes, and any capital investments needed to create future

growth in both fixed assets and working capital, but before financing expenses.

Cash Flow to Firm = EBIT (1-t) – (capital expenditures – depreciation) – Change in working capital

The value of the firm can then be written as

where WACC is the weighted average cost of capital. The firm’s value, then, is function of

the firm’s cash flows and its cost of capital. If we assume that the cash flows to the firm are

unaffected by the choice of financing mix, and the cost of capital is reduced as a consequence

of changing the financing mix, the value of the firm will increase. If the objective in choosing

the financing mix for the firm is the maximization of firm value, we can accomplish it, in this

case, by minimizing the cost of capital. In the more general case where the cash flows to the

firm are a function of the debt-equity mix, the optimal financing mix is the mix that

maximizes firm value.

PriceStock'PreferredDividend Preferred Stock Preferred ofCost =

∑=

= +=

nt

1tt

t

WACC)(1Firm toCF

Firm of Value

Steps in Cost of Capital Approach

We need three basic inputs to compute the cost of capital – the cost of equity, the after-tax

cost of debt, and the weights on debt and equity. The costs of equity and debt change as the

debt ratio changes and the primary challenge of this approach is in estimating each of these

inputs.

Leverage and Cost of Equity

Previously, we argued that the expectations of equity investors changes as the debt ratio

changes. This is captured in the beta which would adjusted according to the level of leverage.

The beta adjustment formula would depend on the financing patter followed by the firm.

(i) If the firm follows a policy of keeping the initial amount of debt constant through the

entire life of the project, then the following formula will be used to adjust beta to the level of

leverage.

(ii) If the firm follows a policy of adjusting debt to the value of the project/firm, then the

following formula will be used to adjust beta to the level of leverage.

[ ]levered unlevered 1 Debt/Equityβ β= +

Thus, if we can estimate the unlevered beta for a firm, we can use it to estimate the levered

beta of the firm at every debt ratio. This levered beta can then be used to compute the cost of

equity at each debt ratio.

These formulas are especially useful when one is required to calculate cost of equity for a

unlisted firm.

Leverage and Cost of Debt

Most texts assume the cost of debt to be constant at all levels of debt. However, cost of debt

for a firm is a function of its default risk. As firms borrow more, their default risk will

increase and so will the cost of debt. If we use bond ratings as our measure of default risk,

we can estimate the cost of debt in three steps. First, we estimate a firm’s dollar debt and

[ ]yDebt/Equit)1(1 unleveredlevered t−+= ββ

Premium)Risk ( cost free-Risk Equity ofCost leveredβ+=

interest expenses at each debt ratio; as firms increase their debt ratio, both dollar debt and

interest expenses will rise. Second, at each debt level, we compute a financial ratio or ratios

that measures default risk, and we use the ratio(s) to estimate a rating for the firm; again, as

firms borrow more, this rating will decline. Third, a default spread, based on the estimated

rating, is added on to the risk-free rate of arrive at the pre-tax cost of debt. Applying the

marginal tax rate to this pre-tax cost yields an after-tax cost of debt.

Once we estimate the costs of equity and debt at each debt level, we weight them based on

the proportions used of each to estimate the cost of capital. Although we have not explicitly

allowed for a preferred stock component in this process, we can have preferred stock as a part

of capital. However, we have to keep the preferred stock portion fixed, while changing the

weights on debt and equity. The debt ratio at which the cost of capital is minimized is the

optimal debt ratio.

In this approach, the effect on firm value of changing the capital structure is isolated by

keeping the operating income fixed and varying only the cost of capital. In practical terms,

this requires us to make two assumptions. First, the debt ratio is decreased by raising new

equity and retiring debt; conversely, the debt ratio is increased by borrowing money and

buying back stock. This process is called recapitalization. Second, the pre-tax operating

income is assumed to be unaffected by the firm’s financing mix and, by extension, its bond

rating. If the operating income changes with a firm’s default risk, the basic analysis will not

change, but minimizing the cost of capital may not be the optimal course of action, since the

value of the firm is determined by both the cash flows and the cost of capital. The value of

the firm will have to be computed at each debt level, and the optimal debt ratio will be that

which maximizes firm value.

Limitations of Cost of Capital Approach There are several reasons why a firm may choose not to view the debt ratio that emerges from

this analysis as optimal.

(i) The firm’s default risk at the point at which the cost of capital is minimized may be

high enough to put the firm’s survival at jeopardy. Stated in terms of bond ratings, the

firm may have a below-investment grade rating

(ii) The assumption that the operating income is unaffected by the bond rating is a key

one. If the operating income declines as default risk increases, the value of the firm

may not be maximized where the cost of capital is minimized.

(iii) The optimal debt ratio was computed using the operating income from the most recent

financial year. To the extent that operating income is volatile and can decline, firms

may want to curtail their borrowing. In this section, we consider how we can bring

each of these consideration into the cost of capital analysis.

(i) Bond Rating Constraint

One way of using the cost of capital approach, without putting firms into financial jeopardy, is to

impose a ‘bond rating constraint’ on the cost of capital analysis. Once this constraint has been

imposed, the optimal debt ratio is the one that has the lowest cost of capital, subject to the constraint

that the bond rating meets or exceeds a certain level.

(ii) Operating Income as a Function of Default Risk

We assumed so far that operating income would remain constant while the debt ratios

changed. Although this assumption simplifies our analysis substantially, it is not realistic. For

many firms, operating income will drop as the default risk increases; this, in fact, is the cost

we labeled an indirect bankruptcy cost in the previous chapter. The drop is likely to become

more pronounced as the default risk falls below an acceptable level. For instance, a bond

rating below investment grade may trigger significant losses in revenues and increases in

expenses.

A general model for optimal capital structure would allow both operating income and cost of

capital to change as the debt ratio changes. We have already described how we can estimate

cost of capital at different debt ratios, but we could also attempt to do the same with operating

income.

If both operating income and cost of capital change, the optimal debt ratio may no longer be

the point at which the cost of capital is minimized. Instead, the optimal leverage has to be

defined as that debt ratio at which the value of the firm is maximized.

(iii) Normalized Operating Income

A key input that drives the optimal capital structure is the current operating income. If this

income is depressed, either because the firm is a cyclical firm or because there are firm-

specific factors that are expected to be temporary, the optimal debt ratio that will emerge

from the analysis will be much lower than the firm’s true optimal. If the drop in operating

income is permanent, however, this lower optimal debt ratio is, in fact, the correct estimate.

When evaluating a firm with depressed current operating income, we must first decide

whether the drop in income is temporary or permanent. If the drop is temporary, we must

estimate the normalized operating income for the firm. The normalized operating income is

an estimate of how much the firm would earn in a normal year, that is, a year without the

specific events that are depressing earnings this year. Most analysts normalize earnings by

taking the average earnings over a period of time (usually five years). This approach may not

be appropriate for firms that have changed in size over time. The right way to normalize

income will vary across firms.

1. For cyclical firms whose current operating income may be overstated (if the economy is

booming) or understated (if the economy is in recession), we can estimate the normalized

operating income using the average operating margin for these firms over an entire economic

cycle (about 10 years):

Normalized Operating Income = Average Operating Margin over cycle * Current Sales

2. For firms that have had a bad year in terms of operating income due to firm specific

factors such as the loss of a contract, we can use the operating margin for the industry in

which the firm operates to calculate the normalized operating income:

Normalized Operating Income = Average Operating Margin for the Industry * Current Sales

We can also estimate the normalized operating income using returns on capital across an

economic cycle (for cyclical firms) or an industry (for firms with firm-specific problems.)

Case of Banks and Insurance Companies

Applying the cost of capital approach to financial service firms, such as banks and insurance

companies, presents several problems. The first is that the interest coverage ratio spreads,

which are critical in determining the bond ratings, have to be estimated separately for

financial service firms; applying manufacturing company spreads will result in absurdly low

ratings for even the safest banks and very low optimal debt ratios. Furthermore, the

relationship between interest coverage ratios and ratings tend to be much weaker for financial

service firms than it is for manufacturing firms. The second is a measurement problem that

arises partly from the difficulty in estimating the debt on a financial service company’s

balance sheet.

Given the mix of deposits, repurchase agreements, short-term financing, and other liabilities

that may appear on a financial service firm’s balance sheet, one solution is to focus only on

long-term debt, defined tightly, and to use interest coverage ratios defined using only long-

term interest expenses. The third problem is that financial service firms are regulated and

have to meet capital ratios that are defined in terms of book value. If, in the process of

moving to an optimal market value debt ratio, these firms violate the book capital ratios they

could put themselves in jeopardy.

Illustration: Applying the Cost of Capital Approach to ABC Bank Ltd.

We analyze the optimal capital structure for ABC Bank Ltd. using data from1994. To begin,

we make the following assumption:

• The earnings before long-term interest expenses and taxes amounted to Rs. 2,448 million.

• The Bank was ranked AA+ and paid 8.20 per cent on its long-term debt in 1999. It had

Rs. 9 billion in long-term debt outstanding at the end of the year

• It had 187.10 million shares outstanding, trading at Rs.70 per share, and had a beta of

1.15. (The treasure bond rate at that time was 8.00 per cent.). The tax rate for the firm was

36 per cent.

• The interest coverage ratios used to estimate the bond ratings were adjusted to reflect the

ratings of financial service firms.

• The operating income is assumed to drop if its rating drops. Table 3.1 summarizes the

interest coverage ratios and estimated operating income drops for different ratings classes.

Table 3.1 Interest Coverage Ratios, Ratings, and Operating Income Declines for ABC

Bank, 1999

Long term Interest Coverage Ratio Rating Spread ( per cent) Operating Income

Decline ( per cent) <0.25 D 12.00 -50

0.25-0.50 C 9.00 -40

0.50-0.75 CC 7.50 -40

0.75-0.90 CCC 6.00 -40

0.90-1.00 B- 5.00 -25

1.00-1.25 B 4.00 -20

1.25-1.50 B+ 3.00 -20

1.50-2.00 BB 2.50 -20

2.00-2.25 BBB 2.00 -10

2.25-3.00 A- 1.50 -5

3.00-3.90 A 1.25 -5

3.90-4.85 A+ 1.00 -5

4.85-6.65 AA 0.70 -5

>6.65 AAA 0.30 0

Table 3.2 Debt Ratios, Cost of Capital, and Firm Value for the Bank

Debt Ratio (%) Cost of Capital (%) Firm Value (millions)

0 12.39 19,333

10 11.97 20,315

20 11.54 20,332

30 11.19 21,265

40 10.93 20,858

50 10.80 18,863

60 10.68 19,198

70 11.06 13,658

80 13.06 10,790

90 15.76 7,001

Thus, we assume that the operating income will drop 5% if the bank’s rating drops to AA and

20 per cent if it drops to BB. The drops in operating income were estimated by looking at the

effects of ratings downgrades on banks.

Based on these assumptions, we estimate the optimal long term debt ratio for ABC to be 30

per cent, close to the current debt ratio of 40 per cent. Table 3.2 summarizes the cost of

capital and firm values at different debt ratios for the firm.

The optimal debt ratio is the point at which the firm value is maximized. Note that the cost of

capital is actually minimized at 60 per cent debt. This is because the operating income

changes as the debt ratio change. While the cost of capital continues to decline as the debt

ratio increases beyond 30 per cent, the decline in operating income more than offsets this

drop.

3.3 Leverage and the Return Differential

One way to ascertain the quality of a firm’s projects is by measuring the differential between

the return earned by the projects and the firm’s cost of financing. Firms that earn a high

return on equity, relative to their cost of equity, have invested in good projects. Extending

this criterion to the financing decision, we can view the optimal debt ratio as that mix of debt

and equity at which the differential between the return on equity and the cost of equity is

maximized.

Steps in the Return Differential Approach

The two inputs that we need for the return differential approach are the return and the cost of

equity at different debt ratios. The return on equity for a firm can be written in terms of its

return on capital and its after-tax cost of borrowing.

ROE = ROC + D/E [ROC – i (1 – t)]

Fig. 1.: Effect of Leverage on RoE

Where

ROE = Return on equity

ROC = Return on capital

D/E = Debt to equity ratio

i = Interest rate on debt

t = Tax rate

The return on capital is defined as the after-tax earnings before interest and taxes, divided by

the book value of capital invested in the firm (either at the beginning of the year or the

average for the year).

fEquityBookvalueofDebtbookvalueo

tEBITROC+

−=

)1(

If the return on capital is greater than the after-tax cost of borrowing, the return on equity will

increase as the leverage increases. This is the benefit of borrowing, as illustrated in figure 3.1.

This benefit has to be weighed against the additional risk equity investors face as a

consequence of the borrowing. In the capital asset pricing model, this additional risk can be

measured by adjusting the beta for the higher debt ratio, as shown in figure 3.2. As the firm

borrows more money, the beta will increase, as will the cost of equity.

We can present the differential between the return and the cost of equity as a function of the

debt ratio. At the risk of oversimplifying the capital structure decision, if the increase in

leverage increases the differential between return on equity and cost of equity, the firm

should use debt rather than equity.

Fig. 2.: Effect of Leverage on β and Ke

Effects of Leverage, ROE, and Cost of Equity on The Home Depot

In this illustration, we consider the effects of increasing debt on both return on equity and the

cost of equity for XYZ Ltd. in 1999. We first estimate the return on equity at different levels

of debt, based on the return on capital earned by XYZ in 1998:

1998

1997

EBIT (1-t)Return on Capital at XYZ (Debt PV of Operating Leases Equity)

=+ +

%16.1512,9681,829

==

Note that both the operating income and the book value of capital are adjusted to reflect the

conversion of operating leases into debt, and the book value is from the end of 1997. Table

3.3 tracks the interest rates and tax rates estimated at different levels of debt. We use the

return on capital, interest rates, and tax rates to estimate the return on equity at each level of

debt. Note that the interest rate increases as the default risk increases and that the tax rate

drops once XYZ’s interest expenses exceed its earnings before interest and taxes.

In addition, the betas and costs of equity can be estimated at different levels of debt for the

company, using the unlevered beta of 0.84, estimated earlier, as shown in Table 3.4. The

treasuring bond rate used was 5 per cent, and the risk premium was 5.5per cent.

The differential between the return on equity and cost of equity at different debt levels can be

computed as shown in Table 3.5. The differential is positive for the entire range of debt

ratios, but it is maximized at a debt ratio of 30per cent. Although the optimal debt ratios

under the cost of capital approach and this approach are the same for XYZ Ltd., this will not

always be true. In fact, this approach will tend to break down for firms with very high returns

on capital.

Table 3.3 Interest Rates, Tax Rates, ROE, and Debt Ratios

Debt Ratio ( per cent)

Interest Rate on Debt (%) Tax Rate (%) ROE (%)

0 5.20 35.00 15.16

10 6.00 35.00 16.41

20 7.00 35.00 17.81

30 10.00 35.00 18.87

40 11.00 24.95 19.76

50 12.50 17.56 20.02

60 12.50 14.63 21.89

70 12.50 12.54 25.03

80 12.50 10.98 31.29

90 12.50 9.76 50.08

Table 3.4 Betas, Costs of Equity and Debt Ratios

Debt Ratio (%) Beta Cost of Equity (%) 0 0.84 9.64

10 0.90 9.98

20 0.98 10.40

30 1.08 10.93

40 1.27 11.96

50 1.54 13.47

60 1.92 15.58

70 2.57 19.11

80 3.85 26.17

90 7.70 47.34

Table 3.5 Return Differential and Debt Ratios

Debt Ratio (%) ROE (%) Cost of Equity (%)

ROE – Cost of Equity (%)

0 15.16 9.64 5.52

10 19.41 9.98 6.43

20 17.81 10.40 7.42

30 18.87 10.93 7.94

40 19.76 11.96 7.80

50 20.02 13.47 6.55

60 21.89 15.58 6.31

70 25.03 19.11 5.91

80 31.29 26.17 5.12

90 50.08 47.34 2.74

Limitations of the Return Differential Approach

There are two limitations to this approach. First, by measuring the return differential in

percentage terms between return on equity and the cost of equity, the firm might under invest.

In other words, a firm may choose not to invest in a good project, with a return greater than

its cost of equity, simply because investing in the project will bring down the return

differential. Second, the return differential measures the difference between project returns in

the current period and its cost of equity. If project earnings are expected to grow over time,

the return differential can provide a misleading view of the quality of a firm’s projects.

3.4 Comparative Analysis

The most common approach to analyzing the debt ratio of a firm is to compare its leverage to

that of similar firms. A simple way to perform this analysis is to compare a firm’s debt ratio

to the average debt ratio for the industry in which the firm operates. A more complete

analysis would consider the differences between a firm and the rest of the industry, when

determining debt ratios.

The underlying assumptions in this comparison are that firms within the same industry are

comparable and that, on average, these firms are operating at/or close to their optimal. Both

assumptions can be questioned. However, firms within the same industry can have different

product mixes, amounts of operating risk, tax rates, and project returns. Since firms try to

mimic the industry average, the average debt ratio across an industry might not be at/or even

close to its optimal.

Controlling for Differences among Firms

Firms within she same industry can exhibit wide differences in tax rates, capacity to generate

operating income & cash flows. Consequently, it can be dangerous to compare a firm’s debt

ratio to the industry and draw conclusions about the optimal financing mix. The simplest way

to control for differences across firms, using the maximum information available in the

market, is to run a regression, regressing debt ratios against these variables, across the firms

in an industry.

income operatingin Variance Returnstax -Pre RateTax RatioDebt 3210 αααα +++=

The cross-sectional approach has several advantages. Once the regression has been run and

the basic relationship has been established (i.e., the intercept and coefficients have been

estimated), the predicted debt ratio for any firm can be computed quickly using the measures

of the independent variables for this firm. If a task involves calculating the optimal debt ratio

for a large number of firms in a short time period, this may be the only practical way of

approaching the problem, since the other approaches described in this chapter are time

intensive.

This approach also has some limitations. The coefficients tend to shift over time. Besides

some standard statistical problems and errors in measuring the variables, these regressions

also tend to explain only a portion of the differences in debt ratios between firms. However,

the regressions provide significantly more information than does a naïve comparison of a

firm’s debt ratio to the industry average.

Example 3.1. Say we are looking at ABC Ltd.’s poposed bond issue of Rs. 50,00,000. The

debt is rated A, which is lower than ABC’s current debt rating of AA. Based on Table 3.1,

once would estimate the interest rate on debt to be 6 per cent. Determined to prove its credit

worthiness, ABC, sets aside 5 percent of the principle of the new debt as sinking fund every

year. The interest payment on existing debt is Rs. 5,00,000. If the current EBITDA of the

firm is Rs. 40,00,000, then find the probability of default.

Table 3.1 Interest rates vis a vis credit rating

Rating Spread Interest Rate on DebtAAA 0.20% 5.20% AA 0.50% 5.50% A+ 0.80% 5.80% A 1.00% 6.00% A- 1.25% 6.25%

BBB 1.50% 6.50% BB 2.00% 7.00% B+ 2.50% 7.50% B 3.25% 8.25% B- 4.25% 9.25%

CCC 5.00% 10.00% CC 6.00% 11.00% C 7.50% 12.50% D 10.00% 15.00%

Now, assume that ABC management decide that the probability of default should not be more

than 5 per cent, then find the maximum amount of debt that they can borrow.

Example 3.2 The cash flow to firm for Pitamber Ltd. is Rs. 200 lacs. Pitamber is into a

relatively stable industry and the cash flows are expected to increase at 6 per cent p.a. till

perpetuity. Given the cost of debt and cost of equity at different levels of debt, find the

optimal financing mix which maximizes firm value.

D/(D+E) Cost of Equity Cost of Debt WACC Firm Value 0 10.50% 4.80%

10% 11.00% 5.10% 20% 11.60% 5.40% 30% 12.30% 5.52% 40% 13.10% 5.70% 50% 14.00% 6.30% 60% 15.00% 7.20% 70% 16.10% 8.10% 80% 17.20% 9.00% 90% 18.40% 10.20% 100% 19.70% 11.40%

Example 3.3 Kalash Ltd. had debt worth of Rs. 6,00,000 whose market value is Rs. 8,00,000

(rated AA) and equity with market value Rs. 32,00,000 (1,00,000 shares of Rs. 32 each). The

beta of Kalash’s stock is estimated to be 1.01 and the 10 year government bond rate was 5 per

cent. The market risk premium in India is estimated to be 8 per cent. Say the firm has an

operating income of Rs. 20,00,000. Find the value of the firm with 0 per cent, 10 per cent and

20 per cent debt.

Numericals

1. You have been asked to estimate the cost of capital for Sarthi Tel, a telecomm firm. The

firm has the following characteristics:

• There are 100 million shares outstanding, trading at Rs. 250 per share.

• The firm has a book value of debt of Rs. 10 billion with a maturity of 6 years and

interest expenses of Rs. 600 million on the debt. The firm is not rated, but it had

operating income of Rs. 2.5 billion last year. Firms with an interest coverage

ratio of 3.5 to 4.5 were rated BBB. (Default spread is 1 per cent).

• The unlevered beta of other telecomm firms is 0.80. T bond rate is 6 per cent,

market risk premium over T Bond rate is 5.5 per cent and the tax rate for the firm is

35 per cent.

a. Based on the synthetic rating, estimate the cost of debt for this firm.

b. Estimate the market value of the debt for this firm.

c. Estimate the cost of capital for this firm.

2. UB Ltd. is examining its capital structure with the intent of arriving at an optimal debt

ratio. It currently has no debt and has a beta of 1.5. The riskless interest rate is 9 per cent.

Your research indicates that the debt rating will be as follows at different debt levels:

D/(D+E) Rating Interest Rate

0% AAA 10%

10% AA 10.5%

20% A 11%

30% BBB 12%

40% BB 13%

50% B 14%

60% CCC 16%

70% CC 18%

80% C 20%

90% D 25%

The firm currently has 1 million shares outstanding at Rs. 20 per share (tax rate =

40%).

a. What is the firm’s optimal debt ratio?

b. Assuming that the firm restructures by repurchasing stock with debt, what

will the value of the stock be after the restructuring?

3. You have been called in as a consultant for Pioma Ind. Ltd., a sporting goods retail firm,

which is examining its debt policy. The firm currently has a balance sheet as follows:

Liability Assets

LT Bonds Rs. 100 Fixed Assets Rs.300

Equity 300 Current Assets 100

Total Rs. 400 Total Rs. 400

The firm’s income statement is as follows:

Revenues Rs. 250

Cost of Goods Sold 175

Depreciation 25

EBIT 50

LT Interest 10

EBT 40

Taxes 16

Net Income 24

The firm currently has 100 shares outstanding, selling at a market price of Rs. 5 per share,

and the bonds are selling at par. The firm’s current beta is 1.12, and the T. Bond rate is 7 per

cent. The company falls in the 40 per cent tax bracket and the market risk premium is 5.5 per

cent.

a. What is the firm’s current cost of equity?

b. What is the firm’s current cost of debt?

c. What is the firm’s current weighted average cost of capital?

Assume that management of Herbert’s Inc. is considering doing a debt equity swap (i.e.,

borrowing enough money to buy back 70 shares of stock at Rs. 5 per share). It is believed that

this swap will lower the firm’s rating to C and raise the interest rate on the company’s debt to

15 per cent.

d. What is the firm’s new cost of equity?

e. What is the effective tax rate (for calculating the after-tax cost of debt) after the swap?

f. What is the firm’s new cost of capital?

4. Crocodile Electric, a company that gets 85 per cent of its revenues form industrial electric

motors, had 27.5 million shares at Rs. 25 per share, and Rs. 25 million in debt

outstanding at the end of 2005. The firm has a beta of 0.70, earnings before interest and

tax of Rs. 63.3 million, and book value of equity of Rs. 200 million. The following table

summarizes the ratings and interest rates for Crocodile Electric at different levels of debt.

Debt Ratio (%) Bond Rating Interest Rate

On Debt (%)

09 AA 6.70

10 A+ 7.00

20 A- 7.50

30 BBB 8.00

40 BB 8.50

50 B+ 9.00

60 B 10.00

70 B- 11.00

80 CCC 12.00

90 C 15.00

The tax rate is 35% and the market risk premium is 5.5 per cent.

a. Estimate the cost of equity at each level of debt.

b. Estimate the return on equity at each level of debt.

c. Estimate the optimal debt ratio based on the differential return.

d. Will the value of the firm be maximized at this level of debt? Why or why not?

5. Konkan Railway Ltd., a railroad company, had debt outstanding of Rs. 985 million and

40 million shares trading Rs. 46.25 per share in March 1995. It earned Rs. 203 million in

earnings before interest and taxes, and faced a marginal tax rate of 36.56 per cent. The

firm was interested in estimating its optimal leverage using the adjusted present value

approach. The following table summarizes the estimated bond ratings and probabilities of

default at each level of debt from 0 per cent to 90 per cent.

Debt Ratio (%) Bond Rating Probability of Default (%)

0 AAA 0.28

10 AAA 0.28

20 A- 1.41

30 BB 12.20

40 B- 32.50

50 CCC 46.61

60 CC 65.00

70 C 80.00

80 C 80.00

90 D 100.00

The direct and indirect bankruptcy cost is estimated to be 25 per cent of the firm values.

Estimate the optimal debt ratio of the firm, based on levered firm value.

6. Battle shoes Ltd., a manufacturer and retailer of footwear and sportswear, is considering a

highly levered status. In 2005, the firm had Rs. 237 million in market value of debt

outstanding and 11 million shares outstanding at Rs. 19.88 per share. The firm had

earnings before interest and tax of Rs. 44 million, a book value of capital of Rs. 250

million, and tax rate of 37 per cent. The treasure bond rate is 7.88 per cent, and the stock

has a beta of 1.26. The following table summarizes the estimated bond ratings and interest

rates at different levels of debt for Battle shoes Ltd.

Debt Ratio (%) Bond Rating Interest Rate On Debt (%)

0 AAA 8.18

10 AAA 8.18

20 A+ 8.88

30 A 9.13

40 A- 9.38

50 BB 10.38

60 BB 10.38

70 B 11.88

80 B- 12.88

90 CCC 13.88

a) Estimate the optimal debt ratio using the cost of capital approach.

b) Estimate the optimal debt ratio using the return differential approach

c) Will the two approaches always give you identical results? Why or why not?

7. MTNL, the phone utility for the Mumbai area, has approached you for advice on its

capital structure. In 2007, MTNL had debt outstanding of Rs. 12.14 billion and equity

outstanding of Rs. 20.55 billion. The firm had earnings before interest and taxes of Rs. 1.7

billion, and faced a corporate tax rate of 36 per cent. The beta for the stock is 0.84, and the

bonds are rated A- (with a market interest rate of 7.5 per cent). The probability of default

for A- rated bonds is 1.41 per cent, and the bankruptcy cost is estimated to be 30 per cent

of firm value.

a. Estimate the unlevered value of the firm

b. Value of the firm if it increases its leverage to 50 per cent. At that debt ratio,

its bond rating would be BBB, and the probability of default would be 2.30 per

cent

c. Assume now that MTNL is considering a move into entertainment, which is

likely to be both more profitable and riskier than the phone business. What

changes would you expect in the optimal leverage?

8. A small, private firm has approached your for advice on its capital structure decision. It is

in the specialty retailing business, and it had earnings before interest and taxes last year of

Rs. 500,000.

• The book value of equity is Rs. 1.5 million, but the estimated market value is Rs.

6 million.

• The firm has Rs. 1 million in debt outstanding and paid an interest expense of Rs.

80,000 on the debt last year. (Based on the interest coverage ratio, the firm would

be rated AA and would be facing an interest rate of 8.25 per cent).

• The equity is not traded, but the average beta for comparable traded firms is 1.05,

and their average debt/equity ratio is 25 per cent.

a) Estimate the current cost of capital for this firm.

b) Assume now that this firm doubles its debt from Rs.1 million to Rs. 2

million and that the interest rate at which it can borrow increases to 9 per

cent. Estimate the new cost of capital and the effect on firm value.

c) You also have run a regression of debt ratios of publicly traded firms

against firm characteristics:

(DR = 0.15 + 1.05 (EBIT/Firm Value) – 0.15 (Beta)

Estimate the debt ratio for the private firm, based on this regression.

d) What are some of the concerns you might have in extending the approaches

used by large publicly traded firms to estimate optimal leverage to smaller

firms?