 − I = m( R − Rb ) − I
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
α < α *,
Where, α * ( pR − I ) + (1 − α * )(qR − I ) = 0
Because the borrower cannot receive a negative compensation ( Rb ≥ 0 ), 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: mR ≥ 1 . 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 α ≥ α * . The
borrower’s compensation Rb is then set so that the investors break even on average.
m( R − Rb ) = I .
This implies that, ex post, investors make money on the good type ( p( R − Rb ) > I ) and lose
money on the bad type (q( R − Rb ) < I ) : there is cross-subsidization.
Note also that
Rb < Rb
G
(and Rb > RbB 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 R − Rb = (1 + r ) I , then
r > r G , where r G is the rate of interest that the good borrower could obtain under symmetric
information: R − Rb = (1 + r G ) I .
G
How much discount is suffered by the good borrower?
mR ≥ I](https://image.slidesharecdn.com/pgdmcapstrucnotes1-120711072348-phpapp02/85/Pgdm-cap-struc_notes-1-30-320.jpg)
 + [1 − p + (1 − α )( p − q)]( R F − RbF ) = I .
The good borrower’s utility is then equal to
pRbS + (1 − p ) RbF = [ pR S + (1 − p) R F − I ] − (1 − α )( p − q)[ R S − RbS ) − ( R F − RbF )]
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 RbF and decreases with RbS , the good
borrower sets
RbF = 0
Then, RbS , is determined by the investor’s breakeven constraint:
m( R S − RbS ) + (1 − m) R F = I](https://image.slidesharecdn.com/pgdmcapstrucnotes1-120711072348-phpapp02/85/Pgdm-cap-struc_notes-1-32-320.jpg)
![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.
β levered = β unlevered [1 + (1 − t )Debt/Equity]
(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.
β levered = β unlevered [1 + Debt/Equity ]
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.
Cost of Equity = Risk - free cost + β levered (Risk Premium)
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](https://image.slidesharecdn.com/pgdmcapstrucnotes1-120711072348-phpapp02/85/Pgdm-cap-struc_notes-1-49-320.jpg)
![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)]](https://image.slidesharecdn.com/pgdmcapstrucnotes1-120711072348-phpapp02/85/Pgdm-cap-struc_notes-1-55-320.jpg)
Pgdm cap struc_notes[1]
- 1. 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.
- 2. (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
- 3. 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., n I F P=∑ + (1) t =1 (1 + kd ) (1 + kd ) n t Where, k d = Pre-tax cost of debt I = Annual interest payment F = Redemption value of debt P = Net amount realized n = Maturity period The k d 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. F −P I+ kd = n F+P 2 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
- 4. 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 ( k p ) is defined as the discount rate which equates the proceeds from preference capital issue to the dividend payment and principal payments. Symbolically, n D F P=∑ + t =1 (1 + k p ) (1 + k p ) n t Where, k p = 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. F−P D+ kp = n F+P 2 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.
- 5. 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 Dt Pe = ∑ t =1 (1 + k e ) t Where, Pe = Price per equity share Dt = Expected dividend per share at the end of year one ke = Rate of return required by the equity shareholders If we know the current market price ( Pe ) and can forecast the future stream of dividends, we can determine the rate of return required by the equity shareholders ( ke ) using the above equation which is nothing but the cost of equity capital.
- 6. 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 ( Ri ) 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 R f and Rm - R f is the slope of the SML. According to this approach, the rate of return required on a security is given by the following equation: k i = R f + β i ( Rm − R f ) Where, ki = Rate of return required on security i R f = Risk-free rate of return β i = Beta of security i Rm = 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
- 7. 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 = ke we + kd (1 − t ) wd ⎛ E ⎞ ⎛ D ⎞ = ke ⎜ ⎟ + kd (1 − 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.
- 8. 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.
- 9. 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
- 10. 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: t =3 Rs.80 Rs.1, 000 PV of Bond = ∑ (1.1) t =1 t + (1.1)3 = Rs.950 The total straight bond value of the Rs. 1 crore in convertible bonds can then be estimated as follows: ⎛ 100, 00, 000 ⎞ Total Straight Bond Value of Convertible Bonds = ⎜ 1, 000 ⎟ *Rs. 950 =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 = ⎛ 100, 00, 000 ⎞ *Rs. 300 = = Rs. 30 lakhs ⎜ 1, 000 ⎟ ⎝ ⎠ 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. ⎛ 2.95 ⎞ ⎛ 3.30 ⎞ Thus, the WACoC is given by ⎜ ⎟ *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
- 11. 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.
- 12. • 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.
- 13. 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.
- 14. 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
- 15. 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. k Ke Ka kd D/V 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.
- 16. k Ke Ka kd D/V 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.
- 17. Ke Ka Cost (per cent) Kd D/V O L ˆ L 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
- 18. 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 rd and re 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 si . Let their current and future incomes & consumption be mi and cio , ci1 respectively. Therefore, cio = mio − si The individual must now decide how to allocate the si dollars between bond ( bi ) and stock ( ei ) investments. The choice is made by maximizing the utility of a given consumption stream, which implies maximizing the end of period wealth wi , for a given savings decision: Maximize wi1 = (1 + rd )bi + (1 + re )ei With the following constraints: 1. Savings must be allocated between bonds and equities 2. Equity cannot be short sold
- 19. 3. If bonds are issued, they cannot exceed the present value of the individuals wealth ⎡ m ⎤ bi ≤ ⎢ mio + i1 ⎥ = wio ⎣ 1 + rd ⎦ ∴ his next period consumption can be defined as cio = mi1 + (1 + rd )bi + (1 + re )ei Now if rd > re then the individual will save by buying only bonds, while if re > rd the individual will invest in equity only. Consequently the individual’s supply of funds to the bond market can be depicted as rd si rt - ⎡ mi 0 + mi1 ⎤ si bi ⎢ ⎥ ⎣ (1 + re ) ⎦ Where si denotes the individuals savings when rd = re Over the entire range where rd = re , the supply of funds. Corporate financing decision and demand for funds in the market Let V j = B j + E j denote the value of securities issued by a (levered) corporation j, where L B j is the value of the firms debt and E j is the value of its equity. Now, let X j depict the corporation’s earnings for the period. The value of the firm’s equity can then be written as:
- 20. X J − (1 + rd ) B j EJ = (1 + rE ) Thus, the value of the levered firms can be expressed as X J − (1 + rd ) B j Xj ⎡ 1 + rd ⎤ VJ = + Bj = + ⎢1 − ⎥ Bj 1 + re (1 + re ) ⎣ 1 + re ⎦ Thus, it can be seen that a corporation’s demand for funds via sale of bonds is perfectly elastic so long as re = rd . And when re = rd the value of the levered firm is equal to the value of the unlevered firm. Xj VjL = = V jU 1 + re If V j L ≠ V j u , 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 VU & V L should also be the same. If the market values of the two firms are not equal Vu ≠ V L , 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 V L > Vu and the arbitrageur hold α proportion of the levered firm’s equity S L . She could sell his stake in the levered firm and borrow equivalent to α proportion of the levered firm’s debt D L 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 αVu − α DL = α (Vu − DL ) and the returns are − − α x − α DL = α ( x − DL ) which is what she would have got if she had stayed put with his α proportion investment in the levered firm.
- 21. In the process she makes arbitrage gain of α (VL − V j ) .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 Vu > VL , then the arbitrage would work in the opposite direction. Say an investor holds α proportion of stocks in the unlevered firm. If Vu > VL the investor would sell the stocks and acquire α proportion of the levered firms debt and equity. _ − Therefore his investment is αVL & his returns α ( x − DL ) + α DL = α x 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 α (Vu − VL ) . 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.
- 22. Table 2.1: Replicating Levered Equity Using Homemade Leverage Date 0: Cash Flows Date 1: Cash Flows (in Rs.) (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 Date 1: Cash Flows (in Rs.) (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.
- 23. 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
- 24. 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 x j − (1 + rd ) B j Ej = (1 + re ) 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 ( x j − rd B j ) and the value of its equity will be x j − (1 + rd ) B j − ( x j − rd B j )tc Ej = (1 + re ) x j (1 − tc ) B j (1 + rd (1 − tc )) = − (1 + re ) (1 + re ) And the value of the levered firms is V j = B j + E j Hence, x j (1 − tc ) ⎡ 1 + rd (1 − tc ) ⎤ Vj = + ⎢1 − ⎥ Bj 1 + re ⎣ 1 + rd ⎦ In the above equation when rd = re ⎡ x j (1 − tc) ⎤ rd tc B j Vj = ⎢ ⎥ + ⎣ 1 + re ⎦ 1 + rd 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 rd = re . 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
- 25. 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 re achieved when rd = 1 − tc rd S re /(1 − tc ) D re Substituting rd = re (1 − tc ) is x j (1 − tc ) ⎡ 1 + rd (1 − tc ) ⎤ VjL = + ⎢1 − ⎥ B j we get 1 + re ⎣ 1 + re ⎦ x j (1 − tc ) VjL = = V ju 1 + re 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.
- 26. 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 rd = re . 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 re /(1 − tc ) . 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 re /(1 − t p ) . 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. rB S re /(1−tc) D re /(1−tp ) b, B 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
- 27. and corporate taxes. The equilibrium rate of interest is again rd = re /(1 − tc ) . 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 x j (1 − tc ) ⎡ 1 + rd * (1 − tc ) ⎤ VjL = + ⎢1 − ⎥ Bj 1 + re ⎣ 1 + re ⎦ If we substitute at equilibrium bond rate rd * = re /(1 − t p ) = re /(1 − tc ) , we get Vj = Vj L u 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 − t pd ) − (1 − tc )(1 − t pe ) (1 − tc )(1 − t pe ) t* = = 1− (1 − t pd ) (1 − t pd )
- 28. 0.65 − 0.525 = = 15% 0.65 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: V L = V u + 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-
- 29. 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, R bG in the case of success, consistent with investors’ breaking even on average: p ( R − Rb ) = I G 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 R bB in the case of success, where q( R − RbB ) = I . Clearly, RbB < Rb . G 2. Asymmetric Information The symmetric information outcome, however, is not robust to asymmetric information, as G the bad borrower can, by mimicking the good borrower, derive utility qRb that is greater than that (either 0 or qRbB ) she obtains by revealing her type. Let us assume that the only feasible financial contracts are contracts that give the borrower a compensation Rb ≥ 0 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
- 30. funded, and conditional on being funded, prefers contracts with a higher compensation. The investor’s profit for such a contract is therefore on average: [αp + (1 − α )q]( R − Rb ) − I = m( R − Rb ) − I 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 α < α *, Where, α * ( pR − I ) + (1 − α * )(qR − I ) = 0 Because the borrower cannot receive a negative compensation ( Rb ≥ 0 ), 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: mR ≥ 1 . 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 α ≥ α * . The borrower’s compensation Rb is then set so that the investors break even on average. m( R − Rb ) = I . This implies that, ex post, investors make money on the good type ( p( R − Rb ) > I ) and lose money on the bad type (q( R − Rb ) < I ) : there is cross-subsidization. Note also that Rb < Rb G (and Rb > RbB 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 R − Rb = (1 + r ) I , then r > r G , where r G is the rate of interest that the good borrower could obtain under symmetric information: R − Rb = (1 + r G ) I . G How much discount is suffered by the good borrower? mR ≥ I
- 31. Can be rewritten as ⎡ ⎛ p − q ⎞⎤ ⎢1 − (1 − α )⎜ ⎜ p ⎟⎥ pR ≥ I ⎟ ⎣ ⎝ ⎠⎦ We can thus define an index of adverse selection: ⎛ p−q⎞ χ ≡ (1 − α ) ⎜ ⎟. ⎝ p ⎠ 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
- 32. 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 mR s + (1 − m) R F > I and so there is enough pledgeable income to secure funding even when the bad borrower pools with the good one. { } Let RbS , RbF 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 m ( R s − R bS ) + (1 − m )( R F − R bF ) ≥ I . The good borrower maximized her expected payoff. pR bS + (1 − p ) R bF subject to the breakeven constraint. At the optimum, the investor’s breakeven condition is satisfied with equality. It can be rewritten as [ p − (1 − α )( p − q )]( R S − RbS ) + [1 − p + (1 − α )( p − q)]( R F − RbF ) = I . The good borrower’s utility is then equal to pRbS + (1 − p ) RbF = [ pR S + (1 − p) R F − I ] − (1 − α )( p − q)[ R S − RbS ) − ( R F − RbF )] 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 RbF and decreases with RbS , the good borrower sets RbF = 0 Then, RbS , is determined by the investor’s breakeven constraint: m( R S − RbS ) + (1 − m) R F = I
- 33. 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 R S − RbS in the case of success ( and 0 in the case of failure) so as to make up for the shortfall in pledgeable income: m( R S − RbS ) = I − R F . Thus, the firm first issues safe debt with a debt obligation D given by D = RF , 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 mR1 = I − D , 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.
- 34. 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.
- 35. 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
- 36. 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.
- 37. (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.
- 38. 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
- 39. 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:
- 40. (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
- 41. 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%
- 42. 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: RHiy Tech = 0.5% + 1.2 RM 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.
- 43. 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.
- 44. 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.
- 45. • 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.)
- 46. 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.
- 47. 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
- 48. 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. Preferred Dividend Cost of Preferred Stock = Preferred Stock' Price 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 t =n CF to Firm t Value of Firm = ∑ t =1 (1 + WACC) t 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.
- 49. 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. β levered = β unlevered [1 + (1 − t )Debt/Equity] (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. β levered = β unlevered [1 + Debt/Equity ] 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. Cost of Equity = Risk - free cost + β levered (Risk Premium) 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
- 50. 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
- 51. (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.
- 52. (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
- 53. 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.
- 54. Table 3.1 Interest Coverage Ratios, Ratings, and Operating Income Declines for ABC Bank, 1999 Long term Interest Operating Income Rating Spread ( per cent) Coverage Ratio 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
- 55. 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)]
- 56. 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). EBIT (1 − t ) ROC = bookvalueofDebt + BookvalueofEquity 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.
- 57. 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: EBIT (1-t)1998 Return on Capital at XYZ = (Debt + PV of Operating Leases + Equity)1997 1,829 = = 15.16% 12,968 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
- 58. 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 Interest Rate on Tax Rate (%) ROE (%) cent) Debt (%) 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
- 59. 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 Cost of Equity ROE – Cost of Debt Ratio (%) ROE (%) (%) 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
- 60. 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. Debt Ratio = α 0 + α 1 Tax Rate + α 2 Pre - tax Returns + α 3 Variance in operating income 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
- 61. 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 Debt AAA 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
- 62. 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.
- 63. 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
- 64. 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
- 65. 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 (%)
- 66. 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.
- 67. • 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?