CHAPTER 16 CAPITAL STRUCTURE: BASIC CONCEPTS Answers to Concepts Review and Critical Thinking Questions 2. False. A reduction in leverage will decrease both the risk of the stock and its expected return. Modigliani and Miller state that, in the absence of taxes, these two effects exactly cancel each other out and leave the price of the stock and the overall value of the firm unchanged. 3. False. Modigliani-Miller Proposition II (No Taxes) states that the required return on a firm s equity is positively related to the firm s debt equity ratio [R S = R 0 + (B/S)(R 0 R B )]. Therefore, any increase in the amount of debt in a firm s capital structure will increase the required return on the firm s equity. 5. Business risk is the equity risk arising from the nature of the firm s operating activity, and is directly related to the systematic risk of the firm s assets. Financial risk is the equity risk that is due entirely to the firm s chosen capital structure. As financial leverage, or the use of debt financing, increases, so does financial risk and, hence, the overall risk of the equity. Thus, Firm B could have a higher cost of equity if it uses greater leverage. 7. Because many relevant factors such as bankruptcy costs, tax asymmetries, and agency costs cannot easily be identified or quantified, it is practically impossible to determine the precise debt equity ratio that maximizes the value of the firm. However, if the firm s cost of new debt suddenly becomes much more expensive, it s probably true that the firm is too highly leveraged. 8. It s called leverage (or gearing in the UK) because it magnifies gains or losses. 9. Homemade leverage refers to the use of borrowing on the personal level as opposed to the corporate level. 10. The basic goal is to minimize the value of non-marketed claims. [i.e., maximize the value of equity by maximizing the value of the firm]
Solutions to Questions and Problems 12. a. With the information provided, we can use the equation for calculating WACC to find the cost of equity. The equation for WACC is: WACC = (S/V)R S + (B/V)R B (1 t C ) The company has a debt equity ratio of 1.5, which implies the weight of debt is 1.5 / 2.5, and the weight of equity is 1 / 2.5, so WACC =.105 = (1 / 2.5)R S + (1.5 / 2.5)(.06)(1.35) R S =.2040, or 20.40% b. To find the unlevered cost of equity, we need to use M&M Proposition II with taxes, so: R S = R 0 + (R 0 R B )(B/S)(1 t C ).2040 = R 0 + (R 0.06)(1.5)(1.35) R 0 =.1329, or 13.29% c. To find the cost of equity under different capital structures, we can again use M&M Proposition II with taxes. With a debt equity ratio of 2, the cost of equity is: R S = R 0 + (R 0 R B )(B/S)(1 t C ) R S =.1329 + (.1329.06)(2)(1.35) R S =.2277, or 22.77% With a debt equity ratio of 1.0, the cost of equity is: R S =.1329 + (.1329.06)(1)(1.35) R S =.1803, or 18.03% And with a debt equity ratio of 0, the cost of equity is: R S =.1329 + (.1329.06)(0)(1.35) 14. a. The value of the unlevered firm is: V = EBIT(1 t C ) / R 0 V = $145,000(1.35) /.14 V = $673,214.29 b. The value of the levered firm is: V = V U + t C B V = $673,214.29 +.35($135,000) V = $720,464.29
15. We can find the cost of equity using M&M Proposition II with taxes. First, we need to find the market value of equity, which is: V = B + S $720,464.29 = $135,000 + S S = $585,464.29 Now we can find the cost of equity, which is: R S = R 0 + (R 0 R B )(B/S)(1 t C ) R S =.14 + (.14.08)($135,000 / $585,464.29)(1.35) R S =.1490, or 14.90% Using this cost of equity, the WACC for the firm after recapitalization is: WACC = (S/V)R S + (B/V)R B (1 t C ) WACC = ($585,464.29 / $720,464.29)(.1490) + ($135,000 / $720,464.29)(.08)(1.35) WACC =.1308, or 13.08% When there are corporate taxes, the overall cost of capital for the firm declines the more highly leveraged is the firm s capital structure. This is M&M Proposition I with taxes. 17. To find the value of the levered firm, we first need to find the value of an unlevered firm. So, the value of the unlevered firm is: V U = EBIT(1 t C ) / R 0 V U = ($67,000)(1.35) /.15 V U = $290,333.33 Now we can find the value of the levered firm as: V L = V U + t C B V L = $290,333.33 +.35($130,000) V L = $335,833.33 Applying M&M Proposition I with taxes, the firm has increased its value by issuing debt. As long as M&M Proposition I holds, that is, there are no bankruptcy costs and so forth, then the company should continue to increase its debt equity ratio to maximize the value of the firm. 24. a. The expected return on a firm s equity is the ratio of annual aftertax earnings to the market value of the firm s equity. The amount the firm must pay each year in taxes will be: Taxes =.40($1,350,000) Taxes = $540,000 So, the return on the unlevered equity will be: R 0 = ($1,350,000 540,000) / $5,900,000 R 0 =.1373, or 13.73%
Notice that perpetual annual earnings of $810,000, discounted at 13.73 percent, yields the market value of the firm s equity. b. The company s market value balance sheet before the announcement of the debt issue is: Debt 0 Assets $5,900,000 Equity $5,900,000 Total assets $5,900,000 Total D&E $5,900,000 The price per share is the total market value of the stock divided by the shares outstanding, or: Price per share = $5,900,000 / 350,000 Price per share = $16.86 c. Modigliani-Miller Proposition I states that in a world with corporate taxes: V L = V U + t C B When Green announces the debt issue, the value of the firm will increase by the present value of the tax shield on the debt. The present value of the tax shield is: PV(Tax Shield) = t C B PV(Tax Shield) =.40($1,800,000) PV(Tax Shield) = $720,000 Therefore, the value of Green Manufacturing will increase by $720,000 as a result of the debt issue. The value of Green Manufacturing after the repurchase announcement is: V L = V U + t C B V L = $5,900,000 +.40($1,800,000) V L = $6,620,000 Since the firm has not yet issued any debt, Green s equity is also worth $6,620,000. Green s market value balance sheet after the announcement of the debt issue is: Old assets $5,900,000 Debt 0 PV(tax shield) 720,000 Equity $6,620,000 Total assets $6,620,000 Total D&E $6,620,000 d. The share price immediately after the announcement of the debt issue will be: New share price = $6,620,000 / 350,000 New share price = $18.91 e. The number of shares repurchased will be the amount of the debt issue divided by the new share price, or: Shares repurchased = $1,800,000 / $18.91
Shares repurchased = 95,166.16 The number of shares outstanding will be the current number of shares minus the number of shares repurchased, or: New shares outstanding = 350,000 95,166.16 New shares outstanding = 254,833.84 f. The share price will remain the same after restructuring takes place. The total market value of the outstanding equity in the company will be: Market value of equity = $18.91(254,833.84) Market value of equity = $4,820,000 The market-value balance sheet after the restructuring is: Old assets $5,900,000 Debt $1,800,000 PV(tax shield) 720,000 Equity 4,820,000 Total assets $6,620,000 Total D&E $6,620,000 g. According to Modigliani-Miller Proposition II with corporate taxes R S = R 0 + (B/S)(R 0 R B )(1 t C ) R S =.1373 + ($1,800,000 / $4,820,000)(.1373.06)(1.40) R S =.1546, or 15.46%
CHAPTER 17 CAPITAL STRUCTURE: LIMITS TO THE USE OF DEBT Answers to Concepts Review and Critical Thinking Questions 1. [Yost says this is not briefly explaining.] Direct costs are potential legal and administrative costs. These are the costs associated with the litigation arising from a liquidation or bankruptcy. These costs include lawyers fees, courtroom costs, and expert witness fees. Indirect costs include the following: 1) Impaired ability to conduct business. Firms may suffer a loss of sales due to a decrease in consumer confidence and loss of reliable supplies due to a lack of confidence by suppliers. 2) Incentive to take large risks. When faced with projects of different risk levels, managers acting in the stockholders interest have an incentive to undertake high-risk projects. Imagine a firm with only one project, which pays $100 in an expansion and $60 in a recession. If debt payments are $60, the stockholders receive $40 (= $100 60) in the expansion but nothing in the recession. The bondholders receive $60 for certain. Now, alternatively imagine that the project pays $110 in an expansion but $50 in a recession. Here, the stockholders receive $50 (= $110 60) in the expansion but nothing in the recession. The bondholders receive only $50 in the recession because there is no more money in the firm. That is, the firm declares bankruptcy, leaving the bondholders holding the bag. Thus, an increase in risk can benefit the stockholders. The key here is that the bondholders are hurt by risk, since the stockholders have limited liability. If the firm declares bankruptcy, the stockholders are not responsible for the bondholders shortfall. 3) Incentive to under-invest. If a company is near bankruptcy, stockholders may well be hurt if they contribute equity to a new project, even if the project has a positive NPV. The reason is that some (or all) of the cash flows will go to the bondholders. Suppose a real estate developer owns a building that is likely to go bankrupt, with the bondholders receiving the property and the developer receiving nothing. Should the developer take $1 million out of his own pocket to add a new wing to a building? Perhaps not, even if the new wing will generate cash flows with a present value greater than $1 million. Since the bondholders are likely to end up with the property anyway, why would the developer pay the additional $1 million and likely end up with nothing to show for it? 4) Milking the property. In the event of bankruptcy, bondholders have the first claim to the assets of the firm. When faced with a possible bankruptcy, the stockholders have strong incentives to vote for increased dividends or other distributions. This will ensure them of getting some of the assets of the firm before the bondholders can lay claim to them. 5. Modigliani and Miller s theory with corporate taxes indicates that, since there is a positive tax advantage of debt, the firm should maximize the amount of debt in its capital structure. In reality, however, no firm adopts an all-debt financing strategy. MM s theory ignores both the financial distress and agency costs of debt. The marginal costs of debt continue to increase with the amount of debt in the firm s capital structure so that, at some point, the marginal costs of additional debt will outweigh its marginal tax benefits. Therefore, there is an optimal level of debt for every firm at the point where the marginal tax benefits of the debt equal the marginal increase in financial distress and agency costs. 9. As in the previous question, it could be argued that using bankruptcy laws as a sword may be the best use of the asset. Creditors are aware at the time a loan is made of the possibility of bankruptcy, and the interest charged incorporates it.