Stockholm School of Economics in Riga Financial Economics, Spring 2010 Tālis Putniņš

Problem Set X: Capital structure policy Exercise 1: Capital structure Companies A and B differ only in their capital structure. A is financed with 30% debt and 70% equity; B is financed with 10% debt and 90% equity. The debt is risk free. Assume perfect capital markets. a) Rosencrantz owns 1% of the common stock of A. What other investment package would produce identical cash flows for Rosencrantz? b) Guildenstern owns 2% of the common stock of B. What other investment package would produce identical cash flows for Guildenstern? c) Show that neither Rosencrantz nor Guildenstern would invest in the common stock of B if the total value of company A were less than that of B.

Exercise 2: Capital structure Brengulis Corp., operating in a perfect capital market, pays no taxes and is financed entirely by common stock. The stock has a beta of 0.8, a price-earnings ratio of 12.5, and is priced to offer an 8% expected return. Brengulis Corp. now decides to repurchase half its common stock and substitute it with an equal amount of debt. The debt yields a risk free 5%. Calculate the following: a) The beta of common stock after the refinancing. b) The required return on the stock after refinancing. c) The required return on the company (i.e., stock and debt combined) after the refinancing. Assume that the operating profit is expected to remain constant in perpetuity. Calculate: d) The percentage increase in expected earnings per share. e) The new price-earnings multiple.

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Exercise 3: Capital structure A manufacturing firm with no debt outstanding and a market value of $100 million is considering borrowing $40 million and buying back stock. The interest rate on debt is 9% and the firm faces a tax rate of 35%. a) Estimate the annual interest tax savings each year from the debt. b) Estimate the present value of the interest tax savings assuming the debt change is permanent. c) Estimate the present value of the interest tax savings assuming the debt will be taken on for 10 years only. d) What will happen to the present value of interest tax savings if interest rates drop tomorrow to 7% but the debt itself is fixed rate debt?

Exercise 4: Capital structure The following are the book and market value balance sheets of Lāčplēšu Corp.: Book values Net working capital Long-term assets

$20 $80

$60 $40

Equity Debt

Market values Net working capital Long-term assets

$20 $140

$120 $40

Equity Debt

Assume that Modigliani and Miller’s theory with taxes holds. There is no growth and the $40 of debt is expected to be permanent. The corporate tax rate is 40%. a) How much of the firm’s value is accounted for by the debt-generated tax shield? b) How much better off will Lāčplēšu Corp.’s shareholders be if the firm borrows $20 more and uses it to repurchase stock? c) Now instead suppose that Congress passes a law, which eliminates the deductibility of interest for tax purposes after a grace period of 5 years. What will be the new value of the firm, other things equal? (Assume an 8% borrowing rate.)

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Exercise 5: Capital structure Tērvetes Corp, an unlevered firm, has EBIT = $2 million per year. Tērvetes’ tax rate is 40% and market value is V = E = $12 million. The stock has a beta of 1, the riskfree rate is 9% and E(Rm) – Rf = 6%. Management is considering the use of debt; debt would be issued and used to buy back stock, leaving the firm’s assets unchanged. The default-free interest rate on debt is 12%. Because interest is tax deductible, the value of the firm would tend to increase as debt is added to the capital structure, but there would be an offset in the form of increasing expected bankruptcy costs. The firm’s analysts have estimated that the present value of any bankruptcy costs is $8 million and that the probability of bankruptcy will increase with leverage according to the following schedule. Value of debt $2.50m $5.00m $7.50m $8.00m $9.00m $10.0m $12.5m

Probability of default 0.00% 8.00% 20.5% 30.0% 45.0% 52.5% 70.0%

a) What is the current cost of equity and WACC (no debt added yet)? b) What is the optimal capital structure when bankruptcy costs are considered? c) What is the value of the firm at the optimal capital structure?

Exercise 6: Capital structure Your boss, the CFO of Valmiermuiža Corp., is fond of saying that what kills a business is the debt burden it chooses to carry. Recently, however, one of the directors questioned the wisdom of this low-debt policy by pointing out the tax savings from debt financing. Your boss instructs you to illustrate the tax savings of debt by comparing the market values of two hypothetical firms that are very similar except in debt policy. You draw up the following parameters for the hypothetical firms: Gaišais Corp. $200m $200m 0% 100% 10% 34% 40% 20%

EBIT Debt Growth rate (of EBIT) Payout ratio Interest rate, rd Corporate tax rate, tc Personal tax rate on interest, ti Personal tax rate on dividends, te

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Tumšais Corp. $200m $0 0% 100% n/a 34% n/a 20%

a) What is the total annual income to equity holders in Tumšais Corp. after both corporate and personal taxes? b) What is the market value of Tumšais Corp. if the required return on equity is 15%? c) What is the total annual income to bond holders in Gaišais Corp. after both corporate and personal taxes? d) What is the total annual income to equity holders in Gaišais Corp. after both corporate and personal taxes? e) What is the total combined annual income to bond holders and equity holders in Gaišais Corp. after both corporate and personal taxes? f) What is the present value of the tax advantage to Gaišais Corp.? g) What is the total market value of the firm and market value of the equity for Gaišais Corp.? h) What is the WACC of Gaišais Corp.? Is it higher or lower than the WACC of Tumšais Corp.?

Exercise 7: Capital structure The total market value of a firm with $500,000 of debt is $1,700,000. Earnings before interest and taxes (EBIT) are expected to be constant in perpetuity. The interest rate on debt is 10%. The company is in the 34% tax bracket. If the company were 100% equity financed, the equity holders would require a 20% return. a) What would the value of the firm be if it were financed entirely with equity? b) What is the net income to the stockholders of this levered firm?

Exercise 8: Capital structure Three companies, A, B and C, operate in the same line of business. A has a long-term target debt/assets ratio of 35%, whereas B has chosen a 50% debt-assets ratio. C has chosen to remain 100% equity financed. Company A has an excellent debt rating paying in effect only the risk free rate for its debt. Company B pays a premium of 0.5% p.a. over the risk-free rate. The beta of company C’s equity is 1.4. However, the equity betas for A and B are unknown. The corporate tax rate is 29% for all companies. The risk-free rate is 4.5% p.a. and the market risk premium is 5% p.a.. a) Estimate the cost of equity for companies A, B and C. b) Estimate the WACC for companies A, B and C.

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Exercise 9: Capital structure Circular File’s market value balance sheet: Net working capital $20 Fixed assets $10 Total assets $30

$5 $25 $30

Common Stock Bonds outstanding (Face value $50) Total value

Who gains and who loses from the following maneuvers? a) Circular scrapes up $5 in cash and pays a cash dividend. b) Circular halts operations, sells its fixed assets, and converts net working capital into $20 cash. Unfortunately the fixed assets fetch only $6 on the second hand market. The $26 in cash are invested in T-bills. c) Circular encounters an acceptable investment opportunity, NPV = $0, requiring an investment of $10. The firm borrows to finance the project. The new debt has the same security, seniority, etc. as the old. d) Suppose the new project has NPV = $2 and is financed by an issue of preferred stock. e) The lenders agree to extend the maturity of their loan from one year to two in order to give Circular a chance to recover.

Exercise 10: Capital structure Recently, your boss, the CFO of Līvu Corp. came across the notion that adjusting the firm’s capital structure might significantly increase its market value. Your boss has asked you to do a preliminary study on this issue. Līvu Corp. currently has a very conservative leverage policy with D/E ratio of only 10%. Regressions of the past 5 years’ data result in an estimated equity beta of 1.05. The marginal tax rate is 34%. The long-term risk-free rate is 8% and the market risk premium is 5.5%. An investment banker recently estimated the pretax cost of debt at various levels of the D/E ratio and the estimates are as follows. D/E 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Pretax cost of debt 10.30% 10.70% 11.30% 12.00% 12.60% 13.40% 15.00% 16.80% 19.00% 23.00%

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From Līvu Corp.’s most recent financial statement you find that EBIT = $120 million, depreciation = $10.5 million, capital expenditure = $15 million and the growth rate of cash flows to the firm is 6% p.a. Based on recent evidence in Schaefer and Strebulaev (2007), your boss instructs you to use the approximation that the beta of the firm’s debt is zero. a) What is the weighted cost of capital (WACC) today when the D/E ratio is 10%? b) What is the total market value of Līvu Corp. today when the D/E ratio is 10%? c) What is the unlevered beta of the firm today? d) Construct a table showing the relation between the D/E ratio, beta of equity and the cost of equity. e) Construct a table showing the relation between the D/E ratio, WACC and market value of the firm. f) What is the optimal capital structure for the firm? What is the minimum WACC and maximum firm value? g) If the firm decides to move to the optimal capital structure, what will be the gain to shareholders? Will debt holders be harmed by the move?

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