Question 1

Your firm is an all-equity firm. The management is debating whether or not to increase the firms leverage ratio from 0 percent to 50 percent. Currently, there are 5,000 shares outstanding and the price per share is $100. Your companys assets generate expected cash flows of $30,000 per year forever. The interest rate on new debt is 4 percent. Assume that the firms cash flows remain the same regardless of its capital structure. Assume a perfect market. (Hint: leverage ratio = D/(D+E) = D/Total firm value)

a) Miss LaLaLa owns 500 shares of your firms stock. That is, she owns 10% of the total equity. What is her expected cash flow per year under the current capital structure, assuming the firm has a dividend payout rate of 100 percent?

b) Suppose that the management issue debt and repurchase shares to increase the firms leverage ratio to 50 percent.

i. What dollar amount of debt should the firm issue? (Hint: The change in the capital structure does not affect the firms cash flows.)

ii. Debt issuance is a zero NPV project in a perfect market. Therefore, the equity share price stays the same after the debt issuance. With the cash raised from the debt issuance, the management buys back stock shares at $100 per share. How many shares will the management buy back? What is the number of remaining shares?

c) Suppose that Miss LaLaLa keeps all 500 of her shares. What percentage of equity would she own?

d) What will Miss LaLaLas expected cash flow be under the new capital structure, assuming that she keeps all 500 of her shares?

Note that the higher leverage ratio increases Miss LaLaLas expected cash flow. However, it also makes the expected cash flows of equity holders risker. As a result, the share price remains at $100 per share after the recapitalization.

e) Suppose Miss LaLaLa prefers the old cash flow to the new cash flow. That is, she prefers a lower expected cash flow with lower risk. Show how she can unlever her shares of stock to recreate the original cash flow. (Hint: before the firm took on debt, she owned 10% of the total firm. To recreate the original cash flow, she needs to hold 10% of the total firm, not just the firms equity.)

Question 2

Your companys operating asset will generate expected EBIT (earnings before interest and taxes) of $100M next year and will become obsolete afterwards. The corporate tax rate is 40%. All earnings after tax are paid out as dividends. Your companys asset has a cost of capital of 10%.

For (a) and (b), assume that your firm is an all-equity firm.

a) Calculate the total expected dividends to the equity holders next year. Assume that your companys asset is already fully depreciated (DEPN = 0 next year), your company does not need working capital (WC = 0 always), and your company will not make any investment next year (CAPEX = 0 next year). (Hint: calculate the free cash flow of your company.)

b) What is the unlevered value of your firm?

For the remaining questions, assume that your firm is a levered firm. Your firm currently has $20M of a par bond outstanding. The bond matures in one year and has a cost of capital of 7.5%.

c) What is the interest rate on the par bond?

d) How much taxes will your company pay next year?

e) Calculate the tax shield of your company next year.

f) Calculate the total cash flows to the bond holders next year.

g) Calculate the total expected dividends to the equity holders next year.

h) Using APV, calculate the levered value of your firm. (Hint: the tax shield next year is already known.)

i) What is the value of the levered equity?

j) What is the levered equity cost of capital? (Hint: Calculate the asset cost of capital of the firm. The firms asset includes PV of tax shields and operating assets.)

k) Calculate your companys WACC (weighted average cost of capital) with taxes. Round the number to four decimal places.

l) Using WACC, recalculate the levered value of your firm. Compare your answers in part (l) and part (k). They should be the same up to rounding errors.