Alpha Corporation and Beta Corporation are identical in every way except their c

Question

Alpha Corporation and Beta Corporation are identical in every way except their capital structures. Alpha Corporation, an all-equity firm, has 15,500 shares of stock outstanding, currently worth $25 per share. Beta Corporation uses leverage in its capital structure. The market value of Beta's debt is $65,500, and its cost of debt is 7 percent. Each firm is expected to have earnings before interest of $75,500 in perpetuity. Neither firm pays taxes. Assume that every investor can borrow at 7 percent per year. What is the value of Alpha Corporation? (Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.) What is the value of Beta Corporation? (Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.) What is the market value of Beta Corporation's equity? (Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.) How much will it cost to purchase 20 percent of each firm's equity? (Do not round intermediate calculations and round your answers to the nearest whole number, e.g., 32.) Assuming each firm meets its earnings estimates, what will be the dollar return to each position in part (d) over the next year? (Do not round intermediate calculations and round your answers to the nearest whole number, e.g., 32.)

Explanation / Answer

a. The value of alpha = 15,500 * 25 = $387,500

b. Since there are no taxes, Value of beta is same as alpha :Vu (value of unlevered firm) = VL (Value of levered firm) according to MM proposition

So Value of beta = $387,500

c. Market Value of beta's equity = 387,500 - Debt = 387,500 - 65,500 = $322,000

d. To purchase 20% of alpha = 0.2* 387,000 = $77,500

To purchase 20% of beta = 0.2*322,000 = $64,400

e. Since Alpha Corporation expects to earn $75,500 this year and owes no interest payments, the dollar return to an investor who owns 20% of the firm’s equity is expected to be $15,100 (= 0.20 * $75,500) over the next year.

While Beta Corporation also expects to earn $75,500 before interest this year, it must pay 7% interest on its debt. Since the market value of Beta’s debt at the beginning of the year is $65,500, Beta must pay $4,585 (= 0.07 * $65,500) in interest at the end of the year. Therefore, the amount of the firm’s earnings available to equity holders is $70,915 (= $75,500 - $4,585). The dollar return to an investor who owns 20% of the firm’s equity is $14,183 (= 0.20 * $70,915).

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