Question

Alpha Corporation and Beta Corporation are identical in every way except their capital structures. Alpha Corporation, an all-equity firm, has 10,000 shares of stock outstanding, currently worth $20 per share. Beta Corporation uses leverage in its capital structure. The market value of Beta's debt is $60,000 and its cost of debt is 8 percent. Each firm is expected to have earnings before interest of $70,000 in perpetuity. Neither firm pays taxes. Assume that every investor can borrow at 8 percent per year.

a. What is the value of Alpha Corporation?
b. What is the value of Beta Corporation?
c. What is the market value of Beta Corporation's equity?
d. How much will it cost to purchase 25 percent of each firm's equity?
e. Assuming each firm meets its earnings estimates, what will be the dollar return to each position in part (d) over the next year?

Answer 1

a. The value of Alpha Corporation is $200,000. b. The value of Beta Corporation is $875,000. c. The market value of Beta Corporation's equity is $815,000. d. It will cost $50,000 to purchase 25 percent of Alpha Corporation's equity and $203,750 to purchase 25 percent of Beta Corporation's equity. e. The dollar return to each position cannot be calculated without information about the return on equity.

Step-by-step explanation:

a. To calculate the value of Alpha Corporation, we can use the formula:

Value of Equity = Number of Shares * Price per Share

Alpha Corporation has 10,000 shares of stock outstanding, currently worth $20 per share. Therefore, the value of Alpha Corporation is:

Value of Alpha Corporation = 10,000 * $20 = $200,000

b. To calculate the value of Beta Corporation, we need to consider both the market value of its debt and the cost of debt. The value of Beta Corporation can be calculated as:

Value of Equity = Earnings before Interest / Cost of Equity

Since Beta Corporation is an all-equity firm, its earnings before interest is $70,000. Therefore, the value of Beta Corporation is:

Value of Beta Corporation = $70,000 / (0.08 - 0) = $875,000

c. The market value of Beta Corporation's equity can be calculated by subtracting the market value of its debt from the value of Beta Corporation:

Market Value of Equity = Value of Beta Corporation - Market Value of Debt

Given that the market value of Beta Corporation's debt is $60,000, the market value of Beta Corporation's equity is: Market Value of Beta Corporation's Equity = $875,000 - $60,000 = $815,000

d. To calculate the cost of purchasing 25 percent of each firm's equity, we can use the formula:

Cost of Equity Purchase = 25% * Market Value of Equity

For Alpha Corporation:

Cost of Alpha Corporation's Equity Purchase = 0.25 * $200,000 = $50,000

For Beta Corporation:

Cost of Beta Corporation's Equity Purchase = 0.25 * $815,000 = $203,750

e. To calculate the dollar return to each position in part (d) over the next year, we need to consider the return on equity. Since the question does not provide information about the return on equity, we cannot calculate the dollar return.