Alpha Corporation and Beta Corporation are identical in every way except their c
ID: 2757667 • Letter: A
Question
Alpha Corporation and Beta Corporation are identical in every way except their capital structures. Alpha Corporation, an all-equity firm, has 9,700 shares of stock outstanding, currently worth $22 per share. Beta Corporation uses leverage in its capital structure. The market value of Beta’s debt is $52,000, and its cost of debt is 15 percent. Each firm is expected to have earnings before interest of $51,000 in perpetuity. Neither firm pays taxes. Assume that every investor can borrow at 15 percent per year.
Requirement 1: What is the value of Alpha Corporation? (Do not include the dollar sign ($).) Value of Alpha $
Requirement 2: What is the value of Beta Corporation? (Do not include the dollar sign ($).) Value of Beta $
Requirement 3: What is the market value of Beta Corporation’s equity? (Do not include the dollar sign ($).) Value of Beta’s equity $
Requirement 4: How much will it cost to purchase 15 percent of each firm’s equity? (Do not include the dollar signs ($).) Cost for Alpha $ Cost for Beta $
Requirement 5: Assuming each firm meets its earnings estimates, what will be the dollar return to each position in requirement 4 over the next year? (Do not include the dollar signs ($). Round your answers to the nearest whole dollar amount. (e.g., 32)) Return on Alpha $ Return on Beta $
Explanation / Answer
a. Since Alpha Corporation is an all-equity firm, its value is equal to the market value of its outstanding
shares. Alpha has 9,700 shares of common stock outstanding, worth $20 per share.
Therefore, the value of Alpha Corporation = 9,000 shares * $22 = $213,400
b. Modigliani-Miller Proposition I states that in the absence of taxes, the value of a levered firm equals the value of an otherwise identical unlevered firm. Since Beta Corporation is identical to Alpha Corporation in every way except its capital structure and neither firm pays taxes, the value of the two firms should be equal.
Modigliani-Miller Proposition I (No Taxes): VL =VU
Alpha Corporation, an unlevered firm, is worth $213,400 (VU).
Therefore, the value of Beta Corporation (VL) is $213,400.
c. The value of a levered firm equals the market value of its debt plus the market value of its equity.
Value of Beta Corporation = Value of Debt + Value of equity
The value of Beta Corporation is $213,400 and the market value of the firm’s debt is $52,000.
The value of Beta’s equity = Value of beta corporation – Value of debt = $213,400 - $52,000 = $161,400
Therefore, the market value of Beta Corporation’s equity (S) is $161,400
d. Since the market value of Alpha Corporation’s equity is $213,400, it will cost $32,010 (= 0.15 * $213,400) to purchase 15% of the firm’s equity.
Since the market value of Beta Corporation’s equity is $161,400, it will cost $24,210 (= 0.15 * $161,400) to purchase 15% of the firm’s equity.
e. Since Alpha Corporation expects to earn $51,000 this year and owes no interest payments, the dollar return to an investor who owns 15% of the firm’s equity is expected to be $7,650 (= 0.15 * $51,000) over the next year.
While Beta Corporation also expects to earn $51,000 before interest this year, it must pay 15% interest on its debt. Since the market value of Beta’s debt at the beginning of the year is $52,000, Beta must pay $7,800 (= 0.15 * $52,000) in interest at the end of the year. Therefore, the amount of the firm’s earnings available to equity holders is $43,200 (= $51,000 - $7,800). The dollar return to an investor who owns 15% of the firm’s equity is $6,480 (= 0.15 * $43,200).
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