Question

Alpha Corporation and Beta Corporation are identical in every way except their capital structures. Alpha Corporation, an all-equity firm, has 9,200 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 $50,000, and its cost of debt is 13 percent. Each firm is expected to have earnings before interest of $62,000 in perpetuity. Neither firm pays taxes. Assume that every investor can borrow at 13 percent per year.

Requirement 1: What is the value of Alpha Corporation? (Do not include the dollar sign ($).) Value of Alpha $_____

2: What is the value of Beta Corporation? (Do not include the dollar sign ($).) Value of Beta $_____

3: What is the market value of Beta Corporation’s equity? (Do not include the dollar sign ($).) Value of Beta’s equity $_____

4: How much will it cost to purchase 16 percent of each firm’s equity? (Do not include the dollar signs ($).) Cost for Alpha $_____, Cost for Beta $______.

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 $ ______.

Answer 1

(1) Firm Alpha:

Number of Shares Outstanding = 9200 and Price per Share = $ 22

Market Capitalization = Firm Value = 22 x 9200 = $ 202400 (Market Capitalization = Firm Value as the firm is all equity-financed)

(2) Firm Beta:

As per Modigliani-Miller Theorem, two identical firms in the absence of taxes will have equal values if they have equal earnings power (have equal earnings in simpler words). Therefore, Alpha and Beta will have equal values as there are no taxes and have equal earnings.

Beta Value = Alpha Value = $ 202400

(3) Market Value of Beta's Debt = $ 50000

Market Value of Beta's Equity = Beta's Value - Market Value of Beta's Debt = 202400 - 50000 = $ 152400

(4) 16% of Firm Alpha = 16 % of Firm Beta = 0.16 x 202400 = $ 32384

(5) Firm Alpha:

EBIT = Net Income = Return to Equity holders = $ 62000 and Equity = $ 202400

% Return to Equityholders = (62000 / 202400) x 100 = 30.63 %

$ Return = Net Income = 62000

Firm Beta:

EBIT = $ 62000

Less: Interest Expense = Market Value of Debt x Cost of Debt = 50000 x 0.13 = $ 6500

Earnings Beforet Tax = $ 55500

Less: Tax = Zero (as there are no taxes)

Net Income = $ 55500

Equity = $ 152400

% Return to Equityholders = (55500 / 152400) x 100 = 36.42 %

$ Return = 55500