Alpha Corporation and Beta Corporation are identical in every way except their c
ID: 2771272 • Letter: A
Question
Alpha Corporation and Beta Corporation are identical in every way except their capital structures. Alpha Corporation, an all equity firm, has 19,500 shares of stock outstanding, currently worth $30 per share. Beta Corporation uses leverage in its capital structure. The market value of Beta’s debt is $69,500, and its cost of debt is 9 percent. Each firm is expected to have earnings before interest of $79,500 in perpetuity. Neither firm pays taxes. Assume that every investor can borrow at 9 percent per year.
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.)
d. How much will it cost to purchase 20 percent of each firm’s equity? (Do not round intermediate calculations.)
Explanation / Answer
Answer (d)
Firm Amount to Invest
Alpha Corporation $ 117,000
Beta Corporation $ 103,500
Calculations
Given
Alpha Corporation (All Equity Firm)
Total Number of shares outstanding = 19500
Current Market Price = $ 30
Beta Corporation
Total Debt = 69500
Cost of Debt = 9%
Earnings before Interest = 79500 in perpetuity
Borrower can borrow at the rate of 9%
Alpha Corporation
Total Number of shares outstanding = 19500
Current Market price = $ 30
Total Capital = Total Equity = 19500 * 30 = $ 585,000
Amount to be invested to acquire 20% of Equity = $ 585,000 * 0.20 = $ 117,000
Beta Corporation
Current Market Value of the Debt = 69500
Total Capital = Debt + Equity = 69500 + Equity
As both Alpha and Beta Corporations are identical in all aspects except the capital structure, the total capital of Beta Corporation is taken at $ 585,000. Substituting this value
585,000 = 69,500 + Equity -> Equity = 585,000 – 69,500
Total Equity of Beta Corporation = $ 515,500
Amount to be invested to purchase 20% of equity = $ 515,500 * 0.20 = $ 103,100
Answer (e)
Dollar Return on Investment
Alpha $ 5,369.95
Beta $ 5,390.69
Calculations
Both firms are assumed to be not paying any taxes.
Assuming that each firm meets the earnings estimates
Alpha Corporation
Earnings Before Interest = Earnings After Interest (since all equity firm) = $ 79,500
Return on Equity = (79500 / 585000) * 100 = 13.5897%
$ Value of Return on $ 117,000 invested in Alpha = 117,000 * 13.5897% = $ 15,899.95
Less : Cost of borrowing 117,000 at 9% = 117,000 * 9% = $ 10,530.00
Net Dollar Return on amount invested in Alpha = $ 5,369.95
Beta Corporation
Earnings Before Interest = $ 79,500
Less : Interest on Debt = $ 69,500 * 0.09 = $ 6,255
Earnings after interest = $ 73,245
Return on Equity for a levered firm can be calculated using the formula
Re (levered) = Re (unlevered) + (D/E) * (Re (unlevered) – cost of debt)
Taking the value of Re (unlevered) same as that for Alpha Corporation which is 13.59%
Re (Beta) = Re(alpha) + (D/E) * (Re (alpha) – cost of debt)
Re(Beta) = 13.5897% + (69500/515500) *(13.5897% - 9%)
Re(Beta) = 13.589% + 0.1348 * 4.5897% = 13.5897% + 0.6187% = 14.2084%
$ Value of Return on investment in Beta = $ 103500 * 14.2084% = $ 14,705.69
Less : Cost of borrowing for investment = 103500* 9% = $ 9,315.00
Net Return on investment in Beta = $ 5,390.69
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