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Assignment2Solutions

Assignment2Solutions - Economics 181 Solutions Individual...

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Question 1: (a) The discount rate is 15% and the statutory corporate tax rate is 40%. Losses can be carried back two years and carried forward twenty years. (a) If the firm optimally uses carry-backs and carry-forwards where applicable, what will its after-tax income be in each year if its taxable income stream is as follows. Year -2 -1 0 1 2 3 4 Taxable income 0 1,000 1,000 1,000 -2,500 -1,000 2,000 After year 4, the firm is expected to have positive income in each year forever. (b) What is this companys economic marginal tax rate today (i.e., at t = 0)? Solutions: (a)The firm will optimally carry as much income back as it can, and carry the rest forward as follows: Year -2 -1 0 1 2 3 4 Income 0.00 1,000.00 1,000.00 1,000.00 -2,500.00 -1,000.00 2,000.00 Taxes at 40% ( T A ) 0.00 400.00 400.00 400.00 -800.00 0.00 200.00 After-tax income 0.00 600.00 600.00 600.00 -1,700.00 -1,000.00 1,800.00 (b) Now suppose that the firm generates an extra dollar of taxable income today (at t = 0). How much extra taxes will it have to pay? Year -2 -1 0 1 2 3 4 Taxable income 0.00 1,000.00 1,001.00 1,000.00 -2,500.00 -1,000.00 2,000.00 Taxes at 40% ( T B ) 0.00 400.00 400.40 400.00 -800.40 0.00 200.40 T B - T A 0.00 0.00 0.40 0.00 -0.40 0.00 0.40 The firms marginal tax rate is the present value of this stream of extra tax liabili- 1
ties: MTR = 0 . 40 - 0 . 40 (1 . 15) 2 + 0 . 40 (1 . 15) 4 = 32 . 62%. Question 2: Knarfappaz Co. pays no taxes and is financed entirely by common stock. The stock has a beta of 0.8 and a price-earnings ratio of 12.5 and is priced to offer an 8% expected return. Knarfappaz now decides to repurchase half the common stock and substitute an equal value of debt. If the debt yields a riskfree 5%, calculate: (a) the beta of the common stock after the refinancing; (b) the required return and risk premium on the stock before the refinancing; (c) the required return and risk premium on the stock after the refinancing; (d) the required return on the debt; (e) the required return on the company (i.e., stock and debt combined) after the refinancing. Assume that the operating profit of the firm is expected to remain constant in perpetuity. Give: (f) the percentage increase in expected earnings per share; (g) the new price/earnings ratio. Solutions: For this solution, all the primed variables denote after-refinancing variables. (a) The asset beta both before and after the refinancing is 0.8. After the refinancing, we have: 0 . 8 = β A = 0 . 5 β E + 0 . 5 β D = 0 . 5 β E + 0 . 5(0), which implies β E = 1 . 6 (b) Before the refinancing, we have r E = 8% and r E - r f = 3%. 2

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(c) Using the fact that r E = r f + ( r m .r f ) β E with r E = 8%, r f = 5%, and β E = 0 . 8, we find r m = 8 . 75%. Therefore, r E = r f + ( r m .r f ) β E = 0 . 05 + (0 . 0875 . 0 . 05)(1 . 6) = 11%, and r E - r f = 6%. (d) Since the debt is risk-free, we have r D = 5%. (e) The return on the total assets of the firm are unaffected by the refinancing, i.e., r A = r A = 8%. (f) Let V denote the value of the firm both before and after the refinancing. Also, if N denotes the number of outstanding shares before the refinancing, the number of outstanding shares after the refinancing is N/2. The price-earnings ratio before the refinancing is 12.5, i.e., V/N EPS = 12 . 5 EPS = 0 . 08 V N .
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