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Unformatted text preview: Economics 181 Solutions: Individual Assignment #2 Wadia Haddaji 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 carrybacks and carryforwards where applicable, what will its aftertax income be in each year if its taxable income stream is as follows. Year21 1 2 3 4 Taxable income 1,000 1,000 1,0002,5001,000 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: Year21 1 2 3 4 Income 0.00 1,000.00 1,000.00 1,000.002,500.001,000.00 2,000.00 Taxes at 40% ( T A ) 0.00 400.00 400.00 400.00800.00 0.00 200.00 Aftertax income 0.00 600.00 600.00 600.001,700.001,000.00 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? Year21 1 2 3 4 Taxable income 0.00 1,000.00 1,001.00 1,000.002,500.001,000.00 2,000.00 Taxes at 40% ( T B ) 0.00 400.00 400.40 400.00800.40 0.00 200.40 T B T A 0.00 0.00 0.40 0.000.40 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 . 40 (1 . 15) 2 + . 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 priceearnings 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 afterrefinancing variables. (a) The asset beta both before and after the refinancing is 0.8. After the refinancing, we have: . 8 = A = 0 . 5 E + 0 . 5 D = 0 . 5 E + 0 . 5(0), which implies E = 1 . 6 (b) Before the refinancing, we have r E = 8% and r E r f = 3%. 2 (c) Using the fact that r E = r f + ( r m .r f ) E with r E = 8%, r f = 5%, and E = 0 . 8, we find r m = 8 . 75%. Therefore, r E = r f + ( r m .r f ) E = 0 . 05 + (0 . 0875 . . 05)(1 . 6) = 11%, and r E r f = 6%....
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This note was uploaded on 09/29/2008 for the course ECON 181 taught by Professor Haddaji during the Spring '07 term at Duke.
 Spring '07
 HADDAJI
 Economics

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