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sol4 - ACTSC 372 Assignment 4 due on 1[3 points You own 100...

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ACTSC 372 – Assignment 4 – due on March 30, 2007 1. [3 points] You own 100 shares of Remko Inc., which will pay a dividend of \$2.50 per share at the end of each year for the next two years. Three years from now, Remko Inc. will close and the liquidating value returned to the shareholders will be \$16.5 per share. The required return on Remko’s stock is 13%. (a) What is the current price of Remko’s stock? (b) If you prefer to receive an equal amount of money every year in each of the next three years, how can you accomplish this (only using transactions on Remko’s stock)? Solution: (a) The current price P 0 is equal to the present value of the future cash flows, and is thus given by P 0 = 2 . 50 1 . 13 + 2 . 50 1 . 13 2 + 16 . 50 1 . 13 3 = 15 . 61 (b) The level amount that can be obtained from the 100 shares is the value x such that 100 P 0 = xa 3 13% , where a 3 13% = (1 - 1 . 13 - 3 ) / 0 . 13 = 2 . 3611. Solving for x , we find x = 660 . 93. To get this amount, we’ll need to sell some shares at time 1 and 2. To determine how much shares we need to sell, we need to figure out (1) the value of the stock at those times (2) how much dividends we get, which in turn depends on how many shares we have. Now, at time 1 (after the dividend is paid), the value of the stock becomes P 1 = 2 . 50 1 . 13 + 16 . 5 1 . 13 2 = 15 . 13 . We get 100 × 2 . 50 = 250 in dividends, and thus we need to sell enough shares to make up for the difference 660.93 - 250 = 410.93, which means we need to sell 410.93/15.13 = 27.15 27 shares. So at time 2, now the stock price is 16.50/1.13 = 14.60, and we get (100 - 27) × 2 . 50 = 182 . 5 in dividends, so we need to sell 660 . 93 - 182 . 50 14 . 60 = 32 . 77 33 shares . Hence at time 3, we’re now left with 100-27-33 = 40 shares, and thus get a total of 40 × 16 . 50 = 660 at time 3 (not exactly 660.93 because of round-off errors). 2. [3 points] Jensen Inc. currently has a debt-to-equity ratio of 30%, and the required return on the firm’s levered equity is 17%. The applicable corporate tax rate is 35%. Jensen Inc. is considering a project that requires an initial investment of 14 million, and that will generate after-tax cash flows of 3, 7 and 8 millions at the end of year 1, 2, and 3, respectively. Jensen is planning to issue 4.5 million in debt to partially finance the project. The company’s borrowing rate is 9%. The loan contract specifies that at the end of each year, Jensen will pay 9% on the outstanding balance at the beginning of the year, and that it will make year-end principal payments of 1.5 million per year. Using the APV method,

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sol4 - ACTSC 372 Assignment 4 due on 1[3 points You own 100...

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