sol3 - ACTSC 372 Assignment 3 Solutions 1[10 points You own...

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ACTSC 372 – Assignment 3 – Solutions 1. [10 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). Accept answers if they use fractional number of shares (not rounded) 2. [10 points] The market value balance sheet for the Archway Company is shown below. The firm has 500 shares outstanding. Assets Liabilities and owners’ equity Cash $1,500 Equity $4,500 Fixed assets $3,000 (a) Archway has declared a dividend of $1.08 per share. The stock goes ex-dividend tomorrow. What is the price of the stock today? What will its price be tomorrow? (Assume that there are no taxes) (b) Archway, instead, has declared a 10% stock dividend. The stock goes ex-dividend tomorrow. What
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