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# CONSTANT GROWTH Your broker offers to sell you some shares of Bahnsen & Co. com- mon stock that paid a dividend of \$2.00 yesterday. Bahnsen’s dividend is expected to grow at 5% per year for the next 3 years. If you buy the stock, you plan to hold it for 3 years and then sell it. The appropriate discount rate is 12%. a. Find the expected dividend for each of the next 3 years; that is, calculate D1, D2, and D3. Note that D0 1⁄4 \$2.00. b. Given that the first dividend payment will occur 1 year from now, find the present value of the dividend stream; that is, calculate the PVs of D1, D2, and D3 and then sum these PVs. c. You expect the price of the stock 3 years from now to be \$34.73; that is, you expect P^3 to equal \$34.73. Discounted at a 12% rate, what is the present value of this expected future stock price? In other words, calculate the PV of \$34.73. d. If you plan to buy the stock, hold it for 3 years, and then sell it for \$34.73, what is the most you should pay for it today? e. Use Equation 9-2 to calculate the present value of this stock. Assume that g 1⁄4 5% and that it is constant. f. Is the value of this stock dependent upon how long you plan to hold it? In other words, if your planned holding period was 2 years or 5 years rather than 3 years, would this affect the value of the stock today, P^0? Explain.

CONSTANT GROWTH Your broker offers to sell you some shares of Bahnsen & Co. com- mon stock that paid a dividend of \$2.00 yesterday. Bahnsen’s dividend is expected to grow at 5% per year for the next 3 years. If you buy the stock, you plan to hold it for 3 years and then sell it. The appropriate discount rate is 12%. a. Find the expected dividend for each of the next 3 years; that is, calculate D1, D2, and D3. Note that D0 1⁄4 \$2.00. b. Given that the first dividend payment will occur 1 year from now, find the present value of the dividend stream; that is, calculate the PVs of D1, D2, and D3 and then sum these PVs. c. You expect the price of the stock 3 years from now to be \$34.73; that is, you expect P^3 to equal \$34.73. Discounted at a 12% rate, what is the present value of this expected future stock price? In other words, calculate the PV of \$34.73. d. If you plan to buy the stock, hold it for 3 years, and then sell it for \$34.73, what is the most you should pay for it today? e. Use Equation 9-2 to calculate the present value of this stock. Assume that g 1⁄4 5% and that it is constant. f. Is the value of this stock dependent upon how long you plan to hold it? In other words, if your planned holding period was 2 years or 5 years rather than 3 years, would this affect the value of the stock today, P^0? Explain.

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