Chapter 9, Problem 17P

CONSTANT GROWTH Your broker offers to sell you some shares of Bahnsen & Co. common 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%.

1. a. Find the expected dividend for each of the next 3 years; that is, calculate D₁, D₂, and D₃. Note that D₀ = $2.00.
2. 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.
3. c. You expect the price of the stock 3 years from now to be $34.73; that is, you expect ${\hat{\text{P}}}_{\text{3}}$ 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.
4. 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?
5. e. Use Equation 9.2 to calculate the present value of this stock. Assume that g = 5% and that it is constant.
6. 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, ${\hat{\text{P}}}_{\text{0}}$? Explain.