Your broker offers to sell you some shares of Bahnsen & Co. common stock that paid a dividend of $2 yesterday. You expect the dividend to grow at the rate of 5 percent per year for the next 3 years, and, if you buy the stock, you plan to hold it for 3 years and then sell it.
a. Find the expected dividend for each of the next 3 years; that is, calculate D1, D2, and D3. Note that D0 = $2.
b. Given that the appropriate discount rate is 12 percent and that the first of these dividend payments will occur 1 year from now, find the present value of the dividend stream; that is, calculate the PV 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 ˆP3 to equal $34.73. Discounted at a 12 percent 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?
e. Use Equation 7-2 to calculate the present value of this stock. Assume that g _ 5%, and 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 were 2 years or 5 years rather than 3 years, would this affect the value of the stock today, ˆP 0?