Question

9-17. 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%. a. Find the expected dividend for each of the next 3 years; that is, calculate D1, D2, and D3. Note that Do = $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 ; 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 = 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, f, Explain.

Answer 1

a, D1=D0*(1+growth) =2*(1+5%) =2.10
D2=D0*(1+growth)^2 =2*(1+5%)^2 =2.205
D3=D0*(1+growth)^3 =2*(1+5%)^3 =2.31525

b. PV of D1 =D1/(1+r)=2.10/(1+12%)=1.8750
PV of D2 =D2/(1+r)^2=2.205/(1+12%)^2=1.7578
PV of D3 =D3/(1+r)^3=2.31525/(1+12%)^3=1.6749
PV of all Dividends =1.8750+1.7578+1.6749=5.2807 or 5.28

c. PV of Future Stock Price=P3/(1+r)^3 =34.73/(1+12%)^3 =24.72

d. Price of Stock Today =PV of all Dividends+PV of Future Stock Price =5.28+24.72 =30.00