Your broke offers to sell you some shares of Bahnsen & Co. common stock that pai
ID: 2634565 • Letter: Y
Question
Your broke 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, D3. Note that D0 = $2.00.
b. Given that the first dividend payment willl occur 1 year from now, find the present value of the dividen stream; that is, calculate the PVs of D1, D2, 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 P3 to equal $34.73. Discounted at a 12% rate, what is the present value of this expected furture 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. 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, P0? Explain.
Explanation / Answer
a. D0 = $2
D1 = $2(1.05) = $2.10
D2 = $2.10(1.03) = $2.205
D3 = $2.205(1.03) = 2.315
b. Ptesent value of dividend stream:
PV (D1) = $2.10/1.12 = $1.875
PV(D2) = $2.205/(1.12)2= 1.7578
PV(D3) = $2.315/(1.12)3= 1.6478
c. P3 = 34.73
PV(P3) = $34.73/(1.12)3= 24.72
d. It will be the present value of P3 = 24.72
e. Present value of stock = 24.72 + 1.875 + 1.7578 +1.6478 = 30
f. Yes, it totally depends on how long you plan to hold it. The value of stock will be different with 2, 3 or 5 years as we considere the present values.
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