Constant growth Your broker offers to sell you some shares of Bahnsen & Co. comm
ID: 2757948 • Letter: C
Question
Constant growth Your broker offers to sell you some shares of Bahnsen & Co. common stock that paid a dividend of $2.75 yesterday. Bahnsen's dividend is expected to grow at 7% 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 13%.
1. Find the expected dividend for each of the next 3 years; that is, calculate D1, D2 and D3. Note that D0 = $2.75. Round your answer to the nearest cent.
2. 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. Round your answer to the nearest cent.
3. You expect the price of the stock 3 years from now to be $60.08; that is, you expect P(hat) 3 to equal $60.08. Discounted at a 13% rate, what is the present value of this expected future stock price? In other words, calculate the PV of $60.08. Round your answer to the nearest cent.
4. If you plan to buy the stock, hold it for 3 years, and then sell it for $60.08, what is the most you should pay for it today? Round your answer to the nearest cent.
Explanation / Answer
1) D1 = 2.75 (1 +.07) = 2.94
D2 = 2.94 (1+.07 ) =3.15
D3 = 3.15 (1+.07) = 3.37
2)PV od D1 = PVF@13%,1 *D1
= .88496* 2.94 = $ 2.60
PV Of D2 = PVF@13%,2 *D2
= .78315* 3.15 = $ 2.47
PV of D3 = PVF@13%,3 *D3
= .69305 * 3.37 =$ 2.34
3)PV of future price = PVF@13%,3 * Price
= .69305 *60.08 = $ 41.64
4)mAximum price to pay today = Total return from stock = 2.60+2.47+ 2.34 + 41.64 =$ 49.05