Problem 9-17 Constant growth Your broker offers to sell you some shares of Bahns
ID: 2646964 • Letter: P
Question
Problem 9-17
Constant growth
Your broker offers to sell you some shares of Bahnsen & Co. common stock that paid a dividend of $3.75 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%.
Find the expected dividend for each of the next 3 years; that is, calculate D1, D2 and D3. Note that D0 = $3.75. Round your answer to the nearest cent.
D1 = $
D2 = $
D3 = $
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.
$
You expect the price of the stock 3 years from now to be $65.12; that is, you expect to equal $65.12. Discounted at a 12% rate, what is the present value of this expected future stock price? In other words, calculate the PV of $65.12. Round your answer to the nearest cent.
$
If you plan to buy the stock, hold it for 3 years, and then sell it for $65.12, what is the most you should pay for it today? Round your answer to the nearest cent.
$
Use equation below to calculate the present value of this stock.
??????
Assume that g = 5% and that it is constant. Round your answer to the nearest cent.
$
Explanation / Answer
Calculation of D1,D2, and D3:
Calculation of Present Value of Dividend:
Present Value of Stock:
Price after 3 Years = $65.12
DF (12%) for 3 Years = 0.71178
Present Value = 65.12 x 0.71178 = $46.35
Present Value of the Stock = D1/ k - g
D1 = Dividend next year, k = Cost of Capital, g = Growth Rate
Present Value = 3.9375 / 0.12 - 0.05
Present Value = $56.25
Year Present Dividend Growth Rate Dividend Next Year 0 3.75 5% 3.9375 D1 1 3.9375 5% 4.134375 D2 2 4.134375 5% 4.34109375 D3Related Questions
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