Your broker offers to sell you some shares of Bahnsen & Co. common stock that pa

Question

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, and, 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 D0 = $2.00. Round answers to the nearest hundredth.
D1 = ________
D2 = ________
D3 = ________

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 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 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 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, P0 ? Explain

Explanation / Answer

a)Find the expected dividend for each of the next 3 years; that is, calculate D1, D2 and D3. Note that D0 = $2.00. Round answers to the nearest hundredth.
D1 = $2(1+.05)^1= $2.10
D2 =$2(1+.05)^2 = $2.21
D3 = $2(1+.05)^3=$2.32

b.Year    Dividend               PV at 12% Present value of dividends
1            $2(1+.05)^1= $2.10     .893                 $1.88
2           $2(1+.05)^2 = $2.21    .797                 $1.76
3            $2(1+.05)^3=$2.32     .712                $1.65
Total $5.29

c. Pv of $34.73= 34.73*.712 = $24.73

d.Present of share today $24.73 +$5.29 =$30.02

e.Pv of share at the end of year 3=Div3(1+g)/r-g
= $2.32(1+.05)/.12-.05 =$34.8

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