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 8% 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 10%. Find the expected dividend for each of the next 3 years; that is, calculate D1, D2, and D3. Note that D0 = $2.00. 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. Do not round your intermediate calculations. $ You expect the price of the stock 3 years from now to be $136.05; that is, you expect to equal $136.05. Discounted at a 10% rate, what is the present value of this expected future stock price? In other words, calculate the PV of $136.05. Round your answer to the nearest cent. Do not round your intermediate calculations. $ If you plan to buy the stock, hold it for 3 years, and then sell it for $136.05, what is the most you should pay for it today? Round your answer to the nearest cent. Do not round your intermediate calculations. $ Use equation below to calculate the present value of this stock.                     Assume that g = 8% and that it is constant. Do not round intermediate calculations. Round your answer to the nearest cent. $ 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, ?

Answer 1

a). D0 = 2.00; g = 8%

D1 = D0*(1+g)^1 = 2*(1+8%) = 2.16

D2 = 2*(1+8%)^2 = 2.33

D3 = 2*(1+8%)^3 = 2.52

b). Present Values (PV) with discount rate (d) of 10%:

PV(D1) = D1/(1+d)^1 = 2.16/(1+10%)^1 = 1.96

PV(D2) = D2/(1+d)^2 = 2.33/(1+10%)^2 = 1.93

PV(D3) = D3/(1+d)^3 = 2.52/(1+10%)^3 = 1.89

c). P3 = 136.05

PV(P3) = 136.05/(1+10%)^3 = 102.22

d). Total share price today = PV(D1) + PV(D2) + PV(D3) + PV(P3) = 1.96+1.93+1.89+102.22 = 108.00

This is the intrinsic value of the stock, as of today. One should not pay more than this for the stock.

e). Present value of the stock using a constant growth rate (g) of 8% and discount rate (k) of 10%:

Current share price = D1/(k-g) = 2.16/(10%-8%) = 108.00 (same as calculated in part d)

f). The holding period is not going to make any difference to the value of the stock because the present value captures all the future cash flows expected from the stock.