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 8% 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 11%.

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.

a. D1 = __________
b. D2 = __________
c. D3 = ___________

d. 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. Round your answer to two decimal places.______________


e. You expect the price of the stock 3 years from now to be $90.70; that is, you expect P ? ?3 to equal $90.70. Discounted at a 11% rate, what is the present value of this expected future stock price? In other words, calculate the PV of $90.70. Round your answer to two decimal places.______________


f. If you plan to buy the stock, hold it for 3 years, and then sell it for $90.70, what is the most you should pay for it today? Round your answer to two decimal places.______________


g. Use Equation 9-2 to calculate the present value of this stock. Assume that g = 8%, and it is constant. Round your answer to two decimal places.______________

Explanation / Answer

a) D1 = D0(1+g) = 2*1.08 =2.16 ($) b) D2 = D1*1.08 = 2.16*1.08 = 2.33 ($) c) D3 = D2*1.08 = 2.3328*1.08 = 2.52 ($) d) PV of div stream= D1/1.11 +D2/1.11^2 + D3/1.11^3 => = 2.16/1.11 + 2.33/1.11^2 + 2.52/1.11^3 =+ = 1.95 + 1.89 + 1.84 => = 5.68 ($) e) PV of P(3) = 90.70/1.11^3 = 66.32 ($) f) P(0) = PV of div. stream + PV of P(3) => = 5.68 + 66.32 = 72.00 ($) g) PV of stock = D0((1+g)/(1+k) + (1+g)^2/(1+k)^2 + (1+g)^3/(1+k)^3) + P(3)/(1+k)^3 => 2(1.08/1.11 + 1.08^2/1.11^2 + 1.08^3/1.11^3) + 90.70/1.11^3 => 72.00 ($)

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