Problem 9-17 Constant growth Your broker offers to sell you some shares of Bahns

Question

Problem 9-17 Constant growth Your broker offers to sell you some shares of Bahnsen & Co. common stock that paid a dividend of $3.50 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 9%. a. Find the expected dividend for each of the next 3 years; that is, calculate D1, D2 and D3. Note that D0 = $3.50. Round your answer to the nearest cent. 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 PV5 of D1, D2, and D3 and then sum these PV5. Round your answer to the nearest cent. c. You expect the price of the stock 3 years from now to be $106.36; that is, you expect P3 to equal $106.36. Discounted at a 9% rate, what is the present value of this expected future stock price? In other words, calculate the PV of $106.36. Round your answer to the nearest cent. d. If you plan to buy the stock, hold it for 3 years, and then sell it for $106.36, what is the most you should pay for it today? Round your answer to the nearest cent. e. 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

Dividend for Year 1 = Dividend for year 0 *( 1+ growth rate)^n

So, D0 = 3.5

D1 = 3.5(1.05) = 3.675

D2 = 3.675 (1.05) = 3.8588

D3 = 3.8588 (1.05) = 4.0517

B)Present Value of the stream of dividend = Divdend for year 1/(1+r)^1 + Dividend for year 2 / (1+r)^2 + Dividend for year 3 / (1+r)^3

=3.675/(1.09) +3.8588/(1.09)^2 + 4.0517/ (1.09)^3

=9.7481

c) Present Value of Expected Future Stock price = Price at year3/ (1+r)^3

                                                                              =106.36/(1.09)^3

                                                                              =82.13

       D) The value payable today is PV of dividends + PV of price after 3 years

                                                     =9.7481+82.13 = 91.88

E) Using Gordon Model, the PV of stock is D0(1+g)/ r-g

=3.5(1.05)/(.09-.05)

= 91.875

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