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 $2.50 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 10%.

Find the expected dividend for each of the next 3 years; that is, calculate D1, D2 and D3. Note that D0 = $2.50. 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 $170.06; that is, you expect to equal $170.06. Discounted at a 10% rate, what is the present value of this expected future stock price? In other words, calculate the PV of $170.06. 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 $170.06, 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.


h. 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, ?
-Select-IIIIIIIVVItem 8
I. No. The value of the stock is not dependent upon the holding period unless the growth rate remains constant for the foreseeable future.
II. Yes. The value of the stock is dependent upon the holding period as long as the growth rate remains constant for the foreseeable future.
III. No. The value of the stock is not dependent upon the holding period. The value calculated in Parts a through d is the value for a 3-year holding period. It is equal to the value calculated in Part e. Any other holding period would produce the same value of .
IV. Yes. The value of the stock is dependent upon the holding period. The value calculated in Parts a through d is the value for a 3-year holding period. It is not equal to the value calculated in Part e. Any other holding period would produce a different value of .
V. Yes. The value of the stock is dependent upon the holding period due to the fact that the value is determined as the present value of all future expected dividends.

Explanation / Answer

a) The dividend is expected to grow at a constant growth rate of 8% per year for the next three years: a) D1 = D0(1+g) = $2.50 (1 + 0.08) = $2.7 b) D2 = D1 (1+g) = $2.7 (1.08) = $2.916 c) D3 = D2(1+g) = $3.15 d) As long as the growth rate is less than the discout rate, the present value of the dividend stream is calculated as: P0 = D1 / (R-g) = $2.7 / (0.1 - 0.08) = $2.7 / 0.02 = $135 Therefore, the present value of the dividend stream is $135 e) Calculting the current price of the stock: P0 = D1 / (1+r) + D2 / (1+r)^2 + D3 / (1+r)^3 + P3 / (1+r)^3 = $2.7 / (1.1) + $2.916 / (1.21) + $3.15 / (1.331) + $170.06 / (1.331) = $2.45 + $2.41 + $2.36 + $127.77 = $134.99 or $135 Therefore, the price of the stock today is $135 f) If he wants to sell the stock after 3 years, then the present value of the stock would be : Step1: Go to excel and click "insert" to insert the function Step2: Select the "PV" function as we are finding the present value of the stock Step3: Enter the values as Rate = 10%; Nper = 3; PMT = -3.15; FV = -170.06 Step4: Click "OK" to get the desired value. The value comes to "$135" The payment is the third year dividend payment and the future value is the selling price of the stock in the third year. Therefore, the price of the stock today is $135 g) There is no complete information for this part f) The correct option is II) yes the value of the stock os dependent on the holding period as long as the growth rate remains constant for the forseeable future.

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