Question

Your broker offers to see 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. 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 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 PVs 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 P3 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 if 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 that 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 was 2 years or 5 years rather than 3 years, would this affect the value of the stock today, Po? Explain

Answer 1

a) D1 = D0 x (1 + g) = $2 x (1 + 0.05) = $2.10

where, D0 = last dividend paid, g = growth rate

D2 = D1 x (1 + g) = $2.10 x (1 + 0.05) = $2.205 or $2.21

D3 = D2 x (1 + g) = $2.205 x (1 + 0.05) = $2.31525 or $2.32

b) PV of an amount is computed as -

PV = Amount / (1 + r)ⁿ where r is the discount rate of 12% and n is the year for which it is calculated

PV of D1 = $2.10 / (1 + 0.12)¹ = $1.875 or $1.88

PV of D2 = $2.205 / (1 + 0.12)² = $1.7578125 or $1.76

PV of D3 = $2.31525 / (1 + 0.12)³ = $1.64794921875 or $1.65

c) PV of P3 = $34.73 / (1 + 0.12)³ = $24.7201280065 or $24.72

d) The intrinsic value of stock is the maximum amount you should pay for the stock. It is the sum of the present value of dividends and price at the end of year 3.

Intrinsic value = PV of D1 + PV of D2 + PV of D3 + PV of P3 = $1.875 + $1.7578125 + $1.64794921875 + $24.7201280065 = $30.0008897252 or $30

e) The equation was not mentioned in the question but since the question says "constant growth rate", I believe it is the following equation -

P0 = D1 / (Ke - g)

where, Ke = discount rate, g = constant growth rate

P0 = $2.10 / (0.12 - 0.05) = $30

f) No, it does not depend upon the holding period in case of constant growth rate because the constant growth equation P0 = D1 / (Ke - g) does not change as per the holding period, i.e., to say the growth rate and discount rate do not change.