Your broker offers to sell you some shares of Bahnsen & Co. common stock that pa
ID: 2664723 • Letter: Y
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 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 [ayment 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 expected 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 it 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 contant.
f) Is the value of this stock dependent upon how long you plan to hold it ? In other words, if you planned holding period was 2 years or 5 years rather than 3 years, would this affect the value of the stock today, P0 ? Explain.
Explanation / Answer
a) Calculating the Dividends for the next three years: The formula for calculating the dividend for the next year is D1 = D0 (1+g) = $2.00 (1 + 0.05) = $2.00 (1.05) = $2.1 D2 = D1 (1+g) = $2.1 (1+ 0.05) = $2.205 D3 = $2.205 (1.05) = $2.315 b) The present value of the dividend stream is calculated as: PV = D1 / (1+R)^1 + D2 / (1+R)^2 + D3 / (1+R)^3 = $2.1 / (1.12) + $2.205 / 1.2544 + $2.315 / 1.45 = $1.875 + $1.76 + $1.6 = $5.235 c) Calculating the present value of the future stock price: P3 = D3 (1+g) / (R-g) = $2.315 (1.05) / (0.12 - 0.05) = $2.43 / 0.07 = $34.73 P0 = D1 / (1+R)^1 + D2 / (1+R)^2 + D3 / (1+R)^3 + P3 / (1+R)^3 = $2.1 / (1.12) + $2.205 / 1.2544 + $2.315 / 1.45 + $34.73 / 1.45 = $1.875 + $1.76 + $1.6 + $23.95 = $29.185 d) The value of the stock in 3 yrs is $34.73, then we can get the present value of the stock by discounting this price back three years at 12%. P0 = $34.73 / 1.45 = $23.95 Therefore, the stock is worth $23.95 today. e) Assuming dividends grow at a constant rate, the present value of the dividend stream is P0 = D1 / (R-g) = $2.1 / (0.12 - 0.07) = $30 Therefore, the price of the stock today is $30 f) As long as the growth rate is less than the discount rate, the present value of this series of cash flows can be simply written as P0 = D0 (1+g) / (R-g) Therefore, this does not change according to the holding period. This is referred to as Dividend growth model and we can use this model to get the stock price at any point, not just today. Therefor, the holding period of 2yrs or 5yrs does not affect the present value of the stock as long as the growth rate is less than the discount rate. P3 = D3 (1+g) / (R-g) = $2.315 (1.05) / (0.12 - 0.05) = $2.43 / 0.07 = $34.73 P0 = D1 / (1+R)^1 + D2 / (1+R)^2 + D3 / (1+R)^3 + P3 / (1+R)^3 = $2.1 / (1.12) + $2.205 / 1.2544 + $2.315 / 1.45 + $34.73 / 1.45 = $1.875 + $1.76 + $1.6 + $23.95 = $29.185 d) The value of the stock in 3 yrs is $34.73, then we can get the present value of the stock by discounting this price back three years at 12%. P0 = $34.73 / 1.45 = $23.95 Therefore, the stock is worth $23.95 today. e) Assuming dividends grow at a constant rate, the present value of the dividend stream is P0 = D1 / (R-g) = $2.1 / (0.12 - 0.07) = $30 Therefore, the price of the stock today is $30 f) As long as the growth rate is less than the discount rate, the present value of this series of cash flows can be simply written as P0 = D0 (1+g) / (R-g) Therefore, this does not change according to the holding period. This is referred to as Dividend growth model and we can use this model to get the stock price at any point, not just today. Therefor, the holding period of 2yrs or 5yrs does not affect the present value of the stock as long as the growth rate is less than the discount rate. P0 = D1 / (1+R)^1 + D2 / (1+R)^2 + D3 / (1+R)^3 + P3 / (1+R)^3 = $2.1 / (1.12) + $2.205 / 1.2544 + $2.315 / 1.45 + $34.73 / 1.45 = $1.875 + $1.76 + $1.6 + $23.95 = $29.185 d) The value of the stock in 3 yrs is $34.73, then we can get the present value of the stock by discounting this price back three years at 12%. P0 = $34.73 / 1.45 = $23.95 Therefore, the stock is worth $23.95 today. e) Assuming dividends grow at a constant rate, the present value of the dividend stream is P0 = D1 / (R-g) = $2.1 / (0.12 - 0.07) = $30 Therefore, the price of the stock today is $30 f) As long as the growth rate is less than the discount rate, the present value of this series of cash flows can be simply written as P0 = D0 (1+g) / (R-g) Therefore, this does not change according to the holding period. This is referred to as Dividend growth model and we can use this model to get the stock price at any point, not just today. Therefor, the holding period of 2yrs or 5yrs does not affect the present value of the stock as long as the growth rate is less than the discount rate.Related Questions
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