SPRING 2011, AUBG
Problem 1 (10 points)
The Duo Growth company just paid a dividend of $1 per share. The dividend is expected to grow at a rate of 25% per year for the next two years and then to level off to 5% per year forever. You think the appropriate market capitalization rate is 20% per year. a. What is your estimate of the intrinsic value of a share of the stock? b. If the market price of a share is equal to this intrinsic value what is the expected dividend yield? c. What do you expect its price to be in one year from now? Is the implied capital gain consistent with your estimate of the dividend yield and the market capitalization rate? (Note: Capital gain = (P1 – P0)/P0)
|Time: |0 |1 |2 |3 | | D t |$1.0000 |$1.2500 |$1.5625 |$1.640625 | |g |25.0% |25.0% |25.0% |5.0% |
a. The dividend to be paid at the end of year 3 is the first installment of a dividend stream that will increase indefinitely at the constant growth rate of 5%. Therefore, we can use the constant growth model as of the end of year 2 in order to calculate intrinsic value by adding the present value of the first two dividends plus the present value of the price of the stock at the end of year 2.
The expected price 2 years from now is:
P2 = D3/(k – g) = $1.640625/(0.20 – 0.05) = $10.9375
The PV of this expected price is: $10.9375/1.202 = $7.5955
The PV of expected dividends in years 1 and 2 is: [pic]
Thus the current price should be: P0 = $7.5955 + $2.1267 = $9.7222
b. Expected dividend yield = D1/P0 = $1.25/$9.7222 = 12.857%
c. The expected price one year from now is the PV at that time of P2 and D2:
P1 = (D2 + P2)/1.20 = ($1.5625 + $10.9375)/1.20 = $10.4167...