Question 8CRS-TP2: In Self-Test Problem 8.1, what would the stock sell for toda...
In Self-Test Problem 8.1, what would the stock sell for today if the dividend was expected to grow at 20 percent per year for the next three years and then settle down to 8 percent per year, indefinitely?
In this scenario, we have supernormal growth for the next three years. We’ll need to calculate the dividends during the rapid-growth period and the stock price in three years. The dividends are:
D_{1} = $2.00 × 1.20 = $2.400
D_{2} = $2.40 × 1.20 = $2.880
D_{3} = $2.88 × 1.20 = $3.456
After three years, the growth rate falls to 8 percent indefinitely. The price at that time, P_{3}, is thus:
P_{3} = D_{3} × (1 + g)/(R – g)
= $3.456 × 1.08/(.16 – .08)
= $3.7325/.08
= $46.656
To complete the calculation of the stock’s present value, we have to determine the present value of the three dividends and the future price:
P_{0}=\frac{D_{1}}{(1+R)^1}+\frac{D_{2}}{(1+R)^2}+\frac{D_{3}}{(1+R)^3}+\frac{P_{3}}{(1+R)^3}
=\frac{\$2.40}{1.16}+\frac{2.88}{1.16^2}+\frac{3.456}{1.16^3}+\frac{46.656}{1.16^3}
=\$2.07+2.14+2.21+29.89
=\$36.31