Question

Synovec co. is growing quickly. dividends are expected to grow at a rate of 24 percent for the next three years, with the growth rate falling off to a constant 5 percent thereafter. if the required return is 12 percent, and the company just paid a dividend of $3.85, what is the current share price?

Answer 1

The dividend yield for the next three years is given by:

$D_1=\ 3.85\times1.24=\ 4.77 \\ \\ D_2=\ 4.77\times1.24=\ 5.92 \\ \\ D_3=\ 5.92\times1.24=\ 7.34$

Given that the growth rate falls off to a constant 5 percent after three years, i.e. g = 0.05 and that the required return is 12 percent, i.e. R = 0.12, then the price of the shares at that time is given by:

$P_3=D_3\left(\frac{1+g}{R-g}\right) \\ \\ =\ 7.34\left(\frac{1+0.05}{0.12-0.05}\right) \\ \\ =\ 7.34\left(\frac{1.05}{0.07}\right)=\ 7.34(15) \\ \\ =\ 110.10$

We then obtain the current price of the stock by determining the present value of the three dividends and the future price as follows:

$P_0= \frac{D_1}{1+R} + \frac{D_2}{(1+R)^2} + \frac{D_3}{(1+R)^3} + \frac{P_3}{(1+R)^3} \\ \\ = \frac{4.77}{1+0.12} + \frac{5.92}{(1+0.12)^2} + \frac{7.34}{(1+0.12)^3} + \frac{110.10}{(1+0.12)^3} \\ \\ =\frac{4.77}{1.12} + \frac{5.92}{(1.12)^2} + \frac{7.34}{(1.12)^3} + \frac{110.10}{(1.12)^3}=\ 4.26+\ 4.72+\ 5.22 +\ 78.37 \\ \\ =\ 92.57$