The dividend yield for the next three years is given by:
[tex]D_1=\$3.85\times1.24=\$4.77 \\ \\ D_2=\$4.77\times1.24=\$5.92 \\ \\ D_3=\$5.92\times1.24=\$7.34[/tex]
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:
[tex]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[/tex]
We then obtain the current price of the stock by determining the present value of the three dividends and the future price as follows:
[tex]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[/tex]
