Answer to Question #185858 in Financial Math for anus

Question

Your company paid a dividend of $2.00 last year. The growth rate is expected to be 4 percent for 1 year, 5 percent the next year, then 6 percent for the following year, and then the growth rate is expected to be a constant 7 percent thereafter. The required rate of return on equity (ks) is 10 percent. What is the current stock price

Answer 1

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

$D_{1}=\$2.00\times1.04=2.08$

$D_{2}=\$2.08\times1.05=2.184$

$D_{3}=\$2.184\times1.06=2.31504$

$P_{3}=D_{3}(\frac{1+g}{R-g})$

$=\$2.31504(\frac{1+0.07}{0.1-0.07})$

$\$2.31504(\frac{1.07}{0.03})=\$2.31504(35.67)$

$=\$82.57$

$\therefore$ The current stock price

$P_{0}=\frac{D_{1}}{1+R}+\frac{D_{2}}{(1+R)^2}+\frac{D_{3}}{(1+R)^3}+\frac{P_{3}}{(1+R)^3}$

$=\frac{2.08}{1+1.1}+\frac{2.184}{(1+1.1)^2}+\frac{2.31504}{(1+1.1)^3}+\frac{82.57}{(1+1.1)^3}$

$=\frac{2.08}{2.1}+\frac{2.184}{(2.1)^2}+\frac{2.31504}{(2.1)^3}+\frac{82.57}{(2.1)^3}=0.99+0.50+0.25+8.92$

$=\$10.66$