Answer to Question #261753 in Financial Math for ray

Question

Yohe Technology’s stock is expected to pay a dividend of $2.00 a share at the end of the year. The stock currently has a price of $40 a share, and the stock’s dividend is expected to grow at a constant rate of g percent a year. The stock has a beta of 1.2. The market risk premium, k_M – k_RF, is 7 percent and the risk-free rate is 5 percent. What is the expected price of Yohe’s stock 5 years from today?

Answer 1

Calculate cost of equity using CAPM model:

(k)=Risk free rate+Beta$\times$ Market risk free premium

$=$ $5\%+1.2 \times7\%$

$=13.4\%$

Calculate growth rate of dividend using Gordon Growth Dividend model:

$P_{o}=\frac{D_{1}}{k-g}$

$\$40=\frac{\$2}{13.4\%-g\%}$

$\$5.36-\$40g=\$2$

$g=8.4\%$

Calculate terminal value at the end of year 5:

$=\frac {D_{1}\times(1+g\%)^5}{k-g}$

$=\frac {\$2\times(1+8.4\%)^5}{13.4\%-8.4\%}$

$=\$59.87$

$\therefore$ the expected price of Yohe’s stock 5 years from today is $\$59.87$