The risk-free rate of return is 7.5%, the expected rate of return on the market portfolio is 17%, and the stock of Xyrong Corporation has a beta coefficient of 2.1. Xyrong pays out 25% of its earnings in dividends, and the latest earnings announced were $9.00 per share. Dividends were just paid and are expected to be paid annually. You expect that Xyrong will earn an ROE of 15% per year on all reinvested earnings forever. a. What is the intrinsic value of a share of Xyrong stock

$15.45

Explanation:

For computing the intrinsic value of a share first we have to determine the required rate of return and the growth rate which is shown below:

Required rate of return is

= Risk free rate of return + Beta × (Market rate of return - required rate of return)

= 7.5% + 2.1 × (17% - 7.5%)

= 27.45%

Now the growth rate is

= Risk free rate of return × Return on equity

= 0.75 × 15%

= 11.25%

Now the intrinsic value of a share is  

= Dividend × (1 + growth rate)  ÷ (required rate of return - growth rate

= $2.25 × 1.1125 ÷ (0.2745 - 0.1125)

= $2.50 ÷ 0.162

= $15.45