Question

The risk-free rate of return is 9.0%, the expected rate of return on the market portfolio is 14%, and the stock of Xyrong Corporation has a beta coefficient of 2.0. Xyrong pays out 50% of its earnings in dividends, and the latest earnings announced were $20 per share. Dividends were just paid and are expected to be paid annually. You expect that Xyrong will earn an ROE of 18% per year on all reinvested earnings forever
a. What is the intrinsic value of a share of Xyrong stock? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Intrinsic valueS
b-1. If the market price of a share is currently $108, and you expect the market price to be equal to the intrinsic value one year from now, calculate the price of the share after one year from now. (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Price
b-2. What is your expected one-year holding-period return on Xyrong stock? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Expected one-year holding-period return

Answer 1

Answer:

$109

$118.81

18.26%

Explanation:

Intrinsic value can be determined using the constant growth dividend model

according to the constant dividend growth model

price = d1 / (r - g)

d1 = next dividend to be paid

r = cost of equity

g = growth rate

dividend, growth rate and cost of equity are not given and they have to be calculated

growth rate = retention rate x ROE  

Retention rate = 1 - payout ratio = 1 - 0.5 = 0.5 = 50%

0.5 x 18% = 9%

According to the capital asset price model: cost of equity = risk free + beta x (market rate of return - risk free rate of return)

9% + 2x (14% - 9%) = 19%

dividend = payout ratio x earnings per share

0.5 x $20 = $10

Intrinsic value = $\frac{10( 1 + 0.09)}{0.19 - 0.09}$ = $109

Stock price in a year

$\frac{10(1 + 0.9)^{2} }{0.19 - 0.09}$ = 118.81

(dividend return + price return)  

price return is the return on investment as a result of appreciation or depreciation of share price  

Dividend return is the return on investment from dividend earned  

price return = price at the end of the year - price at the beginning of the year