The risk-free rate of return is 6.5%, the expected rate of return on the market
ID: 2751889 • Letter: T
Question
The risk-free rate of return is 6.5%, the expected rate of return on the market portfolio is 13%, and the stock of Xyrong Corporation has a beta coefficient of 2.7. 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 25% 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 value $ _______________
b-1. If the market price of a share is currently $96, 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 _________ %
Explanation / Answer
Required rate of return using CAPM model = risk free rate + beta ( expected return - risk free rate)
Required rate of return = 0.065 + 2.7 ( 0.13 - 0.065)
Required rate of return = 0.2405 or 24.05%
Growth rate = ( 1 - dividend payout ratio) *ROE
Growth rate = ( 1 - 0.5) * 0.25
Growth rate = 0.125 or 12.5%
a)
Dividends per share will be $10 since payout ratio is 50%
Intrinsic value of share = D1 / rate - growth
Intrinsic value of share = 10(1.125) / 0.2405 - 0.125
Intrinsic value of share = 11.25 / 0.1155
Intrinsic value of share = $97.40
b)
Price after 1 year = 97.40( 1 + 0.125)
Price after 1 year = $109.58
c)
One year holding period return = ( 109.58 + 11.25 - 96) / 96
One year holding period return = 0.25864 or 25.86%
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