Problem 18-13 The risk-free rate of return is 7.5%, the expected rate of return
ID: 2816671 • Letter: P
Question
Problem 18-13
The risk-free rate of return is 7.5%, the expected rate of return on the market portfolio is 15%, and the stock of Xyrong Corporation has a beta coefficient of 1.1. Xyrong pays out 50% of its earnings in dividends, and the latest earnings announced were $10.00 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.)
b. If the market price of a share is currently $75, and you expect the market price to be equal to the intrinsic value one year from now, what is your expected 1-year holding-period return on Xyrong stock? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Explanation / Answer
Required Rate of Return, r = Risk-free Rate of Return + Beta *(Rate of Return on Market - Risk-free Rate of Return)
Required Rate of Return, r = 7.50% + 1.1 * (15.00% - 7.50%)
Required Rate of Return, r = 15.75%
Payout Ratio = 50%
Plowback Ratio = 50%
Growth Rate, g = ROE * Plowback Ratio
Growth Rate, g = 18% * 50%
Growth Rate, g = 9.00%
Answer a.
Recent Earnings, EPS0 = $10.00
D0 = EPS0 * Payout Ratio
D0 = $10.00 * 50%
D0 = $5.00
D1 = D0 * (1 + g)
D1 = $5.00 * 1.09
D1 = $5.45
Intrinsic Value = D1 / (r - g)
Intrinsic Value = $5.45 / (0.1575 - 0.09)
Intrinsic Value = $80.74
Answer b.
Market Price = $75
Intrinsic Value after 1 year = $80.74 * 1.09
Intrinsic Value after 1 year = $88.01
Holding-period Return = (Intrinsic Value after 1 year + Expected Dividend - Market Price) / Market Price
Holding-period Return = ($88.01 + $5.45 - $75) / $75
Holding-period Return = 24.61%