The risk-free rate of return is 6.5%, the expected rate of return on the market

Question

The risk-free rate of return is 6.5%, the expected rate of return on the market portfolio is 17%, and the stock of Xyrong Corporation has a beta coefficient of 1.8. Xyrong pays out 40% of its earnings in dividends, and the latest earnings announced were $8.50 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.)

b. If the market price of a share is currently $35, 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

Answer a)

Expected return of a stock = Risk free rate + Beta * (Market return - risk free rate)

= 6.5% + 1.8 *(17%-6.5%)

= 25.40%

Growth rate = Retention ratio x Return on equity

= (1-0.40) x 0.25

= 15%

Intrinsic value = Expected dividend / (Required return - Growth)

= 8.5 x 0.40 x (1.15) / (0.2540 - 0.15)

= 37.59615

Answer b) P1 = Vo (1+g) = 37.59615 * (1+0.15) = 43.23558

E(r) = [(8.5*0.4*1.15) + 43.23558 - 35 ] / 35 = 0.347016 or 34.70%

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