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The risk-free rate of return is 10

Finance

The risk-free rate of return is 10.5%, the expected rate of return on the market portfolio is 17%, and the stock of Xyrong Corporation has a beta coefficient of 1.5. Xyrong pays out 50% of its earnings in dividends, and the latest earnings announced were $13 per share. Dividends were just paid and are expected to be paid annually. You expect that Xyrong will earn an ROE of 24% 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-1) If the market price of a share is currently $87, 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.) 

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.) 

 

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a) Computation of the intrinsic value of share:-

Required return = Risk free rate + Beta * (Expected market return - Risk free rate)

= 10.5% + 1.5 * (17% - 10.5%)

= 10.5% + (1.5 * 6.50%)

= 10.5% + 9.75%

= 20.25%

Growth rate = ROE * (1 - Payout ratio)

= 24% * (1 - 50%)

= 12%

Dividend = EPS * Payout ratio

= $13 * 50%

= $6.50

Intrinsic value = D1 / (Required return - Growth rate)

= $6.50 * (1 + 12%) / (20.25% - 12%)

= $7.28 / 8.25%

= $88.24

 

b-1) Computation of the price of share after one year (P1):-

Share price after one year = P0 * (1 + Growth rate)

= $88.24 * (1 + 12%)

= $98.83

 

b-2) Computation of the expected one year holding period return:-

Expected dividend = D0 * (1 + Growth rate)

= $6.50 * (1 + 12%)

= $7.28

Holding-period Return = (Intrinsic Value after 1 year + Expected dividend - Market price) / Market price

= ($98.83 + $7.28 - $87) / $87

= $19.11 / $87

= 21.97%

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