The risk-free rate of return is 7.5%, the expected rate of return on the market

ID: 2769210 • Letter: T

Question

The risk-free rate of return is 7.5%, the expected rate of return on the market portfolio is 14%, and the stock of Xyrong Corporation has a beta coefficient of 2.8. Xyrong pays out 40% of its earnings in dividends, and the latest earnings announced were $25 per share. Dividends were just paid and are expected to be paid annually. You expect that Xyrong will earn an ROE of 16% 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 $67, 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

Cost of equity (Ke) = risk free rate + beta * ( market return - risk free rate)

= 7.5% + 2.8*(14% - 7.5%) = 25.7%

Growth rate = earnings retention * ROE

= (1- DIVIDEND PAYOUT RATIO ) * ROE

= (1-40%) *16% = 9.6%

Current dividend = $25

Dividend for next year = current dividend * (1+ growth rate) = 25*(1.096) = 27.4

Intrinsic = Dividend next year / ( ke-g)

= 27.4 / (25.7% - 9.6%) = $170.19

Intrinsic value after one year = $170.19 * (1.096) = $186.52

as market price will be equal to intrinsci value after one year

so market price after one year $186.52

Expected one-year holding period return = (dividend next year / current price) + (capital gain / current price)

= 27.4 / 67 + (186.52-67)/67 = 146.92/67 = 219.3%

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The risk-free rate of return is 7.5%, the expected rate of return on the market

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