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

a. Calculation of intrinsic value of share by dividend growth model

ROE = D1/P0 + G = Expected return

D1 = Dividend after 1 year = D0 (1+g)

P0= price of share or intrinsic value

G= growth rate = retention ratio * Expected return

Retention ratio = (100-dividend payout) = (100-40%) = 60%

G = 60%*25% = 15%

D0 = Earnings * dividend payout = 8.5*40% = 3.4

D1 = D0(1+G) = 3.4(1+.15) = 3.91

ROE = 25% (Given in question) = D1/P0 + G

0.25 = 3.91/P0 + 0.15

0.25-0.15=3.91/P0

P0= 3.91/0.1 = 39.1

Intrinsic value of share = $ 39.1

b. Calculation on return on stock

ROE = D1/P0+G

P0 =35 (Given in question)

For calculation of growth and dividend after one year we have to use CAPM (Capital Asset Price Model)

ER = Expected return = RF+ Beta (RM- RF)

RF = risk free return = 6.5% (given in question)

Beta = 1.8 (given in question)
RM = Market return = 17% (given in question)
ER = 6.5%+1.8(17%-6.5%) = 25.4%
G = Retention ratio* ER = 60%*25.4% = 15.24%
D1 = D0(1+G) = 3.4(1+15.24%)=3.91816

ROE = D1/P0+G = 3.91816/35 + 15.24% = 26.43%

ROE = 26.43%

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