Question

The risk-free rate of return is 5.5%, the expected rate of return on the market portfolio is 14%, and the stock of Xyrong Corporation has a beta coefficient of 1.9. Xyrong pays out 50% of its earnings in dividends, and the latest earnings announced were $7.50 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. Omit the "$" sign in your response.)

Intrinsic value ---------------$

b. If the market price of a share is currently $27.00, 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. Omit the "%" sign in your response.)

Expected one-year holding-period return    --------------%

Answer 1

a). Calculation of Required rate of return using CAPM equation would be as follows.

Required Return = Risk-free Rate + [Beta * (Expected Market Return - Risk-free Rate)]

= 5.5% + [1.9 * (14% - 5.5%)]

= 5.5% + 16.15% = 21.65%

Calucation of dividend growth rate (g) would be.

g = ROE * (1 - Payout Ratio)

= 18% * (1 - 0.50) = 9%

D0 = EPS0 * Payout Ratio = $7.50 * 0.50 = $3.75

P0 = [D0 * (1 + g)] / [r - g]

= [$3.75 * (1 + 0.09)] / [0.2165 - 0.09]

= $4.0875 / 0.1265 = $32.31

b). Holding Period Return = [P1 + D1 - P0] / P0

= [$32.31 + $4.0875 - $27] / $27 = $9.3975/ $27 = 0.34806, or 34.81%