Question

The risk-free rate of return is 8%, the expected rate of return on the market portfolio is 15%, and the stock of Xyrong Corporation has a beta coefficient of 1.2. Xyrong pays out 40% of its earnings in dividends, and the latest earnings announced were $10 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?


B) If the market price of a share is currently $103, and you expect the market price to be equal to the intrinsic value one year from now, what is your expected one-year holding-period return on Xyrong stock?

Answer 1

Answer:

A)

risk free rate = 8%

market rate = 15%

Xyrong's beta = 1.2

pays 40% of income in dividends

latest EPS = $10

ROE = 18%

k = 8% + (1.2 x 7%) = 16.4%

g = ROE x (1 - 40%) = 10.8%

div1 = [(40% x $10) x (1 + g)] = $4 x 1.108 = $4.432

stock price = $4.432 / (16.4% - 10.8%) = $79.14

B)

div0 = $4

div1 = $4.432

price0 = $103

price1 = $79.14 x (1 + g) = $79.14 x 1.108 = $87.69

holding period return = ($4.43 + $87.69 - $103) / $103] = -0.1056 or -10.56%