Question

The risk-free rate of return is 4%, the expected rate of return on the market portfolio is 12%, and the stock of Xyrong Corporation has a beta coefficient of 1.5. Xyrong pays out 25% of its earnings in dividends, and the latest earnings announced were $6.00 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.) Intrinsic value b. If the market price of a share is currently $70, 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.) Expected one-year holding-period return %

Answer 1

a. The intrinsic value is computed as shown below:

Cost of equity is computed as follows:

= Risk free rate + Beta ( return on market - risk free rate )

= 0.04 + 1.5 ( 0.12 - 0.04 )

= 0.16

The growth rate is computed as follows:

= retention rate x roe

= ( 1 - 0.25 ) x 0.18

= 0.135

Dividend just paid will be:

= $ 6 x 0.25

= $ 1.50

So the price will be:

= Dividend just paid ( 1 + growth rate ) / ( cost of equity - growth rate )

= $ 1.50 ( 1 + 0.135 ) / ( 0.16 - 0.135 )

= $ 68.1

b. The expected one year holding return is computed as follows:

= ( Price at the end of year - Current stock price + Dividend ) / ( Current stock price )

Price at the end of year = $ 68.1

Current stock price = $ 70

Dividend = $ 1.50 x 1.135

= $ 1.7025

So the return will be:

= ( $ 68.1 - $ 70 + $ 1.7025 ) / $ 70

= - 0.28% Approximately

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