Question

The risk-free rate of return is 6%, the expected rate of return on the market portfolio is 15%, and the stock of Xyrong Corporation has a beta coefficient of 2.3. Xyrong pays out 45% of its earnings in dividends, and the latest earnings announced were $9.00 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.)

b. If the market price of a share is currently $22, 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.)

Answer 1

Required rate of return is calculated below using CAPM model:

Required rate of return = Risk free rate + (Market return - Risk free rate) × Beta

= 6% + (15% - 6%) × 2.30

= 6% + (9% × 2.30)

= 6% + 20.70%

= 26.70%

Required rate of return is 26.70%.

Current Year earnings = $9

Payout ratio = 45%

Current Year dividend = $9 × 45%

= $4.05

Current year dividend is $4.05.

Retention ratio = 55%

Return on equity =18%

Sustainable growth rate for the firm is calculated below using following formula:

Sustainable growth rate = Retention Ratio × return on equity

= 55% × 18%

= 9.90%

Hence, Sustainable growth rate is 9.90%.

a.

Current Stock price = Current Dividend × (1 + Growth rate) / (Required rate - Growth rate)

= $4.05 × (1 + 9.90%) / (26.70% - 9.90%)

= $4.45 / 16.80%

= $26.49

intrinsic value of a share of Xyrong stock is $26.49.

b.

if current Market price = $22

Stock price after one year = $26.49.

one year holding period = ($26.49 - $22) / $22

= 20.43%

One year holding period is 20.43%.