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 20% 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 $100, 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

Answer:

a. The intrinsic value of a share of Xyrong stock is $90.91.

b. Your expected 1-year holding-period return on Xyrong stock is 5.82%.

Explanation:

Given in the question are the following:

rf = risk-free rate of return = 8%, or 0.08

rm = expected rate of return on the market portfolio = 15%. or 0.15

b = beta = 1.2

dp = Dividend payout ratio = 40%, or 0.40

e = latest earnings = $10

ROE = Return on equity = 20%, or 0.20

We therefore proceed as follows:

a. What is the intrinsic value of a share of Xyrong stock ? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

This can be calculated using the formula for calculating the intrinsic value of a share as follows:

Intrinsic value = (e * dp) / [rf + b * (rm - rf) - ROE * (1 - dp)] .......... (1)

Substituting the values into equation (1), we have:

Intrinsic value = ($10 * 40%) / [8%+ 1.2 * (15% - 8%) - 20% * (1 - 40%)]

Intrinsic value = $4 / [8% + 1.2 * 7% - 20% * 60%

Intrinsic value = $4 / (8% + 0.084 - 12%)

Intrinsic value = $4 / 0.044

Intrinsic value = $90.91

Therefore, the intrinsic value of a share of Xyrong stock is $90.91.

b. If the market price of a share is currently $100, 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.)

To do this, we first calculate the price of the share after one year from now as follows:

p1 = Intrinsic value * (1 + ROE * (1 - dp)) ............................ (2)

Where p1 denotes the price of the share after one year from now.

Substituting the relevant values into equation (2), we have:

p1 = 90.91 * (1 + 20% * (1-40%))

p1 = 90.91 * (1 + 20% * 60%)

p1 = 90.91 * 1.12

p1 = 101.8192

We can now calculate the expected 1-year holding-period return on Xyrong stock as follows:

Expected 1-year holding-period return = (p1 + e * dp) / 100 - 1 ............ (3)

Substituting the relevant values into equation (3), we have:

Expected 1-year holding-period return = [(101.8192 + 10 * 40%) / 100] - 1

Expected 1-year holding-period return = [105.8192 / 100] - 1

Expected 1-year holding-period return = 1.058192 - 1

Expected 1-year holding-period return = 0.058192, or 5.82%

Therefore, your expected 1-year holding-period return on Xyrong stock is 5.82%.