Answer:
a. The intrinsic value of a share of Xyrong stock is <u>$90.91</u>.
b. Your expected 1-year holding-period return on Xyrong stock is <u>5.82%</u>.
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 <u>$90.91</u>.
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 <u>5.82%</u>.
