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

a.

P0 = $101.82

b.

Holding period return = 18.52%

Step-by-step explanation:

a.

The intrinsic value of the share can be calculated using the constant growth model of DDM. The DDM values the share based on the present value of the expected future dividends from the stock. The formula for Price today under this model is,

P0 = D1 / r - g

Where,

• D1 is the expected dividend for the next period or Year 1 or D0 * (1+g)
• r is the required rate of return
• g is the constant growth rate in dividends

First we need to calculate the r or required rate of return using the CAPM equation.

r = rRF + Beta * (rM - rRF)

Where,

• rRF is the risk free rate and rM is the return on market

r = 0.08 + 1.2 * (0.15 - 0.08)

r = 0.164 or 16.4%

The constant growth rate on the stock can be calculated as follows,

Constant or sustainable growth rate or g = ROE * RR

Where,

• ROE is return on equity
• RR is retention ratio or (1 - Dividend payout ratio)

g = 0.2 * (1 - 0.4)

g = 0.12 or 12%

As the earnings per share were $10 and the payout ratio is 40%, the dividend per share or D0 was 10 * 0.4 = $4

P0 = 4 * (1+0.12) / (0.164 - 0.12)

P0 = $101.8181818 rounded off to $101.82

b.

The price one year from now will be,

P1 = D2 / (r - g)

P1 = 4 * (1+0.12)^2 / (0.164 - 0.12)

P1 = $114.0363636 rounded off to $114.04

Dividend Year 1 = 4 * 1.12 = 4.48

The formula for holding period return is attached.

Holding period return =[ 4.48 + (114.0363636 - 100) ] / 100

Holding period return = 0.185163636 or 18.5163636% rounded off to 18.52%