The risk-free rate of return is 9.0%, the expected rate of return on the market

Question

The risk-free rate of return is 9.0%, the expected rate of return on the market portfolio is 16%, and the stock of Xyrong Corporation has a beta coefficient of 1.5. Xyrong pays out 40% of its earnings in dividends, and the latest earnings announced were $15 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. What is the intrinsic value of a share of Xyrong stock? (Do not round intermediate calculations. Round your answer to 2 decimal places.) If the market price of a share is currently $87, and you expect the market price to be equal to the intrinsic value one year from now, calculate the price of the share after one year from now. (Do not round intermediate calculations. Round your answer to 2 decimal places.) What is your expected one-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

Explanation / Answer

a) Using the Gordon Growth Model,

Intrinsic Value of the stock = D1/ (ke - g)

where, D1 = Dividend per share expected next year

Ke Required Return on Equity

g = Growth rate

g = retention ratio * ROE

Dividend payout Ratio = 40%

Retention Ratio = 1 - Dividend payout Ratio = 1 - 40% = 60%

g = 60% * 20% = 12%

ke is calculate using CAPM

ke = Risk Free Rate + Beta * (Expected Return on Market Portfolio - Risk Free Rate)

     = 9% + 1.5 * (16% - 9%) = 9% + 1.5 * 7% = 19.5%

D1 = Dividend Payout Ratio * Next Year's Earnings per share

Earnings per share this year = $15

Earnings per share next year = 15 * (1+g) = 15 * (1+12%) = 15 * 1.12 = $16.80

D1 = 40% * 16.8 = $6.72

Intrinsic Value = D1/ (ke - g) = 6.72 / (19.5% - 12%) = 6.72 / 0.075 = $89.60

b-1) If market price of the stock is equal to the intrinsic value of the stock one year from now, then

Price of the share one year from now = D2/ (ke - g)

D2 = D1 * (1+g) = 6.72 * ( 1 + 12%) = 6.72 * 1.12 = $7.5264

Price of the share one year from now = 7.5264 / (19.5% - 12%) = 7.5264 / 0.075 = $100.35

b-2) Current Price of the Stock = $87

Expected Price of the stock one year from now = $100.35

Dividend from the stock at the end of year 1 = $6.72

Expected Gain = Dividend + Price of the share after 1 year - Current Price of the share

                           = 100.35 + 6.72 - 87 = $20.07

Expected one-year holding period return on Xyrong stock = (Expected Gain / Current Price) * 100

                                                                                                      = (20.07 / 87) * 100 = 23.07%

                     

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.