Question

Question 4

One year ago, Hangzhou Limited made an announcement that they would not pay out any dividends for the subsequent four years and that the next dividend would be paid out in five years. The stock price at the time of the announcement was $88. Analysts expect the next dividend that will be paid out to grow at 8% for three consecutive years, then at 5% for two years and then at 4% per year forever.

a) Hangzhou stock has a beta of 1.3, the risk free rate is 4% and the market risk premium is 8%. Assume the Capital Asset Pricing Model holds. What is the required rate of return for a stock of Hangzhou Limited?

b) Calculate the next dividend that will be paid out. Use the required rate of return calculated in part a.

c) Sofu bought a stock of Hangzhou Limited one year ago. Suppose she sells it two years from now. What would be her capital gains yield over this entire three-year period?

Answer 1

Answer to Part A

If CAPM holds good it means here we are finding expected return of a stock

Formula of CAPM = Rf + beta(Rm-Rf) Here (Rm-Rf) refers to Risk Premium

Usinf information in question we calulate expected return as follows

CAPM or Expected return = 4% + 1.3*(8%) = 4+10.4 = 14.4% This is the required return from company stock

Answer to Part B

As It is given in question that one year ago company decided not to pay any dividend in coming four years so lets suppose today is Jan 2018 Therefore company decided not to Pay any dividend in Jan 2017.

That means company would not pay dividends for years 2017,2018,2019 and 2020 that is 4 years beginning Jan 2017 means next dividend would be paid in Jan 2021.

we suppose it is Jan 2018 today and share price is $88 and as no dividends are paid for 2018,2019 and 2020 it is safe to assume entire return company earns in these years are reinvested in the business itself.

For example if stock price today that is Jan 2018 is $100 and expected return or CAPM return is 10% it means price after 3 years or at beginning of Jan 2021 would be $100*1.10*1.10*1.10=$133.1

Similarly in our question price is $88 so reinvesting return of 14.4% for 3 years as no dividends are paid price after 3 years at beginning of jan 2021 would be $88*1.144*1.144*1.144 = $131.75

Note that no dividends are paid for 2017 to 2020 that is for 4 years Now dividend would be paid in Jan 2021 based on price of $131.75.

Dividend to be paid = $131.75 * 14.4%= $18.972 as Dividend assuming entire EPS of $18.972 is paid as dividend. Answer to Part C suppose to day is Jan 2018 so the investor the share in Jan 2017 at $88/1.144= $76.92 and sofu would sell in 2 years from now that is in Jan 2020 when price would be $88 * 1.144*1.144 = $115.16 Buy at $76.92 and sell at $115.16 So capital gains = 115.16-76.92= 38.24 Capital gain yield = Capital Gains/ Buy price *100 = 38.24/76.92 *100 = 49.71%