Question

Problem 8-32 Capital Gains versus Income [LO1] Consider four different stocks, all of which have a required return of 20 percent and a most recent dividend of $3.10 per share. Stocks W, X, and Y are expected to maintain constant growth rates in dividends for the foreseeable future of 10 percent, 0 percent, and –5 percent per year, respectively. Stock Z is a growth stock that will increase its dividend by 20 percent for the next two years and then maintain a constant 12 percent growth rate thereafter. What is the di vidend yield and capital gains yield for each of these four stocks? (Leave no cells blank - be certain to enter "0" wherever required. A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to 1 decimal place, e.g., 32.1.)

Answer 1

Price of Stock W =Dividend*(1+g)/(Required Rate-growth) =3.10*(1+10%)/(20%-10%) =34.10
Dividend Yield of Stock W =Dividend/(1+g)/Price =3.10*(1+10%)/34.10=10%
Capital Gain yield of Stock W =Growth =10%

Price of Stock X =Dividend*(1+g)/(Required Rate-growth) =3.10*(1+0%)/(20%-0%) =15.5
Dividend Yield of Stock X =Dividend/(1+g)/Price =3.10*(1+0%)/15.50 =20%
Capital Gain yield of Stock X=Growth =0%

Price of Stock Y =Dividend*(1+g)/(Required Rate-growth) =3.10*(1-5%)/(20%+5%) =11.78
Dividend Yield of Stock Y =Dividend/(1+g)/Price =3.10*(1-5%)/11.78=25%
Capital Gain yield of Stock Y =Growth =-5%

Price of Stock Z =Dividend*(1+g)/(1+r)+Dividend*(1+g)^2/(1+r)^2+Dividend*(1+g)^2*(1+Growth 2)/((Required Rate-growth)*(1+r)^2) =3.10*(1+20%)/(1+20%)+3.10*(1+20%)^2/(1+20%)^2+3.10*(1+20%)^2*(1+12%)/((20%-12%)*(1+20%)^2)=49.60
Dividend Yield =Dividend year 1/Price =3.10*1.20/49.60=7.50%
Capital Gain Yield of Stock Z =Required Rate-Dividend Yield =20%-7.50% =12.50%