Consider four different stocks, all of which have a required return of 20 percen
ID: 2776725 • Letter: C
Question
Consider four different stocks, all of which have a required return of 20 percent and a most recent dividend of $4.10 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 10 percent growth rate thereafter. What is the dividend yield for each of these four stocks?
Explanation / Answer
W.
We have:
D0= 4.10
G=10 %
Ke = 20%
We have following formula for value of a stock:
P = D0(1+g)/ (Ke-g)
= 4.10(1+0.10)/(0.20-0.10)
=45.10
Dividend yield = Do(1+g)/P
= 4.10x(1+0.1)/45.10
=10%
X.
D0= 4.10
G=0 %
Ke = 20%
We have following formula for value of a stock:
P = D0(1+g)/ (Ke-g)
= 4.10(1+0.0)/(0.20-0.0)
=20.50
Dividend yield = Do(1+g)/P
= 4.10x(1+0.0)/20.50
=20%
Y.
D0= 4.10
G=-5 %
Ke = 20%
We have following formula for value of a stock:
P = D0(1+g)/ (Ke-g)
= 4.10(1-0.05)/(0.20+0.05)
=15.58
Dividend yield = Do(1+g)/P
= 4.10x(1-.05)/15.58
=25%
Z
D0= 4.10
G=-5 %
Ke = 20%
We have following formula for value of a stock:
D1 = 4.10x(1+0.20) = 4.92
D2=4.92x(1+0.20) =5.904
P2 = D2(1+g)/ (Ke-g)
= 5.904(1+0.10)/(0.20-0.10)
=64.944
Current price of the stock would be PV of all the future prices and dividend:
year
CF
PV factor 20%
PV
1
4.92
0.8333
4.10
2
5.904+64.944
0.6944
49.20
53.30
Dividend yield = Do(1+g)/P
= 4.10x(1+0.2)/53.30
=9.23%
year
CF
PV factor 20%
PV
1
4.92
0.8333
4.10
2
5.904+64.944
0.6944
49.20
53.30
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