Question

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 dividend yield for each of these four stocks? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) What is the expected 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 2 decimal places, e.g., 32.16.)

Answer 1

Dividend yield is the percentage of dividend earned on the price of the stock
Capital gain yield is the percentage of gain company earns by holding and selling the stock at higher price.
The total return of stock comprises of capital gain yield plus the dividend yield.
Therefore the required return given of 20 percent consists of both dividend yield and capital gain yield
To calculate the dividend yield and capital gain yield we will have to calculate the price of all the four stocks
By using the dividend growth model we would calculate the price of stocks
Formula to calculate price of stocks
P0 = D0(1+g)/(R-g)
where D0 = Dividend declared today
g = growth rate of dividend
R = required return
Formula to calculate dividend yield
Dividend Yield = D1/P0
where D1 = Dividend at year end, calculated as D0(1+g)
P0 = Price of stock today
Formula to calculate capital gains yield
Capital gain yield = Total (required) return - Dividend Yield
Calculation for stock W
P0 = [3.10(1+0.10)]/(0.20-0.10)
P0 = 3.41/0.10
P0 = $34.10
Price of stock W is $34.10
Dividend Yield = [3.10*(1+0.10)]/34.10
Dividend Yield = 3.41/34.10
Dividend Yield = 10%
Dividend yield of stock W is 10%
Capital gain yield = 0.20-0.10
Capital gain yield = 0.10
Capital gain yield of stock W is 10%
Calculation for stock X
P0 = [3.10(1+0)]/(0.20-0.0)
P0 = 3.1/0.20
P0 = $15.50
Price of stock X is $15.50
Dividend Yield = [3.10*(1+0)]/15.50
Dividend Yield = 3.10/15.50
Dividend Yield = 20%
Dividend yield of stock X is 20%
Capital gain yield = 0.20-0.20
Capital gain yield = 0
Capital gain yield of stock X is 0%
Calculation for stock Y
P0 = [3.10(1+(-0.05))]/(0.20-(-0.05)
P0 = 2.945/0.25
P0 = $11.78
Price of stock Y is $11.78
Dividend Yield = [3.10*(1+(-0.05)]/11.78
Dividend Yield = 2.945/11.78
Dividend Yield = 25%
Dividend yield of stock Y is 25%
Capital gain yield = 0.20-0.25
Capital gain yield = -0.05%
Capital gain yield of stock Y is -5%
Calculation for stock Z
P2 = [D0(1+g1)^2]*[(1+g2)/(R-g2)]
P2 = 3.10(1.20^2)(1.12)/(0.20-0.12)
P2 = 62.496
P0 = [3.10*(1.20)/1.20] + [3.10(1.20^2)]/[1.20^2]+62.496/(1.20^2)
P0 = 49.60
Price of stock Z is $49.60
Dividend Yield = [3.10*(1.20)]/49.60
Dividend Yield = 3.72/49.60
Dividend Yield = 7.50%
Dividend yield of stock Z is 7.50%
Capital gain yield = 0.20-0.075
Capital gain yield = 12.50%
Capital gain yield of stock Z is 12.50%