Question

Consider four different stocks, all of which have a required return of 15 percent and a most recent dividend of $4.20 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? (Do not round intermediate calculations. Enter your answers as a percent rounded to 1 decimal place, e.g., 32.1.)

Find Dividend yield For:

Stock W %

Stock X %

Stock Y %

Stock Z %

What is the expected capital gains yield for each of these four stocks? (Leave no cells blank - be certain to enter "0" wherever required. Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 1 decimal place, e.g., 32.1.)

Find Capital gains yield for:

Stock W %

Stock X %

Stock Y %

Stock Z %

Answer 1

Solution:
The dividend yield for each of these four stocks
Stock W	5.0%
Stock X	15.0%
Stock Y	20%
Stock Z	4.6%
The expected capital gains yield for each of these four stocks
Stock W	10.0%
Stock X	0%
Stock Y	-5%
Stock Z	10.4%
Working Notes:
	Dividend yield = Next Dividend (D1)/ Current price of the stock (P0)
	Capital gains yield = Required rate of return - Dividend yield
	from above formulas we can observe that first we have to calculate d current price of stock to get its dividend yields and then Capital gains yield.
Stock W
	P0= D0(1 + g) / (R?g) as per Gordon Dividend growth model.
	R = Required rate of return of the stock or cost of equity = 15%
	Po=current share price = ??
	g= growth rate= 10%
	D0= Current Dividend=$4.20 per share
	P0= D0(1 + g) / (R?g)
	P0=$4.20(1+0.10)/(0.15-0.10)
	P0=$92.40
	Dividend yield = Next Dividend (D1)/ Current price of the stock (P0)
	Dividend yield = D0(1 + g)/ Current price of the stock (P0)
	Dividend yield = $4.20(1 + 0.10)/ $92.40
	Dividend yield = 0.05
	Dividend yield = 0.05
	Dividend yield = 5 %
	Capital gains yield = Required rate of return - Dividend yield
	Capital gains yield = 15% - 5%
	Capital gains yield = 15% - 5%
	Capital gains yield = 10%
Stock X
	P0= D0(1 + g) / (R?g) as per Gordon Dividend growth model.
	R = Required rate of return of the stock or cost of equity = 15%
	Po=current share price = ??
	g= growth rate= 0%
	D0= Current Dividend=$4.20 per share
	P0= D0(1 + g) / (R?g)
	P0=$4.20(1+0.0)/(0.15-0.0)
	P0=$28
	Dividend yield = Next Dividend (D1)/ Current price of the stock (P0)
	Dividend yield = D0(1 + g)/ Current price of the stock (P0)
	Dividend yield = $4.20(1 + 0.0)/ $28
	Dividend yield = 0.15
	Dividend yield = 15%
	Capital gains yield = Required rate of return - Dividend yield
	Capital gains yield = 15% - 15%
	Capital gains yield = 0%
Stock Y
	P0= D0(1 + g) / (R?g) as per Gordon Dividend growth model.
	R = Required rate of return of the stock or cost of equity = 15%
	Po=current share price = ??
	g= growth rate=-5%
	D0= Current Dividend=$4.20 per share
	P0= D0(1 + g) / (R?g)
	P0=$4.20(1-0.05)/(0.15+0.05)
	P0=$19.95
	Dividend yield = Next Dividend (D1)/ Current price of the stock (P0)
	Dividend yield = D0(1 + g)/ Current price of the stock (P0)
	Dividend yield = $4.20(1 -0.05)/ $19.95
	Dividend yield = $3.99/$19.95
	Dividend yield = 0.20
	Dividend yield = 20%
	Capital gains yield = Required rate of return - Dividend yield
	Capital gains yield = 15% - 20%
	Capital gains yield = -5%
Stock Z
	P0= D0(1 + g) / (R?g) as per Gordon Dividend growth model.
	R = Required rate of return of the stock or cost of equity = 15%
	Po=current share price = ??
	g1= growth rate= 20% for next two years
	g2= Constant growth rate after two years = 10%
	D0= Current Dividend=$4.20 per share
	Price of the stock Z at the end of 2nd year P2
	P2= D2(1 + g) / (R?g)
	P2 = D0(1 + g1)^2(1 + g2) / (R?g2)
	P2 = $4.20(1 + 0.20)^2 (1 + 0.10) / (0.15?0.10)
	P2= $133.056
	P0=D0 (1 + g1)/ (1 + R) + D0 (1 + g1)^2/ (1 + R)^2+ P2 / (1+ R)^2
	P0= $4.20 (1.20) / (1.15) + $4.20(1.20)^2/ (1.15)^2+ $133.056 / (1.15)^2
	P0= $4.20 (1.20) / (1.15) + $4.20(1.20)^2/ (1.15)^2+ $133.056 / (1.15)^2
	P0=109.565217
	Dividend yield = Next Dividend (D1)/ Current price of the stock (P0)
	Dividend yield = D0(1 + g)/ Current price of the stock (P0)
	Dividend yield = $4.20(1 +0.20)/ $109.565217
	Dividend yield = 0.046000
	Dividend yield = 4.6%
	Capital gains yield = Required rate of return - Dividend yield
	Capital gains yield = 15% - 4.6%
	Capital gains yield = 10.4%
Please feel free to ask if anything about above solution in comment section of the question.