Question

Consider four different stocks, all of which have a required return of 20% and a most recent dividend of $4.50 per share is paid today. Stocks W, X, and Y are expected to maintain constant growth rates in dividends for the foreseeable future of 10%, 0%, and –5% per year, respectively. Stock Z is a growth stock that will increase its dividend by 30% for the next two years and then maintain a constant 8% growth rate thereafter. What is the dividend yield for each of these four stocks? What is the expected capital gains yield for each stock? Discuss the relationship among the various returns that you find for each of these stocks.

Answer 1

A	B	C	D	E	F	G	H	I	J
2
3			W	X	Y	Z
4		Dividend paid today (Div0)	$4.50	$4.50	$4.50	$4.50
5		Required Rate of Return (r)	20%	20%	20%	20%
6		Terminal growth rate (g)	10%	0%	-5%	8%
7		High growth rate				30%
8		High growth period				2
9
10		Stock price will be the present value of the future dividends.
11
12		Current Stock Price (P0) of W	=Present value of growing perpetuity
13			=Div0*(1+g) / (r-g)
14			=$4.50*(1+10%) / (20% - 10%)
15			$45.00	=D4/(D5-D6)
16
17		Current Stock Price (P0) of X	=Present value of growing perpetuity
18			=Div0*(1+g) / (r-g)
19			=$4.50*(1+0%)/(20% - 0%)
20			$22.50	=E4*(1+E6)/(E5-E6)
21
22		Current Stock Price (P0) of Y	=Present value of growing perpetuity
23			=Div0*(1+g) / (r-g)
24			=$4.50*(1-5%)/ (20% -(-5%))
25			$17.10	=F4*(1+F6)/(F5-F6)
26
27
28		Calculation of current price (P0) of stock Z:
29
30		Required return (r)	20.00%
31		Terminal growth rate (g)	8.00%
32		Year	0	1	2	3	…
33		Dividend	$4.50	$5.40	$6.48	$8.42	$10.95
34		Terminal value = DIV3/(rs-gL)			$70.20
35		Present value of dividends		$4.50	$53.25	=(F33+F34)/((1+$D30)^F32)
36		Price of share at Year 0	$57.75	=SUM(E35:F35)
37
38		Hence Current Price of share Z is	$57.75
39
40		Simillarly Prices of share in Year 1 can be calculated as follows:
41			W	X	Y	Z
42		Price at Year 1 (P1)	$54.45	$22.50	$16.25	$63.90	=(F33+F34)/((1+D30)^1)
43
44		Thus in Summary,
45			W	X	Y	Z
46		Current Dividend	$4.50	$4.50	$4.50	$4.50
47		Dividend next Year	$4.95	$4.50	$4.28	$5.85
48		Current Price (P0)	$45.00	$22.50	$17.10	$57.75
49		Price in Year (1)	$54.45	$22.50	$16.25	$63.90
50		Dividend Yield (Div0/P0)	10.00%	20.00%	26.32%	7.79%	=G46/G48
51		Expected Capital Gain Yield (P1-P0)/P0	21.00%	0.00%	-5.00%	10.65%	=(G49-G48)/G48
52
53		It can be observed from the returns calculated above thath, the
54		higher the dividend yield lower will be the capital gain yield.
55

Formula sheet