Question

Investors expect the following series of dividends from a particular common stock: Year 1 $0.95 Year 2 $1.03 Year 3 $1.18 Year 4 $1.24 Year 5 $1.32 After the 5th year, dividends will grow at a constant rate. If the required rate of return on the stock is 8% and the current market price is $47.86, what is the long-term rate of dividend growth expected by the market?

Answer 1

Let us Assume Price after 5 Years is X.

Value of Stock = PV of Cfs from it.

Year	CF	PVF @8%	Disc CF
1	$      0.95	0.9259	$               0.88
2	$      1.03	0.8573	$               0.88
3	$      1.18	0.7938	$               0.94
4	$      1.24	0.7350	$               0.91
5	$      1.32	0.6806	$               0.90
5	X	0.6806	0.6806X
Price of Stock			4.51 + 0.6806X

Given Stock Price = 47.86

Thus 0.6806X + 4.51 = 47.86

0.6806X = 47.86 - 4.51

= 43.35

X = 43.35 / 0.6806

= 63.69

P5 = D5(1+g) / [ Ke - g ]

D5 = Div after 5 Years

g = growth rate

Ke = required Rate

P5 =Price after 5 Years

63.69 = 1.32 (1+g) / [ 0.08 - g ]

63.69 (0.08 - g ) =1.32 + 1.32g

5.10 - 63.69g = 1.32 + 1.32g

63.69g + 1.32g = 5.10 - 1.32

= 3.78

65.01g = 3.78

g = 3.78 / 65.01

= 0.0581 i.e 5.81%

growth rate after 5 Years is 5.81%