Question

Consider a stock that is planning to pay a dividend of $3 at the end of this year. After that, dividends will grow at a fixed rate of 4.5% per year indefinitely. The required return on the stock is 11%.

a. What is the value of the stock today, in 5 years, and in 8 years?

b. What are dividend yield and capital gains yield yield this year, in 5 years, and in 8 years?

Answer 1

Expected dividend Next year (D1) =			3
Growth rate (g) =		4.5% or	0.045
Required return (Ke) =		11% or	0.11
Value of stock today = D1 / (ke -g)
	3 / (0.11-0.045)
	46.15384615	or $ 46.15
Value of stock in 5 Years = D6/(Ke-g)
D6 = D1(1+g)^5
3 * (1+0.045)^5 =		3.738545813
So, P5 =	3.738545813	/ (0.11 - 0.045)
	57.51608943	or $57.52
Value of stock in 8 Years = D9/(Ke-g)
D9 = D1 * (1+g)^8
3 * (1+0.045)^8 =		4.266301839
So, P8 =	4.266301839	/(0.11 - 0.045)
	65.6354129	or $65.63
So, Value of stock today is $46.15, in 5 years is $57.52, in 8 years is $65.63
Part (b)
P0 =	46.15384615
P1 = D2 / (ke -g)
(3 * (1+g)^1) / (0.11 - 0.045)
48.23077
Dividend Yield this year = D1/ P0
	3/46.15=	6.50%
Capital gains yield this year = (P1 - P0)/P0
	(48.23077 - 46.15384615)/46.15384615
	4.50%
So, Dividend and Capital gains yield will be 6.50% and 4.5% during this year, in 5 years and in 8 Years.
As growth rate and Ke are same for all years, So dividend and capital gains yield will also be same for all year.