Question

The common stock of Bellingham Water Company currently sells for $29.03 a share. The stock is recently paid a dividend of $1.35 per share. The firm has established a pattern of increasing its dividends by 3 percent annually and expects to continue doing so. What is the market rate of return on this stock?

Answer 1

Solution:
Given in the question
Current Price =$29.03

Dividend(D0)=$1.35

Growth = 3% or 0.03

We need to calculate Market Rate(Ke) =?

We know current price can be calculated as

Current Price(P) =D0(1+g)/(1+ke)^1 + D0(1+g)^2/(1+ke)^2 + D0(1+g)^3/(1+ke)^3.....................∞

Therefore...29.03 =1.35(1+.03)/(1+ke) +1.35(1+.03)^2/(1+ke)^2 +1.35(1+.03)^3/(1+ke)^3.........∞

:- 29.03 =1.3905/(1+ke) +1.3905(1+.03)/(1+ke)^2 +1.3905(1+.03)^2/(1+ke)^3...........∞

29.03 = 1.3905(1/(1+ke) +(1+.03)/(1+ke)^2 +(1+.03)^2/(1+ke)3........∞)
As we know (1/(1+ke) +(1+.03)/(1+ke)^2 +(1+.03)^2/(1+ke)3........∞) is the growing annuity dividend = first term/(ke-g)

29.03 = 1.3905(1/ke-0.03)

20.877Ke - 0.6263 = 1

Ke=1.6263/20.8776

Ke=7.789%
market rate of return on this stock = 7.789%