Rayray Records' stock currently sells for $105.00 per share. The dividend is projected to increase at a constant rate of 5.00% per year. The required rate of return on the stock, rs, is 9.00%. What is the stock's expected price 3 years from today

$121.55

Explanation:

Given;

Stock price per share = $105

Required rate of return = 9%

Constant rate of dividend growth = 5%

As per Gordon's Growth Model, the equation for count of the stock cost dependent on profit, cost of value capital (required pace of return) and consistent pace of profit development is:

Stock Price per share = D / (r-g)

where D = dividend

r = cost of equity capital (in this problem, we take the required rate of return)

g = growth rate of dividend

Substituting the values for Stock price per share = $105, r = 0.09, g = 0.05 we need to find dividend, D

105 = D / (0.09 - 0.05)

105 = D / 0.04

105 * 0.04 = D

D = $ 4.20

Now since dividend grows at a constant rate of 5%

Dividend at the end of 3rd year = Dividend * (1 + g)3

Dividend at the end of 3rd year = 4.20 * (1+0.05)3

= 4.20 * 1.053

= 4.862

Stock price per share at the end of the 3rd year = D / (r-g)

Stock price per share at the end of the 3rd year = 4.862 / (0.09 - 0.05) = 4.862 / 0.04 = $121.55