Carnes Cosmetics Co.'s stock price is $51, and it recently paid a $3.00 dividend. This dividend is expected to grow by 25% for the next 3 years, then grow forever at a constant rate, g; and rs = 16%. At what constant rate is the stock expected to grow after Year 3? Do not round intermediate calculations. Round your answer to two decimal places.

The answer is 6.17%.

Explanation:

We apply the Dividend Model for solving the questions.

Denote g as the constant dividend growth rate after 3 years which needs to be found.

The principle in the Dividend model is: Current share price = Projected present value of all expected future dividend discounted at company's cost of equity rs = 16%.

Thus Current share price = Present value of Dividend paid in Y1 + Present value of Dividend paid in Y2 + Present value of Dividend paid in Y3 + Present value of dividend perpetuity growth after Y3.

=> 51 = (3 x 1.25) / 1.16^1 + (3 x 1.25^2) / 1.16^2 + (3 x 1.25^3) / 1.16^3 + [3 x 1.25^3 x (1+g) ] / (0.16-g) / 1.16^3 [5.8594 x (1+g) ] / (0.16-g) / 1.16^3 = 40.5298 [5.8594 x (1+g) ] / (0.16-g) = 63.2628 5.8594 + 5.8594g = 10.1220 - 63.2628g 69.1222g = 4.2626 g = 6.17%.

Thus, the constant rate the stock's dividend expected to grow after Year 3 is 6.17%