# Carnes Cosmetics Co.'s stock price is $52.97, and it recently paid a$2.25 dividend. This...

## Question:

Carnes Cosmetics Co.'s stock price is $52.97, and it recently paid a$2.25 dividend. This dividend is expected to grow by 19% for the next 3 years, then grow forever at a constant rate, g; and rs = 14%.

At what constant rate is the stock expected to grow after Year 3? Round your answer to two decimal places. Do not round your intermediate calculations.

## Two-Step Constant Growth Model:

The two-step constant growth model is appropriate for a stock whose dividends exhibit non-constant growth for a finite period of time, followed by a constant growth. The model first computes the terminal value of the stock and then computes the current price.

According to the dividend discount model, the price of a stock is the discounted present value of future dividends. If the stock is priced according to the dividend discount model, then we have:

• {eq}\displaystyle \sum_{t=1}^{3}{\dfrac{2.25*(1 + 19\%)^t}{(1 + 14\%)^t}} + \sum_{t=4}^{\infty}{\dfrac{2.25*(1 + 19\%)^3*(1 + g)^{t-3}}{(1 + 14\%)^t}} = 52.97\\ 7.3596 + \dfrac{2.25*(1 + 19\%)^3*(1 + g)}{(14\% - g)(1 + 14\%)^3} = 52.97\\ g = 7.94\% {/eq}

That is, the growth rate after year 3 is 7.94%.