# Carnes Cosmetics Co.'s stock price is $38.37, and it recently paid a$2.25 dividend. This...

## Question:

Carnes Cosmetics Co.'s stock price is $38.37, and it recently paid a$2.25 dividend. This dividend is expected to grow by 21% for the next 3 years, then grow forever at a constant rate, g; and rs =15%. At what constant rate is the stock expected to grow after Year 3?

## Constant Growth Model:

The constant growth model is also known as the dividend growth model and the Gordon growth model. This model is a special case of the more general discounted dividend model.

We can use the dividend discount model to answer this question. According to this model, the price of a stock is the discounted present value of future dividends, i.e.,

• {eq}\displaystyle \sum_{t=1}^{3}{\dfrac{2.25*(1 + 21\%)^t}{(1 + 15\%)^t}} + \dfrac{2.25*(1 + 21\%)*(1 + g)}{(15\% - g)(1 + 15\%)^3} = 38.37\\ 7.48 + \dfrac{2.62*(1 + g)}{(11\% - g)} = 38.37\\ g = 6\% {/eq}

That is, the growth rate is 6% after year 3. 