# Carnes Cosmetics Co.'s stock price is $65.66, and it recently paid a$1.50 dividend. This...

## Question:

Carnes Cosmetics Co.'s stock price is $65.66, and it recently paid a$1.50 dividend. This dividend is expected to grow by 28% 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? Do not round your intermediate calculations.

## Dividend Growth Model:

According to the dividend growth model, the price of a stock is the discounted present value of future dividends. Because of stock dividends grow at a constant rate in this model, the discounted present value of dividends has a simple expression.

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{1.50*(1 + 28\%)^t}{(1 + 14\%)^t}} + \dfrac{1.50*(1 + 28\%)^3*(1 + g)}{(14\% - g)(1 + 14\%)^3} = 65.66\\ 5.70 + \dfrac{3.146*(1 + g)}{(14\% - g)} = 65.66\\ g = 8.3\% {/eq}

That is, the growth rate is 8.3% after year 3.