Carnes Cosmetics Co.'s stock price is $69.04, and it recently paid a$2.25 dividend. This...

Question:

Carnes Cosmetics Co.'s stock price is $69.04, and it recently paid a$2.25 dividend. This dividend is expected to grow by 30% 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? Round your answer to two decimal places. Do not round your intermediate calculations.

Terminal Value:

In the discounted dividend model of stock valuation, the terminal value refers to the price of the stock at the point after which dividends will maintain a constant growth rate. This value could be computed by applying the dividend growth 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 + 30\%)^t}{(1 + 16\%)^t}} + \dfrac{2.25*(1 + 30\%)^3*(1 + g)}{(16\% - g)(1 + 16\%)^3} = 69.04\\ 8.51 + \dfrac{4.94*(1 + g)}{(16\% - g)} = 65.66\\ g = 7.24\% {/eq}

That is, the growth rate is 7.24% after year 3.