# 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.

## Answer and Explanation:

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.

#### Learn more about this topic:

The Dividend Growth Model

from Finance 101: Principles of Finance

Chapter 14 / Lesson 3
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