# The stock of Dravo Corporation currently pays a dividend (D0) at the rate of $2 per share. This... ## Question: The stock of Dravo Corporation currently pays a dividend (D0) at the rate of$2 per share. This dividend is expected to increase at a 9 percent annual rate for the next three years, at a 7 percent annual rate for the following two years, and then at 4 percent per year thereafter.

What is the value of a share of stock of Dravo to an investor who demands a 24 percent rate of return on this stock?

## Dividend Discount Model:

The dividend discount model is a general approach to stock valuation, which states that the price of a stock is the discounted present value of future dividends. This approach is less applicable to stocks that are perceived to never pay dividends.

## Answer and Explanation:

The price of the stock is the discounted present value of future dividends, which is given by:

• {eq}\displaystyle \sum_{t=1}^{3}{\dfrac{2*(1 + 9\%)^t}{(1 + 24\%)^t}} + \sum_{t=4}^{5}{\dfrac{2*(1+9\%)^3*(1 + 7\%)^{t-3}}{(1 + 24\%)^t}} + \sum_{t=6}^{\infty}{\dfrac{2*(1+9\%)^3*(1+7\%)*(1 + 4\%)^{t-5}}{(1 + 24\%)^t}}\\ = 4.66 + 2.18 + \dfrac{2*(1 + 9\%)^3*(1+7\%)^2*(1 + 4\%)}{(24\% - 4\%)(1 + 24\%)^5}\\ = 6.84 + 5.26\\ = 12.10 {/eq}

That is, the price of the stock is \$12.10.