# 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.

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. 