Question

the stock of supergro inc. is expected to grow at an annual rate of 28% for the next 2 years, after which growth will return to the normal constant growth rate of 8%. if the last dividend paid (that is, d0) was $2.00 and the required rate of return on stocks of this risk class is 16%, what is the price of the stock today?

Answer 1

The price of the stock of Supergro inc. today is $37.52

The dividend discount model is based on the idea that the intrinsic value of a stock is derived from its stream of future dividends. Accordingly, the model prices a stock to the present value of future dividends discounted at the required return on the stock.

According to the dividend discount model, the price of the stock is discounted present value of future dividends. The dividend for the next two years is:

year 1: 2*(1 + 28%) = 2.56

year 2: 2.56 * (1 + 28%) = 3.28

After year 2, the dividend grows at a constant rate of 8%. Given a discount rate of 16%, the present value of future dividends is:

$\displaystyle \frac{2.56}{(1 + 16\%)} + \frac{3.28}{(1 + 16\%)^2} + \sum_{t=3}^{\infty}{\frac{3.28*(1 + 8\%)^{t-2}}{(1 + 16\%)^t}}\\ = \displaystyle 2.21 + 2.44 + \frac{3.28*(1 + 8\%)}{(16\% - 8\%)(1 + 16\%)^2}\\ = 4.65 + 32.87\\ = 37.52$

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