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Allen, Inc., is expected to pay equal dividends at the end of each of the next two years....

Question:

Allen, Inc., is expected to pay equal dividends at the end of each of the next two years. Thereafter, the dividend will grow at a constant annual rate of four percent, forever. The current stock price is $30.

What is next year's dividend payment if the required rate of return is 12%?

Dividend Growth Model:

The dividend growth model prices a stock to the discounted present value of future dividends. Since dividends are growing at a constant rate indefinitely, the stream of dividends is a growing perpetuity.

Answer and Explanation:

We can use the dividend discount model to answer the question. According to the model, the price of a stock is the discounted present value of future dividends. Denote the next dividend by {eq}D_1 {/eq}, then we have:

  • {eq}\dfrac{D_1}{(1 + 12\%)} + \dfrac{D_1}{(1 + 12\%)^2} + \dfrac{D_1*(1 + 4\%)}{(12\% - 4\%)(1 + 12\%)^2} = 30\\ 1.69 D_1 + 10.36 D_1 = 30\\ D_1(1.69 + 10.36) = 30\\ D_1 = 2.49 {/eq}

That is, dividend next year will be $2.49.


Learn more about this topic:

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The Dividend Growth Model

from Finance 101: Principles of Finance

Chapter 14 / Lesson 3
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