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

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. 