# A company's common stock is selling for $16. The stock just paid a dividend (D0) of$.60 and this...

A company's common stock is selling for $16. The stock just paid a dividend (D0) of$.60 and this dividend is expected to grow by 15% per year for three years. After that it will grow at a constant rate of 4%. The stock's beta is 1.7, the risk-free rate of interest is 1.75% and the market risk premium is 5.25%. According to the DCF model, what is the intrinsic value of the stock today? Given the current stock price today (P0=$16), should you buy the stock and briefly explain why or why not? ## CAPM and Required Return: According to the capital asset pricing mode, the required return on a stock is the sum of the risk free rate and the stock's risk premium. The latter is the product of the stock's beta and the market risk premium. ## Answer and Explanation: We first compute the required return using CAPM: • required return = risk free rate + beta * market risk premium • required return = 1.75% + 1.7 * 5.25% • required return = 10.675% Then we can price the stock to the discounted present value of future dividends, i.e., • {eq}\displaystyle \sum_{t=1}^{3}{\frac{0.6*(1 + 15\%)^t}{(1 + 10.675\%)^t}} + \sum_{t=4}^{\infty}{\frac{0.6*(1 + 15\%)^3*(1 + 4\%)^{t-3}}{(1 + 10.675\%)^t}}\\ = 1.944 + \dfrac{0.6*(1 + 15\%)^3*(1 + 4\%)}{(10.675\% - 4\%)(1 + 10.675\%)^3}\\ = 1.944 + 10.488\\ = 12.432 {/eq} Given that the current stock price is$16, the stock is over-priced relative to its discounted present value of dividends, so you should not buy the stock. 