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.

Learn more about this topic:

The Dividend Growth Model

from Finance 101: Principles of Finance

Chapter 14 / Lesson 3

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