Question

A company is expected to pay a dividend of $1.49 per share one year from now and $1.93 in two years. You estimate the risk-free rate to be 4.2% per year and the expected market risk premium to be 5.6% per year. After year 2, you expect the dividend to grow thereafter at a constant rate of 5% per year. The beta of the stock is 1.4, and the current price to earnings ratio of the stock is 17. What would be an appropriate estimate of the stock price today? (Answer to the nearest penny, i.e. 55.55 but do not use a $ sign).

Answer 1

This is an example of application of dividned growth model.

Let us first calculate the required return on stock of this company

r = Risk free rate + Beta * Market Risk Premium (by CAPM)

r = 4.2% + (1.4 * 5.6%)

r = 12.04%

In order to calculate the stock price today, we need to discount all future dividend to the present year.

D₁ = 1.49

D₂ = 1.93

D₃ = 2.0265 (with growth of 5%

Terminal value of this stock (at t=2) = D₃/(r-g) = 2.0265/(12.04% - 5%) = $27.385

Current Fiar price of stock= $24.53