Question

The risk-free rate is 3.14% and the market risk premium is 6.65%. A stock with a β of 1.77 just paid a dividend of $1.89. The dividend is expected to grow at 23.62% for five years and then grow at 4.18% forever. What is the value of the stock?

Answer 1

To value the stock, we use the CAPM to find the expected return and then apply the Dividend Discount Model for different growth stages. The present value of future dividends is calculated using the growth rates for the high-growth phase and the perpetual growth phase.

Step-by-step explanation:

The student asked about calculating the value of a stock given the risk-free rate, market risk premium, and the stock's beta, along with the dividend growth rates for different periods. This question is related to the Dividend Discount Model (DDM) and the Capital Asset Pricing Model (CAPM), which are used in finance to estimate the value of a stock based on expected future dividends and the expected rate of return respectively.

First, using the CAPM, the expected return (k) on the stock is calculated using the formula k = risk-free rate + (beta x market risk premium), which equates to 3.14% + (1.77 x 6.65%). Then, for the first five years, the future dividends are calculated considering the anticipated growth rate of 23.62% and then discounted back to the present value at the expected return rate. After five years, the formula switches to a perpetual growth model using the 4.18% growth rate. The value of the stock is the sum of the present value of dividends for the first five years and the present value of the perpetual dividends starting from the sixth year.