Question

A stock with a beta of 2.45 is expected to pay a $1.78 dividend over the next year. The dividends are expected to grow at 2.02% per year forever. What is the stock's value per share (to the nearest cent, no $ symbol) if the risk-free rate is 1.25% and the market risk premium (i.e., the difference between the market return and the risk-free rate) is 6.16%? Note: You first need to find the required rate of return (r) using the CAPM equation.

Answer 1

The stock's value per share is calculated using the Dividend Discount Model with the required rate of return derived from the CAPM equation. Using the inputs provided, the stock's value is computed, taking into account the expected dividend, the dividend growth rate, and the required rate of return.

Step-by-step explanation:

The question asks to calculate the value of a stock using the Dividend Discount Model (DDM), factoring in the expected dividend growth rate and the required rate of return calculated via the Capital Asset Pricing Model (CAPM). To find the required rate of return (r), the CAPM equation, r = risk-free rate + (beta * market risk premium), is used. Based on the provided beta of 2.45, the risk-free rate of 1.25%, and the market risk premium of 6.16%, the required rate of return would be r = 1.25% + (2.45 * 6.16%) = 16.242%. Using the DDM, the stock's value (V) is calculated as V = D / (r - g), where D is the expected dividend and g is the expected growth rate of the dividend. Therefore, V = $1.78 / (0.16242 - 0.0202) gives us the stock's value per share.