Question

XYZ, Inc. just paid an annual per share dividend of $3.50. Dividends are expected to grow at a rate of 3% per year from here on out. If the risk-free rate is 2.5%, the expected return on the market is 7% and the beta of the stock is 2, what is the most that you should be willing to pay for a share of this stock today?

Answer 1

P0 = $42.4117 rounded off to $41.41

Step-by-step explanation:

Using the constant growth model of dividend discount model, we can calculate the price of the stock today. The DDM values a stock based on the present value of the expected future dividends from the stock. The formula for price today under this model is,

P0 = D0 * (1+g) / (r - g)

Where,

D0 is the dividend paid recentl

D0 * (1+g) is dividend expected for the next period /year

g is the growth rate

r is the required rate of return or cost of equity

First we need to calculate the required rate of return on this stock using CAPM.

Using the CAPM, we can calculate the required rate of return on a stock. This is the minimum return required by the investors to invest in a stock based on its systematic risk, the market's risk premium and the risk free rate.

The formula for required rate of return under CAPM is,

r = rRF + Beta * (rM - rRF)

Where,

rRF is the risk free rate

rpM is the market return

r = 0.025 + 2 * (0.07 - 0.025)

r = 0.115 or 11.5%

Using the constant growth of dividend formula,

P0 = 3.5 * (1+0.03) / (0.115 - 0.03)

P0 = $42.4117 rounded off to $41.41