Paunch Burger has a beta of 1.2 and just paid a dividend of $2.30 that is expected to grow at 3.2%. If the risk-free rate is 3% and the market risk premium is 6%, what should be the price of the stock

P0 = $33.9085 rounded off to $33.91

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  recently

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 or r using the CAPM.

Using the CAPM, we can calculate the required/expected 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 * rpM

Where,  

rRF is the risk free rate

rpM is the market risk premium

r = 0.03 + 1.2 * 0.06

r = 0.102 or 10.2%

Now using the formula for P0 under the constant dividend growth model,

P0 = 2.3 * (1+0.032)  /  (0.102 - 0.032)

P0 = $33.9085 rounded off to $33.91

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