The stock of Smashburger Inc. is currently trading at a price of $40. Smashburger is expected to pay a dividend of $3.00 per share one year from now (t = 1) and then the dividend is expected to grow at a constant growth rate gL. Assuming that the market is in equilibrium, the risk free rate of return is 5.2%, the market risk premium is 6%, and that the beta of Smashburger is 0.8, what is the long run growth rate gL?

g or gL = 0.025 or 2.5%

Explanation:

The constant growth model of DDM is used to calculate the price of a stock whose dividends are expected to grow at a constant rate. 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 = D1 / r - g

Where,

First we need to calculate the value of r. We will use the CAPM equation to calculate r.

r = rRF + Beta * rpM

Where,

r = 0.052  +  0.8 * 0.06

r = 0.1 or 10%

As we already know the P0, r and D1, we will input these values in the formula of price under constant growth model to calculate teh value of g or gL.

40 = 3 / (0.1 - g)

40 * (0.1 - g)  =  3

4  -  40g  =  3

4 - 3  =  40g

1 / 40 = g

g = 0.025 or 2.5%

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