A company currently pays a dividend of $1.75 per share (D0 = $1.75). It is estimated that the company’s dividend will grow at a rate of 25% per year for the next 3 years, and then at a constant rate of 5% thereafter. The company’s stock has a beta of 1.5, the risk-free rate is 4.5%, and the market risk premium is 7.5%. What is your estimate of the stock’s current price?

The current price of the stock is $27.66

Explanation:

First we need to determine the required rate of return on this stock. The required rate of return (r) can be calculated using the CAPM,

r = rRF + Beta * rpM

Where,

r = 0.045 + 1.5 * 0.075   =  0.1575 or 15.75%

The price of the stock today can be calculated using the dividend discount model which calculates the price of a stock based on the present value of the expected future dividends from the stock. The price of this stock using DDM will be,

P0 = 1.75 * (1+0.25) / (1+0.1575)  +  1.75 * (1+0.25)^2  /  (1+0.1575)^2  +  

1.75 * (1+0.25)^3 / (1+0.1575)^3  +

[(1.75*(1+0.25)^3 *(1+0.05) / (0.1575 - 0.05)) / (1+0.1575)^3 ]

P0 = $27.66

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