The stock pays a dividend of $2 per year and its price is $80. If the market return is 7% and the risk-free rate is 1%, what is the stock beta? A. 0.4 B. 0.5 C. 0.25 D. 0.1

The beta of the stock is 0.25 and option C is the correct answer.

Explanation:

The current price of a stock which pays a constant dividend can be determined using the zero growth dividend model of DDM. The formula to calculate the price under this model is,

P0 = Dividend / r

Where,

As we already know the value of P0 and Dividend, we can plug in these values in the formula and calculate the value of r.

80 = 2 / r

80 * r = 2

r = 2 / 80

r = 2.5% or 0.025

The required rate of return can also be calculated using the CAPM equation. The formula for r under CAPM is,

r = rRF + Beta * (rM - rRF)

Where,

To calculate beta, we will input the values for r, rRf and rM in the CAPM equation.

Let beta be x.

0.025 = 0.01 + x * (0.07 - 0.01)

0.025 - 0.01 = x * 0.06

0.015 / 0.06 = x

x = 0.25

Thus, beta is 0.25

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