A stock has an expected return of 11.85 percent, its beta is 1.24, and the expected return on the market is 10.2 percent. What must the risk-free rate be? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e. g., 32.16.)

The risk free rate is 3.325%

Explanation:

The required rate of return or cost of equity of a stock can be calculated using the CAPM. The CAPM estimates the required rate of return of a stock based on three factors- risk free rate, stock's beta and the market risk premium. The equation of required rate of return under CAPM is,

r = rRF + Beta * (rM - rRF)

Where,

We already have the values for r, Beta and rM. Plugging in these values in the formula, we calculate the rRF to be,

Let rRF be x.

0.1185 = x + 1.24 * (0.102 - x)

0.1185 = x + 0.12648 - 1.24x

1.24x - x  =  0.12648 - 0.1185

0.24x = 0.00798

x = 0.00798/0.24

x = 0.03325 or 3.325%

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