The expected return for a stock, calculated using the CAPM, is 10.5 percent. The market return is 9.5 percent, and the beta of the stock is 1.50. Calculate the implied risk-free rate.
A) 7.50 percent
B) 13.91 percent
C) 17.50 percent
D) 21.88 percent
E) 14.38 percent

Question

Quizplus · Accepted Answer

CAPM formula is:

Expected Return = Risk-Free Rate + Beta*(Market Return - Risk-Free Rate)

Given,

Expected Return = 10.5%
Market Return = 9.5%
Beta = 1.5

Plugging the values in the formula:

10.5% = Risk-Free Rate + 1.5*(9.5% - Risk-Free Rate)

Solving for Risk-Free Rate:

10.5% = Risk-Free Rate + 1.5*9.5% - 1.5*Risk-Free Rate
10.5% = 14.25% - 0.5*Risk-Free Rate
0.5*Risk-Free Rate = 14.25% - 10.5%
0.5*Risk-Free Rate = 3.75%
Risk-Free Rate = 7.50%

Therefore, the implied risk-free rate is 7.50 percent (Option A).

The Expected Return for a Stock, Calculated Using the CAPM