The expected return on the market portfolio is currently 11%. Battmobile Corporation stockholders require a rate of return of 23.0%, and the stock has a beta of 2.5. According to CAPM, determine the risk-free rate.
A) 17.5%
B) 2.75%
C) 3.0%
D) 9.2%

Question

Quizplus · Accepted Answer

The Capital Asset Pricing Model (CAPM) formula is:

required return = risk-free rate + beta (expected return on the market - risk-free rate)

We know that:
- Expected return on the market (rM) = 11%
- Required return on Battmobile Corporation stock (rB) = 23%
- Beta (β) = 2.5

Plugging these into the CAPM formula and solving for the risk-free rate (rF):

23% = rF + 2.5(11% - rF)
23% = rF + 27.5% - 2.5rF
-4.5% = -1.5rF
rF = 3%

Therefore, the risk-free rate is 3%. The best choice is (C).

The Expected Return on the Market Portfolio Is Currently 11