Use the following information to answer the question(s)below.
-If the expected return on the market is 11% and the expected return of investing in Merck is 10.35%,then the risk-free rate must be:
A)3.0%.
B)4.0%.
C)4.5%.
D)5.0%.

Question

Use the following information to answer the question(s)below. 
-If the expected return on the market is 11% and the expected return of investing in Merck is 10.35%,then the risk-free rate must be:
A)3.0%. 
B)4.0%. 
C)4.5%. 
D)5.0%.

Quizplus · Accepted Answer

The risk-free rate can be found by using the Capital Asset Pricing Model (CAPM):

Expected return on stock = Risk-free rate + Beta*(Expected return on market - Risk-free rate)

Rewriting the formula: 
Risk-free rate = (Expected return on stock - Beta*(Expected return on market))/(1-Beta)

Plugging in the values given: 
10.35% = (Risk-free rate) + Beta(11% - Risk-free rate)

Solving for Risk-free rate: 
Risk-free rate = (10.35% - Beta(11%))/(1-Beta)

Since we do not know Beta, we cannot solve for Risk-free rate exactly. However, we do know that Beta is a measure of the stock's volatility compared to the market. Since Merck is a pharmaceutical company, it is likely less volatile than the market as a whole. Therefore, we can assume that Beta is less than 1.

Assuming Beta is 0.8, we get: 
Risk-free rate = (10.35% - 0.8(11%))/(1-0.8) = 4.5%

Therefore, the best choice is C) 4.5%.

Use the Following Information to Answer the Question(s)below