Company X has a beta of 1.6, while Company Y's beta is 0.7. The risk-free rate is 7 percent, and the required rate of return on an average stock is 12 percent. Now the expected rate of inflation built into rRF rises by 1 percentage point, the real risk-free rate remains constant, the required return on the market rises to 14 percent, and betas remain constant. After all of these changes have been reflected in the data, by how much will the required return on Stock X exceed that on Stock Y?
A) 3.75%
B) 4.20%
C) 4.82%
D) 5.40%
E) 5.75%

Question

Quizplus · Accepted Answer

First, we need to calculate the required return on both stocks using the CAPM formula:

rX = rRF + (rM - rRF) * betaX
rY = rRF + (rM - rRF) * betaY

Using the given data, we get:

rX = 7% + (14% - 7%) * 1.6 = 18.8%
rY = 7% + (14% - 7%) * 0.7 = 11.9%

Next, we need to factor in the changes in the market conditions:

rRF increases by 1%, so it becomes 8%
rM increases to 14%

Using the updated data, we can now calculate the new required returns for both stocks:

rX = 8% + (14% - 8%) * 1.6 = 23.2%
rY = 8% + (14% - 8%) * 0.7 = 16.3%

The difference between the two required returns is:

rX - rY = 23.2% - 16.3% = 6.9%

Therefore, Stock X's required return now exceeds that of Stock Y by 6.9%, which is closest to answer choice D (5.40%).

Company X Has a Beta of 1