Company X has beta = 1.6, while Company Y's beta = 0.7.The risk-free rate is 7%, and the required rate of return on an average share is 12%.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%, and betas remain constant.After all of these changes have been reflected in the data, by how much will the required return on Share X exceed that on Share Y?

Question

Quizplus · Accepted Answer

First we need to calculate the required return for Company X and Company Y using the CAPM formula:

Company X:
rX = rRF + βX(rM - rRF)
rX = 0.07 + 1.6(0.12 - 0.07)
rX = 0.19 or 19%

Company Y:
rY = rRF + βY(rM - rRF)
rY = 0.07 + 0.7(0.12 - 0.07)
rY = 0.105 or 10.5%

After the changes, the required return on the market is now 14%, so we need to recalculate the required return for Company X and Company Y:

Company X:
rX = 0.08 + 1.6(0.14 - 0.08)
rX = 0.2 or 20%

Company Y:
rY = 0.08 + 0.7(0.14 - 0.08)
rY = 0.123 or 12.3%

The difference between the required returns is:

rX - rY = 0.2 - 0.123 = 0.077 = 7.7%

Therefore, the required return on Share X will exceed that on Share Y by 5.4%. The correct answer is D) 5.40%.

Company X Has Beta = 1