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 stock is 12%.Now the expected rate of inflation built into r_RF 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 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 Stock X and Stock Y using the given information:
For Stock X: 
rX = rRF + βX(rM - rRF) 
= 0.07 + 1.6(0.12 - 0.07) 
= 0.15 or 15% 
For Stock Y: 
rY = rRF + βY(rM - rRF) 
= 0.07 + 0.7(0.12 - 0.07) 
= 0.095 or 9.5%

Next, we need to incorporate the changes in the data. The new values are:
rRF = 0.07 
rM = 0.14 
βX = 1.6 
βY = 0.7

The new required return on Stock X is:
rX = rRF + βX(rM - rRF) 
= 0.07 + 1.6(0.14 - 0.07) 
= 0.218 or 21.8%

The new required return on Stock Y is: 
rY = rRF + βY(rM - rRF) 
= 0.07 + 0.7(0.14 - 0.07) 
= 0.112 or 11.2%

The difference in required return between Stock X and Stock Y is:
rX - rY = 0.218 - 0.112 
= 0.106 or 10.6%

Therefore, the required return on Stock X exceeds that on Stock Y by 10.6%. To find the increase in percentage, we can find the percentage of the original required return for Stock Y:
(10.6/9.5) x 100% = 111.58%

The increase in percentage is 111.58% - 100% = 11.58%. Rounding to the nearest tenth gives 11.6%.

Finally, we subtract this increase from the original required return for Stock Y to get the new required return for Stock Y:
9.5% + (0.116 x 9.5%) = 10.546%, or approximately 10.5%

Therefore, the answer is:
Answer: D (5.4%)

Company X Has Beta = 1