Question

You are considering an investment in a mutual fund with a 7% load and an expense ratio of 0.5%. You can invest instead in a bank CD paying 3% interest. a. If you plan to invest for 5 years, what annual rate of return must the fund portfolio earn for you to be better off in the fund than in the CD? Assume annual compounding of returns. (Do not round intermediate calculations. Round your answer to 2 decimal places.) b. What annual rate of return must the fund portfolio earn if you plan to invest for 7 years to be better off in the fund than in the CD? (Do not round intermediate calculations. Round your answer to 2 decimal places.) c. Now suppose that instead of a front-end load the fund assesses a 12b-1 fee of .75% per year. What annual rate of return must the fund portfolio earn for you to be better off in the fund than in the CD

Answer 1

A.   Mutual Fund Wealth Index after N years = (1 – FL) (1 + r – Expenses) N
CD Wealth index after N years = (1 + r CD ) N = (1.03) N
The mutual fund is a better investment if its wealth index is greater:
(1 – FL)(1 + r – Expenses) N > 1.03 N
(1 – 0.07)(1 + r – 0.005)2 > 1.032
(0.93)(1 + r – 0.005)2 > 1.0609
(1 + r – 0.005)2 > 1.1407
1 + r – 0.005 > 1.1407
1 + r > 1.1457
r > 14.57%
So if the mutual fund return exceeds 14.57%, it is better than the CD.
B.   (1 – FL)(1 + r – Expenses)7 > 1.037
(1 – 0.07)(1 + r – 0.005)7 > 1.037
r > 32.73%
The cutoff rate of return is lower for the 7-year holding period cost

C.   12b-1 fee instead of a front-end load:
(1 + r – Expenses – Fee) N > 1.03 N
Note that without the one-time fee, we can take each side to the 1/N power and get:
(1 + r – Expenses – Fee) > 1.03
1 + r – 0.005 – 0.0075 > 1.03
r > 4.25%