Question

You are considering an investment in a mutual fund with a 4% front-end load. The fund charges a back-end load of 5, 4, 3, 2, and 1 percent if the shares are redeemed within the first 5 years, respectively. The expense ratio of 0.5%. Alternatively, you can invest instead in a bank saving account paying 6% interest per year.

a. If you plan to invest for 3 years, what annual rate of return must the fund portfolio earn for you to be better off in the fund than in the bank saving account? Assume annual compounding of returns.

b. How does your answer change if you plan to invest for six years? Why does your answer change?

c. Now suppose that instead of a front-end load the fund assesses a 12b-1 fee of 0.75% per year. The back-end load will be 5, 4, 3, 2, and 1 percent if the shares are redeemed within the first 5 years, respectively. Then what annual rate of return must the fund portfolio earn for you to be better off in the fund than in the bank saving account if you plan to invest in 10 years?

Answer 1

Given,

If investment made in mutual fund,

Front end load = 4%

Expense ratio = 0.5%

Back end load for year 1 = 5%

For year 2 = 4%, for year 3 = 3%, for year 4 = 2%, for year 5 = 1%

If investment made in bank savings account, then Interest income will be @6% p.a. compounded annually

(a) If plans to invest for 3 years, annual rate of return fund portfolio should earn to be better than in bank savings account:

Annual rate of return of fund portfolio:

For year 1:

Front end load to be covered = 4%

Expense ratio to be covered = 0.5%

Bank savings Interest rate to be recovered.

[[1+0.06]^3 - 1] ÷3 = 6.37%

Total return Required for year 1 = 10.87%

For year 2:

Bank interest rate to be covered = 6.37%

For year 3:

Back end load to be recovered, if invested for 3 years. = 3%

Bank savings Interest rate. = 6.37%

Total return Required for year 3 = 9.37%

Therefore annual rate of return Required to be covered if investment made in mutual fund

=( 10.87+6.37+9.37)÷3 = 8.87%

(b) If plans to invest for 6 years, then annual rate of return from the mutual fund shall be:

For year 1:

Front load to be covered in return. = 4%

Expense ratio to be covered in return = 0.5%

Bank savings Interest to be recovered by

investing in mutual fund

[(1+0.06)^6 - 1]÷6] = 6.97%

Return required for year 1 = 11.47%  

For year 2 to 6:

​​​​​​Required return = 6.97% p.a.

Annual rate of return Required to be covered if investment made in mutual fund

= (11.47+6.97%×5)÷6 = 7.72%

If plans to invest for 3 years,

Annual rate of return = 8.87%

If plans to invest for 6 years,

Annual rate of return = 7.72%

Here the interest rate required has been changed because there will be no back end load required to be recovered if plans to invest for 6 years and hence annual required rate of return has been changed.

(c) If instead of front end load, there is a charge @0.75% per year, then annual rate of return Required if plans to invest for 10 years:

Annual rate of return:

Fee to be recovered every year = 0.75%

Bank savings Interest rate

[(1+0.06)^10 - 1]÷10 = 7.91%

Annual rate of return = 8.66%