Question

A mutual fund sells Class A shares with a front-end load of 6% and Class B shares with 12b-1 fees of 1% as well as back-end load fees that starts at 6% and fall by 1% for each holding year. Assume that the fund return net of operating costs is 11% annually. What will be the value of a $10,000 investment in Class A and B if the shares are sold after (a) 1 year; (b) 4 years, or (c) 10 years? Which fee structure provide higher net proceeds ?

Answer 1

Net investment in class A shares = 10,000 x (1 - Front end load) = 10,000 x (1 - 6%) = 9,400

Return r = 11%

Hence, the value of investment in class A shares after n years = 9,400 x (1 + r)ⁿ = 9,400 x (1 + 11%)ⁿ = 9,400 x 1.11ⁿ

(a) 1 year; n = 1; value of investment in class A shares = 9,400 x 1.11 = 10,434

(b) 4 years; n = 4; value of investment in class A shares = 9,400 x 1.11⁴ = 14,270

(c) 10 years; n = 10; value of investment in class A shares = 9,400 x 1.11¹⁰ = 26,691

Class B Shares

No front end load; Net return, r = 11% - 12b-1 fees = 11% - 1% = 10%; Back end load fees, b = 6% - n x 1%

Hence, the value of investment in class B shares after n years = 10,000 x (1 + r)ⁿ x (1 - b)

= 10,000 x (1 + 10%)ⁿ x [1 - (6% - n x 1%)] = 10,000 x 1.1ⁿ x [1 - (6% - n x 1%)]

(a) 1 year; n = 1; value of investment in class B shares = 10,000 x 1.1 x [1 - (6% - 1 x 1%)] = 10,000 x 1.1 x (1 - 5%) = 10,450

(b) 4 years; n = 4; value of investment in class B shares = 10,000 x 1.1⁴ x [1 - (6% - 4 x 1%)] = 10,000 x 1.1⁴ x (1 - 2%) = 14,348

(c) 10 years; n = 10; value of investment in class B shares = 10,000 x 1.1¹⁰ = 25,937 (Please note that the back end load would have vanished and become zero by the end of year 6)

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• For a very short horizon such as one year and moderate time frame of 4 years, the Class B shares offer marginally higher value and hence are the better choice. The back-end load is a % lower.
• For long horizons of 10 years or more, Class A shares are better than class B shares. In this case, the one-time front-end load is less expensive than the continuing 12b-1 fees.