Question

You are considering an investment in a mutual fund with a 5% front-end load and an expense ratio of 1.45%. You can invest instead in a bank CD paying 7% interest.

a.	If you plan to invest for two 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. Enter your answer as a percentage rounded to two decimal places.)

Annual rate of return

%

b.	If you plan to invest for six 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. Enter your answer as a percentage rounded to two decimal places.)

Annual rate of return

%

c.

Now suppose that instead of a front-end load the fund assesses a 12b-1 fee of 1.70% per year. If you plan to invest for two years, what annual rate of return must the fund portfolio earn for you to be better off in the fund than in the CD? (Do not round intermediate calculations. Enter your answer as a percentage rounded to two decimal places.)

Annual rate of return

%

Answer 1

Front-end load is deducted from the amount that you want to invest in the funds. So, if you want to invest, say, $10000 then front end load @5% will be $500. So, you'll get mutual fund units for $9500 and then expenses will be deducted out of this amount at the end of the year. Think of the $500 as a initial charge or expense.

a) For us to consider mutual funds, the return must be greater than the return on the CD, i.e., 7%. We have the following equation -

(1 - font end load) x (1 + return - expense ratio)ⁿ > (1 + Return on CD)ⁿ

where, n = no. of years

or, (1 - 0.05) x (1 + return - 0.0145)² > (1 + 0.07)²

or, 0.95 x (return + 0.9855)² > 1.1449

or, (return + 0.9855)² > 1.20515789473

or, (return + 0.9855) > (1.20515789473)^1/2

or, (return + 0.9855) > 1.09779683672

or, Return > 0.1122968 or 11.23%

So, the annual return should be greater than 11.23%.

b) Just change n to 6.

(1 - 0.05) x (1 + return - 0.0145)⁶ > (1 + 0.07)⁶

or, 0.95 x (1 + return - 0.0145)⁶ > 1.50073035184

or, (return + 0.9855)⁶ > 1.57971615983

or, (return + 0.9855) > (1.57971615983)^1/6

or, (return + 0.9855) > 1.0791865154

or, return > 0.0936865 or 9.37%

Therefore, in case of 6 years, the return should be greater than 9.37%.

c) 12b-1 fees will be incurred just like expenses at year end. So, the equation will now become -

(1 + return - expense ratio - 12b-1 fees)ⁿ > (1 + return on CD)ⁿ

or, (1 + return - 0.0145 - 0.017)² > (1 + 0.07)²

or, (1 + return - 0.0145 - 0.017) > 1.07

or, return + 0.9685 > 1.07

or, Return > 0.1015 or 10.15%

Note that in this case the no. of years will not affect the return.