Question

In: Finance

You are considering an investment in a mutual fund with a 7% load and expense ratio...

You are considering an investment in a mutual fund with a 7% load and expense ratio of 0.25%. You can invest instead in a bank CD paying 3% interest.

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 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 1.00% 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? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Solutions

Expert Solution

A) After two years each dollar invested in the fund with 7% load and a porfolio return will grow $ 0.93 X (1+r - 0.0025)3

Each dollar invested In CD will grow $1 X (1.03)3

If mutual fund is to be better investment then porfolio return must satisfy r,

0.93 x (1+r - 0.0025)3> (1.03)3

0.93 x (1+r - 0.0025)3> 1.0927

(1+r - 0.0025)3> 1.1749

1+r - 0.0025 > 1.055

1+r > 1.0575

Therefore r > 0.0575 i.e. 5.75%

B) If you invest for seven years then portfolio must satisfy

0.93 x (1+r - 0.0025)7> (1.03)7

0.93 x (1+r - 0.0025)7> 1.229

(1+r - 0.0025)7> 1.321

1+r - 0.0025 > 1.0405

1+r > 1.043

r> 4.3%

C) With 12b -1 instead of a front end load, the portfolio must earn a rate of return which must satisfy :

1 + r - 0.0025 - 0.01 > 1.03

1 + r > 2.0425

r > 1.0425

In this case investment must exceed 104.25% regardless of the investment horizon.


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