You are considering an investment in a mutual fund with a 4% load and an expense

Question

You are considering an investment in a mutual fund with a 4% load and an expense ratio of 1.4%. You can invest instead in a bank CD paying 6% 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. Round your answer to 2 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. Round your answer to 2 decimal places.)

Annual rate of return             %

c. Now suppose that instead of a front-end load the fund assesses a 12b-1 fee of 1.65% 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.)

Annual rate of return             %

Explanation / Answer

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 The return from CD after 2 years would be (1+r)^2 (1.06)^2 The return from mutual fund after 2 years would be (1-Load)(1+r-expenses)^2 (1-0.04)(1+r-0.014)^2 0.014 Return from mutual fund should be greater than CD for investment in mutual fund Return from mutual fund > Return from CD (1-0.04)(1+r-0.014)^2 > (1.06^2) 0.96*(1 + r - 0.014)^2 > 1.1236 (1+r-0.014)^2 > 1.1704 1+r-0.014 > 1.0819 1 + r > 1.0959 r > 9.59% If mutual fund return is more than 9.59%, than it would be better than the CDs 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 Here, the n = 6 yrs. Therefore, return from CD would be (1.06^6) Return from mutual fund would be (1-0.04)(1+r-0.014)^6 Return from mutual fund > Return from CD (1-0.04)(1+r-0.014)^6 > (1.06^6) 0.96*(1 + r - 0.014)^2 > 1.4185 (1+r-0.014)^6 > 1.4776 1+r-0.014 > 1.0672 1 + r > 1.0812 r > 8.12% c Now suppose that instead of a front end load the fund assesses a 12b-1 of 1.65% 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 Here if the mutual fund levies fee instead of front end load, the return would be (1+r-expenses-fee)^n (1+r-Expenses-Fee)^n > (1.06^n) (1+r-0.014-0.0165)^n > (1.06^n) (1+r-0.014-0.0165) > (1.06) 1+r > (1.06+0.014+0.0165) 1+r > 1.0905 r > 0.0905 r > 9.05% The return should be more than 9.05%, this would be irrespective of the investment years

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