Question

You are considering an investment in a mutual fund with a 3% load and an expense ratio of 0.6%. You can invest instead in a bank CD paying 5% 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 0.85% 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 %

Answer 1

Solution:

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 %

Given details:

Mutual fund with a 3% load and an expense ratio of 0.6%.

Bank CD paying 5% interest

Note: In CD, rate i.e. “r” is given as 5% and we need to ascertain “r” for mutual fund.

In above scenario we need to see what annual rate of return a mutual fund should give if you invest in it and not in CD. Compounding is annual.

In order to understand if mutual funds investment is better than investment in CD we need to see if returns generated by mutual funds are exceeding the returns generated by CD investment.

• CD value after 2 years (1+r)ⁿ -- (1+0.05)² -- 1.1025
• Similarly calculate for mutual fund (1-Load)* (1+r-expenses)ⁿ (1-0.03)* (1+r-0.006)²

Assume if return on mutual fund investment is greater than return on CD investment.

Then start solving below equation:

• (1-0.03)* (1+r-0.006)² > 1.1025
• (0.97)* (1+r-0.006)² > 1.1025
• (1+r-0.006)² > (1.1025/0.97)
• (1+r-0.006)² > 1.14
• 1+r-0.006 > 1.068
• 1+r> 1.068+0.006
• 1+r > 1.074
• r>1.074-1
• r>0.74 OR 7.4%

Therefore, if mutual funds returns exceeds 7.40% then it is better investment than CD.

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 %

In this case we need to change “n” to 6 because in this scenario we note that period of investment has changed:

Hence other things remaining same --- Except “n” which is 6 in this case

• CD value after 2 years-- (1+r)ⁿ -- (1+0.05)⁶ -- 1.030
• Similarly calculate for mutual fundà (1-Load)* (1+r-expenses)ⁿ -- (1-0.03)* (1+r-0.006)⁶
• (1-0.03)* (1+r-0.006)⁶ > 1.030
• (1+r-0.006)⁶ > 1.030/0.97
• (1+r-0.006)⁶ > 1.062
• 1+r-0.006 > 1.0100
• 1+r> 1.0100+0.006
• 1+r > 1.016
• r> 1.016-1
• r>0.016 OR 1.6% Answer is 1.6%

c. Now suppose that instead of a front-end load the fund assesses a 12b-1 fee of 0.85% 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.)

In this case there is no front load but 12b-1 fee of 0.85% is given.

In this case we will not consider “n” and put given data in below equation:

• (1+r-expenses-fee)> (1+r)
• (1+r-0.006-0.0085)>1.05
• r>1.05-1+0.006+0.0085
• r>0.0645 OR 6.45%
• Rate of return on mutual funds investment should be greater than 6.45%