Hi Syuen!
Great question! The important distinction here is that the mutual fund's underlying investments can earn a different return from the return you personally receive after accounting for sales charges and operating expenses.
Let's work through both calculations.
Step 1: Identify the information
We are given:
| ItemValue | |
| Shares purchased | 2,000 |
| Initial offering price | $40 |
| Front-end load | 5% |
| Back-end load | 2% if redeemed within one year |
| Ending NAV | $50 |
| Annual operating expense ratio | 1% |
| Investment period | Approximately 2 years |
Because the shares were purchased in January 2010 and sold at the end of 2011, the investment was held for nearly two years.
Therefore, the 2% back-end load does not apply, since it only applies to redemptions within one year.
Step 2: Calculate the initial investment
You purchased 2,000 shares at an offering price of $40 per share.
[
\text{Initial Investment}=2,000(40)
]
[
\boxed{$80,000}
]
This is the amount you paid to purchase the shares.
Step 3: Account for the front-end load
A front-end load is a sales charge deducted when purchasing mutual fund shares.
Because the $40 is the offering price, which includes the load, the initial net asset value per share is:
[
NAV_0=40(1-0.05)
]
[
\boxed{NAV_0=$38}
]
Therefore, the amount initially invested in the fund's underlying assets was:
[
2,000(38)=$76,000
]
The remaining $4,000 represented the sales charge.
Step 4: Calculate the fund's annual return before operating expenses
The initial NAV was $38, and the ending NAV was $50.
First, calculate the fund's cumulative NAV return:
[
R_{NAV}=\frac{50-38}{38}
]
[
R_{NAV}=0.315789
]
[
\boxed{R_{NAV}=31.58%}
]
This is the cumulative return reflected in NAV over approximately two years, after the fund's operating expenses.
To annualize this return:
[
(1+r_{NAV})^2=\frac{50}{38}
]
Therefore:
[
r_{NAV}=\left(\frac{50}{38}\right)^{1/2}-1
]
[
\boxed{r_{NAV}\approx14.71%}
]
Now account for the 1% annual operating expense ratio.
Assuming operating expenses reduce the fund's assets by 1% each year:
[
(1+r_{\text{assets}})(1-0.01)=1+r_{NAV}
]
Solving:
[
r_{\text{assets}}=\frac{1.1471}{0.99}-1
]
[
\boxed{r_{\text{assets}}\approx15.87%}
]
Therefore, under this expense-ratio convention, the underlying assets earned an annualized return of approximately 15.87% before operating expenses.
Step 5: Calculate the investor's total return
Now let's calculate how much you personally earned.
Your initial investment was:
[
2,000(40)=$80,000
]
At the end of 2011, the shares were worth:
[
2,000(50)=$100,000
]
Since you held the investment for longer than one year, there is no back-end load.
Therefore, your profit was:
[
100,000-80,000=$20,000
]
Your total holding-period return was:
[
R=\frac{20,000}{80,000}
]
[
\boxed{R=25%}
]
Step 6: Calculate the annualized investor return
Because the investment was held for approximately two years, we can also calculate the compound annual growth rate:
[
r=\left(\frac{100,000}{80,000}\right)^{1/2}-1
]
[
r=\sqrt{1.25}-1
]
[
\boxed{r\approx11.80%}
]
Final Answers
| MeasureReturn | |
| Cumulative NAV return after operating expenses | 31.58% |
| Annualized NAV return after operating expenses | 14.71% |
| Annualized underlying asset return before operating expenses | 15.87% |
| Investor's total holding-period return | 25.00% |
| Investor's annualized return | 11.80% |
Important Concept
Notice that the underlying investments earned a higher return than the investor.
Why?
Because the investor paid a 5% front-end sales charge, while the fund's NAV also reflects operating expenses.
This illustrates why mutual fund fees matter, particularly over shorter investment periods.
One final note: This calculation assumes that the fund made no additional distributions that need to be included in total return and that the expense ratio reduces assets multiplicatively. Some introductory finance courses approximate the underlying asset return by adding one percentage point to the annualized NAV return, producing approximately 15.71%.
Hope this helps!
Michael
