Consider a no-load mutual fund with $200 million in assets and 10 million shares at the start of the year and with $250 million in assets and 11 million shares at the end of the year. During the year investors have received income distributions of $2 per share and capital gain distributions of $.25 per share. Assuming that the fund carries no debt, and that the total expense ratio is 1%, what is the rate of return on the fund

273.75%

Explanation:

Note: Capital Gain distribution would be $50.25, NOT $.25 (typing mistake)

This is no-load MF. But there are other two types of MF (Mutual Funds).

If FL MF (Front Load Mutual Fund), investors pay something upfront when investing.

In BL MF (Back Load Mutual Fund), investors pay when exiting the MF.

Here, this is no load, so calulations are easier.

Now,

NAV (Net Asset Value) is the total assets divided by number of shares.

NAV beginning of year and NAV end of year. Total expense ratio will be adjusted from NAV, end of year.

NAV, beginning = 200 million / 10 million shares = $20

NAV, end = 250 - (0.01*250) / 11 million shares = $22.5

Now,

Rate of Return of the Fund = (NAV, end - NAV, beginning + Income Distribution + Capital Gain Distribution - Liabilities) / NAV, beginning

We have:

Rate of Return = ($22.5 - $20 + $2 + $50.25 - $0) / $20 = 2.7375

Converting to percentage:

2.7375 * 100 = 273.75%