Question

Consider a no-load mutual fund with $200 million in assets and 10 million shares at the start of the year, and $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 gains distributions of $0.25 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?

A. 36.25%

B. 24.90%

C. 23.85%

D. There is not sufficient information to answer this question.

Answer 1

Answer: Correct option is C (that is 23.85%)
NAV at the beginning of the year=Total assets value of the mutual fund at the start of the year / Total shares at the start of the year

Total assets value of the mutual fund at the start of the year=$200 million
Total shares at the start of the year= 10 million
Net asset value at the start of the year (NAV0)=$200/10=$20.00

Total assets value of the mutual fund at the end of the year=$250 million
Total shares at the end of the year= 11 million
Expense ratio=1%
Net asset value at the end of the year= [Total assets value at the end of the year-(Total assets value at the end of the year*Expense ratio)]/Total shares at the end of the year

Net asset value at the end of the year (NAV1)= [$250-($250×1%)]/11= [$250-($2.5)]/11=($247.5)/11=$22.50

Gross return=(NAV1-NAV0+Income distribution+Capital gain distribution)/NAV0

Given that, income distribution is $2 per share and capital gain distribution is $0.25 per share
So, gross return=($22.50-$20+$2+$.25)/$20=0.2375 or 23.75%
Now, the closest value available in the options is 23.85%. So we can choose option "C" with the value 23.85%.