Question

Consider a no-load mutual fund with $210 million in assets and 10 million shares at the start of the year and with $260 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 $.30 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? 23.70% 20.09% 22.38% The answer cannot be determined from the information given.

Answer 1

NAV at the start of the year (NAV0)

NAV at the start of the year (NAV0) = Value of total asset at the year beginning / Number of shares outstanding

= $210 Million / 10 Million shares

= $21.00 per share

NAV at the end of the year (NAV1)

NAV at the end of the year (NAV1) = Value of total asset at the year end(1 – Expense Ratio) / Number of shares outstanding

= $260 Million(1 – 0.01) / 11 Million shares

= $257.40 Million / 11 Million shares

= $23.40 per share

Rate of return on the fund

Rate of return on the fund = [(NAV1 – NAV0 + Dividend per share + Capital gain per share) / NAV0] x 100

= [($23.40 - $21.00 + $2.00 + $0.30) / $21.00] x 100

= [$4.70 / $21.00] x 100

= 22.38%

“Therefore, the Rate of return on the fund will be 22.38%”