Question

Consider a mutual fund with $300 million in assets at the start of the year and 12 million shares outstanding. If the gross return on assets is 18% and the total expense ratio is 2% of the year-end value, then the rate of return on the fund is  %.

Please enter your answer with TWO decimal points.

Answer 1

Sol:

Total assets = $300 million

Outstanding shares (S0) = 12 million

Return on Assets (ROA) = 18%

Expense ratio (Er) = 2%

To determine rate of return (ROR) on the fund in %:

Assets value at end of the year = Total assets * (1 + ROA)

Assets value at end of the year = 300,000,000 * (1 + 18%)

Assets value at end of the year = 300,000,000 * 1.18 = $354,000,000

Total expense = Assets value * Er

Total expense = 354,000,000 * 2% = $7,080,000

ROR = (Assets value at end of the year - Total assets - Total expense) / Total assets

ROR = (354,000,000 - 300,000,000 - 7,080,000) / 300,000,000

ROR = 46,920,000 / 300,000,000

ROR = 0.1564 or 15.64%

Therefore rate of return (ROR) on the fund is 15.64%