Answer:
The net annual rate of return is negative, which means there was a loss on the investment. However, the options you provided for the net annual rate of return are positive percentages. Therefore, none of the options (13.6%, 11.7%, 15.2%, 12.9%) accurately represent the net annual rate of return in this case. Impress your teachers ;)
Step-by-step explanation:
To calculate your net annual rate of return, we need to consider the management fee and performance fee charged by the hedge fund.
Management Fee:
The management fee is calculated as a percentage of the total investment. In this case, the management fee is 2% of $30,000,000, which is $600,000.
Performance Fee:
The performance fee is calculated as a percentage of the profit earned by the hedge fund. In this case, the return on the hedge fund's shares after one year is 19%, which corresponds to a profit of 19% * $30,000,000 = $5,700,000. The performance fee is 20% of this profit, which amounts to $5,700,000 * 20% = $1,140,000.
Now, let's calculate the net annual rate of return:
Net Annual Rate of Return = (Profit - Management Fee - Performance Fee) / Total Investment
Profit = Return on Investment - Total Investment
Profit = 19% * $30,000,000 - $30,000,000
Profit = $5,700,000 - $30,000,000
Profit = -$24,300,000 (Negative because the return was less than the initial investment)
Net Annual Rate of Return = (-$24,300,000 - $600,000 - $1,140,000) / $30,000,000
Net Annual Rate of Return = -$26,040,000 / $30,000,000
Net Annual Rate of Return ≈ -0.868 (as a decimal)