Answer-first summary for fast verification
Answer: 27%
## Explanation Let's break this down step by step: **Given:** - Management fee: 2% - Incentive fee: 20% (on net return after management fees) - Target return after fees: 20% - Let R be the required return before fees **Step 1: Calculate return after management fee** After management fee = R - 2% **Step 2: Calculate incentive fee** Incentive fee = 20% × (R - 2%) **Step 3: Calculate return after all fees** Return after fees = (R - 2%) - 20% × (R - 2%) Return after fees = (R - 2%) × (1 - 0.20) Return after fees = (R - 2%) × 0.80 **Step 4: Set equal to target return and solve** (R - 2%) × 0.80 = 20% R - 2% = 20% / 0.80 R - 2% = 25% R = 27% **Verification:** - Before fees: 27% - After 2% management fee: 25% - 20% incentive fee on 25%: 5% - Return after all fees: 25% - 5% = 20% ✓ Therefore, the hedge fund needs to earn **27%** before fees to provide investors with a 20% return after fees.
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A hedge fund charges 2 plus 20%. Investors want a return after fees of 20%. How much does the hedge fund have to earn, before fees, to provide investors with this return? Assume that the incentive fee is paid on the net return after management fees have been subtracted.
A
27%
B
15%
C
21.6%
D
20%
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