Answer: 3.96%

## Explanation To calculate the money-weighted return (MWR), we need to find the internal rate of return (IRR) that equates the present value of cash flows to zero. ### Step 1: Determine cash flows **Year 1:** - Beginning investment: +$2,500 (cash outflow from investor's perspective) - End-of-year value after -20% return: $2,500 × (1 - 0.20) = $2,000 - Withdrawal: $0 - Net cash flow at end of Year 1: $0 **Year 2:** - Beginning investment: +$1,500 (additional cash outflow) - Starting value: $2,000 + $1,500 = $3,500 - End-of-year value after 65% return: $3,500 × (1 + 0.65) = $5,775 - Withdrawal: -$500 (cash inflow to investor) - Net cash flow at end of Year 2: +$500 (inflow) **Year 3:** - Beginning investment: +$1,000 (additional cash outflow) - Starting value: $5,775 - $500 + $1,000 = $6,275 - End-of-year value after -25% return: $6,275 × (1 - 0.25) = $4,706.25 - Withdrawal: -$500 (cash inflow to investor) - Net cash flow at end of Year 3: +$500 (inflow) **Year 4:** - Beginning investment: $0 - Starting value: $4,706.25 - $500 = $4,206.25 - End-of-year value after 10% return: $4,206.25 × (1 + 0.10) = $4,626.875 - Withdrawal: $0 - Final value: $4,626.875 (cash inflow at end of Year 4) ### Step 2: Set up cash flow timeline From investor's perspective: - t=0 (beginning Year 1): -$2,500 - t=1 (beginning Year 2): -$1,500 - t=2 (end Year 2): +$500 - t=3 (beginning Year 3): -$1,000 - t=3 (end Year 3): +$500 - t=4 (end Year 4): +$4,626.875 Combining cash flows at same time points: - t=0: -$2,500 - t=1: -$1,500 - t=2: +$500 - t=3: -$1,000 + $500 = -$500 - t=4: +$4,626.875 ### Step 3: Solve for IRR We need to find r such that: -2,500 + (-1,500)/(1+r) + 500/(1+r)² + (-500)/(1+r)³ + 4,626.875/(1+r)⁴ = 0 Testing the options: - **Option A (2.15%):** NPV = -2,500 - 1,500/1.0215 + 500/1.0215² - 500/1.0215³ + 4,626.875/1.0215⁴ ≈ -$2,500 - $1,468.43 + $479.08 - $469.02 + $4,253.15 ≈ $294.78 - **Option B (3.96%):** NPV = -2,500 - 1,500/1.0396 + 500/1.0396² - 500/1.0396³ + 4,626.875/1.0396⁴ ≈ -$2,500 - $1,442.86 + $462.38 - $444.74 + $3,985.22 ≈ $61.00 - **Option C (7.50%):** NPV = -2,500 - 1,500/1.075 + 500/1.075² - 500/1.075³ + 4,626.875/1.075⁴ ≈ -$2,500 - $1,395.35 + $432.90 - $402.70 + $3,472.43 ≈ -$392.72 The IRR is the rate that makes NPV = 0. At 3.96%, NPV is closest to zero ($61), while at 2.15% it's $294.78 and at 7.50% it's -$392.72. ### Step 4: Verification Using financial calculator or Excel: CF0 = -2500 CF1 = -1500 CF2 = 500 CF3 = -500 CF4 = 4626.875 IRR ≈ 3.96% Therefore, the money-weighted return is closest to **3.96%**.

Author: LeetQuiz .