Answer: 13.2%

## Explanation To calculate the money-weighted rate of return (MWRR), we need to find the discount rate that equates the present value of cash outflows to the present value of cash inflows. **Cash Flows:** - At t=0: Initial investment = -$50 million (outflow) - At t=1: Additional investment = -$125 million (outflow at beginning of Year 2) - At t=2: Terminal value = ? (inflow) **Calculate terminal value:** 1. Year 1: $50 million × (1 + 0.17) = $58.5 million 2. Beginning of Year 2: $58.5 million + $125 million = $183.5 million 3. Year 2: $183.5 million × (1 + 0.12) = $205.52 million **Set up the equation:** The MWRR (r) satisfies: \[ 50 + \frac{125}{(1+r)} = \frac{205.52}{(1+r)^2} \] **Solve for r:** Let x = 1 + r \[ 50 + \frac{125}{x} = \frac{205.52}{x^2} \] Multiply through by x²: \[ 50x^2 + 125x = 205.52 \] \[ 50x^2 + 125x - 205.52 = 0 \] **Solve quadratic equation:** \[ x = \frac{-125 \pm \sqrt{125^2 - 4(50)(-205.52)}}{2(50)} \] \[ x = \frac{-125 \pm \sqrt{15625 + 41104}}{100} \] \[ x = \frac{-125 \pm \sqrt{56729}}{100} \] \[ x = \frac{-125 \pm 238.18}{100} \] Take positive root: \[ x = \frac{-125 + 238.18}{100} = \frac{113.18}{100} = 1.1318 \] Thus, r = 1.1318 - 1 = 0.1318 or 13.18% **Annualized MWRR over 2 years:** Since this is already an annualized rate (it's the discount rate that makes the equation work), the answer is approximately 13.2%. **Verification:** - PV of outflows: $50 + $125/(1.1318) = $50 + $110.41 = $160.41 - PV of terminal value: $205.52/(1.1318)² = $205.52/1.281 = $160.41 ✓ Therefore, the closest answer is **13.2%**.

Author: LeetQuiz .