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%.