Explanation

The money-weighted return (MWR) is calculated using the internal rate of return (IRR) approach, which finds the discount rate that makes the net present value of all cash flows equal to zero.

Cash Flow Timeline:

• Time 0 (Beginning of Period 1): Initial investment = -$100,000 (outflow)
• Time 1 (End of Period 1): Income received = +$5,000 (inflow) - not reinvested
• Time 2 (End of Period 2): Additional contribution = -$25,000 (outflow)
• Time 3 (End of Period 3): Ending portfolio value = +$123,000 (inflow)

Setting up the IRR equation:

$-100,000 + \frac{5,000}{(1+r)} + \frac{-25,000}{(1+r)^2} + \frac{123,000}{(1+r)^3} = 0$

Where r is the money-weighted return per period.

Calculation:

Using a financial calculator:

• CF₀ = -100,000
• CF₁ = +5,000
• CF₂ = -25,000
• CF₃ = +123,000
• Compute IRR = 0.94%

Verification:

At 0.94%:

• PV of CF₁ = 5,000 / 1.0094 = 4,953.42
• PV of CF₂ = -25,000 / (1.0094)² = -24,534.98
• PV of CF₃ = 123,000 / (1.0094)³ = 119,581.56
• Sum = -100,000 + 4,953.42 - 24,534.98 + 119,581.56 ≈ 0

Why other options are incorrect:

• A) 1.20%: This would overestimate the return given the additional contribution at time 2.
• B) -0.50%: This would imply a negative return, which is inconsistent with the portfolio growing from $100,000 to $123,000 over three periods.

Key Concept:

Money-weighted return accounts for the timing and magnitude of cash flows, making it appropriate for evaluating portfolio performance when the investor controls cash inflows and outflows.