Explanation

The money-weighted rate of return (MWRR) 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:

Year 0 (CF0):

• Initial purchase: -$50.00 (cash outflow)

Year 1 (CF1):

• Dividend received: +$5.00 (cash inflow)
• Additional purchase: -$75.00 (cash outflow)
• Net cash flow: $5.00 - $75.00 = -$70.00

Year 2 (CF2):

• Dividends received: 2 shares × $7.50 = +$15.00 (cash inflow)
• Sale proceeds: 2 shares × $100.00 = +$200.00 (cash inflow)
• Net cash flow: $15.00 + $200.00 = +$215.00

IRR Calculation:

The IRR equation is: $-50 + \frac{-70}{(1+r)} + \frac{215}{(1+r)^2} = 0$

Solving this equation gives r = 48.8607%, which rounds to 48.9%.

Verification:

• The investor's required return of 35% is irrelevant to the calculation of the actual money-weighted return.
• The MWRR of 48.9% exceeds the required return of 35%, indicating this was a good investment.

Key Concept: Money-weighted return considers the timing and amount of all cash flows into and out of the investment, making it sensitive to when money is added or withdrawn from the portfolio.