Question

What is the dollar-weighted return (IRR) for the following fund results? Assume initial fund is $2,000 and you withdraw all your account balance at the end of year 4. Each cash inflow occurs at the end of each period. year returns 0.085 0.105 cash inflow $5,000 $6,000 $1,000 $0 -0.05 0.0645 4.10% 3.09% 5.56% 2.95%

Answer 1

The correct answer is the second option showing 3.09%

C0 = 2,000; C1 = 5,000; C2 = 6,000; C3 = 1,000; r1 = 0.085; r2 = 0.105; r3 = -0.05; r4 = 0.0645

Value of all the investments at the end of year 1 = C0 x (1 + r1) + C1 = 2,000 x (1 + 0.085) + 5,000 =  7,170

Value of all the investments at the end of year 2 = 7,170 x (1 + r2) + C2 = 7,170 x (1 + 0.105) + 6,000 =  13,922.85

Value of all the investments at the end of year 3 = 13,922.85 x (1 + r3) + C3 = 13,922.85 x (1 - 0.05) + 1,000 = 14,226.71

Value of all the investments at the end of year 4 = C4 = 14,226.71 x (1 + r4) = 14,226.71 x (1 + 0.0645) = 15,144.33

Hence, the cash flows and IRR are as shown below. Please see the table below. The last row highlighted in yellow is your answer. Figures in parenthesis, if any, mean negative values. All financials are in $. Adjacent cells in blue contain the formula in excel I have used to get the final output.

ДАО 192 Year 1930 194 1 195 2 196 3 197 4 198 IRR 199 АР Cash flows -CO -C1 -C2 -C3 04 AQ Cash flows (2,000.00) (5,000.00) (6,000.00) (1,000.00) 15,144.33 3.09% "=IRR(AQ193:AQ197)