Find the Modified Internal Rate of Return (MIRR) for the following series of future cash flows, given a discount rate of 11%: Year 0: -$22,000; Year 1: $5,000; Year 2: $6,000; Year 3: $7,000; Year 4: $7,500; and, Year 5: $8,000
A) About 12.13%
B) About 12.88%
C) About 13.04%
D) About 13.12%
Answer: D
Explanation: D) Step One. Find the future values of all the cash inflows by reinvesting the cash inflows at the appropriate cost of capital. FV = $5,000 × (1.11)4 + $6,000 × (1.11)3 + $7,000 × (1.11)2 + $7,500 × (1.11)1 + $8,000 × (1.11)0 = $7,590.35 + $8,205.79 + $8,624.70 + $8,325.00 + $8,000.00. Summing these we get: FV = $40,745.84.
Step Two. Find the present value of the cash outflow by discounting at the appropriate cost of capital. This is the initial cash outflow of $22,000 because all investment is made at the start of the project. Expressing the cash outflow in absolute terms: PV = $22,000.
Step Three. Find the interest rate that equates the present value of the cash outflow with the future value of the cash inflow given as: MIRR = (FV/PV)1/n - 1 = ($40,745.84/$22,000)1/5 - 1 = (1.852084)1/5 - 1 = 1.131181 - 1 = 0.131181, or about 13.12%.
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