Find the Modified Internal Rate of Return (MIRR) for the following annual series of cash flows, given a discount rate of 10.50%: Year 0: -$75,000; Year 1: $15,000; Year 2: $16,000; Year 3: $17,000; Year 4: $17,500; and, Year 5: $18,000
A) About 6.35%
B) About 6.88%
C) About 7.35%
D) About 7.88%
Answer: A
Explanation: A) Step One. Find the future values of all the cash inflow by reinvesting the cash inflow at the appropriate cost of capital. FV = $15,000 × (1.1050)4 + $16,000 × (1.1050)3 + $17,000 × (1.1050)2 + $17,500 × (1.1050)1 + $18,000 × (1.1050)0 = $22,363.53 + $21,587.72 + $20,757.43 + $19,337.50 + $18,000.00. Summing these we get: FV = $102,046.18.
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 $75,000 because all investment is made at the start of the project. Expressing the cash outflow in absolute terms: PV= $75,000.
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)n - 1 = ($102,046.18 / $75,000)1/5 - 1 = (1.360616)1/5 - 1 = 1.063524 - 1 = 0.063524 or about 6.35%.
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