2.6 Calculating the MIRR: Negative Interim Outflows
The MIRR may be found by equating the PV of the costs with the terminal values (TV) of the inflows. The TV is calculated, as you will recall, by assuming a future “external” reinvestment rate, which herewith, shall be a “given.”
We shall use for this example, a reinvestment rate of 12%. Note that here there were several negative (out-) flows, or costs. In such cases, the negative values are discounted to their respective PVs, and the positive inflows are compounded to their FVs. Then a time value-based return shall be calculated as before, comparing the PV “cost” (in lieu of or as supplement to the original notion of “initial outlay”) with the TV. This is the same MIRR formula already discussed. Be careful to use the correct exponents in each instance. We shall illustrate the solution using the cash flows for “Project A” given earlier (see Section #2.2).
Project A
PV of costs =
($300) + ($387 ÷ 1.121) + ($193 ÷ 1.122) + ($100 ÷ 1.123) + ($180 ÷ 1.127) =
$952.00
TV of inflows =
($600 × 1.123) + ($600 × 1.122) + ($850 × 1.121) =
$2,547.60
$2,547.60 ÷ $952.00 = 2.6761x
- For every dollar invested, the project will produce $2.67 in the future.
- Remember: the project’s life is 7 years.
MIRRA = (2.6761) 1/7 -1 = 15.1%
Summary: The MIRR is calculated by compounding any positive interim cash flows to a Terminal Value, i.e., a Future Value at the term of the project, and comparing it to the Present Value of the negative cash flows – as shown in the formulations above.