What IRR and MIRR measure
IRR is the discount rate that makes the present value of the inflows equal the present value of the outflows. There is no direct formula for it once there are more than two cash flows, so calculators search for the rate by trial and refinement. This one scans from -99% to 10,000% and reports every rate it finds.
MIRR changes the setup. It compounds all the inflows forward to the final year at a reinvestment rate you choose, discounts all the outflows back to today at a finance rate, and then finds the single rate that links the two amounts.
IRR: the r that solves 0 = CF0 + CF1/(1+r) + ... + CFn/(1+r)^n. MIRR = (FV of inflows at the reinvestment rate / PV of outflows at the finance rate)^(1/n) - 1, where n is the number of periods. Both are standard textbook definitions, found for example in Berk and DeMarzo, Corporate Finance.
A worked example
A project costs $1,000 today and returns $300, $400, $500 and $600 over the next four years. Net present value falls as the discount rate rises, and the IRR is the rate where it reaches zero.
| Discount rate | NPV |
|---|---|
| 0% | $800.00 |
| 10% | $388.77 |
| 20% | $106.48 |
| 24.89% (the IRR) | $0.00 |
| 30% | -$94.88 |
For the MIRR, suppose inflows can be reinvested at 10% and the finance rate is 8%. The inflows grow to $300(1.10)^3 + $400(1.10)^2 + $500(1.10) + $600 = $2,033.30 by year 4. The only outflow is the $1,000 today. MIRR = (2,033.30 / 1,000)^(1/4) - 1 = 19.41%. The finance rate does not matter here because the only outflow is today. The MIRR is lower than the 24.89% IRR because it assumes the interim cash earns 10%, not 24.89%.
When IRR gives two answers or none
Each time the cash flows switch between negative and positive, the NPV curve can cross zero once more. A project with a cost, a payoff and then a cleanup bill is a typical case. The flows -$1,000, +$5,000, -$6,000 have two IRRs, 100% and 200%, and both are correct solutions. The calculator lists them and warns you, because an answer that is not unique cannot rank projects.
Some cash flows have no IRR at all. If every flow is positive, or every flow is negative, no rate can bring NPV to zero. The same happens for some mixed patterns such as +$100, -$50, +$50. In those cases the calculator says there is no solution instead of showing a number. MIRR still works whenever there is at least one inflow and one outflow.
Mistakes to avoid
- Ranking projects of different sizes by IRR. A small project can have a high IRR and add little value. Compare NPVs.
- Reading IRR as the rate you will actually earn. That is true only if every inflow can be reinvested at the IRR, which is why MIRR exists.
- Reporting one IRR when the cash flows change sign more than once.
- Entering the investment as a positive number. The initial outlay must be negative.
- Comparing the IRR against the wrong hurdle rate. The right one is the project's required return, usually the WACC when the risk is average.
Estimate for learning, not financial advice. Inputs stay in your browser and are not sent or stored.