IRR Calculator
The discount rate that makes a project’s NPV exactly zero.
4 cash flows. The IRR is the discount rate that makes NPV exactly zero — here it exceeds the 8.00% hurdle.
Positive NPV — the project creates value at your required return.
IRR assumes interim cash flows are reinvested at the IRR itself, which flatters high-IRR projects. When ranking mutually exclusive projects, NPV is the more reliable criterion.
The internal rate of return is the discount rate at which a project’s NPV equals zero. For an investment of 1,000 returning 400 a year for three years, the IRR is about 9.70% — so the project adds value against any hurdle rate below that.
The break-even discount rate
NPV falls as the discount rate rises: future cash is worth less the more heavily you discount it. Somewhere there is a rate at which the discounted inflows exactly offset the initial outlay and NPV hits zero. That rate is the internal rate of return.
Its appeal is that it comes out as a percentage, which compares directly against a cost of capital without needing any scale context. Saying a project returns 9.7% against an 8% hurdle is immediately meaningful, where saying it has an NPV of 25 requires knowing how large the investment was.
Why there is no formula
IRR cannot be solved algebraically for more than a few periods, because it is the root of a polynomial in the discount rate. Every calculator, spreadsheet included, finds it by iteration — trying rates until NPV is close enough to zero. This tool uses bisection, which is slower than the alternatives but cannot diverge on awkward input.
CF₀ is the initial investment and is negative. There is no closed-form solution beyond simple cases, so r is found numerically.
Worked example: −1,000 then 400 × 3
Test rates until NPV crosses zero:
- 1 Lay out the cash flows. −1,000 at t = 0, then +400 at the end of each of three years.
- 2 Try a low rate. At 5%, NPV is about +89 — positive, so the true IRR is higher.
- 3 Try a higher rate. At 12%, NPV is about −39 — negative, so the IRR sits between 5% and 12%.
- 4 Narrow the range. Bisection repeatedly halves the interval, converging on 9.70%.
- 5 Check the answer. Discounting the three 400s at 9.70% gives almost exactly 1,000, so NPV is zero.
- 6 Compare against the hurdle. 9.70% beats an 8% cost of capital, so the project is worth taking.
NPV of the example at different discount rates
NPV of −1,000 followed by 400 a year for three years. It crosses zero at the IRR.
| Discount rate | NPV | Decision |
|---|---|---|
| 0% | +200.00 | Accept |
| 5% | +89.30 | Accept |
| 8% | +30.84 | Accept |
| 9.70% | 0.00 | Indifferent — this is the IRR |
| 12% | −39.27 | Reject |
| 15% | −86.71 | Reject |
Three ways IRR misleads
Multiple IRRs. A series whose sign changes more than once can have several rates that set NPV to zero, all equally valid mathematically. This happens with projects requiring later reinvestment — a mine that must be restored at the end, for instance. The calculator flags this; when it appears, use NPV instead.
The reinvestment assumption. IRR implicitly assumes interim cash flows are reinvested at the IRR itself. For a project returning 40%, that assumes every payout also earns 40%, which is usually unrealistic. The modified IRR exists to fix this by discounting at an explicit reinvestment rate.
Scale blindness. A project returning 50% on an investment of 10 has a higher IRR than one returning 15% on 10,000, but the second creates far more value. When choosing between mutually exclusive projects, rank by NPV; IRR is a screening tool, not a ranking one.
None of this makes IRR useless — it remains the most intuitive single number for whether a project clears its cost of capital. It simply should not be the only number you look at.