How this calculator works
- Step 1DiscountCF ÷ (1 + r)ᵗEach flow is valued in today’s money.
- Step 2SolveNPV = 0The IRR is the rate where the total is zero.
- Step 3CompareNPV, MIRRBoth use your own discount rate.
The net present value adds every cash flow after discounting it back to today. The internal rate of return is the rate that makes that total exactly zero.
There is no formula for the IRR, so the calculator scans rates from −99.99% to 1,000% per period. It then narrows each place where the NPV changes sign.
Worked example: an embroidery machine
- NPV
Σ CFₜ ÷ (1 + r)ᵗ- IRR
the r where NPV = 0
- Year 0−₹16,000−₹16,000
- Year 1₹2,000 ÷ 1.1^1₹1,818
- Year 2₹4,000 ÷ 1.1^2₹3,306
- Year 3₹5,000 ÷ 1.1^3₹3,757
- Year 4₹5,000 ÷ 1.1^4₹3,415
- Year 5₹5,000 ÷ 1.1^5₹3,105
- Year 6₹5,000 ÷ 1.1^6₹2,822
- NPV at 10%₹2,223
The NPV at 10% is positive, so the project earns more than 10%. The IRR is 14.09%, matching the 14.09% in the OpenStax Principles of Finance example.
Read the result
- IRR14.09%The project’s own break-even rate.
- NPV at 10%₹2,223Value added over a 10% alternative, in today’s rupees.
- MIRR at 10%12.41%Assumes inflows are reinvested at 10%, not at the IRR.
₹1,000 that returns ₹400 a year for four years has an IRR of 21.86% and an NPV of ₹268 at 10%.
For monthly flows, the IRR is per month. An IRR of 1% a month compounds to 12.68% a year.
When there is more than one IRR
−100, then +230, then −132 changes sign twice and has two IRRs: 10% and 20%. Neither is the answer on its own.
When the flows change sign more than once, use the NPV at your discount rate or the MIRR. The calculator lists every rate it finds rather than picking one.
Assumptions and limits
- Equal periodsEvery flow is one period after the last.
- First flow todayLine 1 is not discounted.
- One rateMIRR finances and reinvests at your discount rate.
- Before taxTaxes, fees and inflation are not modelled.
Related return tools
IRR needs evenly spaced cash flows. For other patterns, a different measure fits better.
When cash flows fall on irregular dates, use the XIRR calculator. For a single start and end value, the CAGR calculator is enough, and the payback period calculator shows how long a project takes to repay its cost.
Common mistakes
Mistake: Entering the investment as positive.
Instead: Money paid out is negative; money received is positive.
Mistake: Leaving out a year with no cash flow.
Instead: Enter 0 so later flows keep their timing.
Mistake: Using IRR for dated, uneven flows.
Instead: Use the XIRR Calculator for exact dates.
Mistake: Ranking projects of different sizes by IRR.
Instead: Compare NPVs; a small project can have a high IRR but add little.
Checking the method
A separate script re-works every golden value with Newton’s method and Horner’s rule, and reproduces the OpenStax 14.09% example.
Read how we test our calculators, or browse more money calculators.