The calculation, without hidden assumptions
IRR is the discount rate that makes net present value equal zero. That sounds like a single clean answer, but cash-flow patterns with more than one sign change can have more than one mathematical IRR or none in the searched range. This calculator therefore keeps the cash flows visible, searches for roots numerically, reports how many sign-change roots it detected, and also shows NPV at a separate hurdle rate you control.
How to use this calculator
Paste the time-zero cash flow first and then one amount for each equal-length period.
Optionally enter a hurdle/discount rate to see the NPV of the same stream at that rate.
Read the root warning as well as the displayed IRR, especially when cash flows switch signs more than once.
Where people use it
- •Cross-checking an IRR from a spreadsheet
- •Exploring irregular project cash flows
- •Teaching the relationship between IRR and NPV
Example: one outflow followed by several inflows
For -10,000 at period 0 followed by positive inflows, the solver looks for a rate r where discounting all later cash flows makes their combined present value equal the initial 10,000 outflow.
What the result does not assume
- •IRR can be ambiguous for non-conventional cash flows and can hide project scale or reinvestment assumptions. Review the actual cash-flow stream and NPV alongside it.
- •This numerical result is not an investment recommendation, return forecast or guarantee.
Frequently asked questions
Why can a project have more than one IRR?+
When the cash-flow sequence changes sign multiple times, the NPV equation can cross zero at more than one rate.
What if no IRR is shown?+
The entered cash flows may not create a root in the calculator’s searched rate range, or may not contain both positive and negative values.
How is IRR related to NPV?+
IRR is a rate at which the NPV of the entered cash-flow stream equals zero.
Semantic next steps
Continue the calculation
These links move to a different input, formula or project stage rather than a keyword variation of this page.
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