FinCalcs

IRR Calculator — Internal Rate of Return of a Cash Flow Stream

Who this is for: For finance students who need the IRR of a homework cash flow stream without keystroke hunting, and for operators comparing a project's return to their cost of capital in one number.

Not the right tool for: Cash flows that change sign more than once — multiple IRRs exist and this reports the first root found · Ranking mutually exclusive projects — IRR's reinvestment assumption misranks them; use NPV

Enter a cash flow stream — get the internal rate of return (plus NPV, MIRR, and payback) with the numerical solve done for you.

Quick answer: IRR is the discount rate that sets NPV to zero — the stream's built-in per-period return. −$1,000 today returning $500, $600, $700 over three years has an IRR of 33.87%. It's always solved numerically (no formula exists), and it assumes intermediate cash flows reinvest at the IRR itself — MIRR relaxes that.

Cash flows (CF0 first — outflows negative)
NPV
$533.05
discounted at 8% per period
IRR
33.87%
rate where NPV = 0
MIRR
24.53%
reinvested at 8%
Payback
1.83 periods
undiscounted cumulative
Discounted payback
2.04 periods
at 8% per period
Total inflows
$1,800.00
undiscounted sum of positive flows
PeriodCash flowDiscountedCumulative (discounted)
0 (today)-$1,000.00-$1,000.00-$1,000.00
1$500.00$462.96-$537.04
2$600.00$514.40-$22.63
3$700.00$555.68$533.05
MIRR here applies your discount rate as both the finance rate and the reinvestment rate. IRR shows “no solution” when the stream never crosses zero (all-positive or all-negative flows). Deciding between two projects? Read the NPV vs IRR guide before trusting IRR alone.
Cash flows entered per period (year, month — your choice, kept consistent). CF0 is day zero and is not discounted. Educational reference, not investment advice.
Core facts
DefinitionThe rate r where NPV = 0 (per period)
Worked example−$1,000; $500, $600, $700 → IRR 33.87%
SolvingGrid scan + bisection, −99.99% to 1000%
CaveatMultiple sign changes can produce multiple IRRs — first root reported
CompiledOctober 2026

What the internal rate of return means

IRR is the discount rate that makes NPV exactly zero — the project's built-in compound return, expressed per period. It has no closed-form formula, so it is always solved numerically: guess a rate, compute NPV, use the sign to steer the next guess. This page scans a fine grid of rates (−99.99% to 1000%) for a sign change and bisects to full precision — the same bisection your financial calculator performs when you press CPT IRR. Example: −$1,000 today returning $500, $600, and $700 over three years has an IRR of 33.87% per year; if your cost of capital is 10%, the project clears it by a mile. Two caveats matter: IRR assumes you can reinvest intermediate cash flows at the IRR itself (optimistic — see MIRR), and cash flows that change sign more than once can have more than one IRR.

Common uses

  • Homework: find the IRR of a textbook cash flow stream
  • Comparing a project's return to the cost of capital in one number
  • Checking the return a structured payout (installment sale, royalty) really offers
  • Seeing why MIRR gives a different, more conservative number on the same stream

Where these numbers come from

All results are computed in your browser from the standard closed-form formulas (and a numerical root-finder where no closed form exists — rates, IRR, YTM). Formulas follow the ordinary-annuity (END) convention used by the BA II Plus and HP 12C. Educational reference only — not investment, tax, or accounting advice.

Frequently Asked Questions

What is a good IRR?
Only relative to your alternatives: any IRR above your cost of capital creates value on that project. A 12% IRR is excellent if you borrow at 6% and mediocre if your equity investors demand 20%. Textbook problems usually tell you the hurdle rate to compare against.
Why does IRR assume reinvestment at the IRR?
Mathematically, IRR is just the compound growth rate that connects your outlays to your inflows — using it implicitly treats every intermediate cash flow as if it grew at that same rate until the end. That's fine for small rates, flattering for big ones; MIRR lets you set a realistic reinvestment rate instead.
Can a project have two IRRs?
Yes. Every sign change in the cash flow stream can add a root — a project like −1,000, +2,500, −1,560 (common in mining, decommissioning, or staged investments) crosses zero twice and has two IRRs. This calculator reports the first one it finds; if the stream changes sign more than once, switch to NPV or MIRR to decide.
Why is my IRR 'no solution'?
If cash flows never sum to a crossover — for instance all flows are positive, or the total inflows never exceed the outflows — no discount rate makes NPV zero, and the honest answer is that IRR is undefined rather than a made-up number.
How is this different from the BA II Plus IRR?
Same math, same bisection. The BA II Plus requires the CF worksheet: CF0, then each cash flow with a repeat count. Here you just add rows — and you also see NPV, MIRR, and the discounted table in the same view.

More capital budgeting calculators

NPV Calculator
Paste a cash flow stream and a discount rate — get net present value plus the discounted table that shows where the value comes from.
MIRR Calculator
Modified internal rate of return: reinvests inflows at a rate you choose instead of the IRR — the conservative fix for IRR's optimism.
Payback Period Calculator
How fast does the project pay for itself? Simple and discounted payback from any cash flow stream, with linear interpolation inside the year.
WACC Calculator
Equity and debt values with their costs and the tax rate — get the weighted average cost of capital and the after-tax debt rate.
Break-Even Calculator
Fixed costs, price per unit, variable cost per unit — get break-even units, break-even revenue, and the profit at any volume.