IRR Calculator
The return a project earns on the money it ties up — and when that number misleads.
NPV profile
The NPV of these cash flows at each discount rate. It crosses zero at the IRR; the dashed line is your cost of capital. Hover or tap the curve for values.
Cash flows at the IRR
Each cash flow discounted to today at the IRR. The present values add up to zero — that is what the IRR means.
The same in Excel or Google Sheets
How this was calculated
Results are estimates for general information and planning, not financial advice. Banks and institutions may calculate differently (rounding, fees, rate changes). Confirm figures with your lender or a qualified adviser before deciding.
About the IRR Calculator
The internal rate of return (IRR) is the discount rate at which a project’s net present value is exactly zero: the rate of return the cash flows themselves earn. If it is above your cost of capital, the project earns more than the money costs — for a normal project, where money goes out first and comes back later.
Enter the cash flows one per period (IRR) or on exact dates (XIRR). The calculator solves for the rate the way Excel does — Newton–Raphson from a 10% guess — but also scans every rate from −99.9999% to 1,000,000% and bisects each sign change, so it tells you when more than one IRR fits, or none. It also gives the MIRR with separate finance and reinvestment rates, the NPV at your cost of capital and an NPV profile chart, which shows at a glance where the IRRs are. Nothing you enter leaves your browser.
How to use it
- Choose every period (and the period length) or on dates (XIRR).
- Enter the cash flows: money going out (the investment) negative — the ± button flips the sign on phones — and money coming in positive. Or paste a column or row of numbers, or dates with amounts.
- Optionally enter your cost of capital to compare the IRR with it, and the finance and reinvestment rates for the MIRR.
- Read the IRR, check any warning about multiple rates or a financing pattern, look at the NPV profile, then copy the summary, the Excel formula or the CSV.
Examples
−70,000 today; 12,000, 15,000, 18,000, 21,000 and 26,000 at the end of years 1–5
IRR 8.66% a year · NPV at 10% = −2,683.31 · MIRR 9.87% (finance 10%, reinvestment 12%)
Excel’s =IRR(B1:B6) shows 8.7% with one decimal. The first four years alone give −2.12%.
IRR 10% and 20%
The cash flows change sign twice, and the NPV is zero at both rates (positive between them). Neither is “the” return: judge the project by its NPV at your cost of capital.
IRR 15%
This is the cost of a loan, not a return: at a 10% cost of capital the NPV is −45.45, so it is not worth taking, even though 15% is above 10%.
−10,000 on 1 Jan 2008; 2,750 on 1 Mar 2008; 4,250 on 30 Oct 2008; 3,250 on 15 Feb 2009; 2,750 on 1 Apr 2009
XIRR 37.34% a year
Common uses
- Check whether a project, a machine purchase or an expansion clears your required rate of return.
- Compare the return of investments with different cash-flow patterns — and spot when the IRR is not a fair comparison.
- Find the effective yield of a deal with staged payments on real dates.
- Check a spreadsheet IRR or XIRR, or find out why Excel returns #NUM!.
The IRR and MIRR formulas
The IRR is the rate that solves 0 = CF₀ + CF₁ ÷ (1 + IRR) + CF₂ ÷ (1 + IRR)² + … + CFₙ ÷ (1 + IRR)ⁿ — for dated cash flows (XIRR) each exponent is the days since the first date ÷ 365. There is no algebraic formula, so it is found by trial: Excel’s IRR iterates from the guess until the result is accurate within 0.00001 percent (at most 20 tries) and XIRR within 0.000001 percent (at most 100 tries), returning #NUM! if it fails. This calculator uses Newton–Raphson too, with a bisection search over every bracket as a fallback.
The modified IRR assumes that money received is reinvested at the reinvestment rate and money paid out is financed at the finance rate: MIRR = (FV of the positive cash flows at the reinvestment rate ÷ PV of the negative cash flows at the finance rate)^(1 ÷ (n − 1)) − 1, where n is the number of cash flows. It always has exactly one answer. Formulas as documented on Microsoft’s IRR, XIRR and MIRR help pages.
Four ways the IRR can mislead
Brealey, Myers & Allen (Principles of Corporate Finance) list four pitfalls of the IRR rule:
- Lending or borrowing? When money comes in first and goes out later, the IRR is the rate you pay, so a lower IRR is better. The calculator flags this pattern.
- Multiple rates of return. When the cash flows change sign more than once (an investment, income, then a large closing cost), there can be several IRRs — up to the number of sign changes (Descartes’ rule of signs) — or none. The calculator lists every one it finds.
- Mutually exclusive projects. A small project can have a higher IRR but a lower NPV than a large one, and timing differences can reverse rankings. Choose between alternatives by NPV, or by the IRR of the difference between their cash flows.
- More than one cost of capital. If the right discount rate differs from year to year, there is no single hurdle to compare the IRR with; use NPV with each year’s rate (the NPV calculator accepts a rate per period).
Reading the NPV profile
The NPV profile plots the NPV of the cash flows at each discount rate. For a normal project it slopes down and crosses zero once, at the IRR: at any lower rate the NPV is positive. The vertical dashed line marks your cost of capital, so you can read off the NPV there. A curve that crosses zero twice has two IRRs; one that never crosses has none.
Monthly and quarterly cash flows
With periods shorter than a year the IRR is a rate per period, exactly as Excel’s IRR returns it. The calculator also shows it as a yearly rate, compounded (1 + IRR)^k − 1 and nominal IRR × k, where k is the number of periods in a year. Enter the cost of capital and the MIRR rates per period as well, so like is compared with like. Use the dated mode (XIRR) when the cash flows do not fall at equal intervals; its rates are always yearly.
Limitations
- The search covers rates from −99.9999% to 1,000,000% per period; roots outside that range are not reported.
- The dated MIRR applies Excel’s MIRR idea to dates (365-day years); Excel itself has no dated MIRR, so there is no spreadsheet result to compare it with.
- Cash flows are assumed to arrive at the end of each period (period 0 = today).
- Up to 1,200 periods or dated cash flows at a time.
Privacy
Everything is calculated in your browser. The cash flows, rates and results are never uploaded or stored on a server.
Frequently asked questions
Is a higher IRR always better?
No. For an investment followed by income, yes, compared with the same cost of capital. For a borrowing pattern (money in first) a lower IRR is better, and between projects of different size or timing the higher IRR can belong to the one with the lower NPV. NPV at your cost of capital is the safer rule.
Why does Excel return #NUM! for my IRR?
Either no rate makes the NPV zero (for example all cash flows have the same sign), or Excel’s 20 tries from the guess did not reach one. This calculator searches every rate, so it either finds the IRR or explains why none exists. If it finds one Excel missed, give Excel that rate as the guess.
What is the difference between IRR, XIRR and MIRR?
IRR assumes equal periods between the cash flows. XIRR uses the actual dates and a 365-day year. MIRR replaces the IRR’s implicit assumption — that money received is reinvested at the IRR itself — with explicit finance and reinvestment rates, and always has one answer.
What should the reinvestment rate be?
What you can realistically earn on the money the project returns, often your cost of capital. The finance rate is what you pay to fund the investment, such as your borrowing rate.
How is IRR related to NPV?
The IRR is the discount rate at which the NPV is zero. For a normal project, the NPV at your cost of capital is positive exactly when the IRR is above it. Work out the NPV itself with the NPV calculator.