The IRR Equation and How It Is Solved
IRR is the rate r that solves
0 = CF0 + CF1 ÷ (1 + r) + CF2 ÷ (1 + r)2 + … + CFn ÷ (1 + r)n
With more than a few cash flows there is no closed-form answer, so it is found by search. This calculator brackets the rate between −99.99% and 1,000% and halves the interval 300 times. Check the default result by hand: at 15.32%, $3,000 is worth $2,601.41 today, $4,000 is worth $3,007.70, $5,000 is worth $3,260.11 and $2,000 is worth $1,130.78 (each divided by 1.1532 raised to its year). Those add to about $10,000, the amount invested, so NPV is zero.
Timing Changes IRR More Than the Total
Every row below puts in $10,000, and every row but the last gets $14,000 back. MIRR uses an 8% finance rate and 6% reinvestment rate; NPV is at 8%.
Front-loading the same dollars raises IRR from 14.36% to 17.80%, because money returned sooner is discounted less. MIRR moves far less, since it compounds the early money at only 6% instead of at the IRR. When all the money comes back at the end there is nothing to reinvest, and IRR equals MIRR.
Monthly or Quarterly Cash Flows
Enter one value per period and choose the period length. The IRR per period is annualized by compounding, not by multiplying. Investing $10,000 and receiving $900 a month for 12 months is an IRR of 1.20% a month; (1 + 0.012043)12 − 1 = 15.45% a year, not 14.45%.
Pitfalls and Edge Cases With IRR
- Cash flows that change sign more than once. −$1,600, then +$10,000, then −$10,000 has two IRRs, 25% and 400%: NPV is zero at both. This calculator scans NPV from −99% to 1,000% and reports every rate where it crosses zero, so it shows both. With two answers IRR can’t rank the project; use NPV at your required return, or MIRR, which always has one answer.
- Comparing projects of different sizes. A 40% IRR on $1,000 adds less value than a 15% IRR on $1,000,000. Rank mutually exclusive projects by NPV at your cost of capital.
- Treating IRR as a cash yield. IRR assumes interim cash is reinvested at the IRR. If you cannot reinvest at that rate, MIRR with a realistic rate is the better estimate of what you will earn.
- Uneven gaps between flows. Each value is one period apart. If payments arrive on irregular dates, use a dated method (Excel’s XIRR) instead.
- Typing the investment as positive. The first value is money out and must be negative, or there is no sign change and no IRR.
What IRR Doesn’t Tell You
IRR ignores scale, risk and taxes, and it says nothing about whether the cash-flow forecast is right. It also does not choose the hurdle: compare it with your cost of capital (see the WACC calculator) or another benchmark. For federal cost-benefit work OMB publishes discount rates each year; the 2026 Appendix C nominal rates run from 3.4% for 3 years to 4.1% for 30 years. For an investment decision with tax or legal consequences, have a financial adviser or CPA review the cash flows.
Frequently Asked Questions
What is a good IRR?
One above your cost of capital or the return you could earn elsewhere at similar risk. There is no universal number; it depends on the risk of the cash flows.
What is the difference between IRR and MIRR?
IRR assumes cash is reinvested at the IRR; MIRR compounds inflows at a reinvestment rate you choose and discounts outflows at a finance rate, so it is usually lower and always has one answer.
Why does the calculator show no IRR?
The cash flows need at least one negative and one positive value, and NPV has to reach zero somewhere between −99% and 1,000%. With more than one sign change there can be several IRRs, which the calculator lists; use NPV or MIRR to decide then.
Is IRR the same as annual return?
Only for yearly periods. For monthly or quarterly flows the calculator compounds the per-period IRR to an annual figure.
How is IRR different from ROI?
ROI compares total gain with cost and ignores timing; IRR accounts for when each dollar arrives, so a faster payback raises IRR even with the same total gain.
Why does Excel give a slightly different IRR?
Excel uses an iterative method with a starting guess; with normal cash flows both should agree to two decimals. Check that the cash flows and their order match.
Does IRR work for real estate deals?
Yes: enter the down payment and costs as the first negative flow, each year’s cash flow, and the sale proceeds in the final year.
How to Use This Calculator
- Enter cash flows — the first value is the investment as a negative number; then one value per period, separated by commas. Use 0 for a period with no cash.
- Choose the period length — years, months or quarters; monthly and quarterly results are also shown annualized.
- Set the MIRR rates — the rate you pay to borrow (finance rate) and the rate you can earn on cash received (reinvestment rate).
- Read the results — IRR per period, annualized IRR, MIRR, totals in and out, NPV at 0%, 5% and 10%, and a warning when flows change sign more than once.
📚 Sources & References- [1] Microsoft. IRR function (method and the worked example used to test this calculator; accessed Oct 2026). support.microsoft.com
- [2] OpenStax. Principles of Finance, Chapter 16: How Companies Decide Which Projects to Invest In (NPV, IRR, MIRR, payback, profitability index; 2022). openstax.org
- [3] Office of Management and Budget. Circular A-94, Appendix C: discount rates for 2026 (revised Mar 6, 2026). www.whitehouse.gov
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