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IRR Calculator

Work out the internal rate of return of an investment from what you put in and what it pays back each period, plus its net present value at your required return and how long it takes to pay back.

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How to use the IRR calculator

  1. Enter the initial investment, the amount paid at the start. Enter it as a positive number; the calculator treats it as money going out.
  2. Enter the cash flows, one for each period in order, separated by commas or new lines. Money you receive is positive; money you pay in later (an extra investment or a repair, say) is negative. Use 0 for a period with nothing.
  3. Choose whether each period is a year or a month.
  4. Optionally, enter a discount rate: the yearly return you require. The calculator then shows the net present value (NPV) and the discounted payback period.

The results show the IRR, NPV, payback period and a table of every cash flow with its running total and present value. For monthly periods the IRR is also shown as an annual rate.

How IRR is calculated

NPV(r) = CF0 + CF1 ÷ (1 + r) + CF2 ÷ (1 + r)^2 + … + CFn ÷ (1 + r)^n IRR = the rate r at which NPV(r) = 0

CF0 is the initial investment (negative), and CF1 to CFn are the later cash flows. The IRR is the discount rate that makes the present value of everything you receive exactly equal to what you paid. There is no formula that solves for it directly, so the calculator scans every rate from −99% to +1,000% per period for a point where NPV changes sign, then narrows each one down. For monthly periods, the annual IRR is (1 + monthly IRR)^12 − 1.

The payback period is when the running total of cash flows turns positive, counting a fraction of the period in which it happens. The discounted payback does the same with present values.

Worked example

The defaults are a $10,000 investment that returns $3,000, $3,500, $4,000 and $4,500 over four years, with an 8% discount rate.

  • At 17.09%, the cash flows are worth $3,000 ÷ 1.1709 + $3,500 ÷ 1.1709² + $4,000 ÷ 1.1709³ + $4,500 ÷ 1.1709⁴ = $10,000, so the IRR is 17.09%.
  • NPV at 8%: $3,000 ÷ 1.08 + $3,500 ÷ 1.08² + $4,000 ÷ 1.08³ + $4,500 ÷ 1.08⁴ − $10,000 = $2,777.78 + $3,000.69 + $3,175.33 + $3,307.63 − $10,000 = $2,261.43.
  • Payback: after two years you have $6,500 back, $3,500 short; year 3 brings $4,000, so payback is 2 + 3,500 ÷ 4,000 = 2.88 years. The discounted payback is 3.32 years.

Because the IRR (17.09%) is higher than the 8% you require, the NPV is positive and the project clears your hurdle.

If the same $10,000 returned $2,600 a month for four months, the monthly IRR would be 1.587%, or 20.80% a year.

When IRR can mislead

Multiple IRRs. If the cash flows change sign more than once, there can be more than one IRR. A project costing $1,000 that pays $2,300 next year and then needs $1,320 the year after has two: 10% and 20%. NPV is zero at both and negative at 8%. The calculator lists every rate it finds, and in such cases the NPV at your discount rate is the better guide.

No IRR. If every cash flow has the same sign, no rate can make NPV zero. The calculator says so instead of showing a number.

Reinvestment and scale. IRR quietly assumes cash received is reinvested at the IRR itself, which can flatter high-IRR projects. It also ignores size: a 40% return on $1,000 adds less wealth than 15% on $100,000. When choosing between projects, compare NPVs as well.

Frequently asked questions

What is a good IRR?

One that beats your cost of capital or the return you could get elsewhere at similar risk. If your money would otherwise earn 8%, a project with a 17% IRR is attractive; one with 6% is not, even though it makes money.

What is the difference between IRR and ROI?

ROI is the total gain divided by the amount invested and ignores timing. IRR accounts for when each cash flow arrives, so money back sooner counts for more. The ROI calculator gives the simple total and its annualized rate.

Do the cash flows have to be equal?

No. Each period can have a different amount, including zero or negative values. They must be evenly spaced, though: one per year or one per month. For uneven dates, the IRR would need an XIRR-style calculation with actual dates.

What discount rate should I use for NPV?

Use the return you require from an investment of this risk: often your borrowing cost, your company's cost of capital, or what you could earn in a comparable investment. The present value calculator shows how the discount rate changes what future money is worth today.

Related calculators

  • ROI Calculator — Return on investment as a percentage, the gain or loss, and the annualized ROI from a length or two dates.
  • Present Value Calculator — What a future sum, or a stream of regular payments, is worth today at a given discount rate.
  • Average Return Calculator — Arithmetic and geometric average returns from yearly results, or the CAGR from a start and end value.
  • Payback Period Calculator — How many years an investment takes to pay for itself, with simple and discounted payback and a cumulative table.

Results are estimates for educational purposes and are not financial, tax or legal advice. See our disclaimer.