CalcVerse

IRR Calculator

The internal rate of return is the discount rate at which the cash flows of an investment are worth exactly zero today. List the money going out as negative numbers and the money coming back as positive ones, one per period.

Also called: Internal rate of return calculator

  • Last updated
  • Formula tested against reference values

Your numbers

One number per period, starting with the initial investment as a negative number. Use 0 for periods with no cash flow.

Result

IRR per period
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Calculating…

IRR per year (effective)
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Net gain (money in − money out)
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Money multiple
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How to use this calculator

  1. Enter or choose cash flows, period 0 first.
  2. Enter or choose each period is.
  3. The iRR per period updates as you type. Use Copy result or Share to keep it.

Method

0 = Σ CFₜ ÷ (1 + IRR)ᵗ for t = 0 … n; annual IRR = (1 + IRR)^(periods per year) − 1

CFₜ
cash flow in period t (negative for money paid out)
IRR
the rate found by numerical search
n
number of periods after the first

Worked example

  1. Find r with −1,000 + 600 ÷ (1 + r) + 600 ÷ (1 + r)² = 0.
  2. Put x = 1 ÷ (1 + r): 600x² + 600x − 1,000 = 0, so x = (−600 + √2,760,000) ÷ 1,200 = 0.88444.
  3. r = 1 ÷ 0.88444 − 1 = 13.07%.

Paying 1,000 now for 600 at the end of each of the next two years earns an IRR of 13.07% a year.

What the result means

Accept a project when its IRR is above your required return (cost of capital). IRR assumes interim cash can be reinvested at the IRR itself, so very high IRRs on short projects overstate long-run growth; compare NPV at your required rate when projects differ in size or length.

Assumptions and limits

  • Cash flows occur at regular, equal intervals, with the first at time zero.
  • Rates are found by search between −99% and +1,000% per period.
  • When the cash flows change sign more than once there can be several IRRs; the calculator reports the one nearest 10% and lists the others.
  • Irregular dates need an XIRR-style calculation, which this tool does not do.

Questions

What is the difference between IRR and ROI?

ROI is the total gain divided by the cost and ignores timing. IRR is a yearly (or per-period) rate that accounts for when each amount is paid or received.

Why can there be more than one IRR?

The NPV equation is a polynomial in 1 ÷ (1 + r). Each change of sign in the cash flows can add a root, so a project with a large cost at the end can have two IRRs.

Please note: Returns are illustrations at a constant rate, not predictions or guarantees. Investments can lose value. This is not investment advice.