Help - Internal Rate of Return (IRR) (irrn)
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Internal Rate of Return (IRR)
Purpose
This calculator finds the Internal Rate of Return implied by a series of cash flows over time — the single discount rate at which those cash flows exactly break even (a Net Present Value of zero). It is useful for judging an investment or project's own rate of return, so it can be compared against a required return or against other opportunities.
It supports cash flows at irregular periods, so Period values do not need to be consecutive.
Background
What the IRR tells you
A typical cash flow series starts with an outlay (a negative value — money spent or invested) followed by a series of returns (positive values). The Internal Rate of Return is the break-even discount rate for that series: at exactly that rate, the present value of the returns equals the initial outlay. A project's IRR above your required rate of return suggests it is worth pursuing; an IRR below your required rate suggests it is not. A follow-up Net Present Value button is offered after this calculation, letting you check the present value of the same cash flows at a discount rate of your choosing.
Inputs
Cashflow Interval
The time period between entries in the Cashflows series (for example,
yr for one entry per year).
Cashflows
A table with exactly two columns in this order:
- Period (first column), for example 1, 10, 15, 25, 26.
- Cashflow (second column), the corresponding cash flow amount.
Any renamed, reordered, missing, or extra column is rejected.
Results
Periodic Interest Rate
The break-even discount rate per Cashflow Interval — the rate at which the given cash flow series has a Net Present Value of zero.
Annual Interest Rate
The same rate restated as an equivalent effective annual rate, regardless of the Cashflow Interval used, so it can be compared with annual rates quoted elsewhere.
Understanding the Calculation
The calculator searches for the periodic discount rate r that makes the
Net Present Value of the Cashflows series equal to zero.
where Cashflow_0 is the first entry (typically the initial
outlay) and i counts periods from there. The resulting rate r is the
Periodic Interest Rate; the Annual Interest Rate restates it as an
effective annual rate.
When a Period column is provided, the calculator uses those explicit
period values as numeric timestamps measured in the same unit as
Cashflow Interval (for example, years when Cashflow Interval is
yr). These timestamps are treated as absolute times since time 0 (e.g.
0.0, 0.5, 1.75) and the calculator searches for the periodic discount rate
r that makes the following condition true:
If your cash flows are listed as 1, 2, 3, ... but you intended the first entry to be time 0, supply 0, 1, 2, ... in the Period column. Using consecutive integers 1,2,3 with the period unit chosen appropriately is still equivalent to the consecutive-row model when interpreted consistently.
Example
Using the default cash flow series -40000, 5000, 8000, 12000, 30000 (one entry per year), the calculator finds a Periodic Interest Rate and Annual Interest Rate of approximately 10.58% per year. This means an initial outlay of 40,000 followed by those four annual returns breaks even at a 10.58% annual discount rate — any required return below 10.58% would make this series worth pursuing on an IRR basis; any required return above 10.58% would not.
Important Assumptions and Interpretation
- IRR assumes every positive cash flow it produces is reinvested at the same rate as the IRR itself, which can overstate the attractiveness of projects with large interim cash flows — see the Modified Internal Rate of Return calculator for an alternative that lets you set a separate reinvestment rate.
- A cash flow series with more than one sign change (for example, negative, then positive, then negative again) can have more than one mathematically valid IRR, or none; treat results from such series with caution.
- With irregular Period gaps, the same cash flow amounts can produce a different IRR than the consecutive-row assumption, because timing is part of the return calculation.
- The result describes the rate implied by the cash flows given; it is not a forecast of future project performance.