Saving & investing
Internal rate of return (IRR): Definition, Formula and Example
IRR is a discount rate that makes the net present value of a specified series of cash flows equal to zero.
Scope: General financial concept; examples are hypothetical.
Other names and related labels: IRR; Money-weighted return.
How it works
IRR incorporates the size and timing of contributions and distributions. Periodic IRR assumes equally spaced cash flows; a dated calculation needs an explicit day-count convention. The root may be absent or nonunique when cash flows change sign more than once.
0 = Σ[cash flow at period t / (1 + IRR)^t], including the initial cash flow at t = 0
Use signed cash flows from one consistent viewpoint. A periodic IRR is a rate per cash-flow period unless explicitly annualized.
$1,000 invested and $1,100 received a year later
Treat the investment as an outflow and the receipt as an inflow.
- At 10%: −$1,000 + $1,100 / 1.10 = $0.
- The single-period rate is $1,100/$1,000 − 1 = 10%.
The annual IRR is 10% for these two cash flows.
Exactly one year; no intermediate payments or extra fees.
Try these example inputsA higher IRR is not always the better project
Projects of different scale or timing may rank differently by NPV. For cash flows −100, +230 and −132 at annual intervals, both 10% and 20% are IRRs. A single displayed root is not necessarily an unambiguous investment return.
Explore with a calculator
- IRR Calculator
Calculate periodic or dated cash-flow IRRs and inspect multiple-root warnings.
- Rental Property Calculator
Review the modeled dated investment cash flows, costs and sale assumptions.
Sources and checks
Definition and example arithmetic checked . Sources explain the concepts; numerical examples use the assumptions stated above.
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