Annual internal rate of return and supporting figures
Bisection finds the rate that makes NPV zero. One positive initial cost and nonnegative subsequent inflows make discounted inflows strictly decrease as the rate rises, so the model has a unique solution above −100%.
For growth described only by a beginning and ending value, the CAGR Calculator calculates an annualized rate without an intermediate cash-flow stream.
The formula
Bisection finds the rate that makes NPV zero. One positive initial cost and nonnegative subsequent inflows make discounted inflows strictly decrease as the rate rises, so the model has a unique solution above −100%.
Worked internal rate of return example
An initial investment of 10,000 followed by 11,000 after one year has an annual IRR of 10%. Three end-of-year inflows of 4,000 instead give approximately 9.70%.
How to use this calculator
- Enter initial investment.
- Set annual cash flows after initial investment using the stated units or choices.
- Calculate and compare annual internal rate of return, total undiscounted inflows, undiscounted net surplus, cash-flow years.
Choosing inputs for internal rate of return
Enter the initial outlay as a positive cost in its own control. Each cash-flow position represents one year after that outlay, so a zero entry preserves a year with no receipt. Future inflows can vary, but this solver intentionally rejects additional negative flows to avoid displaying one arbitrary answer when several mathematical IRRs are possible.
IRR is a percentage describing the break-even discount rate of the entered cash flows. It differs from simple ROI because it accounts for when the money arrives. The displayed undiscounted surplus is a separate amount and can help identify whether the receipts exceed the cost before considering timing.
Interpreting annual internal rate of return
A high IRR does not reveal the scale of the investment or guarantee that projected receipts will occur. Compare cash-flow risk and NPV at a justified discount rate when evaluating projects of different sizes. A negative IRR is valid if total receipts are smaller than the initial cost; it should not be replaced by zero merely to make the result look favorable.
Assumptions & limitations
What this calculation assumes
- The initial investment occurs now and positive inflows occur at equal yearly intervals.
- At least one future inflow is positive; later outflows are not supported.
What to keep in mind
- The search supports rates from −99.9999% through 1,000,000%; inputs whose unique root lies outside that range return an error. Irregular dates require XIRR.
Common questions
Why are future negative amounts rejected?
Multiple sign changes can create multiple IRRs. This calculator restricts its model to conventional cash flows with a unique solution.
Can the result be negative?
Yes. For example, paying 10,000 now and receiving 9,000 in one year gives an IRR of −10%.
How do I represent a year with no receipt?
Enter zero in that year’s position. Omitting it would move every later inflow one year earlier and change the IRR.
Sources & further reading
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