What the algorithm solves
With equal periods, IRR is the rate r at which the present value of cash flows is zero: Σ CFₜ / (1 + r)ᵗ = 0. For ordinary interpretation, use r > −1. The initial investment is negative and owner receipts positive, but signs depend on the chosen viewpoint, not the transaction name. The zero-date is the start of the measurement. With irregular dates, exponents must reflect actual time; adding dates beside a monthly series does not make it calendar-based.
Two solutions for one cash flow
In arbitrary currency units: today −100, in one year +230, and in two years −132. The final negative flow may represent a mandatory additional cost; no real project is implied. At 10%, −100 + 230 / 1.10 − 132 / 1.10² = 0. At 20%, −100 + 230 / 1.20 − 132 / 1.20² = 0. Numerical checks leave only machine-level residuals. The equation has two valid roots, not two roundings of one result.
A calculator showing one root may depend on the initial guess or algorithm. Choosing the first result does not prove economic superiority. The simple sum of the three flows is −2, but that does not replace time valuation. Sign changes can warn that multiple roots are possible, but do not promise their number in the relevant economic domain.
When there is no root
If every non-zero cash flow is negative, its present value remains negative for r > −1. No internal rate exists. An error or blank may describe the problem, not a broken program. Do not replace no solution with zero: zero return is a separate substantive claim. Missing dates, wrong signs and an overly narrow search range require different diagnoses.
Scale and horizon
A high rate does not imply a large monetary result: a small short project can have a high percentage and modest absolute gain. For mutually exclusive options, consider amount, timing, risk and decision criterion. NPV at an explicitly chosen rate answers another question and also depends on assumptions. Do not turn annual IRR on a short turnover into a promise of repeating it all year. Removing the final negative flow creates a different problem and removes the source of ambiguity.
Control before publishing a number
Save the cash-flow and date table, owner viewpoint, rate unit and rounding rule. Substitute the root back and verify zero present value. Search for other solutions in the justified domain and check whether the terminal value is unrealised. If ambiguous, say so and show NPV under selected scenarios instead of declaring a favourite root correct. IRR characterises an equation; it does not certify payment reliability, manager skill or suitability for a person.
Terminal value is also a model cash flow
If an investment is unfinished at the reporting date, terminal value enters as an estimated receipt. It need not be cash actually received. An optimistic estimate can improve IRR without another transfer to the owner. Keep actual payouts separate from estimated residual value, its valuation date and basis. FINRA highlights the estimated nature of remaining assets. Do not silently replace an estimated sale with actual repayment or treat an uncertain future payment as fulfilled.
For the alternative question of present monetary value, use [NPV](/glossary/npv/) with an explicitly selected rate; do not call it automatically better without defining the task.