How to use it 01 Type the cash flows separated by commas, starting with period 0. 02 Type the discount rate as a percentage per period. 03 Read NPV and the IRR list; the NPV-vs-rate profile draws the curve from −50% to +100%, marks every real root on the zero line and counts sampled sign changes. The Rule-of-72 card appears when the rate is positive. 04 Change one number and every readout recomputes; the panel lists multiple roots when the signs change more than once. Worked readouts -50,000 then 20,000, 25,000 and 30,000: NPV 13,766.96 at 8% and 1,388.89 at 20%; IRR 21.65% ; the Rule-of-72 card reads 9.0 periods at 8%. A series of -100, 60, 60 at 0% has NPV 20.00 . When the signs change more than once the IRR is not unique: -100, 230, -132 returns 10.00% and 20.00% , and the panel lists both; -100, -50 has no real root and says so instead of inventing one.
Why IRR can multiply NPV is the sum of each flow divided by (1 + r)^t. IRR is the rate that makes that sum zero; a series that changes sign k times can have up to k positive roots, so the panel solves for all of them rather than reporting one. NPV stays single-valued at any rate.
Limits
Even spacing. Every flow is one period apart; irregular dates and gaps are not modelled.
The rate is yours. The panel does not estimate a discount rate, a cost of capital or a market return, and it ignores taxes and inflation. What it does not do. It does not rank projects or recommend one, and it does not build repayment schedules — Loan and Prepayment do that. This page provides general information and scenario estimates based only on the inputs you provide. It is not investment, tax, legal, or other professional advice and does not recommend any rate, product, or institution. Two traps in one series The discount rate moves NPV but not IRR: the same flows are worth 13,766.96 at 8% and 1,388.89 at 20%, while the IRR stays 21.65% . IRR also ignores scale and timing — a small plan can outrank a large one on percentage alone, so read NPV and IRR together. The multiple-root series is the extreme case: 10.00% and 20.00% are both correct answers to "the" IRR, which is why the panel refuses to collapse them into one number.
Where it is used Screening one plan Enter the outlay and the expected inflows at your own discount rate; a positive NPV means the series is worth more than it costs at that rate.
Reading a funding-shaped series A first inflow followed by outflows can produce a root that is not a return at all; the full root list and the slope note keep that visible.
Privacy The cash flows, rate and readouts stay in the browser; nothing is uploaded.
References
Wikipedia, Net present value , en.wikipedia.org （访问日期：2026-10-07）— discounted cash-flow valuation.
Wikipedia, Internal rate of return , en.wikipedia.org （访问日期：2026-10-07）— the IRR definition and the multiple-root problem.
Wikipedia, Time value of money , en.wikipedia.org （访问日期：2026-10-07）— discounting conventions.
OpenStax, Principles of Finance , openstax.org （访问日期：2026-10-07）— capital-budgeting worked examples.
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Updated 2026-10-07