How this calculation works
A single initial outflow followed only by non-negative future inflows gives a monotone present-value balance and one IRR above −100%. A bounded search solves the rate and reports its remaining NPV residual.
Find r such that Σ CFt/(1+r)^t = 0A worked example
For ₹1,000 invested now and ₹600 received at each of the next two year ends, the annual IRR is approximately 13.066239%.
Good to know
Equal annual periods only. Later negative flows are rejected because a different sign pattern can have several or no roots. Supported IRR range is −99.99% through 10,000%. This is not dated XIRR, a reinvestment forecast or a guaranteed yield.
Reference: OpenStax: internal rate of return method (opens in a new tab) ↗
Solve the discount rate instead of supplying it
For the default −1,000, 600, 600 stream, the tool finds an annual rate near 13.066239% at which the present value of both future receipts equals the initial outflow. The NPV residual is shown so the numerical balance can be inspected.
The annual cash flow NPV calculator instead evaluates a rate you choose. An IRR above or below a decision-maker’s required return can be informative, but it does not establish the size, risk or certainty of the future cash flows.
The annual cash flow NPV calculator takes a chosen discount rate. This conventional cash flow IRR solves the rate at which the signed present values balance.
One sign change makes this root well defined
The first amount must be negative. Every later amount must be non-negative and at least one must be positive. For this conventional pattern, increasing the discount rate reduces the future receipts’ present value, yielding a single crossing.
Zero receipts in intermediate years preserve their timing. Trailing zero years can be removed without changing the root, so the table stops at the final nonzero receipt. The supported annual-rate range is explicitly bounded.
A more complicated stream can need another method
A later cleanup cost or another investment outflow creates a different sign pattern. Such streams can have several IRRs or no meaningful IRR. This tool rejects them rather than selecting one root and hiding the ambiguity.
IRR alone can also rank projects differently from NPV when scale and timing differ. It is not a reinvestment forecast or a promise that the same annual rate can be earned elsewhere.
A few questions, answered
Can the annual IRR be negative?
Yes. A conventional stream that returns less than the initial outflow can have a unique negative IRR.
Why is a later negative cash flow rejected?
It violates the single-initial-outflow scope and can make the root ambiguous.
Is this XIRR?
No. Receipts occur at equally spaced annual year ends, not on supplied calendar dates.