Cash Flows
Tip: Period 0 is usually the initial investment (often negative). Subsequent periods represent cash inflows or outflows.
Results
IRR: 8.896339%
A higher rate indicates a stronger return for the sequence of cash flows shown.
NPV vs Discount Rate
The IRR occurs where the NPV crosses zero.
What Is Internal Rate of Return (IRR)?
Definition: Internal Rate of Return (IRR) is the discount rate that sets the Net Present Value (NPV) of a series of cash flows to zero. In practice, it summarizes a project’s or asset’s expected return as a single annualized percentage. Analysts use IRR to compare mutually exclusive projects, rank investment alternatives, and sanity-check hurdle rates.
How IRR Works
Given an initial outlay followed by future inflows and outflows, the time value of money discounts each period’s cash flow back to today. The IRR is the rate where the discounted inflows exactly offset the discounted outflows. Because there is no closed-form solution for most cash-flow patterns, numerical methods iterate to find the rate. This calculator uses a hybrid approach—Newton’s method with a robust bisection fallback—for stability across common capital budgeting scenarios.
When to Use IRR
IRR shines when comparing projects of similar scale and timing. It is especially helpful for screening opportunities against a required rate of return or cost of capital. For long-tail queries like “how to calculate internal rate of return with uneven cash flows,” this tool accepts arbitrary sequences and visualizes the NPV curve so you can see where it crosses zero.
Limitations and Best Practices
Some cash-flow streams can produce multiple IRRs or none at all, especially when signs change more than once. In those cases, rely on NPV at the firm’s discount rate and consider metrics like Modified Internal Rate of Return (MIRR) or Payback Period. Always pair IRR with scenario analysis, sensitivity checks, and a realistic assessment of risk, reinvestment assumptions, and scale.
Why This Calculator Helps
Beyond computing IRR, it displays the full NPV profile across discount rates, provides exportable PDF and CSV outputs for documentation, and supports custom currencies and precision. Use it to build investor-ready reports, compare projects consistently, and communicate capital budgeting choices with clarity.
FAQs
1) What inputs do I need?
Enter the currency, decimal precision, an initial rate guess, and a list of period-indexed cash flows starting at period 0.
2) Why does IRR sometimes say “Not found”?
If all cash flows are the same sign or if the pattern produces no real solution, the equation may have no valid IRR. Check the NPV chart and consider MIRR.
3) Can there be multiple IRRs?
Yes. When cash-flow signs change more than once, multiple rates can satisfy NPV = 0. Use NPV at your discount rate or MIRR to resolve conflicts.
4) What does the NPV chart show?
It plots NPV against discount rates from roughly −90% to 150%. The zero crossing indicates the IRR when it exists.
5) How should I choose the guess?
A guess near your cost of capital typically converges faster. The solver adapts and falls back to a robust bracket search if needed.
6) What units are cash flows in?
Any consistent unit works. The currency symbol is only for display formatting and does not affect calculations.
7) Is IRR comparable across projects of different sizes?
Not always. A small project can have a high IRR but low absolute value. Compare NPV and IRR together for a complete picture.
8) How do I export my results?
Click Download CSV for a structured file of periods and flows. Click Download PDF to capture the results card for sharing.