IRR Calculator

Free online IRR (Internal Rate of Return) calculator. Enter any series of cash flows, choose an initial guess, and get the IRR plus NPV at the calculated rate. Supports Newton-Raphson with bisection fallback.

Find the discount rate that makes NPV zero. Add an initial outlay (optional), then enter one cash flow per period — positive for inflows, negative for outflows. The calculator solves for the internal rate of return that drives NPV to zero and shows total inflows, outflows and the running cumulative cash flow.

Internal Rate of Return (IRR)
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Net Present Value (at IRR)
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Total Inflows
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Total Outflows
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Net Cash Flow
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Understanding IRR

What Is IRR?

The Internal Rate of Return (IRR) is the discount rate at which the net present value (NPV) of a series of cash flows equals zero. In plain English, it's the constant annual return that makes the project's inflows exactly repay its outflows. \[ 0 = \sum \frac{CF_t}{(1 + IRR)^{t}} \]

Where \(CF_t\) is the cash flow at period \(t\). The first period (\(t=0\)) is typically the initial investment and is not discounted.

IRR vs. NPV vs. ROI

  • IRR — a rate, comparable directly to your hurdle rate (cost of capital, required return).
  • NPV — a dollar amount, dependent on the discount rate you choose.
  • ROI — a simple ratio, ignores the time value of money.

IRR is the rate where NPV equals zero, so they answer complementary questions.

Worked Example

A project costs $10,000 today and returns $3,000, $4,200 and $6,800 over the next three years:

\[ NPV(r) = -10000 + \frac{3000}{1+r} + \frac{4200}{(1+r)^{2}} + \frac{6800}{(1+r)^{3}} \]

Setting NPV = 0 and solving gives IRR ≈ 25.65% — the project's break-even annual return.

How We Solve It

IRR has no closed-form solution, so we use:

  1. Newton-Raphson (fast, requires a reasonable starting guess). Convergence is quadratic near the root.
  2. Bisection fallback if Newton-Raphson stalls. Robust but slower.

Both converge to within 1e-7 of the true IRR or terminate after 200 iterations.

Multiple IRRs

When cash flows switch sign more than once (e.g., one negative followed by positive, then negative again), the polynomial NPV(r) = 0 can have multiple real roots. In that case, IRR is ambiguous and you should fall back to NPV at your cost of capital.

Common Pitfalls

  1. Reinvestment assumption: IRR implicitly assumes intermediate cash flows are reinvested at the IRR itself, which is rarely true in practice. The Modified IRR (MIRR) fixes this by using a separate reinvestment rate.
  2. Scale blindness: A $1,000 project returning $2,000 has the same 100% IRR as a $1M project returning $2M. Always compare to scale and NPV.
  3. Timing matters: IRR rewards projects that return money early, which can bias you away from long-horizon value creation.
  4. Hurdle rate comparison: IRR is only useful compared to your required return. A 15% IRR is bad if your cost of capital is 12%; great if it is 8%.

When to Use IRR

  • Comparing mutually exclusive projects with similar scale and timing.
  • Communicating returns to non-financial stakeholders (IRR is intuitive as a percentage).
  • Quick screening before a full NPV / DCF analysis.

For capital budgeting and valuation, prefer NPV as the primary metric and use IRR as a sanity check.

About This Tool

IRR is solved with Newton-Raphson followed by a bisection fallback. NPV at the solved rate is reported to confirm convergence. The chart shows each period's cash flow as a coloured bar (green inflow, red outflow) and the cumulative cash flow as an amber line so you can see when the project breaks even.

Open-Source License: IRR / NPV math implemented directly using Newton-Raphson with bisection fallback. Charts use Chart.js by Chart.js contributors (MIT), bundled locally.

Frequently Asked Questions

What is a good IRR?
It depends on your cost of capital and the project's risk. A high-risk startup might require 30%+; a mature utility bond might be acceptable at 6%. Compare IRR to your hurdle rate, not to absolute numbers.
Why does my IRR say 'no solution'?
Either the cash flows never switch sign (all positive or all negative), or the IRR equation has no real root. Add both an outflow and an inflow, or check that you haven't entered the initial investment twice.
Why does NPV at IRR show a small number instead of zero?
We stop iterating when the change between successive estimates is below 1e-9. Tiny residuals (fractions of a cent) are normal and indicate the solver has converged.
What's the difference between IRR and annualised ROI?
ROI is the total return divided by the initial outlay, ignoring time. IRR is the equivalent constant annual rate that delivers the same cash flow pattern. IRR is the time-aware version.
Why does my project show two different IRRs?
When cash flows flip sign more than once, the polynomial NPV(r) = 0 can have multiple real roots. IRR becomes ambiguous; NPV at your cost of capital is the safer metric.
What does the cumulative line tell me?
It tracks running total cash flow. The point where the line crosses zero is the project's payback period — when cumulative inflows finally equal cumulative outflows.
Should I include the initial outlay in the cash flow list or as a separate input?
Either works — the calculator treats the optional 'Initial Outlay' field as period 0, then the cash flow list as periods 1, 2, 3, … If you include the initial outlay in the cash flow list instead, set the separate input to 0.