IRR Calculator — NPV Roots, MIRR & Payback
Solve the IRR of any cash-flow schedule, detect multiple roots, and compare MIRR, profitability index, NPV at your hurdle rate, and payback periods.
Internal Rate of Return (IRR) Calculator
A clear path from inputs to results.
For anyone evaluating a project, property, or private investment with irregular cash flows. The solver finds the discount rate that sets NPV to zero, flags schedules that produce multiple IRRs, and pairs the answer with MIRR, profitability index, NPV at your hurdle rate, and both payback measures — the numbers an investment committee actually asks for.
How to use
- Enter the cash-flow schedule with the six sliders: the t = 0 outlay (negative) and the flows at t = 1 through 5.
- Set your hurdle rate; it serves both as the benchmark the IRR must beat and as the finance rate used by MIRR and the profitability index.
- Set the reinvestment rate you believe interim cash flows can actually earn; MIRR uses it to compound inflows to the final period.
- Read the headline block: the primary IRR, how many IRR roots were detected, NPV at the hurdle rate, and MIRR.
- Check the diagnostics row: profitability index, nominal and discounted payback, and the sign-change count that warns when multiple IRRs are possible.
- Inspect the NPV profile to see where it crosses zero, then use the future cash-flow scale surface to see how far the inflows can fall before NPV turns negative.
The formula
Reference: Brealey, Myers, and Allen, Principles of Corporate Finance — capital budgeting with NPV and IRR; modified IRR as presented in Chan S. Park, Contemporary Engineering Economics.
Worked example
Six-period project versus a 12% hurdle
- Cash flows: -100,000 at t = 0; then 28,000; 32,000; 35,000; 26,000; and 42,000 at t = 1 through 5. Hurdle rate 12%, reinvestment rate 10%.
- 1
Discounting the inflows at the 12% hurdle gives a positive NPV of 15,777.91, so the IRR must lie above 12%. Solving NPV(r) = 0 by bracketing and bisection yields a single root at 17.9079%. For MIRR, compounding every inflow to t = 5 at the 10% reinvestment rate accumulates 196,536.80, so MIRR = (196,536.80 / 100,000)^(1/5) - 1 = 14.4692%. The profitability index is 1.1578 (PV of inflows 115,777.91 over the 100,000 outlay), nominal payback lands at 3 + 5,000/26,000 = 3.19 years, and discounted payback at 4.34 years.
One IRR root at 17.908%; NPV at the 12% hurdle +15,778; MIRR 14.469%; profitability index 1.158; payback 3.19 years; discounted payback 4.34 years.
Interpreting the result
An IRR above your hurdle rate means the schedule earns more than a risk-equivalent alternative, and the NPV at the hurdle quantifies that surplus in currency. If MIRR sits well below IRR, as it does here, the gap measures how much the IRR relies on reinvesting interim cash at the IRR itself. A root count above one means the schedule is non-conventional: treat any single displayed IRR with suspicion and lean on NPV at the hurdle rate instead.
Assumptions & limitations
- Cash flows occur at integer periods t = 0 through 5 on the fixed six-row schedule, with periods interpreted as years.
- The IRR implicitly assumes interim cash flows are reinvested at the IRR itself; MIRR is provided to replace that assumption with explicit finance and reinvestment rates.
- With more than one sign change in the cash-flow stream, multiple IRRs can exist; the solver enumerates every root it can bracket, and the primary IRR is the detected root closest to your hurdle rate, preferring positive roots.
- No taxes, financing costs, or inflation adjustments are applied: enter amounts in nominal, after-tax terms if you want after-tax decisions.
- Payback interpolates linearly within a period and treats flows as arriving at period boundaries.
Frequently asked questions
What is a good IRR?
There is no universal number: an IRR is only good or bad relative to your cost of capital and the returns available on alternatives of similar risk. Compare it with your own hurdle rate, and remember that IRR ignores scale — a 20% return on a small outlay can add less value than an 8% return on a large one. That is exactly why this solver shows NPV at your hurdle rate next to the rate itself.
Why does MIRR differ from IRR?
IRR implicitly assumes every interim cash flow is reinvested at the IRR itself, which is often optimistic for strong projects. MIRR compounds positive flows to the final period at your reinvestment rate, discounts negative flows at your finance rate, and annualizes the ratio. In the worked example, assuming reinvestment at 10% pulls the 17.9% IRR down to a 14.5% MIRR — a more conservative compounding story.
Is IRR the same as a CAGR?
Only when there is exactly one outflow followed by one inflow, in which case IRR reduces to the compound annual growth rate between the two. With interim cash flows, IRR is the rate at which all discounted flows net to zero, which silently assumes those interim flows are reinvested at the IRR. That distinction is precisely what MIRR is designed to fix.
Why can a project have two IRRs?
The IRR is a root of the NPV polynomial, and every sign change in the cash-flow stream can add a root. A project that pays out for years and then requires a large cleanup or follow-on investment changes sign twice and can cross zero at two different rates. The solver brackets every sign change on the rate grid and reports the full root count, so a single displayed IRR is not hiding a second one.
IRR versus NPV: which should decide?
NPV measures value added in currency and is the theoretically correct ranking rule, especially for mutually exclusive projects of different sizes or timings. IRR is a convenient, scale-free rate that is easy to communicate, but it can misrank alternatives and breaks down entirely with multiple sign changes. A common discipline is to accept if IRR clears the hurdle but to choose between competing projects by NPV.
What does the future cash-flow scale control do?
It multiplies every cash flow after t = 0 by a scaling factor in the NPV sensitivity surface while holding the initial outlay fixed. Scanning the surface shows, at each discount rate, how far the inflows can shrink before NPV turns negative — a break-even margin on your forecast rather than a single-point answer.
Methodology last reviewed 2026-10-06. Results are informational and not financial or engineering advice — see our disclaimer.