IRR & MIRR Calculator

What the IRR Calculator does

This tool takes a series of cash flows — typical project, investment, or loan streams — and computes the discount rate at which their Net Present Value equals zero. That rate is the Internal Rate of Return, and it's the most widely used measure of project profitability after NPV itself. Alongside IRR we compute MIRR (Modified IRR), NPV at a rate you choose, simple payback, discounted payback, and a full NPV profile so you can see the shape of the curve.

IRR in one formula

IRR is the rate r that solves:

Σ CF_t / (1 + r)^t  =  0    for t = 0, 1, 2, …, N

There is no closed-form solution for N > 4, so the value is found numerically — this tool uses Newton-Raphson from several starting guesses and falls back to bisection on the interval (−0.99, 10) when Newton fails to converge. For well-behaved streams (one sign change in the cash flows) convergence is near-instant and the answer is unique. For non-conventional streams with multiple sign changes, we report the root closest to 0 and flag the presence of additional solutions.

Why MIRR is usually the better number

IRR assumes interim positive cash flows are reinvested at the IRR itself. For a project returning 35%, that assumption means every dollar paid out must immediately be redeployed at 35% — rarely realistic. MIRR separates the assumptions:

• Finance rate — the cost of capital applied to negative cash flows (typically your weighted average cost of capital, or the borrowing rate).
• Reinvestment rate — the rate at which positive cash flows earn interest (typically your opportunity cost of capital, or safe rate).

Mathematically:

MIRR = ( FV(positives @ reinvest rate) / | PV(negatives @ finance rate) | )^(1/N)  − 1

MIRR is always unique, lies between the finance rate and the reinvest rate, and eliminates the multiple-IRR pathology. If you only report one rate to a CFO, make it MIRR.

Reading the NPV profile

The NPV profile (the chart on the right) plots NPV against discount rate. Where it crosses zero is an IRR. The slope at the crossing tells you how sensitive the project is to cost-of-capital changes: a steep curve means small rate moves cause big NPV swings. A curve that never crosses zero (always above) means unconditionally profitable; always-below means the project loses money at any positive discount rate.

Common use cases

• Capital budgeting — accept a project if IRR > hurdle rate (usually WACC). Prefer MIRR when interim cash flows are material.
• Real estate — a typical commercial deal: negative in year 0 (purchase + closing), positive in years 1-N (NOI), big positive in year N (sale). IRR across the hold period is the industry-standard return metric.
• Private equity / venture — LPs judge fund managers on realised IRR (money-multiples + timing), though TVPI / DPI are increasingly reported alongside.
• Bonds — for a bond held to maturity the IRR of the cash flow stream equals the yield to maturity. Try the “Bond” preset.
• Personal investing — compute the money-weighted return of a brokerage account by entering deposits, withdrawals, and current value as cash flows.

Tips & gotchas

• Sign convention matters. Money out is negative. Most IRR mistakes come from forgetting this.
• Sign changes > 1. If your stream switches sign more than once, prefer MIRR. The “Mining project” preset demonstrates this: two sign changes, two real IRR solutions.
• Periods must be equal. IRR and MIRR assume periods are of equal length (years, quarters, months). For irregular dates use XIRR (day-count-based) — which isn't computed here.
• Scaling. IRR doesn't care about absolute scale; a $10k and a $10M project with identical time-scaled CFs have the same IRR. Use NPV to pick between mutually exclusive projects.

Related tools

• Bond YTM — yield to maturity, duration, convexity.
• Compound Interest — future value with periodic contributions.
• FIRE / Retirement — Monte Carlo retirement projection.
• Mortgage Calculator — amortization & extra-payment scenarios.
• HP 12C RPN Clone — full TVM, NPV, IRR on an emulator.