IRR Calculator — Internal Rate of Return

IRR is the discount rate that makes the net present value (NPV) of a cash flow series exactly equal zero. The formula: the sum of CF_t divided by (1+r)^t for t = 0 to n-1, equals 0 — then solve for r. Example: an initial investment of -1,000 with cash flows of 300 per year for 4 years has an IRR of 7.7138% — at that discount rate, the present value of all cash flows exactly recovers the initial outlay.

There is no direct algebraic formula for IRR, so it is computed numerically — this calculator uses the bisection method: take lower and upper bounds whose NPV changes sign, then halve the range repeatedly until NPV at the midpoint approaches zero. Mode 1 shows the full iteration table for transparency. As a cross-check, NPV computed at the resulting IRR is always near zero, e.g. 0.0000 for the -1,000 and 300 × 4 years example.

Each measures something different. IRR is the implied percentage rate of a cash flow series (the root of NPV = 0). NPV is the absolute value in currency at a specific discount rate — e.g. the -1,000 and 300 × 4 years series has NPV -49.04 at a 10% discount. CAGR only connects two points (start value to end value) regardless of interim cash flows; for pure two-point CAGR, use the annualized rate of return calculator. For pure NPV valuation with variable discount rates or retirement mode, use the net present value calculator.

Non-conventional cash flows — those changing sign more than once, e.g. -100, then +250, then -150 — can have more than one IRR. That example has two roots: 0% and 50%, because both discount rates make NPV = 0. This calculator’s convention: report ALL roots found by scanning the -99.99% to 1000% range, show a multiple-IRR warning, and use the smallest root for ranking. An alternative that avoids this problem is MIRR.

IRR math implicitly assumes every interim cash flow is reinvested at the same rate as the IRR itself. If a project’s IRR is 25% but actual surplus cash can only be placed at 8%, IRR overstates the realistic outcome. IRR is therefore most honestly used alongside NPV at a realistic hurdle rate, or replaced by MIRR, which uses separate finance and reinvestment rates.

First, IRR is a percentage and therefore blind to scale: a small project with 40% IRR can create less absolute value than a large project with 12% IRR. Second, when ranking two projects, IRR and NPV can disagree — example: project A (-1,000; 300 × 4) has IRR 7.7138% while project B (-2,000; 700 × 4) has IRR 14.9625%; at a 10% hurdle, NPV A = -49.04 and NPV B = 218.91. Here both agree on B, but when they disagree, the finance literature generally uses NPV as the tiebreaker. Third, IRR is not a measure of risk.

No. This calculator is an educational tool for practicing cash-flow math — it computes figures from the inputs you enter, without knowing your risk, taxes, liquidity, or market conditions. A high IRR figure does not mean an investment is right for you. For real-money decisions, discuss them with a licensed financial planner.