NPV & IRREasy

Two numbers that decide whether money moves: what future cash is worth today, and what return a stream of cash flows actually earns.

4 min read · 774 words · Updated 4 Sep 2026

The one idea: money has a time price

A euro next year is worth less than a euro today — not philosophy, but arithmetic: today's euro can be invested at the going rate and become more than a euro by next year. Discounting runs that logic backwards, translating every future cash flow into today's money:

• Net present value (NPV): discount every cash flow — the negative ones too — and add them up. Positive NPV: the project creates value at that discount rate. Negative: it destroys it.
• The discount rate r is the decision's whole personality: it encodes what the money could earn elsewhere at similar risk (the "opportunity cost of capital", or hurdle rate).
• Every bond price in this atlas is an NPV; every yield curve point is a discount rate with a maturity attached.

IRR: the break-even discount rate

Ask the reverse question: at what discount rate would this project's NPV be exactly zero? That rate is the internal rate of return — the return the cash-flow stream itself earns:

The decision rule follows from the picture: invest when IRR > hurdle rate (equivalently, when NPV at the hurdle is positive). The two rules agree for ordinary projects — one outflow, then inflows — and that covers most of life.

Where IRR misleads — the professional's checklist

• The reinvestment assumption: IRR implicitly assumes interim cash flows are reinvested at the IRR. A 40% IRR fund did not compound your money at 40% unless you re-deployed every distribution at 40% — you didn't.
• IRR vs. MOIC: a quick 1.5× flip in one year is a 50% IRR; a patient 3× over ten years is ~12%. Which was better? MOIC measures wealth created, IRR measures speed — private equity quotes both because either alone can flatter (the MOIC/IRR and waterfall calculators show the interplay).
• Timing games: subscription credit lines delay capital calls, mechanically boosting reported fund IRRs without creating a cent — a now-standard practice that makes early-life IRRs largely marketing.
• Multiple sign changes: mining projects with cleanup costs, structured deals with capital returns — multiple IRRs or none. Descartes' rule of signs, applied to your term sheet.
• Scale blindness: a 100% IRR on €1,000 is worth less than a 15% IRR on €1m. NPV in euros ranks projects; IRR in percent ranks percentages.

The same machine everywhere

• Bonds: yield to maturity is the IRR of the bond's cash flows at its price — the YTM solver is this page's solver wearing a bond costume.
• Equities: the dividend discount model is an NPV with an infinite horizon.
• Private markets: fund returns are IRRs on called-and-distributed cash — with every caveat above, at scale.
• Corporate life: every capex committee meeting is an argument about which hurdle rate, applied to whose cash-flow forecast.