Why NPV Wins Every Argument With IRR
IRR is the number executives quote. NPV is the number that is right when they disagree.
What each measure actually says
NPV discounts every cash flow to today at your cost of capital and adds them up. A positive result means the project creates value beyond what the money could earn elsewhere. It is denominated in currency, so it accounts for scale.
IRR is the discount rate at which NPV equals zero — the project's own break-even return. It is a percentage, which makes it intuitive and comparable across projects of any size, and that is also its weakness.
Net present value
NPV = Σ CFₜ ÷ (1 + r)ᵗ
- t = 0 is today and is not discounted
- IRR is the r that makes this sum zero
The reinvestment problem
IRR quietly assumes every interim cash inflow is reinvested at the IRR itself. For a project showing 45%, that means assuming you have an endless supply of other 45% opportunities to park the cash in. You do not.
MIRR separates the assumptions: inflows compound forward at a selected reinvestment rate, and outflows discount back at a selected financing rate. It is single-valued and can provide a useful comparison when IRR's reinvestment assumption does not fit the project.
Watch the two figures in the tool. When the reinvestment rate is well below the IRR, the gap is large — and the IRR is the one flattering the project.
When IRR breaks entirely
Descartes' rule of signs bounds the number of positive roots by the number of sign changes in the cash flow series. A conventional project — one outflow followed by inflows — has exactly one sign change and one IRR.
A project with a later outflow — a mine that must be decommissioned, equipment needing mid-life replacement — has two or more sign changes and can have several mathematically valid IRRs. The calculator flags this. When it does, IRR may be ambiguous; NPV evaluates project value at the selected discount rate and can provide a clearer comparison.
Scale, and why ratios mislead
A one-year project that turns $10,000 into $18,000 has an IRR of 80%. One that turns $10 million into $11.2 million has an IRR of 12%. IRR ranks the first higher. At a 10% discount rate, NPV ranks the second far higher — about $181,800 against $6,400 — because a rate of return says nothing about scale. IRR expresses a rate; NPV expresses value.
Where NPV and IRR rank two mutually exclusive projects differently, take NPV. The academic consensus on this is unusually unanimous.