Why is discounted payback longer than simple payback?

Because later cash is worth less. Simple payback counts a dollar in year four as a full dollar; discounted payback counts it as what it is worth today. Discounted payback is the more honest measure, though both ignore everything that happens after the payback point.

What is a good profitability index?

Above 1.0 means the project creates value, which is the same signal as a positive NPV. PI is most useful when capital is rationed and you must rank projects by value created per unit invested rather than by total value.

Should I include sunk costs?

No. Money already spent is irrecoverable and irrelevant to whether to continue. Include only future incremental cash flows. Including sunk costs is how organisations talk themselves into finishing projects that should be abandoned.

NPV, IRR & MIRR Calculator

Capital Budgeting8 min readSanguine Straphanger

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 fixes this by separating the assumptions: inflows compound forward at a realistic reinvestment rate, outflows discount back at your financing rate. It is always closer to the truth than IRR, and it is single-valued.

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 is meaningless and NPV is the only reliable answer.

Scale, and why ratios mislead

A project returning 80% on $10,000 has a magnificent IRR and adds $8,000 of value. One returning 12% on $10 million adds $1.2 million. IRR prefers the first; NPV prefers the second; the shareholders prefer the second.

Where NPV and IRR rank two mutually exclusive projects differently, take NPV. The academic consensus on this is unusually unanimous.

Frequently Asked Questions & Quantitative Reference

Your weighted average cost of capital for a project of typical risk, adjusted upward for a riskier one. For personal decisions, the return you could reliably get on the same money elsewhere. Note how sensitive the answer is — move the slider and watch the verdict flip. If a project only works at a very low discount rate, that is worth knowing.