Three numbers get used interchangeably to describe whether an investment worked. They are not interchangeable, they frequently disagree, and the disagreement is always informative. Understanding what each one measures — and what each one silently assumes — is most of what separates a useful projection from a persuasive one.
ROI: one percentage, and everything it hides
Return on investment is the simplest of the three:
ROI = (gain − cost) ÷ cost
$500 returned on $400 is a 25% ROI. Simple, and immediately useful for a single round-trip investment. The problem is that it collapses an entire timeline into one number, and two things get lost.
Timing. Consider two investments, each returning 20%. The first returns everything in year 1. The second returns nothing for four years and everything in year 5. ROI says they are identical. They are not: the first gave you four extra years of use, and if you reinvested it at 8% those four years are worth about 36% on their own. Timing is the whole difference, and ROI cannot see it.
Scale. A 200% ROI on $1,000 and a 200% ROI on $100,000 both print "200%", and the second made you $200,000 while the first made you $2,000. Percentages compare poorly across different-sized investments, which is why the ROI calculator reports the absolute gain alongside the percentage.
ROI is not wrong — it is incomplete. Treat it as the headline number for a simple comparison, never as a decision criterion on its own.
IRR: percentage return that respects timing
Internal rate of return solves for the discount rate that makes an investment's net present value exactly zero. Put differently: it is the constant annual return that would produce the same cash flows you actually received.
That is a genuine improvement on ROI, because it accounts for when money arrived. The same 20% over five years has a materially different IRR than the same 20% over one year, and IRR captures that correctly.
The IRR calculator solves it numerically, and for a conventional investment — initial outflow, then all inflows — it works well.
What IRR assumes, and why it quietly misleads
Reinvestment at the IRR. The math treats every intermediate cash flow as though it could be reinvested at exactly the IRR. In reality you reinvest at whatever is available. Over a 15-year project, that assumption alone can move the reported return substantially — it flatters high-return and penalises low-return investments, and it systematically overstates long-horizon results.
A single known discount rate. IRR compares your return to nothing. It never asks whether the return beats the alternative. A 15% IRR is excellent if your other option is 4% bonds and terrible if the same project exists at 25%.
One sign change in the cash flows. This is the fatal one. IRR only has a unique solution when the cash flows switch sign exactly once — money out, then money in. A project that invests, withdraws, and invests again switches sign multiple times, and the equation can then have no solution, or several. This is not exotic: most real multi-phase projects hit it. The NPV of the same project is always well defined.
NPV: the only one that answers "should I?"
Net present value discounts every cash flow back to today and sums them, net of the initial outlay:
NPV = −C₀ + Σ [ CFₜ / (1+r)ᵗ ]
where r is the cost of capital — the return you could get elsewhere for the same risk.
The result is not a percentage, it is an amount of value created. A positive NPV means the project earns more than your opportunity cost; a negative one means you would be better off with the alternative. That makes NPV directly additive: two positive-NPV projects are better together, whereas two 20% ROIs cannot simply be combined.
Worked example — a five-year project costing $100,000 and returning $30,000 a year at a 10% cost of capital:
- Year 1: 30,000 / 1.10 = 27,273
- Year 2: 30,000 / 1.21 = 24,794
- Year 3: 30,000 / 1.331 = 22,540
- Year 4: 30,000 / 1.4641 = 20,491
- Year 5: 30,000 / 1.61051 = 18,628
Sum = 113,726. NPV = 113,726 − 100,000 = $13,726 positive. So the project creates $13,726 of value. The IRR of the same cash flows is about 19.6% — which sounds impressive until you notice the cost of capital is 10% and the NPV is what carries that comparison. The NPV calculator returns both, which is the point.
Where they disagree, and who is right
For conventional projects, NPV and IRR rank options identically. They diverge in two situations, and NPV wins both times:
Different scales. A small project at 40% IRR and a large one at 15% IRR are ranked differently by IRR than by NPV. The percentage measure cannot compare them, because the larger project creates more absolute value. If you can only do one, take the larger NPV.
Unconventional cash flows. When signs flip more than once, IRR can return multiple answers or none. NPV remains unambiguous.
Which to use
ROI for a single, simple, one-off comparison where timing and scale do not matter — "did this trade make money".
IRR to communicate the return on one conventional project to a non-specialist. It is intuitive, it is a percentage, and for that one job it is the best tool.
NPV for the actual decision. It is the only one that references an opportunity cost, handles scale, survives weird cash flow patterns, and is additive. Every textbook agrees on this, and it is the recommendation worth following.
Two places these numbers are routinely misused
IRR as a hurdle rate. Setting a project "IRR hurdle" and then ignoring that the hurdle should itself reflect the opportunity cost can approve projects that destroy value. The correct test is always NPV against the cost of capital.
IRR on savings decisions. An investment that lifts your return by 2 percentage points is not automatically good — if it requires selling investments in a taxable account, or locking up the money past the point you might need it, the NPV of the added complexity can easily be negative. This is the quantitative version of the advice that a 0.1% fee is not free.
Frequently asked questions
Why is ROI misleading?
ROI is a single percentage that ignores when money comes and goes. Two investments can both return 20% while one delivered it in year 1 and the other in year 5, and the second is worse because the money was tied up longer. ROI also ignores scale, so 100% on $500 looks identical to 100% on $50,000.
What does IRR assume that breaks in practice?
It assumes a single known discount rate for all cash flows and that intermediate flows can be reinvested at the IRR itself. Both are rarely true, and IRR becomes unreliable outright when an investment has multiple sign changes in its cash flows.
When should I use NPV over IRR?
Whenever cash flows are uneven or you are comparing mutually exclusive projects. NPV gives an absolute amount of value created rather than a percentage, and it never hits the multiple-IRR problem. The rule of thumb: NPV for decisions, IRR for explaining a single project.
Why do the two methods disagree, and which is right?
When a project's return exceeds the discount rate they rank projects the same way. They disagree on scale and on unconventional cash flows, and in both cases NPV is correct because IRR's percentage scale hides absolute value.