NPV vs IRR: Which Should You Use? A CFA Guide
NPV and IRR agree on accept-or-reject and disagree on ranking. Where the conflict comes from — scale, timing, multiple roots — and which number to defend.
The short answer
Use NPV to decide. It measures the value a project adds in money at a stated cost of capital, and it is additive across projects, so it ranks them correctly. IRR reports the rate at which NPV reaches zero, which is easier to quote but throws away scale, assumes every interim cash flow is reinvested at the IRR itself, and can have several values or none when the cash flows change sign more than once. On a single accept-or-reject question the two always agree; when ranking competing projects, follow NPV.
Ask a finance committee which project to fund and someone will quote an IRR. Ask a textbook and it will say NPV. Both are reading the same cash flows, and most of the time they reach the same conclusion — which is exactly why the cases where they diverge are worth knowing cold.
This is not a tie. NPV is the correct rule and IRR is the popular one. But “use NPV” is a poor answer on its own, because you still have to explain to the person holding the IRR why their number is misleading, and that argument is winnable only if you know precisely where it breaks.
Two readings of one curve
Every project has an NPV profile: a curve of net present value plotted against discount rate. It starts at the undiscounted sum of the cash flows, slopes downward, and for a conventional project crosses zero once.
- NPV is the height of that curve at the rate you chose.
- IRR is where the curve crosses zero, and it does not depend on any rate you chose.
That is the whole relationship. NPV needs an input IRR does not, and in exchange NPV answers a question IRR cannot: how much.
| Discount rate | NPV | What it tells you |
|---|---|---|
| 0% | £290,000.00 | The raw cash surplus |
| 8% | £132,633.52 | Comfortable |
| 11% | £86,606.78 | The actual decision |
| 15% | £33,541.10 | Thinner |
| 17.9049% | £0.00 | The IRR — where the curve crosses |
| 18.5% | −£6,415.83 | Reject |
On accept-or-reject, they cannot disagree
For a single project with one sign change, the two rules are mathematically the same statement:
-
NPV at r > 0 ⟺ IRR > r
The curve slopes downward and crosses zero once. If it is above zero at r, then r must be to the left of the crossing.
So if a colleague’s IRR says accept and your NPV says reject, one of you has a data entry error — not a methodological disagreement. That is worth knowing because it saves an argument: check the inputs first.
The disagreements are all about ranking, and they come in three flavours.
Conflict one: scale
Two projects, both worth doing, only enough capital for one.
| Project A | Project B | |
|---|---|---|
| Initial outlay | −£100,000 | −£300,000 |
| Annual inflow | £32,000 | £85,000 |
| IRR | 18.0307% | 12.8585% |
| NPV at 8% | £27,766.72 | £39,380.35 |
| Profitability index | 1.2777 | 1.1313 |
A wins on rate by five points. B creates £11,613.63 more value. Both facts are true, and only one of them is a reason to do anything.
The test that settles it: if you took A, you would have £200,000 of unspent capital. What does it earn? By assumption, the cost of capital — 8%, which has an NPV of zero. So A plus £200,000 of nothing is worth £27,766.72, and B is worth £39,380.35. There is no arrangement of A that catches up.
The crossover rate, and why it is the number to bring
Ranking arguments run in circles because everyone is arguing about the cost of capital without saying so. The crossover rate ends that, because it converts a disagreement about method into a single testable number: the rate at which the two projects have identical NPVs.
Compute it as the IRR of the difference between the two series. Here that is B minus A: an extra £200,000 out at time zero, and an extra £53,000 a year for five years.
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CPT
F01 = 5 does the repetition. The answer is the crossover rate for the pair.
Crossover = 10.1783%. Below it, B wins. Above it, A wins.
| Discount rate | NPV of A | NPV of B | B − A |
|---|---|---|---|
| 0% | £60,000.00 | £125,000.00 | £65,000.00 |
| 6% | £34,795.64 | £58,050.92 | £23,255.28 |
| 8% | £27,766.72 | £39,380.35 | £11,613.63 |
| 10.1783% | £20,754.6 | £20,754.6 | £0.00 |
| 12% | £15,352.84 | £6,405.98 | −£8,946.86 |
| 14% | £9,858.59 | −£8,188.12 | −£18,046.71 |
Now the conversation is useful. At an 8% cost of capital you have more than two percentage points of headroom before the ranking flips, so B is the answer and it is not a close call. If your WACC estimate were 11%, the honest report is that the two projects are within a hair of each other and the choice should turn on something other than arithmetic.
Conflict two: timing
Scale is not the only way to disagree. Two projects of identical size can rank differently because their cash arrives at different times.
| Quick | Patient | |
|---|---|---|
| Cash flows | −50,000 then +60,000 | −50,000, four zeros, then +95,000 |
| IRR | 20.0000% | 13.6974% |
| NPV at 5% | £7,142.86 | £24,434.99 |
| NPV at 8% | £5,555.56 | £14,655.40 |
| NPV at 15% | £2,173.91 | −£2,768.21 |
Quick has the higher IRR at every cost of capital, because IRR has no way to express that Patient earns its return over five years rather than one. Their crossover is 12.1742%, where both are worth £3,488.
Below 12.1742% the long project is worth more; above it the short one is. A percentage per period cannot carry that, because it says nothing about how many periods you get to earn it for.
Conflict three: IRR may not exist, or may not be unique
The third failure is not a ranking problem. It is IRR having no well-defined answer at all.
Pay £4,000 for a film option, collect £25,000 on release, pay £25,000 in profit share.
Two sign changes, and two rates that both set NPV to exactly zero: 25% and 400%. The BA II Plus reports one of them and says nothing about the other. Neither is “the return on this deal” — the project is only worth doing at rates between them, which no single percentage can express.
| Discount rate | NPV |
|---|---|
| 0% | −£4,000.00 |
| 25% | £0.00 |
| 100% | £2,250.00 |
| 400% | £0.00 |
| 500% | −£527.78 |
NPV has no equivalent failure. At any rate you name, the discounting produces one number, and its sign is the decision. That robustness is the strongest argument for NPV and it is structural rather than a matter of preference: NPV evaluates a function, IRR solves an equation, and equations can have zero solutions or several.
Why NPV is the correct rule
Three properties, in order of how often they actually matter.
It is additive. The NPV of A and B taken together is the NPV of A plus the NPV of B. That is what makes NPV usable across a capital budget — you can sum a portfolio of projects, compare bundles, and drop the worst until the money runs out. Two IRRs cannot be added, averaged or weighted into anything meaningful.
It is denominated in the thing you care about. Shareholders own money, not rates. £39,380 of value is the objective; 18% is a description of how efficiently some of it was produced.
It makes one honest assumption instead of one hidden one. NPV assumes interim cash earns the discount rate — the rate you stated, out loud, and can be challenged on. IRR assumes interim cash earns the IRR, which nobody stated and which gets more optimistic the better the project looks.
| IRR | MIRR at 8% | Change | |
|---|---|---|---|
| Project A | 18.0307% | 13.4246% | −4.61 pts |
| Project B | 12.8585% | 10.6973% | −2.16 pts |
The five-point gap between A and B on IRR is 2.7 points on MIRR. Over half of A’s apparent superiority was the assumption, not the project. B still has the higher NPV, and now the rates no longer contradict it as loudly.
Where IRR is genuinely the better tool
Being the wrong decision rule does not make it useless.
It needs no discount rate. When the cost of capital is contested — a startup, a new market, a cross-border deal — IRR is a fact about the cash flows that survives the argument about WACC. Report it first and let the reader supply their own hurdle.
It communicates headroom. “IRR is 17.9% against an 11% hurdle” tells a listener how much the assumptions could be wrong before the answer changes. “NPV is £86,607” does not, unless you also give them the profile.
It is scale-free on purpose. For comparing the efficiency of capital deployment across a portfolio of similarly sized projects, or for reporting fund performance where the investor chose the amount, a rate is the right unit.
The rule that follows: decide with NPV, communicate with IRR, and quote MIRR when the sign pattern is awkward or the reinvestment assumption is doing too much work.
What the exams actually test
The CFA curriculum is unambiguous — NPV is the theoretically correct criterion — but the questions are rarely a straight “which is better”. They test whether you can spot the conflict and name its cause.
| The question looks like | What it is testing |
|---|---|
| Two projects, different sizes, IRR favours the small one | That you rank on NPV and can say why |
| “At what discount rate are you indifferent?” | The crossover rate as the IRR of the differences |
| A project with a decommissioning cost at the end | Sign changes, and that IRR may be non-unique |
| An IRR quoted on monthly flows | That a periodic rate must be compounded, not multiplied |
| Independent projects, unlimited capital | That both rules agree, and there is no conflict to find |
The last row is the trap. Given two independent projects and enough money for both, there is nothing to rank: take every project with a positive NPV. Candidates who have drilled the conflict cases sometimes manufacture one that is not there.
The working rule
- Load the cash flows once. The
CFworksheet feeds bothNPVandIRR, so computing both costs one extra keystroke. There is no reason to have only one. - Count the sign changes before you trust the IRR. More than one and the rate is decoration.
- Rank on NPV at your stated cost of capital. In money, not percentages.
- Compute the crossover rate for any close pair. It converts a methodological argument into a sensitivity you can defend.
- Present the IRR too. Leaving it out invites someone to compute it themselves and lead with it.
If you want the keystrokes rather than the argument, NPV on the cash flow worksheet and the IRR walkthrough both work through this same £450,000 project, and the NPV calculator adds NFV, payback and discounted payback to the same set of flows.