Skip to main content
Guides 10 min read

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 BA II Plus Calculator Team

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
One project: £450,000 out, then £120,000, £135,000, £150,000, £160,000, £175,000.

On accept-or-reject, they cannot disagree

For a single project with one sign change, the two rules are mathematically the same statement:

Equivalent for a conventional project
  1. 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
Cost of capital 8%. Five years of level inflows each.

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.

IRR of the incremental cash flows
  1. CF
  2. 2ND
  3. CLR WORK
  4. 200000
  5. +|−
  6. ENTER
  7. 53000
  8. ENTER
  9. 5
  10. ENTER
  11. 2ND
  12. QUIT
  13. IRR
  14. 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
The two profiles crossing. Below 10.1783% B is ahead; above it, A.

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
Both cost £50,000. One pays next year, one pays in year five.

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
The film deal's NPV crosses zero twice.

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
Strip out the reinvestment assumption with MIRR and both rates fall — the higher one further.

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 patterns that come up, and what each one is really checking.

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

  1. Load the cash flows once. The CF worksheet feeds both NPV and IRR, so computing both costs one extra keystroke. There is no reason to have only one.
  2. Count the sign changes before you trust the IRR. More than one and the rate is decoration.
  3. Rank on NPV at your stated cost of capital. In money, not percentages.
  4. Compute the crossover rate for any close pair. It converts a methodological argument into a sensitivity you can defend.
  5. 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.

Share X LinkedIn
  • #npv
  • #irr
  • #capital budgeting
  • #cfa
  • #project appraisal

Do it without the keystrokes

The calculators used in this guide

Same arithmetic, same sign convention, with every substitution written out underneath the answer.

FAQ

Frequently asked questions

What is the main difference between NPV and IRR?

NPV is an amount of money and IRR is a rate. NPV answers "how much value does this add at the rate I have to beat", so it needs a discount rate as an input. IRR answers "what rate does this project earn", so it needs no rate at all — but that independence is what makes it unable to tell a large project from a small one.

Why does NPV give a better decision than IRR?

Because NPV is additive and IRR is not. The NPV of two projects taken together is the sum of their individual NPVs, which means NPV ranks correctly and can be aggregated across a whole capital budget. Two IRRs cannot be added or averaged in any meaningful way, and a higher percentage on a smaller base is not a better outcome.

When do NPV and IRR disagree?

Only when you are ranking two or more projects, never on a single accept-or-reject question. The three triggers are a difference in scale, a difference in the timing of the cash flows, and a series that changes sign more than once. For one project against a hurdle rate, IRR above the hurdle and positive NPV always arrive together.

What is the crossover rate?

The discount rate at which two projects have identical NPVs, so the ranking between them flips. Compute it as the IRR of the difference between the two cash flow series. It is the single most useful number in a ranking argument, because it tells you exactly how wrong your cost of capital would have to be for your choice to change.

Should I use MIRR instead of IRR?

MIRR fixes IRR's two structural faults — it produces one answer regardless of sign changes, and it uses a reinvestment rate you state rather than the IRR itself. It is the better rate to quote. It still cannot rank projects of different sizes, because it is still a percentage, so it replaces IRR rather than replacing NPV.

Keep reading

Related guides

All articles