CFA Level I Exam · Capital Investments and Capital Allocation

Conflicts Between NPV and IRR Rankings for Mutually Exclusive Projects

Updated 7 October 2026 · Fact-checked

NPV and IRR can rank mutually exclusive projects differently because of differences in project scale, cash flow timing, or non-conventional cash flows. To resolve it, choose the project with the higher positive NPV. NPV measures the value added in currency terms and assumes reinvestment at the discount rate.

Understand Conflicts Between NPV and IRR Rankings

A mutually exclusive choice means you can take only one project. Both NPV and IRR say "accept" for any single independent project with conventional cash flows. The trouble starts when you must rank projects. NPV and IRR can then point to different winners.

There are two main causes. The first is scale: a small project can have a high IRR but a small NPV, while a large project has a lower IRR but adds more money. The second is timing: one project returns cash early, the other later. The NPV profiles (NPV plotted against the discount rate) of the two projects cross at a rate called the crossover rate. If the required rate is below the crossover rate, the project with later, larger cash flows has the higher NPV. If the required rate is above it, the project with earlier cash flows has the higher NPV. IRR may favour the other project at the same time.

Why NPV wins: NPV measures the expected change in firm value in currency terms, which is the goal of the firm. IRR gives a percentage, which ignores size. NPV also implicitly assumes interim cash flows are reinvested at the required rate of return, which is generally considered more realistic. IRR implicitly assumes reinvestment at the IRR itself, which can be too optimistic for a high-IRR project.

The second problem is non-conventional cash flows, where the sign changes more than once (for example outflow, inflow, outflow). Such a project can have multiple IRRs or no IRR at all. The number of real IRRs above −100% (the economically meaningful ones) is at most the number of sign changes. When this happens the IRR rule is unreliable. NPV still gives one clear answer at your chosen discount rate.

Key formulas to remember

Net present value: NPV = Σ CFt ÷ (1 + r)^t, for t = 0 to n; CF0 is usually negative. Accept if NPV > 0. For mutually exclusive projects, pick the highest positive NPV.
Internal rate of return: IRR is the r that makes NPV = 0; Accept an independent project with conventional cash flows if IRR > required rate of return.
Crossover rate: Crossover rate: the r at which NPV(A) = NPV(B); Find it as the IRR of the difference in cash flows. The sign of the difference does not affect the crossover rate, so you can use A − B or B − A.
Multiple IRR condition: Number of real IRRs above −100% ≤ number of sign changes in the cash flows; This is an upper limit, not an exact count. Conventional flows have one sign change, so at most one such IRR. More sign changes allow several IRRs, or none.
Decision rule for mutually exclusive projects: Choose the project with the highest NPV, if NPV > 0; Use NPV when the rankings conflict.

How to solve Conflicts Between NPV and IRR Rankings questions

Use this method for any question asking which project to choose or why rankings disagree.

1Check whether the projects are mutually exclusive or independent. Independent projects with conventional flows: NPV and IRR agree on accept or reject.
2Count the sign changes in each cash flow series. More than one change means multiple IRRs or no IRR may exist, so rely on NPV.
3Compare scale: is one initial outlay much larger? Compare timing: are cash flows front-loaded or back-loaded?
4Compute NPV for each project at the stated required rate of return.
5Rank by NPV and reject any project with a negative NPV.
6If asked about the crossover rate, compare the required rate with it. Below the crossover, the back-loaded project has the higher NPV. Above it, the front-loaded project does.
7State the conclusion: follow NPV, because it measures value added and its reinvestment assumption is generally considered more realistic.

Quickest way: Pick the higher NPV, then check the trap

When to use it: Use when the stem gives both IRRs and NPVs, or asks which rule to trust.

If the stem gives NPVs, choose the highest positive NPV. Ignore the IRR ranking. If every NPV is negative, reject all the projects.
If the stem mentions several sign changes in cash flows, note that IRR may be multiple or undefined, so NPV is the answer.
If the stem asks for the cause of a conflict, look for scale or timing differences.
Eliminate any option that chooses by the highest IRR for mutually exclusive projects, and any option that accepts a project with a negative NPV.
On a calculator, enter cash flows in CF mode (BA II Plus: CF, then NPV with I = rate, CPT) to get NPV fast.

Common mistakes in Conflicts Between NPV and IRR Rankings

Choosing the project with the higher IRR when the projects are mutually exclusive
A percentage looks like a better measure than a currency amount.
Fix: For mutually exclusive projects, rank by NPV. IRR ignores project size and timing.
Saying a project with several sign changes always has several IRRs
Students read the rule as exact rather than as a maximum.
Fix: Sign changes set an upper limit on the number of real IRRs above −100%. The project may have fewer, or none.
Applying the crossover logic the wrong way round
Confusion over which project is more sensitive to the discount rate.
Fix: Back-loaded cash flows are more sensitive to r. Below the crossover rate the back-loaded project has the higher NPV. Above it the front-loaded project does.
Stating that IRR assumes reinvestment at the required rate of return
Students mix up the two rules.
Fix: NPV assumes reinvestment at the required rate, which is generally considered more realistic. IRR assumes reinvestment at the IRR itself.
Using NPV and IRR as rivals for independent projects
Students over-generalise the conflict.
Fix: For an independent project with conventional flows, both rules give the same accept or reject decision. Conflicts only arise when you rank.

Worked examples

Example 1

A firm with a required return of 10% must choose one of two mutually exclusive projects. Project A: outlay €100, inflow €120 at the end of year 1. Project B: outlay €1,000, inflow €1,150 at the end of year 1. Which should it choose, and which rule would mislead?

Show the solution

IRR of A = 120 ÷ 100 − 1 = 20%.
IRR of B = 1,150 ÷ 1,000 − 1 = 15%.
NPV of A = 120 ÷ 1.10 − 100 = 109.09 − 100 = €9.09.
NPV of B = 1,150 ÷ 1.10 − 1,000 = 1,045.45 − 1,000 = €45.45.
IRR ranks A first. NPV ranks B first. The conflict comes from scale.
Both NPVs are positive. Choose the higher NPV.

Answer: Choose Project B (NPV €45.45 versus €9.09). The IRR ranking would mislead because it ignores scale.

Example 2

A project has cash flows of −$100 at t = 0, +$300 at t = 1 and −$200 at t = 2. How many IRRs can it have, and what does the exam expect you to conclude? Check whether 0% and 100% are IRRs.

Show the solution

Signs are −, +, −: two sign changes, so up to two IRRs.
Test r = 0%: NPV = −100 + 300 − 200 = 0. So 0% is an IRR.
Test r = 100%: NPV = −100 + 300 ÷ 2 − 200 ÷ 4 = −100 + 150 − 50 = 0. So 100% is an IRR.
The project therefore has two IRRs, 0% and 100%, and the IRR rule gives no clear single decision.
The firm should compute NPV at its required rate of return instead.

Answer: The project has two IRRs (0% and 100%) because of two sign changes. IRR is unreliable here, so use NPV at the required rate.

Exam tips

Mutually exclusive plus conflicting rankings: the answer is to choose the project with the highest positive NPV. If every NPV is negative, reject all the projects.
Learn the two causes of conflict cold: differences in scale and differences in timing of cash flows.
Count sign changes first when a stem shows non-conventional cash flows. It signals multiple or no IRRs.
Know the reinvestment assumptions: NPV at the required rate, IRR at the IRR itself.
Remember the options are three only, so eliminate any choice favouring IRR for mutually exclusive ranking, and any choice that accepts a project with a negative NPV.

Practice questions from Capital Investments and Capital Allocation

Conflicts Between NPV and IRR Rankings in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Conflicts Between NPV and IRR Rankings: frequently asked questions

Why is NPV better than IRR for mutually exclusive projects?

NPV shows the currency value a project adds to the firm, so it accounts for scale. It also assumes reinvestment at the required rate of return, which is generally considered more realistic than reinvestment at the IRR. Because the firm aims to maximise value, the highest NPV is the right choice.

What causes multiple IRRs?

Non-conventional cash flows, where the sign changes more than once, such as an outflow, then inflows, then a final outflow. The number of real IRRs above −100% is at most the number of sign changes. Some projects have fewer, or none.

What is the crossover rate?

It is the discount rate at which two projects have equal NPV. At rates below it, the project with later cash flows usually has the higher NPV. Above it, the project with earlier cash flows does.

How do I resolve a conflict between NPV and IRR?

Compute NPV at the required rate of return and pick the project with the highest positive NPV. Use the IRR only as supporting information. If the projects are independent with conventional flows, the two rules already agree.