NPV vs IRR: When the Two Disagree, and Which One Is Right
A percentage is easier to talk about than a dollar amount, which is why IRR wins meetings and loses money. Here are two projects where IRR picks one and NPV picks the other, the crossover rate that explains it, and the case with two valid IRRs.
NPV vs IRR
Net present value tells you how much value a project adds, in currency, given a discount rate you supply. Internal rate of return tells you the discount rate at which that value would be exactly zero. They are computed from the same cash flows and they usually agree.
When they disagree, NPV is right. Not usually right: right. IRR is a rearrangement of the same equation that discards the information about size, and that discarded information is often the whole decision. This article shows the disagreement happening on real numbers.
Try the capital expenditure ROI calculatorEnter an outlay and a stream of returns to get payback, return on investment, and discounted value together.Where they always agree
For a single project with a normal cash flow shape, one outlay followed by inflows, the two metrics give the same accept or reject answer. This is a mathematical consequence, not a coincidence.
The trouble starts the moment you rank two projects against each other, because ranking requires a comparison of magnitude and IRR has thrown magnitude away.
The disagreement, on numbers
Two mutually exclusive projects. You can fund one. Your cost of capital is 10%.
Swipe sideways to compare columns.
| Project Small | Project Large | |
|---|---|---|
| Initial outlay | −$50,000 | −$400,000 |
| Annual inflow | $25,000 | $150,000 |
| Years of inflow | 3 | 4 |
| NPV at 10% | $12,171 | $75,480 |
| IRR | 23.4% | 18.5% |
| IRR ranks | First | Second |
| NPV ranks | Second | First |
The instinct that the higher rate must be better assumes you have somewhere else to put the other $350,000 at a comparable rate. If you do, fund Small and say what the other $350,000 is doing. If you do not, that assumption is fiction and Large is worth $63,309 more.
The crossover rate explains exactly when each wins
Subtract Small's cash flows from Large's and you get the incremental project: what you actually buy by choosing Large. Its IRR is the crossover rate, the discount rate at which the two projects have equal NPV.
Swipe sideways to compare columns.
| Year | Large | Small | Difference |
|---|---|---|---|
| 0 | −$400,000 | −$50,000 | −$350,000 |
| 1 | $150,000 | $25,000 | $125,000 |
| 2 | $150,000 | $25,000 | $125,000 |
| 3 | $150,000 | $25,000 | $125,000 |
| 4 | $150,000 | $0 | $150,000 |
The IRR of that difference is about 18%. That is the crossover. Below an 18% cost of capital, the extra $350,000 earns more than it costs and Large wins. Above 18%, capital is expensive enough that the smaller, faster project wins.
Swipe sideways to compare columns.
| Discount rate | NPV Small | NPV Large | Choose |
|---|---|---|---|
| 5% | $18,081 | $131,893 | Large |
| 10% | $12,171 | $75,480 | Large |
| 15% | $7,081 | $28,247 | Large |
| 18% | $4,357 | $3,509 | Crossover, near-identical |
| 20% | $2,662 | −$11,690 | Small |
| 23.4% | $0 | −$35,424 | Small, marginally |
The reinvestment assumption
IRR implicitly assumes every interim cash flow is reinvested at the IRR itself. Project Small returning 23.4% assumes you can redeploy each $25,000 at 23.4% for the remaining years. If that were available, you would already be doing it.
NPV assumes reinvestment at the discount rate, which is your cost of capital, which is a claim you can actually defend. Where IRR is high, the reinvestment assumption is where it overstates the return, and the overstatement grows with both the rate and the term.
The case where IRR has more than one answer
IRR solves a polynomial. A polynomial can have as many roots as the cash flows have sign changes, and a project with a mid-life outlay has two. Take a project costing $100,000, returning $290,000 in year one, then requiring $195,000 of remediation in year two.
Swipe sideways to compare columns.
| Discount rate | NPV |
|---|---|
| 0% | −$5,000 |
| 5% | −$680 |
| 5.95% | $0, an IRR |
| 10% | $2,479 |
| 40% | $7,653 |
| 84.05% | $0, also an IRR |
| 100% | −$3,750 |
Both 5.95% and 84.05% are correct IRRs. A spreadsheet returns whichever it converges on from your starting guess, with no warning that another exists. Neither is a meaningful description of the project, and the NPV column tells you everything you need: at a 10% cost of capital the project adds $2,479.
What IRR is genuinely good for
- Communicating. A percentage compares directly against a borrowing rate or a hurdle rate, and everyone in the room understands it without being told the discount rate.
- Screening when you have no discount rate. IRR needs no assumption about the cost of capital, so it can rank a long list before anyone agrees on one.
- Measuring realised performance. XIRR on actual dated cash flows is the standard way to state what an investment actually returned.
- Sizing the margin of safety. An IRR of 22% against a 9% cost of capital tells you how far the assumptions can be wrong before the project stops working.
The working rules
Swipe sideways to compare columns.
| Question | Use | Why |
|---|---|---|
| Should we do this project at all? | Either | They agree on conventional cash flows |
| Which of these two projects? | NPV | Only NPV accounts for size |
| Which projects fit a fixed budget? | NPV per dollar invested | Ranks by value density, then take from the top |
| Cash flows change sign more than once | NPV | IRR may have several answers or none |
| Projects with different lifespans | NPV, then equivalent annual value | Raw NPV favours the longer project unfairly |
| Reporting what an investment returned | IRR or XIRR | A rate is the natural way to state realised performance |
| Explaining it to a board | Both | NPV for the decision, IRR for the intuition |
What neither metric tells you
- Whether the cash flow forecast is any good. Both are exact arithmetic on numbers somebody guessed. A 10% error in year-four revenue moves the answer more than the choice of metric ever will.
- What discount rate to use. NPV is only as defensible as the cost of capital you supply, and reasonable people disagree by several points on the same business.
- Anything about risk profile. Two projects with identical NPV can have completely different distributions of outcomes, and neither metric distinguishes them.
- The value of flexibility. Being able to abandon, delay, or expand a project has real value that a fixed cash flow schedule cannot express.
- Whether you have the cash. A project can have a large positive NPV and still be unfundable, which is why payback period survives alongside these two.
- Strategic fit or opportunity cost beyond the modelled alternatives. The best project may be one nobody put in the spreadsheet.
If NPV and IRR disagree, which do I follow?
NPV, without exception. The disagreement arises because IRR ignores scale and timing differences between projects. NPV measures value added in currency at your actual cost of capital, which is the quantity you are trying to maximise.
Why does a higher IRR not always mean a better project?
Because a high rate on a small base can be worth less than a moderate rate on a large one. Earning 23.4% on $50,000 adds $12,171 of value; earning 18.5% on $400,000 adds $75,480. The percentage is higher and the outcome is worse.
What is the crossover rate?
The discount rate at which two projects have equal NPV. It is the IRR of the difference between their cash flows. Below it, the larger project wins; above it, the smaller one does. Computing it tells you exactly how sensitive the ranking is to your cost of capital.
When does a project have more than one IRR?
When the cash flows change sign more than once, such as an outlay, then inflows, then a decommissioning cost. Each sign change can add a root. Use NPV or MIRR on those projects and ignore the IRR entirely.
Is MIRR better than IRR?
It is more honest, because it makes the reinvestment rate an explicit input rather than an implicit assumption. It still cannot rank projects of different sizes, so it does not replace NPV. Use it when you want a rate and the IRR looks implausibly high.
How do I compare projects with different lifespans?
Raw NPV favours the longer project because it accumulates more years of value. Convert each NPV to an equivalent annual value by dividing by the annuity factor for its own life, then compare those. It answers the right question: which project is worth more per year.
Written by
Do The Calculation Team
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