Head-to-head
NPV vs IRR
Both metrics judge the same stream of cash flows, and both usually agree on whether a single project is worth doing. They disagree the moment you have to choose between projects, because they measure different things: NPV measures how much value a project adds in today's money, while IRR measures the rate at which the money grows.
That difference sounds cosmetic and is not. A dollar figure can be added across projects, so two positive NPV projects are worth their sum. A rate cannot be added, so picking the project with the highest IRR can leave value on the table — a small project returning 40% may add less wealth than a large one returning 15%.
The two also carry different hidden assumptions. NPV discounts interim cash flows at the rate you supplied, which is normally your cost of capital. IRR implicitly assumes interim cash flows are reinvested at the IRR itself, which is optimistic when the IRR is high and is the standard criticism of the metric.
Finally, IRR is not always defined. Cash flows that change sign more than once can produce several IRRs or none, and a project that pays out early and then costs money later is a realistic example. NPV has no such failure mode: one discount rate in, one number out.
NPV
How To Calculate NPV
Net present value asks a single sharp question: after discounting every future cash flow back at the rate you require, does the investment create or destroy value? It is the most reliable single test in capital budgeting because it works in money rather than in ratios.
IRR
How To Calculate IRR
The internal rate of return is the discount rate that makes an investment's net present value exactly zero. It is the break-even rate the project must beat, and it lets you compare projects of different sizes on a single percentage scale.
How They Differ
| Attribute | NPV | IRR |
|---|---|---|
| What it returns | A dollar amount — value added today | A percentage — the rate earned |
| Decision rule | Accept anything above zero | Accept anything above the hurdle rate |
| Comparing two projects | Add them; take the larger NPV | Cannot be added; ranking can mislead |
| Reinvestment assumption | Interim cash flows earn the discount rate | Interim cash flows earn the IRR |
| Sensitivity to the discount rate | Moves continuously as the rate changes | Does not move at all — it ignores your rate |
| Scale of the project | Captured; bigger projects give bigger numbers | Ignored; a tiny project can have a huge IRR |
| When it breaks down | Only if the discount rate is wrong | Multiple or no solutions when signs flip twice |
The Same Numbers, Both Ways
A $100,000 outlay returning $30,000 a year for five years, discounted at 8%.
- Initial outlay
- $100,000
- Annual cash flow
- $30,000
- Term
- 5 years
- Discount rate
- 8%
| Line | NPV | IRR |
|---|---|---|
| Headline result | $19,781.30 | 15.2% |
| At a 5% discount rate | $29,884.30 | 15.2% |
| At a 12% discount rate | $8,143.29 | 15.2% |
| At a 20% discount rate | -$10,281.64 | 15.2% |
| Reinvestment assumption | Interim cash flows earn the discount rate | Interim cash flows earn the IRR |
| Two projects of different size | Add the surpluses | Ranking can pick the smaller one |
The same five payments are worth $19,781.30 of surplus at an 8% discount rate and represent a 15.2% return. Both say accept, but only one of them says how much: raise the discount rate to 20% and the surplus falls to -$10,281.64 while the IRR stays at 15.2%, which is exactly why IRR alone cannot rank projects of different size.
When To Use Each
NPV
- You need to choose between mutually exclusive projects, where only the dollar surplus is additive.
- Your cost of capital is known and you want value measured in today's money.
- Cash flows change sign more than once, which can leave IRR with no unique answer.
IRR
- You need a rate to compare against a hurdle rate, a borrowing cost, or another investment's return.
- The audience thinks in percentages and the project sizes are similar.
- You are communicating the result rather than optimising a portfolio.
Common Questions
Can NPV and IRR disagree on whether to accept a project?
For a single conventional project, no — if the IRR is above the discount rate then the NPV is positive, because the two are the same calculation solved for different unknowns. They disagree only when you rank competing projects, or when cash flows are unconventional.
Why can a high IRR be a worse choice?
Because IRR ignores scale. A $1,000 project returning 40% adds $400; a $100,000 project returning 15% adds a great deal more even after discounting. Ranking by IRR would pick the first and destroy value.
What does the reinvestment assumption really mean?
NPV assumes each interim cash flow is reinvested at your discount rate, usually your cost of capital. IRR assumes each one is reinvested at the IRR itself. If a project's IRR is 30% but your money realistically earns 8%, the IRR figure is flattering the project.
What is MIRR and does it fix this?
The modified internal rate of return discounts outflows and compounds inflows at explicit finance and reinvestment rates. It gives a rate that is still communicable but no longer assumes reinvestment at the IRR, and it is unique even when cash flows flip sign.
What discount rate should I use?
The rate you could earn elsewhere at the same risk, which for a company is its weighted average cost of capital. Using too low a rate makes long-dated projects look better than they are, because discounting is what suppresses distant cash flows.
More Comparisons
- Present Value vs Future Value
Present value discounts a future sum back to today; future value compounds today's money forward. At 6% over ten years, $10,000 promised later is $5,583.95 now, and $5,583.95 invested now is $10,000 later.
- ROI vs CAGR
ROI measures the whole return; CAGR turns it into a compound annual rate. A 100% return over five years is 20% a year by division but 14.87% a year in reality.
- Simple Interest vs Compound Interest
Simple interest charges the principal only; compound interest charges the balance. On $10,000 at 5% over 10 years that gap is $1,288.95 — here is where it comes from.
Sources
- Net present value — capital budgeting basics — Corporate Finance Institute
- Internal rate of return — definition and limitations — Corporate Finance Institute
- Cost of capital and discount rate guidance — NYU Stern, Damodaran data pages
Both methods sit in Finance.