NPV vs IRR: choosing projects that create value
The two capital-budgeting workhorses, their decision rules, a fully worked 198.21 / 19.09% example, and the sign-change trap that breaks IRR.
A project is a signed list of cash flows: an investment today (negative) followed by returns (positive). Capital budgeting asks which lists are worth signing. Two criteria dominate — NPV, the value created in currency, and IRR, the rate the project internally earns. Used correctly they agree; used carelessly they fight, and IRR usually loses the argument.
The decision rules
- NPV > 0 → accept: the project adds value over and above the cost of capital.
- IRR > hurdle rate → accept: the project earns more than the alternative use of funds.
- Independent projects: both rules accept or reject together (for conventional flows).
- Mutually exclusive projects: rank by NPV, never by IRR.
A fully worked example
Take the flow CF₀ = −1000, then 300, 500, 500 and 200, discounted at 10%. The FinScope cash-flow worksheet — engine-verified — reports: NPV = 198.2105, IRR = 19.0862%, plain payback 2.4 periods, discounted payback 2.836 periods and profitability index 1.1982. One row of inputs, five complementary verdicts: the project creates 198 units of value, earns 19.09% against a 10% cost of capital, returns cash by mid-period-3 on a discounted basis and multiplies every invested unit into 1.198.
| t | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| Cash flow | −1,000 | 300 | 500 | 500 | 200 |
| NPV @10% | 198.2105 | ||||
| IRR | 19.0862% |
Compare it with the classic flow −1000, 500, 400, 300, 100: NPV 78.8197 and IRR 14.4890%. Larger, later inflows can carry a lower IRR yet a higher NPV — depending on the discount rate, the two rankings genuinely diverge, and when they do, NPV is the one that pays the bills.
The multiple-IRR trap
−1000, 500, −300, 400 has 3 sign changes, and the engine flags it before you waste a decision on a meaningless rate.If the sign-change count exceeds one, trust NPV or MIRR instead. And if the flow never changes sign at all — say all positive — there is no IRR whatsoever: the engine returns 'not found' rather than inventing one.
Why NPV wins the tie-breaks
- NPV is measured in currency: NPVs of different projects simply add up; IRRs do not.
- NPV assumes reinvestment at the discount rate — the realistic cost-of-capital assumption; IRR implicitly assumes reinvestment at the (often unrealistically high) IRR itself.
- NPV handles changing discount rates and non-conventional flows gracefully.
- Scale matters: a 50% return on 10 rials is not better than 12% on a million.
Frequently asked questions
Can IRR be negative or not exist?
Yes to both. A project that never recovers its cost has a negative IRR, and a flow with no sign change (e.g. all inflows) has no IRR at all — the equation's root is undefined, and a solver correctly reports 'not found'. Multiple sign changes can even produce several valid-looking IRRs for the same flow.
Why do mutually exclusive projects favor NPV?
IRR is a percentage and blind to size. A small project can show a dazzling IRR on a trivial investment while a large project with a lower IRR adds far more absolute wealth. When you can pick only one, the goal is maximizing value — the NPV ranking, not the return ratio.
What discount rate should I use for NPV?
The opportunity cost of capital for projects of comparable risk — commonly the WACC, adjusted upward for riskier ventures and downward for safer ones. The verified example uses 10%; at that rate NPV is 198.2105. If a project's NPV is positive at your true cost of funds, it creates value; IRR merely restates the same test as a percentage.
Practice it live
Open the matching worksheet and reproduce every number in this article.
Open calculator