NPV vs IRR — When They Agree, When They Fight, Which Wins
NPV and IRR are computed from the same equation — IRR is literally the discount rate where NPV hits zero. Yet the two methods disagree often enough that corporate finance spends a whole lecture on it. Here is the disagreement, on one worked stream.
Quick answer: On −$1,000 returning $500, $600, $700: NPV at an 8% discount rate is $533.05 and IRR is 33.87% — both say accept. They fight when projects compete: IRR flatters early-cash projects by assuming reinvestment at the IRR itself; NPV prices everything at your real opportunity cost. When in doubt, take the higher NPV.
One stream, both verdicts
Take the project −$1,000 today, then $500, $600, $700. Discounted at 8%, the inflows are worth $462.96 + $514.40 + $555.68 = $1,533.05, so NPV = $533.05 — the project creates that much value over and above 8%. The IRR, the rate where NPV equals zero, is 33.87% — the project's own built-in return. Both flags are green: any stream with IRR above the discount rate has positive NPV. The math guarantees agreement on the accept/reject question for conventional streams.
Where they fight: the reinvestment assumption
IRR's arithmetic quietly assumes each intermediate cash flow compounds at the IRR until the end — the $500 arriving in year 1 is treated as growing at 33.87% for two more years. That's rarely possible. NPV assumes intermediate flows earn the discount rate, which is what you can actually approximate by parking them at your cost of capital. MIRR makes the assumption explicit and lands between the two: on this stream at 8% for both rates, MIRR = 24.53%.
Where they fight: two projects, one slot
Mutually exclusive projects of different sizes or shapes can rank differently: the big, slow project can have the higher NPV while the small, fast one has the higher IRR. Picking by IRR then leaves value on the table — the IRR winner earns a higher rate on less money; the NPV winner adds more dollars. Scale matters, and only NPV sees it. This is the classic exam question, and the answer is always: choose the higher NPV when the projects are truly mutually exclusive.
Where IRR breaks outright
- Multiple sign changes → multiple IRRs; the calculator reports one and hides the other
- No-crossover streams → no IRR at all, even though NPV works fine
- Very different project lengths → IRR's per-period number misleads across unequal horizons
The decision rule
Screen with IRR if you like — it's intuitive and comparable to financing costs. Decide with NPV: it measures value created in dollars, prices risk with the rate you chose, and never produces two answers. Practitioner consensus (and the CFA curriculum) treats NPV as the primary criterion precisely because it wins every disagreement.