NPV vs. IRR - what's the difference

Net present value and internal rate of return are taught together in almost every intro finance course, for the reason that they answer the same underlying question from two different directions - and usually, but not always, agree with each other.

NPV: what a project is worth today, at a rate you pick

Net present value discounts every future cash flow back to today at a rate you choose (your cost of capital, or a required return), then sums them. A positive NPV means the project creates more value than that rate demands; a negative NPV means it destroys value at that rate. NPV is expressed in dollars, and it directly answers "is this worth doing" once you already know what rate you're measuring against.

IRR: the rate at which a project breaks exactly even

Internal rate of return is the discount rate that would make a project's NPV exactly zero. It's a percentage, not a dollar figure, and it answers a slightly different question: "how good is this project's own return, independent of any external rate I might compare it to." IRR is solved numerically rather than with a closed-form formula (outside of a two-cash-flow project), which is why every real IRR calculation - including the NPV & IRR calculator - searches for the rate rather than computing it directly.

Where they can disagree

For a single, straightforward project, a positive NPV and an IRR above your required rate always agree - accept the project either way. The disagreement shows up when comparing two mutually exclusive projects of different sizes or cash flow timing: one project can have a higher IRR while the other has a higher NPV at your actual cost of capital. When that happens, NPV is the correct tiebreaker for choosing between them, because IRR implicitly assumes cash flows get reinvested at the IRR itself, which is often an unrealistic assumption for a very high IRR project.

Why case studies pair them instead of picking one

A case study that only reports NPV hides how sensitive the project is to a wrong estimate of the discount rate; one that only reports IRR hides the actual dollar value at stake. Together, they show both the size of the opportunity and its rate of return, which is why business courses drill both instead of treating one as strictly better.

Once you can see the mechanics, the actual arithmetic is worth checking against your own numbers - see the break-even point calculator for the related question of how many units a project needs to sell before either number turns positive, and how case-method courses actually grade you for how this fits into a typical b-school syllabus.