NPV vs IRR: which capital budgeting rule to trust
A company deciding whether to build a factory, launch a product or buy a rival is comparing money spent now with money earned later. Net present value and internal rate of return are the two standard ways to compare them. They usually point the same way, but when they do not, you need to know which to believe.
Net present value
NPV discounts every cash flow of a project to today and adds them up, counting the initial outlay as a negative:
NPV = Σ cash flow in year t ÷ (1 + r)t, from t = 0
The discount rate r is the return the company could earn elsewhere on investments of similar risk, usually the cost of capital. The decision rule is simple:
- NPV above zero: the project earns more than the cost of capital, so it adds value. Accept.
- NPV below zero: it earns less. Reject.
NPV has a very useful property: it is measured in money. A project with an NPV of 243 is expected to add 243 to the value of the firm, and the NPVs of independent projects simply add.
Internal rate of return
The IRR is the discount rate at which a project's NPV is exactly zero. It is the project's own rate of return. The rule: accept if the IRR is above the required return, reject if below.
For a project that costs 1,000 and returns 300, 420 and 680 in years one to three, the NPV at 10% is 130.73 and the IRR is 16.3%. Both say accept. Try your own cash flows in the NPV and IRR calculator.
Why they agree, usually
For a conventional project, with one outflow at the start and inflows afterwards, NPV falls steadily as the discount rate rises, and crosses zero once, at the IRR. So NPV is positive exactly when the required return is below the IRR. The two rules give the same accept-or-reject answer.
When they disagree
Two situations break the agreement.
Mutually exclusive projects
When you can only pick one, the IRR can rank the projects differently from NPV. Compare these two projects, each costing 1,000:
- Project A returns 500 a year for three years. NPV at 10% is 243.43 and the IRR is 23.4%.
- Project B returns nothing for two years, then 1,800 in year three. NPV at 10% is 352.37 and the IRR is 21.6%.
A has the higher IRR, but B has the higher NPV. Which is right? It depends on the discount rate. The two NPVs are equal at a crossover rate of 18.8%. At any rate below that, B has the higher NPV; above it, A does. Since the company's cost of capital is 10%, B creates more value, even though its IRR is lower.
The reason is that IRR ignores scale and timing in a way NPV does not. It also quietly assumes each interim cash flow is reinvested at the IRR itself, while NPV assumes reinvestment at the cost of capital, which is far more plausible for a company that can earn the cost of capital elsewhere.
Unconventional cash flows
If the cash flows change sign more than once, for instance an outflow, then inflows, then a large closing outflow for decommissioning, there can be more than one IRR, or none. A polynomial in (1 + r) can have several roots. NPV never has this problem: it is always a single number at any given rate.
The practical rule
- Use NPV to choose between mutually exclusive projects.
- Use IRR as a communication tool: "the project returns 17%" is easy to grasp.
- When the two disagree, trust NPV.
- Always check how many times the cash flows change sign before relying on an IRR.
Mistakes to avoid
- Discounting the first cash flow. The initial outlay is at time zero and is not discounted.
- Comparing IRRs of mutually exclusive projects without checking the NPVs.
- Using the wrong rate. NPV needs a discount rate that reflects the project's risk.
- Reading a high IRR as a large gain. A tiny project can have a huge IRR and a small NPV.
Where this is tested
Capital budgeting is part of corporate issuers, and NPV logic returns throughout valuation. The learning outcomes below set out the decision rules and the calculations.