NPV vs IRR (CFA): Why They Disagree and Which One Wins

Capital budgeting questions look like calculation questions and are usually decision questions. The arithmetic is a calculator function. The mark is in knowing which rule to trust when the two disagree, and why.

The two rules

Net present value is the sum of a project's cash flows discounted at the required rate of return, less the initial investment. The rule: accept if NPV is positive.

NPV is expressed in currency, and it is a direct estimate of how much value the project adds to the firm. An NPV of $4m means the project is expected to make shareholders $4m better off in today's terms.

Internal rate of return is the discount rate at which NPV equals exactly zero — the project's own implied return. The rule: accept if IRR exceeds the required rate of return.

IRR is expressed as a percentage, which is why practitioners like it. It communicates instantly and compares across projects of different sizes without any context.

When they agree

For a single conventional project — one initial outflow followed by inflows — the two rules always give the same accept or reject decision. If NPV is positive at the required return, the IRR must be above that return. The relationship is definitional.

So for independent projects, where you can accept all that qualify, the choice of rule does not matter.

When they conflict

Conflicts arise only for mutually exclusive projects, where accepting one means rejecting the other. Two causes:

Scale differences. A small project can post a spectacular percentage return while adding little absolute value. A 60% IRR on a $100,000 investment produces less wealth than a 15% IRR on $10m. IRR is blind to size; NPV is not.

Timing differences. A project front-loading its cash flows will show a higher IRR than one delivering more cash later, even if the second creates more total value. IRR implicitly rewards early cash disproportionately.

Worked example

Required return 10%.

• Project A: invest $10,000, receive $12,000 in one year. IRR = 20%. NPV = 12,000/1.10 − 10,000 = $909
• Project B: invest $100,000, receive $118,000 in one year. IRR = 18%. NPV = 118,000/1.10 − 100,000 = $7,273

A has the higher IRR. B adds eight times more value. If they are mutually exclusive, take B.

The reasoning: a firm cannot spend a percentage. It can spend money, and shareholders are made better off by the absolute amount created, not the rate at which a small sum grew.

The reinvestment rate assumption

This is the deeper reason NPV wins, and it appears in conceptual questions.

NPV implicitly assumes interim cash flows are reinvested at the required rate of return — the firm's cost of capital. IRR implicitly assumes they are reinvested at the IRR itself.

The NPV assumption is realistic: the cost of capital is, by construction, the return available on projects of comparable risk. The IRR assumption is not: a project with a 40% IRR does not imply the firm has an endless supply of 40% opportunities to redeploy cash into. The higher the IRR, the more unrealistic the assumption becomes — so IRR overstates attractiveness precisely where it looks most attractive.

The IRR pathologies

Multiple IRRs. A project whose cash flows change sign more than once can have more than one IRR — mathematically, as many as there are sign changes. A mining project with an initial outflow, years of inflows, then a large restoration cost at the end is the standard example. With two IRRs, the decision rule is meaningless: neither number is "the" return.

No IRR. Some unconventional cash flow patterns produce no real solution at all.

NPV has neither problem. It produces exactly one value for any set of cash flows and any discount rate. A question describing non-conventional cash flows is signalling that IRR should be distrusted.

The crossover rate

Plot NPV against discount rate for two projects and the lines will often intersect. That intersection is the crossover rate — the discount rate at which both projects have equal NPV.

It matters because it tells you where the conflict lives:

• Below the crossover rate, the project with more distant cash flows has the higher NPV
• Above it, the front-loaded project wins
• The ranking conflict between NPV and IRR only exists when the required return sits below the crossover rate

You find it by computing the IRR of the differential cash flows — the year-by-year difference between the two projects.

What the exam wants you to say

The expected answer, stated cleanly:

NPV is theoretically superior because it measures absolute value added, uses a realistic reinvestment assumption, always produces a single unambiguous value, and directly reflects the goal of maximising shareholder wealth.

IRR remains widely used because a percentage is intuitive, comparable across projects without further context, and does not require the analyst to specify a discount rate before computing it.

Where they conflict for mutually exclusive projects, choose the higher NPV. There is no situation in the curriculum where IRR should override NPV.

Related measures

• Profitability index = PV of future cash flows / initial investment. Accept above 1.0. Useful when capital is rationed, since it ranks by value created per unit of capital deployed.
• Payback period — how long to recover the investment. Ignores the time value of money and everything after the payback point. Useful as a liquidity screen, never as a decision rule.
• Discounted payback — fixes the time value flaw but still ignores post-payback cash flows.

The discount rate feeding all of this is normally the firm's WACC, adjusted where the project's risk differs from the firm's typical activity — a point questions test alongside the NPV calculation itself.