ACCA FM: What To Do When NPV and IRR Give Conflicting Decisions

One of the quieter traps in ACCA FM is the assumption that Net Present Value (NPV) and Internal Rate of Return (IRR) always point to the same investment decision. For a single, stand-alone project with conventional cash flows, they usually do agree on whether to accept or reject. The trouble starts with mutually exclusive projects — where a company can only choose one option, such as which of two machines to buy — because NPV and IRR can rank those options in a different order. Candidates who have only ever practised the simple accept/reject case often freeze, or worse, default to whichever answer feels more familiar, when a question asks them to choose between two competing projects.

Why NPV and IRR usually agree, and where that breaks down

NPV discounts a project’s cash flows at the company’s cost of capital and expresses the result as an absolute amount of money: a positive NPV means the project is expected to add that much value for shareholders. IRR instead finds the discount rate at which NPV becomes exactly zero, and expresses the result as a percentage return. For a single conventional project (one initial outflow followed only by inflows), both methods will normally agree on whether to accept it: if NPV is positive at the cost of capital, the IRR will be above the cost of capital too, and vice versa.

The conflict appears specifically when you are ranking two or more mutually exclusive projects against each other, for three main reasons.

1. Different reinvestment rate assumptions

NPV implicitly assumes that cash flows generated by a project are reinvested at the cost of capital — a realistic, conservative assumption, since the cost of capital reflects the return available elsewhere on projects of similar risk. IRR implicitly assumes that cash flows are reinvested at the project’s own IRR, which for a very profitable project can be an unrealistically high rate to assume the company can keep earning on future cash as it comes in.

2. Differences in scale

A small project can easily show a higher percentage return (IRR) than a large project, while the large project still generates more total value in money terms (NPV). Percentage returns do not account for how much capital is actually being put to work.

3. Non-conventional cash flows and multiple IRRs

If a project’s cash flows change sign more than once — for example, an initial outflow, followed by inflows, followed by a further outflow such as a decommissioning or environmental remediation cost at the end of the project’s life — the IRR equation can mathematically produce more than one valid discount rate that sets NPV to zero. When there is more than one IRR, the IRR technique breaks down as a decision rule altogether: there is no single percentage figure left to compare against the cost of capital. NPV has no equivalent problem, because it simply produces one number at the company’s actual cost of capital, whatever the shape of the cash flows.

Worked example: two mutually exclusive projects

A company has a cost of capital of 10% and can only afford to run one of two mutually exclusive projects, both lasting one year.

Project A’s IRR is found by solving 130,000 / (1 + r) = 100,000, giving r = 30%. Project B’s IRR is found the same way: 480,000 / (1 + r) = 400,000, giving r = 20%. Project A’s NPV at 10% is −100,000 + 130,000 / 1.10 = £18,182. Project B’s NPV at 10% is −400,000 + 480,000 / 1.10 = £36,364.

IRR ranks Project A above Project B, because 30% is a higher percentage return than 20%. NPV ranks Project B above Project A, because £36,364 of added value is more than £18,182. The two methods genuinely disagree on which project is better, purely because Project B is four times the scale of Project A. This is exactly the kind of conflict ACCA FM questions are built to test: a scenario where you must know which method to trust, not just how to calculate both of them.

Which number should decide: NPV

When NPV and IRR conflict for mutually exclusive projects, ACCA FM examiners expect the NPV decision rule to be followed. Project B should be chosen, even though its IRR is lower, because NPV directly measures the absolute increase in shareholder wealth in money terms, using the company’s actual cost of capital as the reinvestment assumption. A shareholder is better off with an extra £36,364 of value than with an extra £18,182 of value, regardless of which project achieved a higher percentage return getting there. Maximising shareholder wealth, not maximising percentage return, is the objective that both FM theory and most corporate finance decision rules are built around.

There is also a practical point worth remembering under exam pressure: NPV is additive across projects (the NPV of undertaking two projects together is simply the sum of their individual NPVs), while IRR is not. That additivity property is part of why NPV is treated as the theoretically superior technique whenever the two methods disagree, and it is worth stating explicitly in a written answer, not just calculating both figures and picking one without justification.

Exam technique checklist

• For a single stand-alone project with conventional cash flows, NPV and IRR will normally agree on accept or reject — no conflict to resolve there.
• For mutually exclusive projects, always calculate both NPV and check whether the ranking differs from IRR before writing a recommendation.
• If the two methods disagree, state explicitly that NPV should be preferred, and explain why: it measures absolute wealth added at a realistic reinvestment rate, and it is additive across projects.
• If cash flows change sign more than once, flag that multiple IRRs may exist and that NPV is the only reliable decision rule in that situation.
• Do not stop at the calculation — ACCA FM marks the written justification for choosing NPV over IRR just as heavily as the numbers themselves.

Getting comfortable with when NPV and IRR can disagree, and being ready to justify NPV as the tiebreaker, turns a topic candidates often find confusing into an easy source of marks. For more exam-technique traps in this part of the syllabus, see our posts on overtrading warning signs and the WACC book vs market value weights mistake, two more areas where a small conceptual slip costs disproportionate marks.