Advanced Financial Management · Discounted cash flow techniques

NPV and IRR Investment Appraisal Rules in ACCA AFM

Updated 11 October 2026 · Fact-checked

NPV is the present value of a project's cash flows at the cost of capital. Accept if it is positive, because that adds to shareholder wealth. IRR is the discount rate that gives an NPV of zero. Accept if it exceeds the cost of capital. When the two rankings conflict, trust NPV.

Understand NPV and IRR Investment Appraisal Rules

A project is worth doing if it earns more than the return investors require. Discounted cash flow (DCF) tests this by moving every cash flow to today's value. Money received later is worth less, so you discount it at the project's cost of capital.

Net present value (NPV) is the sum of discounted inflows less the initial outlay. A positive NPV is the extra value, in today's money, that the project adds. That is why NPV links directly to shareholder wealth maximisation. If the discount rate is right and the cash flows are right, an NPV of ₹/$ 100 means shareholder wealth rises by about that amount.

Internal rate of return (IRR) is the discount rate at which NPV equals zero. It is the project's break-even cost of capital. If the company's cost of capital is below the IRR, NPV is positive. IRR is a percentage, so many managers find it easier to understand. The gap between IRR and the cost of capital also shows how much margin of safety there is.

The two methods agree for a single, conventional project (one outflow, then inflows). They can disagree when you rank mutually exclusive projects. The usual causes are different project sizes, different timing of cash flows, or non-conventional cash flows. Then NPV is the better guide. It measures absolute wealth, and it assumes surplus cash is reinvested at the cost of capital. That is more realistic than IRR's implicit assumption that cash is reinvested at the IRR itself.

IRR has other weaknesses. A project with more than one change in the sign of cash flows (for example, a cash outflow at the end of its life) can have multiple IRRs or none that make sense. IRR also cannot cope easily with discount rates that change over the life of the project. In the exam you must calculate, decide, and then explain these limits in the context of the scenario.

Key rules to remember

Net present value: NPV = Σ [CFt ÷ (1 + r)^t], t = 0 to n; CF0 is normally the initial outflow (negative). r is the cost of capital or a project-specific rate.
NPV decision rule: Accept if NPV > 0; for mutually exclusive projects, choose the highest positive NPV; With no capital rationing, accepting all positive-NPV projects maximises wealth.
IRR by interpolation: IRR ≈ L + [NPV_L ÷ (NPV_L − NPV_H)] × (H − L); L is the lower rate with positive NPV (NPV_L), H is the higher rate with negative NPV (NPV_H). The result is an estimate, because NPV is not a straight line against the rate. Choose two rates close together for accuracy.
IRR decision rule: Accept if IRR > cost of capital; Reliable only for a single project with conventional cash flows. For mutually exclusive projects, use NPV or the incremental IRR.
Incremental IRR: IRR of (larger project cash flows − smaller project cash flows); If this exceeds the cost of capital, the larger project is better. It gives the same choice as NPV.
Number of IRRs: Maximum number of IRRs = number of sign changes in the cash flows; Conventional flows (− then +) have one sign change. More changes can mean multiple IRRs.
Perpetuity PV: PV = annual cash flow ÷ r; Use for level cash flows that go on indefinitely, with the first one a year from now. Not valid for growth.

How to solve NPV and IRR Investment Appraisal Rules questions

Use this order for any NPV or IRR question. It keeps your workings clear and earns marks even if one figure is wrong.

1Identify the relevant cash flows and their timing. Include tax, working capital and scrap value as the question gives them. Ignore sunk costs and non-cash items.
2Choose the discount rate. Use the company's cost of capital unless the question gives a project-specific rate.
3Discount each cash flow, add them up and state the NPV with its sign. Show the discount factors or the formula.
4If IRR is needed, calculate NPV at two rates, one giving a positive NPV and one giving a negative NPV. Interpolate, and state that the answer is an estimate.
5Apply the rule. For a single project, accept if NPV > 0 or IRR > cost of capital. For mutually exclusive projects, rank on NPV. If the rankings conflict, say why (scale or timing) and choose by NPV.
6Comment in context. Mention the assumptions, the margin of safety (IRR − cost of capital), risk, any capital rationing and the effect on shareholder wealth. Then recommend.

Quickest way: Fast NPV and IRR under time pressure

When to use it: Use when you have to compare projects quickly or when the IRR figure is only needed as a supporting measure.

Set out the cash flows in one row with years across the top. Put the NPV at the cost of capital first.
For IRR, pick a second rate by judgement. If the NPV at the cost of capital is small and positive, try a rate 3 to 5 points higher. Do not guess far away.
Interpolate with the formula, and round to one decimal place.
If projects conflict, do not calculate IRR for every project. Compare NPVs, and if asked about the conflict, find the incremental cash flows and their IRR.
Write the recommendation in one sentence tied to shareholder wealth, then add one or two caveats.

Common mistakes in NPV and IRR Investment Appraisal Rules

Choosing the project with the higher IRR when projects are mutually exclusive
A percentage looks like a better return, and students forget the size of the investment.
Fix: Rank on NPV. A smaller project with a higher IRR can add less wealth than a larger project with a lower IRR. Use the incremental IRR if asked.
Interpolating IRR using two rates that both give positive (or both negative) NPVs
Students stop at the first two rates they try.
Fix: Check that one NPV is positive and one is negative. If not, try another rate. Extrapolating outside the two rates gives a poorer estimate.
Treating the interpolated IRR as exact
The formula produces a precise-looking number.
Fix: Say it is an estimate, as the NPV curve is not a straight line. The closer the two rates, the better the estimate.
Assuming a non-conventional project has just one IRR
Students use the rule IRR > cost of capital without checking the sign pattern.
Fix: Count the sign changes in the cash flows. If there is more than one, say that multiple IRRs are possible and rely on NPV at the cost of capital.
Including financing costs, interest or sunk costs in the cash flows
Students copy every figure in the question into the appraisal.
Fix: Include only incremental future cash flows. The cost of finance is already in the discount rate.
Giving a calculation without a recommendation or comment
Students run out of time or treat the question as numbers only.
Fix: Always finish with a decision, link it to shareholder wealth, and add assumptions and risks. Professional skills marks reward this.

Worked examples

Example 1

A company with a cost of capital of 10% is considering a project with these cash flows ($000): Year 0: (1,000); Year 1: 400; Year 2: 500; Year 3: 450. Calculate the NPV at 10%, estimate the IRR using rates of 15% and 20%, and advise whether to accept the project.

Show the solution

NPV at 10%: 400 ÷ 1.10 = 363.64; 500 ÷ 1.21 = 413.22; 450 ÷ 1.331 = 338.09.
Total PV of inflows = 363.64 + 413.22 + 338.09 = 1,114.95. NPV = 1,114.95 − 1,000 = 114.95, so about $115,000.
NPV at 15%: 400 ÷ 1.15 = 347.83; 500 ÷ 1.3225 = 378.07; 450 ÷ 1.520875 = 295.89. Total = 1,021.79. NPV = +21.79.
NPV at 20%: 400 ÷ 1.20 = 333.33; 500 ÷ 1.44 = 347.22; 450 ÷ 1.728 = 260.42. Total = 940.97. NPV = −59.03.
IRR ≈ 15% + [21.79 ÷ (21.79 + 59.03)] × (20% − 15%) = 15% + 0.2696 × 5% = 15% + 1.35% = 16.35%, or about 16.3% to 16.4%.
The cash flows have one sign change, so there is a single IRR and the rules agree.

Answer: NPV at 10% is about +$115,000 and the IRR is about 16.3%, above the 10% cost of capital. Accept the project. It adds about $115,000 to shareholder wealth. The IRR is an interpolated estimate, and the result depends on the forecast cash flows.

Example 2

Two mutually exclusive projects have a one-year life and a cost of capital of 10%. Project P: outlay $100,000 at Year 0, inflow $125,000 at Year 1. Project Q: outlay $400,000 at Year 0, inflow $480,000 at Year 1. Calculate each project's NPV and IRR, explain the conflict, and recommend one.

Show the solution

P: IRR = 125,000 ÷ 100,000 − 1 = 25%. NPV = 125,000 ÷ 1.10 − 100,000 = 113,636 − 100,000 = $13,636.
Q: IRR = 480,000 ÷ 400,000 − 1 = 20%. NPV = 480,000 ÷ 1.10 − 400,000 = 436,364 − 400,000 = $36,364.
The IRR ranks P first (25% against 20%). The NPV ranks Q first ($36,364 against $13,636). This is a scale conflict. Q needs a larger investment, and its return is lower in percentage terms but larger in absolute value.
Check with incremental cash flows (Q − P): Year 0 = −300,000; Year 1 = +355,000. Incremental IRR = 355,000 ÷ 300,000 − 1 = 18.33%. This is above 10%, so the extra investment in Q is worthwhile.
Incremental NPV = 355,000 ÷ 1.10 − 300,000 = 322,727 − 300,000 = $22,727. This equals 36,364 − 13,636, confirming the result.

Answer: Choose Project Q. It has the higher NPV ($36,364 against $13,636), so it adds more to shareholder wealth, even though P has the higher IRR. The extra $300,000 invested in Q earns 18.33%, above the 10% cost of capital. This assumes no capital rationing. If funds are limited, the other projects available would need to be considered.

Exam tips

In AFM, state the decision rule and its link to shareholder wealth. Marks are given for the reasoning as well as the figures.
When asked to compare NPV and IRR, cover both strengths and weaknesses. Use points such as scale and timing conflicts, multiple IRRs and different reinvestment assumptions, and apply them to the scenario's cash flows.
If cash flows change sign more than once, say so early and show NPV at more than one rate if time allows. This supports your point about multiple IRRs.
Always add a closing recommendation with caveats. Mention the accuracy of forecasts, the discount rate and capital rationing. These show commercial judgement for the professional skills marks.
Keep the workings tidy: a cash flow table, discount factors and a labelled NPV for each rate. Part marks are given for method.

Practice questions from Discounted cash flow techniques

NPV and IRR Investment Appraisal Rules in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

NPV and IRR Investment Appraisal Rules: frequently asked questions

What is the difference between NPV and IRR in ACCA AFM?

NPV is the value added in money terms at the cost of capital. IRR is the discount rate at which NPV is zero, shown as a percentage. NPV is the preferred measure because it directly shows the change in shareholder wealth.

How do I calculate IRR in the AFM exam?

Calculate the NPV at two discount rates, one positive and one negative, then interpolate. Use IRR ≈ L + [NPV_L ÷ (NPV_L − NPV_H)] × (H − L). The answer is an estimate, so say so.

Why can NPV and IRR give different rankings?

They can differ for mutually exclusive projects when the projects have different sizes or different timing of cash flows. IRR ignores scale, and it implicitly assumes reinvestment at the IRR. NPV assumes reinvestment at the cost of capital, so it is the better guide.

What are multiple IRRs and when do they occur?

Multiple IRRs arise when a project's cash flows change sign more than once, for example a large cleanup cost at the end of a project's life. The number of IRRs can be up to the number of sign changes. In that case, use NPV at the cost of capital to decide.