Net present value (NPV) discounts every future cash flow of a project back to today at the business’s required rate of return and adds them up; a positive NPV means the project earns more than that rate. The internal rate of return (IRR) is the discount rate at which the NPV is exactly zero. Both use the same cash flows, but where they disagree on which of two projects to choose, NPV is the measure to rely on.
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What does net present value actually measure?
A pound received in three years is worth less than a pound today, because today’s pound could be invested, used to repay debt or spent now. Discounting converts future cash into today’s money so that an outlay now can be compared fairly with savings or income that arrive over several years. NPV is the total of those discounted amounts, with the initial outlay entered as a negative figure at time zero.
The result is an absolute amount in pounds. An NPV of £6,000 means that, after recovering the outlay and earning the required return on it, the project is expected to add about £6,000 of value in today’s money. ACCA’s Financial Management syllabus treats NPV as the most important of the four standard appraisal methods (payback, accounting rate of return, NPV and IRR), in practice as well as in the exam.
The same arithmetic appears in the accounting standards. FRS 102 paragraph 27.15 defines value in use, which is used when testing assets for impairment, as the present value of the future cash flows expected from an asset, found by estimating those cash flows and applying an appropriate discount rate.
How do you calculate NPV step by step?
- List the relevant cash flows. Only future, incremental cash counts: extra sales receipts, cost savings, the purchase price, extra working capital, and any sale proceeds at the end. ACCA calls this the golden rule. Money already spent on research is a sunk cost and is left out, and so are apportioned overheads that would be incurred anyway.
- Leave out financing costs. Interest and loan repayments are excluded because the cost of finance is already reflected in the discount rate. Counting interest as well would charge for the money twice.
- Time each flow. The usual convention puts the outlay at time 0 and treats each year’s operating cash as arising at the end of that year.
- Discount. Multiply each flow by 1 divided by (1 + r) raised to the power of the year number, where r is the required return.
- Add up. The total is the NPV. Accept the project if it is positive, reject if negative.
Working capital needs care. An increase in stock or debtors is a cash outflow when it happens, and the same amount normally comes back as an inflow when the project ends, so it costs the time value of the money tied up.
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How do you choose the discount rate?
The rate should reflect what the business could earn elsewhere at similar risk, or what its finance costs, whichever is higher. A larger company often uses its weighted average cost of capital. An owner managed business more often sets a hurdle rate that sits comfortably above its borrowing rate, with a higher rate for riskier projects such as a new product line than for a like for like replacement.
For comparison, HM Treasury’s Green Book (2026) discounts public sector projects at a social time preference rate of 3.5% in real terms for years 1 to 30, falling to 3% for years 31 to 75. That is a public policy rate, not a commercial one. Energy efficiency guidance for the Energy Savings Opportunity Scheme uses 6% as a typical commercial rate in its worked example and notes that the rates companies use vary widely.
Inflation must be treated consistently. Either inflate the cash flows and use a money (nominal) rate, or keep everything in today’s prices and use a real rate. The two are linked by the Fisher formula: (1 + money rate) = (1 + real rate) × (1 + inflation rate). ACCA recommends the money method whenever different cash flows inflate at different rates or tax is involved. The Green Book makes the same point from the other side: its real rate must only be applied to real cash flows, and adding the inflation rate to the discount rate gives a mathematically incorrect answer.
What is the internal rate of return and how is it found?
The IRR is the discount rate that makes the NPV equal to zero. It answers a slightly different question: what return does this project earn on the money tied up in it? If the IRR exceeds the hurdle rate, the project is acceptable, which for a normal project (outlay first, inflows afterwards) gives the same accept or reject answer as NPV.
Spreadsheets calculate IRR directly. By hand, the usual method is linear interpolation. Calculate the NPV at two rates, one giving a positive answer and one a negative answer, then estimate:
IRR ≈ low rate + (high rate minus low rate) × NPV at low rate ÷ (NPV at low rate minus NPV at high rate)
Because the true relationship between rate and NPV is curved, interpolation is only an approximation, and the wider the gap between the two trial rates, the less accurate it is.
What does a worked example look like?
Illustration only. A company is considering a machine costing £50,000 that will save £15,000 of cash a year for five years, with no value at the end. Its hurdle rate is 10%.
| Year | Cash flow (£) | Factor at 10% | Present value (£) |
|---|---|---|---|
| 0 | (50,000) | 1.000 | (50,000) |
| 1 to 5 | 15,000 a year | 3.791 (cumulative) | 56,862 |
| NPV | 6,862 |
At 20% the cumulative factor for five years is 2.991, giving a present value of £44,859 and an NPV of minus £5,141. Interpolating: 10% + 10% × 6,862 ÷ (6,862 + 5,141) ≈ 15.7%. The exact IRR, from a spreadsheet, is about 15.2%, which shows the interpolation error. Either way the project clears the 10% hurdle.
Why can NPV and IRR rank projects differently?
Suppose the same company could instead spend £10,000 on a smaller project returning £13,000 after one year. Its IRR is 30%, double the machine’s, but its NPV at 10% is only £1,818. If only one can be chosen, IRR points to the small project and NPV to the machine. NPV is the better guide, because it measures the value added in pounds; a high percentage return on a small sum can be worth less than a lower percentage on a larger one.
IRR has other known weaknesses:
- Projects whose cash flows change sign more than once, such as those with large decommissioning or reinstatement costs at the end, can have more than one IRR, or none.
- IRR implicitly assumes interim cash can be reinvested at the IRR itself, which may be unrealistic for a very high return project.
- It ignores scale and, on its own, says nothing about how long the money is at risk.
IRR is still popular because a percentage is easy to compare with a borrowing rate. A sound approach is to report both, and decide on NPV.
How should tax and capital allowances be included?
For a company, extra profits attract corporation tax and qualifying capital spending attracts capital allowances, so both belong in the cash flows. gov.uk currently states that the small profits rate is 19% on profits up to £50,000 and the main rate is 25% above £250,000, with marginal relief between. Relief from the annual investment allowance or full expensing can bring much of the tax saving on plant into the first year, which improves the NPV compared with relief spread over many years. Model the tax at the time it is actually paid, not when the profit is earned. The accounting standard takes a different line for impairment: FRS 102 paragraph 27.18 excludes tax and financing flows from value in use and paragraph 27.20 requires a pre tax discount rate, so do not reuse an impairment model for a tax affected investment decision without adjusting it.
What mistakes come up most often?
- Using accounting profit instead of cash, so that depreciation is deducted and the asset cost is counted twice.
- Deducting interest as well as discounting at a rate that already includes the cost of borrowing.
- Mixing a real discount rate with inflated cash flows, or the reverse.
- Forgetting working capital, or forgetting to release it at the end.
- Including sunk costs or reallocated overheads that would be incurred anyway.
- Treating one NPV figure as certain. The inputs are forecasts, so test them with scenario and sensitivity analysis and set the result alongside the simpler payback period where cash is tight.
Investment appraisal is a decision tool, not a figure in the statutory accounts, but the cash flow forecasts behind it should tie back to the business’s own cash flow forecast and budget so that the assumptions are consistent.
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Related Accountapedia entries
- Weighted average cost of capital (WACC)
- Lease or buy: comparing the cost
- Residual income vs ROI for divisions
- Calculating value in use
- Business valuation methods
Sources
- ACCA: Advanced investment appraisal
- GOV.UK: The green book 2026
- GOV.UK: Appendix c advice for complying with esos
- Financial Reporting Council: FRS 102 September 2024 tmKYWO6
- GOV.UK: Corporation tax rates
Reviewed by Christine Anderson, Broker, Solar Protect. Last reviewed 8 October 2026. Part of Accountapedia, the Solar Protect guide to UK tax and accounting. This page is general information, not personalised advice.