NPV Calculator
Last updated: 27 June 2026
Reviewed by Gavin Meiring, Lead research and primary author · Doctoral Candidate (Corporate Governance) · Research and drafting assisted by AI
- Net present value is the gold standard of capital budgeting: discount all future cash flows back to today, subtract the cost, and if the answer is positive the project creates value.
- The technique was formalised by economist Irving Fisher in his 1930 book 'The Theory of Interest' — and its logic quietly governs everything from house purchases to corporate takeovers.
- NPV has a sharp edge over the IRR: it tells you how much value is created in dollars, not just as a percentage — so a 10% IRR on a $10 billion project beats a 40% IRR on a $1 million one, even though the rate looks worse.
NPV Calculator
A net present value (NPV) calculator determines whether an investment or project will generate value by discounting future cash flows back to today's pounds. It is used by businesses, investors, and analysts to evaluate capital projects, acquisitions, and any decision involving cash flows spread over time.
How to Use the NPV Calculator
- Enter the initial investment as a negative number in period zero.
- Enter the expected cash inflows (and any outflows) for each future period.
- Enter your discount rate, which typically represents your cost of capital or required rate of return.
- The calculator discounts each future cash flow back to its present value using the discount rate.
- It then sums all present values including the initial outlay. A positive NPV means the project creates value; a negative NPV means it destroys it.
The Formula
NPV = -Initial Investment + CF1/(1+r)^1 + CF2/(1+r)^2 + ... + CFn/(1+r)^n
Where CF1, CF2, CFn are the cash flows in each period, r is the discount rate per period, and n is the number of periods. The initial investment is typically a cash outflow and is therefore negative. The sum of all discounted cash flows plus the initial outflow gives the net present value.
Real-World Example
A company is considering a project requiring an initial investment of £80,000. It expects cash inflows of £25,000 in year 1, £30,000 in year 2, £35,000 in year 3, and £20,000 in year 4. The company's cost of capital is 10%.
Year 1: £25,000 / (1.10)^1 = £22,727 Year 2: £30,000 / (1.10)^2 = £24,793 Year 3: £35,000 / (1.10)^3 = £26,296 Year 4: £20,000 / (1.10)^4 = £13,660
Sum of present values = £87,476
NPV = £87,476 - £80,000 = £7,476
The positive NPV of £7,476 indicates that the project is expected to create value above the cost of capital and should be pursued, assuming the projections are reliable.
Choosing the Right Discount Rate
The discount rate is the most critical and subjective input in any NPV calculation. It should reflect the riskiness of the cash flows and the opportunity cost of capital. For a company, this is typically the weighted average cost of capital (WACC). For personal investment decisions, it might be the return available from the next best alternative. Using a rate that is too low makes bad projects look attractive; using one that is too high rejects good ones. Sensitivity analysis, where you recalculate NPV at several different rates, helps test how reliable the conclusion is to this key assumption.
Frequently Asked Questions
What is the difference between NPV and IRR? NPV tells you the absolute value created by an investment in today's pounds. IRR tells you the discount rate at which NPV equals zero. Both use the same discounted cash flow mechanics, but NPV is generally more reliable for project ranking because it considers the scale of investment.
Can NPV be negative? Yes. A negative NPV means the project is expected to return less than the required rate of return, destroying value. It should generally be rejected unless there are strategic reasons beyond the financial numbers.
What if cash flows are uncertain? NPV is only as good as the underlying projections. Scenario analysis and Monte Carlo simulation can be used to model a range of outcomes. Managers typically run NPV at base, optimistic, and pessimistic assumptions to understand the range of possible outcomes.
Should I always choose the project with the highest NPV? When comparing mutually exclusive projects, the one with the highest positive NPV is usually preferred, as it creates the most value. When projects have very different scales or timelines, additional metrics such as the profitability index (NPV divided by initial investment) can help with ranking.
The four years, line by line
The example above gives the present value of each year to the nearest pound. Carried out to the full discount factors, the same four years look like this.
| Year | Cash flow | Discount factor at 10% | Present value |
|---|---|---|---|
| 1 | £25,000 | 0.909091 | £22,727.27 |
| 2 | £30,000 | 0.826446 | £24,793.39 |
| 3 | £35,000 | 0.751315 | £26,296.02 |
| 4 | £20,000 | 0.683013 | £13,660.27 |
| Sum of the present values | £110,000 | £87,476.95 | |
| Less the initial outlay | £80,000.00 | ||
| Net present value | £7,476.95 |
Each discount factor is one divided by 1.10 raised to the year number. Year three is 1 divided by 1.331, which gives 0.751315. The initial outlay sits in period zero and is not discounted at all, which is why it is subtracted at the end rather than carried through the table.
The summary above prints £87,476 and £7,476 because it adds the four rounded present values: 22,727 plus 24,793 plus 26,296 plus 13,660 gives 87,476. Carrying the unrounded figures gives £7,476.95. Both routes agree to the nearest pound, and the difference of 95 pence is the accumulated rounding, not a disagreement about the method.
What the discount rate does to the answer
Nothing in the cash flows changes here. Only the rate moves.
| Discount rate | Present value of the inflows | Net present value | Decision |
|---|---|---|---|
| 5% | £97,708.77 | £17,708.77 | Accept, comfortably positive |
| 8% | £91,353.04 | £11,353.04 | Accept |
| 10% | £87,476.95 | £7,476.95 | Accept |
| 12% | £83,859.92 | £3,859.92 | Accept, but the margin is thin |
| 15% | £78,871.57 | minus £1,128.43 | Reject |
The rate at which the net present value falls to zero is 14.29%, and that figure is the internal rate of return for the same four cash flows. Below 14.29% the project adds value; above it the project destroys value. The consequences of getting the rate wrong are severe and asymmetric in feeling: a rise of five percentage points, from 10% to 15%, turns a decision to invest into a decision to refuse.
The two other measures from the same table
The same arithmetic supports two further figures, and both are worth having because each answers a question that the net present value does not.
| Measure | Calculation | Result | What it answers |
|---|---|---|---|
| Profitability index | £87,476.95 divided by £80,000 | 1.0935 | Value created per pound invested |
| Payback, undiscounted | The year in which the running cash total passes £80,000 | 2.71 years | How long the money is tied up |
| Payback, discounted | The year in which the running present value passes £80,000 | 3.45 years | The same, allowing for the time value of money |
The undiscounted payback passes £80,000 partway through the third year, since the first three years bring in £90,000. The discounted payback is slower: the present values reach £73,816.68 by the end of year three and cross £80,000 during the fourth year. The two figures differ by nearly nine months, and the discounted version is the one that belongs in a decision about money.
A profitability index of 1.0935 means the project returns about £1.09 of present value for every £1 committed. Where two projects compete for the same £80,000 and both have a positive net present value, the index gives a way to compare them when their sizes differ, which a bare net present value does not.
The timing convention that shifts the answer
The formula above discounts each cash flow from the end of its year. Most projects receive money through the year rather than in a single payment on the last day, and the mid-year convention corrects for that by discounting each flow from the middle of its period instead, which is an exponent of n minus 0.5.
Applied here, the mid-year convention lifts the net present value at 10% from £7,476.95 to £11,746.60, an uplift of £4,269.65. The project was already worth doing under the stricter assumption, so the convention does not change the decision. It does change the size of the margin, and a project close to the line can cross it purely on the choice of convention. The honest course is to state which convention was used rather than to present the more flattering one without a label.
Government appraisal takes a different route to the same problem. The Green Book sets a social time preference rate of 3.5% in real terms for the first 30 years of a project, falling to 3.0% for years 31 to 75 and 2.5% after that. The 3.5% is built from a pure time preference of 0.5%, an allowance for catastrophic risk of 1.0%, and a wealth effect of 2.0%, where the last of those reflects the expectation that future consumption will be higher than consumption today. On the same four cash flows, a real rate of 3.5% gives a net present value of £21,156.75, though the comparison is only fair if the cash flows themselves are stated in real terms.
Method and what the calculation assumes
Six conventions hold the arithmetic together, and each of them can be broken.
The rate must match the period. A rate quoted as an annual figure and applied to monthly cash flows gives an answer that is wrong by a large factor; the monthly rate that matches a 10% annual rate is not 10% divided by 12 unless the compounding convention says so.
The flows are cash, not profit. Depreciation, provisions for future costs and accrued income belong in an accounting result and not in this table. What counts is money moving in or out in the period named.
The outlay is a flow in period zero. It is entered as a negative number in the period before the first receipt, and it is not discounted, which is the same as discounting it by a factor of one.
Real rates go with real flows, and nominal rates with nominal flows. Mixing the two produces a figure that looks plausible and means nothing. Where the flows were estimated in today's prices, the rate should be a real one.
The rate is a single number standing for risk. It is the most subjective input in the calculation, and it is doing a great deal of work: it carries the cost of capital, the risk of the specific project and the opportunity cost of the funds all at once. A sensitivity table is the cheapest protection against being wrong about it.
The horizon ends where the table ends, and no value is assigned to anything after that. Where a project continues to generate cash beyond the last period shown, the omission understates the case, and the usual remedy is a terminal value stated as an explicit assumption rather than a number hidden in the final year.
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