How do you calculate NPV?
Net present value (NPV) is the value today of every cash flow a project produces, after taking off what it costs, with each future amount discounted for the time you wait for it. The formula is NPV = CF0 + CF1 / (1 + r) + CF2 / (1 + r)^2 + ... + CFn / (1 + r)^n. CF0 is the year 0 cash flow, usually the investment and therefore negative; CFt is the net cash flow at the end of year t; r is the discount rate, normally the cost of capital.
A positive NPV means the cash flows repay the investment and also beat the discount rate. A negative NPV means they fall short of it. That is the decision rule used in investment appraisal: at the cost of capital, a project with a positive NPV adds value and one with a negative NPV destroys it.
Worked example: an NPV answer laid out like an exam script
The calculator opens on a project that costs $100,000 today and brings in $30,000, $40,000, $50,000 and $20,000 at the end of years 1 to 4, discounted at 10%. On paper the answer is a four-column table, with each discount factor read from a present value table to three decimal places:
| Year | Cash flow | Factor at 10% | Present value |
|---|---|---|---|
| 0 | -$100,000 | 1.000 | -$100,000 |
| 1 | $30,000 | 0.909 | $27,270 |
| 2 | $40,000 | 0.826 | $33,040 |
| 3 | $50,000 | 0.751 | $37,550 |
| 4 | $20,000 | 0.683 | $13,660 |
| NPV | $11,520 |
The table method gives an NPV of $11,520. Unrounded factors (0.909091, 0.826446, 0.751315 and 0.683013) give $11,556.59, and that exact value is the headline above the chart. The calculator prints both, so you can check a textbook or practice answer line by line and still see the precise figure.
Why is the table NPV different from the exact NPV?
Rounding a factor to three decimals moves that year's present value by up to half a thousandth of the cash flow. On the default project all four rounded factors sit slightly below the exact ones, so the table total comes out $36.59 lower. On big numbers the gap grows: a factor that is off by 0.0005 on a $2 million cash flow shifts that year by $1,000.
Neither figure is wrong. The exact NPV is what a spreadsheet returns. The 3-decimal figure is what you get by hand from printed tables, such as the present value and annuity tables in ACCA's published formulae sheet, which cover 1% to 20% and 1 to 15 periods. Outside those limits the calculator still rounds its factors to three decimals, so the layout works the same way at 23.5% or over 20 years.
How do you calculate NPV when the cash flow is the same every year?
Use one annuity factor instead of discounting each year separately. The present value of 1 received at the end of each year for n years is (1 - (1 + r)^-n) / r. Multiply the yearly cash flow by that factor, then add the year 0 flow.
An example in pounds: a machine costs £250,000 and saves £70,000 a year for 5 years, with a 12% cost of capital. The 5-year annuity factor at 12% is 3.605 to three decimals (3.604776 unrounded). NPV = -£250,000 + £70,000 x 3.605 = £2,350 from the table, or £2,334.33 exact. The project only just clears 12%, and its IRR is 12.38%. Pick Same each year above to use this layout; the table then shows the single annuity line a written answer would use.
What about cash flows that grow each year?
When a cash flow rises at a steady rate g, the year t amount is the first-year amount x (1 + g)^(t - 1). The Growing tab builds those years and discounts each one. An example in euros: an outlay of €80,000, a first-year cash flow of €20,000 growing 3% a year for 6 years, and a 9% discount rate.
| Year | Cash flow | Factor at 9% | Present value |
|---|---|---|---|
| 1 | €20,000.00 | 0.917 | €18,340.00 |
| 2 | €20,600.00 | 0.842 | €17,345.20 |
| 3 | €21,218.00 | 0.772 | €16,380.30 |
| 4 | €21,854.54 | 0.708 | €15,473.01 |
| 5 | €22,510.18 | 0.650 | €14,631.61 |
| 6 | €23,185.48 | 0.596 | €13,818.55 |
Those present values add up to €95,988.67, so the table NPV is €15,988.67; the exact NPV is €16,008.54. A growing annuity also has a closed form, C1 / (r - g) x (1 - ((1 + g) / (1 + r))^n), which gives the same €96,008.54 present value for years 1 to 6 before the outlay comes off. These flows have an IRR of 15.28%.
How do you calculate NPV in Excel or Google Sheets?
Excel's NPV function treats every value it receives as arriving at the end of a period, starting one period after today. Microsoft's help page says a cost at the start of the first period has to be added to the result, not included in the values. So with year 0 in B1 and years 1 to 4 in B2:B5, the correct formula is =NPV(10%, B2:B5) + B1, which returns 11,556.59 for the default project.
The usual error is =NPV(10%, B1:B5). That pushes the whole project one year later, so the investment gets discounted too and the result is 10,505.99, the right answer divided by 1.10. Google Sheets uses the same argument order, NPV(discount, cashflow1, ...), and calls cashflow1 the first future cash flow, so the same fix applies there.
For cash flows on real calendar dates, use XNPV(rate, values, dates). It discounts each amount by its exact number of days from the first date on a 365-day year, so it differs slightly from the yearly NPV even for flows twelve months apart, because some years have 366 days.
How do you work out NPV on a BA II Plus or another financial calculator?
The Texas Instruments guidebook for the BA II Plus puts uneven cash flows in its Cash Flow worksheet. For the default project: press CF, then 2nd and CLR WORK to clear old entries. Key 100000, press +|- and ENTER, so CFo shows -100,000. Press the down arrow, key 30000 and ENTER for C01, then the down arrow again; F01 shows 1, the number of years that amount repeats. Enter 40000, 50000 and 20000 the same way. Then press NPV, key 10 and ENTER for I, press the down arrow and CPT. For this project the display reads 11,556.59, the same NPV this page works out above.
The frequency entry saves time on level cash flows: £70,000 for five years is one entry with F01 set to 5. HP models such as the 10bII+ and 12C, and the Sharp EL-738, follow the same pattern of a year 0 entry, later entries with a repeat count, a rate and a compute key, but the key names and order differ by model. Follow the cash-flow chapter of your own calculator's manual; this page does not reproduce those makers' keystrokes.
How does each input change the NPV?
Discount rate. NPV falls as the rate rises, because later cash is worth less today. The default project is worth $40,000 at 0%, $24,498.54 at 5%, $11,556.59 at 10%, $643.58 at 15% and -$8,641.98 at 20%. The chart beside the result plots this NPV profile and marks where it crosses zero, at the IRR of 15.32%.
Timing. Earlier cash is worth more even when the total is unchanged. Reverse the four inflows to $20,000, $50,000, $40,000 and $30,000 and the NPV at 10% drops to $10,047.13, which is $1,509.46 less for the same $140,000 of cash. The outlay. Each extra dollar spent at year 0 cuts NPV by exactly one dollar, since year 0 is never discounted. Project length. Extra years add less and less: at 10% the factor falls to 0.386 by year 10 and 0.239 by year 15.
Common NPV mistakes
- Discounting year 0. The investment happens today, so its factor is 1.000.
- Putting the outlay inside the spreadsheet NPV function. Add it outside, as shown above.
- Mixing real and money rates. Cash flows that include inflation need a money (nominal) rate; flows in today's prices need a real rate. The Fisher formula links them: (1 + money rate) = (1 + real rate) x (1 + inflation rate).
- Counting sunk costs or depreciation. Only future incremental cash flows count. Depreciation is not cash, although the tax relief on it is.
- Forgetting money that comes back at the end. A scrap value or released working capital belongs in the final year's row.
- Reading an NPV as certain. It is only as good as the cash flow estimates and the rate behind it.
What this NPV calculator leaves out, and a short glossary
It works on the cash flows and the single rate you enter. Tax, capital allowances, inflation, working capital and risk all change real projects, and each needs its own row or its own rate. Cash is assumed to arrive at year ends, and the rate is assumed to be the right hurdle; to estimate a cost of capital, see the WACC calculator. The answer is arithmetic on assumptions, not a forecast that the cash will arrive.
Discount factor: 1 / (1 + r)^t, the value today of 1 received in year t. Annuity factor: the sum of the discount factors for years 1 to n. Cost of capital: the return the providers of finance require, used as the discount rate. IRR: the rate at which NPV is zero. Profitability index: the present value of the future cash flows divided by the initial investment, 1.116 on the default project.
Frequently asked questions
How do you calculate NPV by hand?
Multiply each year's cash flow by its discount factor, 1 / (1 + r)^t, add the results and subtract the investment at year 0. With factors from a 3-decimal table, a $100,000 project returning $30,000, $40,000, $50,000 and $20,000 has an NPV of $11,520 at 10%. With unrounded factors it is $11,556.59.
Why does Excel give a different NPV from my written answer?
There are two usual causes. Your written answer used factors rounded to three decimals, which moves the total slightly, or the Excel formula included the year 0 investment inside NPV(), which discounts everything one year too far. Use =NPV(rate, years 1 to n) plus the year 0 cell.
Is a positive NPV always worth accepting?
In theory, a positive NPV at the cost of capital means the project adds value. In practice the answer depends on how reliable the cash flow estimates are, whether capital is limited, and whether the project competes with another one, in which case the higher NPV is normally preferred.
What discount rate goes into an NPV calculation?
Normally the cost of capital: the return that lenders and shareholders require, often estimated as a weighted average cost of capital. A project that is riskier than the business as a whole may justify a higher, risk-adjusted rate.
What is the difference between NPV and IRR?
NPV is an amount of money: the value added at a chosen rate. IRR is a percentage: the rate at which NPV would be zero. For the default project the NPV at 10% is $11,556.59 and the IRR is 15.32%, so both say the project beats a 10% cost of capital.
How do I include a scrap value or working capital?
Add them to the rows for the years they happen. Working capital paid in at the start is an outflow at year 0, and the same amount coming back at the end is an inflow in the final year, alongside any scrap or resale value.
Can I use monthly cash flows?
Yes, as long as the rate matches the period. Enter each month as a row and use a monthly rate: a 10% annual rate is (1.10)^(1/12) - 1, or 0.7974% a month. Each row then stands for a month, although the table still labels it a year.
What is the difference between NPV and XNPV in Excel?
NPV assumes equal periods, with the first value one period from now. XNPV takes a date for every cash flow and discounts each one by its exact number of days on a 365-day year, measured from the first date, which suits irregular timing.
Why does the calculator show two NPV figures?
The headline uses exact discount factors, the figure a spreadsheet returns. The table and the first tile use factors rounded to three decimals, the figure you reach by hand from printed tables. The gap is usually small, $36.59 on the default project.
Can I calculate NPV in pounds, euros or dirhams?
Yes. Choose any of 24 currencies; symbols, separators and decimal places change, and nothing is converted. Amounts typed in the year-by-year list stay exactly as entered when you switch currency.
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See what the course coversSources and review
Last reviewed 13 November 2026 by the NIFM Academy editorial team. Next review by 13 November 2027.
- ACCA, Financial Management (FM) formulae sheet and maths tables (accaglobal.com, file S23_FM_Formulae.pdf, the version linked from the FM exam formulae and maths tables page), present value table (1 + r)^-n and annuity table (1 - (1 + r)^-n) / r, factors printed to 3 decimal places for rates of 1% to 20% and 1 to 15 periods. Checked 14 November 2026.
- Microsoft Support, NPV function, values occur at the end of each period and the investment begins one period before value1; a cost at the start of the first period is added to the result, not included in the values. Checked 13 November 2026.
- Microsoft Support, XNPV function, XNPV(rate, values, dates); payments after the first are discounted on a 365-day year. Checked 13 November 2026.
- Google Docs Editors Help, NPV function for Google Sheets, NPV(discount, cashflow1, ...), cashflow1 being the first future cash flow. Checked 13 November 2026.
- Texas Instruments, BA II PLUS guidebook (online edition), Cash Flow worksheet, CFo, Cnn, Fnn, I, NPV and IRR variables, clearing with 2nd CLR WORK, up to 24 cash flows after CFo, NPV computed with CPT. Checked 13 November 2026.