NPV Calculator – What Future Cash Is Worth in Today’s Money
A project that pays you $14,000 over three years sounds better than one that pays $10,000 today — until you price the wait. Net present value does that pricing: it shrinks every future cash flow by your discount rate, adds what is left, and tells you in one honest number whether the deal creates value or quietly destroys it. Enter the rate and each year’s cash flow — the first row is the money that moves today — and every discounted flow is laid out underneath, so the answer never has to be taken on faith.
The rate and the cash flows
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The verdict, in today’s money
The full picture
What this means
At a 10% discount rate this series clears the bar: the future cash flows are worth $1,307.29 more in today’s money than the $10,000.00 they cost to set in motion. In plain terms, the deal pays its way and leaves $1,307.29 of value on the table for you — over and above the 10% a year you demanded for waiting.
How to read the index. The profitability index divides the present value of everything that comes back by what goes out at the start. Above 1.00 the deal creates value, at exactly 1.00 it breaks even in today’s money, and below 1.00 it falls short — the same verdict as the NPV sign, expressed per dollar instead of in dollars.
- Net present value shrinks every future cash flow by one plus the rate, raised to its year, then adds what survives — the price of waiting, stated as a percentage.
- The default series pays out $10,000 today and receives $3,000, $4,200 and $6,800 over three years at 10%, giving an NPV of $1,307.29 and a profitability index of 1.13.
- The rate is an argument, not a fact: the same series gives $2,540.76 at 5% and thins to $255.61 at 15%, flipping negative by 20%.
- Every flow, shrunk to today’s money
- How it works, in 3 steps
- How each figure is worked out
- Deep dives
- Four rates, one series — and a verdict that flips twice
- The variation table, at a glance
- Reading the verdict, and the index that patches its blind spot
- Three mistakes the table catches
- NPV questions, answered
Every flow, shrunk to today’s money
The calculation, line by line. Each future amount is divided by (1 + rate) raised to its year — that divisor is the discount factor — and what survives the shrinking is its present value. Add the present values and the NPV falls out; nothing is hidden inside a single formula.
| Year | Cash flow | Discount factor | Present value |
|---|---|---|---|
| Year 0 · today | -$10,000.00 | 1.0000 | -$10,000.00 |
| Year 1 | $3,000.00 | 0.9091 | $2,727.27 |
| Year 2 | $4,200.00 | 0.8264 | $3,471.07 |
| Year 3 | $6,800.00 | 0.7513 | $5,108.94 |
| Net present value | $4,000.00 | — | $1,307.29 |
The middle column of the totals row is deliberately blank: discount factors belong to single years, not to sums. The $4,000.00 beside it is the undiscounted total — what the flows add up to if you ignore time completely — and the gap between it and the NPV is the price of the wait.
How it works, in 3 steps
List the flows, in order
Write down what moves, year by year, starting with today. Year 0 is the money that changes hands now — for a project, the build cost or purchase price, entered negative. Each year after that gets one row: what comes in positive, what goes out negative. Add rows until the last flow is on the list.
Set the discount rate
The rate is the yearly return you could demand elsewhere — your cost of capital, the rate on the loan funding the project, or the hurdle your firm sets. It is the price of waiting, stated as a percentage, and it decides how hard each future flow gets shrunk on its way back to today.
Read the verdict, then stress it
A positive NPV means the flows are worth more today than they cost — the deal clears your bar. Then do what every analyst does: nudge the rate up and down and watch when the verdict flips. A deal that only survives at exactly your rate deserves a harder look than one still standing at twice it.
How each figure is worked out
The default, worked through. Pay out $10,000 today, then receive $3,000, $4,200 and $6,800 over the next three years, discounted at 10%. Year 1: $3,000 ÷ 1.1 = $2,727.27. Year 2: $4,200 ÷ 1.21 = $3,471.07. Year 3: $6,800 ÷ 1.331 = $5,108.94. The three future flows, shrunk to today, are worth $11,307.29; set against the $10,000 that starts them, the net present value is +$1,307.29. Notice that the raw flows add up to $14,000 coming back — a $4,000 surplus on paper. Discounting removes $2,692.71 of that surplus as the price of waiting three years for the last of it.
The profitability index. Divide the present value of the future flows by the size of the starting outlay: $11,307.29 ÷ $10,000 = 1.13. Every dollar committed today brings back $1.13 of present value. The index and the NPV always agree on the verdict — 1.00 is exactly the border where NPV is zero — but the index speaks in ratios, which makes it the fairer way to compare a small project against a large one.
Why year 0 is never discounted. Its discount factor is (1 + r) raised to the power zero, which is 1: money that moves today is already in today’s money. That is also why the order of the rows matters and the calculator never sorts them — a flow dragged a year earlier or later is a different deal, not a tidier one.
Deep dives
Time eats money at a compounding pace. At 10% a year, a dollar due in one year is worth 90.9 cents today. In five years it is worth 62.1 cents, in ten years 38.6 cents, and in twenty years just 14.9 cents. The shrinking is not linear — each year multiplies by the same factor, so distant flows fade fast. That is why the last row of a long project can look enormous on paper and still contribute little to the verdict, and why pushing a payment one year further out always costs more than the year before did.
Which means the rate is an argument, not a fact. Run the calculator’s default series at different rates and the verdict moves with it: at 5% the NPV is $2,540.76, at 15% it thins to $255.61, and by 20% it has flipped to -$648.15 — the same cash flows, three different answers, all of them arithmetically correct. The discount rate smuggles in your judgement about risk and opportunity: a safe, bond-like flow deserves a low rate; a speculative one earns a high rate or a sceptical haircut to the flows themselves. Anyone presenting you an NPV owes you the rate it was computed at — without it, the number is decoration.
The honest habit is sensitivity. Compute the NPV at your expected rate, then at a rate a few points higher that prices in things going wrong, and note the rate where the answer crosses zero. That crossing point is the project’s internal rate of return, and the distance between it and your rate is the project’s margin for error, stated as a single percentage.
NPV is blind to scale. A project that turns $1,000 into an NPV of $300 and a project that turns $1,000,000 into an NPV of $3,000 can both be “positive”, and if you can only pick one, raw NPV points at the bigger one — which is correct if capital is unlimited and wrong when it is not. The profitability index patches this by pricing value per dollar committed: the small project scores 1.30, the giant 1.003, and ranked by index the small one wins the scarce capital. The two tools are not rivals; they answer “how much value?” and “how efficiently?” respectively, and serious appraisals quote both.
NPV quietly assumes the in-between money works. The maths treats every interim flow as if it could be reinvested at the discount rate the moment it arrives. If your realistic reinvestment rate is lower — because the cash will sit in a deposit account — the true return lands somewhere between the NPV story and a more conservative one. This is the same assumption that makes the internal rate of return flattering on projects with big early inflows, and it is a reason to treat all these figures as a comparison language rather than a promise.
And NPV prices only what you typed. Flexibility — the option to expand a hit product, abandon a failing one, or delay a launch — has real value that never appears in a cash flow row. Two projects with identical NPVs are not identical if one can be walked away from cheaply and the other cannot. The calculator gives you the arithmetic floor of the decision; the strategic value sits on top of it, and no formula on this page pretends otherwise.
Four rates, one series — and a verdict that flips twice
The default, year by year. The series is −$10,000 today, then $3,000 in year 1, $4,200 in year 2 and $6,800 in year 3, at a 10% discount rate. Each future dollar is worth less today by a factor of 1 ÷ 1.10 for every year it must wait: year 1’s $3,000 is worth $3,000 × 0.9091 = $2,727.27, year 2’s $4,200 is worth $4,200 × 0.8264 = $3,471.07, and year 3’s $6,800 is worth $6,800 × 0.7513 = $5,108.95. The present value of the future flows is the sum, $11,307.29; subtract the $10,000 cost and the NPV is $1,307.29, with a profitability index of 1.13 — each dollar invested returns $1.13 in today’s money. The undiscounted total is $4,000 ($3,000 + $4,200 + $6,800 − $10,000), and the gap between $4,000 and $1,307.29 is exactly the price of waiting three years at 10%.
At 0%, waiting is free — and the answer is the undiscounted total. Set the rate to 0% and every discount factor becomes 1.0000, so the present value of the future flows is the plain sum $14,000, the NPV is $4,000 and the index is 1.40. The 0% case is the calculator’s honesty check: it proves the discounting is the only thing standing between the $4,000 headline and the $1,307.29 verdict, and it is the case to run whenever an NPV looks surprising, because any series whose 0% NPV does not equal its undiscounted total has a typing error in it. No real project discounts at 0% — money always has a price — but the boundary case is where the arithmetic shows its working.
At 5% the project looks twice as good; at 15% it barely clears the bar. Lower the rate to 5% and the present value rises to $12,540.76, the NPV to $2,540.76 and the index to 1.25 — nearly double the default’s NPV from a five-point rate change. Raise it to 15% and the figures fall to $10,255.61, $255.61 and 1.03: still positive, but a verdict that a single delayed payment or a slightly higher cost of capital would overturn. The year-by-year table at 15% shows why: the factors are 0.8696, 0.7561 and 0.6575, so year 3’s $6,800 — the largest flow — is worth only $4,471.11 today, and the back-loaded shape of this series is precisely what a high rate punishes. Two projects with the same undiscounted total and different shapes are different projects, and the rate is what reveals it.
The same series, one smaller flow, a negative verdict. Keep the rate at 5% but cut the final flow from $6,800 to $3,000, and the present value falls to $9,258.18, the NPV to −$741.82 and the index to 0.93 — while the undiscounted total is still positive at $200 ($3,000 + $4,200 + $3,000 − $10,000). This is the case that teaches the whole calculator: a project can take in more than it spends and still destroy value, because the money arrives late and the discount rate charges for the wait. The index says it plainly — $0.93 back for each dollar invested in today’s money — and no rearrangement of the undiscounted figures rescues it. When someone quotes you a project’s total inflows, ask for the timing; the timing is the verdict.
The variation table, at a glance
Each row uses the default series (−$10,000, $3,000, $4,200, $6,800) unless the row says otherwise.
| Variation | Present value of future flows | NPV | Profitability index |
|---|---|---|---|
| Rate 0% | $14,000.00 | $4,000.00 | 1.40 |
| Rate 5% | $12,540.76 | $2,540.76 | 1.25 |
| Rate 10% (default) | $11,307.29 | $1,307.29 | 1.13 |
| Rate 15% | $10,255.61 | $255.61 | 1.03 |
| Rate 5%, final flow $3,000 | $9,258.18 | −$741.82 | 0.93 |
Read the table down the NPV column and the sensitivity is stark: five points of rate move the verdict by roughly $1,200 in either direction, and one flow cut of $3,800 moves it by more than $3,200 at the same rate. The rate and the late flows are the two levers that matter; everything else is commentary.
Reading the verdict, and the index that patches its blind spot
What the verdict actually claims. A positive NPV says the future flows, priced at today’s money, exceed the cost of setting them in motion — nothing more. It does not say the project is the best use of the money, the least risky use, or the use that returns the most per dollar: NPV is blind to scale. Consider two projects: one that turns $1,000 into $1,100 of present value and one that turns $1,000,000 into $1,001,000 of present value. That is why the calculator prints the profitability index beside the NPV: the index divides the present value of the inflows by the cost, so 1.13 means $1.13 back per dollar, 1.03 means $1.03, and 0.93 means $0.93. When two projects compete for the same capital, rank by the index; when one project stands alone, the NPV’s sign is enough.
Why the discount rate is a judgement, not a fact. Every figure in the variation table comes from the same series, and the only input that moves between the first four rows is the rate — yet the NPV ranges from $4,000 to $255.61. The rate is the price of waiting, and its honest value depends on what the money would otherwise earn: a risk-free return for a safe series, a higher rate for a risky one, the firm’s cost of capital for a corporate project. There is no rate printed on the cash flows themselves, which means two honest analysts can run the same series and reach different verdicts, and the difference is entirely in the rate they chose. The calculator’s job is to make that sensitivity visible — run the series at two or three rates, watch the verdict move, and notice how close to zero it gets — not to certify one rate as correct. A verdict of $255.61 at 15% is not “barely positive”; it is a verdict that changes sign if the rate rises a little further, and that fragility is itself information.
The table is the audit trail. The year-by-year table is not decoration: it is where an NPV error is found. Each row shows the flow, its discount factor and its present value, and the present values sum to the headline — at 15%, $2,608.70 + $3,175.80 + $4,471.11 = $10,255.61, and $10,255.61 − $10,000 = $255.61. If a flow was mistyped, the row shows it; if a year was skipped, the factors show it; if the rate was entered as 15 instead of 0.15, every factor collapses and the table shows that too. The page accepts rates as percentages (10 means 10%, not 1,000%), and the table is the place to confirm the entry did what you meant. A calculator that hides its intermediate steps asks to be trusted; this one shows them, so it can be checked instead.
What NPV cannot see. NPV prices the flows you enter and nothing else: it does not know about the option to expand, abandon or delay the project, the strategic value of entering a market, the risk that a late flow never arrives, or the tax treatment of the flows. A negative NPV does not always mean “do not do it” — it means “on these flows, at this rate, the project destroys value” — and the gap between those two sentences is where judgement lives. What NPV does, better than any single alternative, is force the timing into the open: the undiscounted total flatters every back-loaded project, and discounting is the correction. Use it for that, use the index for ranking, and let the things it cannot see be decided elsewhere, explicitly, rather than smuggled into the rate.
Three mistakes the table catches
Entering the rate as a decimal. This page takes the rate as a percentage: 10 means 10%, not 1,000%. Enter 0.1 meaning “ten percent” and the calculator faithfully reads it as one tenth of one percent — the present value becomes $13,968.26 and the NPV $3,968.26, nearly the undiscounted figures, because at 0.1% waiting is almost free. The year-by-year table exposes the error at once: the discount factors sit at 0.9990, 0.9980 and 0.9970 instead of 0.9091, 0.8264 and 0.7513, and any factor that close to 1.0000 for a multi-year flow is a rate entered in the wrong units. The fix is one keystroke — 10, not 0.1 — but the check is the table, because the headline alone ($3,968.26) looks like a plausible, even attractive, verdict.
Forgetting Year 0. Delete the −$10,000 cost row, leaving only the three inflows, and the NPV becomes $11,307.29 — the present value of the future flows standing alone, overstated by exactly the $10,000 that was forgotten — while the profitability index collapses to a dash, because there is no cost left to divide by. The dash is the tell: an index that cannot be computed means the series has no investment in it, and a series with no investment is not a project but a wish list. Whenever the index shows a dash, or the NPV equals the present value of the inflows to the dollar, check that Year 0 is present and negative. The calculator treats a blank flow as zero, so a missing cost row and a deliberately zero cost row look identical — only the table, and the dash, distinguish them.
Comparing NPVs computed at different rates. The variation table’s first four rows are the same series at four rates, and their NPVs run from $4,000 down to $255.61 — a range wider than most projects’ entire NPV. Comparing one project’s NPV at 5% with another’s at 10% is therefore meaningless: the comparison measures the rates, not the projects. The rule is simple and non-negotiable — one rate for every project in a comparison, chosen before the numbers are run, and the sensitivity shown separately by re-running all of them at a second rate. A ranking that survives two rates is a ranking worth acting on; a ranking that flips when the rate moves was never a ranking at all, only a rate difference in disguise.
NPV and IRR together: why both matter
IRR, the discount rate at which NPV is zero, is a useful companion to NPV because it expresses the verdict as a rate rather than a money amount. A project with NPV of $30,000 at an 8% discount rate and an IRR of 12% beats the hurdle by 4 percentage points. But IRR has traps NPV does not: non-conventional cash flows, with sign changes more than once, can produce multiple IRRs or none, and IRR assumes interim cash flows are reinvested at the IRR itself, which is often unrealistic.
Report both, and let NPV decide when they conflict. NPV measures value created in money terms at a stated rate, which is the question a decision-maker actually asks, while IRR measures the rate at which value creation stops, which is a useful sensitivity check.
Terminal value: the assumption that swallows the project
For long projects, the terminal value, the value assumed at the end of the explicit forecast period, often exceeds the present value of all the forecast cash flows combined. That makes the whole verdict depend on one assumption, usually a perpetual growth rate or an exit multiple, and a small change in that assumption can flip the decision.
Handle terminal value transparently: state the assumption, test the verdict without terminal value, and test it at lower growth rates. A project that only passes because of a heroic terminal value is not a good project; it is a forecast with a project attached.
Nominal, real, and the inflation trap
Cash flows and discount rates must both be nominal, including inflation, or both real, excluding it. Mixing them is the commonest NPV error after bad forecasts: nominal cash flows discounted at a real rate understate present value, and real cash flows discounted at a nominal rate overstate it. If inflation is 3% and the nominal rate is 10%, the real rate is roughly 6.8%, not 7% exactly, though the approximation is close enough for most decisions.
State which basis you are using at the top of any NPV calculation, so a reader can check the consistency without reconstructing your assumptions.
NPV questions, answered
What is net present value (NPV)?
Net present value is the value of a series of future cash flows translated into today’s money, minus what it costs to start. Each future flow is discounted — shrunk by the discount rate for every year it is away — and the shrunk values are added to the starting flow, which needs no shrinking because it moves today. A positive NPV means the deal returns more, in today’s money, than it costs; zero means it exactly breaks even once the wait is priced; negative means it hands back less than it takes, however impressive the raw totals look.
How do you calculate NPV?
For each cash flow, divide the amount by (1 + discount rate) raised to the number of years from today, then add all the results together, including the year-0 flow at full value. A $6,800 flow three years out at 10% divides by 1.331 and is worth $5,108.94 today. This calculator does exactly that, row by row — the table under it shows every division, so any figure on the page can be checked with a pocket calculator.
What is a good NPV?
Any NPV above zero is good in the strict sense: the project pays back its starting cost and beats the return built into your discount rate. How far above zero it needs to be is a judgement call — a bigger cushion means more room for forecasts to be wrong. When projects compete for limited money, compare profitability indexes as well: an index of 1.13 creates the same value per dollar whether the project is small or large, while raw NPV always favours the bigger project.
What discount rate should I use for NPV?
Use the return you genuinely give up by choosing this project: for a company, its weighted average cost of capital or an internal hurdle rate; for a personal investment, the return on the realistic alternative — a bond yield, an index fund’s expected return, or the interest rate on debt you could pay down instead. Riskier flows deserve a higher rate. Because the answer moves with the rate, honest appraisals test a range: the default series on this page is worth $2,540.76 at 5%, $1,307.29 at 10% and -$648.15 at 20%.
What is the difference between NPV and IRR?
IRR is the discount rate at which a series of flows has an NPV of exactly zero — for the default series here, about 16.34%. NPV answers in money: how much value, in today’s dollars, the deal creates above your required return. IRR answers in percent: the yearly rate the flows themselves imply. The two usually agree on yes-or-no for a single project, but they can rank competing projects differently, because a percentage ignores scale — a 40% return on $100 is $40, and a 15% return on $10,000 is $1,500. When they disagree, NPV is the safer referee.
Can this calculator handle monthly flows or a flow part-way through?
Yes, with one adjustment: the rows are periods, not necessarily years. For monthly flows, enter the monthly discount rate — a yearly rate divided by 12 is the usual shortcut — and read each row as a month. What the maths requires is that every row is the same distance apart and the rate matches that distance. A single flow arriving off-schedule, halfway between two rows, has no exact row of its own; the common, honest fix is to place it in the nearer period and know the answer is a close approximation rather than exact.
Why does the same project look twice as good at 5% as at 10%?
Because the discount rate is the price of waiting, and this series is back-loaded — its largest flow, $6,800, arrives in year 3, where discounting bites hardest. At 10% the present value of the future flows is $11,307.29 and the NPV is $1,307.29; at 5% they are $12,540.76 and $2,540.76, nearly double, from a five-point rate change alone. At 15% they fall to $10,255.61 and $255.61. Two honest analysts can reach different verdicts on the same series purely by choosing different rates, which is why you should always run a series at two or three rates and watch how close the verdict gets to zero.
Can a project take in more than it spends and still have a negative NPV?
Yes — and this page’s own series proves it. Cut the final flow from $6,800 to $3,000 at a 5% rate, and the undiscounted total is still positive at $200 ($3,000 + $4,200 + $3,000 − $10,000), yet the present value is only $9,258.18, the NPV is −$741.82 and the index is 0.93. The money arrives late and the rate charges for the wait. When someone quotes a project’s total inflows, ask for the timing; the timing is the verdict.
What does the profitability index add that NPV does not?
Scale. NPV is blind to it: a project returning $1,100 of present value on $1,000 invested and one returning $1,001,000 on $1,000,000 invested both show positive NPVs, but the first returns ten cents on the dollar and the second a tenth of a cent. The index divides the present value of the inflows by the cost, so 1.13 means $1.13 back per dollar, 1.03 means $1.03, and 0.93 means $0.93. When one project stands alone, the NPV’s sign is enough; when two compete for the same capital, rank by the index.
How do I check an NPV instead of trusting it?
Use the year-by-year table and the 0% case. Each row shows the flow, its discount factor and its present value, and the present values must sum to the headline — at 15%, $2,608.70 + $3,175.80 + $4,471.11 = $10,255.61, and $10,255.61 − $10,000 = $255.61. Then set the rate to 0%: every factor becomes 1.0000, the present value becomes the plain sum $14,000 and the NPV becomes the undiscounted total $4,000. If the 0% NPV does not equal the undiscounted total, a flow was mistyped; if a factor looks wrong, the rate was entered wrongly.
What is IRR and how does it relate to NPV?
IRR is the discount rate at which NPV is zero. A project with positive NPV at your rate has an IRR above your rate, but IRR can mislead with non-conventional cash flows, so let NPV decide conflicts.
Why is terminal value dangerous in NPV?
Because it often exceeds the present value of all forecast cash flows combined, so the whole verdict can depend on one growth or exit assumption. Test the verdict without it.
Should NPV use nominal or real figures?
Either, but consistently: nominal cash flows with a nominal rate, or real cash flows with a real rate. Mixing them is a common and serious error.
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The results assume the cash flows arrive exactly as entered, at the end of each period, and that the discount rate stays constant — real projects slip, rates move, and taxes, fees and inflation all take their cut. NPV is a comparison tool: it ranks the figures you give it, and it cannot vouch for the forecasts behind them. For commitments that matter, test the flows and the rate against evidence, run the pessimistic version as well as the hopeful one, and take professional advice where the sums justify it.
Future money, honestly priced in today’s.
↑ 📖NPV Explained
Formula, discount rate, and two worked examples.