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Engineering Economics
Net Present Value (NPV) Calculator
In short: Net present value discounts every future cash flow of a project back to today at your required rate of return and subtracts the initial investment. A positive NPV means the investment earns more than that rate and creates value; a negative NPV means it falls short. This calculator handles uniform or uneven cash flows, shows the full discounted schedule, and reports the profitability index, discounted payback, and the break-even rate (the IRR).
The NPV formula
NPV = −Initial investment + Σ [ Cash flowt ÷ (1 + r)t ] , where r is the discount rate and t is the year.
Net present value, or NPV, is the most trusted single measure in engineering economics for deciding whether an investment is worth making. It takes every future cash flow a project is expected to produce, discounts each one back to today at a rate that reflects your required return, adds them up, and subtracts what you have to spend at the outset.
The result is a figure in today money that tells you, directly, how much value the project creates or destroys. A positive NPV means the investment earns more than your required return and adds wealth; a negative NPV means it falls short.
Because it converts a stream of costs and revenues spread across years into one comparable number, NPV lets you weigh a machine against a building, a five year project against a fifteen year one, or one supplier proposal against another, on a genuinely like for like basis.
The idea behind net present value
The whole method rests on the time value of money, the principle that a sum of money available today is worth more than the same sum promised in the future. There are three reasons for this. First, money on hand can be invested to earn a return, so a dollar today can grow into more than a dollar next year. Second, inflation erodes purchasing power, so a future dollar buys less.
Third, a promised future payment carries risk that it may not arrive in full. Discounting is the arithmetic that turns future amounts into their equivalent value today, and the discount rate is the yardstick that expresses how much less a future dollar is worth.
NPV simply applies this discounting to every cash flow a project generates and nets the results against the initial cost.
Because distant cash flows are discounted more heavily than near ones, NPV automatically rewards projects that return money sooner and penalises those whose payoffs are pushed far into the future. This is exactly what a rational investor wants: two projects that return the same total amount are not equally valuable if one pays back quickly and the other slowly. NPV captures that difference, whereas cruder measures that simply add cash flows without discounting cannot.
How the NPV formula works
The formula states that net present value equals the sum over every period of the cash flow in that period divided by one plus the discount rate raised to the power of the period number, minus the initial investment.
In practice you take year one cash flow and divide it by one plus the rate; you take year two cash flow and divide it by one plus the rate squared; you continue for every year of the forecast; you add all those present values together; and finally you subtract the amount spent at the start, which sits at year zero and is therefore not discounted.
The quantity one divided by one plus the rate raised to the year is called the discount factor for that year, and multiplying a cash flow by its discount factor gives its present value. The calculator on this page lays out the discount factor, present value, and running cumulative present value for every year, so the arithmetic is fully visible rather than hidden inside a single number.
Consider a concrete case. Suppose a piece of equipment costs ten thousand and is expected to generate net cash flows of three thousand, four thousand, five thousand, four thousand, and three thousand over the next five years, and your required return is ten percent.
Discounting each flow gives present values of roughly 2,727 in year one, 3,306 in year two, 3,757 in year three, 2,732 in year four, and 1,863 in year five. These add to about 14,385, and subtracting the ten thousand outlay leaves a net present value of roughly 4,385. Because that number is positive, the equipment earns more than the ten percent you require, and on the NPV rule you should buy it.
Change the required return to a higher figure and the present values shrink, the NPV falls, and at a high enough rate the decision flips.
Choosing the discount rate
The discount rate is the single most influential input in an NPV analysis, and choosing it well matters more than almost anything else. Conceptually it is the return you require to tie up money in the project, which has two parts: the opportunity cost of capital, meaning the return you could earn on a comparable alternative, and a premium for the risk that the project cash flows may not materialise as forecast.
For a company the usual starting point is the weighted average cost of capital, the blended after tax cost of the debt and equity that finance the business, adjusted upward for projects that are riskier than the firm as a whole. For a smaller enterprise or an individual, the rate might simply be the return on the best alternative use of the money.
In Brazilian practice this required rate is known as the minimum attractive rate of return, and it fills exactly the same role in the calculation.
Because a higher rate discounts future cash flows more severely, it lowers the NPV and makes projects with distant or slow payoffs harder to justify, while a lower rate does the opposite. The effect compounds over time, so even a small change in the rate can move the NPV substantially and occasionally reverse the decision.
For that reason a disciplined analysis never rests on a single rate. Instead it tests a range, asking how the NPV behaves if the rate is a point or two higher or lower than the base case, which reveals how sensitive the conclusion is to an assumption that is, after all, an estimate.
The calculator makes this easy: change the rate and the NPV, the schedule, and the chart all update at once.
Reading the results: NPV, profitability index and payback
The headline figure is the NPV itself, and its sign is the decision rule: accept a positive NPV, reject a negative one, and treat a value near zero as a project that earns exactly your required return, where the choice then turns on strategic rather than financial grounds. When comparing several independent projects of similar risk, the one with the highest NPV creates the most value and should rank first.
The profitability index, which the calculator reports alongside NPV, expresses the same information as a ratio: the present value of the inflows divided by the initial investment. An index above one corresponds to a positive NPV, and the higher it is, the more value each unit of investment produces.
The index comes into its own when capital is rationed and you must choose among competing projects, because it ranks them by value created per dollar invested rather than by absolute size.
The calculator also reports the discounted payback period, the year in which the cumulative present value first turns positive, and the break-even discount rate, which is the rate that would drive the NPV to zero.
That break-even rate is precisely the internal rate of return of the cash flows, and comparing it against your required return gives a second, percentage based view of the same decision: if the break-even rate comfortably exceeds your required return, the project has a margin of safety against an error in your rate assumption.
Together these four measures paint a fuller picture than any one of them alone, and because the calculator shows the year by year schedule you can see exactly where the value comes from and when the project moves into the black.
NPV versus IRR
The internal rate of return is NPV closest companion and its most common rival. Where NPV asks how much value a project creates at a rate you specify, IRR asks what rate the project itself earns, defined as the discount rate at which the NPV equals zero. Both use the same cash flows, and for a single conventional project, one with an initial outlay followed by inflows, they usually agree on the accept or reject decision.
Problems arise in two situations. When cash flows change sign more than once, as they do when a project requires a major reinvestment partway through, the IRR equation can have several solutions, and it becomes unclear which one to use.
And when ranking mutually exclusive projects of different sizes, IRR can favour a small project with a high percentage return over a large one that creates far more total value, because a percentage ignores scale.
NPV suffers from neither flaw: it always yields a single figure and it measures value in absolute terms, so it correctly prefers the project that adds the most wealth. There is also a subtler difference in what each method assumes about the cash you receive along the way.
NPV implicitly assumes interim cash flows are reinvested at your discount rate, the cost of capital, which is a realistic assumption because that is roughly what you could earn on them elsewhere. IRR implicitly assumes reinvestment at the IRR itself, which for a high return project is optimistic and overstates the true return.
For all these reasons finance theory treats NPV as the more reliable rule, while acknowledging that IRR communicates well as a percentage. The practical advice is to compute both, as this calculator does, and to let NPV break any tie.
Uneven cash flows, negative years and terminal value
Real projects rarely deliver the same amount every year. A new production line might lose money while it ramps up, hit its stride in the middle years, and taper as the product ages; a mine might require a large closure cost at the end; a software product might need a costly rebuild halfway through its life.
NPV handles all of this without difficulty because each cash flow is discounted on its own terms regardless of size or sign. The custom entry mode in the calculator lets you type one cash flow per line, positive or negative, so you can model the actual shape of a project rather than forcing it into a flat average.
The uniform mode is a convenience for the genuinely level case, such as a lease or a simple annuity, where the same figure repeats each year.
For investments that continue producing cash well beyond the period you can forecast in detail, such as an ongoing business rather than a fixed life project, a terminal value captures everything after the explicit forecast in a single figure.
The calculator uses the perpetuity growth approach: it assumes the final forecast year cash flow continues indefinitely, growing at a constant rate, and computes its value at the forecast horizon as the last cash flow times one plus the growth rate, divided by the difference between the discount rate and the growth rate. That horizon value is then discounted back to today like any other future amount.
Terminal value can dominate a long horizon valuation, so use it deliberately, keep the growth rate modest and below the discount rate, and omit it entirely for projects with a clear end date.
Real versus nominal rates and inflation
Inflation quietly shapes every NPV, and handling it consistently is essential. There are two correct ways to build the analysis, and the only rule is not to mix them. The nominal approach forecasts cash flows in the actual money of each future year, including the effect of rising prices, and discounts them at a nominal rate that also contains an inflation component; this is the more common method in practice because forecasts and quoted interest rates are usually nominal.
The real approach forecasts cash flows in today constant purchasing power, stripped of inflation, and discounts them at a real rate that excludes inflation. Both, applied correctly, give the same NPV, because inflation is either included on both sides or excluded on both sides. The mistake to avoid is discounting real cash flows at a nominal rate, which double counts inflation and understates the NPV, or the reverse, which overstates it.
When you take the rate from a bank quote or a market yield it is almost always nominal, so pair it with nominal cash flows.
The link between the two rates is that one plus the nominal rate equals one plus the real rate times one plus the inflation rate, which for small figures is roughly the real rate plus inflation. If your required real return is five percent and you expect three percent inflation, your nominal required rate is about eight percent. Being explicit about which world you are working in prevents a subtle but common error, and it matters most for long horizon projects where even a modest inflation assumption compounds into a large difference by the final year.
A worked comparison of two investments
NPV proves its worth most clearly when two options compete. Suppose a plant must choose between two machines. Machine A costs twelve thousand and returns four thousand a year for four years; machine B costs twenty thousand and returns six thousand a year for four years. At first glance B returns more in total, twenty four thousand against sixteen thousand, but it also costs more and the question is which creates more value.
Discounting at ten percent, the four annual payments of four thousand from machine A have a present value of about twelve thousand six hundred eighty, so its NPV is roughly six hundred eighty. Machine B six thousand a year discounts to about nineteen thousand twenty, giving an NPV of about minus nine hundred eighty.
Machine A, the cheaper option, is the better investment despite returning less in raw dollars, because its outlay is far lower relative to what it earns.
This is the kind of conclusion that intuition and undiscounted totals get wrong and NPV gets right. Notice too that the ranking can depend on the discount rate: at a very low rate machine B larger absolute returns might overtake machine A, while at a high rate A advantage widens. That sensitivity is exactly why the calculator lets you change the rate and re-read the schedule, and why a careful analyst checks the decision across the plausible range of rates rather than at a single point. When two projects have different lives, NPV alone can mislead and the annual worth method, which converts each to a yearly equivalent, is the right companion tool.
Sensitivity and scenario analysis
An NPV is only as trustworthy as the forecast behind it, and every forecast is uncertain, so a single point estimate can give false confidence. Sensitivity analysis addresses this by changing one input at a time and watching the NPV respond, which reveals the variables that matter most.
In most projects the NPV is highly sensitive to the size and timing of the early cash flows and to the discount rate, and much less sensitive to small changes far in the future, because those are heavily discounted anyway.
Knowing which inputs move the answer tells you where to focus your forecasting effort and where to negotiate hardest, whether that is the sales volume, the unit margin, or the up front cost.
Scenario analysis goes a step further by changing several inputs together into a coherent story, typically a base case, an optimistic case, and a pessimistic case. If the NPV stays positive even in the pessimistic scenario, the project has a robust margin of safety; if it turns sharply negative under mild pessimism, the apparent value is fragile and rests on assumptions that may not hold. The break-even discount rate the calculator reports is itself a form of sensitivity analysis, since it tells you how far the discount rate would have to rise before the project no longer adds value. Using these techniques turns a lone number into a genuine understanding of the risks in a decision.
Where NPV fits in capital budgeting
NPV does not operate in isolation; it is the centrepiece of the broader capital budgeting process by which an organisation decides which long term investments to fund.
That process begins with generating and screening ideas, moves to forecasting the incremental after tax cash flows each idea would produce, applies NPV and its companions to value them, and ends with selecting a portfolio of projects that fits the available capital and the firm strategy.
Within that flow NPV is the primary financial gatekeeper, but it is not the only consideration: strategic fit, regulatory constraints, environmental and social factors, and the option value of being able to expand or abandon later all bear on the final choice. A project with a modest NPV that opens a strategic door may beat one with a larger NPV that leads nowhere.
Because capital is usually limited, firms also rank accepted projects, and this is where the profitability index earns its place, since it measures value per unit of scarce capital. Understanding that NPV is one input to a structured decision, rather than an automatic verdict, keeps the number in perspective. The calculator gives you a rigorous, transparent NPV and its supporting measures; the judgment about whether to proceed weaves that result together with everything a spreadsheet cannot capture. Used this way, NPV disciplines the conversation without pretending to end it.
Computing NPV in a spreadsheet and by hand
It helps to know how the same calculation is done in the tools you already use, because it makes the result easier to check and to reproduce in a report. In a spreadsheet the built in NPV function discounts a range of cash flows, but there is a subtlety that trips up many users: the function treats the first value in the range as occurring at the end of period one, not at time zero.
That means you should not include the initial investment inside the function; instead you compute the NPV of the future cash flows and then add the initial outlay, entered as a negative number, outside the function. Written out, the pattern is the outlay plus the discounted future flows, which matches the definition used here exactly.
When cash flows fall on irregular calendar dates rather than at neat annual intervals, a dated variant of the function discounts each flow by the actual number of days elapsed, which is more precise for real world timing.
By hand, the work is the same as the schedule this calculator prints. For each year you form the discount factor, one divided by one plus the rate raised to the year number, multiply it by that year cash flow to get the present value, and keep a running total.
Subtracting the initial investment from the sum of the present values gives the NPV, and tracking the running total shows you the year in which the cumulative present value turns positive, which is the discounted payback.
Doing this once by hand for a small example is the fastest way to build intuition for why later cash flows contribute so much less than early ones, and why the discount rate has such leverage over the result. After that, letting the calculator lay out the full table for any set of inputs saves the arithmetic while keeping every step visible for review.
Assumptions and limitations of NPV
For all its strengths, NPV rests on assumptions that are worth stating plainly so you know where it can mislead. It assumes you can estimate the future cash flows with reasonable accuracy, yet those forecasts are the least certain part of any analysis, and a confident looking NPV built on shaky projections is still shaky.
It assumes a single discount rate applies across the whole life of the project, whereas in reality the appropriate rate can change as risk resolves or financing conditions shift. It assumes interim cash flows can be reinvested at that discount rate, which is usually reasonable but not guaranteed.
And it treats the project as a fixed plan, whereas managers can often adapt, expanding a success or abandoning a failure, and that flexibility has value that a static NPV does not capture.
These limitations do not undermine NPV; they define how to use it well. Because forecasts are uncertain, pair NPV with the sensitivity and scenario analysis described above so you see a range rather than a false point. Because the discount rate is an estimate, check the break-even rate to gauge your margin for error.
Because managerial flexibility has value, recognise that for projects rich in options, such as staged research or projects that can be scaled up later, a plain NPV may understate the true worth, and more advanced real options methods exist for those cases. And because NPV speaks only to financial value, remember that strategic, regulatory, and human factors sit alongside it in any real decision.
Understood with its assumptions in view, NPV is not a black box that dictates an answer but a disciplined, transparent way to reason about value over time, which is exactly why it has remained the cornerstone of engineering economics and corporate finance for decades.
Common mistakes to avoid
Several errors recur often enough to be worth naming. The first is discounting the initial investment: the outlay happens now, at year zero, and is not discounted; only future cash flows are. The second is mismatching the rate and the period, for example applying an annual rate to monthly cash flows; the rate and the periods must use the same time unit. The third is confusing accounting profit with cash flow.
NPV works on cash, the actual money moving in and out, not on profit figures that include non cash items such as depreciation; depreciation matters only through the tax it saves. The fourth is double counting or omitting working capital and salvage values, which are genuine cash flows that belong in the forecast. And the fifth is treating the discount rate as a fact rather than an estimate, which is why testing a range of rates is essential.
Avoiding these traps is usually the difference between an NPV that guides a good decision and one that misleads.
Five worked examples of net present value
Example 1: a project that creates value
Invest 10,000 today; receive 3,000 a year for 5 years; discount rate 10%. The 5-year annuity factor is 3.7908, so PV of inflows = 3,000 × 3.7908 = 11,372. NPV = 11,372 − 10,000 = +1,372. Positive NPV — accept.
Example 2: raising the discount rate
Same cash flows at 15%. The annuity factor falls to 3.3522, PV of inflows = 10,057, so NPV = 10,057 − 10,000 = +57. Almost break-even — the higher the rate, the lower the NPV.
Example 3: a project that destroys value
Same cash flows at 20%. Annuity factor 2.9906, PV = 8,972, NPV = 8,972 − 10,000 = −1,028. Negative NPV — the return falls short of the 20% hurdle, so reject.
Example 4: the profitability index
Back to Example 1: PI = PV of inflows ÷ investment = 11,372 ÷ 10,000 = 1.14. Every dollar invested returns 1.14 dollars of present value — a useful way to rank projects when capital is limited.
Example 5: uneven cash flows
Invest 10,000; receive 2,000, 4,000, 6,000 in years 1–3 at 10%. PV = 2,000/1.1 + 4,000/1.21 + 6,000/1.331 = 1,818 + 3,306 + 4,508 = 9,632. NPV = −368 — front-loading matters, and this timing just misses.
Three expert tips for a reliable NPV
Match the discount rate to the risk
Use a rate that reflects the project’s risk and financing — often the WACC for average-risk projects, higher for riskier ones. The rate is the single biggest driver of the result.
Keep rate and cash flows on the same basis
Discount nominal cash flows with a nominal rate and real cash flows with a real rate. Mixing the two silently biases the NPV, usually by the inflation rate.
Don’t forget the terminal value and working capital
Salvage value, the release of working capital, and any terminal value are real year-end cash flows. Omitting them understates NPV on long-lived assets.
Frequently asked questions
What is net present value (NPV)?
Net present value is the value today of a series of future cash flows minus the initial investment, discounted at a rate that reflects your required return.
It answers a single question in money terms: does this investment earn more than the return you demand from it? Each future cash flow is divided by one plus the discount rate raised to the power of the year in which it arrives, which shrinks distant money more than near money because a sum received later is worth less than the same sum today.
Those present values are added up and the initial outlay is subtracted. A positive NPV means the project creates value over and above your required return, a negative NPV means it destroys value, and an NPV of zero means it earns exactly your required return and no more.
How is NPV calculated with the formula?
The formula is NPV equal to the sum, over every period t from one to n, of the cash flow in period t divided by one plus the rate r raised to the power t, minus the initial investment made at time zero. In plain terms you discount each year cash flow back to today and add them, then subtract what you paid up front.
For example, an outlay of ten thousand that returns three thousand, four thousand, five thousand, four thousand, and three thousand over five years, discounted at ten percent, gives present values of about 2,727, 3,306, 3,757, 2,732, and 1,863, summing to roughly 14,385; subtracting the ten thousand leaves an NPV near 4,385.
Because the total is positive, the project earns more than ten percent and is worth doing. The calculator above shows this full schedule for any inputs you enter.
What discount rate should I use for NPV?
The discount rate should be the return you require to commit money to the project, which is usually your cost of capital plus a margin for the project specific risk.
For a company this often means the weighted average cost of capital, the blended after tax cost of its debt and equity; for a smaller business or a personal decision it might be the return available on a comparable alternative investment. In Brazil this required rate is commonly called the minimum attractive rate of return, and it plays exactly the same role.
The important point is that a higher rate discounts future cash flows more heavily and lowers the NPV, so the rate you choose can decide whether a project looks attractive. Because of this, test a range of rates rather than trusting a single figure.
What does a positive or negative NPV mean?
A positive NPV means the present value of the inflows exceeds the initial investment when both are measured at your discount rate, so the project earns more than the return you require and adds wealth; the size of the positive number is, in principle, the value created in today money.
A negative NPV means the inflows do not cover the outlay at that rate, so the project earns less than you require and should normally be rejected, even if it still makes an accounting profit. An NPV of exactly zero means the project earns precisely your required return, no better and no worse, and the decision then rests on strategic factors rather than the number itself.
When ranking several projects with similar risk, the one with the highest NPV creates the most value.
What is the difference between NPV and IRR?
NPV and IRR use the same discounted cash flows but report different things. NPV gives a dollar amount, the value created above your required return at a rate you choose. IRR gives a percentage, the discount rate at which the NPV would be exactly zero, so it is the return the project itself earns; you then compare it against your hurdle rate.
In the calculator above, the break-even discount rate we report is this IRR. NPV is generally the more reliable of the two because it always scales correctly with project size and it gives a single answer even when cash flows change sign more than once, a situation in which IRR can produce several values.
IRR remains popular because a percentage is intuitive to communicate, so most analysts compute both and let NPV settle any conflict.
What is the profitability index and how do I read it?
The profitability index is the present value of a project future cash flows divided by the initial investment, so it expresses the same information as NPV as a ratio rather than an amount. An index above one means the discounted inflows are larger than the outlay, which is the same as a positive NPV, and the higher the index the more value each unit of investment produces.
An index below one signals a negative NPV. The index is most useful when you must choose among projects under a capital constraint, because it ranks them by value created per dollar invested rather than by absolute value, helping you get the most from a limited budget.
The calculator reports the profitability index alongside NPV so you can see both the total value and the value per dollar.
What is discounted payback and why does it differ from simple payback?
Discounted payback is the time it takes for the discounted cash flows of a project to recover the initial investment, that is, the year in which the cumulative present value first turns positive. It differs from simple payback, which ignores the time value of money and just adds the raw cash flows until they equal the outlay.
Because discounting shrinks later cash flows, the discounted payback is always longer than the simple payback, and it is the more honest measure because it counts a dollar returned in year five as worth less than a dollar returned in year one.
Payback of either kind is a useful liquidity and risk screen, since a project that repays quickly ties up money for less time, but it should support NPV rather than replace it, because payback ignores everything that happens after the money is recovered.
Can NPV handle uneven or negative cash flows?
Yes. NPV is defined for any pattern of cash flows, and the calculator accepts a different amount for each year, including negative values for years in which the project consumes cash rather than generating it, such as a mid life overhaul or an expansion.
Each cash flow is discounted by its own year factor regardless of sign, and the results are summed, so an irregular stream is handled just as rigorously as a smooth one. This flexibility is one reason NPV is preferred over simpler measures: real projects rarely produce identical cash flows every year, and NPV reflects the actual timing and size of each flow.
Use the custom entry mode to type one cash flow per line, and the uniform mode only when the annual figure genuinely repeats.
What is terminal value and when should I include it?
Terminal value captures the worth of all cash flows beyond the last year you forecast explicitly, compressed into a single figure placed at the end of the forecast.
The calculator uses the perpetuity growth method, which assumes the final year cash flow continues forever while growing at a steady rate; its value at the forecast horizon is the last cash flow times one plus the growth rate, divided by the discount rate minus the growth rate, and that figure is then discounted back to today.
Include a terminal value when the project or business realistically continues generating cash well past your explicit forecast, as in a company valuation, and leave it out for a project with a definite end, such as a machine that is scrapped after its useful life. The method requires the discount rate to exceed the growth rate, or the formula has no finite value.
Are these results suitable for a real investment decision?
The NPV, profitability index, payback, and break-even rate here use the standard formulas of engineering economy and corporate finance and are accurate for the inputs you provide, so they are well suited to learning, screening ideas, and preparing a justification.
They are, however, only as good as your assumptions: the cash flow forecast, the discount rate, and the treatment of tax, inflation, and risk all shape the answer, and a general calculator cannot know the specifics of your situation. For a binding financial, tax, or accounting decision, confirm the figures and assumptions with a qualified professional and your own organisation policies.
Treat the tool as a fast, transparent way to run the numbers and understand the sensitivities, not as a substitute for professional judgment.
Does this calculator store the numbers I enter?
No. The calculator runs entirely in your browser. The cash flows, rate, and other values you enter are never sent to our servers, stored, or shared. You can use it freely for confidential figures. See our Privacy Policy for details.
Is the NPV calculator free to use?
Yes. This calculator, like every tool on OpsCalculators, is free and needs no account or sign up. There is no paywall and no limit on how many calculations you can run, and you can export the schedule to CSV or save a PDF at no cost.
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Sources, disclaimer and editorial transparency
Method follows the standard treatment of discounted cash flow and net present value in engineering economy and corporate finance, including the texts by Blank and Tarquin, Newnan, and Park, and the definitions used by the CFA Institute and Corporate Finance Institute. See our Editorial Policy for how we research and review each tool.
This calculator is for education and planning and does not constitute financial, tax, investment, or accounting advice. Confirm any figure that informs a real decision with a qualified professional. OpsCalculators is operated by MAFHH INTERNATIONAL LTD; see our Privacy Policy.