NPV Calculator

Net present value = [ Σ ( cash flow in year t ÷ (1 + discount rate)ᵗ ) ] − initial investment; profitability index = discounted total ÷ initial investment

Cash flows

The series of amounts expected in each period, entered in order from the first period onward — they do not have to be positive or equal, and a negative figure is how a later cost is entered

Discount rate

The rate each future cash flow is divided by, once per period it is away — the annual rate, also called the hurdle rate or the cost of capital, and the one input on this page that is a judgement rather than a fact

t

How many periods away a cash flow is: 1 for the first one entered, 2 for the second, and so on, which is what makes a later amount count for less

Initial investment

The price paid today to acquire the stream, subtracted in full because it happens at time zero and is therefore not discounted

Profitability index

The discounted total divided by the initial investment — the same accept-or-reject answer as the net present value, expressed as a ratio so that deals of different sizes can be compared

Use it when the question is whether to commit money rather than what the commitment is worth, which is a narrower question than it sounds: the two are the same arithmetic, but only one of them ends in a decision. It is the right page for comparing a project against the rate you could earn elsewhere, because the discount rate is where that alternative lives — discounting at 8 percent is a statement that 8 percent is what the money would otherwise do. It is also the page for a price negotiation, since the initial investment is an input rather than a fact and the break-even point where the net present value reaches zero is the most you can pay before the answer changes. Three things to get right. The cash flows are entered in period order and the first one is discounted by one full period, so if the first receipt arrives today rather than a year from now, add it to the initial investment side instead. The discount rate is a single constant for the whole horizon, which is a real simplification because the rate you would actually demand for a payment five years out is not the rate you would demand for one next month. And the initial investment must be positive here, because the profitability index divides by it; a page that allowed zero would print an index of infinity rather than refusing the input.

1. 205,000 over six years at 8%, against a price of 100,000

   1. Discount each flow by one more period than the one before: 25,000 ÷ 1.08 = 23,148.15, 28,000 ÷ 1.08² = 24,005.49, and so on
   2. Add the six discounted amounts: 153,968.13
   3. Net present value: 153,968.13 − 100,000 = 53,968.13
   4. Profitability index: 153,968.13 ÷ 100,000 = 1.540

   The verdict is accept, and the index says why in a way the amount cannot: for every unit of currency put in, 1.54 comes back. Note that the undiscounted total is 205,000, so more than a quarter of the apparent profit is the discount rate doing its work — 51,031.87 of the 105,000 gross gain never arrives in present-value terms.

2. The same cash flows for 160,000 — the verdict flips

   1. The discounted total does not move with the price: it is still 153,968.13
   2. Net present value: 153,968.13 − 160,000 = −6,031.87
   3. Profitability index: 153,968.13 ÷ 160,000 = 0.962

   Only the price changed and the answer went from 53,968.13 to −6,031.87. This is the pair worth reading twice, because the discounted total is identical in both: what moved is what you are being asked to pay for it. An index below 1 and a net present value below zero are the same statement, and the break-even price sits between these two examples — at 153,968.13 the net present value is zero and the index is exactly 1.

3. Uneven flows with a later cost — 40,000, −25,000, 60,000 at 8%

   1. Year 1: 40,000 ÷ 1.08 = 37,037.04
   2. Year 2: −25,000 ÷ 1.08² = −21,433.47
   3. Year 3: 60,000 ÷ 1.08³ = 47,629.93
   4. Discounted total: 63,233.50; net present value 63,233.50 − 50,000 = 13,233.50
   5. Profitability index: 63,233.50 ÷ 50,000 = 1.265

   The cash flows do not have to be positive, and entering a later cost as a negative amount is how a project that needs a second injection of money is modelled. A payback-period calculation on this stream would be misleading, because a simple running total turns positive in year 1 and never looks back, while the discounted answer has to absorb the year-2 outflow.

The discount rate is a single constant applied to every period, and that is the assumption most likely to be wrong: real projects face a different cost of money at different horizons, and a single rate either over-discounts the near years or under-discounts the far ones. It is also a number you choose, not a number the calculator can find for you, and the verdict moves with it — the default cash flows clear a price of 150,000 at 8 percent and would not at a higher rate. Everything is in nominal terms with no inflation adjustment, so discounting at a rate that does not include an inflation premium quietly overstates a long stream. The cash flows are treated as arriving at the end of each period, exactly one period apart, which is a convention rather than a description of reality: receipts that arrive monthly, or partway through a year, are approximated. The initial investment is assumed to happen entirely at time zero and to be positive, so a project with staged funding, or one where the net outlay is recovered and then spent again, is not this calculation. Nothing here handles taxes, depreciation, financing costs or working capital, all of which change the cash flows rather than the arithmetic, and none of them are modelled. Finally, the profitability index ranks projects that are independent of each other: it can rank a small project above a large one when both are acceptable, which is the right answer for capital rationing and the wrong answer when the two projects are mutually exclusive.

What is net present value?

It is what a series of future cash flows is worth today, minus what you have to pay to receive them. Each flow is divided by the discount rate once for every period it is away, the results are added, and the initial investment is subtracted from that total. On the default case, six flows adding to 205,000 are worth 153,968.13 today at 8 percent, so against a price of 100,000 the net present value is 53,968.13. A positive figure means the deal returns more than the discount rate; a negative one means it returns less.

What is the profitability index and why show it as well?

It is the discounted total divided by the initial investment — 1.540 on the default case, meaning every unit of currency committed comes back as 1.54. It answers the same accept-or-reject question as the net present value, and when the initial investment is positive the two can never disagree, because dividing by a positive number preserves the sign. It is worth showing beside the amount because it carries the scale: a net present value of 3,968.13 reads like a success until the index beside it reveals that it took 150,000 to earn.

How do I calculate net present value?

Discount each cash flow by the rate raised to the number of periods it is away, add the results, then subtract the initial investment. For a single flow one year out at 8 percent, divide by 1.08; for one two years out, divide by 1.08². The default case discounts six flows into 153,968.13 and, against a price of 100,000, leaves 53,968.13. The profitability index is that same discounted total divided by the price, so it costs nothing extra to compute once the total is known.

What discount rate should I use?

The rate you could earn on the money elsewhere at comparable risk, since that is what you are giving up by committing it here — often called the hurdle rate or the cost of capital. It is a judgement, not a measurement, and it is the input the verdict is most sensitive to: the same six cash flows are worth 153,968.13 at 8 percent and would be worth less at a higher rate. This page will not pick one for you, and the reference table is built to show what changing the price rather than the rate does to the answer.

What does a break-even net present value mean?

It means the discounted total and the price are the same number, so the deal neither adds nor destroys value at the rate you chose — the profitability index is exactly 1 and the badge reads break-even. It is the most you can pay before the answer turns, which makes it the useful number in a negotiation. On the default cash flows it falls at 153,968.13, and the table walks from 40,000 up to 200,000 so the transition is visible rather than hidden between two rows.

Can I enter a negative cash flow?

Yes, and on most real projects you should expect to. A negative figure is how a later cost is entered: a project that needs a second injection of money in year two, or one with a decommissioning cost at the end, is modelled by putting that outflow in its own period. The third worked example does exactly this, with 40,000 in year one, −25,000 in year two and 60,000 in year three. What the page will not accept is an initial investment of zero, because the profitability index divides by it.

Is this the same as the net present value calculator on this site?

The two discount the same way, and given the same cash flows and rate they agree on the discounted total. They differ in what they print and in what they are for. The other page reports the discount amount alongside the present value, which answers what the stream is worth today. This page reports the profitability index and a three-tier verdict, which answers whether to commit the money, and its reference table varies the price rather than the rate — the question you ask when someone names a number and you want to know if it is too high.

• OMB Circular A-94, Guidelines and Discount Rates for Benefit-Cost Analysis of Federal Programs (revised November 9, 2023) — section 5a states that projects with positive discounted net benefits are generally preferred and those with negative discounted net benefits should generally be avoided, and directs that a break-even analysis be considered — Office of Management and Budget, Executive Office of the President (United States)
• Interest — Investor.gov glossary, for the rate every cash flow here is discounted at — U.S. Securities and Exchange Commission, Investor.gov (United States)
• Compound Interest Calculator — the SEC's own tool, useful as the inverse of this page: it grows a lump sum forward where this one discounts a stream back — U.S. Securities and Exchange Commission, Investor.gov (United States)