Net Present Value Calculator

NPV = Σ [ CF(k) ÷ (1 + r)^k ] − Initial investment (k = 1 … n)

CF(k)

The cash flow received at the end of year k; it may be negative if that year is a net cost rather than a receipt

r

The discount rate per year, entered as a percentage — the rate the project has to beat to be worth doing

k

The year number, starting at 1 for the first number in the list, which is why the initial investment is not part of the list

Initial investment

The money spent today, at year zero, so its discount factor is exactly 1 and it comes off undiscounted

NPV

The present value of every future cash flow minus the initial investment; above zero means the project clears the rate

Use it to decide whether a project clears a rate you have already chosen, and to compare projects that pay back on completely different schedules — a machine that returns 40,000 a year for five years and a licence that returns 200,000 in year six are not comparable by their totals, but they are comparable once both are discounted. Two things it deliberately does not do. It does not choose the discount rate for you: the rate is the cost of the money or the return available elsewhere, and it belongs to your situation rather than to this page. And it does not find the rate at which the net figure crosses zero — that rate is the internal rate of return, which is a different calculation and is not on this page. A useful sensitivity test instead is to run the same project at a few rates and watch the answer change sign; the reference table below is exactly that for one project.

1. 100,000 in, six rising years out, discounted at 8%

   1. Year 1: 25,000 ÷ 1.08 = 23,148.15
   2. Year 2: 28,000 ÷ 1.08² = 24,005.49
   3. Year 3: 32,000 ÷ 1.08³ = 25,402.63
   4. Year 4: 36,000 ÷ 1.08⁴ = 26,461.07
   5. Year 5: 40,000 ÷ 1.08⁵ = 27,223.33
   6. Year 6: 44,000 ÷ 1.08⁶ = 27,727.46
   7. Sum of the six: 153,968.13
   8. Net: 153,968.13 − 100,000 = 53,968.13

   This is the page's default. The row worth checking by hand is the subtraction, because it is the one place this page can quietly disagree with other calculators: the 100,000 is not discounted, so the net figure is 53,968.13 rather than 46,259.38, which is what discounting it once would give. The discount amount of 51,031.87 is the other half of the story — waiting six years costs more than half of the 105,000 the project appears to earn before discounting.

2. One payment of 100,000 five years out, discounted at 5%

   1. One number in the list means one cash flow, at the end of year 1: 100,000 ÷ 1.05 = 95,238.10
   2. Net: 95,238.10 − 100,000 = −4,761.90

   A negative net present value is the answer this page exists to be able to give. Getting exactly your money back in a year's time is a loss when money costs five percent, and the size of the loss is the rate times the amount. Notice that the flow is discounted once, not five times, because the list has one entry and the first entry is year one — five years out would be five numbers with the last one carrying the amount.

3. A project that spends again in year 2

   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. Sum: 63,233.50
   5. Net: 63,233.50 − 50,000 = 13,233.50

   A negative entry in the list is allowed and it is not a typo: buildings get reroofed, machinery gets overhauled, and a project that costs money again in year two is a normal shape. The undiscounted total of the three flows is 75,000, so the discount amount of 11,766.50 is the part of that 75,000 which is really just the cost of waiting.

The net figure is only as good as three inputs you supplied, and it is silent about all three. The cash flows are assumed to arrive at the end of each year, all of them, which is a convention rather than a fact: a project that collects its money in January is worth slightly more than this page says, and one that collects in December slightly less. The discount rate is assumed to be the same for every year, so a project with a rate that steps up after an introductory period is not modelled. Nothing here accounts for inflation, tax or the risk that the flows do not arrive at all — the discount rate is where all of that is supposed to live, and choosing it is your job rather than this page's. Cash flows are also assumed to be independent of each other, so the calculator cannot express a project that only continues if the year two figure comes in above some level. Finally, the answer is a number of currency units with no currency attached, and comparing net present values across projects is only meaningful when the projects need roughly the same amount of money up front: a project with a net present value of 10,000 on a 20,000 investment and one with 10,000 on a 2,000,000 investment are not equally attractive.

How do I calculate net present value?

Discount every future cash flow back to today at the discount rate, add those present values up, and then subtract the money you spend up front. For a project costing 100,000 that returns 25,000 a year for six years at eight percent, the six discounted flows come to 153,968.13 and the net present value is 53,968.13. The initial investment is not discounted, because it is spent today and today's money is already in today's units.

Why is the initial investment not discounted?

Because it happens at year zero, and the discount factor for year zero is 1 ÷ (1 + r)^0, which is exactly 1. Money spent today needs no adjustment to be expressed in today's money. If the same 100,000 were instead treated as a year one cash flow it would be discounted once and come off at 92,592.59 at eight percent, which would raise the net present value by 7,407.41 and turn a marginal project into a good-looking one.

What discount rate should I use?

The rate your money costs you or the rate it could earn somewhere else, which is why this page asks for it rather than assuming one. A safe project is usually tested against a low rate and a speculative one against a high rate, and the same cash flows can be worth 105,000 at a discount rate of zero and 6,968.02 at twenty percent. If you are not sure, run the project at several rates and find the one where the net present value crosses zero — that rate is the internal rate of return, which this page does not compute but which the table below lets you read off approximately.

Can net present value be negative?

Yes, and a negative answer is the useful kind. It means the project does not return as much as the rate you asked it to clear, so the money would do better elsewhere at that rate. A negative net present value is not an arithmetic failure and the calculator does not treat it as one — the present value of the flows is simply smaller than the amount invested. The size of the negative figure is how much value the project destroys at that rate.

Can a cash flow be negative in the middle of the list?

Yes. A negative number means that year costs you money rather than paying you: a refit, an overhaul, a regulatory upgrade. It is discounted exactly like a positive flow and subtracts from the total. What it cannot express is the initial investment, which has a field of its own, because the first number in the list is year one while the initial investment is year zero, and those are a full year apart.

What is UNDISCARDED cash flow worth here?

The page calls it the discount amount: the difference between the plain sum of the cash flows and their present value. For the default project the flows add up to 205,000 and are worth 153,968.13 today, so 51,031.87 of the apparent profit is really the cost of waiting. That gap widens with the discount rate and with how far out the money arrives, which is why a long project can look excellent by its totals and be worth very little today.

• 10 CFR 436.14 — Methodological assumptions (how future cash flows are discounted to present values) — U.S. Department of Energy rule, via the Electronic Code of Federal Regulations (United States)
• 31 CFR Part 356, Appendix B — Formulas and Tables: present value factors and the price formula for Treasury notes and bonds — U.S. Department of the Treasury rule, via the Electronic Code of Federal Regulations (United States)
• H.15 Selected Interest Rates — the published benchmark rates a computed rate is compared against — Board of Governors of the Federal Reserve System (United States)