Net Present Value Calculator: Is This Investment Worth It?

What does an NPV of $1,372.36 mean?

On the defaults — $10,000 of investment, $3,000 a year coming back for 5 years at a 10% discount rate — the net present value is $1,372.36, which is positive — the investment creates value. The PV of inflows is $11,372.36: the five yearly inflows, discounted back to today, are worth $11,372.36 now. After the $10,000 outlay, the investment is worth $1,372.36 more than doing nothing. A positive NPV means the project earns more than the discount rate demands; a negative NPV means it earns less; and an NPV of zero means it earns exactly the discount rate. The internal rate of return is 15.24% — the discount rate at which this investment’s NPV is exactly zero.

Three things about the model are worth stating plainly.

First, the arithmetic is −$10,000 + $3,000 × 3.790786769 = $1,372.36, and the PV of inflows is $3,000 × 3.790786769 = $11,372.36 — the NPV, the PV of inflows and the annuity factor are three outputs, never the same number. Second, the meaning is $1,372.36 of value created — the value today of the future cash inflows, minus the investment, not the profit itself, and the IRR is the rate where that value is zero. And third, the NPV is displayed to two decimals, half-up, and a figure that displays as $0.36 can sit a hair above zero: $11,372 of investment gives an NPV of 0.360308, which displays as $0.36 — and $11,373 gives −0.639692, which displays as −$0.64 — all listed in Accuracy & limitations.

The worked example, line by line

Setup: investment $10,000, annual cash inflow $3,000, discount rate 10%, years 5.

Line 1 — the annuity factor. (1 − 1.10⁻⁵) ÷ 0.10 = 3.790786769.

Line 2 — the PV of inflows, year by year. Year 1 $2,727.27, year 2 $2,479.34, year 3 $2,253.94, year 4 $2,049.04, year 5 $1,862.76 — added before rounding they come to $11,372.36. The rounded yearly figures add to $11,372.35, one cent of rounding.

Line 3 — the NPV. $11,372.36 − $10,000 = $1,372.36.

Line 4 — the IRR. The discount rate where the NPV is zero is 15.24% (unrounded 15.238237%).

Line 5 — the check. At $11,372 of investment the NPV is 0.360308 — above zero; and at $11,373 it is −0.639692 — below zero.

Every branch, checked

Investment $12,500: initial investment $12,500.00; annual cash inflow $3,000.00; discount rate 10.00%; years 5; net present value −$1,127.64 — More investment to win back, so a lower NPV.

Investment $7,500: initial investment $7,500.00; annual cash inflow $3,000.00; discount rate 10.00%; years 5; net present value $3,872.36 — Less investment to win back, so a higher NPV.

Inflow $3,500: initial investment $10,000.00; annual cash inflow $3,500.00; discount rate 10.00%; years 5; net present value $3,267.75 — More cash coming back each year, so a higher NPV.

Inflow $2,500: initial investment $10,000.00; annual cash inflow $2,500.00; discount rate 10.00%; years 5; net present value −$523.03 — Less cash coming back each year, so a lower NPV.

Rate 8%: initial investment $10,000.00; annual cash inflow $3,000.00; discount rate 8.00%; years 5; net present value $1,978.13 — A lower discount rate, so the future is worth more today.

Rate 12%: initial investment $10,000.00; annual cash inflow $3,000.00; discount rate 12.00%; years 5; net present value $814.33 — A higher discount rate, so the future is worth less today.

Years 6: initial investment $10,000.00; annual cash inflow $3,000.00; discount rate 10.00%; years 6; net present value $3,065.78 — One more year of inflows, so a higher NPV.

Years 4: initial investment $10,000.00; annual cash inflow $3,000.00; discount rate 10.00%; years 4; net present value −$490.40 — One fewer year of inflows, so a lower NPV.

The reverses, worked backwards

Largest investment for the NPV to STAY at or above 0: At the displayed $11,372 the figures are initial investment $11,372.00; annual cash inflow $3,000.00; discount rate 10.00%; years 5; net present value $0.36 (unrounded 0.360308). At the upper neighbor the figures are initial investment $11,373.00; annual cash inflow $3,000.00; discount rate 10.00%; years 5; net present value −$0.64 (unrounded −0.639692) — below zero — so $11,372 is the largest investment for the NPV to STAY at or above 0.

Smallest inflow for the NPV to STAY at or above 0: At the displayed $2,637.98 the figures are initial investment $10,000.00; annual cash inflow $2,637.98; discount rate 10.00%; years 5; net present value $0.02 (unrounded 0.019682). At the lower neighbor the figures are initial investment $10,000.00; annual cash inflow $2,637.97; discount rate 10.00%; years 5; net present value −$0.02 (unrounded −0.018226) — below zero — so $2,637.98 is the smallest inflow for the NPV to STAY at or above 0.

Highest discount rate for the NPV to STAY at or above 0: At the displayed 15% the figures are initial investment $10,000.00; annual cash inflow $3,000.00; discount rate 15.00%; years 5; net present value $56.47 (unrounded 56.465294). At the upper neighbor the figures are initial investment $10,000.00; annual cash inflow $3,000.00; discount rate 16.00%; years 5; net present value −$177.12 (unrounded −177.119039) — below zero — so 15% is the highest discount rate for the NPV to STAY at or above 0.

Shortest years for the NPV to STAY at or above 0: At the displayed 5 years the figures are initial investment $10,000.00; annual cash inflow $3,000.00; discount rate 10.00%; years 5; net present value $1,372.36 (unrounded 1372.360308). At the lower neighbor the figures are initial investment $10,000.00; annual cash inflow $3,000.00; discount rate 10.00%; years 4; net present value −$490.40 (unrounded −490.403661) — below zero — so 5 years is the shortest years for the NPV to STAY at or above 0.

Largest investment for the NPV to STAY at or above $2,000: At the displayed $9,372 the figures are initial investment $9,372.00; annual cash inflow $3,000.00; discount rate 10.00%; years 5; net present value $2,000.36 (unrounded 2000.360308). At the upper neighbor the figures are initial investment $9,373.00; annual cash inflow $3,000.00; discount rate 10.00%; years 5; net present value $1,999.36 (unrounded 1999.360308) — below $2,000 — so $9,372 is the largest investment for the NPV to STAY at or above $2,000.

Smallest inflow for the NPV to STAY at or above $1,000: At the displayed $2,901.78 the figures are initial investment $10,000.00; annual cash inflow $2,901.78; discount rate 10.00%; years 5; net present value $1,000.03 (unrounded 1000.029232). At the lower neighbor the figures are initial investment $10,000.00; annual cash inflow $2,901.77; discount rate 10.00%; years 5; net present value $999.99 (unrounded 999.991324) — below $1,000 — so $2,901.78 is the smallest inflow for the NPV to STAY at or above $1,000.

A warning about the neighbours: every neighbour above sits one dollar, one cent or one percent from the star, and every neighbour figure is a hair below or above the target even though it displays as the target — a one-dollar move in the investment moves the NPV by exactly $1.00, and a one-cent move in the inflow moves it by about $0.04, so the displayed two-decimal figure cannot tell the star from its neighbour. The page prints the unrounded six-decimal NPV in full so the rounding does not mislead you: R1 0.360308 / −0.639692; R2 0.019682 / −0.018226; R3 56.465294 / −177.119039; R5 2000.360308 / 1999.360308; R6 1000.029232 / 999.991324. The R2 neighbour sits a hair below $0 while displaying as −$0.02, and the R6 neighbour sits a hair below $1,000 while displaying as $999.99.

What the defaults assume

The defaults are $10,000 of investment, $3,000 of annual cash inflow, a 10% discount rate and 5 years — initial investment $10,000.00; annual cash inflow $3,000.00; discount rate 10.00%; years 5; net present value $1,372.36. With Investment $12,500, initial investment $12,500.00; annual cash inflow $3,000.00; discount rate 10.00%; years 5; net present value −$1,127.64. With Investment $7,500, initial investment $7,500.00; annual cash inflow $3,000.00; discount rate 10.00%; years 5; net present value $3,872.36. With Inflow $3,500, initial investment $10,000.00; annual cash inflow $3,500.00; discount rate 10.00%; years 5; net present value $3,267.75. With Inflow $2,500, initial investment $10,000.00; annual cash inflow $2,500.00; discount rate 10.00%; years 5; net present value −$523.03. With Rate 8%, initial investment $10,000.00; annual cash inflow $3,000.00; discount rate 8.00%; years 5; net present value $1,978.13. With Rate 12%, initial investment $10,000.00; annual cash inflow $3,000.00; discount rate 12.00%; years 5; net present value $814.33. With Years 6, initial investment $10,000.00; annual cash inflow $3,000.00; discount rate 10.00%; years 6; net present value $3,065.78. With Years 4, initial investment $10,000.00; annual cash inflow $3,000.00; discount rate 10.00%; years 4; net present value −$490.40. With Investment $0, initial investment $0.00; annual cash inflow $3,000.00; discount rate 10.00%; years 5; net present value $11,372.36 (unrounded 11372.360308) — the whole PV of the inflows, with no outlay. With Rate 0%, initial investment $10,000.00; annual cash inflow $3,000.00; discount rate 0.00%; years 5; net present value $5,000.00 — the no-discounting limit — inflows added straight, NOT undefined. With Investment $9,876.54, inflow $2,345.67, rate 9.5%, 5 years (NPV unrounded −869.850291), initial investment $9,876.54; annual cash inflow $2,345.67; discount rate 9.50%; years 5; net present value −$869.85 (unrounded −869.850291) — the unrounded NPV rounds to the displayed figure. With Investment $1,000,000, inflow $300,000, initial investment $1,000,000.00; annual cash inflow $300,000.00; discount rate 10.00%; years 5; net present value $137,236.03 (unrounded 137236.030823) — the same shape at a much bigger size. With Inflow below zero, initial investment $10,000.00; annual cash inflow −$3,000.00; discount rate 10.00%; years 5; net present value −$21,372.36 (unrounded −21372.360308) — each year loses money, so the NPV is negative: a real figure, shown with the U+2212 minus sign. With 1 year, initial investment $10,000.00; annual cash inflow $3,000.00; discount rate 10.00%; years 1; net present value −$7,272.73 (unrounded −7272.727273) — one year of inflow cannot cover the investment. With Inflow $1, initial investment $10,000.00; annual cash inflow $1.00; discount rate 10.00%; years 5; net present value −$9,996.21 (unrounded −9996.209213) — a single dollar a year barely dents the investment. With Investment $33,333, inflow $7,777, rate 7.25%, 7 years (NPV unrounded 8216.656827), initial investment $33,333.00; annual cash inflow $7,777.00; discount rate 7.25%; years 7; net present value $8,216.66 (unrounded 8216.656827) — the unrounded NPV rounds to the displayed figure. With Negative investment, initial investment −$10,000.00; annual cash inflow $3,000.00; discount rate 10.00%; years 5; net present value $21,372.36 (unrounded 21372.360308) — a grant or credit against the investment: a real figure, shown with the U+2212 minus sign. With Rate 50%, initial investment $10,000.00; annual cash inflow $3,000.00; discount rate 50.00%; years 5; net present value −$4,790.12 (unrounded −4790.123457) — a high discount rate shrinks the future to almost nothing. With 10 years, initial investment $10,000.00; annual cash inflow $3,000.00; discount rate 10.00%; years 10; net present value $8,433.70 (unrounded 8433.701317) — ten years of inflows, discounted, still leave value.

A note on the rounding: the NPV is displayed to two decimals, half-up. With the fractional inputs the unrounded NPV is −869.850291 — it displays as −$869.85. With one year the unrounded NPV is −7272.727273 — it displays as −$7,272.73. With the other fractional inputs the unrounded NPV is 8216.656827 — it displays as $8,216.66. At a 50% rate the unrounded NPV is −4790.123457 — it displays as −$4,790.12. The page prints the unrounded values so the rounding does not mislead you.

Output · formula · meaning

Who uses this

• The small-business owner weighing a new machine: they learn $10,000 of investment and $3,000 a year coming back for 5 years at 10% has an NPV of $1,372.36 — and they check the $11,372 reverse to see the most they can invest and still break even.
• The landlord pricing a renovation: they learn the PV of inflows is $11,372.36 — and they check the $2,637.98 reverse to see the smallest inflow that still leaves the NPV at or above zero.
• The investor comparing two projects: they learn the NPV falls when the discount rate rises — and they check the 15% reverse to see the highest rate that still leaves the NPV at or above zero.
• The student learning investment appraisal: they learn the NPV is the discounted inflows minus the investment — and they check the $9,372 reverse to see the most they can invest and still clear $2,000 of value.

Accuracy & limitations

The math is first-principles: the NPV is minus the initial investment plus the annual cash inflow times the annuity factor, where the annuity factor is (1 − (1 + rate)^−years) ÷ rate — all in dollars, percent and years, the NPV displayed to two decimals half-up. There IS division in this calculator — the annuity factor divides by the rate, so the formula as written is undefined at a 0% rate — but the LIMIT is real: at 0% the inflows are not discounted at all, so the NPV is simply −investment + inflow × years ($5,000.00 at the headline inputs) — the calculator shows $5,000.00 with a note, never hides it. When the inflow is below zero the NPV goes NEGATIVE: a −$3,000 inflow against a $10,000 investment gives −$21,372.36 — a real figure, shown with the U+2212 minus sign, because each year loses money. When the investment is negative the NPV rises above the PV of inflows: −$10,000 of investment gives $21,372.36 — a real figure, shown with the U+2212 minus sign, a grant or credit against the investment. At $0 of investment the NPV is $11,372.36 — the whole PV of the inflows, a real figure, not undefined. With the fractional inputs the unrounded NPV is −869.850291 — it displays as −$869.85. With one year the unrounded NPV is −7272.727273 — it displays as −$7,272.73. With the other fractional inputs the unrounded NPV is 8216.656827 — it displays as $8,216.66. At a 50% rate the unrounded NPV is −4790.123457 — it displays as −$4,790.12. The largest investment for the NPV to stay at or above 0 is $11,372 — the page shows the displayed $11,372 input and the forward at that input is 0.360308, which displays as $0.36. The smallest inflow for the NPV to stay at or above 0 is $2,637.98 — the page shows the displayed $2,637.98 input only, and the forward at that input is 0.019682, which displays as $0.02. What the model cannot do is say whether 10% is the right discount rate: it says nothing about the risk — whether the cash is certain or a guess — and it says nothing about uneven cash flows — whether the inflow is $3,000 every year or $0 in year one and $6,000 in year two. Use it to see whether the investment creates value — then check the payback period, future value and break-even point calculators before you decide the investment is right.

Frequently asked questions