What does an IRR of 15.24% mean?
On the defaults — $10,000 of investment, $3,000 a year coming back for 5 years at a 10% discount rate — the internal rate of return is 15.24%, which is above the 10% hurdle — the project earns 15.24% a year, and the NPV at 10% is $1,372.36. The IRR is the discount rate at which this investment’s NPV is exactly zero: at 15% the NPV is still $56.47, and at 16% it is −$177.12, so the rate where it crosses zero sits between them, at 15.24% (unrounded 15.238237%). A project whose IRR beats your hurdle creates value; one whose IRR falls short destroys it; and one whose IRR equals your hurdle breaks even.
Three things about the model are worth stating plainly.
First, the arithmetic is −$10,000 + $3,000 × 3.790786769 = $1,372.36 at a 10% rate, and the IRR is the rate where that arithmetic gives zero — 15.24% — the NPV, the IRR and the profit are three outputs, never the same number. Second, the meaning is 15.24% a year earned on the money — the rate the project itself earns, not the value it creates, and the NPV is the value in dollars at your hurdle. And third, the IRR is displayed to two decimals, half-up, and a figure that displays as 15.00% can sit a hair above or below 15%: $2,983.16 of inflow gives an IRR of 15.000063%, which displays as 15.00% — and $2,983.15 gives 14.999922%, which also displays as 15.00% — 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 at 10%. $11,372.36 − $10,000 = $1,372.36 — positive, so the IRR is above 10%.
Line 4 — the trial at 15%. At a 15% discount rate the NPV is $56.47 (unrounded 56.465294) — still positive, so the IRR is above 15%.
Line 5 — the trial at 16%. At a 16% discount rate the NPV is −$177.12 (unrounded −177.119039) — negative, so the IRR is below 16%.
Line 6 — the IRR. The rate where the NPV is zero sits between 15% and 16%, at 15.24% (unrounded 15.238237%).
Line 7 — the check. At $2,983.16 of inflow the IRR is 15.000063% — above 15%; and at $2,983.15 it is 14.999922% — below 15%.
Every branch, checked
Investment $12,500: initial investment $12,500.00; annual cash inflow $3,000.00; discount rate 10.00%; years 5; IRR 6.40%; NPV −$1,127.64; total inflows $15,000.00; profit $2,500.00 — More investment to earn back, so a lower rate of return.
Investment $7,500: initial investment $7,500.00; annual cash inflow $3,000.00; discount rate 10.00%; years 5; IRR 28.65%; NPV $3,872.36; total inflows $15,000.00; profit $7,500.00 — Less investment to earn back, so a higher rate of return.
Inflow $3,500: initial investment $10,000.00; annual cash inflow $3,500.00; discount rate 10.00%; years 5; IRR 22.11%; NPV $3,267.75; total inflows $17,500.00; profit $7,500.00 — More cash coming back each year, so a higher rate of return.
Inflow $2,500: initial investment $10,000.00; annual cash inflow $2,500.00; discount rate 10.00%; years 5; IRR 7.93%; NPV −$523.03; total inflows $12,500.00; profit $2,500.00 — Less cash coming back each year, so a lower rate of return.
Rate 8%: initial investment $10,000.00; annual cash inflow $3,000.00; discount rate 8.00%; years 5; IRR 15.24%; NPV $1,978.13; total inflows $15,000.00; profit $5,000.00 — A lower hurdle, so a higher NPV — but the IRR itself does not move.
Rate 12%: initial investment $10,000.00; annual cash inflow $3,000.00; discount rate 12.00%; years 5; IRR 15.24%; NPV $814.33; total inflows $15,000.00; profit $5,000.00 — A higher hurdle, so a lower NPV — but the IRR itself does not move.
Years 6: initial investment $10,000.00; annual cash inflow $3,000.00; discount rate 10.00%; years 6; IRR 19.91%; NPV $3,065.78; total inflows $18,000.00; profit $8,000.00 — One more year of inflows, so a higher rate of return.
Years 4: initial investment $10,000.00; annual cash inflow $3,000.00; discount rate 10.00%; years 4; IRR 7.71%; NPV −$490.40; total inflows $12,000.00; profit $2,000.00 — One fewer year of inflows, so a lower rate of return.
The reverses, worked backwards
Smallest inflow for the IRR to STAY at or above 15%: At the displayed $2,983.16 the figures are initial investment $10,000.00; annual cash inflow $2,983.16; discount rate 10.00%; years 5; IRR 15.00% (unrounded 15.000063%); NPV $1,308.52 (unrounded 1308.523459); total inflows $14,915.80; profit $4,915.80. At the lower neighbor the figures are initial investment $10,000.00; annual cash inflow $2,983.15; discount rate 10.00%; years 5; IRR 15.00% (unrounded 14.999922%); NPV $1,308.49 (unrounded 1308.485551); total inflows $14,915.75; profit $4,915.75 — below 15% — so $2,983.16 is the smallest inflow for the IRR to STAY at or above 15%.
Smallest inflow for the IRR to STAY at or above 10%: 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; IRR 10.00% (unrounded 10.000077%); NPV $0.02 (unrounded 0.019682); total inflows $13,189.90; profit $3,189.90. At the lower neighbor the figures are initial investment $10,000.00; annual cash inflow $2,637.97; discount rate 10.00%; years 5; IRR 10.00% (unrounded 9.999929%); NPV −$0.02 (unrounded −0.018226); total inflows $13,189.85; profit $3,189.85 — below 10% — so $2,637.98 is the smallest inflow for the IRR to STAY at or above 10%.
Largest investment for the IRR to STAY at or above 15%: At the displayed $10,056 the figures are initial investment $10,056.00; annual cash inflow $3,000.00; discount rate 10.00%; years 5; IRR 15.00% (unrounded 15.001954%); NPV $1,316.36 (unrounded 1316.360308); total inflows $15,000.00; profit $4,944.00. At the upper neighbor the figures are initial investment $10,057.00; annual cash inflow $3,000.00; discount rate 10.00%; years 5; IRR 15.00% (unrounded 14.997754%); NPV $1,315.36 (unrounded 1315.360308); total inflows $15,000.00; profit $4,943.00 — below 15% — so $10,056 is the largest investment for the IRR to STAY at or above 15%.
Shortest years for the IRR to STAY at or above 15%: 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; IRR 15.24% (unrounded 15.238237%); NPV $1,372.36 (unrounded 1372.360308); total inflows $15,000.00; profit $5,000.00. At the lower neighbor the figures are initial investment $10,000.00; annual cash inflow $3,000.00; discount rate 10.00%; years 4; IRR 7.71% (unrounded 7.713847%); NPV −$490.40 (unrounded −490.403661); total inflows $12,000.00; profit $2,000.00 — below 15% — so 5 years is the shortest years for the IRR to STAY at or above 15%.
Smallest inflow for the IRR to STAY at or above 20%: At the displayed $3,343.80 the figures are initial investment $10,000.00; annual cash inflow $3,343.80; discount rate 10.00%; years 5; IRR 20.00% (unrounded 20.000040%); NPV $2,675.63 (unrounded 2675.632800); total inflows $16,719.00; profit $6,719.00. At the lower neighbor the figures are initial investment $10,000.00; annual cash inflow $3,343.79; discount rate 10.00%; years 5; IRR 20.00% (unrounded 19.999904%); NPV $2,675.59 (unrounded 2675.594892); total inflows $16,718.95; profit $6,718.95 — below 20% — so $3,343.80 is the smallest inflow for the IRR to STAY at or above 20%.
Largest investment for the IRR to STAY at or above 12%: At the displayed $10,814 the figures are initial investment $10,814.00; annual cash inflow $3,000.00; discount rate 10.00%; years 5; IRR 12.00% (unrounded 12.001227%); NPV $558.36 (unrounded 558.360308); total inflows $15,000.00; profit $4,186.00. At the upper neighbor the figures are initial investment $10,815.00; annual cash inflow $3,000.00; discount rate 10.00%; years 5; IRR 12.00% (unrounded 11.997494%); NPV $557.36 (unrounded 557.360308); total inflows $15,000.00; profit $4,185.00 — below 12% — so $10,814 is the largest investment for the IRR to STAY at or above 12%.
A warning about the neighbours: every neighbour above sits one dollar, one cent or one year from the star, and every neighbour figure is a hair below or above the target even though it displays as the target — a one-cent move in the inflow moves the IRR by only about 0.0001 points, so the displayed two-decimal figure cannot tell the star from its neighbour. The page prints the unrounded six-decimal IRR in full so the rounding does not mislead you: R1 15.000063% / 14.999922%; R2 10.000077% / 9.999929%; R3 15.001954% / 14.997754%; R5 20.000040% / 19.999904%; R6 12.001227% / 11.997494%. The R1 neighbour sits a hair below 15% while displaying as 15.00%, and the R5 neighbour sits a hair below 20% while displaying as 20.00%.
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; IRR 15.24%; NPV $1,372.36; total inflows $15,000.00; profit $5,000.00. With Investment $12,500, initial investment $12,500.00; annual cash inflow $3,000.00; discount rate 10.00%; years 5; IRR 6.40%; NPV −$1,127.64; total inflows $15,000.00; profit $2,500.00. With Investment $7,500, initial investment $7,500.00; annual cash inflow $3,000.00; discount rate 10.00%; years 5; IRR 28.65%; NPV $3,872.36; total inflows $15,000.00; profit $7,500.00. With Inflow $3,500, initial investment $10,000.00; annual cash inflow $3,500.00; discount rate 10.00%; years 5; IRR 22.11%; NPV $3,267.75; total inflows $17,500.00; profit $7,500.00. With Inflow $2,500, initial investment $10,000.00; annual cash inflow $2,500.00; discount rate 10.00%; years 5; IRR 7.93%; NPV −$523.03; total inflows $12,500.00; profit $2,500.00. With Rate 8%, initial investment $10,000.00; annual cash inflow $3,000.00; discount rate 8.00%; years 5; IRR 15.24%; NPV $1,978.13; total inflows $15,000.00; profit $5,000.00. With Rate 12%, initial investment $10,000.00; annual cash inflow $3,000.00; discount rate 12.00%; years 5; IRR 15.24%; NPV $814.33; total inflows $15,000.00; profit $5,000.00. With Years 6, initial investment $10,000.00; annual cash inflow $3,000.00; discount rate 10.00%; years 6; IRR 19.91%; NPV $3,065.78; total inflows $18,000.00; profit $8,000.00. With Years 4, initial investment $10,000.00; annual cash inflow $3,000.00; discount rate 10.00%; years 4; IRR 7.71%; NPV −$490.40; total inflows $12,000.00; profit $2,000.00. With Investment $0, initial investment $0.00; annual cash inflow $3,000.00; discount rate 10.00%; years 5; IRR no IRR; NPV $11,372.36 (unrounded 11372.360308); total inflows $15,000.00; profit $15,000.00 — no rate to earn back — there is no IRR, and the NPV is the whole PV of the inflows. With Rate 0%, initial investment $10,000.00; annual cash inflow $3,000.00; discount rate 0.00%; years 5; IRR 15.24% (unrounded 15.238237%); NPV $5,000.00; total inflows $15,000.00; profit $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 (IRR unrounded 6.015911%, NPV unrounded −869.850291), initial investment $9,876.54; annual cash inflow $2,345.67; discount rate 9.50%; years 5; IRR 6.02% (unrounded 6.015911%); NPV −$869.85 (unrounded −869.850291); total inflows $11,728.35; profit $1,851.81 — the unrounded IRR and NPV round to the displayed figures. 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; IRR 15.24% (unrounded 15.238237%); NPV $137,236.03 (unrounded 137236.030823); total inflows $1,500,000.00; profit $500,000.00 — the same rate at a much bigger size — scale does not change the IRR. With Inflow below zero, initial investment $10,000.00; annual cash inflow −$3,000.00; discount rate 10.00%; years 5; IRR no IRR; NPV −$21,372.36 (unrounded −21372.360308); total inflows −$15,000.00; profit −$25,000.00 — each year loses money, so no rate makes the NPV zero: 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; IRR no IRR; NPV −$7,272.73 (unrounded −7272.727273); total inflows $3,000.00; profit −$7,000.00 — one year of inflow cannot return the investment, so no rate makes the NPV zero. With Inflow $1, initial investment $10,000.00; annual cash inflow $1.00; discount rate 10.00%; years 5; IRR no IRR; NPV −$9,996.21 (unrounded −9996.209213); total inflows $5.00; profit −$9,995.00 — a single dollar a year barely dents the investment, so no rate makes the NPV zero. With Investment $33,333, inflow $7,777, rate 7.25%, 7 years (IRR unrounded 14.016834%, NPV unrounded 8216.656827), initial investment $33,333.00; annual cash inflow $7,777.00; discount rate 7.25%; years 7; IRR 14.02% (unrounded 14.016834%); NPV $8,216.66 (unrounded 8216.656827); total inflows $54,439.00; profit $21,106.00 — the unrounded IRR and NPV round to the displayed figures. With Negative investment, initial investment −$10,000.00; annual cash inflow $3,000.00; discount rate 10.00%; years 5; IRR no IRR; NPV $21,372.36 (unrounded 21372.360308); total inflows $15,000.00; profit $25,000.00 — 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; IRR 15.24% (unrounded 15.238237%); NPV −$4,790.12 (unrounded −4790.123457); total inflows $15,000.00; profit $5,000.00 — a high discount rate shrinks the future to almost nothing — but the IRR does not move. With 10 years, initial investment $10,000.00; annual cash inflow $3,000.00; discount rate 10.00%; years 10; IRR 27.32% (unrounded 27.319842%); NPV $8,433.70 (unrounded 8433.701317); total inflows $30,000.00; profit $20,000.00 — ten years of inflows, discounted, still leave value — and a much higher rate.
A note on the rounding: the IRR is displayed to two decimals, half-up. With the fractional inputs the unrounded IRR is 6.015911% — it displays as 6.02% — and the unrounded NPV is −869.850291 — it displays as −$869.85. With one year there is no IRR at all and the unrounded NPV is −7272.727273 — it displays as −$7,272.73. With the other fractional inputs the unrounded IRR is 14.016834% — it displays as 14.02% — and 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 — and the IRR is still 15.24%. The page prints the unrounded values so the rounding does not mislead you.
Output · formula · meaning
| Output | Formula | What it means |
|---|
| Initial investment | input | $10,000.00. |
| Annual cash inflow | input | $3,000.00. |
| Discount rate | input | 10.00%. |
| Years | input | 5 years. |
| IRR | the discount rate where the NPV is zero | 15.24%. |
| NPV at 10% | −initial investment + annual cash inflow × annuity factor | $1,372.36. |
| PV of inflows | annual cash inflow × annuity factor | $11,372.36. |
| Annuity factor | (1 − (1 + rate)−years) ÷ rate | 3.790786769. |
| Total inflows | annual cash inflow × years | $15,000.00. |
| Profit | total inflows − initial investment | $5,000.00. |
| Verdict | whether the IRR beats the hurdle | Beats a 10.00% hurdle — IRR 15.24%; NPV $1,372.36. |
| Reverse: Smallest inflow for the IRR to STAY at or above 15% | step | $2,983.16: initial investment $10,000.00; annual cash inflow $2,983.16; discount rate 10.00%; years 5; IRR 15.00% (unrounded 15.000063%); NPV $1,308.52 (unrounded 1308.523459); total inflows $14,915.80; profit $4,915.80. |
| Reverse: Smallest inflow for the IRR to STAY at or above 10% | step | $2,637.98: initial investment $10,000.00; annual cash inflow $2,637.98; discount rate 10.00%; years 5; IRR 10.00% (unrounded 10.000077%); NPV $0.02 (unrounded 0.019682); total inflows $13,189.90; profit $3,189.90. |
| Reverse: Largest investment for the IRR to STAY at or above 15% | step | $10,056: initial investment $10,056.00; annual cash inflow $3,000.00; discount rate 10.00%; years 5; IRR 15.00% (unrounded 15.001954%); NPV $1,316.36 (unrounded 1316.360308); total inflows $15,000.00; profit $4,944.00. |
| Reverse: Shortest years for the IRR to STAY at or above 15% | step | 5 years: initial investment $10,000.00; annual cash inflow $3,000.00; discount rate 10.00%; years 5; IRR 15.24% (unrounded 15.238237%); NPV $1,372.36 (unrounded 1372.360308); total inflows $15,000.00; profit $5,000.00. |
| Reverse: Smallest inflow for the IRR to STAY at or above 20% | step | $3,343.80: initial investment $10,000.00; annual cash inflow $3,343.80; discount rate 10.00%; years 5; IRR 20.00% (unrounded 20.000040%); NPV $2,675.63 (unrounded 2675.632800); total inflows $16,719.00; profit $6,719.00. |
| Reverse: Largest investment for the IRR to STAY at or above 12% | step | $10,814: initial investment $10,814.00; annual cash inflow $3,000.00; discount rate 10.00%; years 5; IRR 12.00% (unrounded 12.001227%); NPV $558.36 (unrounded 558.360308); total inflows $15,000.00; profit $4,186.00. |
| Investment $12,500 | same model | initial investment $12,500.00; annual cash inflow $3,000.00; discount rate 10.00%; years 5; IRR 6.40%; NPV −$1,127.64; total inflows $15,000.00; profit $2,500.00. |
| Investment $7,500 | same model | initial investment $7,500.00; annual cash inflow $3,000.00; discount rate 10.00%; years 5; IRR 28.65%; NPV $3,872.36; total inflows $15,000.00; profit $7,500.00. |
| Inflow $3,500 | same model | initial investment $10,000.00; annual cash inflow $3,500.00; discount rate 10.00%; years 5; IRR 22.11%; NPV $3,267.75; total inflows $17,500.00; profit $7,500.00. |
| Inflow $2,500 | same model | initial investment $10,000.00; annual cash inflow $2,500.00; discount rate 10.00%; years 5; IRR 7.93%; NPV −$523.03; total inflows $12,500.00; profit $2,500.00. |
| Rate 8% | same model | initial investment $10,000.00; annual cash inflow $3,000.00; discount rate 8.00%; years 5; IRR 15.24%; NPV $1,978.13; total inflows $15,000.00; profit $5,000.00. |
| Rate 12% | same model | initial investment $10,000.00; annual cash inflow $3,000.00; discount rate 12.00%; years 5; IRR 15.24%; NPV $814.33; total inflows $15,000.00; profit $5,000.00. |
| Years 6 | same model | initial investment $10,000.00; annual cash inflow $3,000.00; discount rate 10.00%; years 6; IRR 19.91%; NPV $3,065.78; total inflows $18,000.00; profit $8,000.00. |
| Years 4 | same model | initial investment $10,000.00; annual cash inflow $3,000.00; discount rate 10.00%; years 4; IRR 7.71%; NPV −$490.40; total inflows $12,000.00; profit $2,000.00. |
| Investment $0 | same model | initial investment $0.00; annual cash inflow $3,000.00; discount rate 10.00%; years 5; IRR no IRR; NPV $11,372.36 (unrounded 11372.360308); total inflows $15,000.00; profit $15,000.00. |
| Rate 0% | same model | initial investment $10,000.00; annual cash inflow $3,000.00; discount rate 0.00%; years 5; IRR 15.24% (unrounded 15.238237%); NPV $5,000.00; total inflows $15,000.00; profit $5,000.00. |
| Investment $9,876.54, inflow $2,345.67, rate 9.5%, 5 years (IRR unrounded 6.015911%, NPV unrounded −869.850291) | same model | initial investment $9,876.54; annual cash inflow $2,345.67; discount rate 9.50%; years 5; IRR 6.02% (unrounded 6.015911%); NPV −$869.85 (unrounded −869.850291); total inflows $11,728.35; profit $1,851.81. |
| Investment $1,000,000, inflow $300,000 | same model | initial investment $1,000,000.00; annual cash inflow $300,000.00; discount rate 10.00%; years 5; IRR 15.24% (unrounded 15.238237%); NPV $137,236.03 (unrounded 137236.030823); total inflows $1,500,000.00; profit $500,000.00. |
| Inflow below zero | same model | initial investment $10,000.00; annual cash inflow −$3,000.00; discount rate 10.00%; years 5; IRR no IRR; NPV −$21,372.36 (unrounded −21372.360308); total inflows −$15,000.00; profit −$25,000.00. |
| 1 year | same model | initial investment $10,000.00; annual cash inflow $3,000.00; discount rate 10.00%; years 1; IRR no IRR; NPV −$7,272.73 (unrounded −7272.727273); total inflows $3,000.00; profit −$7,000.00. |
| Inflow $1 | same model | initial investment $10,000.00; annual cash inflow $1.00; discount rate 10.00%; years 5; IRR no IRR; NPV −$9,996.21 (unrounded −9996.209213); total inflows $5.00; profit −$9,995.00. |
| Investment $33,333, inflow $7,777, rate 7.25%, 7 years (IRR unrounded 14.016834%, NPV unrounded 8216.656827) | same model | initial investment $33,333.00; annual cash inflow $7,777.00; discount rate 7.25%; years 7; IRR 14.02% (unrounded 14.016834%); NPV $8,216.66 (unrounded 8216.656827); total inflows $54,439.00; profit $21,106.00. |
| Negative investment | same model | initial investment −$10,000.00; annual cash inflow $3,000.00; discount rate 10.00%; years 5; IRR no IRR; NPV $21,372.36 (unrounded 21372.360308); total inflows $15,000.00; profit $25,000.00. |
| Rate 50% | same model | initial investment $10,000.00; annual cash inflow $3,000.00; discount rate 50.00%; years 5; IRR 15.24% (unrounded 15.238237%); NPV −$4,790.12 (unrounded −4790.123457); total inflows $15,000.00; profit $5,000.00. |
| 10 years | same model | initial investment $10,000.00; annual cash inflow $3,000.00; discount rate 10.00%; years 10; IRR 27.32% (unrounded 27.319842%); NPV $8,433.70 (unrounded 8433.701317); total inflows $30,000.00; profit $20,000.00. |
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 earns 15.24% — and they check the $2,983.16 reverse to see the smallest inflow that still earns 15%.
- The landlord pricing a renovation: they learn the IRR beats a 10% hurdle — and they check the $10,056 reverse to see the most they can invest and still earn 15%.
- The investor comparing two projects: they learn one project earns 15.24% and the other earns 12% — and they check the $3,343.80 reverse to see the inflow that would earn 20%.
- The student learning investment appraisal: they learn the IRR is the rate where the NPV is zero — and they check the 5-year reverse to see the shortest term that still earns 15%.
Accuracy & limitations
The math is first-principles: the IRR is the discount rate at which the net present value is exactly zero, where the net present value is minus the initial investment plus the annual cash inflow times the annuity factor, and the annuity factor is (1 − (1 + rate)−years) ÷ rate — all in dollars, percent and years, the IRR 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 there is no rate at which the NPV is zero the calculator says so plainly: at $0 of investment there is no outlay to earn back, so there is no IRR — and the NPV is $11,372.36, the whole PV of the inflows. At a −$3,000 inflow each year loses money, so no rate makes the NPV zero — and the NPV is −$21,372.36, a real figure, shown with the U+2212 minus sign. At one year the inflow cannot return the investment, so there is no IRR — and the NPV is −$7,272.73. At a −$10,000 investment the NPV is positive at every rate, so there is no IRR — and the NPV is $21,372.36, a real figure, a grant or credit against the investment. With the fractional inputs the unrounded IRR is 6.015911% — it displays as 6.02% — and the unrounded NPV is −869.850291 — it displays as −$869.85. With the other fractional inputs the unrounded IRR is 14.016834% — it displays as 14.02% — and the unrounded NPV is 8216.656827 — it displays as $8,216.66. The smallest inflow for the IRR to stay at or above 15% is $2,983.16 — the page shows the displayed $2,983.16 input only, and the forward at that input is 15.000063%, which displays as 15.00%. The largest investment for the IRR to stay at or above 15% is $10,056 — the page shows the displayed $10,056 input only, and the forward at that input is 15.001954%, which displays as 15.00%. What the model cannot do is say whether 15.24% is a good return: it says nothing about the risk — whether the cash is certain or a guess — and it says nothing about scale — a $10,000 project earning 15.24% and a $1,000,000 project earning 15.24% have the same IRR, and the bigger one creates far more value. Use it to see the rate — then check the net present value, payback period and break-even point calculators before you decide the investment is right.
Cite this calculatorBright Side Kit. “Internal Rate of Return Calculator: Is It Worth It?” brightoolbox.com, 2026. Method: internal rate of return = the discount rate at which the net present value is zero; net present value = −initial investment + annual cash inflow × annuity factor; annuity factor = (1 − (1 + rate)−years) ÷ rate. Reverses: smallest inflow for the IRR to STAY at or above 15% is $2,983.16 (at $2,983.16 the figures are initial investment $10,000.00; annual cash inflow $2,983.16; discount rate 10.00%; years 5; IRR 15.00% (unrounded 15.000063%); NPV $1,308.52 (unrounded 1308.523459); total inflows $14,915.80; profit $4,915.80; at $2,983.15 the figures are initial investment $10,000.00; annual cash inflow $2,983.15; discount rate 10.00%; years 5; IRR 15.00% (unrounded 14.999922%); NPV $1,308.49 (unrounded 1308.485551); total inflows $14,915.75; profit $4,915.75 — below 15%); smallest inflow for the IRR to STAY at or above 10% is $2,637.98 (at $2,637.98 the figures are initial investment $10,000.00; annual cash inflow $2,637.98; discount rate 10.00%; years 5; IRR 10.00% (unrounded 10.000077%); NPV $0.02 (unrounded 0.019682); total inflows $13,189.90; profit $3,189.90; at $2,637.97 the figures are initial investment $10,000.00; annual cash inflow $2,637.97; discount rate 10.00%; years 5; IRR 10.00% (unrounded 9.999929%); NPV −$0.02 (unrounded −0.018226); total inflows $13,189.85; profit $3,189.85 — below 10%); largest investment for the IRR to STAY at or above 15% is $10,056 (at $10,056 the figures are initial investment $10,056.00; annual cash inflow $3,000.00; discount rate 10.00%; years 5; IRR 15.00% (unrounded 15.001954%); NPV $1,316.36 (unrounded 1316.360308); total inflows $15,000.00; profit $4,944.00; at $10,057 the figures are initial investment $10,057.00; annual cash inflow $3,000.00; discount rate 10.00%; years 5; IRR 15.00% (unrounded 14.997754%); NPV $1,315.36 (unrounded 1315.360308); total inflows $15,000.00; profit $4,943.00 — below 15%); shortest years for the IRR to STAY at or above 15% is 5 years (at 5 years the figures are initial investment $10,000.00; annual cash inflow $3,000.00; discount rate 10.00%; years 5; IRR 15.24% (unrounded 15.238237%); NPV $1,372.36 (unrounded 1372.360308); total inflows $15,000.00; profit $5,000.00; at 4 years the figures are initial investment $10,000.00; annual cash inflow $3,000.00; discount rate 10.00%; years 4; IRR 7.71% (unrounded 7.713847%); NPV −$490.40 (unrounded −490.403661); total inflows $12,000.00; profit $2,000.00 — below 15%); smallest inflow for the IRR to STAY at or above 20% is $3,343.80 (at $3,343.80 the figures are initial investment $10,000.00; annual cash inflow $3,343.80; discount rate 10.00%; years 5; IRR 20.00% (unrounded 20.000040%); NPV $2,675.63 (unrounded 2675.632800); total inflows $16,719.00; profit $6,719.00; at $3,343.79 the figures are initial investment $10,000.00; annual cash inflow $3,343.79; discount rate 10.00%; years 5; IRR 20.00% (unrounded 19.999904%); NPV $2,675.59 (unrounded 2675.594892); total inflows $16,718.95; profit $6,718.95 — below 20%); largest investment for the IRR to STAY at or above 12% is $10,814 (at $10,814 the figures are initial investment $10,814.00; annual cash inflow $3,000.00; discount rate 10.00%; years 5; IRR 12.00% (unrounded 12.001227%); NPV $558.36 (unrounded 558.360308); total inflows $15,000.00; profit $4,186.00; at $10,815 the figures are initial investment $10,815.00; annual cash inflow $3,000.00; discount rate 10.00%; years 5; IRR 12.00% (unrounded 11.997494%); NPV $557.36 (unrounded 557.360308); total inflows $15,000.00; profit $4,185.00 — below 12%). Defaults: initial investment $10,000.00; annual cash inflow $3,000.00; discount rate 10.00%; years 5; IRR 15.24%; NPV $1,372.36; total inflows $15,000.00; profit $5,000.00 Bright Side Kit. "Internal Rate of Return Calculator: Is It Worth It?" https://brightoolbox.com/internal-rate-of-return-calculator/ Accessed October 27, 2026.
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Frequently asked questions
What is the internal rate of return?
The discount rate at which an investment’s NPV is exactly zero. The IRR is the rate the project itself earns. On $10,000 invested with $3,000 a year coming back for 5 years, the IRR is 15.24% — the project earns 15.24% a year.
How do I calculate the internal rate of return?
Find the rate where the NPV is zero. At 10% the NPV is $1,372.36 — positive, so the IRR is above 10%. At 15% the NPV is $56.47 — still positive. At 16% the NPV is −$177.12 — negative. The rate where it crosses zero sits between 15% and 16%, at 15.24%.
What does an IRR of 15.24% mean?
The project earns 15.24% a year. If your hurdle is 10%, the project beats it and creates value — the NPV at 10% is $1,372.36. If your hurdle were 16%, the project would fall short and destroy value.
How much cash do I need each year to earn 15%?
$2,983.16 a year. The smallest inflow for the IRR to stay at or above 15% is $2,983.16. At $2,983.16 the IRR is 15.000063% — above 15% — and at $2,983.15 it is 14.999922% — below 15%.
How much can I invest and still earn 15%?
$10,056. The largest investment for the IRR to stay at or above 15% is $10,056. At $10,056 the IRR is 15.001954% — above 15% — and at $10,057 it is 14.997754% — below 15%.
What if there is no IRR?
Some investments have no rate at which the NPV is zero. At $0 of investment there is no outlay to earn back. At a −$3,000 inflow each year loses money. At one year the inflow cannot return the investment. The calculator says so plainly — there is no IRR — and shows the NPV instead.
Does the discount rate change the IRR?
No. The discount rate is the hurdle you compare the IRR against, not part of the project. At 8% the NPV is $1,978.13 and at 12% it is $814.33, but the IRR is 15.24% in both cases.
What is the difference between IRR and NPV?
One is a rate, the other is a value in dollars. The IRR is the rate the project earns — 15.24% here. The NPV is the value it creates at your hurdle — $1,372.36 at 10%. A project can earn a high rate on a small investment and still create less value than a bigger project earning a lower rate. Work it out in the net present value calculator.