IRR Calculator
Internal rate of return for up to six years of cash flows, plus NPV at your discount rate.
What it does
The internal rate of return compresses a project into a single percentage: the annual rate at which the present value of its inflows exactly pays back the initial outlay. It is the break-even cost of capital, and investors like it because percentages travel well in conversation.
The tool above takes an initial investment, up to six years of annual cash flows, and your discount rate. It finds the IRR by bisection, reports the NPV at your own rate, and prints the classic accept or reject call. Enter 0 for any year after the project ends.
The defaults model a $10,000 machine returning $3,000 a year for five years against a 10 % cost of capital: IRR 15.24 %, NPV $1,372.36, accept. The OpenStax Principles of Finance embroidery machine example, $16,000 followed by $2,000, $4,000, and then $5,000 four times, reproduces the textbook's 14.09 % IRR and $2,835.62 NPV at a 9 % rate.
The method, worked examples, and caveats follow OpenStax's chapter on capital budgeting: the reinvestment assumption, the possibility of multiple IRRs with unusual flow patterns, and the rule that IRR and NPV only disagree in interesting ways when projects differ in scale or timing.
How to use
- Enter the initial investment as a positive number; the tool applies the minus sign at time zero.
- Fill in the annual cash flows for years 1 through 6.
- Use 0 in any year with no flow, including all unused years at the end.
- Set the discount rate to your cost of capital or hurdle rate.
- Read the IRR, then the NPV and the decision line underneath.
Formula
- CF0
- Initial investment, at time zero.
- CF1 to CF6
- Cash flow in years 1 through 6.
- r
- Discount rate, the annual cost of capital.
- IRR
- The rate r where the project's NPV crosses zero.
No formula solves for IRR in closed form, so the tool searches between -99.99 % and 1000 % by bisection: it tests the midpoint, keeps the half where the NPV changes sign, and repeats 200 times, which pins the rate to far more precision than the two decimals shown. If the NPV never changes sign across that range, no IRR exists and the tool says so. IRR quietly assumes every interim cash flow is reinvested at the IRR itself, and flow patterns that alternate signs can cross zero twice, producing two IRRs; this tool reports one.
Worked example
Example: $10,000 machine, $3,000 a year for five years
Defaults: $10,000 initial, $3,000 in years 1 to 5, $0 in year 6, 10 % discount rate.
- At 0 % the flows return $15,000 against $10,000, an NPV of $5,000.00.
- At 10 % each flow is discounted: NPV = $1,372.36, so the project clears the cost of capital.
- Keep raising the rate: at 15 % the NPV is down to $56.47.
- At 16 % it turns negative at -$177.12, so the crossing sits between 15 % and 16 %.
- Bisection pins the crossing at 15.24 %: the IRR.
Reference table
| Discount rate | NPV | Verdict |
|---|---|---|
| 0 % | $5,000.00 | Accept |
| 5 % | $2,988.43 | Accept |
| 10 % | $1,372.36 | Accept |
| 15 % | $56.47 | Accept |
| 16 % | -$177.12 | Reject |
| 20 % | -$1,028.16 | Reject |
Limits
- Models an initial outlay followed by annual inflows, one flow per year.
- Assumes interim cash flows are reinvested at the IRR itself.
- Reports a single IRR even when the flows imply more than one.
- Ignores taxes, inflation adjustments, and mid-year timing.
Common mistakes
- Comparing IRRs across projects of very different sizes.
- Ignoring NPV when choosing between mutually exclusive projects.
- Feeding revenue instead of net cash flow into the years.
- Sliding the initial investment into year 1.
- Leaving unused years blank instead of entering 0.
Try it yourself
Quick checks. Answers sit tucked under each question.
Same $10,000 project, but a 16 % hurdle rate?
Reject: the IRR of 15.24 % falls short, and NPV at 16 % is -$177.12.
OpenStax embroidery machine: $16,000 in, then $2,000, $4,000, and $5,000 four times?
IRR 14.09 %; at a 9 % cost of capital the NPV is $2,835.62.
$10,000 in, $1,000 a year for five years?
IRR -19.4 %: the flows return less than the outlay, and NPV at 10 % is -$6,209.21.
Questions
What does IRR stand for?
Internal rate of return: the discount rate that sets the project's net present value to zero.
How is IRR used next to NPV?
NPV tells you how many dollars a project adds at your cost of capital; IRR tells you the break-even rate. Accept when IRR exceeds the rate and NPV is positive.
Can the IRR be negative?
Yes. If the project returns less than the initial outlay over its life, the break-even rate sits below zero.
Why might a project have two IRRs?
Every time the cash flows change sign, the NPV curve can cross zero again. A big cleanup cost after profitable years is the classic trigger.
What discount rate should I enter?
Your cost of capital: what the money costs you, or the return you could get on the next best project of similar risk.
Does IRR account for project size?
No. It is a percentage, so a tiny project and a huge one can show the same IRR while adding very different dollar values.
Sources
- OpenStax Principles of Finance 2e, 16.3 Internal Rate of Return (IRR) Method
- OpenStax Principles of Finance 2e, 16.2 Net Present Value (NPV) Method
- OpenStax Principles of Finance 2e, Chapter 16 Summary