IRR Calculator
The internal rate of return is the discount rate at which a project breaks even in present-value terms. It expresses a project as a single annual percentage.
Formula
IRR is the rate r where Σ ( cash flow ÷ (1 + r)ᵗ ) = initial cost
- Equivalently, the discount rate at which NPV equals zero
- There is no closed form; it is found by iteration
£1,000 a year for 5 years on £3,500 gives an IRR near 13.2%
What IRR Represents
IRR is the rate r that makes net present value exactly zero:
0 = ∑ [ Cash flowt ÷ (1 + r)t ]
There is no closed-form solution for most cash flow patterns, so it is found by iteration — trying rates until NPV lands on zero.
The decision rule is simple: accept if IRR exceeds your cost of capital.
Why It Is Popular
A percentage is intuitive. "This project returns 15% a year" communicates instantly in a way that "this project has an NPV of £42,000" does not, and it compares directly against borrowing costs and other opportunities.
Where IRR Misleads
- It ignores scale. A 50% return on £1,000 beats 20% on £1,000,000 by IRR, and loses badly in pounds.
- It assumes reinvestment at the IRR itself, which is usually unrealistic for high figures. MIRR exists to address this.
- Multiple IRRs are possible when cash flows change sign more than once, making the result ambiguous.
Use IRR alongside NPV rather than instead of it. Where the two disagree on mutually exclusive projects, NPV is the more reliable guide.
Quick Reference
| NPV | IRR | |
|---|---|---|
| Answers | How much value is added | What rate the project earns |
| Units | Currency | Percentage |
| Needs a discount rate | Yes | No |
| Compares different sizes | Poorly | Well |
| Multiple answers possible | No | Yes, if cash flows change sign |
Frequently Asked Questions
- What is a good IRR?
- Anything comfortably above your cost of capital. The threshold depends on risk: a stable project might justify 8 per cent while a speculative one needs far more.
- Why can there be more than one IRR?
- When cash flows switch between negative and positive more than once, the equation can have several valid roots, making IRR ambiguous.
- Should I use IRR or NPV?
- NPV when choosing between mutually exclusive projects, because it accounts for scale. IRR is a useful summary but can favour small projects with high percentage returns.
- What is MIRR?
- Modified internal rate of return. It assumes reinvestment at your actual cost of capital rather than at the IRR, which is usually more realistic.