IRR in 3 Easy Steps
The internal rate of return (IRR) is the discount rate that makes a project's NPV exactly zero. Think of it as the project's own annual rate of return. If the IRR is higher than what your money costs you, such as a bank loan rate or required return, the project is worth doing.
IRR explained simply
The internal rate of return (IRR) is the discount rate that makes a project's NPV exactly zero: its own yearly rate of return. If IRR is above your cost of capital, the project adds value. In the example, a $1,000 project paying $600 for 2 years has an IRR of about 13.1%.
What this IRR lesson covers
- What IRR means in plain English
- The IRR formula: set NPV equal to zero
- How to find IRR by trial and error
- How to estimate IRR with linear interpolation
- How to compare IRR with your cost of capital
IRR formula, explained
- C₀
- initial investment today
- CFₜ
- cash flow in year t
- IRR
- the rate that makes NPV equal zero
- r₁
- lower trial rate, giving a positive NPV₁
- r₂
- higher trial rate, giving a negative NPV₂
How to calculate IRR step by step (worked example)
A project costs $1,000 today and pays $600 at the end of each of the next 2 years. What is its IRR?
- Try 10%: NPV = 600 ÷ 1.10 + 600 ÷ 1.10² − 1,000 = 41.32
- Try 15%: NPV = 600 ÷ 1.15 + 600 ÷ 1.15² − 1,000 = −24.57
- The IRR is between 10% and 15% because NPV changes sign
- Interpolate: 10% + [41.32 ÷ (41.32 + 24.57)] × 5% ≈ 13.14%
Answer: IRR ≈ 13.1%. Interpolation gives about 13.14%; the exact answer from a financial calculator is about 13.07%. If the cost of capital is below that, accept the project.
IRR vs NPV
| IRR | NPV | |
|---|---|---|
| What it gives | A percentage return | Value added in dollars |
| Decision rule | Accept if IRR > cost of capital | Accept if NPV > 0 |
| Easy to explain | Yes | Fairly |
| Weak spots | Can mislead when ranking projects; can have several answers | Needs a discount rate up front |
Harder IRR questions
What is the project's NPV at an 8% cost of capital?
600 ÷ 1.08 + 600 ÷ 1.08² − 1,000 ≈ $69.96. Positive, which agrees with the IRR rule, since 13.07% is above 8%.
Can a project have more than one IRR?
Yes, when cash flows change sign more than once (for example, a big clean-up cost at the end). Then IRR can give two or more answers, and NPV is the safer guide.
Why is the interpolated IRR slightly off?
Interpolation draws a straight line between two points on a curve. The real NPV curve bends, so the estimate (13.14%) is a little above the exact 13.07%.
Common IRR questions
What is the formula for IRR?
There is no direct formula you can rearrange. IRR is the rate that solves 0 = −C₀ + Σ CFₜ ÷ (1 + IRR)ᵗ. You find it by trial and error, by interpolation between two rates, or with a financial calculator or Excel's IRR function.
How do you calculate IRR by hand?
Pick a discount rate and compute NPV. If NPV is positive, try a higher rate; if negative, try a lower one. Once you have one positive and one negative NPV, interpolate between the two rates to estimate where NPV equals zero.
What is a good IRR?
A good IRR is one above the project's cost of capital or hurdle rate. If money costs you 8% and the project's IRR is 13%, it earns more than it costs. There is no single magic number, because it depends on risk.
What is the difference between IRR and NPV?
NPV gives the dollar value a project adds at a chosen discount rate. IRR gives the percentage return at which NPV is zero. They usually agree on accept or reject decisions, but NPV is more reliable when ranking projects.