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.
What you will learn
- 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
The formulas
- 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
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.
Common 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.