Internal Rate of Return
Aussi : IRR, Internal Rate of Return, discounted cash flow rate of return
The Internal Rate of Return is the discount rate that makes a project's net present value equal zero. It expresses an investment's expected annualized return.
What It Is
The Internal Rate of Return (IRR) is the discount rate at which the net present value (NPV) of all cash flows from an investment equals zero. In plain terms, it is the annualized rate of return a project is expected to generate, accounting for the timing of every cash inflow and outflow.
Mathematically, IRR is the rate *r* that solves:
`0 = CF0 + CF1/(1+r) + CF2/(1+r)^2 + ... + CFn/(1+r)^n`
Because this equation rarely has a clean algebraic solution, IRR is found numerically (by iteration), which is why spreadsheets and financial tools compute it for you.
Why it matters
IRR gives finance teams a single percentage to compare against a hurdle rate or cost of capital:
- If IRR is above the hurdle rate, the project is generally accepted.
- If IRR is below the hurdle rate, the project is generally rejected.
Its intuitive percentage format makes it easy to communicate to executives and boards who think in terms of returns rather than absolute dollar amounts.
How it is used in practice
- Capital budgeting: ranking competing projects or equipment purchases.
- Private equity and venture capital: measuring fund and deal performance.
- Real estate: evaluating acquisitions across different holding periods.
Watch the limitations:
- IRR assumes interim cash flows are reinvested at the IRR itself, which can overstate returns. The Modified IRR (MIRR) corrects this.
- Projects with alternating positive and negative cash flows can produce multiple IRRs or none.
- IRR ignores project scale, so a high-percentage small project may add less value than a lower-percentage large one. Pair it with NPV.
Concrete Example
You invest $100,000 today and receive $40,000 per year for three years (total $120,000).
- Cash flows: -100,000, +40,000, +40,000, +40,000
- Solving for the rate that sets NPV to zero gives an IRR of about 9.7%.
If your cost of capital is 8%, the project clears the hurdle and creates value. If your cost of capital is 12%, the project destroys value despite the positive total dollars received.