Internal Rate of Return
Also: 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.
See also
Frequently asked questions
What does an IRR of 9.7% actually tell me?
It means the project is expected to return 9.7% per year, accounting for when each cash flow arrives. The Internal Rate of Return is the discount rate that sets the net present value of all inflows and outflows to zero, so 9.7% is the break-even cost of money for that project. Above your cost of capital, it creates value; below it, it destroys value.
What is the difference between IRR and NPV?
IRR gives you a percentage, NPV gives you an amount. The Internal Rate of Return tells you the annualized return rate; net present value tells you how much value the project adds in currency terms at a given discount rate. Because IRR ignores project size, a small project at 25% can add less value than a large one at 12%, which is why finance teams read both together.
How do I decide whether to accept a project based on its IRR?
Compare the IRR to your hurdle rate or cost of capital. If the Internal Rate of Return sits above it, the project generally goes ahead; if it sits below, it is generally rejected. A project returning $120,000 on a $100,000 investment over three years has an IRR near 9.7%: it clears an 8% cost of capital but fails a 12% one, despite the positive total in dollars.
Why can a project show several IRRs, or none at all?
Because the IRR equation is a polynomial: cash flows that alternate between positive and negative can produce multiple roots, or no real solution. This happens with projects requiring reinvestment mid-life, such as a mid-period overhaul. In those cases the Internal Rate of Return stops being a usable decision signal and net present value should drive the call.
When should I use MIRR instead of IRR?
Use MIRR when interim cash flows will realistically be reinvested at a rate well below the IRR. Standard IRR assumes every intermediate inflow earns the IRR itself, which inflates the result on high-return projects. The Modified IRR replaces that assumption with an explicit reinvestment rate, typically the cost of capital, and gives a more defensible figure for private equity or real estate deals with long holding periods.