What Is Internal Rate of Return? IRR Formula

What is internal rate of return

The internal rate of return (IRR) is the discount rate at which the net present value (NPV) of all cash flows of an investment equals zero.

Put simply, at the IRR the money you put in and the money you get back are worth the same in today's terms. A discount rate is the rate used to convert a future payment into its value today.

IRR formula

Formally, the IRR is the rate r that solves:

Present value of all inflows at rate r = Present value of all outflows at rate r

Each cash flow is divided by its discount factor. The discount factor is (one plus r) raised to the power of the number of periods until that payment. Payments further in the future are reduced more.

The equation cannot be rearranged to give r directly. It is solved by trial and error, or by numerical methods such as bisection or Newton's method. In spreadsheets, the functions IRR (equal periods) and XIRR (exact dates) do this for you.

How to calculate IRR: a worked example

This is a hypothetical case. Ayesha pays a lump sum today for a small business stake. In return she receives a fixed payment at the end of each year for a set number of years, and nothing after that.

List the cash flows with their dates. The payment today is negative. The payments she receives are positive.
Pick a trial rate and compute the NPV.
If the NPV is positive, the trial rate is too low, so raise it. If the NPV is negative, the rate is too high, so lower it.
Repeat until the NPV is close enough to zero. That rate is the IRR.

To try this with your own figures, use a spreadsheet or the tools on the calculators page.

Where you see IRR

Bonds: yield to maturity is the IRR of the bond's price, its coupons and its face value.
Fund and private-equity reports: these often quote "net IRR" to investors.
Project finance and company reports: IRR is set against a hurdle rate, which is the minimum return required.
Pakistani business news: project returns are often compared with the policy rate. The latest SBP decision: SBP policy rate raised by 50 bps to 12% with effect from 27.10.2026 (MPC). Rate changes are usually quoted in basis points.

Edge cases experienced readers should know

Several or no IRRs: if the cash flows change sign more than once, for example outflow, inflow, then outflow again, the equation can have several solutions or none.
Reinvestment assumption: IRR implicitly assumes interim cash flows are reinvested at the IRR itself. Modified IRR (MIRR) replaces this with an explicit reinvestment rate.
Ranking projects: IRR ignores size. A small project can have a higher IRR but a lower NPV than a large one. When you can only choose one project, NPV is the usual tie-breaker.
Period vs annual rate: IRR from monthly cash flows is a monthly rate and must be annualised. See annualized return.
Risk: IRR says nothing about how likely the cash flows are. A high IRR on uncertain payments is not the same as a modest IRR on safe ones.

CAGR: this is the IRR of a case with a single payment in and a single payment out.
Annualized return
Bond duration
Amortization
Accrued interest
Saving, investing, loans
Trading glossary

Frequent questions

What does IRR mean in simple words?

IRR is the yearly rate of return that makes an investment's future cash flows worth exactly what was paid for them.

Is a higher IRR always better?

Not always. IRR ignores the size of the project and its risk. It can also be misleading when cash flows change sign more than once.

What is the difference between IRR and XIRR?

IRR assumes equally spaced periods. XIRR uses the actual date of each cash flow.

Is IRR the same as yield to maturity?

Yes. Yield to maturity is the IRR of a bond held to maturity, assuming every payment is made on time.

Internal rate of return (IRR)