What is Internal Rate of Return (IRR)?
Internal rate of return (IRR) is the discount rate at which a project's net present value equals zero — in other words, the annualized rate of return the investment is expected to earn. For a simple investment with a single cash outflow today and a single cash inflow later, IRR has a direct formula; more complex cash flow patterns require trial and error or financial software.
IRR is the break-even discount rate where NPV = 0. For a single-cash-flow investment, IRR = (Future cash flow / Initial investment)^(1/n) − 1.
- 1↓Estimate cash flowsProject the initial outlay and each period's expected cash inflow.
- 2↓Pick a trial discount rateStart with a reasonable guess, such as the company's cost of capital.
- 3↓Calculate NPV at that rateDiscount all cash flows and sum them to find NPV.
- 4↓Adjust the rateIf NPV is positive, try a higher rate; if negative, try a lower rate.
- 5Converge on IRRRepeat until NPV is approximately zero — that rate is the IRR.
Try it: interactive calculator
Step-by-step worked examples
You invest $10,000 today and expect to receive $20,000 in 5 years. What is the IRR?
IRR = (CF/C0)^(1/n) − 1 IRR = (20,000/10,000)^(1/5) − 1 IRR = 2^0.2 − 1 = 1.1487 − 1 IRR ≈ 14.87%
An investment of $5,000 grows to $15,000 in 8 years. Find the IRR.
IRR = (15,000/5,000)^(1/8) − 1 IRR = 3^0.125 − 1 = 1.1472 − 1 IRR ≈ 14.72%
$100,000 invested today returns $250,000 in 10 years. What is the IRR?
IRR = (250,000/100,000)^(1/10) − 1 IRR = 2.5^0.1 − 1 = 1.0960 − 1 IRR ≈ 9.60%
Flashcards
Quick quiz
Q1.IRR is defined as the discount rate where…
Q2.A project has an IRR of 14% and the company's cost of capital is 10%. What should the company do?
Q3.$10,000 today grows to $20,000 in 5 years. Approximately what is the IRR?
Q4.Why can IRR be hard to calculate for multi-year, uneven cash flows?
The full card deck, worked steps and AI-tutor support for “What is Internal Rate of Return (IRR)?” are in Notek — study by hand before your exam.
Common mistakes
Confusing IRR with the discount rate used in NPV. — Correct: The discount rate is an input you choose (cost of capital); IRR is a rate the project itself generates.
Assuming higher IRR always means a better project regardless of size. — Correct: IRR ignores project scale — a small project can have a high IRR but create less total value than a large one.
Applying the single-cash-flow IRR formula to a project with many yearly cash flows. — Correct: Multi-period cash flows need iterative NPV-solving (trial and error or software), not the simple (CF/C0)^(1/n)−1 formula.
Ignoring that some cash flow patterns can produce multiple IRRs. — Correct: Projects with cash flows that change sign more than once can have more than one mathematically valid IRR.
FAQ
What is internal rate of return?
IRR is the discount rate that makes a project's net present value equal zero — effectively its expected annualized return.
What is the IRR formula?
For a single cash flow: IRR = (CF/C₀)^(1/n) − 1. For multiple cash flows, IRR is found by solving NPV = 0 iteratively.
How do you calculate IRR?
Find the discount rate that sets the sum of discounted cash flows equal to the initial investment, often via trial and error or a financial calculator.
What are examples of IRR in practice?
Comparing the profitability of two capital projects, evaluating a private equity deal, or deciding whether to expand a business line.