Internal Rate of ReturnIRR
The internal rate of return is the discount rate at which the present value of an investment’s cash flows equals zero. It is a single annual return figure for investments with irregular cash flows, such as private funds or projects.
Two investments both turn $1,000 into $1,100 of cash — yet one is clearly better because you get your money back sooner. The internal rate of return captures that difference in a single annual percentage.
- Category
- Accounting, Tax and Operations
- Reading time
- 4 min
- Also called
- Discounted cash flow return
- Updated
IRR in plain words
HM Treasury defines IRR as the discount rate that makes the net present value of the cash outflows and inflows zero.1
Intuitively, it is the constant interest rate your money would have to earn to produce the same cash inflows.1
The SEC staff describes a private fund's IRR the same way: the rate that sets the NPV of all its cash flows to zero.2
How to find an IRR, step by step
List cash flows
Write outflows as negative and inflows as positive, by date.
Check the shape
IRR suits outflows first, then inflows.1
Guess a rate
Pick a trial discount rate.
Discount and sum
Compute NPV at that rate; the target is zero.1
Adjust and repeat
Raise the rate if NPV is positive, lower it if negative; a spreadsheet's IRR function does this.
Cross-check with NPV
IRR is not a reliable substitute for NPV.1
Worked examples
Example 1 — Even cash flows
IRR ≈ 13.07%A hypothetical $1,000 investment pays $600 at the end of years 1 and 2.
| Try 13.07% | 600 ÷ 1.1307 = 530.66; 600 ÷ 1.1307² = 469.34 |
| NPV | −1,000 + 530.66 + 469.34 = 0 |
| IRR | ≈ 13.07% |
That rate returns an NPV of zero, which is the definition of IRR.1
Example 2 — Timing matters
Earlier cash ⇒ higher IRRHypothetical A pays 700 then 400; B pays 400 then 700, each on $1,000.
| A: IRR | ≈ 7.28% (652.47 + 347.53 = 1,000) |
| B: IRR | ≈ 6.02% (377.28 + 622.72 = 1,000) |
| Total cash | Both 1,100 |
The timing of cash flows has a big effect on the IRR.1
Example 3 — Alternating flows
Use NPV insteadA hypothetical project's cash flows go −, +, −, + over four years.
| Sign changes | 3 |
| Possible IRRs | More than one |
When positive and negative cash flows alternate, the IRR is not uniquely determinate.1
IRR vs NPV
| Aspect | IRR | NPV |
|---|---|---|
| Output | A percentage | A money amount |
| Needs a discount rate | No — it solves for one | Yes |
| Scale | Ignores size | Reflects size |
| Alternating flows | Can give several answers | Always one answer |
Where IRR is used
Private equity
Funds with unpredictable cash flows.
Projects
Comparing capital projects.
Your own account
Measuring a return that includes your deposits and withdrawals.
Bonds
Yield to Maturity is an IRR on a bond's cash flows.
Advantages and disadvantages
Advantages
- One annual figure for irregular cash flows.
- Reflects the timing of money in and out.
- No discount rate is needed upfront.
- Works well for private equity-style flows.
Disadvantages
- Highly sensitive to timing.
- Multiple answers with alternating flows.
- Ignores the size of the investment.
- Not a reliable replacement for NPV.
Going deeper
Read as far as you need. Each level builds on the one before it.
Common mistakes
Ranking by IRR alone
A small project with a high IRR can create less value.
Ignoring timing
Early distributions inflate IRR.
Mixing gross and net
Compare IRRs before and after fees over the same periods.
Trusting one answer
Check sign changes in the cash flows.
Check your understanding
Test yourself before moving on. Each answer comes with an explanation.
Key points to remember
- IRR is the discount rate that sets NPV to zero.
- It is one annual figure for irregular flows.
- Timing heavily affects it.
- Alternating flows can break it.
- Pair it with NPV.
Frequently asked questions
Is a higher IRR always better?
Can I calculate IRR in a spreadsheet?
Is IRR the same as annual return?
Further learning
- Yield to Maturity
IRR applied to bonds.
- Interest Rate
The discounting idea.
- Dollar-Cost Averaging
Regular cash flows into investments.
- Profit and Loss
The raw result IRR annualises.
Sources
This article is written in our own words. The sources below support the specific facts, rules and figures marked with a number in the text. Links open the original publisher’s page.
- GOV.UK (HM Treasury). Guidance note: the use of internal rates of return in PFI projects (opens in a new tab) Checked .
- U.S. Securities and Exchange Commission. Marketing Compliance – Frequently Asked Questions (opens in a new tab) Checked .
- CFA Institute. Using Brinson Attribution to Explain the Differences between Time-Weighted (TWR) and Money-Weighted (IRR) Returns (Digest Summary) (opens in a new tab) Checked .
Educational content, not financial advice. Examples use hypothetical prices and simplified costs; actual fees, margin rules and regulations vary by broker, market and country. We are not affiliated with any publisher linked above. Last reviewed . Report an error or request a source credit.