IRR Calculator — Internal Rate of Return
Calculate the Internal Rate of Return (IRR) for a series of cash flows. Enter your initial investment (negative) and subsequent returns to find the discount rate that makes the NPV zero. See also ROI Calculator and Compound Interest Calculator.
How to Calculate IRR
The Internal Rate of Return (IRR) is the discount rate that makes the Net Present Value (NPV) of all cash flows equal to zero. It represents the annualized effective compounded return rate of an investment. To calculate IRR, you need a series of cash flows: typically a negative initial investment followed by positive returns over time. The IRR is found iteratively using numerical methods like Newton's method, since there is no closed-form solution for most cash flow series.
IRR Formula
NPV = Σ (CFₜ / (1 + IRR)ᵗ) = 0
Where:
CFₜ = Cash flow at time t
IRR = Internal Rate of Return (the unknown)
t = Time period (0, 1, 2, ...)
Solved iteratively using Newton's method:
IRR(n+1) = IRR(n) − NPV(IRR(n)) / NPV'(IRR(n))
Example Calculation
Cash Flows: -$10,000, $3,000, $4,000, $5,000, $3,000
Find rate r where:
-10000 + 3000/(1+r) + 4000/(1+r)² + 5000/(1+r)³ + 3000/(1+r)⁴ = 0
IRR ≈ 16.82%
Total invested: $10,000 | Total returned: $15,000
IRR Reference Table
| Scenario | Cash Flows | IRR |
|---|---|---|
| Even returns | -10K, 3K, 3K, 3K, 3K | 7.71% |
| Growing returns | -10K, 1K, 2K, 4K, 8K | 13.07% |
| Front-loaded | -10K, 8K, 4K, 2K, 1K | 22.30% |
| Single payoff | -10K, 0, 0, 0, 15K | 10.67% |
| Quick return | -5K, 6K | 20.00% |
Frequently Asked Questions
What is a good IRR?
A good IRR depends on the context. For venture capital, 25-35% is typical. For real estate, 15-20% is considered strong. For corporate projects, any IRR above the company's cost of capital (often 8-12%) is generally acceptable.
What is the difference between IRR and ROI?
ROI measures total return as a percentage of the initial investment without considering the time value of money. IRR accounts for when cash flows occur, giving a time-weighted annualized return. IRR is more useful for comparing investments with different timing patterns.
Can IRR be negative?
Yes. A negative IRR means the investment lost money — the total returns were less than the initial investment. This happens when the sum of positive cash flows is less than the absolute value of the initial investment.
What are the limitations of IRR?
IRR assumes reinvestment at the IRR rate itself, which may be unrealistic. It can also produce multiple solutions when cash flows change sign more than once. For mutually exclusive projects, NPV is often a better decision metric than IRR.
Solved Examples
Example 1: Small business investment evaluation
Solution:
Initial investment: -$100,000 (Year 0)
Cash flows: Year 1 = $30,000, Year 2 = $35,000, Year 3 = $40,000, Year 4 = $45,000
Find rate r where: -100,000 + 30,000/(1+r) + 35,000/(1+r)² + 40,000/(1+r)³ + 45,000/(1+r)⁴ = 0
Using iterative calculation (Newton's method): IRR ≈ 15.24%
Answer: IRR = 15.24%. Since this exceeds the 10% cost of capital, the project is viable.
Example 2: Comparing two projects with different scales
Solution:
Project A: Invest $50,000, receive $20,000/year for 3 years → IRR = 9.70%
Project B: Invest $200,000, receive $70,000/year for 4 years → IRR = 14.96%
Despite lower absolute investment, Project B has higher IRR
Project B is preferred if capital is available and risk is acceptable
Answer: Project B (IRR 14.96%) is the better investment compared to Project A (IRR 9.70%).
Example 3: Real estate development project
Solution:
Year 0: -$500,000 (land + construction), Year 1: -$200,000 (construction continues)
Year 2: $150,000 (rental income), Year 3: $160,000, Year 4: $170,000
Year 5: $850,000 (rental + property sale)
IRR calculation yields ≈ 12.8%
Answer: IRR = 12.8%. The project is marginally attractive for a required return of 12%.
Practice Questions
Try these on your own:
- An investment of $25,000 returns $8,000, $9,000, $10,000, and $11,000 over 4 years. What is the IRR? (Answer: ≈16.5%)
- You invest $80,000 and receive $30,000 annually for 3 years. Is the IRR above or below 6%? (Answer: Above — IRR ≈ 6.13%)
- A project costs $150,000 upfront and returns $50,000/year for 5 years. Calculate the IRR. (Answer: ≈19.86%)
- If a project's IRR is 8% and your cost of capital is 10%, should you invest? (Answer: No, IRR < cost of capital)
- Investment: -$40,000, then $15,000, $15,000, $15,000, $15,000. What is the IRR? (Answer: ≈18.45%)
Common Mistakes to Avoid
The biggest mistake with IRR is using it as the sole decision criterion. IRR doesn't account for project scale — a small project with 50% IRR may generate less total value than a large project with 15% IRR. Another common error is applying IRR to projects with non-conventional cash flows (alternating positive and negative), which can produce multiple IRR values or no solution at all. People also confuse IRR with actual return — IRR assumes all intermediate cash flows are reinvested at the IRR rate, which may not be realistic (this is the "reinvestment rate assumption" problem). When comparing mutually exclusive projects with different lifespans, IRR can be misleading — use NPV or equivalent annual annuity instead. Finally, never compare the IRR to nominal rates without adjusting for inflation and risk.
Key Takeaways
- IRR is the discount rate that makes the Net Present Value (NPV) of all cash flows equal to zero.
- Accept a project if IRR exceeds your required rate of return (cost of capital).
- IRR cannot be solved algebraically for more than 2 periods — it requires iterative numerical methods.
- Non-conventional cash flows (multiple sign changes) can produce multiple or no IRR solutions.
- IRR ignores scale: always check NPV alongside IRR when comparing projects of different sizes.
- Modified IRR (MIRR) addresses the reinvestment rate assumption by using a more realistic reinvestment rate.