IRR Calculator
Find the discount rate that makes the net present value of a series of cash flows equal to zero, helping you evaluate project profitability
Formula
0 = Σ [CFt / (1 + IRR)^t]
IRR is the discount rate that makes NPV equal to zero. Higher IRR indicates higher annualized return.
Worked Examples
Example 1: Simple Investment
Problem:Invest $50,000, receive $15,000/year for 5 years.
Solution:Cash flows: -50000, 15000, 15000, 15000, 15000, 15000 Total returns: $75,000 Profit: $25,000 IRR calculation yields ~15.2%
Result:IRR = 15.2%
Example 2: Real Estate
Problem:Buy property for $200,000, rent for 5 years, sell for $250,000.
Solution:Year 0: -$200,000 Years 1-5: $18,000/year rent Year 5: +$250,000 sale Total inflows: $340,000 IRR ≈ 12.5%
Result:IRR = 12.5%
Example 3: Compare Projects
Problem:Project A: -$100k, +$150k in year 3. Project B: -$100k, +$40k/year for 3 years.
Solution:Project A IRR: (150/100)^(1/3) - 1 = 14.5% Project B IRR: ~9.7% (iterative) A has higher IRR but B has better cash flow timing.
Result:A: 14.5%, B: 9.7%
Frequently Asked Questions
What is IRR?
Internal Rate of Return is the discount rate that makes NPV equal to zero. It represents the annualized return of an investment considering the time value of money.
How is IRR different from ROI?
ROI = (Gain - Cost) / Cost, ignoring timing. IRR accounts for when cash flows occur. $100 returned in year 1 is worth more than $100 in year 5.
What are IRR limitations?
IRR assumes reinvestment at the IRR rate, which may be unrealistic. Multiple IRRs possible with alternating cash flows. Doesn't account for project size or timing preferences.
How does IRR relate to NPV?
IRR is the discount rate where NPV = 0. If your required return < IRR, NPV is positive (good investment). If required return > IRR, NPV is negative (reject).
What is Modified IRR (MIRR)?
MIRR assumes reinvestment at a specified rate (usually cost of capital), not at IRR. More realistic for comparing projects but requires additional assumptions.
Can IRR be negative?
Yes, if total cash inflows are less than outflows. This means you lose money even ignoring time value. Negative IRR = bad investment.
What if there's no IRR?
Some cash flow patterns have no IRR (NPV never crosses zero) or multiple IRRs (crosses zero multiple times). Use NPV analysis in these cases.
How is IRR calculated?
There's no closed-form solution. Use iteration (guess and check) or numerical methods like Newton-Raphson. Spreadsheets and calculators use these algorithms.
What does IRR actually represent in plain terms?
IRR is the annualized percentage return at which the present value of a project's or investment's cash inflows exactly equals the present value of its cash outflows — in other words, the discount rate that makes NPV equal to zero. It provides a single, comparable percentage figure that summarizes the effective yield of a series of cash flows over time.
Why can a project have more than one valid IRR?
When a project's cash flows change sign more than once — for example, an initial outflow, followed by inflows, followed by another large outflow such as a decommissioning cost — the underlying polynomial equation used to solve for IRR can mathematically have multiple valid roots. In these cases, IRR can be ambiguous or misleading, and NPV (evaluated directly at your actual required rate of return) is the more reliable decision tool.