Internal Rate of Return (IRR) Calculator
Calculate the periodic and annualized internal rate of return for a series of cash flows occurring at regular, equal time intervals.
Enter your periodic flows on the left and click calculate.
Understanding IRR (Internal Rate of Return)
The Internal Rate of Return (IRR) is the annual rate of growth an investment is expected to generate. Unlike XIRR, standard IRR assumes that all transaction payments occur at completely regular, periodic intervals (yearly, quarterly, or monthly). It represents the discount rate that makes the net present value (NPV) of all cash flows equal to zero.
The Mathematical Formula
The IRR solver calculates the periodic interest rate r for which NPV equals zero:
Where:
- Ct = The cash flow transaction at period t (Negative for outflows, Positive for inflows).
- t = The index period number (from 0 to N).
- r = The periodic Internal Rate of Return (IRR).
To calculate the Annualized IRR from a periodic rate:
Where m represents the number of compounding periods in a single year (e.g. 12 for monthly, 4 for quarterly).
Worked Example
Scenario: 3-Year Project Cash Flows (Annual Periods)
| Period (Year) | Transaction | Amount ($) |
|---|---|---|
| Period 0 (Start) | Outflow (-) | -100,000 |
| Period 1 (End of Yr 1) | Inflow (+) | +30,000 |
| Period 2 (End of Yr 2) | Inflow (+) | +40,000 |
| Period 3 (End of Yr 3) | Inflow (+) | +50,000 |
By running our numerical iteration on the cash flow series, the equation converges to r = 9.70%. This indicates the project yields a yearly compounded return of 9.70%.