XIRR Calculator
Calculate the Extended Internal Rate of Return (XIRR) for your recurring investments and SIPs.
What is the XIRR Calculator?
The Extended Internal Rate of Return (XIRR) is a standard metric used to calculate the annualized rate of return for a series of cash flows occurring at irregular or regular intervals. Unlike Simple CAGR (which only looks at the initial and final values), XIRR accounts for the exact timing and amount of every single transaction.
For systematic investment plans (SIPs), recurring deposits, or multi-installment equity portfolios, XIRR is the most accurate method to measure real portfolio performance because it gives time-weighted importance to each deposit.
Practical Examples & Reference Guide
Here is a reference table demonstrating the calculated XIRR for a recurring monthly investment of $5,000 over different timeframes and maturity outcomes:
| Monthly Deposit | Start Date | Maturity Date | Maturity Value | Calculated XIRR (%) |
|---|---|---|---|---|
| $5,000 | 2023-01-01 | 2024-01-01 | $64,000 | 12.60% |
| $5,000 | 2023-01-01 | 2025-01-01 | $135,000 | 11.23% |
| $5,000 | 2020-01-01 | 2025-01-01 | $380,000 | 9.64% |
| $5,000 | 2023-01-01 | 2024-01-01 | $55,000 | -15.02% |
These examples illustrate that XIRR adapts to both gains and losses based on the real time duration of the investment.
In-Depth Technical Guide
The Mathematical Formula of XIRR
To compute XIRR, we solve for the rate r that satisfies the Net Present Value (NPV) equation of all cash flows set to zero:
$$\sum_{i=1}^{N} \frac{C_i}{(1 + r)^{\frac{d_i - d_1}{365}}} = 0$$
Where:
- $C_i$ = the amount of the $i$-th cash flow (investments are entered as negative values, while final maturity or redemptions are positive values).
- $d_i$ = the date of the $i$-th cash flow.
- $d_1$ = the date of the first cash flow (Start Date).
- $r$ = the annualized rate of return (XIRR).
- $N$ = the total number of transactions including the maturity payout.
Why Do We Need a Numerical Solver?
Because r is raised to varying fractional exponents depending on the number of days between dates, this equation cannot be solved algebraically. Instead, financial tools use numerical approximation algorithms:
- Newton-Raphson Method: An iterative solver using the function's derivative to quickly converge on the root of the equation.
- Bisection Method: A fallback search algorithm that repeatedly cuts an interval in half to locate the rate when Newton-Raphson encounters convergence limits.