Finance & InvestmentEntry № 01.23Documented Formula

XIRR Calculator (Extended Internal Rate of Return)

Determines the annualized internal rate of return for irregular cash inflows, SIPs, and periodic portfolio redemptions via Newton-Raphson iteration.

Popular Searches:How to calculate XIRR of irregular mutual fund investments?XIRR vs CAGR differencePortfolio annual return with withdrawals

XIRR Irregular Cashflow Engine (Newton-Raphson)

Cash Flow Entries (Negative = Invest, Positive = Current Value)

Annualized XIRR Return

13.76%

Internal rate of return equating discounted cash flows to zero.

Total Invested$200,000.00

Current Portfolio Valuation$245,000.00

Absolute Net Gain$45,000.00

Mathematical Proof & FormulaStandard Mathematical Notation

How This Calculation Formula is Formulated

Extended Internal Rate of Return (XIRR) solves for the discount rate (r) that sets the net present value of all irregular cash inflows and outflows to zero, solved using the Newton-Raphson numerical method.

Standard Algebraic Representation

Σ [ CFᵢ / (1 + r)^( (dᵢ − d₀) / 365 ) ] = 0

Documented algebraic formula with transparent derivation and reference notes.

Variable Definitions & Measurement Units

CFᵢ

Cash Flow Amount

Positive for redemptions/current value, negative for investments.

dᵢ

Cash Flow Date

Calendar date on which transaction occurred.

XIRR Annualized Rate

Annualized internal rate of return.

Step-by-Step Calculation Example

Three-Installment Irregular Mutual Fund Portfolio

An investor deposits ₹1,00,000 on Jan 15, ₹50,000 on Jun 15, ₹50,000 on next Jan 15, and redeems ₹2,45,000 on Dec 15.

Discounting Cashflows

NPV(r) = -100k - 50k/(1+r)^0.41 - 50k/(1+r)^1.0 + 245k/(1+r)^1.91

Equation setup

Newton-Raphson Iteration

r_{n+1} = r_n - NPV(r_n) / NPV'(r_n)

Iterative root-finding converges in 5 steps

Solved Annualized Rate

r ≈ 15.68%

Exact annualized return

Conclusion: The portfolio achieved an annualized XIRR of 15.68%, capturing exact holding periods for each distinct cash installment.

In-Depth Editorial Analysis

Why CAGR Fails for Multiple Cash Flows and XIRR is Mandatory

CAGR only measures returns between two discrete points: an initial investment and an ending valuation. When investors make recurring SIP installments, irregular top-ups, dividend payouts, or partial redemptions, CAGR cannot mathematically account for the varying durations each rupee spent in the market.

XIRR normalizes every cashflow to exact day counts, applying individual compounding discount factors. This makes XIRR the universal regulatory standard used by mutual fund AMCs and portfolio managers worldwide.

Frequently Asked Questions

Frequently Asked Questions About XIRR Calculator (Extended Internal Rate of Return)

What is the difference between IRR and XIRR?

IRR assumes strictly equal periodic intervals (e.g., exactly 30 days apart), whereas XIRR supports irregular calendar dates with exact day-count fractions (d_i / 365).

Why can XIRR show extreme values for short holding periods?

Because XIRR annualizes returns, a 5% gain realized in 5 days will extrapolate mathematically to an absurd annualized percentage. XIRR is most reliable for holding periods exceeding 6 to 12 months.

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Deterministic Precision & 100% Client-Side Privacy

All calculations execute in your local browser using IEEE 754 double-precision floating-point arithmetic. Your figures and financial metrics remain private and are never uploaded or saved to any cloud servers.