IRR (Internal Rate of Return) Calculator

Compute the IRR for equally spaced periods or the XIRR for irregular, date-based cash flows. Robust solver with validation and clear diagnostics.

Author: Ugo Candido Reviewed by: Finance Content Editor Last updated: Category: Finance → Investment

Monthly 12 · Quarterly 4 · Annual 1

Solver is robust even without a guess; this may speed convergence.

Period Amount Actions

Enter a negative initial outflow at time 0, then positive inflows.

Results

IRR (per period) —
Annualized IRR —
NPV at solution —
Iterations / Method —
Mode: Periodic Freq: 1/yr

Data Source and Methodology

The IRR is the discount rate that makes NPV equal to zero. This tool solves the root of the NPV function using a robust bracketed bisection algorithm with a safe Newton assist when a well-behaved derivative is detected. XIRR uses Actual/365 time fractions and annualizes directly. :contentReference[oaicite:1]{index=1}

The Formula Explained

Periodic IRR (equal spacing):

\[ \text{Find } r \text{ such that } \mathrm{NPV}(r)=\sum_{t=0}^{n}\frac{CF_t}{(1+r)^t}=0 \]

Irregular IRR (XIRR):

\[ \text{Find } R \text{ such that } \mathrm{NPV}(R)=\sum_{i=0}^{m}\frac{CF_i}{\left(1+R\right)^{\frac{d_i-d_0}{365}}}=0 \]

Here \(CF\) are cash flows, \(t\) is the period index; \(d_i\) are calendar dates (Actual/365). :contentReference[oaicite:2]{index=2}

How to Use

  1. Choose Periodic (equal spacing) or Irregular (XIRR) (specific dates).
  2. Enter a negative initial outflow, then positive inflows.
  3. If periodic, set Periods per year to annualize: \( \text{Annualized}=(1+r)^{\text{freq}}-1 \).
  4. Click Calculate IRR to solve; review diagnostics.

Worked Example

Periodic: −10,000 at \(t=0\); +3,000, +4,200, +6,800 at \(t=1,2,3\); freq=1.

\[ \frac{-10{,}000}{(1+r)^0}+\frac{3{,}000}{(1+r)^1}+\frac{4{,}200}{(1+r)^2}+\frac{6{,}800}{(1+r)^3}=0 \]

The solution is \(r\approx 18.1\%\) per period. With 1 period/year, annualized = 18.1%. :contentReference[oaicite:3]{index=3}

In-Content Ad Unit

Frequently Asked Questions (FAQ)

Why do I get “No sign change”?

IRR requires at least one negative and one positive cash flow; otherwise the NPV function will not cross zero. :contentReference[oaicite:4]{index=4}

Multiple IRRs?

Non-conventional cash flows with sign changes more than once may yield multiple IRRs. Consider NPV profiles or MIRR for ranking. :contentReference[oaicite:5]{index=5}

How does XIRR annualize?

By raising \(1+R\) to the Actual/365 time fractions between dates. :contentReference[oaicite:6]{index=6}

Full original guide (expanded)

Your previous explanatory sections are preserved here (lightly edited for consistency and accessibility) and reflected in the integrated sections above. :contentReference[oaicite:7]{index=7}

Authoritative reference (Original)

Richard A. Brealey, Stewart C. Myers, Franklin Allen, Principles of Corporate Finance, 13th ed., McGraw-Hill (2019), Chapter 5: Net Present Value and Other Investment Criteria. (Publisher page linked in the original.) :contentReference[oaicite:8]{index=8}

The Formula Explained (Original)

\[\mathrm{NPV}(r)=\sum_{t=0}^{n}\frac{CF_t}{(1+r)^t}=0\]
\[\mathrm{NPV}(R)=\sum_{i=0}^{m}\frac{CF_i}{\left(1+R\right)^{\frac{d_i-d_0}{365}}}=0\]

Text and notation harmonized with this page. :contentReference[oaicite:9]{index=9}

Glossary of Variables (Original)

  • CF: Cash flow; negative for outflows, positive for inflows.
  • t: Period index in periodic mode.
  • d0, di: Start and cash-flow dates for XIRR (Actual/365).
  • r: IRR per period (periodic).
  • R: Annual IRR (irregular/XIRR).
  • freq: Periods/year used to annualize \(r\): \((1+r)^{\text{freq}}-1\).

How It Works: Example (Original)

Same 3-year example detailed above, yielding about 18.1% IRR. :contentReference[oaicite:10]{index=10}

FAQ (Original)

Key Q&A retained and merged into the FAQ section above (no-sign-change, multiple IRRs, date basis). :contentReference[oaicite:11]{index=11}

Authorship and Review (Original)

Tool developed by Ugo Candido. Content verified by CalcDomain Editorial Team. Last reviewed: September 13, 2025. :contentReference[oaicite:12]{index=12}