IRR (Internal Rate of Return) Calculator
This professional IRR calculator computes the Internal Rate of Return for both equally spaced (periodic) and date-specific (XIRR) cash flows. It is designed for finance professionals, analysts, founders, and students who need fast, accurate, and accessible results on any device.
Calculator
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Enter a negative initial investment (time 0) followed by positive inflows. In Irregular mode, use dates.
Validation runs automatically on blur; you can also press Calculate IRR anytime.
Results
Data Source and Methodology
Authoritative reference: Richard A. Brealey, Stewart C. Myers, and Franklin Allen, “Principles of Corporate Finance,” 13th Edition, McGraw‑Hill Education (2019), Chapter 5: Net Present Value and Other Investment Criteria. Publisher page.
Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.
Computation notes: we solve for the discount rate that sets NPV = 0 using a robust bracketed bisection method with adaptive bracketing and a Newton-Raphson assist when safe. For XIRR, continuous compounding is not assumed; exponents use Actual/365 time fractions.
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, $CF$ represents cash flows, $t$ is the period index, and $d_i$ are calendar dates; time fractions use Actual/365.
Glossary of Variables
- CF: Cash flow amount at a given period or date. Negative for outflows (investments), positive for inflows (returns).
- t: Period index (0, 1, 2, …) used in Periodic mode.
- d0, di: Start date and subsequent cash flow dates used in Irregular (XIRR) mode.
- r: IRR per period (Periodic mode).
- R: Annual IRR (Irregular mode).
- Periods per year: Frequency used to annualize periodic IRR: Annualized = (1+r)freq − 1.
How It Works: A Step‑by‑Step Example
Assume an initial outlay of −10,000 at time 0 and three annual inflows: 3,000 at t=1, 4,200 at t=2, and 6,800 at t=3. Frequency = 1 (annual).
Solve for $r$:
$\\frac{-10{,}000}{(1+r)^0} + \\frac{3{,}000}{(1+r)^1} + \\frac{4{,}200}{(1+r)^2} + \\frac{6{,}800}{(1+r)^3} = 0$
Using the calculator, the IRR per period is approximately 18.1%. With 1 period per year, the annualized IRR equals 18.1% as well. If periods per year were 12 (monthly), the annualized IRR would be $(1+r)^{12}-1$.
Frequently Asked Questions (FAQ)
What inputs are required?
At least one negative and one positive cash flow. In Periodic mode, provide amounts per period. In Irregular mode, provide amounts and dates.
How precise is the result?
The solver targets a tolerance of 1e−7 on the rate with up to 200 bisection iterations and a Newton assist for faster convergence when safely bracketed.
Does the tool handle multiple IRRs?
If cash flow signs change multiple times, multiple IRRs may exist. The tool finds one IRR within the bracketed range. Review the NPV profile or use MIRR for decision-making.
How are dates handled in XIRR?
Time fractions use Actual/365: the exponent for each cash flow is (date − first date)/365, without continuous compounding.
What if I get a “No sign change” error?
Ensure that the series includes both outflows (negative) and inflows (positive). Otherwise, the NPV cannot cross zero and IRR is undefined.
Can I rely on IRR for ranking projects?
IRR is useful but can be misleading for mutually exclusive projects or non-conventional cash flows. Use NPV at your cost of capital as the primary criterion.