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The documentation below is generated from the system.functions system table

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financialInternalRateOfReturn

Introduced in: v25.7.0 Calculates the Internal Rate of Return (IRR) for a series of cash flows occurring at regular intervals. IRR is the discount rate at which the Net Present Value (NPV) equals zero. IRR attempts to solve the following equation: ∑i=0ncashflowi(1+irr)i=0\sum_{i=0}^n \frac{cashflow_i}{(1 + irr)^i} = 0 Syntax
Arguments
  • cashflows — Array of cash flows. Each value represents a payment (negative value) or income (positive value). Array(Int8/16/32/64) or Array(Float*)
  • [, guess] — Optional initial guess (constant value) for the internal rate of return (default 0.1). Float*
Returned value Returns the internal rate of return or NaN if the calculation cannot converge, input array is empty or has only one element, all cash flows are zero, or other calculation errors occur. Float64 Examples simple_example
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simple_example_with_guess
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financialInternalRateOfReturnExtended

Introduced in: v25.7.0 Calculates the Extended Internal Rate of Return (XIRR) for a series of cash flows occurring at irregular intervals. XIRR is the discount rate at which the net present value (NPV) of all cash flows equals zero. XIRR attempts to solve the following equation (example for ACT_365F): ∑i=0ncashflowi(1+rate)(datei−date0)/365=0\sum_{i=0}^n \frac{cashflow_i}{(1 + rate)^{(date_i - date_0)/365}} = 0 Arrays should be sorted by date in ascending order. Dates need to be unique. Syntax
Arguments
  • cashflow — An array of cash flows corresponding to the dates in second param. Array(Int8/16/32/64) or Array(Float*)
  • date — A sorted array of unique dates corresponding to the cash flows. Array(Date) or Array(Date32)
  • [, guess] — Optional. Initial guess (constant value) for the XIRR calculation. Float*
  • [, daycount] — Optional day count convention (default ‘ACT_365F’). Supported values:
  • ‘ACT_365F’ - Actual/365 Fixed: Uses actual number of days between dates divided by 365
  • ‘ACT_365_25’ - Actual/365.25: Uses actual number of days between dates divided by 365.25 String
Returned value Returns the XIRR value. If the calculation cannot be performed, it returns NaN. Float64 Examples simple_example
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simple_example_with_guess
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simple_example_daycount
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financialNetPresentValue

Introduced in: v25.7.0 Calculates the Net Present Value (NPV) of a series of cash flows assuming equal time intervals between each cash flow. Default variant (start_from_zero = true): ∑i=0N−1valuesi(1+rate)i\sum_{i=0}^{N-1} \frac{values_i}{(1 + rate)^i} Excel-compatible variant (start_from_zero = false): ∑i=1Nvaluesi(1+rate)i\sum_{i=1}^{N} \frac{values_i}{(1 + rate)^i} Syntax
Arguments
  • rate — The discount rate to apply. Float*
  • cashflows — Array of cash flows. Each value represents a payment (negative value) or income (positive value). Array(Int8/16/32/64) or Array(Float*)
  • [, start_from_zero] — Optional boolean parameter indicating whether to start the NPV calculation from period 0 (true) or period 1 (false, Excel-compatible). Default: true. Bool
Returned value Returns the net present value as a Float64 value. Float64 Examples default_calculation
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excel_compatible_calculation
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financialNetPresentValueExtended

Introduced in: v25.7.0 Calculates the Extended Net Present Value (XNPV) for a series of cash flows occurring at irregular intervals. XNPV considers the specific timing of each cash flow when calculating present value. XNPV equation for ACT_365F: XNPV=∑i=1ncashflowi(1+rate)(datei−date0)/365XNPV=\sum_{i=1}^n \frac{cashflow_i}{(1 + rate)^{(date_i - date_0)/365}} Arrays should be sorted by date in ascending order. Dates need to be unique. Syntax
Arguments
  • rate — The discount rate to apply. Float*
  • cashflows — Array of cash flows. Each value represents a payment (negative value) or income (positive value). Must contain at least one positive and one negative value. Array(Int8/16/32/64) or Array(Float*)
  • dates — Array of dates corresponding to each cash flow. Must have the same size as cashflows array. Array(Date) or Array(Date32)
  • [, daycount] — Optional day count convention. Supported values: 'ACT_365F' (default) — Actual/365 Fixed, 'ACT_365_25' — Actual/365.25. String
Returned value Returns the net present value as a Float64 value. Float64 Examples Basic usage
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Using different day count convention
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Last modified on June 19, 2026