Financial functions

financialInternalRateOfReturn

Introduced in: v25.7

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:

$$\sum_{i=0}^n \frac{cashflow_i}{(1 + irr)^i} = 0$$

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

simple_example_with_guess

financialInternalRateOfReturnExtended

Introduced in: v25.7

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):

$$\sum_{i=0}^n \frac{cashflow_i}{(1 + rate)^{(date_i - date_0)/365}} = 0$$

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

simple_example_with_guess

simple_example_daycount

financialNetPresentValue

Introduced in: v25.7

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):

$$\sum_{i=0}^{N-1} \frac{values_i}{(1 + rate)^i}$$

Excel-compatible variant (start_from_zero = false):

$$\sum_{i=1}^{N} \frac{values_i}{(1 + rate)^i}$$

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

excel_compatible_calculation

financialNetPresentValueExtended

Introduced in: v25.7

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:

$$XNPV=\sum_{i=1}^n \frac{cashflow_i}{(1 + rate)^{(date_i - date_0)/365}}$$

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

Using different day count convention