atoti.finance.irr()#

atoti.finance.irr(*, cash_flows, market_value, date, precision=0.001)#

Return the Internal Rate of Return based on the underlying cash flows and market values.

Warning

This feature is experimental, its key is "finance.irr".

The IRR is the rate r that nullifies the Net Present Value:

\[NPV = \sum_{{i=0}}^{{T}} CF_i (1 + r)^{{\frac{{T - t_i}}{{T}}}} = 0\]

With:

\(T\) the total number of days since the beginning
\(t_i\) the number of days since the beginning for date \(i\)
\(CF_i\) the enhanced cashflow for date \(i\)
- CF of the first day is the opposite of the market value for this day: \(CF_0 = - MV_0\).
- CF of the last day is increased by the market value for this day: \(CF_T = cash\_flow_T + MV_T\).
- Otherwise CF is the input cash flow: \(CF_i = cash\_flow_i\).

This equation is solved using the Newton’s method.

Parameters:

cash_flows (VariableMeasureConvertible) – The measure representing the cash flows.
market_value (VariableMeasureConvertible) – The measure representing the market value, used to enhanced the cashflows first and last value. If the cash flows don’t need to be enhanced then 0 can be used.
date (Hierarchy) – The date hierarchy. It must have a single date level.
precision (float) – The precision of the IRR value.

Return type:

MeasureDefinition