Function InvestmentVariableInternalRateReturnInPeriodicAll(Value, Date, Mode, IRR, NumberSolutions, Basis)

InvestmentVariableInternalRateReturnInPeriodicAll

The procedure InvestmentVariableInternalRateReturnInPeriodicAll returns the internal rate of return for an investment based on a series of in-periodic cash flows. The internal rate of return is the interest rate received for an investment.

InvestmentVariableInternalRateReturnInPeriodicAll(
    Value,                   ! (input) one-dimensional numerical expression
    Date,                    ! (input) one-dimensional string expression
    Mode,                    ! (input) numerical expression
    IRR,                     ! (output) one-dimensional numerical expression
    NumberOfSolutions,       ! (output) numerical expression
    [Basis]                  ! (optional) numerical expression
    )

Arguments

Value

The payments (positive or negative). Value is an one-dimensional parameter of real numbers. Value given by positive numbers represent incoming amounts and Value given by negative numbers represent outgoing amounts. Value must contain at least one positive and at least one negative number.

Date

The dates on which the payments occur. Date and Value must have the same order. Date is an one-dimensional parameter of dates given in a date format. The first payment date indicates the beginning of the schedule of payments. All other dates must be later than this date, but they may occur in any order. Date should contain as many dates as the number of values given by Value.

Mode

Indicates whether all the solutions need to be found or just one. \(Mode = 0\): the search for solutions stops after one solution is found. \(Mode = 1\): the search for solutions continues till all solutions are found.

IRR

The internal rate of return for the investment. There is not always a unique solution for IRR. Dependent on Mode one solution or all the solutions will be given. Solutions smaller than -1 are not supposed to be relevant, so the search for solutions is limited to the area greater than -1.

NumberSolutions

The number of solutions found. When \(Mode = 0\) the NumberSolutions will be 1.

Basis

The day-count basis method to be used. The default is 1.

Equation

The internal rate of return \(r\) is a solution of the equation

\[\sum_{i=1}^n \frac{p_i}{(1+r)^{f_i}} = 0\]

where \(p_i\) are the periodic payments, and \(f_i\) is the difference between date \(i\) and the first date (so, \(f_1 = 0\)), according to the selected day-count basis method.

Note

Example

Often, internal rate of return is an investment first, (period 0, negative value), and then return cashflows in following periods.

_s_periods := ElementRange(0,4);
_p_val('0') := -100 ;
_p_val('1') := 25 ;
_p_val(_i_per | _i_per > '1') := _p_val(_i_per-1) * 1.1 ;
_sp_startQuarter(_i_per) := MomentToString(
    Format        :  "%c%y-%m-%d",
    unit          :  [month],
    ReferenceDate :  "2024-01-01",
    Elapsed       :  ((ord(_i_per)-1)*3)[month]);
_s_sols := ElementRange(1,5);

InvestmentVariableInternalRateReturnInPeriodicAll(
    value             :  _p_val,
    date              :  _sp_startQuarter,
    Mode              :  1,
    NumberOfSolutions :  _p_sols,
    IRR               :  _p_irr(_i_sol) );
block where single_column_display := 1, listing_number_precision := 6 ;
    display { _p_val, _sp_startQuarter }, _p_sols, _p_irr ;
endblock ;

This results in the following IRR:

Composite table:
    _i_per         _p_val  _sp_startQuarter
!   ------    -----------  ----------------
         0    -100.000000  "2024-01-01"
         1      25.000000  "2024-04-01"
         2      27.500000  "2024-07-01"
         3      30.250000  "2024-10-01"
         4      33.275000  "2025-01-01"
    ;

    _p_sols := 1 ;


    _p_irr := data
    { 1 : 0.258815 } ;

References