Function InvestmentVariablePresentValueInPeriodic(Value, Date, InterestRate, Basis)

# InvestmentVariablePresentValueInPeriodic

The function InvestmentVariablePresentValueInPeriodic returns the net present value on the date of the first cash flow for an investment based on a series of in-periodic cash flows and a constant interest rate.

InvestmentVariablePresentValueInPeriodic(
Value,                   ! (input) one-dimensional numerical expression
Date,                    ! (input) one-dimensional string expression
InterestRate,            ! (input) 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.

InterestRate

The interest rate per period for the investment. InterestRate must be a numerical expression in the range $$(-1, 1)$$.

Basis

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

## Return Value

The function InvestmentVariablePresentValueInPeriodic returns the net present value of an investment, which is the total value of all the future cash flows at this moment.

## Equation

The net present value $$v_p$$ is computed through the equation

$v_p = \sum_{i=1}^n \frac{p_i}{(1+r)^{f_i}}$

where $$p_i$$ are the periodic payments, $$r$$ is the (constant) interest rate, 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

• This function can be used in an objective function or constraint and the input parameters Value and InterestRate can be used as a variable.

• The function InvestmentVariablePresentValueInPeriodic is similar to the Excel function XNPV.

## Example

Given the local declarations:

Set _s_qs {
SubsetOf: Integers;
Index: _i_q;
}
Parameter _p_val {
IndexDomain: _i_q;
}
StringParameter _sp_startQuarter {
IndexDomain: _i_q;
}
Parameter _p_npv;

Net present value, with contributions made at the start of each quarter, can be computed as follows:

! Prepping some data:
_s_qs := ElementRange(1,4);
_p_val(_i_q) := 3 + 2 * ord(_i_q)  ;
_sp_startQuarter(_i_q) := MomentToString(
Format        :  "%c%y-%m-%d",
unit          :  [month],
ReferenceDate :  "2024-01-01",
Elapsed       :  ((ord(_i_q)-1)*3)[month]);

! NPV computation
_p_npv := InvestmentVariablePresentValueInperiodic(
value        :  _p_val,
date         :  _sp_startQuarter,
InterestRate :  0.07,
Basis        :  1);

! Putting input and result in listing file
block where single_column_display := 1, listing_number_precision := 6 ;
display { _p_val, _sp_startQuarter }, _p_npv ;
endblock ;

With the following result in the listing file:

Composite table:
_i_q    _p_val  _sp_startQuarter
!   ----    ------  ----------------
1         5  "2024-01-01"
2         7  "2024-04-01"
3         9  "2024-07-01"
4        11  "2024-10-01"
;

_p_npv := 31.038963 ;