Function InvestmentVariablePresentValue(Value, InterestRate)

# InvestmentVariablePresentValue

The function InvestmentVariablePresentValue returns the net present value for an investment based on a series of periodic cash flows at the end of the periods and a constant interest rate.

InvestmentVariablePresentValue(
Value,                   ! (input) one-dimensional numerical parameter
InterestRate             ! (input) numerical expression
)


## Arguments

Value

The periodic payments (positive or negative), which must be equally spaced in time and occur at the end of each period. The order of the payments in Value must be the same as the order in which the cash flows occur. Value is an one dimensional parameter of real numbers. Value should contain at least one nonzero number. Value given by positive numbers represent incoming amounts and Value given by negative numbers represent outgoing amounts.

InterestRate

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

## Return Value

The function InvestmentVariablePresentValue returns the net present value of an investment, which is the total value of all the future cash flows at the beginning of the first period.

## Equation

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

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

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

Note

• When all payments are constant, the net present value computed here is equal to the negative value of the present value computed by the function InvestmentConstantPresentValue with the future value set to 0.0.

• 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 InvestmentVariablePresentValue is similar to the Excel function NPV.

## Example

Given the local declarations:

Set _s_years {
SubsetOf: Integers;
Index: _i_year;
}
Parameter _p_value {
IndexDomain: _i_year;
}
Parameter _p_npv;


Net present value can be computed as follows:

_s_years := ElementRange(2005,2008);
_p_value(_i_year) := ord(_i_year) * 100 + 50 ;
_p_npv := InvestmentVariablePresentValue( _p_value, 0.07 );
block where single_column_display := 1, listing_number_precision := 6 ;
display _p_npv ;
endblock ;


With the following result in the listing file:

_p_npv := 987.553700 ;