Function InvestmentVariableInternalRateReturnAll(Value, Mode, NumberSolutions, IRR)

# InvestmentVariableInternalRateReturnAll

The procedure InvestmentVariableInternalRateReturnAll returns the internal rate of return for an investment based on a series of periodic cash flows. The internal rate of return is the rate received for an investment consisting of payments (negative values) and income (positive values).

InvestmentVariableInternalRateReturnAll(
Value,                   ! (input) one-dimensional numerical expression
Mode,                    ! (input) numerical expression
NumberSolutions,         ! (output) numerical expression
IRR                      ! (output) one-dimensional numerical expression
)

## Arguments

Value

The periodic payments (positive or negative), which must be equally spaced in time. 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 given by positive numbers represent incoming amounts and Value given by negative numbers represent outgoing amounts. em Value must contain at least one positive and at least one negative number.

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.

NumberSolutions

The number of solutions found. When $$Mode = 0$$ the NumberSolutions will be 1.

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.

## Equation

The internal rate of return $$r$$ is a solution of the equation

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

where $$p_i$$ are the periodic payments.

Note

• The internal rate of return is the interest rate at which the investment has a zero net present value.

• When you want to use this procedure in an objective function or constraint you have to use InvestmentVariableInternalRateReturn.

• The function InvestmentVariableInternalRateReturnAll is similar to the Excel function IRR.

## 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') := 50 ;
_p_val(_i_per | _i_per > '1') := _p_val(_i_per-1) * 1.5 ;
_s_sols := ElementRange(1,5);
_p_sols := 0 ;
InvestmentVariableInternalRateReturnAll(
value           :  _p_val,
Mode            :  1,
NumberSolutions :  _p_sols,
IRR             :  _p_irr(_i_sol) );

block where single_column_display := 1, listing_number_precision := 6 ;
display _p_val, _p_sols, _p_irr ;
endblock ;

This results in the following IRR:

_p_val := data
{ 0 : -100.000000,
1 :   50.000000,
2 :   75.000000,
3 :  112.500000,
4 :  168.750000 } ;

_p_sols := 1 ;

_p_irr := data
{ 1 : 0.688847 } ;