Function InvestmentVariableInternalRateReturnModified(Value, FinanceRate, ReinvestRate)

# InvestmentVariableInternalRateReturnModified

The function InvestmentVariableInternalRateReturnModified returns the modified internal rate of return for an investment based on a series of periodic cash flows. It considers both the cost made for the investment and the interest received on the reinvestment of cash flows.

InvestmentVariableInternalRateReturnModified(
Value,                   ! (input) one-dimensional numerical expression
FinanceRate,             ! (input) numerical expression
ReinvestRate             ! (input) 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. Value must contain at least one positive and at least one negative number.

FinanceRate

Interest rate you pay on money used in negative cash flows. FinanceRate must be a numerical expression in the range $$[-1, \infty)$$.

ReinvestRate

Interest rate you receive on the positive cash flows as you reinvest them. ReinvestRate must be a numerical expression in the range $$[-1, \infty)$$.

## Return Value

The function InvestmentVariableInternalRateReturnModified returns the modified internal rate of return for the investment.

## Equation

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

$(1+r)^{n-1} = -\frac{\mbox{NPV}(v^+,r_r)(1+r_r)^n}{\mbox{NPV}(v^-,r_f)(1+r_f)}$

where $$n$$ is the number of periods considered, $$v_i = v^+_i - v^-_i$$ (with $$v^+_i, v^-_i \geq 0$$), $$r_f$$ the finance rate, $$r_r$$ the reinvestment rate, and NPV the function InvestmentVariablePresentValue.

Note

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

• There should be at least one negative and one positive Value.

• The function InvestmentVariableInternalRateReturnModified is similar to the Excel function MIRR <https://support.microsoft.com/en-us/office/mirr-function-28b62fff-b057-47ee-9ff9-13ea2628a007>_.

## 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 ;
_p_irr := InvestmentVariableInternalRateReturnModified(
value        :  _p_val,
FinanceRate  :  0.07,
ReinvestRate :  0.04 );
block where single_column_display := 1, listing_number_precision := 6 ;
display _p_val, _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_irr := 0.434215 ;