| Property | Value |
|---|---|
| Hex Value | $BB01 |
| Categories | |
| Localizations |
|
irr(
Overview
Returns the interest rate at which the net present value of the cash flow is equal to zero.
Availability: Token available everywhere.
Syntax
irr(CF0,CFList[,CFFreq])
Arguments
| Name | Type | Optional |
|---|---|---|
| CF0 | ||
| CFList | ||
| CFFreq | Yes |
Location
apps, 1:Finance, CALC, 8:irr(
Description
The irr( command finds the Internal Rate of Return of an investment, which is a measure of its efficiency. Its mathematical interpretation is the interest rate for which npv( will return 0 for the same cash flows.
irr( takes three arguments: an initial cash flow (CF0), a list of further cash flows (CFList), and an optional frequency list.
Advanced Uses
irr( can be used to find a root of a polynomial of any degree, give by a list of its coefficients:
1+.01irr(0,{list of coefficients})
However, this method is limited to finding roots greater than 0, and will throw an error (ERR:NO SIGN CHG or ERR:DIVIDE BY 0) if it can't find such roots. By reversing the list of coefficients and taking the reciprocal of the roots found, you could find roots less than 0, but this would still result in errors if such roots don't exist either.
Using solve( to find roots of polynomials is less efficient, but more reliable, since it doesn't throw an error unless there are no roots at all to be found.
Formulas
Solving for irr( requires solving a polynomial with degree equal to the total number of cash flows. As such, there is no general formula for calculating irr(, though numerical methods are possible for finding an approximate solution.
The polynomial associated with the calculation is:
(1) \(\begin{align} \sum_{i=0}^{N}{C_i\left(1+\frac{\mathrm{Irr}}{100}\right)^{N-i}}=0 \end{align}\)
Here, Irr is the internal rate of return, N is the number of cash flows, and Ct is the t th cash flow.
To the calculator, only roots for which Irr>0 are considered to be viable.
Error Conditions
- ERR:DIM MISMATCH is thrown if the frequency list's size doesn't match the cash flow list's size.
- ERR:DIVIDE BY 0 is thrown if the solution that is found is Irr=0.
- ERR:NO SIGN CHG is thrown if no positive real solution is found.
Related Commands
Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, kg583.
History
| Calculator | OS Version | Description |
|---|---|---|
| TI-83 | 0.01013 | Added |
Created: February 23, 2023 23:15:01