numpy.
irr
Return the Internal Rate of Return (IRR).
Deprecated since version 1.18: irr is deprecated; for details, see NEP 32 [1]. Use the corresponding function in the numpy-financial library, https://pypi.org/project/numpy-financial.
This is the “average” periodically compounded rate of return that gives a net present value of 0.0; for a more complete explanation, see Notes below.
decimal.Decimal type is not supported.
decimal.Decimal
Input cash flows per time period. By convention, net “deposits” are negative and net “withdrawals” are positive. Thus, for example, at least the first element of values, which represents the initial investment, will typically be negative.
Internal Rate of Return for periodic input values.
Notes
The IRR is perhaps best understood through an example (illustrated using np.irr in the Examples section below). Suppose one invests 100 units and then makes the following withdrawals at regular (fixed) intervals: 39, 59, 55, 20. Assuming the ending value is 0, one’s 100 unit investment yields 173 units; however, due to the combination of compounding and the periodic withdrawals, the “average” rate of return is neither simply 0.73/4 nor (1.73)^0.25-1. Rather, it is the solution (for
System Message: WARNING/2 (r)
latex exited with error [stdout] This is pdfTeX, Version 3.14159265-2.6-1.40.18 (TeX Live 2017/Debian) (preloaded format=latex) restricted \write18 enabled. entering extended mode (./math.tex LaTeX2e <2017-04-15> Babel <3.18> and hyphenation patterns for 3 language(s) loaded. (/usr/share/texlive/texmf-dist/tex/latex/base/article.cls Document Class: article 2014/09/29 v1.4h Standard LaTeX document class (/usr/share/texlive/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texlive/texmf-dist/tex/latex/base/inputenc.sty (/usr/share/texlive/texmf-dist/tex/latex/base/utf8.def (/usr/share/texlive/texmf-dist/tex/latex/base/t1enc.dfu) (/usr/share/texlive/texmf-dist/tex/latex/base/ot1enc.dfu) (/usr/share/texlive/texmf-dist/tex/latex/base/omsenc.dfu))) (/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsmath.sty For additional information on amsmath, use the `?' option. (/usr/share/texlive/texmf-dist/tex/latex/amsmath/amstext.sty (/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsgen.sty)) (/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsbsy.sty) (/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsopn.sty)) (/usr/share/texlive/texmf-dist/tex/latex/amscls/amsthm.sty) (/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.sty (/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amsfonts.sty)) ! LaTeX Error: File `anyfontsize.sty' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: sty) Enter file name: ! Emergency stop. <read *> l.8 \usepackage {bm}^^M No pages of output. Transcript written on math.log.
System Message: WARNING/2 (-100 + \frac{39}{1+r} + \frac{59}{(1+r)^2} + \frac{55}{(1+r)^3} + \frac{20}{(1+r)^4} = 0 )
In general, for values
System Message: WARNING/2 (= [v_0, v_1, ... v_M])
System Message: WARNING/2 (\sum_{t=0}^M{\frac{v_t}{(1+irr)^{t}}} = 0 )
References
NumPy Enhancement Proposal (NEP) 32, https://numpy.org/neps/nep-0032-remove-financial-functions.html
L. J. Gitman, “Principles of Managerial Finance, Brief,” 3rd ed., Addison-Wesley, 2003, pg. 348.
Examples
>>> round(np.irr([-100, 39, 59, 55, 20]), 5) 0.28095 >>> round(np.irr([-100, 0, 0, 74]), 5) -0.0955 >>> round(np.irr([-100, 100, 0, -7]), 5) -0.0833 >>> round(np.irr([-100, 100, 0, 7]), 5) 0.06206 >>> round(np.irr([-5, 10.5, 1, -8, 1]), 5) 0.0886
