NumPy

numpy.irr

numpy.irr(values)[source]

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.

Parameters
valuesarray_like, shape(N,)

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.

Returns
outfloat

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 r) of the equation:

-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 = [v_0, v_1, ... v_M], irr is the solution of the equation: [2]

\sum_{t=0}^M{\frac{v_t}{(1+irr)^{t}}} = 0

References

1

NumPy Enhancement Proposal (NEP) 32, https://numpy.org/neps/nep-0032-remove-financial-functions.html

2

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

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