internalRateSchedule¶

Evaluates the internal rate of return for a schedule of cash flows. It is not necessary that the cash flows be periodic.

Synopsis¶

internalRateSchedule (values, dates)

Required Arguments¶

float values[] (Input): Array of size count of cash flows, which includes the initial investment.
struct tm dates[] (Input): Array of size count of dates cash flows are made see the Usage Notes section of this chapter.

Return Value¶

The internal rate of return for a schedule of cash flows that is not necessarily periodic. If no result can be computed, NaN is returned.

Optional Arguments¶

xguess, float (Input)

Initial guess at the internal rate of return.

highest, float (Input)

Maximum value of the internal rate of return allowed.

Default: 1.0 (100%)

Description¶

Function internalRateSchedule computes the internal rate of return for a schedule of cash flows that is not necessarily periodic. The internal rate such that the stream of payments has a net present value of zero.

It can be found by solving the following:

\[0 = \sum_{i=1}^{\mathit{count}} \frac{\mathit{value}_i}{(1 + \mathit{rate})^{\frac{d_i-d_{\mathit{1}}}{365}}}\]

In the equation above, $d_i$ represents the i-th payment date. $d_1$ represents the 1st payment date. $value_i$ represents the i-th cash flow. rate is the internal rate of return.

Example¶

In this example, internalRateSchedule computes the internal rate of return for nine cash flows, -$800, $800, $800, $600, $600, $800, $800, $700 and $3,000, with an initial investment of $4,500.

from __future__ import print_function
from numpy import *
from datetime import date
from pyimsl.math.internalRateSchedule import internalRateSchedule

values = [-4500., -800., 800., 800., 600.,
          600., 800., 800., 700., 3000.]
dates = [date(1998, 1, 1),
         date(1998, 10, 1),
         date(1999, 5, 5),
         date(2000, 5, 5),
         date(2001, 6, 1),
         date(2002, 7, 1),
         date(2003, 8, 30),
         date(2004, 9, 15),
         date(2005, 10, 15),
         date(2006, 11, 1)]

xirr = internalRateSchedule(values, dates)
print("After  approximately 9 years, the internal")
print("rate of return on the cows is %.2f%%." % (xirr * 100.))

Output¶

After  approximately 9 years, the internal
rate of return on the cows is 7.69%.