internal_rate_of_return

Evaluates the internal rate of return for a schedule of cash flows.

Synopsis

#include <imsl.h>

float imsl_f_internal_rate_of_return (int count, float values[], …, 0)

The type double function is imsl_d_internal_rate_of_return.

Required Arguments

int count (Input)
Number of cash flows in values. count must be greater than one.

float values[] (Input)
Array of size count of cash flows which occur at regular intervals, which includes the initial investment.

Return Value

The internal rate of return for a schedule of cash flows. If no result can be computed, NaN is returned.

Synopsis with Optional Arguments

#include <imsl.h>

float imsl_f_internal_rate_of_return (int count, float values[],

IMSL_XGUESS, float guess,

IMSL_HIGHEST, float max,

IMSL_MAX_EVALS, int max_evals,

IMSL_ABERTH_METHOD,

IMSL_TOLERANCE_ABERTH, float tol_aberth,

0)

Optional Arguments

IMSL_XGUESS, float guess (Input)
Initial guess at the internal rate of return.

IMSL_HIGHEST, float max (Input)
Maximum value of the internal rate of return allowed.
Default: max = 1.0 (100%).

IMSL_MAX_EVALS, int max_evals (Input)
The maximum number of function evaluations allowed in the computation of the internal rate of return. If IMSL_ABERTH_METHOD is used, max_evals denotes the number of iterations allowed in the Ehrlich-Aberth method.
Default: max_evals = 1000.

IMSL_ABERTH_METHOD (Input)
Compute the internal rate of return using the Ehrlich-Aberth method. If IMSL_ABERTH_METHOD is present, optional argument IMSL_XGUESS is ignored.

IMSL_TOLERANCE_ABERTH, float tol_aberth (Input)
Tolerance value used in the Ehrlich-Aberth method to decide if a complex root of the internal rate of return related polynomial is a candidate for a real-valued root.
Default:
tol_aberth = 1000 * imsl_f_machine(4)in single precision.
tol_aberth = 1000 * imsl_d_machine(4)in double precision.

Description

Function imsl_f_internal_rate_of_return computes the internal rate of return for a schedule of cash flows. The internal rate of return is the interest rate such that a stream of payments has a net present value of zero.

It is found by solving the following equation:

where n is the number of cash flows, Ci is the i-th cash flow (including the initial investment C0), and r is the internal rate of return.
If optional argument IMSL_ABERTH_METHOD is used, the roots of the polynomial with real coefficients

are computed by the Ehrlich-Aberth method from function imsl_f_zeros_poly. Since the roots returned from zeros_poly are complex, a root of the polynomial is considered potentially real-valued if the imaginary part of x satisfies the condition

tol_aberth

If the additional condition

with u the unit roundoff and

is satisfied, is considered close enough to a real root of and therefore accepted as a real root of . If have been identified as real roots of , then the related rates of return are computed via the transformation . The internal rate of return is defined as the maximum of the values that is less than or equal to the value max from optional argument IMSL_HIGHEST.

Example

In this example, imsl_f_internal_rate_of_return 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.

#include <stdio.h>
#include <imsl.h>
 
int main()
{
 float values[] = { -4500., -800., 800., 800., 600.,
                  600., 800., 800., 700., 3000. };
 float internal_rate;
 
 internal_rate = imsl_f_internal_rate_of_return (10, values, 0);
 printf ("After 9 years, the internal rate of return on the ");
 printf ("cows is %.2f%%.\n", internal_rate * 100.);
}

Output

After 9 years, the internal rate of return on the cows is 7.21%.

Warning Errors

Fatal Errors