78 Section 4: Additional Financial Functions
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 78 of 275
Printed Date: 2005/8/1
Dimension: 14.8 cm x 21 cm
Calculating Internal Rate of Return (IRR)
1. Enter the cash flows using either of the methods described above under
Calculating Net Present Value.
2. Press
fL
.
The calculated value of
IRR
appears in the display and also is automatically stored
in the
i
register.
Note:
Remember that the
fL
function may take a significant amount of
time to produce an answer, during which the calculator displays
running
.
Example:
The NPV calculated in the preceding example was positive, indicating
that the actual rate of return (that is, the
IRR
) was greater than the 13.5 used in the
calculation. Find the
IRR
.
Assuming the cash flows are still stored in the calculator, we need only press
fL
:
Keystrokes Display
fL
13.72
IRR
is 13.72%.
Note that the value calculated by
fL
is the
periodic
rate of return. If the cash
flow periods are other than years (for example, months or quarters), you can
calculate the nominal annual rate of return by multiplying the periodic
IRR
by the
number of periods per year.
As noted above, the calculator may take several seconds or even minutes to
produce an answer for
IRR
. This is because the mathematical calculations for
finding
IRR
are extremely complex, involving a series of iterations — that is, a
series of successive calculations. In each iteration, the calculator uses an estimate
of
IRR
as the interest rate in a computation of
NPV
. The iterations are repeated
until the computed
NPV
reaches about zero.
*
The complex mathematical characteristics of the
IRR
computation have an
additional ramification: Depending on the magnitudes and signs of the cash flows,
the computation of
IRR
may have a single answer, multiple answers, a negative
answer or no answer.
†
For additional information regarding
fL
, refer to Appendix C. For an
alternative method of calculating
IRR
, refer to Section 13.
*
In practice, because the complex mathematical calculations inside the calculator are done
with numbers rounded to 10 digits,
NPV
may never reach exactly zero. Nevertheless, the
interest rate that results in a very small
NPV
is very close to the actual
IRR
.
†
In the case of multiple answers for
IRR
, the decision criteria listed on page 72 should be
modified accordingly.
