Section 4: Additional Financial Functions
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.
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
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
IRR is 13.72%.