78 Section 4: Additional Financial FunctionsCalculating 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 fLfunction 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 fLis 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.

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