Q. I have prepared projections for a proposed project, and I want to calculate the internal rate of return. Instead of using Excel's IRR function, should I use simple math formulas so others can follow my calculations?

**A. **Excel offers three functions for calculating the internal rate of return, and I recommend you use all three. The problem with using math to calculate the internal rate of return is that the necessary calculations are both complicated and time-consuming. Basically, a math-based solution involves calculating the net present value (NPV) for each cash flow amount (in a series of cash flows) using various guessed interest rates on a trial-and-error basis, and then those NPVs are added together. This process is repeated using various interest rates until you find/stumble upon the exact interest rate that produces NPV amounts that sum to zero. The interest rate that produces a zero-sum NPV is then declared the internal rate of return.

To simplify this process, Excel offers three functions for calculating the internal rate of return, each of which represents a better option than using the math-based formulas approach. These Excel functions are IRR, XIRR, and MIRR. Explanations and examples for these functions are presented below. You can download the example workbook at carltoncollins.com/irr.xlsx.

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1. Excel's IRR function. **Excel's IRR function calculates the internal rate of return for a series of cash flows, assuming equal-size payment periods. Using the example data shown above, the IRR formula would be =IRR(D2:D14,.1)*12, which yields an internal rate of return of 12.22%. However, because some months have 31 days while others have 30 or fewer, the monthly periods are not exactly the same length, therefore, the IRR will always return a slightly erroneous result when multiple monthly periods are involved.

**2. Excel's XIRR function. **Excel's XIRR function calculates a more accurate internal rate of return because it takes into consideration different-size time periods. To use this function, you must supply both the cash flow amounts as well as the specific dates in which those cash flows are paid. In the example pictured below left, the XIRR formula would be =XIRR(D2:D14,B2:B14,.1), which yields an internal rate of return of 12.97%.

**3. Excel's MIRR function.** Excel's MIRR function (modified internal rate of return) works similarly to the IRR function, except that it also considers the cost of borrowing the initial investment funds as well as compounded interest earned by reinvesting each cash flow. The MIRR function is flexible enough to accommodate separate interest rates for borrowing and investing cash. Because the MIRR function calculates compound interest on project earnings or cash shortfalls, the resulting internal rate of return is usually significantly different from the internal rate of return produced by the IRR or XIRR function. In the example at left, the MIRR formula would be =MIRR(D2:D14,D16,D17)*12, which yields an internal rate of return of 17.68%.

**Note: **Some CPAs maintain that the MIRR function's results are less valid because a project's cash flows are rarely fully reinvested. However, clever CPAs can compensate for partial investment levels simply by adjusting the interest rate according to the expected levels of reinvestment. For instance, if it is assumed that reinvested cash flows will earn 3.0%, but only half the cash flows are expected to be reinvested, then the CPA can use an interest rate of 1.5% (half of 3.0%) as the interest rate to compensate for the partial investment of cash flows.

Rather than worrying about which method produces the more accurate result, I believe the best approach is to include all three calculations (IRR, XIRR, and MIRR) so the financial reader can consider them all. A few comments about these calculations follow.

**1. Negative and positive cash flow values required.** All three functions require at least one negative and at least one positive cash flow to complete the calculation. The first number in the cash flow series is typically a negative number that is assumed to be the project's initial investment.

**2. Monthly versus annual yields.** When calculating the IRR or MIRR of monthly cash flows, the results must be multiplied by 12 to produce an annual yield; however, the XIRR function automatically produces an annual result that does not need to be multiplied. When calculating the IRR, XIRR, or MIRR of annual cash flows, the results do not need to be multiplied. (Because the XIRR function includes date ranges, it annualizes the results automatically.)

**3. Guess. **The IRR and XIRR functions allow you to enter a guess as the beginning rate where the function starts calculating incrementally, up to 20 cycles for the IRR function and 100 cycles for the XIRR function, until an answer within 0.00001% is found. If an answer is not determined within the allotted number of cycles, then the #NUM! error message is returned.

**4. The #NUM! error. **If the IRR function returns a #NUM! error value or if the result is not close to what you expected, Excel's help files suggest you try again with a different value for your guess.

**5. If you don't enter a guess.** If you don't enter a guess for the IRR or XIRR function, Excel assumes 0.1, or 10%, as the initial guess.

**6. Dates.** The dates you enter must be entered as date values, not text, for the XIRR function to accurately use those dates.

**About the author**

**J. Carlton Collins** (carlton@asaresearch.com) is a technology consultant, a CPE instructor, and a *JofA *contributing editor.

*Note: *Instructions for Microsoft Office in “Technology Q&A” refer to the 2007 through 2016 versions, unless otherwise specified.

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