Rate of return with excel

What Is the Internal Rate of Return (IRR)?

The internal rate of return (IRR) is the discount rate providing a net value of zero for a future series of cash flows. Both the IRR and net present value (NPV) are used when selecting investments based on their returns.

Excel has three functions for calculating the internal rate of return that include Internal Rate of Return (IRR), Modified Internal Rate of Return (MIRR), and Internal Rate of Return with time periods (XIRR).

The IRR function calculates the internal rate of return for a series of cash flows, the MIRR function works with interest rates for borrowing and investing, and the XIRR function calculates a more accurate internal rate of return as it considers time periods.

What Is Net Present Value?

NPV is the difference between the present value of cash inflows and the present value of cash outflows over time.

The net present value of a project depends on the discount rate used. So when comparing two investment opportunities, the choice of the discount rate, which is often based on a degree of uncertainty, will have a considerable impact.

In the example below, using a 20% discount rate, investment #2 shows higher profitability than investment #1. When opting instead for a discount rate of 1%, investment #1 shows a return bigger than investment #2. Profitability often depends on the sequence and importance of the project’s cash flow and the discount rate applied to those cash flows.

How IRR and NPV Differ

The main difference between the IRR and NPV is that NPV is an actual amount while the IRR is the interest yield as a percentage expected from an investment.

Investors typically select projects with an IRR that is greater than the cost of capital. However, selecting projects based on maximizing the IRR as opposed to the NPV could result in suboptimal economic outcomes.

IRR represents the actual annual return on investment only when the project generates zero interim cash flows, or if those investments can be invested at the current IRR.

Calculating IRR in Excel

The IRR is the discount rate that can bring an investment’s NPV to zero. When the IRR has only one value, this criterion becomes more interesting when comparing the profitability of different investments.

In our example, the IRR of investment #1 is 48% and, for investment #2, the IRR is 80%. This means that in the case of investment #1, with an investment of $2,000 in 2013, the investment will yield an annual return of 48%. In the case of investment #2, with an investment of $1,000 in 2013, the yield will bring an annual return of 80%.

If no parameters are entered, Excel starts testing IRR values differently for the entered series of cash flows and stops as soon as a rate is selected that brings the NPV to zero. If Excel does not find any rate reducing the NPV to zero, it shows the error «#NUM.»

If the second parameter is not used and the investment has multiple IRR values, we will not notice because Excel will only display the first rate it finds that brings the NPV to zero.

In the image below, for investment #1, Excel does not find the NPV rate reduced to zero, so we have no IRR. 

The image below also shows investment #2. If the second parameter is not used in the function, Excel will find an IRR of -10%. On the other hand, if the second parameter is used (i.e., = IRR ($ C $ 6: $ F $ 6, C12)), there are two IRRs rendered for this investment, which are -10% and 216%.

If the cash flow sequence has only a single cash component with one sign change (from + to — or — to +), the investment will have a unique IRR. However, most investments begin with a negative flow and a series of positive flows as the first investments come in. Profits then, hopefully, subside, as was the case in our first example.

In the image below, we calculate the IRR. To do this, we simply use the Excel IRR function:

Calculating MIRR in Excel

When a company uses different borrowing rates of reinvestment, the modified internal rate of return (MIRR) applies.

In the image below, we calculate the IRR of the investment as in the previous example but taking into account that the company will borrow money to plow back into the investment (negative cash flows) at a rate different from the rate at which it will reinvest the money earned (positive cash flow). The range C5 to E5 represents the investment’s cash flow range, and cells D10 and D11 represent the rate on corporate bonds and the rate on investments.

The image below shows the formula behind the Excel MIRR. We calculate the MIRR found in the previous example with the MIRR as its actual definition. This yields the same result: 56.98%. 



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begin{aligned}left(frac{-text{NPV}(textit{rrate, values}[textit{positive}])times(1+textit{rrate})^n}{text{NPV}(textit{frate, values}[textit{negative}])times(1+textit{frate})}right)^{frac{1}{n-1}}-1end{aligned}

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Calculating XIRR in Excel

The XIRR function takes into consideration different periods. To use this function, Excel requires both the cash flow amounts as well as the dates on which those cash flows are paid.

In the example below, the cash flows are not disbursed at the same time each year – as is the case in the above examples. Rather, they are happening at different periods. We use the XIRR function below to solve this calculation. We first select the cash flow range (C5 to E5) and then select the range of dates on which the cash flows are realized (C32 to E32).

For investments with cash flows received or cashed at different moments in time for a firm that has different borrowing rates and reinvestments, Excel does not provide functions that can be applied to these situations although they are probably more likely to occur.

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.

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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