## Don’t Ask Me to Explain!

**Most business professionals outside of finance readily admit they do not really understand the meaning or use of internal rate of return (IRR).**

*
For a complete introduction to IRR and MIRR, see the article Internal Rate of Return (IRR).*Nevertheless, many are required, by their CFOs or other financial specialists, to deliver internal rate of return IRR figures to support funding requests, business case results, or proposals for projects, acquisitions, or other actions.

It is surprising, however, that many of the same finance people who require IRRs with incoming proposals are themselves unable to explain in practical terms:

- The meaning of IRR % values.
- How IRR compares to other financial metrics such as NPV or ROI.

Regarding IRR, almost everyone knows that a larger IRR is better than a smaller IRR. Beyond that, however, the meaning of the IRR percentage is a mystery.

### How Many Really Understand?

A recent Duke University study shows, for instance, that 75% of CFOs almost always evaluate capital spending proposals with IRR. Yet this same study found that only about 20% of these people fully understand IRR’s most serious deficiencies. They simply cannot usefully interpret the meaning of, say, a 30% IRR.

Business people in our business case seminars bring the same message. Their management considers IRR when deciding the fate of their proposals. However these professionals have never been told *why*.

When asked for the meaning of IRR, unfortunately, financial specialists and senior managers tend to *define* IRR instead of explaining it. Or they simply repeat the belief that IRR is useful because it “shows directly how returns from a proposed action compare to inflation, current interest rates, and to financial investment alternatives.” T

his last statement is arguably true, sometimes, but it provides no guidance on how to make these comparisons.

As a result, most of our business case seminars include a serious discussion on the use and misuse of IRR. These discussions, by the way, usually end by recommending another financial metric. We recommend avoiding IRR and using instead the **modified internal rate of return (MIRR). **MIRR is easier to interpret than the familiar IRR.

## Two IRR Definitions and the Temptation to Overstate Return Rates

IRR is more easier to define and explain with an example. Consider two investment proposals computing for funding: Case A and Case B. The expected net cash flow streams for A and B are shown in the image.

Initial cash outflow for both investments is $220. Case A ends 7 years later with a net gain of $200 while case B ends with a net gain of $240. Which is the better investment? If the company can make only one investment now, which one should it be?

### Internal Rate of Return: Spreadsheet Results

Spreadsheet analysis of both net cash flow streams shows an IRR of 30.6% for Case A and an IRR of 20.8% for Case B. But what do those figures mean?

The best known IRR definition explains this comparison in terms that call for a basic understanding of discounted cash flow terms present value, net present value (NPV), and the role of the discount rate in determining NPV.

### Internal Rate of Return First Definition

IRR Definition 1: The internal rate of return (IRR) for a cash flow stream is the interest rate (discount rate) that produces a net present value of 0 for the cash flow stream.

That definition, however, can be less than satisfying when first heard. Many ask: “What does *that* tell me about returns and costs?” A second IRR definition comes closer to providing some guidance for interpretation.

### Internal Rate of Return Second Definition

Internal Rate of Return Definition 2:This definition assumes that investment costs will be financed at a certain annual rate,andthat incoming returns will be reinvested at a certain annual rate. IRR is defined as the single rate that equates total investment costs (including financing) with total investment gains including interest earnings from reinvestment.

The second-definition example above should begin to suggest a reason that financial people look to IRR and trust it as an important decision criterion: IRR has built into it the presumption that investment costs (opportunity costs or borrowing) are financed at a cost, and that incoming returns are reinvested, earning additional gains. This view provides meaning for another IRR interpretation. Many assume the analyst will compare the IRR rate to actual financing rates and actual reinvestment rates. This comparison, however, has to be interpreted carefully. It is easy to over interpret or misinterpret IRR at this point.

### Faulty IRR Reasoning

When a proposed investment produces IRR’s like those shown above—30.6% for example—many are tempted to reason as follows:

For this investment, we will

actually borrow at the IRR rate. Our real financing cost will be lower. Our real financing cost will be closer to our cost of capital, probably less than 10%.notTherefore [the reasoning goes], the investment is a net gain because financing rates will really be under 10%, while returns represent earnings at a much higher rate, something like 30.6%.

This reasoning may or may not be valid.

- The reasoning is most valid when IRR is close to the real cost of capital and real investment rate.
- The reasoning is is not valid when IRR greatly exceeds those rates.

IRR in such cases overstates the real rate of return. This is especially true when comparing competing mutually exclusive investments. In such cases the overstatement can be much greater for one investment versus the other when the two cash flow streams have different profiles. For this reason, IRR is usually *not* recommended for such comparisons.

In brief, one can conclude that an investment is a net gain when its IRR exceeds the investor’s cost of capital. It is also reasonable, to view the investment with the higher IRR is the greater gain. However, the magnitude of the real gain depends on the real cost of capital and the real reinvestment rate, as well as the timing of individual net cash flow events factors that are not visible in the IRR results.

## Modified Internal Rate of Return:

Clear and Easily Understood Meaning

IRR magnitudes are difficult to interpret, as shown, because IRR can differ from the actual financing and reinvestment rates. It is natural to ask, therefore, “Why not calculate an internal return metric that *does* reflect the real financing cost rate and real reinvestment rate?” In fact, this solution is readily available as the **modified internal rate of return **(**MIRR**) metric. Input data for MIRR includes the same net cash flow figures as IRR, but the MIRR also requires as input a **financing rate** and a **reinvestment rate**. Here for comparison are the IRR and MIRR results for example investments A and B from above. MIRR here is based on a reinvestment rate of 8% and a financing rate of 6%:

Investment A: IRR_{A}= 30.6% and MIRR_{A} = 15.1%

Investment B: IRR_{B}= 20.8% and MIRR_{B} = 14.7%

Here, at last is an investment metric with a clear meaning! MIRR rates show investment value growing the same way that compound interest earnings build value. The MIRR message for investment A is this: **Making investment A brings the same results as putting the investment costs in the bank for 7 years and earning interest at a 15.1% annual rate** (assuming the given financing and reinvestment rates are applied). Investment A still shows a greater return rate (MIRR rate) than B, but A’s MIRR advantage is very small, compared to the IRR differences between investments .

MIRR rates have a meaning that is clear and explainable by anyone who understands the basics of interest compounding.

## To Use IRR or Not To Use IRR?

The most straightforward way to avoid problems with IRR is to avoid it altogether.

— J. Kelleher and J. MacCormack, McKinsey & Co., in

CFO, 2007.

Some kinds of investments are very appropriate for IRR analysis. Cash flow streams from interest-paying bonds, for instance, fit the assumptions under IRR definitions. Going by the name **yield to maturity**, IRR in fact has a central role in bond investment analysis. The meaning of **YTM/IRR** results is clear because the cash flow stream has the profile that IRR expects early cash outflows followed by cash inflows.

However, when routinely using IRR for other investments or project proposals, the clear meaning of IRR results shrinks or disappears altogether. This is because the cash flow streams in these cases may differ substantially from the investment curve profile that IRR expects (early costs and later gains). This is also because the resulting IRRs can differ greatly from real the cost of capital and reinvestment rates.

Consequently, there is a case to be made for obeying the **Four Commandments of IRR Use**:

- IRR is not appropriate when the net cash flow stream differs from the investment curve profile. That profile shows early net cash outflows and later net cash inflows.
**Do not**use IRR to compare competing cash flow streams whose profiles differ greatly from each other. Not even if both are roughly*investment curves*.**Do not**over interpret IRR return rates when IRR differs substantially from the real cost of capital and reinvestment rates.**IRR is impossible**when the net cash flow stream is entirely positive or negative. There*is*no IRR in such cases.

## The Emperor’s New Clothes

In the popular Hans Christian Andersen story, no one—including the Emperor—calls it as it is. Admitting they cannot see the Emperor’s fine new clothes would brand them as fools. That would show them unfit for their positions. Or so they hear and so they believe. Only one young child cries out: “He’s not wearing any clothes!”

A mild form of this vanity appears with financial people. And, also with senior managers. Many in both camps seem refrain from exposing IRR’s weaknesses, poor applicability, and difficult interpretability.

For the present, the person who must support proposals or plans with IRR needs to know fully what the IRRs mean, what they do not mean, and how to use instead MIRR and other financial metrics.

### Where to Go From Here: Take Action!

Visit the complete introduction to IRR and MIRR in Internal Rate of Return (IRR).

Order and download the premier business case books and software from the Master Case Builder Shop.

For a more on IRR and MIRR, see Internal Rate of Return (IRR).

See Financial Metrics for a complete overview of cash flow metrics and financial statement metrics (financial ratios).

Learn and practice the leading case building methods at a Business Case Master Class Seminar. Learn case design from our ebooks, the Business Case Guide or the best selling authority in print, Business Case Essentials.

By Marty Schmidt. Copyright © 2004-2017.

Solution Matrix Limited, Publisher.

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