Internal Rate of Return.doc

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Internal Rate of Return (IRR) and Modified Internal Rate of Return (MIRR): Definition,Meaning, and Usage.

Encyclopedia of Business Terms and Methods, ISBN 978-1-929500-10-9. Revised 2013-02-06.

Internal Rate of Return (IRR) is a financial metric for cash flow analysis, often used forevaluating proposed investments, funding requests, acquisitions, or the results of businesscase analysis. Like several other cash flow metrics (such as net present value, paybackperiod, and return on investment), IRR takes an "investment view" of expected financialresults. This means, essentially, that the magnitude and timing of cash flow returns arecompared to the magnitude and timing of cash flow costs. Each of these financialmetricscompares returns to costs in its own way and each carries a unique messageabout the value of the investment.

IRR analysis begins with a cash flow stream, a series ofnet cash flow figures expectedto follow from the investment (or action, acquisition, or business case scenario). The

expected cash flow stream for IRR analysis might appear something like this:Each barrepresents thenet of inflowsand outflowsfor one two-month period.The completeset of net cashflow events isa cash flow

stream. If thiscash flowstreamrepresents oneinvestment, another investment might show a different cash flow profile. IRRs for eachinvestment can be compared to help decide which is the better business decision. Otherthings being equal, the investment with the higher IRR is viewed as the better choice.

Notice especially the shape, or profile of this example cash flow stream. The figure showsa typical investment curve. Net cash outflows at the outset and net cash inflows in laterperiods mean that costs initially exceed incoming returns, but if the investment performs

as expected, returns eventually outweigh the costs. The IRR metric, in fact, "expects" thiskind of cash flow profileearly costs and later benefits. When the cash flow stream hasthis kind of profile, an IRR can probably be found and usefully interpreted. When thecash flow stream deviates substantially from this profile, however, it may not be possibleto find an IRR for the stream. Or, other strange IRR results may appear, such as multipleIRRs for the same stream, or a negative IRR for the cash flow stream. In such cases, theresulting IRRs are either very difficult to interpret or meaningless.

Most people in business have heard of "internal rate of return." Some are required by
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thier financial officers to produce an IRR to support budget requests or action proposals.IRR is in fact a favorite metric of many CFOs, Controllers, and other financial specialists.There is a widespread belief in the financial community, for instance, that IRR is a more"objective" metric than NPV, because NPV depends on an arbitrarily chosen discountrate, whereas IRR is determined eintirely by the cash flow figures and their timing. Many

also believe that IRR allows investment returns to be compared readily with inflation,current interest rates, and financial investment alternatives. Many organizations establishan IRRhurdle rate, that is, an IRR rate that must be reached or exceeded by incomingproposals if they are to be approved and funded.

It should no surprise to learn that most business people who are not in finance have alimited or poor understanding of IRR and its meaning. It may be more surprising,however, to learn that research on professional competencies finds consistently that mostof the same financial specialists who require IRRs with proposals or funding requests arethemselves largely unaware of IRR's serious deficiences and unprepared to explain itsmeaning and proper use.

For that reason, this entry puts a special emphasis on understanding IRR meaning andinterpretation, as well as common misconceptions and misuses of IRR. And, incomparing IRR to other financial metrics, this entry also presents the modified internalrate of return(MIRR), a more easily interpreted alternative to the better known IRR.

Internal rate of return (IRR) defined and illustrated with an example

- First IRR Interpretation: IRR as a measure of risk

- Finding IRR: Can IRR be calculated?

IRR re-defined: Why is it called internal rate of return?

- Second IRR interpretation: Financing costs and reinvestment gains

Modified Internal Rate of Return (MIRR): A better metric? Internal rate of return compared to other financial metrics

- IRR vs. MIRR, NPV, ROI, and Payback Period

- IRR disgused as yield to maturity (YTM) for bond investing

Lease vs. buy and other problem IRR results

- Lease vs. Buy vs. IRR

-Negative, multiple, and impossible IRRs

Internal rate of return (IRR) defined and illustrated with an example

As the word "return" in its name implies, an IRR view of the cash flow stream isessentially an investment view: paid out funds are compared to returns. The best knownIRR definition explains this comparison in terms that call for a basic understanding ofdiscounted cash flow conceptspresent value, net present value (NPV), and the role ofthediscount rate(interest rate) in determining NPV:

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

That definition, however, can be less than satisfying when first heard. Many ask: "Whatdoesthat tell me about returns and costs?

A first interpretation of IRR meaning is illustrated with an example. Consider twoproposed investments compting for funding: Case A and Case B. The expected net cashflow streams for A and B are as follows:

Both cases call for an initial cash outlay of $220. Case A brings a net gain of $200 over 7

years while case B brings a net gain of $240 over the same 7 years. Before finding IRRsand other metrics, note in the image below how the two cash flow streams streams differ:

Both streams have theinvestment curveprofile describedabove. Case A (bluebars) has large earlyreturns but thesediminish year by year.A's profile could

represent aninvestment in anincome producingasset that becomesless productive ormore costly tomaintain each year. Case B (yellow bars) has smaller returns at first, but B's returns groweach year. B's profile could result from investing in a product launch that returns greaterprofits each year. The analyst will thus compare two different kinds of investments withthe same metric, IRR, to address questions like these: Which is the better investment?Which is the better business decision? The net cash flow figures above, when analyzed

with a spreadsheet function or another IRR program, show an IRR of 30.6% for Case Aand an IRR of 20.8% for Case B.

The next table and figure below show the result of applying IRR Definition 1 (thediscount rate that brings an NPV of 0). Only one of the above cash flow streams is shownhere, Case A. The first table row shows net cash flow each year, and the second rowshows the discounted values (present values) of the same cash flows. Discounting isapplied using the IRR rate found by the analyst for this cash flow stream, 30.6%.


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Notice in the tablethat this discount rateleads to a total presentvalue (NPV) of 0. Thechart at left alsoshows the same thingin visual terms.

Dark blue bars are

future valuenet cashflows for Case A . Light blue bars arepresent values of thesame cash flows at the IRR discount rate of 30.6%.

You may just be able to see or imagine that the heights of the seven positive (upwardpointing) light blue bars starting with Yr 1 add up exactly to the height of the onenegative (downward pointing) light blue bar at "Now." In other words, at the IRRdiscount rate, the sum of positive PVs excactly cancels the sum of negative PVs.

First IRR interpretation: IRR as a measure of risk

In the example above, which is the better Investment, Case A or Case B? Case A has anIRR of 30.6%, Case B has an IRR of 20.8%. Other things being equal, and using IRR asthe decision criterion, the one with the higher IRR (Case A) is considered the betterchoice. One reason for this conclusion is that a higher IRR indicates less risk. That is,IRR indicates just how high inflation rates or risk probabilities have to rise in order toeliminate the present value of this investment.

For the Investment A cash flow, the prevailing discount rate (which includes aninflation component and a risk component) would have to rise all the way to 30.6% todrain this investment of present value.

The B investment would lose all present value if the discount rate rose to 20.8%.

Most people, however, find this first interpretation of IRR of little value for evaluting andcomparing proposed investments. The sections below, therefore, move torward a second,more useful IRR interpretation, a comparison of IRR with other cash flow metrics, and adescription of a more easily interpreted metric, the modified internal rate of return(MIRR).


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Finding IRR: Can IRR be calculated?

Other cash flow metrics such as NPV, ROI, and even payback period, can be calculateddirectly from simple formulas, assuming you have the proper input data. However, theverbal IRR Definition 1 above does not lend itself readily to presentation in formulaform. The best that can be done for producing an IRR formula is this: Consider theformula for calculating net present value (NPV) for a cash flow stream, using end ofperiod discounting:

The "FVs" in theformula are thenet cash flowfigures for eachyear. For Case A and Case B above, n = 7 (7 periods). The person who wants a "formula"for IRR can be handed the above formula along with the FVs (net cash flow values) andthen asked to do the following:

Set NPV equal to 0, then solve the formula for i. i = IRR when NPV = 0.

In fact, there is no easily applied analytic solution to the above request, and it is moreaccurate to say that IRR is "found" rather than "calculated." IRR can be found either bygraphical analysis oras Excel doesby "trial and error" (more precisely, by"successive approximations").

Consider first the plotting data for a graphcial IRR solution:

Using the formulaabove, NPV wascalculated for A and Bcash flow streams at

10 different discountrates. The table showsthe calculated NPVvalues. These areplotted below,showing therelationship betweendiscount rate(horizontal axis) andresulting NPV(vertical axis).

As you would expect, increasing discount rates brings lower NPVs for both streams.However, Case A's NPV reaches 0 at a discount rate of 30.6%, while B's NPV reaches 0at a discount rate of 20.8%. Therefore, IRRA = 30.6%. and IRRB = 20.8%

Instead of finding a graphical solution for IRR, most people use Microsoft Excel or a pre-programmed calculator. Either way, the software starts with an arbitrarily chosen discountrate and finds the NPV for a given cash flow stream. It then keeps changing the rate untilit finds a rate that produces a 0 NPV. This occurs very quickly, so that the IRR result


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seems to appear as soon as the data are entered. The analyst, for example, might enter theExcel IRR function into a formula like this: =IRR (B3:B10, .1)

The spreadsheet cell with this formula shows the IRR for a range of cells with net cashflow figures in cells B3 through B10. These could be, for instance, the eight cash flowvalues for Case A in the example above The ".1" figure is simply the analyst's first

"guess" at the IRR. The guess is simply a starting discount rate for calculating NPV onthe first iteration and it can be almost anything or even omitted. The analyst will probablyformat the spreadsheet cell as a percentage, so that the IRR result looks like this: 30.6%

IRR re-defined: Why is it called internal rate of return?

The textbook IRR Definition 1 above explains how to find an IRR but says very littleabout what it represents. IRR's more important meaning is easier to understand in termsof another definition, one that refers investment financing costs and reinvested returns.

IRR Definition 2: The internal rate of return (IRR) for a cash flow stream is based on twoassumptions:

1 There is a financing cost (or opportunity cost) for using the funds to make theinvestment. Investment costs will be financed across the time until the final cash flowevent.

and

2 Incoming returns will be reinvested for the time remaining until the last cash flowevent.

IRR is then defined as the single interest rate (for financing costs and for reinvestmentearnings) that sets the total gains exactly equal to total costs.

The example below shows how IRR can be defined as the interest rate that balances thesetwo factors. Cash flow figures in blue cells are from example Case A above.


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In the example, an initial cash outflow of $220 (at "Now") represents initial investmentcosts. Each year after that, the investment brings positive net cash flow returns. Excel'sIRR function has been entered in the yellow cell below Year 7 net cash flow and it reportsthat a discount rate of 30.63% produces an NPV of 0 for the cash flow stream. The IRRfor this cash flow stream is thus 30.63%.

Consider first the interest earned by re-investing the incoming cash flows from Years 1through 7. If each incoming return is reinvested with for the remaining years, at an annualinterest rate of 30.63%, the total seven year gains would be $1,428.17 (inflows + interestearned).

Now, assume that the initial cash outflow of $220 is borrowed and financed at the same30.63% annual rate. The example shows shows the total cost of repaying this loan is also$1,428.17 (initial cash outflow plus financing). The IRR rate exactly balances totalinvestment costs with total investment gains.

Second IRR Interpretation: Financing costs and reinvestment gains

The second-definition example above should begin to suggest a reason that financialpeople look to IRR and often trust it as an important decision criterion: IRR has built intoit the presumption that investment costs (opportunity costs or borrowing) are financed ata cost, and that incoming returns are reinvested, earning additional gains. This viewprovides meaning for another IRR interpretation, namely that the analyst will comparethe IRR rate to actual financing rates and actual reinvestment rates. This comparison,however, has to be interpreted carefully. It is easy to overinterpret or misinterpret IRR atthis point.

When a proposed investment produces IRR's like those shown above30.6% forexamplemany are tempted to reason as follows:

"For this investment, we will not actually borrow (or pay an opportunity cost) at the IRRrate. Our real cost will be subject to rates closer to our cost of capital, probably less than10%. Therefore [the reasoning goes], the investment is a net gain because financing rateswill really be under 10%, while returns represent earnings at a much higher rate,something like 30.6%."

In reality, that conclusion may or not be supportable, depending on the company'sactualfinancing cost rates (or opportunity cost rates) and the actual reinvestment rates tobe applied. The conclusion is most supportable when the IRR rate is close to actual costof capital and actual reinvestment rate. The conclusion is most likely misleading orwrong when IRR is quite different from actual cost of capital and reinvestment rates.

This reasoning can grossly overstate the value of investments like, for example, Case Aabove. Suppose, for instance, that the company's real reinvestment rate is closer to 8%,even though the cash flow stream has an IRR of 30.6%. Notice especially that cash flowstream A expects large returns in the first and second years of the 7-year investment (thatis, Investment A is "front loaded," or "biased" towards the early years). The high IRRassumes year 1 and year 2 gains will be reinvested at 30.6% for all the remaining yearsbut in fact, this long term of high-rate reinvestment will be absent. Cash flow stream B,on the other hand has a lower IRR than A, but when real investment returns are compared


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to the reinvestment earnings presumed by the IRR, B in fact has less "missing" returns ofthis kind than A. IRR overstates the real value of investment A far more than it overstatesthe value of investment B for two reasons: First, stream A is front loaded and stream B is"back loaded," and second, because A's IRR is further from the real reinvestmen rate thanB's IRR.

In brief, it is reasonable to view a proposed investment as a net gain when IRR is greaterthan the company's cost of capital. However, using IRR to assess the magnitude of the netgain is problematic, especially when (a) IRR greatly exceeds cost of capital and the realreinvestment rate, and (b) when comparing two cash flow streams with different profilesas in the example above. The latter point (b) is illustrated again in the discussion belowon IRR in "Lease vs. buy" comparisions.

Modified Internal Rate of Return (MIRR): A better metric?

The meaning of IRR magnitude is difficult to interpret, as shown, because IRR can differfrom 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 realreinvestment rate?" In fact, this solution is readily available as the modified internal rateof return (MIRR) metric.

Input data for MIRR include the same net cash flow figures as IRR, but the MIRRcalculation also requires as input a financing rate and a reinvestment rate. Here forcomparison are the IRR and MIRR results forexample Cases A and B from above.MIRR for this example is based on a reinvestment rate of 8% and a financing rate of 6%:

Investment Case A: IRR = 30.6% MIRR = 15.1%Investment Case B: IRR = 20.8% MIRR = 14.7%

Notice immediately that Case A also has a higher MIRR value than Case B, but bothMIRR values are much closer to each other than are the two IRR values.

The full meaning of MIRR is easier to explain after showing how the MIRR results arederived. MIRRunlike IRRcan be computed directly from a formula:

Future values ofcash inflows arecalculated usingthe reinvestmentrate. Present values of the cash outflows are calculated using the financing rate. Theradical sign calls for the nth root of the Future value/Present value ratio. nis the numberof periods, here 7. Subtracting 1.0 from the resulting root yields MIRR. For example cashflow stream A using a reinvestment rate of 8% . . .

FV (Positive CFs) = $120(1.08)6 + $100(1.08)5 + $80(1.08)4 + $55(1.08)3 + . . .. . . +35(108)2 + $20(1.08)1 + 10(1.08)0

= $190.42 + $146.93 + $108.84 + $69.28 + $40.82 + $21.60$ +$10.00

= $587.91
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Present values of negative cash flows are also calculated using the financing rate, whichis 6% in this case. However, for this particular example there is only one negative cashflow and because that occurs immediately ("Now") its present value shows 0 discountingeffect.

PV (Negative CFs) = ($220)(1.06)0 = ($220.00)

Negative cash outflows will have a negative present value, so the formula preceeds thePresent Value sum with a "" making it a poisitive number. Using the above formula,MIRR for Investment Case A is thus:

Here, at last, is an investment result with a clear, easily understood meaning:

If the original $220 investment is simply put on deposit, earning interest at the MIRR

annual rate of 15.1% for 7 years, the total value with compound interest would be$587.91. Or, if instead the projected cash inflows from the Investment Case A werereinvested at 8.0%, the total investment value with compound interest would be the same$587.91.

Similarly, Case B has a MIRR of 14.7%. If B's initial cash outflow is simply put ondeposit for 7 years, earning interest compounded at the MIRR rate, the total investmentvalue would be 573.76. Or, if instead, the projected incoming cash flows from investmentB were reinvested at the reinvestment rate of 8.0%, the total investment value after 7years would be the same $573.76.

Note: To check these calculations yourself, use the more precise MIRRA rate of

15.0757% and MIRRB rate of 14.6732%.

In other words, making these investments brings the same result as simply putting theinvestment costs in the bank and receiving interest at the MIRR rate.

Note that IRR results show a larger advantage for Case A over Case B. The realtiveinvestment advanage of A over B is much smaller with MIRR. However, most people caneasily compare MIRR results with compound interest growth and understand themagnitude of the MIRR difference. As shown, understanding the meaning of the IRRdifference is more problematic.

Incidentally, the MIRR formula is really a geometric meanexactly the same formulaused to find comulative average growth rate for figures that grow exponentially, such ascompound interest earnings. And, calculations like those above can be avoided entirelyby simply using Excel's MIRR function. For Case A, whose cash flows are located incells B3 through B10, using a reinvestment rate of 8% and financing rate of 6%, Excel'sMIRR function would be: =MIRR(B3:B10, 0.06, 0.08).

Internal rate of return compared to other financial metrics

Referring to the example cases above, which is the better business investment: Case A or
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Case B? In many organizations, IRRs may play a role in answering such questions, butgenerally, such questions should not be answered on the basis of a single financial metric.The prudent financial specialist, investor, or business analyst will compare bothinvestments with several financial metrics. As shown below, different metrics maysuggest different answers to the question.

This section compares A and B investmentson the basis of net cash flow, internal rate ofreturn, modified internal rate of return, net present value, return on investment, andpayback period. For more coverage of the individual metrics in this encyclopedia, pleasefollow the links provided with each metric.

IRR vs. Net Cash Flow, MIRR, NPV, ROI, and Payback period

IRR results in the above examples required only the net cash flow figures for eachinvestment each period. In order to compare investments with a wider range of cash flowmetrics, however, the analyst needs to see individual cash inflows and outflows as well asthe net figures:

Before looking at the individual metrics, notice some of the most apparent differencesbetween Case A and Case B cash flow. First, A's inflows and outflows are much largerthan B's. A actually brings in larger inflows but these come at larger costs. This differenceis not apparent when viewing only the annual net cash flow figures. Secondly, as alreadynoted, A's large returns arrive early, whereas B's larger returns occur in later years. It willtake more than one financial metric to fully develop the implications of these differences.

Financial metrics results for Case A and Case B based on these data are as follows:


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Total Net Cash Flow

Thenet cash flow metric favors investment B over investment A: A brings a $200 netgain over 7 years, while B brings in $240. Case B thus has a $40 (20%) advantage in netcash flow over A. For situations where cash flow and working capital are problematic,

this could be an important advantage for Case B. However, see the discussion on PaybackPeriod, below, for a different view of these cash flow consequences.

Internal Rate of Return (IRR)

Investment A outscores Investment B on the IRR metric, 30.6% to 20.8%. Both IRRfigures are very likely above the company's cost of capital, and both investments can thusbe viewed as net gains. A's larger IRR can be taken as a signal that A provides a betterrate of return than B (assuming that incoming cash flows are reinvested). Beyond that,however, the IRR figures themselves do not show the magnitude of A's real rate of returnadvantage over B. When IRRs are several times larger than cost of capital, or more, the

real rate of return difference between two different investments depends heavily on thetiming of cash flows, the cash flow stream profiles, and the actual rates available for costof capital and reinvestmentnone of which can be seen in the IRR figures.

Modified Internal Rate of Return (MIRR)

With an 8% real reinvestment rate, investment A slightly outscores investment B ontheMIRR metric, 15.1% to 14.7%. The MIRR's meaning is easily understood: MIRRessentially compares investment results to the growth ofcompound interest earnings.Assuming that incoming returns are reinvested at 8%, investment A, for instance givesthe investor exactly the same result as putting the initial cash outflow on deposit for seven

years and receiving compound interest earnings at the MIRR annual rate, 15.1%.

Net Present Value (NPV)

The better business decisionor preferred investmentA or B, according to net presentvalue depends on the discount rate. At a 5% discount rate, B's NPV of $155 exceeds A's$149 NPV. However, NPV leadership reverses at higher discount rates. With discountingat 10%, A's NPV of $107 is higher than B's $91. As the discount rate rises, B's largereturns in later years suffer greater discounting impact than A's larger returns in the earlyyears. This illustrates one reason some financial specialists prefer IRR to NPV whenchoosing between competing investments: NPV uses an arbitrarily chosen discount rate,

which may determine results of the comparison, as shown. IRR, on the other hand, issometimes seen as more "objective" because it does not rely on an arbitrarily chosen rate.IRR instead uses net cash flow figures themselves to find a rate that satisfies itsdefinition.

Return on Investment (ROI)

According to the ROI metric, it's "no contest!" B's ROI of 52.2% beats A's ROI of 18.7%,
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hands down. The ROI metric shown here is Simple ROI, sometimes called "cash on cash"analysis (incremental gains divided by investment costs). All cash flow metrics above,including ROI, show both investments as net gains for the investor. ROI alone, however,is sensitive to the magnitudes of individual annual inflows and annual outflows. Theother metrics derive only from the net cash flow figures. A's larger total costs ($1,200) are

compared directly to A's incremental gain of $200. B scores much higher on ROI becauseB has a larger incremental gain ($240) and a much smaller total cost ($460). The largedifference in costs is "masked" or hidden in the other metrics. This could be problematicbecause investment costs must be budgeted and paid for, no matter how large the returns,and the investor may simply have trouble providing the larger funding costs.

Payback Period

Thepayback period metric shows that investment A "pays for itself" in 2.0 years, whileit takes 3.4 years for B's incoming gains to fully cover investment costs. Investors preferpayback periods that are shorter rather than longer for at least two reasons. First, the

investment funds are available again for re-use sooner with a shorter payback period.Second, investments with longer payback periods are considered more risky.

Financial Metrics Conclusions

When stating a decision criterion as a general rule, business analysts and finance officersoften borrow a phrase that is a favorite of economist: Other things being equal, theinvestment (or action, or decision, or scenario) with the higher IRR is the better businessdecision. The different financial metrics comparisons above illustrate the point that IRRis blind to many "other things" that may differentiate competing investments, these thingsmay have important financial consequences, and they are very rarely truly equal.

Consequently, it is usually recommended that IRR not be used as a decision criterionwhen comparing competing mutually exlusive investments or actions. When the investorcan or will make only one of the two proposed investments, the choice of one over theother represents so-called constrained financing.

Finally, In business investingas in gamblinga wise investment (or a good gamblingbet) is one where potential rewards compare favorably with investment risks. None of themetrics above fully measures investment risk, although risk considerations are partiallyvisible in IRR, NPV, and payback period:

An Investment with a high IRR can be viewed as less risky than a low IRRinvestment. Interest rates for discounted cash flow include a "risk" component and an

"inflation" component. If inflation rates rise during the investment period, or if theappropriate discount rate for NPV rises because of risk considerations, the high IRRinvestment retains greater NPV than the lower IRR investment.

A longer payback period is considered more risky than a shorter payback, simplybecause of the longer time it takes to recover investment funds.

When using the above metrics as decision criteria, however, the prudent investor willattempt to assess the likelihood that returns actually appear as projected, as well as the
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liklihood that other beter and worse results appear.

IRR disgused as yield to maturity (YTM) for bond investing

Another reason that IRR is a favorite metric for people trained in finance, is that IRR(disguised under a different name) is used in evaluatingbond investments. If the IRR

exercises above remind you of something you have seen beforesolving an NPVequation for an interest rateit is likely you are already familiar with the concept yield tomaturity(YTM) used in bond investing. IRR and YTM are mathematically the sameconcept, with only a slight difference in definition (for a more complete coverage of yieldand other bond concepts, see the encyclopedia entry forbond).

Yield to Maturity is the interest rate, i, that satisfies this version of the NPV equation:

Bond Purchase Price = FV1 / (1+ i )1 + FV2 / (1+ i )2 + ... + FVn / (1 + i )n

This definition for YTM can be changed into Definition 1 for IRR, simply bysubtracting "Bond Purchase Price" from each side of the equation. This way, Bond

Purchase Price becomes the FV0 in the NPV equation that is used for IRR. The formulafor IRR then asks for the same i that solves the equation:

0 = FV0 + FV1 / (1+ i )1 + FV2 / (1+ i )2 + ... + FVn / (1 + i )n

Given the same cash inflows and outflows, the same value of i solves both equations.This is another reason that financial specialists use IRR as a metric for evaluating andcomparing potential business investments, even when the investments are quite differentin nature.

Lease vs. buy and other problem IRR results

IRR can usually be found and usefully interpreted when based on net cash flow streamswith the "investment curve" profile" shown above: Net cash outflows appear very early inthe stream while net cash inflows follow through the rest of the investment life. Thisprofile is common for some kinds of financial investments, such as bond investments orbank deposits. The investment curve profile may also characterize some investments inincome-producing assets, or sometimes even the financial consequences of projects,programs, product launches, and other actions.

In many organizations, however, IRR is routinely calculatedor requiredto supportaction proposals, even when expected cash flows do not fit the investment curve profile.Those who are called upon to provide IRR support for funding requests, project orprogram proposals, orbusiness case analysis are often dismayed when they find that an

IRR does not exist for their cash flow stream, or they find multiple IRRs for a singlestream, or that there is a negative IRR. Or, they may be at a loss to interpret IRR messagewhen one proposed action shows an IRR 10 or 20 times larger than a competing option.

The situations described below illustrate the four "commandments" of IRR Usage.

3 Do not use IRR when the net cash flow stream differs substantially from theinvestment curve profile (early net cash outflows, later net cash inflows).
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4 Do not use IRR to compare competing cash flow streams whose profiles differsubstantially from each other, even if they are both roughly "investment curves."

5 Do not be tempted to over interpret IRR magnitude and suggested return rateswhen IRR differs substantially from the real cost of capital and real reinvestmentrates.

6 Do not even try to find an IRR when the net cash flow stream is entirely positiveor entirely negative. There is no IRR for such situations.

Lease vs. Buy vs. IRR

In a Lease vs. Buy comparison, the "Buy" option typically has a high initial cash outflowto buy the asset. In the remaining years of the asset's life, there should be cash inflows asthe asset earns returns. The "Lease" option for the same asset starts with a very smallinitial cash outlay (if any), followed by almost the same net returns projected, but reducedsomewhat by the periodic leasing fees (this would be the case for a typicaloperatinglease). These cash flow streams fit this pattern

The "Buy" stream has an IRR of 42.6%. The "Leasing" option has an IRR of 1,400.0%.Imagine choosing between these two options, using IRR as the sole decision criterion!

In fact, when results of this kind appear, most people immediatelly ask: "What's wrong

with this picture?" Here are three of the problems:

The Buy option is properly called an "investment," but the Lease option is betterdescribed as a 7-year commitment to a service contract with periodic fees. The twoprofiles difffer substantially from each other. The Lease profile is not an investmentcurve.

IRR looks only at the net cash flow figures each year. The leasing costs each yearare "masked" or hidden from IRR by the larger positive inflows. When these optionsare compared with the Simple ROI metric (cash on cash), which is sensitive toindividual periodic cash inflows and outflows, both options have exactly the sameROI, that is, 226%

Both IRRs are certainly much higher than the company's real cost of capital andreal reinvestment rates, especially the Lease option IRR. The analyst who still insistson taking an "investment" view of both options should probably turn instead to themodified internal rate of return. The MIRR for the Buy option is 22.5%, whileMIRR for the Lease option is 99.3% (basing MIRR on an 8% reinvestment rate.

In brief, a Lease vs. Buy decision based on IRR would always choose leasing as thebetter business decision because IRR views the action as a financial investment.
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However, IRR can be blind to period leasing costs, as shown, and in the Lease vs. Buydecision, other factors can be more important, such as the impact on the company's assetbase, tax consequences, and flexibility to upgrade or replace assets.

Negative, multiple, and impossible IRRs

With certain cash flow streams it is mathematically possible to produce negativeIRRs, or multiple IRRs for the cash stream (more than one discount rate that leads toa 0 NPV). For other cash flow streams, there is simply no mathematically correct IRRsolution.Impossible IRR: There is no possible IRR solution when the cash flowIncludes only positive or only negative net cash flows. As shown above, there may bereal cash outflows in every period, but when the inflows always outwiegh outflows,there will be no negative net cash flows. There is no IRR in such cases. Other patternsof negative and positive net cash flows can also have no IRR solution.

Multiple IRRs: A net cash flow stream will have multiple IRRs when it Includesmore than one sign change. When the first cash flow is negative and the second cash

flow is positive, that is one sign change and there will be one IRR for the stream. Ifanother, later, net cash flow event is negative, that makes 2 sign changes. There willbe one IRR for every sign change in the cash flow stream. In such cases, it is probablybest to consider the IRR closest to the real cost of capital as the "true" IRR.

Negative IRR: It is also possible for some net cash flow streams to produce anegative IRR value. This signals simply that the investment or action should beconsidered a "net loss." Further quantitative analysis of negative IRRs is not advised.Negative IRRs should certainly be diregarded when the analyst prepares IRRaverages, or weighted average IRRs for multiple investments.

Thanks:

Documents

Internal Rate of Return.doc