JOURNAL OF ECONOMICS AND FINANCE EDUCATION ∙ Volume 12∙ Number 1 ∙Summer 2013 - 39 - Teaching MIRR to Improve Comprehension of Investment Performance Evaluation Techniques R. Brian Balyeat 1 , Julie Cagle 2 , and Phil Glasgo 3 ABSTRACT NPV and IRR are frequently used to evaluate investment performance, yet when they conflict many firms base capital budgeting decisions on IRR, though NPV is superior in specific cases. Teaching the MIRR technique should reinforce academia’s preference of the NPV technique. The reinvestment assumptions of NPV and IRR are implicit and hidden from students, while the calculation of the MIRR technique forces explicit decisions regarding the investment and discounting of interim cash flows. Thus, by teaching the MIRR calculation students may gain a better understanding of the differences between the three techniques reinforcing the primacy of NPV. Key Words: NPV, IRR, MIRR Introduction Evaluating investment performance is fundamental to the finance discipline, and taught in both investment andfinancial management courses. 4 A puzzle related to performance evaluation techniques as used in practice is the similar frequency of use of the IRR technique relative to NPV for evaluating capital investments, even though most finance texts argue that NPV is superior in certain cases. 5 NPV is more consistent with wealth maximization when projects have unconventional cash flows, and in the cases of mutually exclusive projects with differences in scale (initial investment size) or timing of cash flows (whether larger cash flows occur later vs. early in project life). Brealy and Myers (2000, p. 108) point out that IRR is a derived figure without any simple economic interpretation and that it cannot be described as anything more than the discount rate that when applied to all cash flows makes NPV equal to zero. Hirshleifer(1958) concludes that anytime there are intermediate cash flows between investment and the termination of the project, the IRR rule is not generally correct. The MIRR (modified IRR) yields decisions identical to the NPV rule unless scale differences are present betweenmutually exclusive projects. Even with scale differencesbetween mutually exclusive projects, Shull (1992) shows an adjusted MIRR technique that leads to identical decisions to the NPV rule. 6 Should it concern finance academics that IRR is used so frequentlyin practice? Yes, given that IRR is not a valid measure of return for many projects, and that IRR may result in investment decisions that conflict with NPV and lead tosub-optimal investment decisions. Burns and Walker (1997)provide evidence 1 Department of Finance, Xavier University 2 Department of Finance, Xavier University 3 Department of Finance, Xavier University 4 See Phalippou (2008) for a discussion of the hazards of using IRR to measure performance in an investment context, particularly the case of private equity. Phalippou points out that the performance evaluation literature is largely found in corporate finance texts rather than investment texts. He also provides a MIRR calculation for measuring investment level and fund level performance. 5 See, for example, Ross, Westerfield, and Jordan (2011) pages 246 and 248. 6 Shull (1992) discusses an adjusted ORR method that is the MIRR technique adjusted so that it can lead to identical ranking decisions to NPV in the case of scale differences between mutually exclusive projects.
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JOURNAL OF ECONOMICS AND FINANCE EDUCATION ∙ Volume 12∙ Number 1 ∙Summer 2013
- 39 -
Teaching MIRR to Improve Comprehension of
Investment Performance Evaluation Techniques
R. Brian Balyeat1, Julie Cagle
2, and Phil Glasgo
3
ABSTRACT
NPV and IRR are frequently used to evaluate investment performance,
yet when they conflict many firms base capital budgeting decisions on
IRR, though NPV is superior in specific cases. Teaching the MIRR
technique should reinforce academia’s preference of the NPV
technique. The reinvestment assumptions of NPV and IRR are implicit
and hidden from students, while the calculation of the MIRR technique
forces explicit decisions regarding the investment and discounting of
interim cash flows. Thus, by teaching the MIRR calculation students
may gain a better understanding of the differences between the three
techniques reinforcing the primacy of NPV.
Key Words: NPV, IRR, MIRR
Introduction
Evaluating investment performance is fundamental to the finance discipline, and taught in both
investment andfinancial management courses.4A puzzle related to performance evaluation techniques as
used in practice is the similar frequency of use of the IRR technique relative to NPV for evaluating capital
investments, even though most finance texts argue that NPV is superior in certain cases.5NPV is more
consistent with wealth maximization when projects have unconventional cash flows, and in the cases of
mutually exclusive projects with differences in scale (initial investment size) or timing of cash flows
(whether larger cash flows occur later vs. early in project life).
Brealy and Myers (2000, p. 108) point out that IRR is a derived figure without any simple economic
interpretation and that it cannot be described as anything more than the discount rate that when applied to
all cash flows makes NPV equal to zero. Hirshleifer(1958) concludes that anytime there are intermediate
cash flows between investment and the termination of the project, the IRR rule is not generally correct. The
MIRR (modified IRR) yields decisions identical to the NPV rule unless scale differences are present
betweenmutually exclusive projects. Even with scale differencesbetween mutually exclusive projects, Shull
(1992) shows an adjusted MIRR technique that leads to identical decisions to the NPV rule.6
Should it concern finance academics that IRR is used so frequentlyin practice? Yes, given that IRR is
not a valid measure of return for many projects, and that IRR may result in investment decisions that
conflict with NPV and lead tosub-optimal investment decisions. Burns and Walker (1997)provide evidence
1 Department of Finance, Xavier University 2 Department of Finance, Xavier University 3 Department of Finance, Xavier University 4 See Phalippou (2008) for a discussion of the hazards of using IRR to measure performance in an investment context,
particularly the case of private equity. Phalippou points out that the performance evaluation literature is largely found in corporate
finance texts rather than investment texts. He also provides a MIRR calculation for measuring investment level and fund level performance.
5 See, for example, Ross, Westerfield, and Jordan (2011) pages 246 and 248. 6 Shull (1992) discusses an adjusted ORR method that is the MIRR technique adjusted so that it can lead to identical ranking
decisions to NPV in the case of scale differences between mutually exclusive projects.
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on how capital budgeting decision criteria are used in practice, and more importantly,how the multiple
decision techniques are treated when they conflict. The survey was sent to CFOs on the Fortune 500
industrials list. Forty-one percent of respondents indicated that IRR took priority in the case of a conflict,
versus 29% for NPV and 2% for MIRR. This is evidence that IRR is being used by practitioners in ways
which result insub-optimal investment decisions that are inconsistent with the recommendation by finance
academics to prioritize NPV in the cases of conflict with IRR. Clearly, these results suggest academics
need to do more to clarify the best use of capital budgeting decision criteria to students that will be future
practitioners.
This paper proceeds to make the case for teaching the MIRR decision rule not only because it is a
superior measure of rate of return in some cases (e.g., when project cash flows change sign more than once)
compared to IRR, but also because teaching MIRR reinforces NPV as the primary decision criteria for
capital budgeting. When students calculate the MIRR for a project, they must explicitly consider how
intermediate cash flows during the life of the project are treated. In so doing, the differences in the
reinvestment assumptions between NPV, IRR, and MIRR can be highlighted. That the three techniques can
lead to inconsistent investment decisions and ranking of projects can also be emphasized and will hopefully
result in practitioners using NPV as the primary decision criteria over IRR in the case of conflict. The latter
may be particularly important if there is a bias by practitioners toward rate of return techniques, like IRR,
over NPV. Further, students and practitioners will become more aware that absent scale differences
between projects, MIRR complements the NPV decision if properly calculated.7
We first examinethe evidence on how alternative decision criteria are used in practice, followed by the
academic perspective on the MIRR technique and how MIRR is calculated. Then, a discussion of
reinvestment rate assumptions is provided, and a comparison of NPV, IRR, and MIRR decision criteria is
made. We conclude than not only is MIRR a superior measure of rate of return to IRR, but that pedagogical
emphasis on the MIRR criterion reinforces the primacy of the NPV technique.
The Practice of Capital Budgeting
The practice of capital budgeting has changed over time. Pike (1996) provides a longitudinal study of
capital budgeting practice between 1975 and 1992 for 100 UK firms. In regards to evaluation techniques,
he finds discounted cash flow methods are well established with 81% of firms reporting using IRR and
74% of firms reporting using NPV. The use of multiple techniques increased over time from one or two
methods to four methods. The greatest growth for any one technique was with NPV with 42% of the
sample introducing it since 1975. While these results are encouraging, Pike cautions that we know very
little about how the discounted cash flow techniques are used in the decision making process.
Burns and Walker (1997)include MIRR in their survey of Fortune 500 industrial CFOs to try and
ascertain more about the “how” of capital budgeting practices. They find NPV and IRR dominate with
more than 70% of firms using each, while MIRR was used by only 3% of respondents. The survey also
asked about emphasis on each of the techniques and IRR received the greatest emphasis (48 of 100 points),
followed by MIRR (45 of 100), and NPV (33 of 100). This suggests that while a small number of firms use
the MIRR technique, of those that do, it receives considerable emphasis. MIRR was also indicated as a
“younger” technique, with the only 50% of firms indicating that have used it for more than 10 years, versus
63% for IRR and 66% for NPV.
Importantly, Burns and Walker (1997)also provide evidence on how the multiple techniques are treated
when they conflict. Forty-one percentof respondents indicated that IRR took priority in the case of a
conflict, versus 29% for NPV and 2% for MIRR. These results are significant because they suggest
decisions are being made with priority placed on IRR instead of NPV when the rules conflict, which can
lead to sub-optimal investment decisions.
Similar to Pike (1996), the results of Burns and Walker (1997) indicate firms have increased their
emphasis on IRR, MIRR, and NPV over the last 5-10 years, while payback, discounted payback, and
average rate of return receive less emphasis. Interestingly, when asked about why a particular technique is
used, “ease of understanding” is indicated more frequently for the MIRR (8.5) and NPV (4.3) techniques
than IRR (3.5). The trend is similar across the three techniques for “ease of computation” and “reliability”.
7 See the section below “MIRR Calculation” for how we define the calculation of MIRR versus other authors and how our
definition may result in a MIRR different from that obtained from the Microsoft Excel MIRR function or a financial calculator. Our definition is based on Lin’s (1976) second definition for MIRR. Also see Shull (1992).
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In terms of “realistic reinvestment rate”, NPV received a composite average of 3.5 versus MIRR which
received 2.0.8Formal education was indicated as the dominant source of familiarity with the various
techniques, suggesting academics have a significant role in regard to how these techniques are used in
practice.
Graham and Harvey (2001) surveyed 392 CFOs in 1998-99 regarding capital budgeting, among other
topics, as well as descriptive information about their firms. NPV and IRR were indicated as the most
frequently used of the capital budgeting techniques listed, in a list that also included payback, discounted
payback, profitability index, accounting rate of return, and adjusted present value. Larger firms were also
more likely to use NPV than small firms. The MIRR technique was not included in the survey.
Ryan and Ryan (2002) survey 205 CFOs of Fortune 1000 companies. Use of seven different capital
budgeting decision techniques including NPV, IRR, and MIRR was examined. While 96% of the firms
reported use of NPV, 85.1% indicated they used it frequently. For IRR the usage rate was 92.1% with
76.7% of the firms using it frequently. By contrast, the MIRR usage rate was just under 50% and the
technique is used frequently by fewer than 10% of respondents. In fact, MIRR ranked seventh out of seven
for frequency of use. The size of the annual capital budget affected use of the various techniques. Firms
with larger capital budgets were more likely to use NPV and IRR, whereas this was not the case for MIRR.
MIRR was more frequently used by firms with mid-sized ($100 - $500 million) annual capital budgets than
small (< $100 million) or large (>$500 million) budgets. The authors puzzle over the lack of use of MIRR
and suggest it may gain acceptance over several decades as did other discounted cash flow techniques.
Academic Perspective on MIRR
The presumed reason for IRR’s frequent use in the field is that managers prefer to make decisions
based on returns rather than dollar amounts. Shull (1994, p. 162) argues that optimal investment decisions
are not the sole objective behind rate of return methods. NPV already provides that, so rate of return
methods are redundant for that reason alone. This suggests rate of return methods provide an advantage
beyond NPV-consistent decisions, but exactly what this additional advantage is remains unclear.
Finance texts now suggest MIRR as an alternative to IRR because it leads to decisions more consistent
with wealth maximization for projects with nonconventional cash flows and mutually exclusive projects
with different timing of cash flows. McDaniel, et al. (1988) credit Lin (1976) with early development of the
term MIRR in a format similar to today’s usage. Biondi(2006)traces the development of MIRR back to
Duvillard in 1787, and the re-emergence in the 1950’s to Lorie and Savage (1955), and Solomon (1956),
among others.
Therefore, MIRR has been around quite some time and is covered in most finance texts. E.g., Brigham
and Daves’(2007)text indicates MIRR is a better measure than IRR of the project’s true rate of return.
However, neither Graham and Harvey (2001) nor Pike (1996) include MIRR in their surveys regarding the
practice of capital budgeting, and when included in surveys, results indicate low use by practitioners.
Kierluff(2008) suggests a lack of academic support has produced graduates relatively unaware of the power
of MIRR. Kierluff(2008) describes MIRR as the more accurate measure of the attractiveness of an
investment because the return depends not only on the investment itself, but also the return expected on the
cash flows it generates.
It is unclear why MIRR hasn’t been embraced as the next best alternative to using NPV, as it is
puzzling why IRR would be the primary decision criteria used in the case that multiple criteria
conflict(Burns and Walker, 1997). One issue may be that MIRR is not an “internal” rate of return in that a
factor external to the project cash flows, the reinvestment rate, is used to determine the rate of return.
Another contributing factor may be the confusion surrounding the academic debate regarding reinvestment
rate assumptions. Carlson, Lawrence and Wort(1974) make this case:
“Note carefully that the most desirable solution to the reinvestment rate problem
is not in selecting either the IRR or NPV methodology, depending on the situation.
Rather, a much better solution is to explicitly select a consistent and accurate
reinvestment rate for the alternatives under consideration (Solomon, 1969).”
8 Although not advocated in this paper, the MIRR technique is sometimes calculated with two different rates for discounting and
compounding. This may explain the different survey results for this item between NPV and MIRR.
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We address the issue of alternative reinvestment rate assumptions below, following the
explanation of how to calculate MIRR.
MIRR Calculation
There is confusion about how to calculate MIRR with some ways to calculate it leading to decisions
more consistent with NPV decisions than alternative calculations. This confusion may be inhibiting the
adoption of MIRR technique. Ross, Westerfield, and Jordan (2011) describe three different possible MIRR
calculations and note that detractors suggest the acronym should stand for “meaningless internal rate of
return”. They point out that since MIRR is based on a modified set of cash flows it is no longer truly an
internal rate of return, which is a legitimate criticism regarding the name of the technique. In the discount
approach, all negative cash flows are discounted back to present, a reinvestment approach where all cash
flows beyond the initial investment are compounded to the end of the project’s life, and a combination
approach where negative cash flows are discounted and positive cash flows are compounded. They also
argue that it is irrelevant what is done with interim cash flows in that how cash flows are spent in the future
does not affect their value today, yet their three approaches result in three different MIRRs. However, we
believe how one deals with interim cash flows is key to understanding why NPV is a superior technique
relative to IRR.
Kierulff(2008), Brigham and Daves(2010), and Emery, Finnertyand Stowe (2007) and others describe
a three step procedure for MIRR similar to Ross, Westerfield, and Jordan’s combination approach. First,
periodic cash flows must be determined for the project life. An issue occurs with simultaneously
occurringinvestment funds (IF) and operating cash flows (OCF). McDaniel et al. (1988) argue that the
flows should be separated and IF discounted at the marginal cost of capital because it measures the cost of
meeting obligations to capital providers. Lin(1976) suggests two alternatives and both use the project’s
opportunity cost of capital as the relevant discount and compounding rate. Alternative oneis to net cash
flows and net negative cash flows are discounted to time zero and net positive cash flows are compounded
until the project’s termination. This calculation is consistent with the Texas Instruments BA II Plus
Professional and Microsoft Excel as long as the same reinvestment and discount rates are used and that rate
is the cost of capital. See Ng’s (2009) and Jones’ (2011) discussions of the inputs necessary to obtain the
correct MIRR with the BAII Plus Professional calculator when the cash flows from the project have more
than one sign change or when the cash flows start with multiple negative cash flows.
With Lin’s secondalternative, positive operating cash flows are invested and used to meet any
subsequent cash outflows during the life of the project, resulting in a net cash flow. If positive operating
cash flows are not available to offset subsequent cash flow, these funds must be obtained externally. Only
net cash flows from external sources are discounted to time zero, and all other cash flows are compounded
to the termination of the project. This is consistent with the notion that a firm would use internal sources of
funds before going to external sources. Using Lin’s second alternative for calculating the MIRR can yield
different results from the first alternative and thus is not always consistent with the MIRR obtained either
with the Texas Instruments BA II Plus Professional calculator or Microsoft Excel. Appendix I highlights
the differences between Lin’s two approaches in a Microsoft Excel Spreadsheet. Note differences only
occur for those projects involving cash outflows that can be funded by previous cash inflows. When
differences do occur, Lin’s second alternative produces MIRRs greater (smaller) than those in Texas
Instruments BA II Plus Professional calculator or Microsoft Excel when the project MIRR exceeds (is less
than) the cost of capital.
While Lin’s two methods provide NPV-consistent accept and reject decisions for projects, the second
approach is clearer to interpret according to Shull (1992, 1994). Shull(1992, p. 9) provides arguments for
why Lin’s latter approach, while resulting in the same investment decisions as the former approach, has
interpretational advantages. The latter approach has an investment base that can be interpreted as the
project’s investment capital that could be invested in alternative opportunities and/or otherwise consumed.
If the investment base has meaning, then the return calculated on this base is likewise meaningful. In turn,
the terminal value considers all cash flows not in the project’s investment base compounded at the cost of
capital. Denoting a project’s cash flows by ai, we define MIRR with Lin’s latter approach and using Shull
(1992)notation:
MIRR=(TV/IB)(1/n)
– 1. (1)
where
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IB= The project’s investment base ∑
(
and (2)
TV=The project’s terminal value ∑ ( . (3)
The variable n is the horizon period over which projects are evaluated, m is the last period with an
unfunded(external) negative cash flow, and k is the project’s cost of capital/opportunity cost of funds.
TheIBcan be interpreted as the present value of the investment requirements funded by sources external to
the project and the TVcan be thought of as the future value of all cash flows not considered in the
investment base compounded to the project’s termination. The MIRR equation can be rearranged into a
more intuitive version as
IB = TV / (1+MIRR)n (4)
As with IRR, the MIRR is compared to the hurdle rate of the project cost of capital. As discussed in
Shull (1992), the MIRR rule will provide the same investment decisions as the NPV rule when the same
discount rate is used for both criteria. However, MIRR will not always rank mutually exclusive projects
identically to NPV. An adjusted MIRR is needed for NPV-consistent rankings. Bernhard(1980) provides an
incremental rate of return method, but its use may require many pair-wise comparisons. Shull (1992)
provides two alternative adjusted MIRRs that do not require pair-wise comparisons, but may be more
difficult to intuit and are likely beyond the scope of most undergraduate finance classes. If rates of return
provide something beyond NPV-consistent rankings, these modified MIRRsshould be used; otherwise,
NPV can be used for the optimal ranking of projects.
The Reinvestment Rate Assumption
The correct reinvestment rate is an issue of considerable debate. In terms of the reinvestment rate,
McDaniel, et al. (1988), Brigham and Daves(2010), and Emery, Finnerty and Stowe (2007), and
Hirshleifer(1958) all advocate the project cost of capital as the discount rate. The rationale provide by
McDaniel, et al. (1988)is that if firms take all positive NPV projects, then positive cash flows generated by
projects reduce the need for external financing and save the cost of capital that would be required on these
funds. Kierulff(2008) points out that NPV and IRR also make reinvestment rate assumptions. When the
project cost of capital differs from the firm’s cost of capital, NPV assumes that future projects of similar
risk to the project under consideration will be found. Thus, projects will have a discount rate more than or
less than the firm’s cost of capital depending on the risk of the individual project. More commonly
recognized is the IRR reinvestment assumption that noninvestment cash flows from the project will be
reinvested at the same rate of return as the IRR of the project under consideration. For positive NPV
projects this means the NPV reinvestment assumption is more conservative than that of the IRR.
The issue of capital rationing is important in the reinvestment rate assumption. Carlson, Lawrence
and Wort(1974) point out that the implicit reinvestment assumption comes not from the decision criteria,
but from the objective of the investor. If the investor’s objective is the maximize shareholder wealth, then a
reinvestment assumption is included in the calculation of discounted cash flow criteria. Bacon (1977)
indicates that absent capital rationing, the correct reinvestment rate is the firm’s cost of capital since
positive cash flows save the firm the external cost of raising funds. However, if capital is “severely
rationed,” the rate of return on future marginal investments should be used. Bacon acknowledges the
complexity of estimating this future reinvestment rate.
Brealy and Myers (2000) point out that most capital rationing is soft, or self-imposed. The limit on
the capital budget is an aid to financial control adopted by management. Further, Brealy and Meyers (2000)
argue hard rationing would be rare for corporations in the U.S. Gitman and Mercurio(1982) provide survey
evidence consistent with this. While two-thirds of Fortune 1000 firms indicated they were confronted with
capital rationing, the dominant cause was a debt constraint imposed by internal management. Zhang (1997)
suggests this control is related to managerial incentives to shirk. The competition created internally among
managers when capital is limited reduces their likelihood of under-reporting project quality. Given that
hard rationing is uncommon, the project cost of capital is the appropriate discount rate in most cases and we
will proceed with this assumption. This is consistent with Shull (1992), Bernhard (1989), McDaniel, et al.
(1988) and others.
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Comparing NPV, IRR, and MIRR
NPV is calculated as the present value of all cash flows for the project discounted at the project’s
cost of capital. IRR is calculated as the discount rate that makes NPV equal to zero. To compare these two
techniques with MIRR, we will use three mathematical examples. Note that these examples involve
nonconventional cash flows so multiple IRRs can result. For each example, the project cost of capital is