ASTM E1057-15(2020)e1
(Practice)Standard Practice for Measuring Internal Rate of Return and Adjusted Internal Rate of Return for Investments in Buildings and Building Systems
Standard Practice for Measuring Internal Rate of Return and Adjusted Internal Rate of Return for Investments in Buildings and Building Systems
SIGNIFICANCE AND USE
5.1 The IRR method has been used traditionally in finance and economics to measure the percentage yield on investment.
5.1.1 The IRR method is appropriate in most cases for evaluating whether a given building or building system will be economically efficient, that is, whether its time-adjusted benefits will exceed its time-adjusted costs over the period of concern to the decision-maker. However, it has deficiencies that limit its usefulness in choosing among projects competing for a limited budget.
5.2 The AIRR method is a measure of the overall rate of return that an investor can expect from an investment over a designated study period. It is appropriate both for evaluating whether a given building or building system will be economically efficient and for choosing among alternatives competing for a limited budget.
5.2.1 The AIRR method overcomes some, but not all, of the deficiencies of the IRR. The AIRR is particularly recommended over the IRR for allocating limited funding among competing projects.
SCOPE
1.1 This practice covers a procedure for calculating and interpreting the internal rate of return (IRR) and adjusted internal rate of return (AIRR) measures in the evaluation of building designs, systems, and equipment.
1.2 The values stated in inch-pound units are to be regarded as standard. The values given in parentheses are mathematical conversions to SI units that are provided for information only and are not considered standard.
1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.
1.4 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
General Information
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Standards Content (Sample)
This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
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Designation: E1057 − 15 (Reapproved 2020)
Standard Practice for
Measuring Internal Rate of Return and Adjusted Internal
Rate of Return for Investments in Buildings and Building
Systems
This standard is issued under the fixed designation E1057; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
ε NOTE—Adjunct title and stock number in 2.2 were updated editorially in April 2020.
INTRODUCTION
The internal rate-of-return (IRR) and adjusted internal rate-of-return (AIRR) methods are members
of a family of economic evaluation methods that provide measures of economic performance of an
investmentovertime.Othermethodsinthisfamilyofevaluationmethodsarelife-cyclecostanalysis,
net benefits and net savings analysis, benefit-to-cost and savings-to-investment ratio analysis, and
payback analysis.
The IRR andAIRR methods are the topic of a single standard practice because they both measure
economic performance as a compound yield on investment.The IRR is the compound rate of interest
that,whenappliedasadiscountratetoaproject’sstreamofdollarbenefitsandcosts,willequatethem.
The AIRR is the overall yield taking into account earnings on receipts reinvested to the end of the
study period.The IRR orAIRR is compared against the investor’s minimum acceptable rate of return
(MARR), and the investment is considered economically attractive if the calculated yield exceeds the
MARR. If an investment entails an initial outlay and a single receipt at the end of the study period,
there is no difference between the IRR and the AIRR. But if cash flows occur over multiple time
periods, the two will normally be different. This arises because theAIRR includes in its measure the
return on reinvestment of receipts, whereas the IRR does not.
The AIRR is recommended for most applications in which a measure of yield is desired. Caution
is recommended in applying either measure, however, because problems arise under certain
conditions.
1. Scope responsibility of the user of this standard to establish appro-
priate safety, health, and environmental practices and deter-
1.1 This practice covers a procedure for calculating and
mine the applicability of regulatory limitations prior to use.
interpreting the internal rate of return (IRR) and adjusted
1.4 This international standard was developed in accor-
internal rate of return (AIRR) measures in the evaluation of
dance with internationally recognized principles on standard-
building designs, systems, and equipment.
ization established in the Decision on Principles for the
1.2 Thevaluesstatedininch-poundunitsaretoberegarded
Development of International Standards, Guides and Recom-
as standard. The values given in parentheses are mathematical
mendations issued by the World Trade Organization Technical
conversions to SI units that are provided for information only
Barriers to Trade (TBT) Committee.
and are not considered standard.
2. Referenced Documents
1.3 This standard does not purport to address all of the
safety concerns, if any, associated with its use. It is the
2.1 ASTM Standards:
E631Terminology of Building Constructions
E833Terminology of Building Economics
This practice is under the jurisdiction of ASTM Committee E06 on Perfor-
mance of Buildings and is the direct responsibility of Subcommittee E06.81 on
Building Economics. For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Current edition approved April 1, 2020. Published May 2020. Originally contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
approved in 1985. Last previous edition approved in 2015 as E1057-15. DOI: Standards volume information, refer to the standard’s Document Summary page on
10.1520/E1057-15R20E01. the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
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E1057 − 15 (2020)
E917Practice for Measuring Life-Cycle Costs of Buildings 4.1.9 Section 9, IRR Calculation—Describes the third step,
and Building Systems performing calculations, as it applies to the IRR.
E964Practice for Measuring Benefit-to-Cost and Savings- 4.1.10 Section 10, AIRR Calculation—Describes the third
to-Investment Ratios for Buildings and Building Systems step, performing calculations, as it applies to the AIRR.
E1074Practice for Measuring Net Benefits and Net Savings 4.1.11 Section 11, Choosing Between the IRR and AIRR—
for Investments in Buildings and Building Systems Discusses how to choose between the IRR and the AIRR.
E1121Practice for Measuring Payback for Investments in 4.1.12 Section 12, Limitations—Discusses limitations and
Buildings and Building Systems shortcomings of the IRR and AIRR.
E1185Guide for Selecting Economic Methods for Evaluat- 4.1.13 Section 13, Analysis of IRR or AIRR Results and the
ing Investments in Buildings and Building Systems Decision—Discussesthedecisioncriterionandthetreatmentof
E1369Guide for Selecting Techniques for Treating Uncer- uncertainty, risk, and unqualified effects.
tainty and Risk in the Economic Evaluation of Buildings 4.1.14 Section 14, Applications—Describes the types of
and Building Systems decisions to which the IRR and AIRR are applicable.
E1765Practice for Applying Analytical Hierarchy Process 4.1.15 Section 15, Report—Identifies information that shall
(AHP) to Multiattribute DecisionAnalysis of Investments be included in a report of an IRR or AIRR application.
Related to Projects, Products, and Processes
5. Significance and Use
E1946Practice for Measuring Cost Risk of Buildings and
Building Systems and Other Constructed Projects
5.1 The IRR method has been used traditionally in finance
E2204Guide for Summarizing the Economic Impacts of
and economics to measure the percentage yield on investment.
Building-Related Projects
5.1.1 The IRR method is appropriate in most cases for
2.2 ASTM Adjunct:
evaluating whether a given building or building system will be
Discount Factor Tables - Adjunct to E917 Practice for
economically efficient, that is, whether its time-adjusted ben-
Measuring Life-Cycle Costs of Buildings and Building
efits will exceed its time-adjusted costs over the period of
Systems - Includes Excel and PDF Files
concern to the decision-maker. However, it has deficiencies
that limit its usefulness in choosing among projects competing
3. Terminology
for a limited budget.
3.1 Definitions—For definitions of general terms related to
5.2 The AIRR method is a measure of the overall rate of
building construction used in this practice, refer to Terminol-
return that an investor can expect from an investment over a
ogyE631;andforgeneraltermsrelatedtobuildingeconomics,
designated study period. It is appropriate both for evaluating
refer to Terminology E833.
whether a given building or building system will be economi-
cally efficient and for choosing among alternatives competing
4. Summary of Practice
for a limited budget.
4.1 This practice is organized as follows:
5.2.1 TheAIRRmethodovercomessome,butnotall,ofthe
4.1.1 Section 1, Scope—Identifies coverage.
deficiencies of the IRR. The AIRR is particularly recom-
4.1.2 Section 2, Applicable Documents—Lists ASTM stan-
mended over the IRR for allocating limited funding among
dards that are referenced.
competing projects.
4.1.3 Section 3, Terminology—Addresses definitions of
terms. 6. Procedure
4.1.4 Section 4, Summary of Practice—Outlines the con-
6.1 The recommended steps for applying the IRR or the
tents.
AIRR method to an investment decision are summarized as
4.1.5 Section 5, Significance and Use—Explains the rel-
follows:
evance of the IRR and AIRR and indicates their appropriate
6.1.1 Identify objectives, constraints, and alternatives.
uses.
6.1.2 Compile data and establish assumptions.
4.1.6 Section 6, Procedure—Summarizes the steps in IRR
6.1.3 Compute IRR orAIRR based on a comparison of two
and AIRR analysis.
alternatives (one of which may be to do nothing).
4.1.7 Section 7, Objectives, Constraints, and Alternatives—
6.1.4 Compare the computed IRR or AIRR against the
Discusses the first step in an analysis, that is, the identification
MARR to determine the acceptability of the alternative with
of the objectives of the analysis, any constraints that must be
the higher investment cost.
taken into account in finding a solution, and technically
6.1.5 Ifalimitedbudgetistobeallocatedamongcompeting
feasible project alternatives.
alternatives, select alternatives in descending order of their
4.1.8 Section 8, Data and Assumptions—Discusses the sec-
IRR or AIRR measures until the budget is exhausted.
ondstepinananalysis;thatisthedataandassumptionsthatare
6.1.6 Report the results.
typically required for calculating the IRR and AIRR, and, in
particular, the requirement of the AIRR for specification of a
7. Objectives, Constraints, and Alternatives
reinvestment rate.
7.1 Specify clearly the objective of the economic analysis.
7.1.1 Suppose, for example, an individual or organization
hasfundsonhandtoinvestinrealestateprojects.Theproblem
Available from ASTM International Headquarters. Order Adjunct No.
ADJE091717-EA. Original adjunct produced in 1984.Adjunct last revised in 2003. is which projects to choose from potential candidates. The
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E1057 − 15 (2020)
N
objectiveoftheeconomicanalysisinthiscaseistoidentifythe
t
¯
PVNB 5 ~B 2 C !/ 11i* 50 (1)
~ !
( t t
project or set of projects within the budget that is expected to
t50
maximize profits over the long run.
where:
7.2 Identify any constraints that narrow the field of candi-
PVNB = present value of net benefits (or, if applied to a
dates.
cost-reducing investment, present value of net
7.2.1 Constraints, for example, might include a budget of
savings (PVNS)),
$1000000; a geographical limitation to buildings located
N = number of discounting periods in the study period,
within 100 km from downtown; and a strong preference for
B = dollar value of benefits in period t for the building
t
nonresidential property.
or system evaluated less the counterpart benefits in
period t for the mutually exclusive alternative
7.3 Identify feasible alternatives.
against which it is compared,
7.3.1 Feasible alternatives include an office building in the
¯
C = dollar costs, including investment costs, in period t
suburbs costing $1000000; convenience shopping strips in t
for the building or system evaluated less the
nearby towns costing a total of $900000; two medical/dental
counterpart costs in period t for the mutually
offices costing $500000 each; and a $1000000 investment
exclusive alternative against which it is compared,
share in a downtown shopping complex.
and
i* = interest rate for which PVNB=0, that is, the IRR
8. Data and Assumption
measure expressed as a decimal.
8.1 To calculate the IRR or AIRR, data are needed.
9.2 An algebraic solution of i* is not possible with Eq 1 for
8.2 Benefit and cost data that are often relevant when
allvaluesofN.Useacomputerprogramwithbuilt-informulas
calculating the IRR or AIRR are revenues, resale or salvage
to calculate IRR and AIRR. Or, use a manual approach to
value, subsidies (for example, grants), and costs of planning,
approximate the IRR such as the trial-and-error approach, the
design,engineering,construction,purchase,installation,opera-
graphical approach, and an approach that uses simple payback
tion and maintenance, utilities, and repairs and replacement.
and uniform present value (UPV) factor tables. (See Practice
E1121 for a description of payback and the Adjunct on
8.3 The time of occurrence of each benefit and cost is also
Discount Factor Tables for UPV factors.)
needed.
9.2.1 Trial and Error Solution:
8.4 Taxes such as tax credits, property taxes, and income
9.2.1.1 The trial-and-error approach to calculating the IRR
taxes are also often relevant because they affect benefits and
entails choosing a trial rate of interest that is expected
costs. If benefits and costs are adjusted for taxes, the IRR or
approximately to balance benefits and costs over the project
AIRR measure gives the after-taxrate of return.
studyperiod.Thenpresentvaluecalculationsaremadeforthat
8.5 If the terms of financing are unique to each alternative,
trial rate. (For an illustration of discounting calculations, see
financingcosts(andassociatedtaxeffects)shouldalsobetaken
Practice E917.) If the PVNB is zero, then the trial rate is the
into account.
solution value of the internal rate of return. If the PVNB is
negative,thetrialrateistoohigh,andasecond,lowertrialrate
8.6 Choose a minimum acceptable rate of return (MARR)
is then used. If the PVNB is positive for the original trial rate,
for comparison against the calculated IRR or AIRR.
then the IRR is higher than the trial rate, and a second, higher
8.6.1 TheappropriateMARRindicatestheinvestor’soppor-
trial rate is used. When two trial rates are found such that one
tunity cost of foregoing the return on the next best investment
yields a PVNB greater than zero and the other a PVNB less
opportunity in order to invest in the project in question.
than zero, the IRR lies between those rates and can be
8.7 If the AIRR is used, a reinvestment rate is needed.
approximated by interpolation, provided the investment has a
8.7.1 The reinvestment rate is usually set equal to the
unique IRR. Considerable time is saved in the trial-and-error
MARR; hence, it equals the discount rate. This is because the
approach if the first trial rate is close to the true rate. One
reinvestmentrateisanindicatoroffutureopportunitycost,and
approach is to start with the MARR as the trial rate. If the
that is also the purpose of the discount rate. Setting the
PVNB is negative with the MARR, then the project is not
reinvestment rate and the discount rate equal makes the
economically feasible, and no further calculations are neces-
reinvestment rate assumption in the AIRR method consistent
sary.IfthePVNBispositive,thenselecthighertrialratesinan
withthereinvestmentrateassumptionthatisimplicitinthenet
attempt to bound the true rate.
benefits (net savings) method (Practice E1074).
9.2.1.2 The UPV factor tables are useful in finding a trial
rate. The first step is to sum the undiscounted cash flows (not
9. IRR Calculation
including the initial cost) and divide the sum by the number of
9.1 The IRR is the compound rate of interest that, when years in the study period (excluding any planning/design/
used to discount a project’s cash flows,
...
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