# ASTM E1057-15

Designation: E1057 − 15Standard Practice forMeasuring Internal Rate of Return and Adjusted InternalRate of Return for Investments in Buildings and BuildingSystems1This standard is issued under the fixed designation E1057; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (´) indicates an editorial change since the last revision or reapproval.INTRODUCTIONThe internal rate-of-return (IRR) and adjusted internal rate-of-return (AIRR) methods are membersof a family of economic evaluation methods that provide measures of economic performance of aninvestment over time. Other methods in this family of evaluation methods are life-cycle cost analysis,net benefits and net savings analysis, benefit-to-cost and savings-to-investment ratio analysis, andpayback analysis.The IRR and AIRR methods are the topic of a single standard practice because they both measureeconomic performance as a compound yield on investment. The IRR is the compound rate of interestthat, when applied as a discount rate to a project’s stream of dollar benefits and costs, will equate them.The AIRR is the overall yield taking into account earnings on receipts reinvested to the end of thestudy period. The IRR or AIRR is compared against the investor’s minimum acceptable rate of return(MARR), and the investment is considered economically attractive if the calculated yield exceeds theMARR. 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 timeperiods, the two will normally be different. This arises because the AIRR includes in its measure thereturn on reinvestment of receipts, whereas the IRR does not.The AIRR is recommended for most applications in which a measure of yield is desired. Cautionis recommended in applying either measure, however, because problems arise under certainconditions.1. Scope1.1 This practice covers a procedure for calculating andinterpreting the internal rate of return (IRR) and adjustedinternal rate of return (AIRR) measures in the evaluation ofbuilding designs, systems, and equipment.1.2 The values stated in inch-pound units are to be regardedas standard. The values given in parentheses are mathematicalconversions to SI units that are provided for information onlyand are not considered standard.1.3 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2E631 Terminology of Building ConstructionsE833 Terminology of Building EconomicsE917 Practice for Measuring Life-Cycle Costs of Buildingsand Building SystemsE964 Practice for Measuring Benefit-to-Cost and Savings-to-Investment Ratios for Buildings and Building SystemsE1074 Practice for Measuring Net Benefits and Net Savingsfor Investments in Buildings and Building SystemsE1121 Practice for Measuring Payback for Investments inBuildings and Building Systems1This practice is under the jurisdiction of ASTM Committee E06 on Perfor-mance of Buildings and is the direct responsibility of Subcommittee E06.81 onBuilding Economics.Current edition approved May 1, 2015. Published June 2015. Originallyapproved in 1985. Last previous edition approved in 2010 as E1057 – 06 (2010).DOI: 10.1520/E1057-15.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at service@astm.org. For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1E1185 Guide for Selecting Economic Methods for Evaluat-ing Investments in Buildings and Building SystemsE1369 Guide for Selecting Techniques for Treating Uncer-tainty and Risk in the Economic Evaluation of Buildingsand Building SystemsE1765 Practice for Applying Analytical Hierarchy Process(AHP) to Multiattribute Decision Analysis of InvestmentsRelated to Buildings and Building SystemsE1946 Practice for Measuring Cost Risk of Buildings andBuilding Systems and Other Constructed ProjectsE2204 Guide for Summarizing the Economic Impacts ofBuilding-Related Projects2.2 ASTM Adjuncts:3Discount Factor Tables, Adjunct to Practices E917, E964,E1057, E1074, and E11213. Terminology3.1 Definitions—For definitions of general terms related tobuilding construction used in this practice, refer to Terminol-ogy E631; and for general terms related to building economics,refer to Terminology E833.4. Summary of Practice4.1 This practice is organized as follows:4.1.1 Section 1, Scope—Identifies coverage.4.1.2 Section 2, Applicable Documents—Lists ASTM stan-dards that are referenced.4.1.3 Section 3, Terminology—Addresses definitions ofterms.4.1.4 Section 4, Summary of Practice—Outlines the con-tents.4.1.5 Section 5, Significance and Use—Explains the rel-evance of the IRR and AIRR and indicates their appropriateuses.4.1.6 Section 6, Procedure—Summarizes the steps in IRRand AIRR analysis.4.1.7 Section 7, Objectives, Constraints, and Alternatives—Discusses the first step in an analysis, that is, the identificationof the objectives of the analysis, any constraints that must betaken into account in finding a solution, and technicallyfeasible project alternatives.4.1.8 Section 8, Data and Assumptions—Discusses the sec-ond step in an analysis; that is the data and assumptions that aretypically required for calculating the IRR and AIRR, and, inparticular, the requirement of the AIRR for specification of areinvestment rate.4.1.9 Section 9, IRR Calculation—Describes the third step,performing calculations, as it applies to the IRR.4.1.10 Section 10, AIRR Calculation—Describes the thirdstep, performing calculations, as it applies to the AIRR.4.1.11 Section 11, Choosing Between the IRR and AIRR—Discusses how to choose between the IRR and the AIRR.4.1.12 Section 12, Limitations—Discusses limitations andshortcomings of the IRR and AIRR.4.1.13 Section 13, Analysis of IRR or AIRR Results and theDecision—Discusses the decision criterion and the treatment ofuncertainty, risk, and unqualified effects.4.1.14 Section 14, Applications—Describes the types ofdecisions to which the IRR and AIRR are applicable.4.1.15 Section 15, Report—Identifies information that shallbe included in a report of an IRR or AIRR application.5. Significance and Use5.1 The IRR method has been used traditionally in financeand economics to measure the percentage yield on investment.5.1.1 The IRR method is appropriate in most cases forevaluating whether a given building or building system will beeconomically efficient, that is, whether its time-adjusted ben-efits will exceed its time-adjusted costs over the period ofconcern to the decision maker. However, it has deficiencies thatlimit its usefulness in choosing among projects competing fora limited budget.5.2 The AIRR method is a measure of the overall rate ofreturn that an investor can expect from an investment over adesignated study period. It is appropriate both for evaluatingwhether a given building or building system will be economi-cally efficient and for choosing among alternatives competingfor a limited budget.5.2.1 TheAIRR method overcomes some, but not all, of thedeficiencies of the IRR. The AIRR is particularly recom-mended over the IRR for allocating limited funding amongcompeting projects.6. Procedure6.1 The recommended steps for applying the IRR or theAIRR method to an investment decision are summarized asfollows:6.1.1 Identify objectives, constraints, and alternatives.6.1.2 Compile data and establish assumptions.6.1.3 Compute IRR or AIRR based on a comparison of twoalternatives (one of which may be to do nothing).6.1.4 Compare the computed IRR or AIRR against theMARR to determine the acceptability of the alternative withthe higher investment cost.6.1.5 If a limited budget is to be allocated among competingalternatives, select alternatives in descending order of theirIRR or AIRR measures until the budget is exhausted.6.1.6 Report the results.7. Objectives, Constraints, and Alternatives7.1 Specify clearly the objective of the economic analysis.7.1.1 Suppose, for example, an individual or organizationhas funds on hand to invest in real estate projects. The problemis which projects to choose from potential candidates. Theobjective of the economic analysis in this case is to identify theproject or set of projects within the budget that is expected tomaximize profits over the long run.7.2 Identify any constraints that narrow the field of candi-dates.7.2.1 Constraints, for example, might include a budget of$1 000 000; a geographical limitation to buildings located3Available from ASTM International Headquarters. Order Adjunct No.ADJE091703.E1057 − 152within 100 km from downtown; and a strong preference fornonresidential property.7.3 Identify feasible alternatives.7.3.1 Feasible alternatives include an office building in thesuburbs costing $1 000 000; convenience shopping strips innearby towns costing a total of $900 000; two medical/dentaloffices costing $500 000 each; and a $1 000 000 investmentshare in a downtown shopping complex.8. Data and Assumption8.1 To calculate the IRR or AIRR, data are needed.8.2 Benefit and cost data that are often relevant whencalculating the IRR or AIRR are revenues, resale or salvagevalue, subsidies (for example, grants), and costs of planning,design, engineering, construction, purchase, installation, opera-tion and maintenance, utilities, and repairs and replacement.8.3 The time of occurrence of each benefit and cost is alsoneeded.8.4 Taxes such as tax credits, property taxes, and incometaxes are also often relevant because they affect benefits andcosts. If benefits and costs are adjusted for taxes, the IRR orAIRR measure gives the after-tax rate of return.8.5 If the terms of financing are unique to each alternative,financing costs (and associated tax effects) should also be takeninto account.8.6 Choose a minimum acceptable rate of return (MARR)for comparison against the calculated IRR or AIRR.8.6.1 The appropriate MARR indicates the investor’s op-portunity cost of foregoing the return on the next best invest-ment opportunity in order to invest in the project in question.8.7 If the AIRR is used, a reinvestment rate is needed.8.7.1 The reinvestment rate is usually set equal to theMARR; hence, it equals the discount rate. This is because thereinvestment rate is an indicator of future opportunity cost, andthat is also the purpose of the discount rate. Setting thereinvestment rate and the discount rate equal makes thereinvestment rate assumption in the AIRR method consistentwith the reinvestment rate assumption that is implicit in the netbenefits (net savings) method (Practice E1074).9. IRR Calculation9.1 The IRR is the compound rate of interest that, whenused to discount a project’s cash flows, will reduce the presentvalue of net benefits (PVNB) to zero. (See Practice E1074 fora discussion of how to compute the PVNB.) The solution valueof i*inEq 1 is the IRR. It is computed as a decimal, thenexpressed as a percent.9.1.1 Find the value of i* for which:PVNB 5(t50N~Bt2 C¯t!/~11i*!t5 0 (1)where:PVNB = present value of net benefits (or, if applied to acost-reducing investment, present value of netsavings (PVNS)),N = number of discounting periods in the study period,Bt= dollar value of benefits in period t for the buildingor system evaluated less the counterpart benefits inperiod t for the mutually exclusive alternativeagainst which it is compared,C¯t= dollar costs, including investment costs, in period tfor the building or system evaluated less thecounterpart costs in period t for the mutuallyexclusive alternative against which it is compared,andi* = interest rate for which PVNB = 0, that is, the IRRmeasure expressed as a decimal.9.2 An algebraic solution of i* is not possible with Eq 1 forall values of N. Use a computer program with built-in formulasto calculate IRR and AIRR. Or, use a manual approach toapproximate the IRR such as the trial-and-error approach, thegraphical approach, and an approach that uses simple paybackand uniform present value (UPV) factor tables. (See PracticeE1121 for a description of payback and the Adjunct onDiscount Factor Tables for UPV factors.)9.2.1 Trial and Error Solution:9.2.1.1 The trial-and-error approach to calculating the IRRentails choosing a trial rate of interest that is expectedapproximately to balance benefits and costs over the projectstudy period. Then present value calculations are made for thattrial rate. (For an illustration of discounting calculations, seePractice E917.) If the PVNB is zero, then the trial rate is thesolution value of the internal rate of return. If the PVNB isnegative, the trial rate is too high, and a second, lower trial rateis then used. If the PVNB is positive for the original trial rate,then the IRR is higher than the trial rate, and a second, highertrial rate is used. When two trial rates are found such that oneyields a PVNB greater than zero and the other a PVNB lessthan zero, the IRR lies between those rates and can beapproximated by interpolation, provided the investment has aunique IRR. Considerable time is saved in the trial-and-errorapproach if the first trial rate is close to the true rate. Oneapproach is to start with the MARR as the trial rate. If thePVNB is negative with the MARR, then the project is noteconomically feasible, and no further calculations are neces-sary. If the PVNB is positive, then select higher trial rates in anattempt to bound the true rate.9.2.1.2 The UPV factor tables are useful in finding a trialrate. The first step is to sum the undiscounted cash flows (notincluding the initial cost) and divide the sum by the number ofyears in the study period (excluding any planning/design/construction period) to obtain an average annual cash flow.Then divide the initial project cost by the average to obtain arough estimate of simple payback (SPB). The second step is tosearch the UPV discount factor tables in the row that corre-sponds to the study period for the UPV factor that is closest tothe estimated SPB. (Again exclude any years in the planning/design/construction period.) The rate that appears at the top ofthe column in which the UPV factor is found is a promisingtrial rate. The more uniform the annual cash flow, the morelikely that this trial rate will be close to the solution rate.9.2.1.3 Table 1 illustrates the trial-and-error approach forcalculating the IRR for an initial investment that yields anuneven yearly cash flow over four years. Columns 2 and 3 listE1057 − 153the dollar v