# ASTM E1369-15

Designation: E1369 − 15Standard Guide forSelecting Techniques for Treating Uncertainty and Risk inthe Economic Evaluation of Buildings and BuildingSystems1This standard is issued under the fixed designation E1369; 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.1. Scope1.1 This guide covers techniques for treating uncertainty ininput values to an economic analysis of a building investmentproject. It also recommends techniques for evaluating the riskthat a project will have a less favorable economic outcome thanwhat is desired or expected.21.2 The techniques include breakeven analysis, sensitivityanalysis, risk-adjusted discounting, the mean-variance criterionand coefficient of variation, decision analysis, simulation, andstochastic dominance.1.3 The techniques can be used with economic methods thatmeasure economic performance, such as life-cycle costanalysis, net benefits, the benefit-to-cost ratio, internal rate ofreturn, and payback.2. Referenced Documents2.1 ASTM Standards:3E631 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 SystemsE1057 Practice for Measuring Internal Rate of Return andAdjusted Internal Rate of Return for Investments inBuildings 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 SystemsE1185 Guide for Selecting Economic Methods for Evaluat-ing Investments in 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 Adjuncts:Discount Factor Tables Adjunct to Practices E917, E964,E1057, E1074, and E112143. Terminology3.1 Definitions—For definitions of general terms related tobuilding construction used in this guide, refer to TerminologyE631; and for general terms related to building economics,refer to Terminology E833.4. Summary of Guide4.1 This guide identifies related ASTM standards and ad-juncts. It describes circumstances when measuring uncertaintyand risk may be helpful in economic evaluations of buildinginvestments. This guide defines uncertainty, risk exposure, andrisk attitude. It presents nonprobabilistic and probabilistictechniques for measuring uncertainty and risk exposure. Thisguide describes briefly each technique, gives the formula forcalculating a measure where appropriate, illustrates the tech-niques with a case example, and summarizes its advantagesand disadvantages.4.2 Since there is no best technique for measuring uncer-tainty and risk in every economic evaluation, this guideconcludes with a discussion of how to select the appropriatetechnique for a particular problem.4.3 This guide describes in detail how risk exposure can bemeasured by probability functions and distribution functions1This guide is under the jurisdiction of ASTM Committee E06 on Performanceof Buildings and is the direct responsibility of Subcommittee E06.81 on BuildingEconomics.Current edition approved Oct. 1, 2015. Published October 2015. Originallyapproved in 1990. Last previous edition approved in 2011 as E1369 – 11. DOI:10.1520/E1369-15.2For an extensive overview of techniques for treating risk and uncertainty, seeMarshall, H.E., Techniques for Treating Uncertainty and Risk in the EconomicEvaluation of Building Investments, National Institute of Standards and Technology,Special Publication 757, 1988.3For 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.4Available from ASTM International Headquarters. Order Adjunct No.ADJE091703. Original adjunct produced in 1984.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1(see Annex A1). It also describes how risk attitude can beincorporated using utility theory and other approaches (seeAnnex A2).5. Significance and Use5.1 Investments in long-lived projects such as buildings arecharacterized by uncertainties regarding project life, operationand maintenance costs, revenues, and other factors that affectproject economics. Since future values of these variable factorsare generally not known, it is difficult to make reliableeconomic evaluations.5.2 The traditional approach to project investment analysishas been to apply economic methods of project evaluation tobest-guess estimates of project input variables as if they werecertain estimates and then to present results in single-value,deterministic terms. When projects are evaluated withoutregard to uncertainty of inputs to the analysis, decision makersmay have insufficient information to measure and evaluate therisk of investing in a project having a different outcome fromwhat is expected.5.3 Risk analysis is the body of theory and practice that hasevolved to help decision makers assess their risk exposures andrisk attitudes so that the investment that is the best bet for themcan be selected.NOTE 1—The decision maker is the individual or group of individualsresponsible for the investment decision. For example, the decision makermay be the chief executive officer or the board of directors.5.4 Uncertainty and risk are defined as follows. Uncertainty(or certainty) refers to a state of knowledge about the variableinputs to an economic analysis. If the decision maker is unsureof input values, there is uncertainty. If the decision maker issure, there is certainty. Risk refers either to risk exposure orrisk attitude.5.4.1 Risk exposure is the probability of investing in aproject that will have a less favorable economic outcome thanwhat is desired (the target) or is expected.5.4.2 Risk attitude, also called risk preference, is the will-ingness of a decision maker to take a chance or gamble on aninvestment of uncertain outcome. The implications of decisionmakers having different risk attitudes is that a given investmentof known risk exposure might be economically acceptable toan investor who is not particularly risk averse, but totallyunacceptable to another investor who is very risk averse.NOTE 2—For completeness, this guide covers both risk averse and risktaking attitudes. Most investors, however, are likely to be risk averse. Theprinciples described herein apply both to the typical case where investorshave different degrees of risk aversion and to the atypical case where someinvestors are risk taking while others are risk averse.5.5 No single technique can be labeled the best technique inevery situation for treating uncertainty, risk, or both. What isbest depends on the following: availability of data, availabilityof resources (time, money, expertise), computational aids (forexample, computer services), user understanding, ability tomeasure risk exposure and risk attitude, risk attitude ofdecision makers, level of risk exposure of the project, and sizeof the investment relative to the institution’s portfolio.6. Procedures6.1 The recommended steps for carrying out an evaluationof uncertainty or risk are as follows:6.1.1 Determine appropriate economic measure(s) forevaluating the investment (see Guide E1185).6.1.2 Identify objectives, alternatives, and constraints (seePractices E917, E964, E1057, E1074, and E1121).6.1.3 Decide whether an uncertainty and risk evaluation isneeded, and, if so, choose the appropriate technique (seeSections 5, 7, 8, and 10).6.1.4 Compile data and establish assumptions for the evalu-ation.6.1.5 Determine risk attitude of the decision maker (seeSection 7 and Annex A2).6.1.6 Compute measures of worth5and associated risk (seeSections 7 and 8).6.1.7 Analyze results and make a decision (see Section 9).6.1.8 Document the evaluation (see Section 11).7. Techniques: Advantages and Disadvantages7.1 This guide considers in detail three nonprobabilistictechniques (breakeven analysis, sensitivity analysis, and risk-adjusted discounting) and four probabilistic techniques (mean-variance criterion and coefficient of variation, decisionanalysis, simulation, and stochastic dominance) for treatinguncertainty and risk. This guide also summarizes severaladditional techniques that are used less frequently.7.2 Breakeven Analysis:7.2.1 When an uncertain variable is critical to the economicsuccess of a project, decision makers frequently want to knowthe minimum or maximum value that variable can reach andstill have a breakeven project; that is, a project where benefits(savings) equal costs. For example, the breakeven value of aninput cost variable is the maximum amount one can afford topay for the input and still break even compared to benefitsearned. A breakeven value of an input benefit variable is theminimum amount the project can produce in that benefitcategory and still cover the projected costs of the project.NOTE 3—Benefits and costs are treated throughout this guide on adiscounted cash-flow basis, taking into account taxes where appropriate.(See Practice E917 for an explanation of discounted cash flows consid-ering taxes.)7.2.2 To perform a breakeven analysis, an equation isconstructed wherein the benefits are set equal to the costs for agiven investment project, the values of all inputs except thebreakeven variable are specified, and the breakeven variable issolved algebraically.7.2.3 Suppose a decision maker is deciding whether or notto invest in a piece of energy conserving equipment for agovernment-owned building. The deviation of the formula forcomputing breakeven investment costs for the equipment is asfollows:5The NIST Building Life-Cycle Cost (BLCC) Computer Program helps userscalculate measures of worth for buildings and building components that areconsistent with ASTM standards. The program is downloadable from http://energy.gov/eere/femp/building-life-cycle-cost-programs.E1369 − 152S 5 C (1)C 5 I1O or acombination might include optimistic values for some vari-ables in conjunction with pessimistic or expected values forothers. Examining different combinations is required if theuncertain variables are interrelated.7.3.3 The following illustration of sensitivity analysis treatsan accept/reject decision. Consider a decision on whether ornot to install a programmable time clock to control heating,ventilating, and air conditioning (HVAC) equipment in abuilding. The time clock reduces electricity consumption byturning off that part of the HVAC equipment that is not neededduring hours when the building is unoccupied. Using thebenefit-to-cost ratio (BCR) as the economic method, the timeclock is acceptable on economic grounds if its BCR is greaterthan 1.0. The energy reduction benefits from the time clock,however, are uncertain.They are a function of three factors: theinitial price of energy, the rate of change in energy prices overthe life cycle of the time clock, and the number of kilowatthours saved. Assume that the initial price of energy and thenumber of kilowatt-hours saved are relatively certain, and thatthe sensitivity of the BCR is being tested with respect to thefollowing three values of energy price change: a low rate ofenergy price escalation (slowly increasing benefits from energysavings); a moderate rate of escalation (moderately increasingbenefits); and a high rate of escalation (rapidly increasingbenefits). These three assumed values of energy price changemight correspond to our projections of pessimistic, expected,and optimistic values. Three BCR estimates result from repeat-ing the BCR computation for each of the three energy priceescalation rates. For example, BCRs of 0.8, 2.0, and 4.0 mightresult. Whereas a deterministic approach might have generateda BCR estimate of 2.0, now it is apparent that the BCR couldbe significantly less than 2.0, and even less than 1.0. Thusaccepting the time clock could lead to an inefficient outcome.7.3.4 There are several advantages of sensitivity analysis.First, it shows how significant a single input variable is indetermining project outcomes. Second, it recognizes the un-certainty associated with the input. Third, it gives informationabout the range of output variability. And fourth, it does all ofthese when there is little information, resources, or time to usemore sophisticated techniques.7.3.5 Disadvantages of sensitivity analysis in evaluatingrisk are that it gives no explicit probabilistic measure of riskexposure and it includes no explicit treatment of risk attitude.The findings of sensitivity analysis are ambiguous. How likelyis a pessimistic or expected or optimistic value, for example,and how likely is the corresponding outcome value? Sensitivityanalysis can in fact be misleading if all pessimistic assumptionsor all optimistic assumptions are combined in calculatingeconomic measures. Such combinations of inputs are unlikelyin the real world.7.3.6 Sensitivity results can be presented in text, tables, orgraphs. One type of graph that is useful in showing thesensitivity of project worth to a critical variable is illustrated inFig. 1. Net benefits (NB) for Projects A and B decrease as thediscount rate increases. The slopes of the functions show thatNB is more sensitive to discount rate changes for Project Athan for Project B, assuming other variables remain unchanged.These functions also help in making comparisons as to whichproject is more cost effective.At a discount rate below 7 %, forE1369 − 153example, Project A has the greater NB. At a rate above 7 %,Project B yields the greater NB. And at 7 %, the two projectsprovide identical NB.7.3.7 Note that the functions indicate the potential values ofNB if different values of the discount rate occur. If decisionmakers have some idea as to the likelihood of specific discountrates, the graph will help them evaluate the NB implications forthese two projects. The sensitivity graph in this sense contrib-utes to an implicit description of risk exposure. Yet the graphfails to provide a quantitative measure of the probability of anygiven NB occurring.7.3.8 Another special graph for sensitivity analysis thatpresents a snapshot of potential impacts of uncertain inputvariables on project outcomes is the spider diagram. The oneillustrated in Fig. 2 shows for a prospective commercialbuilding investment the sensitivity of the adjusted internal rateof return (AIRR) to three variables: operation, maintenance,and replacement costs (OM project life (PL); and thereinvestment rate (RR). Each variable is represented by alabeled