ASTM E1369-15(2020)e1

Standard Guide for Selecting Techniques for Treating Uncertainty and Risk in the Economic Evaluation of Buildings and Building Systems

SIGNIFICANCE AND USE
5.1 Investments in long-lived projects such as buildings are characterized by uncertainties regarding project life, operation and maintenance costs, revenues, and other factors that affect project economics. Since future values of these variable factors are generally not known, it is difficult to make reliable economic evaluations.  
5.2 The traditional approach to project investment analysis has been to apply economic methods of project evaluation to best-guess estimates of project input variables as if they were certain estimates and then to present results in single-value, deterministic terms. When projects are evaluated without regard to uncertainty of inputs to the analysis, decision-makers may have insufficient information to measure and evaluate the risk of investing in a project having a different outcome from what is expected.  
5.3 Risk analysis is the body of theory and practice that has evolved to help decision-makers assess their risk exposures and risk attitudes so that the investment that is the best bet for them can be selected.
Note 1: The decision-maker is the individual or group of individuals responsible for the investment decision. For example, the decision-maker may 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 variable inputs to an economic analysis. If the decision-maker is unsure of input values, there is uncertainty. If the decision-maker is sure, there is certainty. Risk refers either to risk exposure or risk attitude.  
5.4.1 Risk exposure is the probability of investing in a project that will have a less favorable economic outcome than what is desired (the target) or is expected.  
5.4.2 Risk attitude, also called risk preference, is the willingness of a decision-maker to take a chance or gamble on an investment of uncertain outcome. The implications of decision-makers having different risk attitudes i...
SCOPE
1.1 This guide covers techniques for treating uncertainty in input values to an economic analysis of a building investment project. It also recommends techniques for evaluating the risk that a project will have a less favorable economic outcome than what is desired or expected.2  
1.2 The techniques include breakeven analysis, sensitivity analysis, risk-adjusted discounting, the mean-variance criterion and coefficient of variation, decision analysis, simulation, and stochastic dominance.  
1.3 The techniques can be used with economic methods that measure economic performance, such as life-cycle cost analysis, net benefits, the benefit-to-cost ratio, internal rate of return, and payback.  
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

• Status: Published
• Publication Date: 31-Mar-2020
• ICS: 91.010.20 - Contractual aspects
• Technical Committee: E06 - Performance of Buildings
• Drafting Committee: E06.81 - Building Economics

Relations

• Replaces: ASTM E1369-15 - Standard Guide for Selecting Techniques for Treating Uncertainty and Risk in the Economic Evaluation of Buildings and Building Systems
• Effective Date: 01-Apr-2020
• Refers: ASTM E1057-15(2020)e1 - Standard Practice for Measuring Internal Rate of Return and Adjusted Internal Rate of Return for Investments in Buildings and Building Systems
• Effective Date: 01-Apr-2020
• Refers: ASTM E1074-15(2020)e1 - Standard Practice for Measuring Net Benefits and Net Savings for Investments in Buildings and Building Systems
• Effective Date: 01-Apr-2020
• Refers: ASTM E964-15(2020)e1 - Standard Practice for Measuring Benefit-to-Cost and Savings-to-Investment Ratios for Buildings and Building Systems
• Effective Date: 01-Apr-2020
• Refers: ASTM E1121-15(2020)e1 - Standard Practice for Measuring Payback for Investments in Buildings and Building Systems
• Effective Date: 01-Apr-2020
• Refers: ASTM E1185-15(2020)e1 - Standard Guide for Selecting Economic Methods for Evaluating Investments in Buildings and Building Systems
• Effective Date: 01-Apr-2020
• Refers: ASTM E917-17 - Standard Practice for Measuring Life-Cycle Costs of Buildings and Building Systems
• Effective Date: 01-Sep-2017
• Refers: ASTM E1121-15 - Standard Practice for Measuring Payback for Investments in Buildings and Building Systems
• Effective Date: 01-Oct-2015
• Refers: ASTM E1185-15 - Standard Guide for Selecting Economic Methods for Evaluating Investments in Buildings and Building Systems
• Effective Date: 01-Oct-2015
• Refers: ASTM E917-15 - Standard Practice for Measuring Life-Cycle Costs of Buildings and Building Systems
• Effective Date: 01-Oct-2015
• Refers: ASTM E2204-15 - Standard Guide for Summarizing the Economic Impacts of Building-Related Projects
• Effective Date: 01-Aug-2015
• Refers: ASTM E1057-15 - Standard Practice for Measuring Internal Rate of Return and Adjusted Internal Rate of Return for Investments in Buildings and Building Systems
• Effective Date: 01-May-2015
• Refers: ASTM E1074-15 - Standard Practice for Measuring Net Benefits and Net Savings for Investments in Buildings and Building Systems
• Effective Date: 01-May-2015
• Refers: ASTM E964-15 - Standard Practice for Measuring Benefit-to-Cost and Savings-to-Investment Ratios for Buildings and Building Systems
• Effective Date: 01-May-2015
• Refers: ASTM E631-15 - Standard Terminology of Building Constructions
• Effective Date: 01-Mar-2015

Overview

ASTM E1369-15(2020)e1 is a comprehensive standard guide developed by ASTM International to assist decision-makers in treating uncertainty and risk during the economic evaluation of buildings and building systems. Investments in buildings and construction projects carry significant risks due to uncertainties in project lifespan, operational and maintenance costs, revenues, and other economic factors. This standard equips professionals with recommended techniques to analyze and manage uncertainty, enabling more reliable and informed investment decisions.

By leveraging ASTM E1369-15(2020)e1, organizations can systematically assess the potential for less favorable outcomes and factor in the varying risk attitudes of stakeholders. The standard supports the application of both nonprobabilistic and probabilistic techniques, improving the robustness of life-cycle cost analysis and other economic performance measures.

Key Topics

• Investment Uncertainty in Buildings: Recognition that future values of input variables such as costs and revenues are generally unknown, leading to challenges in reliable economic evaluations.

• Risk and Uncertainty Management: Differentiation between uncertainty (knowledge state regarding variable inputs) and risk (probability of less favorable economic outcomes or risk attitudes of decision-makers).

• Techniques for Risk Analysis:

  • Breakeven Analysis: Identifies critical points where benefits equal costs.
  • Sensitivity Analysis: Evaluates how changes in input variables affect economic outcomes.
  • Risk-Adjusted Discounting: Adjusts discount rates to factor in risk exposure and risk attitudes.
  • Mean-Variance Criterion & Coefficient of Variation: Compares project alternatives based on expected values and variability.
  • Decision Analysis: Utilizes decision trees and probabilistic assessments to evaluate alternative scenarios and maximize expected value.
  • Simulation and Stochastic Dominance: Advanced statistical approaches for risk evaluation in complex projects.

• Selection of Appropriate Techniques: Guidance on selecting the most suitable technique based on data availability, resources, expertise, risk attitude, and project scale.

• Integration with Economic Methods: Recommended use of these techniques alongside established economic performance metrics such as life-cycle cost analysis, net benefits, benefit-to-cost ratio, internal rate of return, and payback period.

Applications

ASTM E1369-15(2020)e1 serves as a vital resource for:

• Facility Managers and Asset Owners: Supporting investment decisions for new constructions, renovations, or retrofits by accounting for the full range of possible outcomes and risk exposures.
• Engineers, Economists, and Financial Analysts: Systematically applying risk analysis tools to improve the accuracy and transparency of economic evaluations.
• Policy Makers and Project Boards: Understanding the impact of uncertainty and aligning project selections with organizational risk preferences.
• Consultants and Auditors: Recommending and documenting best practices in project evaluation, funding proposals, and feasibility studies.
• Building Lifecycle Assessment: Integrating with life-cycle costing, net benefits analysis, and payback calculations to optimize long-term investment value.

Related Standards

ASTM E1369-15(2020)e1 references and complements several other ASTM standards to create a comprehensive framework for economic evaluation and risk analysis in building projects, including:

• ASTM E917: Practice for Measuring Life-Cycle Costs of Buildings and Building Systems
• ASTM E964: Practice for Measuring Benefit-to-Cost and Savings-to-Investment Ratios for Buildings and Building Systems
• ASTM E1057: Practice for Measuring Internal Rate of Return for Investments in Buildings and Building Systems
• ASTM E1074: Practice for Measuring Net Benefits and Net Savings
• ASTM E1121: Practice for Measuring Payback for Investments in Buildings and Building Systems
• ASTM E1185: Guide for Selecting Economic Methods for Evaluating Investments in Buildings
• ASTM E1946: Practice for Measuring Cost Risk of Buildings and Building Systems
• ASTM E2204: Guide for Summarizing Economic Impacts of Building-Related Projects

By following ASTM E1369-15(2020)e1, professionals can improve decision-making, reduce financial risk, and maximize the economic performance of buildings and building systems.

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.
ϵ1
Designation: E1369 − 15 (Reapproved 2020)
Standard Guide for
Selecting Techniques for Treating Uncertainty and Risk in
the Economic Evaluation of Buildings and Building
Systems
This standard is issued under the fixed designation E1369; 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.
1. Scope E917Practice for Measuring Life-Cycle Costs of Buildings
and Building Systems
1.1 This guide covers techniques for treating uncertainty in
E964Practice for Measuring Benefit-to-Cost and Savings-
input values to an economic analysis of a building investment
to-Investment Ratios for Buildings and Building Systems
project. It also recommends techniques for evaluating the risk
E1057Practice for Measuring Internal Rate of Return and
thataprojectwillhavealessfavorableeconomicoutcomethan
2 Adjusted Internal Rate of Return for Investments in
what is desired or expected.
Buildings and Building Systems
1.2 The techniques include breakeven analysis, sensitivity
E1074Practice for Measuring Net Benefits and Net Savings
analysis,risk-adjusteddiscounting,themean-variancecriterion
for Investments in Buildings and Building Systems
and coefficient of variation, decision analysis, simulation, and
E1121Practice for Measuring Payback for Investments in
stochastic dominance.
Buildings and Building Systems
E1185Guide for Selecting Economic Methods for Evaluat-
1.3 Thetechniquescanbeusedwitheconomicmethodsthat
measure economic performance, such as life-cycle cost ing Investments in Buildings and Building Systems
E1946Practice for Measuring Cost Risk of Buildings and
analysis, net benefits, the benefit-to-cost ratio, internal rate of
return, and payback. Building Systems and Other Constructed Projects
E2204Guide for Summarizing the Economic Impacts of
1.4 This international standard was developed in accor-
Building-Related Projects
dance with internationally recognized principles on standard-
2.2 ASTM Adjunct:
ization established in the Decision on Principles for the
Discount Factor Tables - Adjunct to E917 Practice for
Development of International Standards, Guides and Recom-
Measuring Life-Cycle Costs of Buildings and Building
mendations issued by the World Trade Organization Technical
Systems - Includes Excel and PDF Files
Barriers to Trade (TBT) Committee.
3. Terminology
2. Referenced Documents
3.1 Definitions—For definitions of general terms related to
2.1 ASTM Standards:
building construction used in this guide, refer to Terminology
E631Terminology of Building Constructions
E631; and for general terms related to building economics,
E833Terminology of Building Economics
refer to Terminology E833.
4. Summary of Guide
This guide is under the jurisdiction ofASTM Committee E06 on Performance
of Buildings and is the direct responsibility of Subcommittee E06.81 on Building 4.1 This guide identifies related ASTM standards and ad-
Economics.
juncts. It describes circumstances when measuring uncertainty
Current edition approved April 1, 2020. Published May 2020. Originally
and risk may be helpful in economic evaluations of building
approved in 1990. Last previous edition approved in 2015 as E1369-15. DOI:
investments.This guide defines uncertainty, risk exposure, and
10.1520/E1369-15R20E01.
For an extensive overview of techniques for treating risk and uncertainty, see
risk attitude. It presents nonprobabilistic and probabilistic
Marshall, H. E., Techniques for Treating Uncertainty and Risk in the Economic
techniques for measuring uncertainty and risk exposure. This
Evaluation of Building Investments,NationalInstituteofStandardsandTechnology,
guide describes briefly each technique, gives the formula for
Special Publication 757, 1988.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
Standards volume information, refer to the standard’s Document Summary page on Available from ASTM International Headquarters. Order Adjunct No.
the ASTM website. ADJE091717-EA. Original adjunct produced in 1984.Adjunct last revised in 2003.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
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E1369 − 15 (2020)
havedifferentdegreesofriskaversionandtotheatypicalcasewheresome
calculating a measure where appropriate, illustrates the tech-
investors are risk taking while others are risk averse.
niques with a case example, and summarizes its advantages
and disadvantages. 5.5 Nosingletechniquecanbelabeledthebesttechniquein
every situation for treating uncertainty, risk, or both. What is
4.2 Since there is no best technique for measuring uncer-
best depends on the following: availability of data, availability
tainty and risk in every economic evaluation, this guide
of resources (time, money, expertise), computational aids (for
concludes with a discussion of how to select the appropriate
example, computer services), user understanding, ability to
technique for a particular problem.
measure risk exposure and risk attitude, risk attitude of
4.3 This guide describes in detail how risk exposure can be
decision-makers, level of risk exposure of the project, and size
measured by probability functions and distribution functions
of the investment relative to the institution’s portfolio.
(see Annex A1). It also describes how risk attitude can be
6. Procedures
incorporated using utility theory and other approaches (see
Annex A2).
6.1 The recommended steps for carrying out an evaluation
of uncertainty or risk are as follows:
5. Significance and Use
6.1.1 Determine appropriate economic measure(s) for
evaluating the investment (see Guide E1185).
5.1 Investments in long-lived projects such as buildings are
6.1.2 Identify objectives, alternatives, and constraints (see
characterized by uncertainties regarding project life, operation
Practices E917, E964, E1057, E1074, and E1121).
and maintenance costs, revenues, and other factors that affect
6.1.3 Decide whether an uncertainty and risk evaluation is
projecteconomics.Sincefuturevaluesofthesevariablefactors
needed, and, if so, choose the appropriate technique (see
are generally not known, it is difficult to make reliable
Sections 5, 7, 8, and 10).
economic evaluations.
6.1.4 Compile data and establish assumptions for the evalu-
5.2 The traditional approach to project investment analysis
ation.
has been to apply economic methods of project evaluation to
6.1.5 Determine risk attitude of the decision-maker (see
best-guess estimates of project input variables as if they were
Section 7 and Annex A2).
certain estimates and then to present results in single-value, 5
6.1.6 Compute measures of worth and associated risk (see
deterministic terms. When projects are evaluated without
Sections 7 and 8).
regardtouncertaintyofinputstotheanalysis,decision-makers
6.1.7 Analyze results and make a decision (see Section 9).
may have insufficient information to measure and evaluate the
6.1.8 Document the evaluation (see Section 11).
risk of investing in a project having a different outcome from
7. Techniques: Advantages and Disadvantages
what is expected.
7.1 This guide considers in detail three nonprobabilistic
5.3 Risk analysis is the body of theory and practice that has
techniques (breakeven analysis, sensitivity analysis, and risk-
evolvedtohelpdecision-makersassesstheirriskexposuresand
adjusted discounting) and four probabilistic techniques (mean-
riskattitudessothattheinvestmentthatisthebestbetforthem
variance criterion and coefficient of variation, decision
can be selected.
analysis, simulation, and stochastic dominance) for treating
NOTE 1—The decision-maker is the individual or group of individuals
uncertainty and risk. This guide also summarizes several
responsible for the investment decision. For example, the decision-maker
additional techniques that are used less frequently.
may be the chief executive officer or the board of directors.
7.2 Breakeven Analysis:
5.4 Uncertainty and risk are defined as follows. Uncertainty
7.2.1 When an uncertain variable is critical to the economic
(or certainty) refers to a state of knowledge about the variable
success of a project, decision-makers frequently want to know
inputstoaneconomicanalysis.Ifthedecision-makerisunsure
the minimum or maximum value that variable can reach and
of input values, there is uncertainty. If the decision-maker is
still have a breakeven project; that is, a project where benefits
sure, there is certainty. Risk refers either to risk exposure or
(savings) equal costs. For example, the breakeven value of an
risk attitude.
input costvariable is the maximum amount one can afford to
5.4.1 Risk exposure is the probability of investing in a
pay for the input and still break even compared to benefits
project that will have a less favorable economic outcome than
earned. A breakeven value of an input benefitvariable is the
what is desired (the target) or is expected.
minimum amount the project can produce in that benefit
5.4.2 Risk attitude, also called risk preference, is the will-
category and still cover the projected costs of the project.
ingness of a decision-maker to take a chance or gamble on an
investmentofuncertainoutcome.Theimplicationsofdecision-
NOTE 3—Benefits and costs are treated throughout this guide on a
makershavingdifferentriskattitudesisthatagiveninvestment
discounted cash-flow basis, taking into account taxes where appropriate.
(See Practice E917 for an explanation of discounted cash flows consid-
of known risk exposure might be economically acceptable to
ering taxes.)
an investor who is not particularly risk averse, but totally
unacceptable to another investor who is very risk averse.
The NIST Building Life-Cycle Cost (BLCC) Computer Program helps users
NOTE 2—For completeness, this guide covers both risk averse and risk
calculate measures of worth for buildings and building components that are
takingattitudes.Mostinvestors,however,arelikelytoberiskaverse.The consistent with ASTM standards. The program is downloadable from http://
principles described herein apply both to the typical case where investors energy.gov/eere/femp/building-life-cycle-cost-programs.
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E1369 − 15 (2020)
7.2.2 To perform a breakeven analysis, an equation is nomic analysis for each of the three values to see how the
constructed wherein the benefits are set equal to the costs for a outcome changes as they change, with other things held the
given investment project, the values of all inputs except the same.
breakeven variable are specified, and the breakeven variable is
7.3.2 Sensitivity analysis also applies to different combina-
solved algebraically.
tionsofinputvalues.Thatis,alterseveralvariablesatonceand
7.2.3 Suppose a decision-maker is deciding whether or not
then compute a measure of worth. For example, one scenario
to invest in a piece of energy conserving equipment for a
might include a combination of all pessimistic values, another
government-owned building. The deviation of the formula for
all expected values, and a third all optimistic values; or a
computing breakeven investment costs for the equipment is as
combination might include optimistic values for some vari-
follows:
ables in conjunction with pessimistic or expected values for
others. Examining different combinations is required if the
S 5 C (1)
uncertain variables are interrelated.
C 5 I1O&M1R
7.3.3 The following illustration of sensitivity analysis treats
an accept/reject decision. Consider a decision on whether or
S 5 I1O&M1R
not to install a programmable time clock to control heating,
ventilating, and air conditioning (HVAC) equipment in a
I 5 S 2O&M 2 R
building. The time clock reduces electricity consumption by
where:
turning off that part of the HVAC equipment that is not needed
S = savings (benefits) in reduced energy costs from
during hours when the building is unoccupied. Using the
using the equipment,
benefit-to-cost ratio (BCR) as the economic method, the time
C = all costs associated with the equipment,
clock is acceptable on economic grounds if its BCR is greater
I = initial investment costs of the equipment,
than 1.0. The energy reduction benefits from the time clock,
O&M = operation and maintenance costs of the equipment,
however,areuncertain.Theyareafunctionofthreefactors:the
and
initial price of energy, the rate of change in energy prices over
R = replacement costs required to keep the equipment
the life cycle of the time clock, and the number of kilowatt
functional over the study period, and where all cost
hours saved. Assume that the initial price of energy and the
and benefit cash flows are discounted to present
number of kilowatt-hours saved are relatively certain, and that
values.
the sensitivity of the BCR is being tested with respect to the
7.2.4 By rearranging terms, the breakeven investment un-
following three values of energy price change: a low rate of
known is isolated on the left side of the equation. Substitution
energypriceescalation(slowlyincreasingbenefitsfromenergy
of known values for the terms on the right side allows the
savings); a moderate rate of escalation (moderately increasing
analyst to solve for the breakeven value. For example, if S
benefits); and a high rate of escalation (rapidly increasing
=$20000, O&M=$2500, and R=$1000,
benefits). These three assumed values of energy price change
then
might correspond to our projections of pessimistic, expected,
andoptimisticvalues.ThreeBCRestimatesresultfromrepeat-
I 5$20000 2$2500 2$1000 (2)
ing the BCR computation for each of the three energy price
or
escalation rates. For example, BCRs of 0.8, 2.0, and 4.0 might
result.Whereasadeterministicapproachmighthavegenerated
I 5$16500 (3)
a BCR estimate of 2.0, now it is apparent that the BCR could
7.2.5 This means that $16500, the breakeven value, is the
besignificantly less than 2.0, and even less than 1.0. Thus
maximum amount that can be paid for the energy-conserving
accepting the time clock could lead to an inefficient outcome.
equipment and still recover all costs through energy savings.
7.3.4 There are several advantages of sensitivity analysis.
7.2.6 An advantage of breakeven analysis is that it can be
First, it shows how significant a single input variable is in
computed quickly and easily with limited information. It also
determining project outcomes. Second, it recognizes the un-
simplifies project evaluation in that it gives just one value to
certainty associated with the input. Third, it gives information
decision-makers to use as a benchmark for comparison against
about the range of output variability.And fourth, it does all of
the predicted performance of that uncertain variable.
these when there is little information, resources, or time to use
Breakevenanalysishelpsdecision-makersassessthelikelihood
more sophisticated techniques.
of achieving the breakeven value and thereby contributes
7.3.5 Disadvantages of sensitivity analysis in evaluating
implicitly to the analysis of project risk.
risk are that it gives no explicit probabilistic measure of risk
7.2.7 A disadvantage is that it provides no probabilistic
exposure and it includes no explicit treatment of risk attitude.
pictureofinputvariableuncertaintyorofprojectriskexposure.
The findings of sensitivity analysis are ambiguous. How likely
Furthermore, it includes no explicit treatment of risk attitude.
is a pessimistic or expected or optimistic value, for example,
7.3 Sensitivity Analysis:
andhowlikelyisthecorrespondingoutcomevalue?Sensitivity
7.3.1 Sensitivity analysis measures the impact on project analysiscaninfactbemisleadingifallpessimisticassumptions
outcomes of changing a key input value about which there is or all optimistic assumptions are combined in calculating
uncertainty. For example, choose a pessimistic, expected, and economic measures. Such combinations of inputs are unlikely
optimistic value for an uncertain variable. Then do an eco- in the real world.
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E1369 − 15 (2020)
7.3.6 Sensitivity results can be presented in text, tables, or
graphs. One type of graph that is useful in showing the
sensitivityofprojectworthtoacriticalvariableisillustratedin
Fig. 1. Net benefits (NB) for ProjectsAand B decrease as the
discount rate increases. The slopes of the functions show that
NB is more sensitive to discount rate changes for Project A
thanforProjectB,assumingothervariablesremainunchanged.
These functions also help in making comparisons as to which
projectismorecosteffective.Atadiscountratebelow7%,for
example, Project A has the greater NB. At a rate above 7%,
Project B yields the greater NB. And at 7%, the two projects
provide identical NB.
7.3.7 Notethatthefunctionsindicatethepotentialvaluesof
NOTE 1—PL=project life,
NB if different values of the discount rate occur. If decision-
RR=reinvestment rate, and
makershavesomeideaastothelikelihoodofspecificdiscount
OM&R=operation, maintenance, and replacement costs.
rates,thegraphwillhelpthemevaluatetheNBimplicationsfor
FIG. 2 Spider Diagram Showing Sensitivity of the Adjusted Inter-
these two projects. The sensitivity graph in this sense contrib-
nal Rate of Return to Variations in Uncertain Variables
utes to an implicit description of risk exposure. Yet the graph
failstoprovideaquantitativemeasureoftheprobabilityofany
the AIRR value. Thus a 30% increase in the best-guess
given NB occurring.
reinvestment rate would yield a 25% AIRR, assuming other
7.3.8 Another special graph for sensitivity analysis that
values remain unchanged.
presents a snapshot of potential impacts of uncertain input
7.3.9 Thecontributionofthespiderdiagramisitspictureof
variables on project outcomes is the spider diagram. The one
the relative importance of the different uncertain variables. It
illustrated in Fig. 2 shows for a prospective commercial
shows immediately that the lesser the slope of a function, the
building investment the sensitivity of the adjusted internal rate
more sensitive is the AIRR to that variable. For example, any
of return (AIRR) to three variables: operation, maintenance,
given percent change in OM&R will have a greater impact on
and replacement costs (OM&R); project life (PL); and the
the AIRR than will an equal percent change in RR or PL.
reinvestment rate (RR). Each variable is represented by a
7.3.10 Spider diagrams can be helpful when comparing
labeled function that shows what AIRR values would result
competing projects as long as the decision-maker keeps in
from different values of the uncertain variable. For example,
mind that extreme values of the measure of worth reflect
the downward-sloping OM&R function indicates that the
variations in one variable only. For example, look at the spider
AIRRisinverselyproportionaltoOM&Rcosts.Bydesign,the
diagram for ProjectsAand B in Fig. 3.The NB of ProjectAis
OM&R function (as well as the other two functions) passes
a function of variablesA1 andA2, and the NB of Project B is
through the horizontal axis at the best-guess estimate of the
afunctionofvariablesB1andB2.Thehorizontalaxissuggests
AIRR (15% in this case), based on the best-guess estimates of
thatProjectBhasahigherpresentvaluenetbenefits($90000)
the three uncertain variables. Since each of the variables is
than Project A ($50000). That is, if only best-guess values
measured by different units (money, years, and percent), the
were used in a single-value, deterministic approach, Project B
vertical axis is denominated in positive and negative percent
would be the preferred project. However, if we assign, say a
changesfromthebest-guessvaluesfixedatthehorizontalaxis.
50% confidence interval about the uncertain variablesA1,A2,
TheAIRR value corresponding to any given percent variation
B1, and B2, as shown by X’s on the functions, there appears
indicated by a point on the function is found by extending a
the possibility that Project A could yield a higher NB than
line perpendicular to the horizontal axis and reading directly
Project B. That is, within that confidence interval, if the
FIG. 1 Sensitivity of Net Benefits of Projects A and B to Discount
Rate FIG. 3 Spider Diagrams for Competing Projects
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E1369 − 15 (2020)
extreme B1 value to the left were to occur, Project B would the discount rate to make the project look less desirable. For
yield a lesser NB than would Project A for A1 or A2 extreme cost streams, AR1 and AR2 are adjusted downwards as
values to the left. Furthermore, if A1 and B1 were the same perceived risk increases; that is, as future costs become more
input variable, we would know that Project A would be uncertain, the correct application of the RADR technique
preferred at values of A1 and B1 above 10% over the
requires lowering the discount rate to make the project look
best-guessvalue,andProjectBwouldbepreferredatvaluesof less cost effective. It follows then that the appropriate adjust-
A1 and B1 below 10%.
ment for risk when using life cycle cost (LCC) analysis is a
7.3.11 Once again, however, sensitivity analysis gives no decrease in the discount rate for each cost stream to make
indication of the probability of any given value of NB. project costs appear higher. Otherwise LCC analysis will be
Furthermore,becauseonlyonevariableisallowedtochangeat biased in favor of projects with a greater risk of higher-than-
a time, and NB is a function of more than one variable,
anticipated costs.
sensitivity analysis gives an incomplete description of the
7.4.7 Let us look once again at the BCR of the time clock
possible outcomes.
for an illustration of the RADR when making an accept/reject
decision. If no unusual risk is associated with the time clock,
7.4 Risk-Adjusted Discounting:
the discount rate is equal to the sum of RF andAR1 as shown
7.4.1 One technique used by the business community to
under Eq 4. Let us suppose that the BCR for the time clock is
accountforriskistherisk-adjusteddiscountrate(RADR).The
1.1 in this case. Thus it appears economically sound.
objective of using the RADR technique is to raise the likeli-
hood that the investor will earn a return over time sufficient to 7.4.8 Now let us assume instead that the economic perfor-
compensate for extra risk associated with specific projects.
manceofthetimeclockismoreriskythanaverage.Thismight
7.4.2 Projects with anticipated high variability in distribu- arise, for example, from the impact of uncertain kilowatt-hour
tions of project worth have their net benefits or returns reductions or uncertain future energy prices. Furthermore, let
discounted at higher rates than projects with low variability. us assume that the decision-maker is risk averse. Using the
Thus in computing net benefits or the benefit-to-cost ratio, the
RADR technique, we raise the discount rate for evaluating
discountrateishigherforbenefitstreamsofriskyprojectsthan
energy cost savings by some positive value of AR2. If the
for those with certain outcomes. Or when applying rate-of-
resulting BCR falls below 1.0, the project no longer appears
return methods, the minimum acceptable rate of return
economically acceptable.
(MARR) is raised above the risk-free rate to compensate for
7.4.9 Advantages of the RADR technique are that it is
the higher variability of returns in risky projects.
relatively simple to understand; it is easy to compute; and it
7.4.3 Calculate the RADR as follows:
accounts to some extent for uncertainty of inputs, risk
exposure, and risk attitude.
RADR 5RF1AR11AR2 (4)
7.4.10 Amajor limitation in using the RADR is the lack of
where:
any accepted procedure for establishing the RADR value. It is
RF = risk-free rate,
typically estimated based on the decision-maker’s best judg-
AR1 = adjustment for normal risk encountered in the firm’s
ment. One common approach is to simply lump projects into
operations, and
riskcategories,eachofwhichhasanassignedRADR.Thereis
AR2 = adjustmentforextrariskaboveorbelownormalrisk.
little fine tuning. Furthermore, there is no distinction between
All terms are expressed as percents.
adjustments for handling risk exposure and risk attitude.
7.4.4 The risk-free rate (RF) component accounts for the
7.4.11 Acommonmistakeinapplicationistouseaconstant
time value of money. It is what might be earned, for example,
AR2 over the entire study period.This distorts risk adjustment
on government treasury bills, the closest thing to a riskless
when there are periods for which no special adjustment is
investment available to most investors. The adjustment for
necessary above or below what is considered normal risk. A
normalrisk(AR1)istheriskpremiumthatafirmmightimpose
constantAR2alsodistortsriskadjustmentbecauseitimpliesin
to cover the average riskiness of its normal operations. The
effect that returns become exponentially more uncertain over
sum of RF andAR1 should equal the MARR the firm requires
time, which is often not the case. Thus a discount rate that
on typical investments. The AR2 component adjusts for proj-
includes a constant AR2 severely reduces the weight of net
ects with more or less risk than what is normally associated
benefits accrued in later years, regardless of the certainty of
with the firm. The adjustment can be positive or negative.
their occurrence. This biases selection towards projects with
7.4.5 For discounting benefit streams,AR2 is an increasing
earlypayoffs.Toavoidthiscommonmistakeinapplicationand
function of (1) the perceived variability in project outcomes
its resulting bias, use a variable AR2.
(riskexposure)and(2)thedegreetowhichthedecision-maker
7.5 Mean-Variance Criterion and Coeffıcient of Variation:
is risk averse (risk attitude). For coststreams, AR2 is a
decreasing function of those same risk factors. 7.5.1 Comparing mean values and standard deviations of
7.4.6 For computing the RADR, each benefit and cost measures of project worth can help decision-makers evaluate
streamshouldbediscountedwithauniqueRADRthatincludes returns and risk exposure of one project versus another and
AR1 and AR2 values that describe that stream’s uncertainty. determine stochastic dominance. If two projects competing for
For benefit or savings streams, AR1 and AR2 are adjusted limiting funds are compared on the basis of BCRs, for
upwards as perceived risk increases; that is, as future benefits example,themean-variancecriteriondictatesthattheonewith
become more uncertain, the RADR technique requires raising the higher mean (that is, expected value) and lower standard
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best judgments available on the likelihood of uncertain events.
deviation be chosen. This presumes that decision-makers
prefer higher BCRs to lower BCRs and less risk to more risk.
7.6.4 DecisionAnalysis of Energy Conservation Investment:
7.5.2 If one project has a higher mean and higher standard
7.6.4.1 This illustration examines an energy investment
deviation of the measure of project worth, then the choice is
problem facing a state energy office. The office has been
not clear with the mean-variance criterion. In this case, the
directed to make a choice regarding an energy conservation
coefficient of variation can be computed to determine the
project from among six possibilities for retrofitting two public
relative risk of the two projects. The coefficient of variation is
buildings. The purpose of the conservation project is to
found by dividing the standard deviation by the mean as
demonstrate to private companies that energy conservation is
follows:
profitable. The objective of the decision analysis exercise is to
choose the retrofit package that yields the maximum expected
CV 5 σ/µ, (5)
net benefits (NB), that is, shows the greatest profit potential. If
where:
none of the packages yields a positive NB, the choice will be
CV = coefficient of variation,
not to invest at all.
σ = standard deviation, and
7.6.4.2 Twotypesofretrofitcostsareconsidered.Thefirstis
µ = mean or expected value.
a fixed retrofit investment cost that is incurred for energy
conservationworkineachbuildingregardlessofwhichretrofit
7.5.3 The project with the lower coefficient of variation has
package is chosen. The second is the cost of implementing the
the lesser risk per unit of return or project worth. It will be
individual retrofits in each package. The present value fixed
preferred by risk-averse decision-makers. Risk-taking
investment (F1 and F2) costs and retrofit package (R1 through
decision-makers,ontheotherhand,willprefertheprojectwith
R6) costs are shown in Table 1. All costs are assumed to be
the higher coefficient.
certain.
7.5.4 An advantage of the coefficient of variation is that it
7.6.4.3 The predicted benefit outcomes (dollar energy sav-
providesanexplicitmeasureofrelativeriskexposure.Another
ings in present value terms) are uncertain for the different
is that risk attitude is considered when the decision-maker
retrofit packages. Table 2 shows estimates of these possible
evaluates the coefficients of variation to choose among alter-
benefit outcomes with their respective probabilities of occur-
native projects. The major limitation is in acquiring the σ and
rence. Since the state is assumed to be risk neutral and act so
µ values for the measure of project worth.
astomaximizetheexpectedmonetaryvalueofitsinvestments,
7.6 Decision Analysis:
thereisnoneedtoconsiderriskattitudeandthecorresponding
7.6.1 Decision analysis is one of the few techniques for
utilitymeasuresofoutcomes.Furthermore,sincethestatepays
making economic decisions in an uncertain environment that
no taxes, they are not included in the analysis.
treats formally both risk exposure and risk attitude. It provides
7.6.4.4 The decision tree in Fig. 4 clarifies the possible
a methodology that allows a decision-maker to include alter-
alternatives and outcomes listed in Table 1 and Table 2. The
native outcomes, risk attitudes, and subjective impressions
following explanation describes the potential paths of the
about uncertain events in an evaluation of investments.
decision tree starting from the left side.
7.6.2 Decision analysis typically uses decision trees to
NOTE 5—The procedure for finding the package that yields maximum
represent all possible outcomes, costs, and probabilities asso-
net benefits requires starting from the right side of the tree, as will be
ciated with a given decision problem. A decision tree is a
shown later. It is easier to explain the tree structure, however by starting
decision-flow diagram that serves as a road map to clarify
from the left.
possible alternatives and outcomes of sequential decisions. A
7.6.4.5 Thebasicalternativeofnotinvestingisindicatedby
decision tree is used in this section to illustrate how it helps
the top line segment coming out of the box on the left side of
bring order to complex decisions about risky investments.
Fig.4.Thefixedinvestmentof$500000inBuildingIisshown
7.6.3 In general, the decision analysis approach has three
by the next line, and the investment of $800000 in Building II
steps. The first is to structure the problem. This includes
is shown by the bottom line. Each box in a decision tree
defining variables, describing with models their relationships,
represents a decision juncture or node, and the line segments
assigning values to possible outcomes, and measuring the
represent alternative branches on the decision tree. The state
importance of variables through sensitivity analysis. The sec-
energy office will select that branch sequence that they expect
ond step is to assign subjective probabilities to important
will maximize the present value of net benefits from conser-
variables and possible outcomes, and to find the best bet
vation.
alternative. This includes describing uncertainty with subjec-
7.6.4.6 Associated with each building is another decision
tive probability distributions, describing risk attitude with a
node, requiring a decision regarding a specific set of retrofit
utilityfunction(seeAnnexA2),andfindingthealternativethat
choices,R1throughR3orR4throughR6.Theknowncostsof
is expected to yield the greatest economic return (or utility if
each retrofit package are shown under each alternative branch.
thedecision-makerisnotriskneutral).Thethirdstep,whichis
not always taken, is to determine whether obtaining additional
TABLE 1 Fixed Investment and Retrofit Package Cost for
information is worth the cost. If it is, then the information is
Buildings I and II (Cost in Millions of Dollars)
collected, and steps 1 and 2 are repeated.
Building I Building II
NOTE 4—Subjective probability distributions are developed by the
F1 R1 R2 R3 F2 R4 R5 R6
decision analyst asking the decision-maker or an expert(s) designated by 0.5 2.0 3.0 4.0 0.8 3.0 4.0 4.5
the decision-maker a series of probing questions designed to reveal the
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E1369 − 15 (2020)
TABLE 2 Possible Benefit Outcomes and Their Estimated
7.6.4.9 Letustraceoutonesetofdecisionswithitspossible
Probabilities of Occurrence for the Six Retrofit Packages
outcomes. If the state energy office chooses the R1 package of
Possible Benefit
retrofits in Building I for a total cost of $2500000, there is a
Retrofit Estimated
Outcomes,
Packages Probabilities
90% probability that the outcome (payoff) will be $3000000
millions of dollars
and a 10% chance it will be only $2000000.
R1 3.0 0.9
2.0 0.1
7.6.4.10 Let us also examine how some of the outcome and
probability values might have been derived. The 90% prob-
R2 4.5 0.6
abilityassociatedwithR1fora$3000000payoffmightbedue
3.0 0.3
−1.0 0.1 to the R1 conservation package being a well-tested one with
predictable results. On the other hand, R2 might contain
R3 6.0 0.7
conservationoptionsthatarenewanduntried,therebyexplain-
4.0 0.2
2.0 0.1
ing the spread of possible outcomes and the lower probabili-
ties.And since there is no record of performance, and there is
R4 4.0 0.8
some chance of the conservation options not working, a 10%
3.0 0.1
2.5 0.1
probability of a loss of $1000000 is included in R2, as shown
on the bottom outcome branch.
R5 7.0 0.5
7.6.4.11 The outcome values at the tips of the outcome
4.5 0.4
4.0 0.1
branches, the probabilities on the outcome branches, and the
retrofit and fixed building costs on the alternative branches are
R6 7.0 0.5
estimated (see Table 1 and Table 2).The values shown at each
4.5 0.3
1.0 0.2
decision node and chance node, on the other hand, must be
calculated. The following steps describe the calculation pro-
cess for the node values and how to determine the retrofit
choice that maximizes expected net benefits. Note that the
calculation process starts from the right side of the tree and
works backwards to the left side.
7.6.4.12 Starting from the right-hand side of the tree,
average out for each chance node its expected value; that is,
calculate the weighted average for each probability fan by
summing the products of the possible outcomes weighted by
their respective probabilities. The expected value of the prob-
ability fan of R1, for example, is computed as follows:
0.9 $3000000 10.1 $2000000 5$2900000 (6)
~ ! ~ !
Writetheexpectedvalueatopeachchancenode,asshownin
Fig. 4.
NOTE 1—□=decision node, 7.6.4.13 Next,foldbacktothenextprecedingstage.Thatis,
O=chance node, and
ateachsquaredecisionnode,comparethealternativebranches
R=retrofit package.
with respect to their costs and expected benefits. Choose the
FIG. 4 Decision Tree for Conservation Investment (Dollar Values
one with the highest expected net benefits and write it atop the
are in Millions)
decision node box. For example, if you fold back the decision
node values on the Building II path sequence, expected NB
7.6.4.7 The benefit outcomes (dollar energy savings) are
values (before subtracting the $800000 Building II fixed cost)
uncertain for the different retrofit packages. Thus at the end of
for retrofit packages R4 through R6 are as follows:
each retrofit package branch is a chance node or juncture
R4 5$3800000 2$3000000 5$800000 (7)
NB
followed by alternative outcomes. Retrofit package R1, for
example, is followed by a chance node, indicated by a circle,
R5 5$5700000 2$4000000 5$1700000 (8)
NB
with two potential outcomes. The probability of each alterna-
R6 5$5100000 2$4500000 5$600000 (9)
NB
tiveoutcomeisindicatedontopofitslineandthevalueofeach
7.6.4.14 The preferred (that is, maximum expected NB)
alternative outcome at the tip of its line.
alternative branch is R5. Write its value, $1700000, atop the
7.6.4.8 One way to establish the probability and outcome
decision node box. Truncate the other two paths by parallel
values is for the analyst to discuss with engineers, architects,
slash marks to indicate that they are less economical choices.
building managers, equipment manufacturers, and other
knowledgeable people the implications of alternative retrofit 7.6.4.15 The final step is to fold back one more time.
packages in Buildings I and II. The outcome values at the Retrofit package R5 in Building II is the most efficient choice
branch tips will be based on anticipated potential impacts of because its expected value of net benefits is $900000 (that is,
changes in uncertain input variables, including energy prices, $1 700 000 − $800 000) compared to $700 000 (that is,
lengthofsystemlife,performanceoftheconservationretrofits, $1200000−$500000) for retrofit package R3 in Building I
and the quantity of energy saved. and zero dollars for having no project. Enter the maximum
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expected value at the initial decision node box at the far left of 7.7.3.2 Contingencies are often estimated simply as a per-
the decision tree. Use parallel slash marks to truncate the no cent of the base estimate of project cost. Historical data on the
project and Building I alternatives. The decision tree, once all differences between actual and estimated costs for similar
values are written in, shows explicitly the economically effi- projects can be used to determine an average percent of
cient path sequence (Building II/R5 in this case) and the underestimation (or overestimation). The percent can apply to
expected value of net benefits ($900000) for that path se- theoverallprojectortospecificelementsoftheprojectthatare
quence. estimated separately. This simple approach is typical in esti-
mating costs of small projects. There is no distinction,
7.6.4.16 Note that risk attitude was not addressed explicitly
however, between accounting for risk exposure and risk
withutilityvaluesinthisexamplebecausethestateisassumed
attitude in the contingency estimate.
to be risk neutral. If the decision-maker were risk averse or a
7.7.3.3 For large construction projects with many uncertain
risktaker,however,theprojectedearningsandcostsassociated
with each decision branch could be converted to utility values. variables, a sophisticated risk-analysis technique based on
simulations is sometimes employed in estimating contingen-
Autilityfunction(seeFig.A2.5)isusedtofindtheutilityvalue
correspondingtothesebenefitsandcosts.Theaveragingoutto cies. It provides decision-makers with the probabilities of cost
overruns (that is, risk exposure) associated with every possible
find expected values (now expected utility values) and the
contingency markup in the relevant range. The following
rollingbackprocessarethesameasdescribedearlier.Oncethe
example adapted from S.H. Zaheer illustrates how to use
alternative that maximizes utility is identified, the certain
simulation to measure risk exposure when making a cost
equivalent dollar value corresponding to that alternative’s
estimateforaspecificconstructionproject.Notethattheintent
utility is found on the utility function. The certain equivalent
hereistoshowhowusefulsimulationcanbeindescribingrisk
value shows what the risky investment is worth, taking into
of an investment and not to describe every step the computer
consideration the decision-maker’s risk attitude.
program takes to do the simulation.
7.7 Simulation:
7.7.3.4 ConstructioncostisbeingestimatedforProjectX.It
7.7.1 Simulation is a well-documented technique used to
isexpectedtocost$140millionexclusiveofcontingencies.Of
determine risk exposure from an investment decision. To
the $140 million, $60 million are spent dollars or firm
perform a simulation, probability functions of significant input
commitments. Being relatively certain, they require no consid-
variables must be estimated. The simulation process for build-
eration for contingency. The other $80 million are uncertain
ing a probability density function (pdf) and cumulative distri-
and make up the base on which the contingency is calculated.
bution function (cdf) of the measure of project worth is as
7.7.3.5 The process for carrying out a contingency/risk
follows:drawavalueforeachinputvariablerandomlyfromits
analysis is as follows. Generate subjective probability distri-
probability function, substitute the set of input values for that
butionsforeveryactivitythatisdeemedparticularlyuncertain.
round of draws into the formula for computing the measure of
The distributions describe the percent of estimated costs of
economic worth, and repeat the process over and over until a
these activities, where the midpoint is 100% of the estimated
pdf and cdf can be constructed for the measure of worth.
value.Enterthesedata,alongwiththeestimateddollarcostsof
7.7.2 For example, in analyzing the time clock, the initial
bothcertainanduncertainactivitiesintoacomputersimulation
energy price, the rate of energy price escalation, and the
package. It generates a probability distribution of the contin-
kilowatt hour savings are uncertain input variables. If each of
gency percent of total project cost and a graph that plots
these inputs could be described by a probability distribution, a
probability of cost overrun against contingency percent and
simulation could be used to arrive at a probability distribution
amount.
of the time clock’s BCR (or some other measure of worth).
7.7.3.6 Fig. 5 shows how the probability of a cost overrun
Specifically, a random combination of each of the three
(that is, risk exposure) varies with the contingency adjustment
variableswouldbeselectedandcombinedwithconstantinputs
for this construction project. To use the contingency/risk
to compute a BCR. By repeating this random sampling over
analysis to select a single cost estimate, the decision-maker
and over, typically 500 to 1000 times, and computing the BCR
considers risk exposure and risk attitude. Risk exposure, as
for each combination, a pdf and cdf can be generated for
indicatedbytherisingprobabilityofcostoverrun,increasesas
evaluating the cost effectiveness of the time clock.
the percent contingency markup goes down. Risk exposure
7.7.3 Construction Contingency Simulation Example:
decreases as the percent contingency markup increases. Risk
7.7.3.1 Contingency analysis is routinely used by cost
attitudeenterswhenthedecision-makerchoosesacontingency
engineers in estimating the costs of construction projects. A
amount, thereby establishing a probability of overrun that will
contingency is a cost element included in project cost estima-
be acceptable.
tiontocovercoststhathavesomelikelihoodofoccurrence,but
7.7.3.7 The risk neutral decision-maker will choose the
whose amounts cannot be predicated with certainty. By adding
most likely cost estimate of $144 million, which includes the
the contingency to the line-item estimate of project cost, the
$140 million without contingency plus a contingency of $4
costengineerhopestoprojectthemostlikelyfinalcost.Typical
million (0.05·$80 million of uncertain costs). That is, the
uses of contingencies are to cover possible increases in
materialorlaborcostsbeyondnormalescalation,unanticipated
developments in applying a first-time technology, changes in
Zaheer, S.H., “Contingency and Capital Cost Estimates,” Cost Engineers’
project scope due to omission or error, or unforeseen work
Notebook,AmericanAssociationofCostEngineers,Morgantown,WV,March1983,
disruptions from operating in a volatile foreign country. p. 13.
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decision-makerselectsprojectsonthebasisofcdfs,inherentin
that selection is an implicit assessment of risk attitude.
7.7.8 The disadvantage of simulation is tha
...