# ASTM E1121-15

Designation: E1121 − 15Standard Practice forMeasuring Payback for Investments in Buildings andBuilding Systems1This standard is issued under the fixed designation E1121; 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 practice provides a recommended procedure forcalculating and applying the payback method in evaluatingbuilding designs and building systems.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 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 SystemsE1185 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 Systems2.2 Adjuncts:Discount Factor Tables Adjunct to Practices E917, E964,E1057, E1074, and E112133. 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 2, Referenced Documents—Lists ASTM stan-dards and adjuncts referenced in this practice.4.1.2 Section 3, Definitions—Addresses definitions of termsused in this practice.4.1.3 Section 4, Summary of Practice—Outlines the con-tents of the practice.4.1.4 Section 5, Significance and Use—Explains the signifi-cance and use of this practice.4.1.5 Section 6, Procedures—Describes step-by-step theprocedures for making economic evaluations of buildings.4.1.6 Section 7, Objectives, Alternatives, and Constraints—Identifies and gives examples of objectives, alternatives, andconstraints for a payback evaluation.4.1.7 Section 8, Data and Assumptions—Identifies dataneeded and assumptions that may be required in a paybackevaluation.4.1.8 Section 9, Compute Payback Period—Presents alter-native approaches for finding the payback period.4.1.9 Section 10, Applications—Explains the circumstancesfor which the payback method is appropriate.4.1.10 Section 11, Limitations—Discusses the limitations ofthe payback method.5. Significance and Use5.1 The payback method is part of a family of economicevaluation methods that provide measures of economic perfor-mance of an investment. Included in this family of evaluationmethods are life-cycle costing, benefit-to-cost and savings-to-investment ratios, net benefits, and internal rates of return.5.2 The payback method accounts for all monetary valuesassociated with an investment up to the time at which cumu-lative net benefits, discounted to present value, just pay offinitial investment costs.5.3 Use the method to find if a project recovers its invest-ment cost and other accrued costs within its service life orwithin a specified maximum acceptable payback period(MAPP) less than its service life. It is important to note that the1This 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 Oct. 1, 2015. Published October 2015. Originallyapproved in 1986. Last previous edition approved in 2012 as E1121 – 12. DOI:10.1520/E1121-15.2For 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.3Available from ASTM International Headquarters. Order Adjunct No.ADJE091703.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1decision to use the payback method should be made with care.(See Section 11 on Limitations.)6. Procedures6.1 The recommended steps for making an economic evalu-ation of buildings or building components are summarized asfollows:6.1.1 Identify objectives, alternatives, and constraints,6.1.2 Select an economic evaluation method,6.1.3 Compile data and establish assumptions,6.1.4 Convert cash flows to a common time basis, and6.1.5 Compute the economic measure and compare alterna-tives.6.2 Only the step in 6.1.5, as applied to measuring payback,is examined in detail in this practice. For elaboration on thesteps in 6.1.1 – 6.1.4, consult Practices E964 and E917, andGuide E1185.7. Objectives, Alternatives, and Constraints7.1 Specify the kind of building decision to be made. Makeexplicit the objectives of the decision maker. And identify thealternative approaches for reaching the objectives and anyconstraints to reaching the objectives.7.2 An example of a building investment problem thatmight be evaluated with the payback method is the installationof storm windows. The objective is to see if the costs of thestorm windows are recovered within the MAPP. The alterna-tives are (1) to do nothing to the existing windows or (2)toinstall storm windows. One constraint might be limited avail-able funds for purchasing the storm windows. If the paybackperiod computed from expected energy savings and windowinvestment costs is equal to or less than the specified MAPP,the investment is considered acceptable using this method.7.3 Whereas the payback method is appropriate for solvingthe problem cited in 7.2, for certain kinds of economicproblems, such as determining the economically efficient levelof insulation, Practices E917 and E1074 are the appropriatemethods.8. Data and Assumptions8.1 Data needed to make payback calculations can becollected from published and unpublished sources, estimated,or assumed.8.2 Both engineering data (for example, heating loads,equipment service life, and equipment efficiencies) and eco-nomic data (for example, tax rates, depreciation rates andperiods, system costs, energy costs, discount rate, project life,price escalation rates, and financing costs) will be needed.8.3 The economic measure of a project’s worth variesconsiderably depending on the data and assumptions. Usesensitivity analysis to test the outcome for a range of the lesscertain values in order to identify the critical parameters.Consult Guide E1369 for guidance on how to use sensitivityanalysis to measure the impact on the payback period fromchanging one or more values about which there is uncertainty.9. Compute Payback Period9.1 The payback method finds the length of time (usuallyspecified in years) between the date of the initial projectinvestment and the date when the present value of cumulativefuture earnings or savings, net of cumulative future costs, justequals the initial investment. This is called the payback period.When a zero discount rate is used, this result is referred to asthe “simple” payback (SPB). The payback period can bedetermined mathematically, from present-value tables, orgraphically.9.2 Mathematical Solution:9.2.1 To determine the payback period, find the minimumsolution value of PB in Eq 1.(t51PB@~Bt2 C˜t!/~11i!t# 5 Co(1)where:Bt= dollar value of benefits (including earnings, costreductions or savings, and resale values, if any, andadjusted for any tax effects) in period t for thebuilding or system being evaluated less the coun-terpart benefits in period t for the mutually exclu-sive alternative against which it is being compared.C˜t= dollar value of costs (excluding initial investmentcost, but including operation, maintenance, andreplacement costs, adjusted for any tax effects) inperiod t for the building or system being evaluatedless the counterpart cost in period t for the mutuallyexclusive alternative against which it is beingcompared.Bt2C˜t= net cash flows in year t,Co= initial project investment costs, as of the base time,i = discount rate per time period t, and1~11i!t= formula for determining the single present valuefactor,NOTE 1—Eq 1 and all others that follow assume the convention ofdiscounting from the end of the year. Cash flows are assumed to be spreadevenly over the last year of payback so that partial year answers can beinterpolated.9.2.2 Uniform Net Cash Flows:9.2.2.1 For the case where ~Bt2 C˜t! is the same from yearto year, denoted by ~B 2 C˜!, the payback period (PB) corre-sponding to any discount rate (i) other than zero can be foundusing Eq 2.PB 5log@1/~1 2 ~ SPB·i!!#log~11i!(2)where:SPB 5 Co/~B 2 C˜!. (3)When the discount rate is equal to zero,PB 5 SPB (4)However PB is undefined when (SPB · i) ≥ 1; that is, theproject will never pay for itself at that discount rate.9.2.2.2 A calculation using Eq 2 is presented for thefollowing investment problem. What would be the paybackperiod for a project investment of $12 000, earning uniformannual net cash flows of $4500 for six years? A 10 % discountE1121 − 152rate applies. First solve for the SPB: $12 000⁄$4500 = 2.6667.Eq 2 would yield the following:PB 5log@1/~1 2 ~2.6667·0.10!!#log1.105 ~log1.3636/log1.1000!5 ~0.1347/0.0414! 5 3.259.2.2.3 Since the payback period (3.25 years) is less than thesix years over which the project earns constant net benefitreturns, and since a shorter MAPP has not been specified, theproject is considered acceptable.9.2.3 Unequal Net Cash Flows:9.2.3.1 For problems with unequal annual net cash flows, acommon approach to calculating the payback period is toaccumulate the present value of net cash flows year-by-yearuntil the sum just equals or exceeds the original investmentcosts. The number of years required for the two to becomeequal is the payback period.9.2.3.2 This approach is illustrated in Table 1.Aproject withseven years of unequal cash flows (Column 2) is evaluated ata discount rate of 12 %. The net cash flow in each year isdiscounted at 12 % to present value (Column 3). Each year’saddition to the present value is accumulated in Column 4. Thepresent value of net benefits (PVNB) in Column 6 is derived bysubtracting the investment costs (Column 5) from thecumulative, discounted, future net cash flows (Column 4). Thepresent value of net cash flows equals investment costs at somepoint in the fifth year. The payback period can be interpolatedas follows:PB 5 4 years10 2 ~2$3011!$4933 2 ~2$3011!5 4.389.2.3.3 Since the payback period is less than the period overwhich the project earns positive net benefits (seven years), andsince a shorter MAPP has not been specified, the project isconsidered acceptable.9.2.4 Net Cash Flows Escalating at a Constant Rate:9.2.4.1 To determine the payback period when net cashflows escalate at a constant rate, find the minimum solution ofPB in Eq 5.~B 2 C˜!*(t51PB@~11e!/~11i!#t5 Co(5)where:~B 2 C˜!*= initial value of an annual, uniformly escalating,net cash flow, ande = constant price escalation rate per period t appli-cable to net cash flows.9.2.4.2 When e is not equal to i, the payback period can becalculated by using Eq 6.PB 5log@11~SPB!~1 2 ~11i!/~11e!!#log@~11e!/~11i!#(6)where SPB = C0⁄~B 2 C˜!*.When e is equal to i,PB 5 SPB (7)However PB is undefined and the project will never pay foritself at discount rate i ifSPB~1 2 ~11i!/~11e!! # 21 (8)9.2.4.3 If the payback period is less than the period overwhich the project yields returns, the project is considered to beeconomically acceptable.9.2.4.4 Eq 6 can be illustrated with the following problem.An energy conservation investment of $40 000 yielding energysavings initially worth $8000 annually is to be evaluated withan 8 % energy price escalation and a 12 % discount rate.Applying Eq 6 yields the following:PB 5log@11~$40000/$8000!~1 2 ~1.12/1.08!!#log~1.08/1.12!5log@115~20.0370!#log0.96435log0.8150log0.964355.63 years9.3 Estimating Payback Periods with Present-Value Tables:TABLE 1 Payback Problem With Unequal Annual Cash Flows(1) (2) (3) (4) (5) (6) = (4) − (5)Years(t, s)Net Cash Flows($)(Bt−Ct)DiscountedNet Cash FlowsA($)FBt2C˜ts11idtGCumulativeDiscountedNet Cash Flows($)ot51sFBt2 C˜ts11idtGInvestmentCost($)(Co)Cumulative PVNB($)ot51sFBt2 C˜ts11idtG 2 Co0 0 0 0 50 000 −50 0001 10 000 8 929 8 929 −41 0712 20 000 15 944 24 873 −25 1273 15 000 10 677 35 550 −14 4504 18 000 11 439 46 989 −3 0115 14 000 7 944 54 933 +4 9336 12 000 6 080 61 013 +11 0137 8 000 3 619 64 632 +14 632AThe discount rate = 12 %.E1121 − 1539.3.1 Present-value tables, such as those found in DiscountFactor Tables, can be used in certain cases to estimate paybackperiods without a calculator.9.3.2 Uniform Net Cash Flows:9.3.2.1 The payback period for a project with uniformannual net cash flows ~B 2 C˜! can be estimated by firstfinding, in a table of Uniform Present Value (UPV) factors forthe given discount rate, that UPV factor closest to the ratio ofInitial Investment⁄~B 2 C˜!* (9)The appropriate payback period is the number of periods (n)corresponding to that UPV factor. Interpolation can be usedto more closely approximate the payback period.9.3.2.2 As an example, when the discount rate is 12 %, thepayback period for an initial investment of $100 which returns$15 per year is found as follows: The ratio of $100/$15 = 6.67.This ratio corresponds to a time period (n) of approximately14.2 years in a table of Uniform Present Value factors based ona 12 % discount rate.9.3.3 Net Cash Flows Escalating at a Constant Rate:9.3.3.1 The payback period for a project with annual netcash flows escalating at a constant rate can be estimated by firstfinding, in a table of Modified Uniform Present Value (UPV*)factors for the given discount rate and escalation rates, thatUPV* factor closest to the ratio of:Initial Investment⁄~B 2 C˜!* (10)The appropriate payback period is the number of periods (n)corresponding to that UPV* factor. Interpolation can be usedto more closely approximate the payback period.9.3.3.2 As an example, when the discount rate is 12 %, thepayback period for an investment of $100 that returns net cashflows initially valued at $15 per year and increasing at 6 % peryear is found as follows: The ratio of $100/$15 = 6.67. Thisratio corresponds to a time period (n) of approximately 8.6years in a table of Modified Uniform Present Value factorsbased on a 12 % discount rate and 6 % escalation.9.4 Graphical Solutions:9.4.1 The payback period for projects with uniform annualnet cash flows or flows that increase at a constant rate can befound using graphs. The payback graphs described belowpresent payback as a function of SPB.9.4.2 Uniform Net Cash Flows:9.4.2.1 Fig. 1 plots payback periods up to ten years as afunction of SPB values