1、Designation: E 1121 07Standard Practice forMeasuring Payback for Investments in Buildings andBuilding Systems1This standard is issued under the fixed designation E 1121; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of l
2、ast revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) 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 de
3、signs and building systems.2. Referenced Documents2.1 ASTM Standards:2E 631 Terminology of Building ConstructionsE 833 Terminology of Building EconomicsE 917 Practice for Measuring Life-Cycle Costs of Buildingsand Building SystemsE 964 Practice for Measuring Benefit-to-Cost and Savings-to-Investment
4、 Ratios for Buildings and Building SystemsE 1057 Practice for Measuring Internal Rate of Return andAdjusted Internal Rate of Return for Investments in Build-ings and Building SystemsE 1074 Practice for Measuring Net Benefits and Net Sav-ings for Investments in Buildings and Building SystemsE 1185 Gu
5、ide for Selecting Economic Methods for Evalu-ating Investments in Buildings and Building Systems2.2 ASTM Adjuncts:Discount Factor Tables, Adjunct to Practice E 91733. Terminology3.1 DefinitionsFor definitions of terms used in thispractice, refer to Terminologies E 631 and E 833.4. Summary of Practic
6、e4.1 This practice is organized as follows:4.1.1 Section 2, Referenced DocumentsLists ASTM stan-dards and adjuncts referenced in this practice.4.1.2 Section 3, DefinitionsAddresses definitions of termsused in this practice.4.1.3 Section 4, Summary of PracticeOutlines the con-tents of the practice.4.
7、1.4 Section 5, Significance and UseExplains the signifi-cance and use of this practice.4.1.5 Section 6, ProceduresDescribes step-by-step theprocedures for making economic evaluations of buildings.4.1.6 Section 7, Objectives, Alternatives, and ConstraintsIdentifies and gives examples of objectives, a
8、lternatives, andconstraints for a payback evaluation.4.1.7 Section 8, Data and AssumptionsIdentifies dataneeded and assumptions that may be required in a paybackevaluation.4.1.8 Section 9, Compute Payback PeriodPresents alter-native approaches for finding the payback period.4.1.9 Section 10, Applica
9、tionsExplains the circumstancesfor which the payback method is appropriate.4.1.10 Section 11, LimitationsDiscusses 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
10、 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
11、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 t
12、o note that thedecision 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
13、.1.2 Select an economic evaluation method,6.1.3 Compile data and establish assumptions,1This 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 April 1, 2007. Publ
14、ished April 2007. Originallyapproved in 1986. Last previous edition approved in 2002 as E 1121 02.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Docu
15、ment Summary page onthe ASTM website.3Available from ASTM International Headquarters. Order Adjunct No.ADJE091703.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.6.1.4 Convert cash flows to a common time basis, and6.1.5 Compute the e
16、conomic 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 E 964 and E 917, andGuide E 1185.7. Objectives, Alternatives, and Constraints7.1 Specify the kin
17、d 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
18、 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
19、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 economicpro
20、blems, such as determining the economically efficient levelof insulation, Practices E 917 and E 1074 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 (
21、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
22、projects 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.9. Compute Payback Period9.1 The payback method finds the length of time (usuallyspecified in years)
23、 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 “si
24、mple” 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.(t 5 1PBBt2 Ct!/1 1 i!t#5Co(1)where:Bt= dollar value of benefits (including
25、earnings,cost reductions or savings, and resale values,if any, and adjusted for any tax effects) inperiod t for the building or system beingevaluated less the counterpart benefits in pe-riod t for the mutually exclusive alternativeagainst which it is being compared.Ct= dollar value of costs (excludi
26、ng initial invest-ment cost, but including operation, mainte-nance, and replacement costs, adjusted for anytax effects) in period t for the building orsystem being evaluated less the counterpartcost in period t for the mutually exclusivealternative against which it is being compared.BtCt= net cash f
27、lows in year t,Co= initial project investment costs, as of the basetime,i = discount rate per time period t, and11 1 i!t= formula for determining the single presentvalue factor,NOTE 1 Eq 1 and all others that follow assume the convention ofdiscounting from the end of the year. Cash flows are assumed
28、 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 (BtCt) is the same from yearto year, denoted by (B C), the payback period (PB) corre-sponding to any discount rate (i) other than zero can be foun
29、dusing Eq 2.PB 5log1/1 2 SPB i!#log 1 1 i!(2)whereSPB 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 investm
30、ent 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 % discountrate applies. First solve for the SPB: $12 000/$4500 = 2.6667.Eq 2 would yield the following:PB 5log1/1 2 2.6667 0.10!#log 1.105log 1.3636/log
31、 1.1000!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
32、unequal annual net cash flows, acommon approach to calculating the payback period is toE1121072accumulate 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
33、.2.3.2 This approach is illustrated inTable 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 yearsaddition to the present value is accumulated in Column 4. Thepres
34、ent value of net benefits (PVNB) in Column 6 is derived bysubtracting the investment costs (Column 5) from the cumula-tive, discounted, future net cash flows (Column 4). The presentvalue of net cash flows equals investment costs at some pointin the fifth year. The payback period can be interpolated
35、asfollows:PB 5 4 years 10 22$3011!$4933 22$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 Con
36、stant 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.B2 C!*(t 5 1PB1 1 e!/1 1 i!#t5 Co(5)where:(B C)*= initial value of an annual, uniformly escalating,net cash flow, ande = constant price escalation rate per period
37、 tapplicable 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 5log1 1 SPB!1 2 1 1 i!/1 1 e!#log1 1 e!/1 1 i!#(6)where SPB = Co/(B C)*.When e is equal to i,PB 5 SPB (7)However PB is undefined and the project will never pay foritself at discount
38、rate i ifSPB 121 1 i!/1 1 e!# 2 1 (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 ene
39、rgysavings 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 5log1 1 $40 000/$8000!1 2 1.12/1.08!#log 1.08/1.12!5log1 1 520.0370!#log 0.96435log 0.8150log 0.96435 5.63 years9.3 Estimating Payback Period
40、s with Present-Value Tables:9.3.1 Present-value tables, such as those found in DiscountFactor Tables,Adjunct to Practice E 917, can be used in certaincases to estimate payback periods without a calculator.9.3.2 Uniform Net Cash Flows:9.3.2.1 The payback period for a project with uniformannual net ca
41、sh flows (B C) can be estimated by first finding,in a table of Uniform Present Value (UPV) factors for the givendiscount 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. Interpolati
42、on can be used tomore 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/$15 = 6.67.This ratio corresponds to a time period (n) of approxima
43、tely14.2 years in a table of Uniform Present Value factors based ona 12 % discount rate.9.3.3 Net Cash Flows Escalating at a Constant Rate:TABLE 1 Payback Problem With Unequal Annual Cash Flows(1) (2) (3) (4) (5) (6) = (4) (5)Years(t, s)Net Cash Flows($)(BtCt)DiscountedNet Cash FlowsA($)FBt2 Ct1 1 i
44、!tGCumulativeDiscountedNet Cash Flows($)(i 5 1sFBt2 Ct1 1 i!tGInvestmentCost($)(Co)Cumulative PVNB($)(t 5 1sFBt2 Ct1 1 i!tGCo0 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 08
45、0 61 013 +11 0137 8 000 3 619 64 632 +14 632AThe discount rate = 12 %.E11210739.3.3.1 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
46、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 used tomore closely approximate the payback period.9.3.3.2 As an example, when the discount rate
47、 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 Prese
48、nt 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 discounted payback as a funct
49、ion 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 from zero to four years and discountrates from 1 to 25 %, in 2 % increments. Fig. 2 is similar to Fig.1 except that payback periods are plotted for even values of thediscount rate, 2 to 24 %. Figs. 3 and 4 are the same respectivelyas Figs. 1 and 2, except that SPB values range from 4 to 12years and payback values range from 4 to 24 years. All of thecurves are derived
