ASTM E1121-15(2020)e1

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: E1121 − 15 (Reapproved 2020)
Standard Practice for
Measuring Payback for Investments in Buildings and
Building Systems
This standard is issued under the fixed designation E1121; 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 2.2 ASTM Adjunct:
Discount Factor Tables - Adjunct to E917 Practice for
1.1 This practice provides a recommended procedure for
Measuring Life-Cycle Costs of Buildings and Building
calculating and applying the payback method in evaluating
Systems - Includes Excel and PDF Files
building designs and building systems.
1.2 This international standard was developed in accor-
3. Terminology
dance with internationally recognized principles on standard-
3.1 Definitions—For definitions of general terms related to
ization established in the Decision on Principles for the
building construction used in this practice, refer to Terminol-
Development of International Standards, Guides and Recom-
ogyE631;andforgeneraltermsrelatedtobuildingeconomics,
mendations issued by the World Trade Organization Technical
refer to Terminology E833.
Barriers to Trade (TBT) Committee.
4. Summary of Practice
2. Referenced Documents
4.1 This practice is organized as follows:
2.1 ASTM Standards:
4.1.1 Section 2, Referenced Documents—Lists ASTM stan-
E631Terminology of Building Constructions
dards and adjuncts referenced in this practice.
E833Terminology of Building Economics
4.1.2 Section 3, Definitions—Addresses definitions of terms
E917Practice for Measuring Life-Cycle Costs of Buildings
used in this practice.
and Building Systems
4.1.3 Section 4, Summary of Practice—Outlines the con-
E964Practice for Measuring Benefit-to-Cost and Savings-
tents of the practice.
to-Investment Ratios for Buildings and Building Systems
4.1.4 Section 5, Significance and Use—Explains the signifi-
E1057Practice for Measuring Internal Rate of Return and
cance and use of this practice.
Adjusted Internal Rate of Return for Investments in
4.1.5 Section 6, Procedures—Describes step-by-step the
Buildings and Building Systems
procedures for making economic evaluations of buildings.
E1074Practice for Measuring Net Benefits and Net Savings
4.1.6 Section 7, Objectives, Alternatives, and Constraints—
for Investments in Buildings and Building Systems
Identifies and gives examples of objectives, alternatives, and
E1185Guide for Selecting Economic Methods for Evaluat-
constraints for a payback evaluation.
ing Investments in Buildings and Building Systems
E1369Guide for Selecting Techniques for Treating Uncer- 4.1.7 Section 8, Data and Assumptions—Identifies data
needed and assumptions that may be required in a payback
tainty and Risk in the Economic Evaluation of Buildings
and Building Systems evaluation.
4.1.8 Section 9, Compute Payback Period—Presents alter-
native approaches for finding the payback period.
1 4.1.9 Section 10, Applications—Explains the circumstances
This practice is under the jurisdiction of ASTM Committee E06 on Perfor-
mance of Buildings and is the direct responsibility of Subcommittee E06.81 on for which the payback method is appropriate.
Building Economics.
4.1.10 Section 11, Limitations—Discusses the limitations of
Current edition approved April 1, 2020. Published May 2020. Originally
the payback method.
approved in 1986. Last previous edition approved in 2015 as E1121-15. DOI:
10.1520/E1121-15R20E01.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
contact ASTM Customer Service at service@astm.org. 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
ϵ1
E1121 − 15 (2020)
5. Significance and Use 8.2 Both engineering data (for example, heating loads,
equipment service life, and equipment efficiencies) and eco-
5.1 The payback method is part of a family of economic
nomic data (for example, tax rates, depreciation rates and
evaluation methods that provide measures of economic perfor-
periods, system costs, energy costs, discount rate, project life,
mance of an investment. Included in this family of evaluation
price escalation rates, and financing costs) will be needed.
methods are life-cycle costing, benefit-to-cost and savings-to-
investment ratios, net benefits, and internal rates of return.
8.3 The economic measure of a project’s worth varies
considerably depending on the data and assumptions. Use
5.2 The payback method accounts for all monetary values
sensitivity analysis to test the outcome for a range of the less
associated with an investment up to the time at which cumu-
certain values in order to identify the critical parameters.
lative net benefits, discounted to present value, just pay off
Consult Guide E1369 for guidance on how to use sensitivity
initial investment costs.
analysis to measure the impact on the payback period from
5.3 Use the method to find if a project recovers its invest-
changing one or more values about which there is uncertainty.
ment cost and other accrued costs within its service life or
within a specified maximum acceptable payback period
9. Compute Payback Period
(MAPP)lessthanitsservicelife.Itisimportanttonotethatthe
decision to use the payback method should be made with care.
9.1 The payback method finds the length of time (usually
(See Section 11 on Limitations.)
specified in years) between the date of the initial project
investment and the date when the present value of cumulative
6. Procedures
future earnings or savings, net of cumulative future costs, just
6.1 Therecommendedstepsformakinganeconomicevalu-
equalstheinitialinvestment.Thisiscalledthepaybackperiod.
ation of buildings or building components are summarized as
When a zero discount rate is used, this result is referred to as
follows:
the “simple” payback (SPB). The payback period can be
6.1.1 Identify objectives, alternatives, and constraints,
determined mathematically, from present-value tables, or
6.1.2 Select an economic evaluation method,
graphically.
6.1.3 Compile data and establish assumptions,
9.2 Mathematical Solution:
6.1.4 Convert cash flows to a common time basis, and
9.2.1 To determine the payback period, find the minimum
6.1.5 Compute the economic measure and compare alterna-
solution value of PB in Eq 1.
tives.
PB
6.2 Only the step in 6.1.5, as applied to measuring payback,
t
˜
@~B 2 C !/ 11i # 5 C (1)
~ !
( t t o
is examined in detail in this practice. For elaboration on the t51
steps in 6.1.1 – 6.1.4, consult Practices E964 and E917, and
where:
Guide E1185.
B = dollar value of benefits (including earnings, cost
t
7. Objectives, Alternatives, and Constraints reductions or savings, and resale values, if any, and
adjusted for any tax effects) in period t for the
7.1 Specify the kind of building decision to be made. Make
building or system being evaluated less the coun-
explicit the objectives of the decision-maker. And identify the
terpart benefits in period tfor the mutually exclu-
alternative approaches for reaching the objectives and any
sive alternative against which it is being compared.
constraints to reaching the objectives.
˜
= dollar value of costs (excluding initial investment
C
t
7.2 An example of a building investment problem that
cost, but including operation, maintenance, and
might be evaluated with the payback method is the installation
replacement costs, adjusted for any tax effects) in
of storm windows. The objective is to see if the costs of the
period t for the building or system being evaluated
storm windows are recovered within the MAPP. The alterna-
lessthecounterpartcostinperiod tforthemutually
tives are (1) to do nothing to the existing windows or (2)to
exclusive alternative against which it is being
install storm windows. One constraint might be limited avail-
compared.
able funds for purchasing the storm windows. If the payback ˜
= net cash flows in year t,
B 2C
t t
period computed from expected energy savings and window
C = initial project investment costs, as of the base time,
o
investment costs is equal to or less than the specified MAPP,
i = discount rate per time period t, and
the investment is considered acceptable using this method.
= formula for determining the single present value
t
~11i!
factor,
7.3 Whereas the payback method is appropriate for solving
NOTE 1—Eq 1 and all others that follow assume the convention of
the problem cited in 7.2, for certain kinds of economic
discountingfromtheendoftheyear.Cashflowsareassumedtobespread
problems, such as determining the economically efficient level
evenly over the last year of payback so that partial year answers can be
of insulation, Practices E917 and E1074 are the appropriate
interpolated.
methods.
9.2.2 Uniform Net Cash Flows:
8. Data and Assumptions ˜
~ !
9.2.2.1 For the case where B 2 C is the same from year
t t
˜
8.1 Data needed to make payback calculations can be to year, denoted by ~B 2 C!, the payback period (PB) corre-
collected from published and unpublished sources, estimated, sponding to any discount rate (i) other than zero can be found
or assumed. using Eq 2.
ϵ1
E1121 − 15 (2020)
log 1/ 1 2 SPB·i 0 2 2$3011
@ ~ ~ !!# ~ !
PB 5 (2) PB 5 4 years1 5 4.38
log~11i! $4933 2 ~2$3011!
where:
9.2.3.3 Sincethepaybackperiodislessthantheperiodover
˜
SPB 5 C /~B 2 C!. (3)
which the project earns positive net benefits (seven years), and
o
When the discount rate is equal to zero,
since a shorter MAPP has not been specified, the project is
considered acceptable.
PB 5 SPB (4)
However PB is undefined when (SPB · i)≥1; that is, the
9.2.4 Net Cash Flows Escalating at a Constant Rate:
project will never pay for itself at that discount rate.
9.2.4.1 To determine the payback period when net cash
flows escalate at a constant rate, find the minimum solution of
9.2.2.2 A calculation using Eq 2 is presented for the
PB in Eq 5.
following investment problem. What would be the payback
PB
period for a project investment of $12000, earning uniform
˜ t
~B 2 C!* @~11e!/~11i!# 5 C (5)
( o
annual net cash flows of $4500 for six years?A10% discount
t51
rate applies. First solve for the SPB: $12000⁄$4500=2.6667.
where:
Eq 2 would yield the following:
˜
= initial value of an annual, uniformly escalating,
~B 2 C!*
log 1/ 1 2 2.6667·0.10
@ ~ ~ !!#
net cash flow, and
PB 5 5 log1.3636/log1.1000
~ !
log1.10
e = constant price escalation rate per period t appli-
5 ~0.1347/0.0414! 5 3.25
cable to net cash flows.
9.2.2.3 Sincethepaybackperiod(3.25years)islessthanthe
9.2.4.2 When e is not equal to i, the payback period can be
six years over which the project earns constant net benefit
calculated by using Eq 6.
returns, and since a shorter MAPP has not been specified, the
log@11~SPB!~1 2 ~11i!/~11e!!#
project is considered acceptable.
PB 5 (6)
log 11e / 11i
@~ ! ~ !#
9.2.3 Unequal Net Cash Flows:
˜
~ !
where SPB= C ⁄ B 2 C *.
9.2.3.1 For problems with unequal annual net cash flows, a
When e is equal to i,
common approach to calculating the payback period is to
accumulate the present value of net cash flows year-by-year
PB 5 SPB (7)
However PB is undefined and the project will never pay for
until the sum just equals or exceeds the original investment
itself at discount rate i if
costs. The number of years required for the two to become
equal is the payback period.
SPB 1 2 11i / 11e # 21 (8)
~ ~ ! ~ !!
9.2.3.2 ThisapproachisillustratedinTable1.Aprojectwith
9.2.4.3 If the payback period is less than the period over
seven years of unequal cash flows (Column 2) is evaluated at
which the project yields returns, the project is considered to be
a discount rate of 12%. The net cash flow in each year is
economically acceptable.
discounted at 12% to present value (Column 3). Each year’s
9.2.4.4 Eq 6 can be illustrated with the following problem.
addition to the present value is accumulated in Column 4. The
Anenergyconservationinvestmentof$40000yieldingenergy
presentvalueofnetbenefits(PVNB)inColumn6isderivedby
savings initially worth $8000 annually is to be evaluated with
subtracting the investment costs (Column 5) from the
an 8% energy price escalation and a 12% discount rate.
cumulative, discounted, future net cash flows (Column 4). The
Applying Eq 6 yields the following:
presentvalueofnetcashflowsequalsinvestmentcostsatsome
point in the fifth year. The payback period can be interpolated log 11 $40000/$8000 1 2 1.12/1.08
@ ~ !~ ~ !!#
PB 5
as follows: log~1.08/1.12!
TABLE 1 Payback Problem With Unequal Annual Cash Flows
(1) (2) (3) (4) (5) (6) = (4) − (5)
Cumulative
Discounted
Cumulative PVNB
Discounted
Net Cash Flows
Investment
A
Net Cash Flows
($)
Net Cash Flows
($)
Years Cost
($) ($)
(t, s) ($) s
˜
˜ B 2 C
(B −C )
s ˜ t t
t t B 2C
t t B 2 C
t t (C ) F G 2 C
o o t o
F G
t F G s11id
t51
11i o t
s d
11i
t51 s d
0 0 0 0 50 000 −50 000
1 10 000 8 929 8 929 −41 071
2 20 000 15 944 24 873 −25 127
3 15 000 10 677 35 550 −14 450
4 18 000 11 439 46 989 −3 011
5 14 000 7 944 54 933 +4 933
6 12 000 6 080 61 013 +11 013
7 8 000 3 619 64 632 +14 632
A
The discount rate = 12 %.
ϵ1
E1121 − 15 (2020)
log 115 20.0370 ˜
@ ~ !#
InitialInvestment⁄~B 2 C!* (10)
log0.9643
The appropriate payback period is the number of periods (n)
corresponding to that UPV* factor. Interpolation can be used
log0.8150
5 to more closely approximate the payback period.
log0.9643
9.3.3.2 As an example, when the discount rate is 12%, the
55.63years
payback period for an investment of $100 that returns net cash
9.3 Estimating Payback Periods with Present-Value Tables:
flows i
...