ASTM C1131-10(2015)
(Practice)Standard Practice for Least Cost (Life Cycle) Analysis of Concrete Culvert, Storm Sewer, and Sanitary Sewer Systems
Standard Practice for Least Cost (Life Cycle) Analysis of Concrete Culvert, Storm Sewer, and Sanitary Sewer Systems
SIGNIFICANCE AND USE
3.1 The significance of the LCA method is that it is a comprehensive technique for taking into account all relevant monetary values over the project design life and provides a measure of the total cost of the material, system, or structure.
3.2 The LCA method can be effectively applied in both the preconstruction and bid stages of projects. After bids are taken, real costs can be used instead of estimates.
SCOPE
1.1 This practice covers procedures for least cost (life cycle) analysis (LCA) of materials, systems, or structures proposed for use in the construction of concrete culvert, storm sewer, and sanitary sewer systems.
Note 1: As intended in this practice, examples of analyses include, but are not limited to the following: (1) materials-pipe linings and coatings, concrete wall thicknesses, cements, additives, etc.; (2) systems-circular pipe, box sections, multiple lines, force mains, etc.; and (3) structures-wet and dry wells, pump and lift stations, etc.
1.2 The LCA method includes costs associated with planning, engineering, construction (bid price), maintenance, rehabilitation, replacement, and cost deductions for any residual value at the end of the proposed project design life.
1.3 For each material, system, or structure, the LCA method determines in present value constant dollars, the total of all initial and future costs over the project design life, and deducts any residual value.
1.4 Major factors in the LCA method include project design life, service life, and relevant interest and inflation rates.
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Designation: C1131 − 10 (Reapproved 2015)
Standard Practice for
Least Cost (Life Cycle) Analysis of Concrete Culvert, Storm
Sewer, and Sanitary Sewer Systems
This standard is issued under the fixed designation C1131; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope tion and testing of replacements materials, systems, or struc-
tures; backfill; surface restoration, traffic rerouting, safety,
1.1 Thispracticecoversproceduresforleastcost(lifecycle)
utility relocations; and additional future costs required by new
analysis (LCA) of materials, systems, or structures proposed
land uses, population growth.
foruseintheconstructionofconcreteculvert,stormsewer,and
2.1.4 discount rate—accounts for the time value of money
sanitary sewer systems.
andreflectstheimpartialityofpayingorreceivingadollarnow
NOTE1—Asintendedinthispractice,examplesofanalysesinclude,but
or at a future time.
are not limited to the following: (1) materials-pipe linings and coatings,
2.1.4.1 Discussion—The discount rate is used to convert
concrete wall thicknesses, cements, additives, etc.; (2) systems-circular
pipe, box sections, multiple lines, force mains, etc.; and (3) structures-wet
costs occurring at different times to equivalent costs at a
and dry wells, pump and lift stations, etc.
common time. Discount rates may be expressed in nominal or
1.2 The LCA method includes costs associated with real terms.
planning, engineering, construction (bid price), maintenance,
2.1.5 future costs—costs incurred after a project has been
rehabilitation, replacement, and cost deductions for any re-
constructed and operating, such as maintenance, rehabilitation,
sidual value at the end of the proposed project design life.
and replacement costs.
1.3 For each material, system, or structure, the LCAmethod
2.1.6 indirect costs—the costs to the owner that users pay in
determines in present value constant dollars, the total of all
terms of delayed time.
initial and future costs over the project design life, and deducts
2.1.7 inflation rate—an increase in the volume of money
any residual value.
and credit relative to available goods and services resulting in
1.4 Major factors in the LCAmethod include project design
a continuing rise in the general price level.
life, service life, and relevant interest and inflation rates.
2.1.7.1 Discussion—In this practice, inflation refers to
yearly change in the Producer Price Index (1).
2. Terminology
2.1.8 interest rate—the cost of borrowed money.
2.1 Definitions:
2.1.9 maintenance costs—the annual or periodic direct and
2.1.1 constant dollars—dollars of uniform purchasing
indirect costs of keeping a material, system, or structure
power exclusive of inflation or deflation.
functioning for the project design life; such maintenance does
2.1.1.1 Discussion—Constant dollars are costs stated at
not extend the service life of the material, system, or structure.
price levels for a specific reference year, usually the particular
time that the LCA is being conducted.
2.1.10 nominal discount rate—adiscountratethattakesinto
account both the effects of inflation and the real earning
2.1.2 current dollars—dollars of purchasing power in which
potential of money invested over time.
actual prices are stated, including inflation or deflation.
2.1.10.1 Discussion—When future costs and values are
2.1.2.1 Discussion—Current dollars are costs stated at price
expressed in current dollars, after having been adjusted for
levels in effect whenever the costs are incurred. In the absence
inflation, a nominal discount rate is used to convert the future
of inflation or deflation, current dollars are equal to constant
costs and values to present value constant dollars. Users of this
dollars.
practice should consult with their accountant or client to
2.1.3 direct costs—the costs of excavation, removal, and
determine the appropriate discount rate for a given project.
disposal of existing materials, systems, or structures; installa-
2.1.11 original costs—costsincurredinplanning,designing,
and constructing a project.
This practice is under the jurisdiction of ASTM Committee C13 on Concrete
Pipe and is the direct responsibility of Subcommittee C13.05 on Special Projects.
Current edition approved Oct. 15, 2015. Published October 2015. Originally
ɛ1
approved in 1995. Last previous edition approved in 2010 as C1131 – 10 . DOI:
10.1520/C1131–10R15. The boldface numbers refer to the list of references at the end of the standard.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
C1131 − 10 (2015)
2.1.12 project design life—thenumberofyearsofusefullife indirect costs and timing of maintenance, rehabilitation and
the material, system, or structure must provide. replacement; real or nominal discount rate; and the compre-
hensiveness of the LCA evaluation.
2.1.13 real discount rate—a discount rate that takes into
account only the real earning potential of money over time and
4.4 Compile Data—Compile basic data required to compute
is the differential between the interest and inflation rates.
the LCA of potential alternatives, including costs of planning,
2.1.13.1 Discussion—When future costs and values are
design, engineering and construction; maintenance costs; reha-
expressed in future constant dollars, a real discount rate is used
bilitation costs; replacement costs; residual values; and the
to convert constant dollars to present value dollars. Life cycle
time periods for all future costs.
economic analyses conducted in constant dollars and a real
4.5 Compute LCA—The LCA of a material, system, or
discount rate are often preferred to similar analyses conducted
structure can be formulated in simple terms with all costs and
in current dollars using nominal discount rates because no
values in present value constant dollars:
forecast of the inflation rate is required.
LCA 5 C 2 S1 M1N1R (1)
~ !
(
2.1.14 rehabilitation costs—the direct and indirect costs of
rehabilitating a material, system, or structure to extend the
where:
service life of the material, system, or structure.
C = original cost,
2.1.15 replacement costs—the direct and indirect costs of S = residual value,
M = maintenance cost,
replacing a material, system, or structure before the end of the
N = rehabilitation cost, and
project design life, so it will again function as originally
R = direct and indirect replacement cost.
intended.
4.5.1 Original Cost—Original cost is defined in Section 2
2.1.16 residual value—the remaining value of the material,
and is normally developed from the engineer’s estimate or is
system, or structure at the end of the project design life.
the actual bid price. A material, system, or structure may have
2.1.17 service life—the number of years of service a
a service life longer than the project design life and,
material, system, or structure will provide before rehabilitation
consequently,wouldhavearesidualfuturecurrentdollarvalue,
or replacement is required.
which must be discounted back to a present constant dollar
2.1.17.1 Discussion—Project design life and service life are
value, and subtracted from the original cost. Since
usually established by the owner or controlling agency.
maintenance, rehabilitation, and replacement costs may be
incurred several times during the life of the project, the future
3. Significance and Use
current dollar value of each occurrence must be discounted
3.1 The significance of the LCA method is that it is a
back to a present constant dollar value and the values summed.
comprehensive technique for taking into account all relevant
4.5.2 Future Costs—Future costs are normally estimated in
monetary values over the project design life and provides a
constant dollar values, which are then converted to future
measure of the total cost of the material, system, or structure.
current dollar values by an inflation factor and then discounted
3.2 The LCA method can be effectively applied in both the
back to present constant dollar values by an interest factor:
preconstruction and bid stages of projects.After bids are taken,
n
FV 5 A 11I (2)
~ !
real costs can be used instead of estimates.
where:
4. Procedures
FV = future current dollar value,
A = constant dollar value,
4.1 The procedures for determining the LCA of a material,
I = inflation rate, and
system, or structure can be summarized in five basic steps.
n = number of years in the future at which costs are
4.1.1 Identify Objective, Alternatives, and Constraints.
incurred.
4.1.2 Establish Basic Criteria.
4.1.3 Compile Data. FV
PV 5 (3)
n
4.1.4 Compute LCA for Each Material, System, or Struc- ~11i!
ture.
where:
4.1.5 Evaluate Results.
PV = present constant dollar value, and
4.2 Objectives, Alternatives, and Constraints—Establish the
I = interest or nominal discount rate.
specific objectives of the project and identify alternative ways
Combining Eq 2 and Eq 3:
of accomplishing the objectives. For example, alternatives for
n
11I
a sanitary sewer system may include a gravity flow system
PV 5 A (4)
S D
11i
versus a gravity flow system with life stations versus a single
forcemain.Identifyconstraints,suchasmaximumculverthead
Eq 4 is usable, but requires assumptions of both interest and
or tail water, maximum and minimum slopes and depths of
inflation rates. Although interest and inflation rates can vary
burial, installation methods, etc.
widely, historical records indicate that the differential between
4.3 Criteria—Establish basic criteria that should be fol- interest and inflation rates has been relatively stable over the
lowed in applying the LCA method, including project design long term.Therefore, by defining an inflation/interest factor, F,
life; the material, system, or structure service life; direct and as:
C1131 − 10 (2015)
11I an annual basis, the total present value of all maintenance costs
F 5 (5)
S D
11i can be determined by:
mn
1 2 F
~ !
where:
M 5 C (9)
F G
M
1/F 2 1
F = inflation/interest factor.
4.5.5 Rehabilitation Costs—If a material, system, or struc-
Restating Eq 4:
ture has durability or structural problems before the end of the
n
PV 5 A F (6)
~ !
project design life, it may be possible to extend its service life
by rehabilitation repairs. If the extended service life does not
The inflation/interest factor is virtually constant for specific
equal or exceed the project design life, the material, system, or
differentials between interest and inflation rates. Therefore,
structure would probably require replacement at the end of the
utilizing the inflation/interest factor in present value calcula-
extended service life. A material, system, or structure may
tions eliminates the uncertainties and distortions due to selec-
require rehabilitation or replacement several times during the
tion of possibly incompatible individual interest and inflation
project design life. The present value of rehabilitation costs is
rates (2).
calculated by determining the future value of each cost
NOTE 2—Table X1.1 presents the inflation/interest factor for a range of
occurrence, discounting each to a present value and summing
inflation rates from 4 through 18 % and differentials between interest and
all values:
inflation rates of 1 through 5 %. For different sources of financing, the
n
differential between interest and inflation rates significant in construction
N 5 C F (10)
( N
over a 30-year period is presented in Table X1.2.
where:
4.5.3 Residual Value—If a material, system, or structure has
N = present value of rehabilitation costs,
a service life greater than the project design life, it would have
C = constant dollar cost estimated for a rehabilitation
N
a residual future current dollar value, which should be dis-
project,
counted back to a present constant dollar value and subtracted
n = number of years after the project is completed that
from the original cost. Using a straight-line depreciation, the
rehabilitation costs will be incurred.
present value of the residual value is:
4.5.6 Replacement Costs:
n
s
n S D
p
S 5 C F n (7)
~ !
4.5.6.1 The present value of replacement costs is zero for a
where: material, system, or structure with a service life equal to or
greater than the project design life.
S = residual value,
C = present constant dollar cost, 4.5.6.2 The present value of replacement costs for a
n = number of years the material, system, or structure
material, system, or structure with a service life less than the
s
service life exceeds the project design life,
projectdesignlifeiscalculatedbydeterminingthefuturevalue
n = service life, and
of each replacement, discounting each to a present value, and
n = project design life.
p summing all values:
With a lack of data to determine the residual value, a salvage n
R 5 C F (11)
( R
value or cash value may be substituted or the term neglected.
where:
If accounting practices dictate, another depreciation method,
other than straight-line, may be used. R = present value of replacement costs,
C = constant dollar cost of direct and indirect replacement,
R
4.5.4 Maintenance Costs—The present value of mainte-
and
nance costs is calculated by determining the future value of
n = number of years after the project is completed that
each cost occurrence, discounting each to a present value, and
replacement costs are estimated to occur.
summing all the values. Maintenance costs may be on an
annual basis or estimated as a total for a periodic cycle or
4.5.6.3 The future value of indirect replacement costs for a
covering a certain number of years, which reduces the number
material, system, or structure with a service life less than the
of computations. The total present value of all maintenance
project design life is calculated by determining user delays
costs is:
during construction (3):
2n mn
M 5 C Fn1F …1F (8) C 5 AADT 3t 3d c 3v 3v 1c 3v (12)
~ ! ~ !
R p p of f f
M(
i
where:
where:
M = total present value of all maintenance costs,
AADT = AnnualAverage DailyTraffic of the roadway which
C = constant dollar cost of a maintenance cycle,
the culvert is being installed,
M
n = number of years in maintenance cycle, and
t = the average increase in delay to each vehicle per
m = number of maintenance cycles in project design life.
day, in hours,
d = the number of days the project will take,
If a maintenance cycle ends in a year in which rehabilitation
c = the average rate of person-delay, in dollars per hour
p
or replacement work is scheduled, then the total present value
(4),
of maintenance costs should be refined by omitting the costs
...
This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
´1
Designation: C1131 − 10 C1131 − 10 (Reapproved 2015)
Standard Practice for
Least Cost (Life Cycle) Analysis of Concrete Culvert, Storm
Sewer, and Sanitary Sewer Systems
This standard is issued under the fixed designation C1131; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
ε NOTE—Editorial changes were made throughout in April 2011.
1. Scope
1.1 This practice covers procedures for least cost (life cycle) analysis (LCA) of materials, systems, or structures proposed for
use in the construction of concrete culvert, storm sewer, and sanitary sewer systems.
NOTE 1—As intended in this practice, examples of analyses include, but are not limited to the following: (1) materials-pipe linings and coatings,
concrete wall thicknesses, cements, additives, etc.; (2) systems-circular pipe, box sections, multiple lines, force mains, etc.; and (3) structures-wet and
dry wells, pump and lift stations, etc.
1.2 The LCA method includes costs associated with planning, engineering, construction (bid price), maintenance, rehabilitation,
replacement, and cost deductions for any residual value at the end of the proposed project design life.
1.3 For each material, system, or structure, the LCA method determines in present value constant dollars, the total of all initial
and future costs over the project design life, and deducts any residual value.
1.4 Major factors in the LCA method include project design life, service life, and relevant interest and inflation rates.
2. Terminology
2.1 Definitions:
2.1.1 constant dollars—dollars of uniform purchasing power exclusive of inflation or deflation.
This practice is under the jurisdiction of ASTM Committee C13 on Concrete Pipe and is the direct responsibility of Subcommittee C13.05 on Special Projects.
Current edition approved Dec. 1, 2010Oct. 15, 2015. Published January 2011October 2015. Originally approved in 1995. Last previous edition approved in 20072010 as
ɛ1
C1131 – 95C1131 – 10 (2007). . DOI: 10.1520/C1131–10E01.10.1520/C1131–10R15.
2.1.1.1 Discussion—
Constant dollars are costs stated at price levels for a specific reference year, usually the particular time that the LCA is being
conducted.
2.1.2 current dollars—dollars of purchasing power in which actual prices are stated, including inflation or deflation.
2.1.2.1 Discussion—
Current dollars are costs stated at price levels in effect whenever the costs are incurred. In the absence of inflation or deflation,
current dollars are equal to constant dollars.
2.1.3 direct costs—the costs of excavation, removal, and disposal of existing materials, systems, or structures; installation and
testing of replacements materials, systems, or structures; backfill; surface restoration, traffic rerouting, safety, utility relocations;
and additional future costs required by new land uses, population growth.
2.1.4 discount rate—accounts for the time value of money and reflects the impartiality of paying or receiving a dollar now or
at a future time.
2.1.4.1 Discussion—
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
C1131 − 10 (2015)
The discount rate is used to convert costs occurring at different times to equivalent costs at a common time. Discount rates may
be expressed in nominal or real terms.
2.1.5 future costs—costs incurred after a project has been constructed and operating, such as maintenance, rehabilitation, and
replacement costs.
2.1.6 indirect costs—the costs to the owner that users pay in terms of delayed time.
2.1.7 inflation rate—an increase in the volume of money and credit relative to available goods and services resulting in a
continuing rise in the general price level.
2.1.7.1 Discussion—
In this practice, inflation refers to yearly change in the Producer Price Index (1).
2.1.8 interest rate—the cost of borrowed money.
2.1.9 maintenance costs—the annual or periodic direct and indirect costs of keeping a material, system, or structure functioning
for the project design life; such maintenance does not extend the service life of the material, system, or structure.
2.1.10 nominal discount rate—a discount rate that takes into account both the effects of inflation and the real earning potential
of money invested over time.
The boldface numbers refer to the list of references at the end of the standard.
2.1.10.1 Discussion—
When future costs and values are expressed in current dollars, after having been adjusted for inflation, a nominal discount rate is
used to convert the future costs and values to present value constant dollars. Users of this practice should consult with their
accountant or client to determine the appropriate discount rate for a given project.
2.1.11 original costs—costs incurred in planning, designing, and constructing a project.
2.1.12 project design life—the number of years of useful life the material, system, or structure must provide.
2.1.13 real discount rate—a discount rate that takes into account only the real earning potential of money over time and is the
differential between the interest and inflation rates.
2.1.13.1 Discussion—
When future costs and values are expressed in future constant dollars, a real discount rate is used to convert constant dollars to
present value dollars. Life cycle economic analyses conducted in constant dollars and a real discount rate are often preferred to
similar analyses conducted in current dollars using nominal discount rates because no forecast of the inflation rate is required.
2.1.14 rehabilitation costs—the direct and indirect costs of rehabilitating a material, system, or structure to extend the service
life of the material, system, or structure.
2.1.15 replacement costs—the direct and indirect costs of replacing a material, system, or structure before the end of the project
design life, so it will again function as originally intended.
2.1.16 residual value—the remaining value of the material, system, or structure at the end of the project design life.
2.1.17 service life—the number of years of service a material, system, or structure will provide before rehabilitation or
replacement is required.
2.1.17.1 Discussion—
Project design life and service life are usually established by the owner or controlling agency.
3. Significance and Use
3.1 The significance of the LCA method is that it is a comprehensive technique for taking into account all relevant monetary
values over the project design life and provides a measure of the total cost of the material, system, or structure.
3.2 The LCA method can be effectively applied in both the preconstruction and bid stages of projects. After bids are taken, real
costs can be used instead of estimates.
C1131 − 10 (2015)
4. Procedures
4.1 The procedures for determining the LCA of a material, system, or structure can be summarized in five basic steps.
4.1.1 Identify Objective, Alternatives, and Constraints.
4.1.2 Establish Basic Criteria.
4.1.3 Compile Data.
4.1.4 Compute LCA for Each Material, System, or Structure.
4.1.5 Evaluate Results.
4.2 Objectives, Alternatives, and Constraints—Establish the specific objectives of the project and identify alternative ways of
accomplishing the objectives. For example, alternatives for a sanitary sewer system may include a gravity flow system versus a
gravity flow system with life stations versus a single force main. Identify constraints, such as maximum culvert head or tail water,
maximum and minimum slopes and depths of burial, installation methods, etc.
4.3 Criteria—Establish basic criteria that should be followed in applying the LCA method, including project design life; the
material, system, or structure service life; direct and indirect costs and timing of maintenance, rehabilitation and replacement; real
or nominal discount rate; and the comprehensiveness of the LCA evaluation.
4.4 Compile Data—Compile basic data required to compute the LCA of potential alternatives, including costs of planning,
design, engineering and construction; maintenance costs; rehabilitation costs; replacement costs; residual values; and the time
periods for all future costs.
4.5 Compute LCA—The LCA of a material, system, or structure can be formulated in simple terms with all costs and values in
present value constant dollars:
LCA 5 C 2 S1 ~M1N1R! (1)
(
where:
C = original cost,
S = residual value,
M = maintenance cost,
N = rehabilitation cost, and
R = direct and indirect replacement cost.
C = original cost,
S = residual value,
M = maintenance cost,
N = rehabilitation cost, and
R = direct and indirect replacement cost.
4.5.1 Original Cost—Original cost is defined in Section 2 and is normally developed from the engineer’s estimate or is the
actual bid price. A material, system, or structure may have a service life longer than the project design life and, consequently, would
have a residual future current dollar value, which must be discounted back to a present constant dollar value, and subtracted from
the original cost. Since maintenance, rehabilitation, and replacement costs may be incurred several times during the life of the
project, the future current dollar value of each occurrence must be discounted back to a present constant dollar value and the values
summed.
4.5.2 Future Costs—Future costs are normally estimated in constant dollar values, which are then converted to future current
dollar values by an inflation factor and then discounted back to present constant dollar values by an interest factor:
n
FV 5 A 11I (2)
~ !
where:
FV = future current dollar value,
A = constant dollar value,
I = inflation rate, and
n = number of years in the future at which costs are incurred.
FV
PV 5 (3)
n
~11i!
where:
PV = present constant dollar value, and
i = interest or nominal discount rate.
PV = present constant dollar value, and
C1131 − 10 (2015)
I = interest or nominal discount rate.
Combining Eq 2 and Eq 3:
n
11I
PV 5 A (4)
S D
11i
Eq 4 is usable, but requires assumptions of both interest and inflation rates. Although interest and inflation rates can vary widely,
historical records indicate that the differential between interest and inflation rates has been relatively stable over the long term.
Therefore, by defining an inflation/interest factor, F, as:
11I
F 5 (5)
S D
11i
where:
F = inflation/interest factor.
F = inflation/interest factor.
Restating Eq 4:
n
PV 5 A F (6)
~ !
The inflation/interest factor is virtually constant for specific differentials between interest and inflation rates. Therefore, utilizing
the inflation/interest factor in present value calculations eliminates the uncertainties and distortions due to selection of possibly
incompatible individual interest and inflation rates (2).
NOTE 2—Table X1.1 presents the inflation/interest factor for a range of inflation rates from 4 through 18 % and differentials between interest and
inflation rates of 1 through 5 %. For different sources of financing, the differential between interest and inflation rates significant in construction over a
30-year period is presented in Table X1.2.
4.5.3 Residual Value—If a material, system, or structure has a service life greater than the project design life, it would have a
residual future current dollar value, which should be discounted back to a present constant dollar value and subtracted from the
original cost. Using a straight-line depreciation, the present value of the residual value is:
n
s
S D
n
p
S 5 C~F! n (7)
where:
S = residual value,
C = present constant dollar cost,
n = number of years the material, system, or structure service life exceeds the project design life,
s
n = service life, and
n = project design life.
p
With a lack of data to determine the residual value, a salvage value or cash value may be substituted or the term neglected. If
accounting practices dictate, another depreciation method, other than straight-line, may be used.
4.5.4 Maintenance Costs—The present value of maintenance costs is calculated by determining the future value of each cost
occurrence, discounting each to a present value, and summing all the values. Maintenance costs may be on an annual basis or
estimated as a total for a periodic cycle or covering a certain number of years, which reduces the number of computations. The
total present value of all maintenance costs is:
2n mn
M 5 C Fn1F …1F (8)
~ !
M(
where:
M = total present value of all maintenance costs,
C = constant dollar cost of a maintenance cycle,
M
n = number of years in maintenance cycle, and
m = number of maintenance cycles in project design life.
If a maintenance cycle ends in a year in which rehabilitation or replacement work is scheduled, then the total present value of
maintenance costs should be refined by omitting the costs of that maintenance cycle. Where future maintenance costs are on an
annual basis, the total present value of all maintenance costs can be determined by:
mn
12 ~F!
M 5 C (9)
F G
M
1/F 2 1
4.5.5 Rehabilitation Costs—If a material, system, or structure has durability or structural problems before the end of the project
design life, it may be possible to extend its service life by rehabilitation repairs. If the extended service life does not equal or exceed
the project design life, the material, system, or structure would probably require replacement at the end of the extended service
C1131 − 10 (2015)
life. A material, system, or structure may require rehabilitation or replacement several times during the project design life. The
present value of rehabilitation costs is calculated by determining the future value of each cost occurrence, discounting each to a
present value and summing all values:
n
N 5 C F (10)
N
(
where:
N = present value of rehabilitation costs,
C = constant dollar cost estimated for a rehabilitation project,
N
n = number of years after the project is completed that rehabilitation costs will be incurred.
4.5.6 Replacement Costs:
4.5.6.1 The present value of replacement costs is zero for a material, system, or structure with a service life equal to or greater
than the project design life.
4.5.6.2 The present value of replacement costs for a material, system, or structure with a ser
...
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