# ASTM C1131-10 (Reapproved 2015)

Designation: C1131 − 10 (Reapproved 2015)Standard Practice forLeast Cost (Life Cycle) Analysis of Concrete Culvert, StormSewer, and Sanitary Sewer Systems1This standard is issued under the fixed designation C1131; 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 covers procedures for least cost (life cycle)analysis (LCA) of materials, systems, or structures proposedfor use in the construction of concrete culvert, storm sewer, andsanitary sewer systems.NOTE 1—As intended in this practice, examples of analyses include, butare not limited to the following: (1) materials-pipe linings and coatings,concrete wall thicknesses, cements, additives, etc.; (2) systems-circularpipe, box sections, multiple lines, force mains, etc.; and (3) structures-wetand dry wells, pump and lift stations, etc.1.2 The LCA method includes costs associated withplanning, engineering, construction (bid price), maintenance,rehabilitation, replacement, and cost deductions for any re-sidual value at the end of the proposed project design life.1.3 For each material, system, or structure, the LCA methoddetermines in present value constant dollars, the total of allinitial and future costs over the project design life, and deductsany residual value.1.4 Major factors in the LCA method include project designlife, service life, and relevant interest and inflation rates.2. Terminology2.1 Definitions:2.1.1 constant dollars—dollars of uniform purchasingpower exclusive of inflation or deflation.2.1.1.1 Discussion—Constant dollars are costs stated atprice levels for a specific reference year, usually the particulartime that the LCA is being conducted.2.1.2 current dollars—dollars of purchasing power in whichactual prices are stated, including inflation or deflation.2.1.2.1 Discussion—Current dollars are costs stated at pricelevels in effect whenever the costs are incurred. In the absenceof inflation or deflation, current dollars are equal to constantdollars.2.1.3 direct costs—the costs of excavation, removal, anddisposal of existing materials, systems, or structures; installa-tion and testing of replacements materials, systems, or struc-tures; backfill; surface restoration, traffic rerouting, safety,utility relocations; and additional future costs required by newland uses, population growth.2.1.4 discount rate—accounts for the time value of moneyand reflects the impartiality of paying or receiving a dollar nowor at a future time.2.1.4.1 Discussion—The discount rate is used to convertcosts occurring at different times to equivalent costs at acommon time. Discount rates may be expressed in nominal orreal terms.2.1.5 future costs—costs incurred after a project has beenconstructed and operating, such as maintenance, rehabilitation,and replacement costs.2.1.6 indirect costs—the costs to the owner that users pay interms of delayed time.2.1.7 inflation rate—an increase in the volume of moneyand credit relative to available goods and services resulting ina continuing rise in the general price level.2.1.7.1 Discussion—In this practice, inflation refers toyearly change in the Producer Price Index (1).22.1.8 interest rate—the cost of borrowed money.2.1.9 maintenance costs—the annual or periodic direct andindirect costs of keeping a material, system, or structurefunctioning for the project design life; such maintenance doesnot extend the service life of the material, system, or structure.2.1.10 nominal discount rate—a discount rate that takes intoaccount both the effects of inflation and the real earningpotential of money invested over time.2.1.10.1 Discussion—When future costs and values areexpressed in current dollars, after having been adjusted forinflation, a nominal discount rate is used to convert the futurecosts and values to present value constant dollars. Users of thispractice should consult with their accountant or client todetermine the appropriate discount rate for a given project.2.1.11 original costs—costs incurred in planning, designing,and constructing a project.1This practice is under the jurisdiction of ASTM Committee C13 on ConcretePipe and is the direct responsibility of Subcommittee C13.05 on Special Projects.Current edition approved Oct. 15, 2015. Published October 2015. Originallyapproved in 1995. Last previous edition approved in 2010 as C1131 – 10ɛ1. DOI:10.1520/C1131–10R15.2The 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 States12.1.12 project design life—the number of years of useful lifethe material, system, or structure must provide.2.1.13 real discount rate—a discount rate that takes intoaccount only the real earning potential of money over time andis the differential between the interest and inflation rates.2.1.13.1 Discussion—When future costs and values areexpressed in future constant dollars, a real discount rate is usedto convert constant dollars to present value dollars. Life cycleeconomic analyses conducted in constant dollars and a realdiscount rate are often preferred to similar analyses conductedin current dollars using nominal discount rates because noforecast of the inflation rate is required.2.1.14 rehabilitation costs—the direct and indirect costs ofrehabilitating a material, system, or structure to extend theservice life of the material, system, or structure.2.1.15 replacement costs—the direct and indirect costs ofreplacing a material, system, or structure before the end of theproject design life, so it will again function as originallyintended.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 amaterial, system, or structure will provide before rehabilitationor replacement is required.2.1.17.1 Discussion—Project design life and service life areusually established by the owner or controlling agency.3. Significance and Use3.1 The significance of the LCA method is that it is acomprehensive technique for taking into account all relevantmonetary values over the project design life and provides ameasure of the total cost of the material, system, or structure.3.2 The LCA method can be effectively applied in both thepreconstruction and bid stages of projects.After bids are taken,real costs can be used instead of estimates.4. Procedures4.1 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 Struc-ture.4.1.5 Evaluate Results.4.2 Objectives, Alternatives, and Constraints—Establish thespecific objectives of the project and identify alternative waysof accomplishing the objectives. For example, alternatives fora sanitary sewer system may include a gravity flow systemversus a gravity flow system with life stations versus a singleforce main. Identify constraints, such as maximum culvert heador tail water, maximum and minimum slopes and depths ofburial, installation methods, etc.4.3 Criteria—Establish basic criteria that should be fol-lowed in applying the LCA method, including project designlife; the material, system, or structure service life; direct andindirect costs and timing of maintenance, rehabilitation andreplacement; real or nominal discount rate; and the compre-hensiveness of the LCA evaluation.4.4 Compile Data—Compile basic data required to computethe LCA of potential alternatives, including costs of planning,design, engineering and construction; maintenance costs; reha-bilitation costs; replacement costs; residual values; and thetime periods for all future costs.4.5 Compute LCA—The LCA of a material, system, orstructure can be formulated in simple terms with all costs andvalues 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, andR = direct and indirect replacement cost.4.5.1 Original Cost—Original cost is defined in Section 2and is normally developed from the engineer’s estimate or isthe actual bid price. A material, system, or structure may havea 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 dollarvalue, and subtracted from the original cost. Sincemaintenance, rehabilitation, and replacement costs may beincurred several times during the life of the project, the futurecurrent dollar value of each occurrence must be discountedback to a present constant dollar value and the values summed.4.5.2 Future Costs—Future costs are normally estimated inconstant dollar values, which are then converted to futurecurrent dollar values by an inflation factor and then discountedback to present constant dollar values by an interest factor:FV 5 A~11I!n(2)where:FV = future current dollar value,A = constant dollar value,I = inflation rate, andn = number of years in the future at which costs areincurred.PV 5FV~11i!n(3)where:PV = present constant dollar value, andI = interest or nominal discount rate.Combining Eq 2 and Eq 3:PV 5 AS11I11iDn(4)Eq 4 is usable, but requires assumptions of both interest andinflation rates. Although interest and inflation rates can varywidely, historical records indicate that the differential betweeninterest and inflation rates has been relatively stable over thelong term. Therefore, by defining an inflation/interest factor, F,as:C1131 − 10 (2015)2F 5S11I11iD(5)where:F = inflation/interest factor.Restating Eq 4:PV 5 A~F!n(6)The inflation/interest factor is virtually constant for specificdifferentials between interest and inflation rates. Therefore,utilizing the inflation/interest factor in present value calcula-tions eliminates the uncertainties and distortions due to selec-tion of possibly incompatible individual interest and inflationrates (2).NOTE 2—Table X1.1 presents the inflation/interest factor for a range ofinflation rates from 4 through 18 % and differentials between interest andinflation rates of 1 through 5 %. For different sources of financing, thedifferential between interest and inflation rates significant in constructionover a 30-year period is presented in Table X1.2.4.5.3 Residual Value—If a material, system, or structure hasa service life greater than the project design life, it would havea residual future current dollar value, which should be dis-counted back to a present constant dollar value and subtractedfrom the original cost. Using a straight-line depreciation, thepresent value of the residual value is:S 5 C~F!npSnsnD(7)where:S = residual value,C = present constant dollar cost,ns= number of years the material, system, or structureservice life exceeds the project design life,n = service life, andnp= project design life.With a lack of data to determine the residual value, a salvagevalue 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 mainte-nance costs is calculated by determining the future value ofeach cost occurrence, discounting each to a present value, andsumming all the values. Maintenance costs may be on anannual basis or estimated as a total for a periodic cycle orcovering a certain number of years, which reduces the numberof computations. The total present value of all maintenancecosts is:M 5 CM(~ Fn1F2n…1Fmn! (8)where:M = total present value of all maintenance costs,CM= constant dollar cost of a maintenance cycle,n = number of years in maintenance cycle, andm = number of maintenance cycles in project design life.If a maintenance cycle ends in a year in which rehabilitationor replacement work is scheduled, then the total present valueof maintenance costs should be refined by omitting the costs ofthat maintenance cycle. Where future maintenance costs are onan annual basis, the total present value of all maintenance costscan be determined by:M 5 CMF1 2 ~F!mn1/F 2 1G(9)4.5.5 Rehabilitation Costs—If a material, system, or struc-ture has durability or structural problems before the end of theproject design life, it may be possible to extend its service lifeby rehabilitation repairs. If the extended service life does notequal or exceed the project design life, the material, system, orstructure would probably require replacement at the end of theextended service life. A material, system, or structure mayrequire rehabilitation or replacement several times during theproject design life. The present value of rehabilitation costs iscalculated by determining the future value of each costoccurrence, discounting each to a present value and summingall values:N 5(CNFn(10)where:N = present value of rehabilitation costs,CN= constant dollar cost estimated for a rehabilitationproject,n = number of years after the project is completed thatrehabilitation costs will be incurred.4.5.6 Replacement Costs:4.5.6.1 The present value of replacement costs is zero for amaterial, system, or structure with a service life equal to orgreater than the project design life.4.5.6.2 The present value of replacement costs for amaterial, system, or structure with a service life less than theproject design life is calculated by determining the future valueof each replacement, discounting each to a present value, andsumming all values:R 5(CRFn(11)where:R = present value of replacement costs,CR= constant dollar cost of direct and indirect replacement,andn = number of years after the project is completed thatreplacement costs are estimated to occur.4.5.6.3 The future value of indirect replacement costs for amaterial, system, or structure with a service life less than theproject design life is calculated by determining user delaysduring construction (3):CRi5 AADT 3 t 3 d ~cp3 vp3 vof1cf3 vf! (12)where:AADT = AnnualAverage Daily Traffic of the roadway whichthe culvert is being installed,t = the average increase in delay to each vehicle perday, in hours,d = the number of days the project will take,cp= the average rate of person-delay, in dollars per hour(4),vp= the percentage of passenger vehicle traffic,C1131 − 10 (2015)3vof= the vehicle occupancy factor,cf= the average rate of freight-delay, in dollars per hour(5), andvf= the percentage of truck traffic.5. Keywords5.1 acceptance criteria; concrete; costs; culvert; inflationrate; interest rate; least cost analysis; life cycle analysis; pipe;procedures; project design life; sanitary sewer; service life;storm sewerAPPENDIXES(Nonmandatory Information)X1. INFLATION/INTEREST FACTORX1.1 History—The