05 Cost Estimation

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5. Cost Estimation

5.1 Costs Associated with Constructed Facilities

The costs of a constructed facility to the owner include both the initial capital cost and thesubsequent operation and maintenance costs. Each of these major cost categories consistsof a number of cost components. The capital cost for a construction project includes theexpenses related to the initial establishment of the facility:

Land acquisition, including assembly, holding and improvement

lanning and feasibility studies

!rchitectural and engineering design

"onstruction, including materials, equipment and labor

#ield supervision of construction

"onstruction financing

$nsurance and taxes during construction

%wner&s general office overhead Equipment and furnishings not included in construction

$nspection and testing

The operation and maintenance cost in subsequent years over the project life cycleincludes the following expenses:

Land rent, if applicable

%perating staff

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Labor and material for maintenance and repairs

eriodic renovations

$nsurance and taxes

#inancing costs

(tilities

%wner&s other expenses

The magnitude of each of these cost components depends on the nature, si)e and locationof the project as well as the management organi)ation, among many considerations. Theowner is interested in achieving the lowest possible overall project cost that is consistentwith its investment objectives. $t is important for design professionals and constructionmanagers to reali)e that while the construction cost may be the single largest componentof the capital cost, other cost components are not insignificant. #or example, landacquisition costs are a major expenditure for building construction in high*density urbanareas, and construction financing costs can reach the same order of magnitude as theconstruction cost in large projects such as the construction of nuclear power plants.

#rom the owner&s perspective, it is equally important to estimate the correspondingoperation and maintenance cost of each alternative for a proposed facility in order toanaly)e the life cycle costs. The large expenditures needed for facility maintenance,especially for publicly owned infrastructure, are reminders of the neglect in the past toconsider fully the implications of operation and maintenance cost in the design stage.

$n most construction budgets, there is an allowance for contingencies or unexpected costsoccurring during construction. This contingency amount may be included within eachcost item or be included in a single category of construction contingency. The amount ofcontingency is based on historical experience and the expected difficulty of a particular

construction project. #or example, one construction firm ma+es estimates of the expectedcost in five different areas:

esign development changes,

-chedule adjustments,

eneral administration changes /such as wage rates0,

iffering site conditions for those expected, and

Third party requirements imposed during construction, such as new permits.

"ontingent amounts not spent for construction can be released near the end ofconstruction to the owner or to add additional project elements. $n this chapter, we shall

focus on the estimation of construction cost, with only occasional reference to other costcomponents. $n "hapter 1, we shall deal with the economic evaluation of a constructedfacility on the basis of both the capital cost and the operation and maintenance cost in thelife cycle of the facility. $t is at this stage that tradeoffs between operating and capitalcosts can be analy)ed.

Example 5-1: Energy project resource demands2'3

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The resources demands for three types of major energy projects investigated during theenergy crisis in the '567&s are shown in Table 8*'. These projects are: /'0 an oil shaleproject with a capacity of 87,777 barrels of oil product per day9 /40 a coal gasificationproject that ma+es gas with a heating value of 47 billions of ;ritish thermal units perday, or equivalent to about 87,777 barrels of oil product per day9 and /0 a tar sand

project with a capacity of '87,777 barrels of oil product per day.

#or each project, the cost in billions of dollars, the engineering manpower requirementfor basic design in thousands of hours, the engineering manpower requirement fordetailed engineering in millions of hours, the s+illed labor requirement for construction inmillions of hours and the material requirement in billions of dollars are shown in Table 8*'. To build several projects of such an order of magnitude concurrently could drive up thecosts and strain the availability of all resources required to complete the projects."onsequently, cost estimation often represents an exercise in professional judgmentinstead of merely compiling a bill of quantities and collecting cost data to reach a totalestimate mechanically.

TA!E 5-1


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"ost estimating is one of the most important steps in project management. ! costestimate establishes the base line of the project cost at different stages of development ofthe project. ! cost estimate at a given stage of project development represents aprediction provided by the cost engineer or estimator on the basis of available data.!ccording to the !merican !ssociation of "ost Engineers, cost engineering is defined as

that area of engineering practice where engineering judgment and experience are utili)edin the application of scientific principles and techniques to the problem of costestimation, cost control and profitability. Dirtually all cost estimation is performedaccording to one or some combination of the following basic approaches:

#roduction $unction. $n microeconomics, the relationship between the output of aprocess and the necessary resources is referred to as the production function. $nconstruction, the production function may be expressed by the relationship between thevolume of construction and a factor of production such as labor or capital. ! productionfunction relates the amount or volume of output to the various inputs of labor, materialand equipment. #or example, the amount of output may be derived as a function of

various input factors x', x4, ..., xnby means of mathematical and>or statistical methods.Thus, for a specified level of output, we may attempt to find a set of values for the inputfactors so as to minimi)e the production cost. The relationship between the si)e of abuilding project /expressed in square feet0 to the input labor /expressed in labor hours persquare foot0 is an example of a production function for construction. -everal suchproduction functions are shown in #igure * of "hapter .

Empirical cost in$erence. Empirical estimation of cost functions requires statisticaltechniques which relate the cost of constructing or operating a facility to a few importantcharacteristics or attributes of the system. The role of statistical inference is to estimatethe best parameter values or constants in an assumed cost function. (sually, this is

accomplished by means of regression analysis techniques.

%nit costs $or &ill o$ 'uantities. ! unit cost is assigned to each of the facilitycomponents or tas+s as represented by the bill of quantities. The total cost is thesummation of the products of the quantities multiplied by the corresponding unit costs.The unit cost method is straightforward in principle but quite laborious in application.The initial step is to disaggregate a process into a number of tas+s. "ollectively, thesetas+s must be completed for the construction of a facility. %nce these tas+s are definedand quantities representing these tas+s are assessed, a unit cost is assigned to each andthen the total cost is determined by summing the costs incurred in each tas+. Thedetailing level of decomposed tas+s will vary considerably from one estimate to another.

Allocation o$ joint costs.!llocations of cost from existing accounts may be used todevelop a cost function of an operation. The basic idea in this method is that eachexpenditure item can be assigned to particular characteristics of the operation. $deally, theallocation of joint costs should be causally related to the category of basic costs in anallocation process. $n many instances, however, a causal relationship between theallocation factor and the cost item cannot be identified or may not exist. #or example, inconstruction projects, the accounts for basic costs may be classified according to /'0

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labor, /40 material, /0 construction equipment, /@0 construction supervision, and /80general office overhead. These basic costs may then be allocated proportionally tovarious tas+s which are subdivisions of a project.

5.( Types o$ Construction Cost Estimates

"onstruction cost constitutes only a fraction, though a substantial fraction, of the totalproject cost. Fowever, it is the part of the cost under the control of the constructionproject manager. The required levels of accuracy of construction cost estimates vary atdifferent stages of project development, ranging from ball par+ figures in the early stageto fairly reliable figures for budget control prior to construction. -ince design decisionsmade at the beginning stage of a project life cycle are more tentative than those made at alater stage, the cost estimates made at the earlier stage are expected to be less accurate.enerally, the accuracy of a cost estimate will reflect the information available at the

time of estimation.

"onstruction cost estimates may be viewed from different perspectives because ofdifferent institutional requirements. $n spite of the many types of cost estimates used atdifferent stages of a project, cost estimates can best be classified into three majorcategories according to their functions. ! construction cost estimate serves one of thethree basic functions: design, bid and control. #or establishing the financing of a project,either a design estimate or a bid estimate is used.

)esign Estimates.#or the owner or its designated design professionals, the types of costestimates encountered run parallel with the planning and design as listed below, noting

that for each of these different estimates, the amount of design information availabletypically increases:

-creening estimates /or order of magnitude estimates0

reliminary estimates /or conceptual estimates0

etailed estimates /or definitive estimates0

Engineer&s estimates based on plans and specifications

id Estimates.#or the contractor, a bid estimate submitted to the owner for competitivebidding or negotiation consists of direct construction cost including field supervision,

plus a mar+up to cover general overhead and profits. The direct cost of construction forbid estimates is usually derived from a combination of the following approaches:

-ubcontractor quotations

uantity ta+eoffs

"onstruction procedures

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Control Estimates.#or monitoring the project during construction, a control estimate isderived from available information to establish:

;udget estimate for financing

;udgeted cost after contracting but prior to construction

Estimated cost to completion during the progress of construction.

)esign Estimates

$n the planning and design stages of a project, various design estimates reflect theprogress of the design. !t the very early stage, the screening estimate or order ofmagnitudeestimate is usually made before the facility is designed, and must thereforerely on the cost data of similar facilities built in the past. ! preliminary estimate orconceptual estimateis based on the conceptual design of the facility at the state when thebasic technologies for the design are +nown. The detailed estimateor definitive estimateis made when the scope of wor+ is clearly defined and the detailed design is in progress

so that the essential features of the facility are identifiable. The engineer's estimate isbased on the completed plans and specifications when they are ready for the owner tosolicit bids from construction contractors. $n preparing these estimates, the designprofessional will include expected amounts for contractors& overhead and profits.

The costs associated with a facility may be decomposed into a hierarchy of levels that areappropriate for the purpose of cost estimation. The level of detail in decomposing thefacility into tas+s depends on the type of cost estimate to be prepared. #or conceptualestimates, for example, the level of detail in defining tas+s is quite coarse9 for detailedestimates, the level of detail can be quite fine.

!s an example, consider the cost estimates for a proposed bridge across a river. !screening estimate is made for each of the potential alternatives, such as a tied archbridge or a cantilever truss bridge. !s the bridge type is selected, e.g. the technology ischosen to be a tied arch bridge instead of some new bridge form, a preliminary estimateis made on the basis of the layout of the selected bridge form on the basis of thepreliminary or conceptual design. Ghen the detailed design has progressed to a pointwhen the essential details are +nown, a detailed estimate is made on the basis of the welldefined scope of the project. Ghen the detailed plans and specifications are completed,an engineer&s estimate can be made on the basis of items and quantities of wor+.

id Estimates

The contractor&s bid estimates often reflect the desire of the contractor to secure the job aswell as the estimating tools at its disposal. -ome contractors have well established costestimating procedures while others do not. -ince only the lowest bidder will be thewinner of the contract in most bidding contests, any effort devoted to cost estimating is aloss to the contractor who is not a successful bidder. "onsequently, the contractor mayput in the least amount of possible effort for ma+ing a cost estimate if it believes that itschance of success is not high.

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$f a general contractor intends to use subcontractors in the construction of a facility, itmay solicit price quotations for various tas+s to be subcontracted to specialtysubcontractors. Thus, the general subcontractor will shift the burden of cost estimating tosubcontractors. $f all or part of the construction is to be underta+en by the generalcontractor, a bid estimate may be prepared on the basis of the quantity ta+eoffs from the

plans provided by the owner or on the basis of the construction procedures devised by thecontractor for implementing the project. #or example, the cost of a footing of a certaintype and si)e may be found in commercial publications on cost data which can be used tofacilitate cost estimates from quantity ta+eoffs. Fowever, the contractor may want toassess the actual cost of construction by considering the actual construction procedures tobe used and the associated costs if the project is deemed to be different from typicaldesigns. Fence, items such as labor, material and equipment needed to perform varioustas+s may be used as parameters for the cost estimates.

Control Estimates

;oth the owner and the contractor must adopt some base line for cost control during theconstruction. #or the owner, a budget estimatemust be adopted early enough for planninglong term financing of the facility. "onsequently, the detailed estimate is often used asthe budget estimate since it is sufficient definitive to reflect the project scope and isavailable long before the engineer&s estimate. !s the wor+ progresses, the budgeted costmust be revised periodically to reflect the estimated cost to completion. ! revisedestimated cost is necessary either because of change orders initiated by the owner or dueto unexpected cost overruns or savings.

#or the contractor, the bid estimate is usually regarded as the budget estimate, which willbe used for control purposes as well as for planning construction financing. The budgeted

cost should also be updated periodically to reflect the estimated cost to completion aswell as to insure adequate cash flows for the completion of the project.

Example 5-": *creening estimate o$ a grouting seal &eneath a land$ill 243

%ne of the methods of isolating a landfill from groundwater is to create a bowl*shapedbottom seal beneath the site as shown in #igure 8*'. The seal is constructed by pumpingor pressure*injecting grout under the existing landfill. Foles are bored at regular intervalsthroughout the landfill for this purpose and the grout tubes are extended from the surfaceto the bottom of the landfill. ! layer of soil at a minimum of 8 ft. thic+ is left between thegrouted material and the landfill contents to allow for irregularities in the bottom of the

landfill. The grout liner can be between @ and 1 feet thic+.

! typical material would be ortland cement grout pumped under pressure through tubesto fill voids in the soil. This grout would then harden into a permanent, impermeableliner. The wor+ items in this project include /'0 drilling exploratory bore holes at 87 ftintervals for grout tubes, and /40 pumping grout into the voids of a soil layer between @and 1 ft thic+. The quantities for these two items are estimated on the basis of the landfillarea:

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A acres H /A0/@,817 ft4>acre0 H @A,@A7 ft4 /!s an approximation, use 17,777 ft4 toaccount for the bowl shape0. The number of bore holes in a 87 ft by 87 ft grid patterncovering 17,777 ft4is given by:

'@@

0870/87/

777,:17 4

=

ftft

ft

Figure 5-1:rout ;ottom -eal Liner at a Landfill

The average depth of the bore holes is estimated to be 47 ft. Fence, the total amount ofdrilling is /'@@0/470 H 4,AA7 ft. The volume of the soil layer for grouting is estimated as:for a @ ft layer, volume H /@ ft0/17,777 ft40 H ',@@7,777 ft

for a 1 ft layer, volume H /1 ft0/17,777 ft4

0 H 4,'17,777 ft

$t is estimated from soil tests that the voids in the soil layer are between 47I and 7I ofthe total volume.Thus, for a @ ft soil layer:grouting in 47I voids H /47I0/',@@7,7770 H 4AA,777 ftgrouting in 7 I voids H /7I0/',@@7,7770 H @4,777 ft

and for a 1 ft soil layer:grouting in 47I voids H /47I0/4,'17,7770 H @4,777 ftgrouting in 7I voids H /7I0/4,'17,7770 H 1@A,777 ft

The unit cost for drilling exploratory bore holes is estimated to be between ? and ?'7per foot /in '56A dollars0 including all expenses. Thus, the total cost of boring will bebetween /4,AA70/0 H ? A,1@7 and /4,AA70/'70 H ?4A,A77.

The unit cost of ortland cement grout pumped into place is between ?@ and ?'7 percubic foot including overhead and profit. $n addition to the variation in the unit cost, thetotal cost of the bottom seal will depend upon the thic+ness of the soil layer grouted andthe proportion of voids in the soil.

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That is:for a @ ft layer with 47I voids, grouting cost H ?','84,777 to ?4,AA7,777for a @ ft layer with 7I voids, grouting cost H ?',64A,777 to ?@,47,777for a 1 ft layer with 47I voids, grouting cost H ?',64A,777 to ?@,47,777for a 1 ft layer with 7I voids, grouting cost H ?4,854,777 to ?1,@A7,777

The total cost of drilling bore holes is so small in comparison with the cost of groutingthat the former can be omitted in the screening estimate. #urthermore, the range of unitcost varies greatly with soil characteristics, and the engineer must exercise judgment innarrowing the range of the total cost. !lternatively, additional soil tests can be used tobetter estimate the unit cost of pumping grout and the proportion of voids in the soil.

-uppose that, in addition to ignoring the cost of bore holes, an average value of a 8 ft soillayer with 48I voids is used together with a unit cost of ? 6 per cubic foot of ortlandcement grouting. $n this case, the total project cost is estimated to be:/8 ft0/17,777 ft40/48I0/?6>ft0 H ?,'87,777

!n important point to note is that this screening estimate is based to a large degree onengineering judgment of the soil characteristics, and the range of the actual cost may varyfrom ? ','84,777 to ? 1,@A7,777 even though the probabilities of having actual costs atthe extremes are not very high.

Example 5-(: Example o$ engineer+s estimate and contractors+ &ids 23

The engineer&s estimate for a project involving '@ miles of $nterstate 67 roadway in (tahwas ?47,587,A85. ;ids were submitted on =arch '7, '5A6, for completing the projectwithin 47 wor+ing days. The three low bidders were:

'. ;all, ;all J ;rosame, $nc., anville "! ?'@,'45,65A

4. Bational rojects, $nc., hoenix, !< ?'8,A',6A5

. Kiewit Gestern "o., =urray, (tah ?'A,'@1,6'@

$t was astounding that the winning bid was 4I below the engineer&s estimate. Even thethird lowest bidder was 'I below the engineer&s estimate for this project. The disparityin pricing can be attributed either to the very conservative estimate of the engineer in the(tah epartment of Transportation or to area contractors who are hungrier than usual towin jobs.

The unit prices for different items of wor+ submitted for this project by /'0 ;all, ;all J;rosame, $nc. and /40 Bational rojects, $nc. are shown in Table 8*4. The similarity oftheir unit prices for some items and the disparity in others submitted by the twocontractors can be noted.

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TA!E 5-":(nit rices in Two "ontractors& ;ids for


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TA!E 5-":(nit rices in Two "ontractors& ;ids for


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diseconomies exist. $f the average cost per unit of capacity is declining, then scaleeconomies exist. "onversely, scale diseconomies exist if average costs increase withgreater si)e. Empirical data are sought to establish the economies of scale for varioustypes of facility, if they exist, in order to ta+e advantage of lower costs per unit ofcapacity. Let x be a variable representing the facility capacity, and y be the resulting

construction cost. Then, a linear cost relationship can be expressed in the form:/8.'0 baxy +=

where a and b are positive constants to be determined on the basis of historical data.Bote that in Equation /8.'0, a fixed cost of y H a corresponds to x H 7 is implied as shownin #igure 8*4.

Figure 5-":Linear "ost


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where a and b are positive constants to be determined on the basis of historical data. #or 7M b M ', Equation /8.40 represents the case of increasing returns to scale, and for b 9gt ',the relationship becomes the case of decreasing returns to scale, as shown in #igure 8*.

Figure 5-(:Bonlinear "ost


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/8.10

=

nn Q

Qm

y

ylnln

The exponential rule can be applied to estimate the total cost of a complete facility or the

cost of some particular component of a facility.

Example 5-,: )etermination o$ m $or the exponential rule

Figure 5-,:Log*Log -cale raph of Exponential n0 and ln/y>yn0 and a linear relationship between these logarithmicratios is shown in #igure 8*@. #or />n0 H ' or ln/>n0 H 7, ln/y>yn0 H 79 and for >nH4 or ln/>n0 H 7.7', ln/y>yn0 H 7.'618. -ince m is the slope of the line in the figure, itcan be determined from the geometric relation as follows:

[email protected]:7'.7

'618.7==m

#or ln/y>yn0 H 7.'618, y>ynH '.8, while the corresponding value of >nis 4. $n words,for m H 7.8A8, the cost of a plant increases only '.8 times when the capacity is doubled.

Example 5-5: Cost exponents $or water and wastewater treatment plants 2@3

The magnitude of the cost exponent m in the exponential rule provides a simple measureof the economy of scale associated with building extra capacity for future growth andsystem reliability for the present in the design of treatment plants. Ghen m is small, thereis considerable incentive to provide extra capacity since scale economies exist asillustrated in #igure 8*. Ghen m is close to ', the cost is directly proportional to thedesign capacity. The value of m tends to increase as the number of duplicate units in asystem increases. The values of m for several types of treatment plants with different

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plant components derived from statistical correlation of actual construction costs areshown in Table 8*.

TA!E 5-( Estimated Dalues of "ost Exponents for Gater Treatment lants

Treatment plant

type

Exponent

m

"apacity range

/millions of gallons per day0'. Gater treatment 7.16 '*'77

4. Gaste treatment

rimary with digestion /small0 7.88 7.'*'7

rimary with digestion /large0 7.68 7.6*'77

Tric+ling filter 7.17 7.'*47

!ctivated sludge 7.66 7.'*'77

-tabili)ation ponds 7.86 7.'*'77

-ource: ata are collected from various sources by .=. ;erthouex. -ee the references in his article forthe primary sources.

Example 5-: *ome istorical Cost )ata $or the Exponential /ule

The exponential rule as represented by Equation /8.@0 can be expressed in a differentform as:

m

n

nm

Q

yKwhereKQy

0/ ==

$f m and K are +nown for a given type of facility, then the cost y for a proposed newfacility of specified capacity can be readily computed.

TA!E 5-, "ost #actors of rocessing (nits for Treatment lants

rocessingunit

(nit ofcapacity

K Dalue/'51A ?0

mvalue

'. Liquid processing

%il separation mgd 8A,777 7.A@

Fydroclone degritter mgd ,A47 7.8

rimary sedimentation ft4 55 7.17

#urial clarifier ft4 677 7.86

-ludge aeration basin mil. gal. '67,777 7.87Tic+ling filter ft4 4',777 7.6'

!erated lagoon basin mil. gal. @1,777 7.16

Equali)ation mil. gal. 64,777 7.84

Beutrali)ation mgd 17,777 7.67

4. -ludge handling

igestion ft 16,877 7.85

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Dacuum filter ft4 5,17 7.A@

"entrifugelb dry

solids>hr'A 7.A'

-ource: ata are collected from various sources by .=. ;erthouex. -ee the references in his article forthe primary sources.

The estimated values of K and m for various water and sewage treatment plantcomponents are shown in Table 8*@. The K values are based on '51A dollars. The rangeof data from which the K and m values are derived in the primary sources should beobserved in order to use them in ma+ing cost estimates. !s an example, ta+e K H ?55and m H 7.17 for a primary sedimentation component in Table 8*@. #or a proposed newplant with the primary sedimentation process having a capacity of '8,777 sq. ft., theestimated cost /in '51A dollars0 is:

y H /?550/'8,77707.17H ?'4A,777.

5.5 %nit Cost 0ethod o$ Estimation

$f the design technology for a facility has been specified, the project can be decomposedinto elements at various levels of detail for the purpose of cost estimation. The unit costfor each element in the bill of quantities must be assessed in order to compute the totalconstruction cost. This concept is applicable to both design estimates and bid estimates,although different elements may be selected in the decomposition. #or design estimates,the unit cost method is commonly used when the project is decomposed into elements atvarious levels of a hierarchy as follows:

'. #reliminary Estimates. The project is decomposed into major structural systemsor production equipment items, e.g. the entire floor of a building or a coolingsystem for a processing plant.

4. )etailed Estimates. The project is decomposed into components of various majorsystems, i.e., a single floor panel for a building or a heat exchanger for a coolingsystem.

. Engineer+s Estimates. The project is decomposed into detailed items of variouscomponents as warranted by the available cost data. Examples of detailed itemsare slabs and beams in a floor panel, or the piping and connections for a heatexchanger.

#or bid estimates, the unit cost method can also be applied even though the contractormay choose to decompose the project into different levels in a hierarchy as follows:

'. *u&contractor uotations. The decomposition of a project into subcontractoritems for quotation involves a minimum amount of wor+ for the generalcontractor. Fowever, the accuracy of the resulting estimate depends on thereliability of the subcontractors since the general contractor selects one amongseveral contractor quotations submitted for each item of subcontracted wor+.

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4. uantity Ta2eo$$s. The decomposition of a project into items of quantities thatare measured /or taken off0 from the engineer&s plan will result in a proceduresimilar to that adopted for a detailed estimate or an engineer&s estimate by thedesign professional. The levels of detail may vary according to the desire of thegeneral contractor and the availability of cost data.

. Construction #rocedures. $f the construction procedure of a proposed project isused as the basis of a cost estimate, the project may be decomposed into itemssuch as labor, material and equipment needed to perform various tas+s in theprojects.

*imple %nit Cost Formula

-uppose that a project is decomposed into n elements for cost estimation. Let ibe thequantity of the ithelement and uibe the corresponding unit cost. Then, the total cost of theproject is given by:

/8.60 ==

n

i ii

Quy'

where n is the number of units. ;ased on characteristics of the construction site, thetechnology employed, or the management of the construction process, the estimated unitcost, uifor each element may be adjusted.

Factored Estimate Formula

! special application of the unit cost method is the Nfactored estimateN commonly used inprocess industries. (sually, an industrial process requires several major equipmentcomponents such as furnaces, towers drums and pump in a chemical processing plant,plus ancillary items such as piping, valves and electrical elements. The total cost of aproject is dominated by the costs of purchasing and installing the major equipmentcomponents and their ancillary items. Let "ibe the purchase cost of a major equipmentcomponent i and fibe a factor accounting for the cost of ancillary items needed for theinstallation of this equipment component i. Then, the total cost of a project is estimatedby:

/8.A0 0'/'''

i

n

i

i

n

i

ii

n

i

i fCCfCy +=+= ===

where n is the number of major equipment components included in the project. The

factored method is essentially based on the principle of computing the cost of ancillaryitems such as piping and valves as a fraction or a multiple of the costs of the majorequipment items. The value of "imay be obtained by applying the exponential rule so theuse of Equation /8.A0 may involve a combination of cost estimation methods.

Formula ased on !a&or3 0aterial and E'uipment

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"onsider the simple case for which costs of labor, material and equipment are assigned toall tas+s. -uppose that a project is decomposed into n tas+s. Let ibe the quantity ofwor+ for tas+ i, =ibe the unit material cost of tas+ i, E ibe the unit equipment rate for tas+i, Libe the units of labor required per unit of i, and Gibe the wage rate associated withLi. $n this case, the total cost y is:

/8.50 ==

++==n

i

iiiii

n

i

i LWEQyy''

0/

Bote that GiLi yields the labor cost per unit of i, or the labor unit cost of tas+ i."onsequently, the units for all terms in Equation /8.50 are consistent.

Example 5-4: )ecomposition o$ a &uilding $oundation into design and construction

elements.

The concept of decomposition is illustrated by the example of estimating the costs of abuilding foundation excluding excavation as shown in Table 8*8 in which thedecomposed design elements are shown on hori)ontal lines and the decomposed contractelements are shown in vertical columns. #or a design estimate, the decomposition of theproject into footings, foundation walls and elevator pit is preferred since the designer caneasily +eep trac+ of these design elements9 however, for a bid estimate, thedecomposition of the project into formwor+, reinforcing bars and concrete may bepreferred since the contractor can get quotations of such contract items moreconveniently from specialty subcontractors.

TA!E 5-5 $llustrative ecomposition of ;uilding #oundation"osts

esignelements

"ontract elements

#ormwor+


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TA!E 5- $llustrative "ost Estimate (sing Labor, =aterial and Equipment hr 7.4 hr>ft4 ?.7>ft4 ?87,@77

lb 7.>lb '8>hr 7.7@ hr>lb 7.1>lb @,@@7

"oncrete 877 yd 8.7>yd 87>yd '8>hr 7.A hr>yd '4.7>yd ,877

Total ?AA,77

5. 0ethods $or Allocation o$ 6oint Costs

The principle of allocating joint costs to various elements in a project is often used in costestimating. ;ecause of the difficulty in establishing casual relationship between each

element and its associated cost, the joint costs are often prorated in proportion to the basiccosts for various elements. %ne common application is found in the allocation of fieldsupervision cost among the basic costs of various elements based on labor, material andequipment costs, and the allocation of the general overhead cost to various elementsaccording to the basic and field supervision cost. -uppose that a project is decomposedinto n tas+s. Let y be the total basic cost for the project and y ibe the total basic cost fortas+ i. $f # is the total field supervision cost and # iis the prorating of that cost to tas+ i,then a typical proportional allocation is:

/8.'70

=

y

y!! ii

-imilarly, let ) be the total direct field cost which includes the total basic cost and thefield supervision cost of the project, and ) ibe the direct field cost for tas+ i. $f is thegeneral office overhead for prorating to all tas+s, and iis the share for tas+ i, then:

/8.''0

="

"## ii

#inally, let w be the grand total cost of the project which includes the direct field cost andthe general overhead cost charged to the project and wibe that attributable tas+ i. Then,

/8.'40 =

+=+=n

i

iy!y!"'

and

'5


20/44

/8.'0 =

+=+=n

i

i"#"#w'

Example 5-7: #rorated costs $or $ield super8ision and o$$ice o8erhead

$f the field supervision cost is ?',4@8 for the project in Table 8*1 /Example 8*A0 with atotal direct cost of ?AA,77, find the prorated field supervision costs for various elementsof the project. #urthermore, if the general office overhead charged to the project is @I ofthe direct field cost which is the sum of basic costs and field supervision cost, find theprorated general office overhead costs for various elements of the project.

#or the project, y H ?AA,77 and # H ?',4@8. Fence:

) H ',4@8 O AA,77 H ?'7',8@8

H /7.7@0/'7',8@80 H ?@,714w H '7',8@8 O @,714 H ?'78,176

The results of the proration of costs to various elements are shown in Table 8*6.

escription;asic cost

yi

!llocatedfield supervision

cost#i

Totalfield cost

)i

!llocatedoverhead

costi

Total costLi

#ormwor+ ?87,@77 ?6,817 ?86,517 ?4,'5 ?17,465


21/44

of the total cost. Even though material costs exceed labor costs, only the labor costs areused in allocating overhead. !lthough this type of allocation method is common inindustry, the arbitrary allocation of joint costs introduces unintended cross subsidiesamong products and may produce adverse consequences on sales and profits. #orexample, a particular type of part may incur few overhead expenses in practice, but this

phenomenon would not be reflected in the standard cost report.

TA!E 5- -tandard "ost


22/44

"atalogs of vendors& data on important features and specifications relating to their

products for which cost quotations are either published or can be obtained. !major source of vendors& information for building products is (weets' Catalogpublished by =craw*Fill $nformation -ystems "ompany.

eriodicals containing construction cost data and indices. %ne source of such

information is E)$, the =craw*Fill "onstruction Gee+ly, which containsextensive cost data including quarterly cost reports. Cost Engineering, a journal ofthe !merican -ociety of "ost Engineers, also publishes useful cost dataperiodically.

"ommercial cost reference manuals for estimating guides. !n example is the

*uilding Construction Cost +atapublished annually by construct process adopted by the owner is fully understood by all.Ghen inflation adjustment provisions have very different ris+ implications to variousparties, the price level changes will also be treated differently for various situations.

5. Cost ndices

-ince historical cost data are often used in ma+ing cost estimates, it is important to notethe price level changes over time. Trends in price changes can also serve as a basis forforecasting future costs. The input price indices of labor and>or material reflect the pricelevel changes of such input components of construction9 the output price indices, whereavailable, reflect the price level changes of the completed facilities, thus to some degreealso measuring the productivity of construction.

44


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! price index is a weighted aggregate measure of constant quantities of goods andservices selected for the pac+age. The price index at a subsequent year represents aproportionate change in the same weighted aggregate measure because of changes inprices. Let ltbe the price index in year t, and l tO'be the price index in the following yeartO'. Then, the percent change in price index for year tO' is:

/8.'@0 0'77/'

'

t

ttt

l

ll,

= ++

or

/8.'80 0'/ '' += += ttt ,--

$f the price index at the base year tH7 is set at a value of '77, then the price indices l ',l4...lnfor the subsequent years tH',4...n can be computed successively from changes in thetotal price charged for the pac+age of goods measured in the index. The best*+nownindicators of general price changes are the ross omestic roduct /0 deflatorscompiled periodically by the (.-. epartment of "ommerce, and the consumer priceindex /"$0 compiled periodically by the (.-. epartment of Labor. They are widelyused as broad gauges of the changes in production costs and in consumer prices foressential goods and services.

-pecial price indices related to construction are also collected by industry sources sincesome input factors for construction and the outputs from construction maydisproportionately outpace or fall behind the general price indices. Examples of specialprice indices for construction input factors are the wholesale ;uilding =aterial rice and;uilding Trades (nion Gages, both compiled by the (.-. epartment of Labor. $naddition, the construction cost index and the building cost index are reported periodicallyin theEngineering )ews.$ecord /E)$0. ;oth EB< cost indices measure the effects ofwage rate and material price trends, but they are not adjusted for productivity, efficiency,competitive conditions, or technology changes.

"onsequently, all these indices measure only the price changes of respective constructioninput factorsas represented by constant quantities of material and>or labor. %n the otherhand, the price indices of various types of completed facilities reflect the price changes ofconstruction output including all pertinent factors in the construction process. Thebuilding construction output indices compiled by Turner "onstruction "ompany andFandy*Ghitman (tilities are compiled in the (.-. (tatistical bstractspublished eachyear.

#igure 8*6 and Table 8*5 show a variety of (nited -tates indices, including the rossBational roduct /B0 price deflator, the EB< building index, the Fandy Ghitman(tilities ;uildings, and the Turner "onstruction "ompany ;uilding "ost $ndex from'567 to '55A, using '554 as the base year with an index of '77.

4


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TA!E 5-7 -ummary of $nput and %utput rice $ndices, '567*'55A

ear '567 '568 '5A7 '5A8 '557 '55 '55@ '558 '551 '556 '55A

Turner"onstruction *

;uildings4A @@ 1' A 5A '74 '78 '75 ''4 ''6 '44

EB< * ;uildings 4A @@ 1A.8 A8.6 58.@ '78.6 '75.A '75.A '' ''A.6 ''5.6

(- "ensus *"omposite

4A @@ 1A.1 A4.5 5A.8 '7.6 '7A ''4.8 ''8 ''A.6 '44

Fandy*Ghitmanublic (tility

' 8@ 6A 57 '7' '78 ''4 ''8 ''A '44 '4

B eflator 8 @5 67 54 5@ '7 '78 '7A ''7 '' ''@

Bote: $ndex H '77 in base year of '554.

Figure 5-4Trends for (- price indices.

4@


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Figure 5-rice and cost indices for construction.

-ince construction costs vary in different regions of the (nited -tates and in all parts ofthe world, locational indicesshowing the construction cost at a specific location relativeto the national trend are useful for cost estimation. EB< publishes periodically the indicesof local construction costs at the major cities in different regions of the (nited -tates aspercentages of local to national costs.

Ghen the inflation rate is relatively small, i.e., less than '7I, it is convenient to select asingle price index to measure the inflationary conditions in construction and thus to dealonly with a single set of price change rates in forecasting. Let j tbe the price change ratein year tO' over the price in year t. $f the base year is denoted as year 7 /tH70, then theprice change rates at years ',4,...t are j',j4,...jt, respectively. Let !tbe the cost in year texpressed in base*year dollars and !t& be the cost in year t expressed in then*currentdollars. Then:

/8.'10

=++++=

7

'4'

&0'0/'0.../'0/'/

-

-',,,,'' tttttt

"onversely

/8.'60

=++++=

t

ttttt-

-',,,,'' 7&''

'

4

'

'

'&0'/0'.../0'/0'/

$f the prices of certain +ey items affecting the estimates of future benefits and costs areexpected to escalate faster than the general price levels, it may become necessary to

48


26/44

consider the differential price changes over and above the general inflation rate. #orexample, during the period between '56 through '565, it was customary to assume thatfuel costs would escalate faster than the general price levels. Gith hindsight in '5A, theassumption for estimating costs over many years would have been different. ;ecause ofthe uncertainty in the future, the use of differential inflation rates for special items should

be judicious.

#uture forecasts of costs will be uncertain: the actual expenses may be much lower ormuch higher than those forecasted. This uncertainty arises from technological changes,changes in relative prices, inaccurate forecasts of underlying socioeconomic conditions,analytical errors, and other factors. #or the purpose of forecasting, it is often sufficient toproject the trend of future prices by using a constant rate j for price changes in each yearover a period of t years, then

/8.'A0 t

tt ,'' 0'/& +=

and

/8.'50 t

tt ,'' += 0'/&

Estimation of the future rate increase j is not at all straightforward. ! simple expedient isto assume that future inflation will continue at the rate of the previous period:

/8.470 '= t,,

! longer term perspective might use the average increase over a hori)on of n past

periods:

/8.4'0 =

=n

i

t

n

,,

'

'

=ore sophisticated forecasting models to predict future cost increases include correctionsfor items such as economic cycles and technology changes.

Example 5-1": Changes in highway and &uilding costs

Table 8*'7 shows the change of standard highway costs from '5@7 to '557, and Table 8*'' shows the change of residential building costs from '567 to '557. $n each case, therate of cost increase was substantially above the rate of inflation in the decade of the'567s.. $ndeed, the real cost increase between '567 and '5A7 was in excess of threepercent per year in both cases.

41


27/44

Fowever, these data also show some cause for optimism. #or the case of the standardhighway, real cost decreasestoo+ place in the period from l567 to l557. (nfortunately,comparable indices of outputs are not being compiled on a nationwide basis for othertypes of construction.

TA!E 5-19 "omparison of -tandard Fighway "osts, '5@7*'557

ear-tandard

highway cost/'564H'770

rice deflator/'564H'770

-tandard highwayreal cost

/'564H'770

ercentagechange

per year

'5@7 41 45 57

'587 @A 8@ A5 *7.'I

'517 8A 15 A@ *7.1I

'567 5' 54 55 O'.AI

'5A7 488 '65 '@ O@.@I

'557 4A@ 4@6 ''8 *4.AI

-ource: (tatistical bstract of the 1nited (tates2 deflator is used for the price deflator index.

TA!E 5-11 "omparison of


28/44

8. !djust for different regulatory constraints1. !djust for local factors for the new facility

-ome of these adjustments may be done using compiled indices, whereas others mayrequire field investigation and considerable professional judgment to reflect differences

between a given project and standard projects performed in the past.

Example 5-1(: *creening estimate $or a re$inery

The total construction cost of a refinery with a production capacity of 477,777 bbl>day inary, $ndiana, completed in 477' was ?'77 million. $t is proposed that a similar refinerywith a production capacity of 77,777 bbl>day be built in Los !ngeles, "alifornia, forcompletion in 477. #or the additional information given below, ma+e an order ofmagnitude estimate of the cost of the proposed plant.

'. $n the total construction cost for the ary, $ndiana, plant, there was an item of ?8million for site preparation which is not typical for other plants.4. The variation of si)es of the refineries can be approximated by the exponential

rule, Equation /8.@0, with m H 7.1.. The inflation rate is expected to be AI per year from '555 to 477.@. The location index was 7.54 for ary, $ndiana and '.'@ for Los !ngeles in '555.

These indices are deemed to be appropriate for adjusting the costs between thesetwo cities.

8. Bew air pollution equipment for the L! plant costs ?6 million in 477 dollars /notrequired in the ary plant0.

1. The contingency cost due to inclement weather delay will be reduced by the

amount of 'I of total construction cost because of the favorable climate in L!/compared to ary0.

%n the basis of the above conditions, the estimate for the new project may be obtained asfollows:

'. Typical cost excluding special item at ary, $B is?'77 million * ?8 million H ? 58 million

4. !djustment for capacity based on the exponential law yields/?580/77,777>477,77707.1 H /580/'.807.1 H ?'4'.4 million

. !djustment for inflation leads to the cost in 477 dollars as/?'4'.40/'.7A0@ H ?'[email protected] million

@. !djustment for location index gives/?'[email protected]/'.'@>7.540 H [email protected] million

8. !djustment for new pollution equipment at the L! plant [email protected] O ?6 H ?4''.1 million

1.


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-ince there is no adjustment for the cost of construction financing, the order of magnitudeestimate for the new project is ?475.8 million.

Example 5-1,: Conceptual estimate $or a chemical processing plant

$n ma+ing a preliminary estimate of a chemical processing plant, several major types ofequipment are the most significant parameters in affecting the installation cost. The costof piping and other ancillary items for each type of equipment can often be expressed as apercentage of that type of equipment for a given capacity. The standard costs for themajor equipment types for two plants with different daily production capacities are asshown in Table 8*'4. $t has been established that the installation cost of all equipment fora plant with daily production capacity between '77,777 bbl and @77,777 bbl can best beestimated by using linear interpolation of the standard data.

TA!E 5-1" "ost ata for Equipment and !ncillary $tems

Equipmenttype

Equipment "ost /?'7770"ost of ancillary items

as I of equipment cost /?'7770

'77,777 bbl @77,777 bbl '77,777 bbl @77,777 bbl

#urnace ,777 '7,777 @7I 7I

Tower 4,777 1,777 @8I 8I

rum ',877 8,777 87I @7I

ump, etc. ',777 @,777 17I 87I

! new chemical processing plant with a daily production capacity of 477,777 bbl is to beconstructed in =emphis, TB in four years. etermine the total preliminary cost estimateof the plant including the building and the equipment on the following basis:

'. The installation cost for equipment was based on linear interpolation from Table8*'4, and adjusted for inflation for the intervening four years. Ge expect inflationin the four years to be similar to the period '557*'55@ and we will use the Beflator index.

4. The location index for equipment installation is 7.58 for =emphis, TB, incomparison with the standard cost.

. !n additional cost of ?877,777 was required for the local conditions in =emphis,TB.

The solution of this problem can be carried out according to the steps as outlined in theproblem statement:

'. The costs of the equipment and ancillary items for a plant with a capacity of477,777 bbl can be estimated by linear interpolation of the data in Table 8*'4, andthe results are shown in Table 8*'.

45


30/44

TA!E 5-1(


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(sing the unit prices in the bid of contractor ' for the quantities specified by the engineerin Table 8*4 /Example 8*0, we can compute the total bid price of contractor ' for theroadway project. The itemi)ed costs for various wor+ items as well as the total bid priceare shown in Table 8*'@.

TA!E 5-1,:;id rice of "ontractor ' in a Fighway roject$tems (nit uantity (nit price $tem cost

=obili)ation ls ' ''8,777 ''8,777

@&& ton 14,477 @.87 ',145,577

Lean concrete, @&& thic+ sy A47,'7 .'7 4,8@4,51'

"", pavement, '7&& thic+ sy 61,7'7 '7.57 6,158,875

"oncrete, ci !! /!E0 ls ' 477,777 477,777

-mall structure cy 87 877 48,777

;arrier, precast lf 6,547 '8.77 ''A,A77

#latwor+, @&& thic+ sy 6,@'7 '7.77 6@,'77

'7&& thic+ sy @,4@' 47.77 A@,A47

-lope protection sy 4,'7@ 48.77 84,177

=etal, end section, '8&& ea 5 '77 ,577

'A&& ea '87 @87

ost, right*of*way, modification lf @,677 .77 '@,'77

-alvage and relay pipe lf ',1A7 8.77 A,@77Loose riprap cy 4 @7.77 ',4A7

;raced posts ea 8@ '77 8,@77

elineators, type $ lb ',7 '4.77 '8,517

type $$ ea '@7 '8.77 4,'77

"onstructive signs fixed sf 84,177 7.'7 8,417

;arricades, type $$$ lf 45,877 7.47 8,577

Garning lights day 1,77 7.'7 17

avement mar+ing, epoxy material

;lac+ gal @68 57.77 @4,687

ellow gal 6@7 57.77 11,177

Ghite gal 5A8 57.77 AA,187

lowable, one*way white ea @4 87.77 '6,'77

Topsoil, contractor furnished cy 417 '7.77 4,177

-eedling, method ! acr '7 '87 '8,@87

Excelsior blan+et sy 877 4.77 ',777

"orrugated, metal pipe, 'A&& lf 8A7 47.77 '',177

'


32/44

TA!E 5-1,:;id rice of "ontractor ' in a Fighway roject

$tems (nit uantity (nit price $tem cost

olyethylene pipe, '4&& lf 4,487 '8.77 ,687

"atch basin grate and frame ea 8 87 '4,487

Equal opportunity training hr 'A,777 7.A7 '@,@77

ranular bac+fill borrow cy 46@ '7.77 4,6@7

rill caisson, 4&x1&& lf 644 '77 64,477

#lagging hr 47,777 A.48 '18,777

restressed concrete member

type $D, '@'&x@&& ea 6 '4,777 A@,777

'4&x@&& ea 1 '',777 11,777


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5.11 Allocation o$ Construction Costs o8er Time

-ince construction costs are incurred over the entire construction phase of a project, it isoften necessary to determine the amounts to be spent in various periods to derive the cashflow profile, especially for large projects with long durations. "onsequently, it is

important to examine the percentage of wor+ expected to be completed at various timeperiods to which the costs would be charged. =ore accurate estimates may beaccomplished once the project is scheduled as described in "hapter '7, but some roughestimate of the cash flow may be required prior to this time.

"onsider the basic problem in determining the percentage of wor+ completed duringconstruction. %ne common method of estimating percentage of completion is based onthe amount of money spent relative to the total amount budgeted for the entire project.This method has the obvious drawbac+ in assuming that the amount of money spent hasbeen used efficiently for production. ! more reliable method is based on the concept ofvalue of work completedwhich is defined as the product of the budgeted labor hours per

unit of production and the actual number of production units completed, and is expressedin budgeted labor hours for the wor+ completed. Then, the percentage of completion atany stage is the ratio of the value of wor+ completed to date and the value of wor+ to becompleted for the entire project.


34/44

The value of wor+ completed at a given time /expressed as a cumulative percentage ofproject cost0 is shown schematically in #igure 8*'7. $n each case /!, ; or "0, the value ofwor+ completed can be represented by an N-*shapedN curve. The effects of rapidmobili)ation and slow mobili)ation are indicated by the positions of curves ; and "relative to curve !, respectively.

Figure 5-19: Dalue of Gor+ "ompleted over roject Time

Ghile the curves shown in #igures 8*5 and 8*'7 represent highly ideali)ed cases, they dosuggest the latitude for adjusting the schedules for various activities in a project. Ghilethe rate of wor+ progress may be changed quite drastically within a single period, such asthe change from rapid mobili)ation to a slow mobili)ation in periods ', 4 and in #igure8*5, the effect on the value of wor+ completed over time will diminish in significance asindicated by the cumulative percentages for later periods in #igure 8*'7. Thus,adjustment of the scheduling of some activities may improve the utili)ation of labor,material and equipment, and any delay caused by such adjustments for individualactivities is not li+ely to cause problems for the eventual progress toward the completionof a project.

$n addition to the speed of resource mobili)ation, another important consideration is theoverall duration of a project and the amount of resources applied. Darious strategies maybe applied to shorten the overall duration of a project such as overlapping design andconstruction activities /as described in "hapter 40 or increasing the pea+ amounts of laborand equipment wor+ing on a site. Fowever, spatial, managerial and technical factors willtypically place a minimum limit on the project duration or cause costs to escalate withshorter durations.

@


35/44

Example 5-1: Calculation o$


36/44

Export utilities to send estimates to cost control and scheduling software. This is

very helpful to begin the management of costs during construction. Dersion control to allow simulation of different construction processes or design

changes for the purpose of trac+ing changes in expected costs. rovisions for manual review, over*ride and editing of any cost element resulting

from the cost estimation system #lexible reporting formats, including provisions for electronic reporting rather

than simply printing cost estimates on paper. !rchives of past projects to allow rapid cost*estimate updating or modification for

similar designs.

! typical process for developing a cost estimate using one of these systems wouldinclude:

'. $f a similar design has already been estimated or exists in the company archive,the old project information is retrieved.

4. ! cost engineer modifies, adds or deletes components in the project information

set. $f a similar project exists, many of the components may have few or noupdates, thereby saving time.. ! cost estimate is calculated using the unit cost method of estimation.

roductivities and unit prices are retrieved from the system databases. Thus, thelatest price information is used for the cost estimate.

@. The cost estimation is summari)ed and reviewed for any errors.

5.1( Estimation o$ >perating Costs

$n order to analy)e the life cycle costs of a proposed facility, it is necessary to estimatethe operation and maintenance costs over time after the start up of the facility. The streamof operating costs over the life of the facility depends upon subsequent maintenancepolicies and facility use. $n particular, the magnitude of routine maintenance costs will bereduced if the facility undergoes periodic repairs and rehabilitation at periodic intervals.

-ince the tradeoff between the capital cost and the operating cost is an essential part ofthe economic evaluation of a facility, the operating cost is viewed not as a separate entity,but as a part of the larger parcel of life cycle cost at the planning and design stage. Thetechniques of estimating life cycle costs are similar to those used for estimating capitalcosts, including empirical cost functions and the unit cost method of estimating the labor,

material and equipment costs. Fowever, it is the interaction of the operating and capitalcosts which deserve special attention.

!s suggested earlier in the discussion of the exponential rule for estimating, the value ofthe cost exponent may influence the decision whether extra capacity should be built toaccommodate future growth. -imilarly, the economy of scale may also influence thedecision on rehabilitation at a given time. !s the rehabilitation wor+ becomes extensive,

1


37/44

it becomes a capital project with all the implications of its own life cycle. Fence, the costestimation of a rehabilitation project may also involve capital and operating costs.

Ghile deferring the discussion of the economic evaluation of constructed facilities to"hapter 1, it is sufficient to point out that the stream of operating costs over time

represents a series of costs at different time periods which have different values withrespect to the present. "onsequently, the cost data at different time periods must beconverted to a common base line if meaningful comparison is desired.

Example 5-14: 0aintenance cost on a roadway213

=aintenance costs for constructed roadways tend to increase with both age and use of thefacility. !s an example, the following empirical model was estimated for maintenanceexpenditures on sections of the %hio Turnpi+e:

" H 851 O 7.77'5 D O 4'.6 !

where " is the annual cost of routine maintenance per lane*mile /in '516 dollars0, D isthe volume of traffic on the roadway /measured in equivalent standard axle loads, E-!L,so that a heavy truc+ is represented as equivalent to many automobiles0, and ! is the ageof the pavement in years since the last resurfacing. !ccording to this model, routinemaintenance costs will increase each year as the pavement service deteriorates. $naddition, maintenance costs increase with additional pavement stress due to increasedtraffic or to heavier axle loads, as reflected in the variable D.

#or example, for D H 877,77 E-!L and ! H 8 years, the annual cost of routinemaintenance per lane*mile is estimated to be:

" H 851 O /7.77'50/877,770 O /4'.60/80 H 851 O 587.8 O '7A.8 H ',188 /in '516 dollars0

Example 5-1: Time stream o$ costs o8er the li$e o$ a roadway263

The time stream of costs over the life of a roadway depends upon the intervals at whichrehabilitation is carried out. $f the rehabilitation strategy and the traffic are +nown, thetime stream of costs can be estimated. (sing a life cycle model which predicts the

economic life of highway pavement on the basis of the effects of traffic and other factors,an optimal schedule for rehabilitation can be developed. #or example, a time stream ofcosts and resurfacing projects for one pavement section is shown in #igure 8*''. !sdescribed in the previous example, the routine maintenance costs increase as thepavement ages, but decline after each new resurfacing. !s the pavement continues to age,resurfacing becomes more frequent until the roadway is completely reconstructed at theend of 8 years.

6
http://www.ce.cmu.edu/pmbook/05_Cost_Estimation.html#fn6http://www.ce.cmu.edu/pmbook/05_Cost_Estimation.html#fn7http://www.ce.cmu.edu/pmbook/05_Cost_Estimation.html#fn6http://www.ce.cmu.edu/pmbook/05_Cost_Estimation.html#fn7


38/44

Figure 5-11: Time -tream of "osts over the Life of a Fighway avement

5.1, /e$erences

'. !huja, F.B. and G.C. "ampbell, Estimating% !rom Concept to Completion,rentice*Fall, $nc., Englewood "liffs, BC, '5A6.

4. "lar+, #.., and !.;. Loren)oni,pplied Cost Engineering, =arcel e++er, $nc.,Bew or+, '56A.

. "lar+, C.E., (tructural Concrete Cost Estimating, =craw*Fill, $nc., Bew or+,'5A.

@. ie+mann, C.


39/44

'. -uppose that the grouting method described in Example 8*4 is used to provide agrouting seal beneath another landfill of '4 acres. The grout line is expected to bebetween @.8 and 8.8 feet thic+ness. The voids in the soil layer are between 48I to8I. (sing the same unit cost data /in '56A dollars0, find the range of costs in ascreening estimate for the grouting project.

4. To avoid submerging part of (.-. 4

where is the daily production capacity of batteries and " is the cost of thebuilding in '5A6 dollars. $f a similar plant is planned for a daily productioncapacity of 477,777 batteries, find the screening estimate of the building in '5A6dollars.

@. #or the cost factor K H ?@1,777 /in '51A dollars0 and m H 7.16 for an aeratedlagoon basin of a water treatment plant in Table 8*@ /Example 8*10, find theestimated cost of a proposed new plant with a similar treatment process having acapacity of @A7 million gallons /in '51A dollars0. $f another new plant wasestimated to cost ?'17,777 by using the same exponential rule, what would be theproposed capacity of that plantP

8. (sing the cost data in #igure 8*8 /Example 8*''0, find the total cost includingoverhead and profit of excavating 57,777 cu.yd. of bul+ material using a bac+hoeof '.8 cu.yd. capacity for a detailed estimate. !ssume that the excavated materialwill be loaded onto truc+s for disposal.

5


40/44

1. The basic costs /labor, material and equipment0 for various elements of aconstruction project are given as follows:

Excavation-ubgrade

;ase course"oncrete pavement Total

?4@7,777?'77,777

?@47,777?1@7,777?',@77,777

6. !ssuming that field supervision cost is '7I of the basic cost, and the generaloffice overhead is 8I of the direct costs /sum of the basic costs and fieldsupervision cost0, find the prorated field supervision costs, general officeoverhead costs and total costs for the various elements of the project.

A. $n ma+ing a preliminary estimate of a chemical processing plant, several majortypes of equipment are the most significant components in affecting theinstallation cost. The cost of piping and other ancillary items for each type ofequipment can often be expressed as a percentage of that type of equipment for agiven capacity. The standard costs for the major equipment types for two plantswith different daily production capacities are as shown in Table 8*'1. $t has beenestablished that the installation cost of all equipment for a plant with dailyproduction capacity between '87,777 bbl and 177,777 bbl can best be estimatedby using liner interpolation of the standard data. ! new chemical processing plantwith a daily production capacity of @77,777 bbl is being planned. !ssuming thatall other factors remain the same, estimate the cost of the new plant.

Ta&le 5-1

Equipmenttype

Equipment cost /?',7770 #actor for ancillary items

'87,777 bbl 177,777 bbl '87,777 bbl 177,777 bbl

#urnace ?,777 ?'7,777 7.4 7.4@

Tower 4,777 1,777 7.@4 7.1

rum ',877 8,777 7.@4 7.4

umps,etc.

',777 @,777 7.8@ 7.@4

5. The total construction cost of a refinery with a production capacity of '77,777bbl>day in "aracas, Dene)uela, completed in '566 was ?@7 million. $t wasproposed that a similar refinery with a production capacity of ?'17,777 bbl>day bebuilt in Bew %rleans, L! for completion in '5A7. #or the additional informationgiven below, ma+e a screening estimate of the cost of the proposed plant.

@7


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'. $n the total construction cost for the "aracus, Dene)uela plant, there wasan item of ?4 million for site preparation and travel which is not typicalfor similar plants.

4. The variation of si)es of the refineries can be approximated by theexponential law with m H 7.1.

. The inflation rate in (.-. dollars was approximately 5I per year from'566 to '5A7.@. !n adjustment factor of '.@7 was suggested for the project to account for

the increase of labor cost from "aracas, Dene)uela to Bew %rleans, L!.8. Bew air pollution equipment for the Bew %rleans, L! plant cost ?@

million in '5A7 dollars /not required for the "aracas plant0.1. The site condition at Bew %rleans required special piling foundation

which cost ?4 million in '5A7 dollars.

'7. The total cost of a sewage treatment plant with a capacity of 87 million gallonsper day completed '5A' for a new town in "olorado was [email protected] million. $t wasproposed that a similar treatment plant with a capacity of A7 million gallons perday be built in another town in Bew Cersey for completion in '5A8. #or additionalinformation given below, ma+e a screening estimate of the cost of the proposedplant.

'. $n the total construction cost in "olorado, an item of ?77,777 for sitepreparation is not typical for similar plants.

4. The variation of si)es for this type of treatment plants can beapproximated by the exponential law with m H 7.8.

. The inflation rate was approximately 8I per year from '5A' to '5A8.

@. The locational indices of "olorado and Bew Cersey areas are 7.58 and'.'7, respectively, against the national average of '.77.8. The installation of a special equipment to satisfy the new environmental

standard cost an extra ?477,777 in '5A8 dollar for the Bew Cersey plant.1. The site condition in Bew Cersey required special foundation which cost

?877,777 in '5A8 dollars.

''. (sing theE)$building cost index, estimate the '5A8 cost of the grouting seal ona landfill described in Example 8*4, including the most li+ely estimate and therange of possible cost.

'4. (sing the unit prices in the bid of contractor 4 for the quantitites specified by theengineer in Table 8*4 /Example 8*0, compute the total bid price of contractor 4for the roadway project including the expenditure on each item of wor+.

'. The rate of wor+ progress in percent of completion per period of a constructionproject is shown in #igure 8*'4 in which ' time periods have been assumed. Thecases !, ; and " represent the normal mobili)ation time, rapid mobili)ation andslow mobili)ation for the project, respectively. "alculate the value of wor+

@'


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completed in cumulative percentage for periods ' through ' for each of the cases!, ; and ". !lso plot the volume of wor+ completed versus time for these cases.

Figure 5-1"

'@. The rate of wor+ progress in percent of completion per period of a constructionproject is shown in #igure 8*' in which '7 time periods have been assumed. Thecases !, ; and " represent the rapid mobili)ation time, normal mobili)ation andslow mobili)ation for the project, respectively. "alculate the value of wor+completed in cumulative percentage for periods ' through '7 for each of the cases!, ; and ". !lso plot the volume of wor+ completed versus time for these cases.

Figure 5-1(

'8. -uppose that the empirical model for estimating annual cost of routinemaintenance in Example 8*'6 is applicable to sections of the ennsylvaniaTurnpi+e in '5A8 if the E)$building cost index is applied to inflate the '516dollars. Estimate the annual cost of maintenance per lane*mile of the tunrpi+e forwhich the traffic volume on the roadway is 687,777 E-!L and the age of thepavement is @ years in '5A8.

@4


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'1. The initial construction cost for a electric rower line is +nown to be a function ofthe cross*sectional area ! /in cm40 and the length L /in +ilometers0. Let " 'be theunit cost of construction /in dollars per cm0. Then, the initial construction cost /in dollars0 is given by

H "'!L/'78

0

The annual operating cost of the power line is assumed to be measured by thepower loss. The power loss - /in +wh0 is +nown to be

0'7/0'7/

'7

448

:

4

'

$L3

'

L$3( =

=

where C is the electric current in amperes, < is the resistivity in ohm*centimeters.Let "4be the unit operating cost /in dollars per +wh0. Then, the annual operatingcost ( /in dollars0 is given by

0'7/ 4

4

4'

$L3C1=

-uppose that the power line is expected to last n years and the life cycle cost T ofthe power line is equal to:

T H O (K

where K is a discount factor depending on the useful life cycle n and the discountrate i /to be explained in "hapter 10. $n designing the power line, all quantities are

assumed to be +nown except ! which is to be determined. $f the owner wants tominimi)e the life cycle cost, find the best cross*sectional area ! in terms of the+nown quantities.

5.1 Footnotes

'. This example was adapted with permission from a paper, N#orecasting $ndustry


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. -ee N(tah $nterstate #orges %n,NE)$, Culy 4, '5A6, p. 5.

@. This and the next example have been adapted from .=. ;erthouex, NEvaluatingEconomy of -cale,N3ournal of the Water 4ollution Control !ederation, Dol. @@, Bo. '',Bovember '564, pp. 4'''*4''A.

8. -ee F.T. Cohnson and

05 Cost Estimation

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