Project Management for Construction Chapter 5

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  1. 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 the subsequent operation and maintenance costs. Each of these major cost categories consists of a number of cost components. The capital cost for a construction project includes the expenses related to the inital establishment of the facility: • Land acquisition, including assembly, holding and improvement • Planning and feasibility studies • Architectural and engineering design • Construction, including materials, equipment and labor • Field supervision of construction • Construction financing • Insurance and taxes during construction • Owner's general office overhead • Equipment and furnishings not included in construction • Inspection and testing The operation and maintenance cost in subsequent years over the project life cycle includes the following expenses: • Land rent, if applicable • Operating staff • Labor and material for maintenance and repairs • Periodic renovations • Insurance and taxes • Financing costs • Utilities • Owner's other expenses The magnitude of each of these cost components depends on the nature, size and location of the project as well as the management organization, among many considerations. The owner is interested in achieving the lowest possible overall project cost that is consistent with its investment objectives. It is important for design professionals and construction managers to realize that while the construction cost may be the single largest component of the capital cost, other cost components are not insignificant. For example, land acquisition costs are a major expenditure for building construction in high-density urban areas, and construction financing costs can reach the same order of magnitude as the construction cost in large projects such as the construction of nuclear power plants. 132
  2. From the owner's perspective, it is equally important to estimate the corresponding operation and maintenance cost of each alternative for a proposed facility in order to analyze the life cycle costs. The large expenditures needed for facility maintenance, especially for publicly owned infrastructure, are reminders of the neglect in the past to consider fully the implications of operation and maintenance cost in the design stage. In most construction budgets, there is an allowance for contingencies or unexpected costs occuring during construction. This contingency amount may be included within each cost item or be included in a single category of construction contingency. The amount of contingency is based on historical experience and the expected difficulty of a particular construction project. For example, one construction firm makes estimates of the expected cost in five different areas: • Design development changes, • Schedule adjustments, • General administration changes (such as wage rates), • Differing site conditions for those expected, and • Third party requirements imposed during construction, such as new permits. Contingent amounts not spent for construction can be released near the end of construction to the owner or to add additional project elements. In this chapter, we shall focus on the estimation of construction cost, with only occasional reference to other cost components. In Chapter 6, we shall deal with the economic evaluation of a constructed facility on the basis of both the capital cost and the operation and maintenance cost in the life cycle of the facility. It is at this stage that tradeoffs between operating and capital costs can be analyzed. Example 5-1: Energy project resource demands [1] The resources demands for three types of major energy projects investigated during the energy crisis in the 1970's are shown in Table 5-1. These projects are: (1) an oil shale project with a capacity of 50,000 barrels of oil product per day; (2) a coal gasification project that makes gas with a heating value of 320 billions of British thermal units per day, or equivalent to about 50,000 barrels of oil product per day; and (3) a tar sand project with a capacity of 150,000 barrels of oil product per day. For each project, the cost in billions of dollars, the engineering manpower requirement for basic design in thousands of hours, the engineering manpower requirement for detailed engineering in millions of hours, the skilled labor requirement for construction in millions of hours and the material requirement in billions of dollars are shown in Table 5-1. To build several projects of such an order of magnitude concurrently could drive up the costs and strain the availability of all resources required to complete the projects. Consequently, cost estimation often represents an exercise in professional judgment instead of merely compiling a bill of quantities and collecting cost data to reach a total estimate mechanically. TABLE 5-1 Resource Requirements of Some Major Energy Projects Oil shale Coal gasification Tar Sands 133
  3. (50,000 (320 billions (150,000 barrels/day) BTU/day) barrels/day) Cost 2.5 4 8 to 10 ($ billion) Basic design (Thousands of 80 200 100 hours) Detailed engineering 3 to 4 4 to 5 6 to 8 (Millions of hours) Construction 20 30 40 (Millions of hours) Materials 1 2 2.5 ($ billion) Source: Exxon Research and Engineering Company, Florham Park, NJ Back to top 5.2 Approaches to Cost Estimation Cost estimating is one of the most important steps in project management. A cost estimate establishes the base line of the project cost at different stages of development of the project. A cost estimate at a given stage of project development represents a prediction provided by the cost engineer or estimator on the basis of available data. According to the American Association of Cost Engineers, cost engineering is defined as that area of engineering practice where engineering judgment and experience are utilized in the application of scientific principles and techniques to the problem of cost estimation, cost control and profitability. Virtually all cost estimation is performed according to one or some combination of the following basic approaches: Production function. In microeconomics, the relationship between the output of a process and the necessary resources is referred to as the production function. In construction, the production function may be expressed by the relationship between the volume of construction and a factor of production such as labor or capital. A production function relates the amount or volume of output to the various inputs of labor, material and equipment. For example, the amount of output Q may be derived as a function of various input factors x1, x2, ..., xn by 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 input factors so as to minimize the production cost. The relationship between the size of a building project (expressed in square feet) to the input labor (expressed in labor hours per square foot) is an example of a production function for construction. Several such production functions are shown in Figure 3-3 of Chapter 3. Empirical cost inference. Empirical estimation of cost functions requires statistical techniques which relate the cost of constructing or operating a facility to a few important characteristics or attributes of 134
  4. the system. The role of statistical inference is to estimate the best parameter values or constants in an assumed cost function. Usually, this is accomplished by means of regression analysis techniques. Unit costs for bill of quantities. A unit cost is assigned to each of the facility components or tasks as represented by the bill of quantities. The total cost is the summation 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 break down or disaggregate a process into a number of tasks. Collectively, these tasks must be completed for the construction of a facility. Once these tasks are defined and quantities representing these tasks are assessed, a unit cost is assigned to each and then the total cost is determined by summing the costs incurred in each task. The level of detail in decomposing into tasks will vary considerably from one estimate to another. Allocation of joint costs. Allocations of cost from existing accounts may be used to develop a cost function of an operation. The basic idea in this method is that each expenditure item can be assigned to particular characteristics of the operation. Ideally, the allocation of joint costs should be causally related to the category of basic costs in an allocation process. In many instances, however, a causal relationship between the allocation factor and the cost item cannot be identified or may not exist. For example, in construction projects, the accounts for basic costs may be classified according to (1) labor, (2) material, (3) construction equipment, (4) construction supervision, and (5) general office overhead. These basic costs may then be allocated proportionally to various tasks which are subdivisions of a project. Back to top 5.3 Types of Construction Cost Estimates Construction cost constitutes only a fraction, though a substantial fraction, of the total project cost. However, it is the part of the cost under the control of the construction project manager. The required levels of accuracy of construction cost estimates vary at different stages of project development, ranging from ball park figures in the early stage to fairly reliable figures for budget control prior to construction. Since design decisions made at the beginning stage of a project life cycle are more tentative than those made at a later stage, the cost estimates made at the earlier stage are expected to be less accurate. Generally, the accuracy of a cost estimate will reflect the information available at the time of estimation. Construction cost estimates may be viewed from different perspectives because of different institutional requirements. In spite of the many types of cost estimates used at different stages of a project, cost estimates can best be classified into three major categories according to their functions. A construction cost estimate serves one of the three basic functions: design, bid and control. For establishing the financing of a project, either a design estimate or a bid estimate is used. 1. Design Estimates. For the owner or its designated design professionals, the types of cost estimates encountered run parallel with the planning and design as follows: o Screening estimates (or order of magnitude estimates) o Preliminary estimates (or conceptual estimates) o Detailed estimates (or definitive estimates) 135
  5. o Engineer's estimates based on plans and specifications For each of these different estimates, the amount of design information available typically increases. 2. Bid Estimates. For the contractor, a bid estimate submitted to the owner either for competitive bidding or negotiation consists of direct construction cost including field supervision, plus a markup to cover general overhead and profits. The direct cost of construction for bid estimates is usually derived from a combination of the following approaches. o Subcontractor quotations o Quantity takeoffs o Construction procedures. 3. 3. Control Estimates. For monitoring the project during construction, a control estimate is derived from available information to establish: o Budget estimate for financing o Budgeted cost after contracting but prior to construction o Estimated cost to completion during the progress of construction. Design Estimates In the planning and design stages of a project, various design estimates reflect the progress of the design. At the very early stage, the screening estimate or order of magnitude estimate is usually made before the facility is designed, and must therefore rely on the cost data of similar facilities built in the past. A preliminary estimate or conceptual estimate is based on the conceptual design of the facility at the state when the basic technologies for the design are known. The detailed estimate or definitive estimate is made when the scope of work is clearly defined and the detailed design is in progress so that the essential features of the facility are identifiable. The engineer's estimate is based on the completed plans and specifications when they are ready for the owner to solicit bids from construction contractors. In preparing these estimates, the design professional will include expected amounts for contractors' overhead and profits. The costs associated with a facility may be decomposed into a hierarchy of levels that are appropriate for the purpose of cost estimation. The level of detail in decomposing the facility into tasks depends on the type of cost estimate to be prepared. For conceptual estimates, for example, the level of detail in defining tasks is quite coarse; for detailed estimates, the level of detail can be quite fine. As an example, consider the cost estimates for a proposed bridge across a river. A screening estimate is made for each of the potential alternatives, such as a tied arch bridge or a cantilever truss bridge. As the bridge type is selected, e.g. the technology is chosen to be a tied arch bridge instead of some new bridge form, a preliminary estimate is made on the basis of the layout of the selected bridge form on the basis of the preliminary or conceptual design. When the detailed design has progressed to a point when the essential details are known, a detailed estimate is made on the basis of the well defined scope of the project. When the detailed plans and specifications are completed, an engineer's estimate can be made on the basis of items and quantities of work. 136
  6. Bid Estimates The contractor's bid estimates often reflect the desire of the contractor to secure the job as well as the estimating tools at its disposal. Some contractors have well established cost estimating procedures while others do not. Since only the lowest bidder will be the winner of the contract in most bidding contests, any effort devoted to cost estimating is a loss to the contractor who is not a successful bidder. Consequently, the contractor may put in the least amount of possible effort for making a cost estimate if it believes that its chance of success is not high. If a general contractor intends to use subcontractors in the construction of a facility, it may solicit price quotations for various tasks to be subcontracted to specialty subcontractors. Thus, the general subcontractor will shift the burden of cost estimating to subcontractors. If all or part of the construction is to be undertaken by the general contractor, a bid estimate may be prepared on the basis of the quantity takeoffs from the plans provided by the owner or on the basis of the construction procedures devised by the contractor for implementing the project. For example, the cost of a footing of a certain type and size may be found in commercial publications on cost data which can be used to facilitate cost estimates from quantity takeoffs. However, the contractor may want to assess the actual cost of construction by considering the actual construction procedures to be used and the associated costs if the project is deemed to be different from typical designs. Hence, items such as labor, material and equipment needed to perform various tasks may be used as parameters for the cost estimates. Control Estimates Both the owner and the contractor must adopt some base line for cost control during the construction. For the owner, a budget estimate must be adopted early enough for planning long term financing of the facility. Consequently, the detailed estimate is often used as the budget estimate since it is sufficient definitive to reflect the project scope and is available long before the engineer's estimate. As the work progresses, the budgeted cost must be revised periodically to reflect the estimated cost to completion. A revised estimated cost is necessary either because of change orders initiated by the owner or due to unexpected cost overruns or savings. For the contractor, the bid estimate is usually regarded as the budget estimate, which will be 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 as well as to insure adequate cash flows for the completion of the project. Example 5-2: Screening estimate of a grouting seal beneath a landfill [2] One of the methods of isolating a landfill from groundwater is to create a bowl-shaped bottom seal beneath the site as shown in Figure 5-0. The seal is constructed by pumping or pressure-injecting grout under the existing landfill. Holes are bored at regular intervals throughout the landfill for this purpose and the grout tubes are extended from the surface to the bottom of the landfill. A layer of soil at a minimum of 5 ft. thick is left between the grouted material and the landfill contents to allow for irregularities in the bottom of the landfill. The grout liner can be between 4 and 6 feet thick. A typical material would be Portland cement grout pumped under pressure through tubes to fill voids in the soil. This grout would then harden into a permanent, impermeable liner. 137
  7. Figure 5-1: Grout Bottom Seal Liner at a Landfill The work items in this project include (1) drilling exploratory bore holes at 50 ft intervals for grout tubes, and (2) pumping grout into the voids of a soil layer between 4 and 6 ft thick. The quantities for these two items are estimated on the basis of the landfill area: 8 acres = (8)(43,560 ft2/acre) = 348,480 ft2 (As an approximation, use 360,000 ft2 to account for the bowl shape) The number of bore holes in a 50 ft by 50 ft grid pattern covering 360,000 ft2 is given by: The average depth of the bore holes is estimated to be 20 ft. Hence, the total amount of drilling is (144)(20) = 2,880 ft. The volume of the soil layer for grouting is estimated to be: for a 4 ft layer, volume = (4 ft)(360,000 ft2) = 1,440,000 ft3 for a 6 ft layer, volume = (6 ft)(360,000 ft2) = 2,160,000 ft3 138
  8. It is estimated from soil tests that the voids in the soil layer are between 20% and 30% of the total volume. Thus, for a 4 ft soil layer: grouting in 20% voids = (20%)(1,440,000) = 288,000 ft3 grouting in 30 % voids = (30%)(1,440,000) = 432,000 ft3 and for a 6 ft soil layer: grouting in 20% voids = (20%)(2,160,000) = 432,000 ft3 grouting in 30% voids = (30%)(2,160,000) = 648,000 ft3 The unit cost for drilling exploratory bore holes is estimated to be between $3 and $10 per foot (in 1978 dollars) including all expenses. Thus, the total cost of boring will be between (2,880)(3) = $ 8,640 and (2,880)(10) = $28,800. The unit cost of Portland cement grout pumped into place is between $4 and $10 per cubic foot including overhead and profit. In addition to the variation in the unit cost, the total cost of the bottom seal will depend upon the thickness of the soil layer grouted and the proportion of voids in the soil. That is: for a 4 ft layer with 20% voids, grouting cost = $1,152,000 to $2,880,000 for a 4 ft layer with 30% voids, grouting cost = $1,728,000 to $4,320,000 for a 6 ft layer with 20% voids, grouting cost = $1,728,000 to $4,320,000 for a 6 ft layer with 30% voids, grouting cost = $2,592,000 to $6,480,000 The total cost of drilling bore holes is so small in comparison with the cost of grouting that the former can be omitted in the screening estimate. Furthermore, the range of unit cost varies greatly with soil characteristics, and the engineer must exercise judgment in narrowing the range of the total cost. Alternatively, additional soil tests can be used to better estimate the unit cost of pumping grout and the proportion of voids in the soil. Suppose that, in addition to ignoring the cost of bore holes, an average value of a 5 ft soil layer with 25% voids is used together with a unit cost of $ 7 per cubic foot of Portland cement grouting. In this case, the total project cost is estimated to be: (5 ft)(360,000 ft2)(25%)($7/ft3) = $3,150,000 An important point to note is that this screening estimate is based to a large degree on engineering judgment of the soil characteristics, and the range of the actual cost may vary from $ 1,152,000 to $ 6,480,000 even though the probabilities of having actual costs at the extremes are not very high. Example 5-3: Example of engineer's estimate and contractors' bids[3] The engineer's estimate for a project involving 14 miles of Interstate 70 roadway in Utah was $20,950,859. Bids were submitted on March 10, 1987, for completing the project within 320 working days. The three low bidders were: 1. Ball, Ball & Brosame, Inc., Danville CA $14,129,798 2. National Projects, Inc., Phoenix, AR $15,381,789 3. Kiewit Western Co., Murray, Utah $18,146,714 It was astounding that the winning bid was 32% below the engineer's estimate. Even the third lowest bidder was 13% below the engineer's estimate for this project. The disparity in pricing can be attributed either to the very conservative estimate of the engineer in the Utah Department of Transportation or to area contractors who are hungrier than usual to win jobs. The unit prices for different items of work submitted for this project by (1) Ball, Ball & Brosame, Inc. and (2) National Projects, Inc. are shown in Table 5-2. The similarity of their unit prices for some items and the disparity in others submitted by the two contractors can be noted. 139
  9. TABLE 5-2: Unit Prices in Two Contractors' Bids for Roadway Construction Unit price Items Unit Quantity 1 2 Mobilization ls 1 115,000 569,554 Removal, berm lf 8,020 1.00 1.50 Finish subgrade sy 1,207,500 0.50 0.30 Surface ditches lf 525 2.00 1.00 Excavation structures cy 7,000 3.00 5.00 Base course, untreated, 3/4'' ton 362,200 4.50 5.00 Lean concrete, 4'' thick sy 820,310 3.10 3.00 PCC, pavement, 10'' thick sy 76,010 10.90 12.00 Concrete, ci AA (AE) ls 1 200,000 190,000 Small structure cy 50 500 475 Barrier, precast lf 7,920 15.00 16.00 Flatwork, 4'' thick sy 7,410 10.00 8.00 10'' thick sy 4,241 20.00 27.00 Slope protection sy 2,104 25.00 30.00 Metal, end section, 15'' ea 39 100 125 18'' ea 3 150 200 Post, right-of-way, modification lf 4,700 3.00 2.50 Salvage and relay pipe lf 1,680 5.00 12.00 Loose riprap cy 32 40.00 30.00 Braced posts ea 54 100 110 Delineators, type I lb 1,330 12.00 12.00 type II ea 140 15.00 12.00 Constructive signs fixed sf 52,600 0.10 0.40 Barricades, type III lf 29,500 0.20 0.20 Warning lights day 6,300 0.10 0.50 Pavement marking, epoxy material Black gal 475 90.00 100 Yellow gal 740 90.00 80.00 White gal 985 90.00 70.00 Plowable, one-way white ea 342 50.00 20.00 140
  10. TABLE 5-2: Unit Prices in Two Contractors' Bids for Roadway Construction Unit price Topsoil, contractor furnished cy 260 10.00 6.00 Seedling, method A acr 103 150 200 Excelsior blanket sy 500 2.00 2.00 Corrugated, metal pipe, 18'' lf 580 20.00 18.00 Polyethylene pipe, 12'' lf 2,250 15.00 13.00 Catch basin grate and frame ea 35 350 280 Equal opportunity training hr 18,000 0.80 0.80 Granular backfill borrow cy 274 10.00 16.00 Drill caisson, 2'x6'' lf 722 100 80.00 Flagging hr 20,000 8.25 12.50 Prestressed concrete member type IV, 141'x4'' ea 7 12,000 16.00 132'x4'' ea 6 11,000 14.00 Reinforced steel lb 6,300 0.60 0.50 Epoxy coated lb 122,241 0.55 0.50 Structural steel ls 1 5,000 1,600 Sign, covering sf 16 10.00 4.00 type C-2 wood post sf 98 15.00 17.00 24'' ea 3 100 400 30'' ea 2 100 160 48'' ea 11 200 300 Auxiliary sf 61 15.00 12.00 Steel post, 48''x60'' ea 11 500 700 type 3, wood post sf 669 15.00 19.00 24'' ea 23 100 125 30'' ea 1 100 150 36'' ea 12 150 180 42''x60'' ea 8 150 220 48'' ea 7 200 270 Auxiliary sf 135 15.00 13.00 Steel post sf 1,610 40.00 35.00 141
  11. TABLE 5-2: Unit Prices in Two Contractors' Bids for Roadway Construction Unit price 12''x36'' ea 28 100 150 Foundation, concrete ea 60 300 650 Barricade, 48''x42'' ea 40 100 100 Wood post, road closed lf 100 30.00 36.00 Back to top 5.4 Effects of Scale on Construction Cost Screening cost estimates are often based on a single variable representing the capacity or some physical measure of the design such as floor area in buildings, length of highways, volume of storage bins and production volumes of processing plants. Costs do not always vary linearly with respect to different facility sizes. Typically, scale economies or diseconomies exist. If the average cost per unit of capacity is declining, then scale economies exist. Conversely, scale diseconomies exist if average costs increase with greater size. Empirical data are sought to establish the economies of scale for various types of facility, if they exist, in order to take advantage of lower costs per unit of capacity. 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: (5.1) where a and b are positive constants to be determined on the basis of historical data. Note that in Equation (5.1), a fixed cost of y = a at x = 0 is implied as shown in Figure 5-2. In general, this relationship is applicable only in a certain range of the variable x, such as between x = c and x = d. If the values of y corresponding to x = c and x = d are known, then the cost of a facility corresponding to any x within the specified range may be obtained by linear interpolation. For example, the construction cost of a school building can be estimated on the basis of a linear relationship between cost and floor area if the unit cost per square foot of floor area is known for school buildings within certain limits of size. 142
  12. Figure 5-2: Linear Cost Relationship with Economies of Scale A nonlinear cost relationship between the facility capacity x and construction cost y can often be represented in the form: (5.2) where a and b are positive constants to be determined on the basis of historical data. For 0 < b < 1, Equation (5.2) represents the case of increasing returns to scale, and for b ;gt 1, the relationship becomes the case of decreasing returns to scale, as shown in Figure 5-3. Taking the logarithm of both sides this equation, a linear relationship can be obtained as follows: 143
  13. Figure 5-3: Nonlinear Cost Relationship with increasing or Decreasing Economies of Scale (5.3) Although no fixed cost is implied in Eq.(5.2), the equation is usually applicable only for a certain range of x. The same limitation applies to Eq.(5.3). A nonlinear cost relationship often used in estimating the cost of a new industrial processing plant from the known cost of an existing facility of a different size is known as the exponential rule. Let yn be the known cost of an existing facility with capacity Qn, and y be the estimated cost of the new facility which has a capacity Q. Then, from the empirical data, it can be assumed that: (5.4) where m usually varies from 0.5 to 0.9, depending on a specific type of facility. A value of m = 0.6 is often used for chemical processing plants. The exponential rule can be reduced to a linear relationship if the logarithm of Equation (5.4) is used: (5.5) or 144
  14. (5.6) 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 5-4: Determination of m for the exponential rule Figure 5-4: Log-Log Scale Graph of Exponential Rule Example The empirical cost data from a number of sewage treatment plants are plotted on a log-log scale for ln(Q/Qn) and ln(y/yn) and a linear relationship between these logarithmic ratios is shown in Figure 5-4. For (Q/Qn) = 1 or ln(Q/Qn) = 0, ln(y/yn) = 0; and for Q/Qn = 2 or ln(Q/Qn) = 0.301, ln(y/yn) = 0.1765. Since m is the slope of the line in the figure, it can be determined from the geometric relation as follows: For ln(y/yn) = 0.1765, y/yn = 1.5, while the corresponding value of Q/Qn is 2. In words, for m = 0.585, the cost of a plant increases only 1.5 times when the capacity is doubled. Example 5-5: Cost exponents for water and wastewater treatment plants[4] The magnitude of the cost exponent m in the exponential rule provides a simple measure of the economy of scale associated with building extra capacity for future growth and system reliability for the present in the design of treatment plants. When m is small, there is considerable incentive to provide extra capacity since scale economies exist as illustrated in Figure 5-3. When m is close to 1, the cost is directly proportional to the design capacity. The value of m tends to increase as the number of duplicate units in a system increases. The values of m for several types of treatment plants with 145
  15. different plant components derived from statistical correlation of actual construction costs are shown in Table 5-3. TABLE 5-3 Estimated Values of Cost Exponents for Water Treatment Plants Treatment plant Exponent Capacity range type m (millions of gallons per day) 1. Water treatment 0.67 1-100 2. Waste treatment Primary with digestion (small) 0.55 0.1-10 Primary with digestion (large) 0.75 0.7-100 Trickling filter 0.60 0.1-20 Activated sludge 0.77 0.1-100 Stabilization ponds 0.57 0.1-100 Source: Data are collected from various sources by P.M. Berthouex. See the references in his article for the primary sources. Example 5-6: Some Historical Cost Data for the Exponential Rule The exponential rule as represented by Equation (5.4) can be expressed in a different form as: where If m and K are known for a given type of facility, then the cost y for a proposed new facility of specified capacity Q can be readily computed. TABLE 5-4 Cost Factors of Processing Units for Treatment Plants Processing Unit of K Value m unit capacity (1968 $) value 1. Liquid processing Oil separation mgd 58,000 0.84 Hydroclone degritter mgd 3,820 0.35 Primary sedimentation ft2 399 0.60 Furial clarifier ft2 700 0.57 Sludge aeration basin mil. gal. 170,000 0.50 Tickling filter ft2 21,000 0.71 146
  16. Aerated lagoon basin mil. gal. 46,000 0.67 Equalization mil. gal. 72,000 0.52 Neutralization mgd 60,000 0.70 2. Sludge handling Digestion ft3 67,500 0.59 Vacuum filter ft2 9,360 0.84 lb dry Centrifuge 318 0.81 solids/hr Source: Data are collected from various sources by P.M. Berthouex. See the references in his article for the primary sources. The estimated values of K and m for various water and sewage treatment plant components are shown in Table 5-4. The K values are based on 1968 dollars. The range of data from which the K and m values are derived in the primary sources should be observed in order to use them in making cost estimates. As an example, take K = $399 and m = 0.60 for a primary sedimentation component in Table 5-4. For a proposed new plant with the primary sedimentation process having a capacity of 15,000 sq. ft., the estimated cost (in 1968 dollars) is: y = ($399)(15,000)0.60 = $128,000. Back to top 5.5 Unit Cost Method of Estimation If the design technology for a facility has been specified, the project can be decomposed into elements at various levels of detail for the purpose of cost estimation. The unit cost for each element in the bill of quantities must be assessed in order to compute the total construction cost. This concept is applicable to both design estimates and bid estimates, although different elements may be selected in the decomposition. For design estimates, the unit cost method is commonly used when the project is decomposed into elements at various levels of a hierarchy as follows: 1. Preliminary Estimates. The project is decomposed into major structural systems or production equipment items, e.g. the entire floor of a building or a cooling system for a processing plant. 2. Detailed Estimates. The project is decomposed into components of various major systems, i.e., a single floor panel for a building or a heat exchanger for a cooling system. 3. Engineer's Estimates. The project is decomposed into detailed items of various components as warranted by the available cost data. Examples of detailed items are slabs and beams in a floor panel, or the piping and connections for a heat exchanger. 147
  17. For bid estimates, the unit cost method can also be applied even though the contractor may choose to decompose the project into different levels in a hierarchy as follows: 1. Subcontractor Quotations. The decomposition of a project into subcontractor items for quotation involves a minimum amount of work for the general contractor. However, the accuracy of the resulting estimate depends on the reliability of the subcontractors since the general contractor selects one among several contractor quotations submitted for each item of subcontracted work. 2. Quantity Takeoffs. The decomposition of a project into items of quantities that are measured (or taken off) from the engineer's plan will result in a procedure similar to that adopted for a detailed estimate or an engineer's estimate by the design professional. The levels of detail may vary according to the desire of the general contractor and the availability of cost data. 3. Construction Procedures. If the construction procedure of a proposed project is used as the basis of a cost estimate, the project may be decomposed into items such as labor, material and equipment needed to perform various tasks in the projects. Simple Unit Cost Formula Suppose that a project is decomposed into n elements for cost estimation. Let Qi be the quantity of the ith element and ui be the corresponding unit cost. Then, the total cost of the project is given by: (5.7) where n is the number of units. Based on characteristics of the construction site, the technology employed, or the management of the construction process, the estimated unit cost, ui for each element may be adjusted. Factored Estimate Formula A special application of the unit cost method is the "factored estimate" commonly used in process industries. Usually, an industrial process requires several major equipment components 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 a project is dominated by the costs of purchasing and installing the major equipment components and their ancillary items. Let Ci be the purchase cost of a major equipment component i and fi be a factor accounting for the cost of ancillary items needed for the installation of this equipment component i. Then, the total cost of a project is estimated by: (5.8) 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 ancillary items such as piping and valves as a fraction or a multiple of the costs of the major equipment items. The value of Ci may be obtained by applying the exponential rule so the use of Equation (5.8) may involve a combination of cost estimation methods. 148
  18. Formula Based on Labor, Material and Equipment Consider the simple case for which costs of labor, material and equipment are assigned to all tasks. Suppose that a project is decomposed into n tasks. Let Qi be the quantity of work for task i, Mi be the unit material cost of task i, Ei be the unit equipment rate for task i, Li be the units of labor required per unit of Qi, and Wi be the wage rate associated with Li. In this case, the total cost y is: (5.9) Note that WiLi yields the labor cost per unit of Qi, or the labor unit cost of task i. Consequently, the units for all terms in Equation (5.9) are consistent. Example 5-7: Decomposition of a building foundation into design and construction elements. The concept of decomposition is illustrated by the example of estimating the costs of a building foundation excluding excavation as shown in Table 5-5 in which the decomposed design elements are shown on horizontal lines and the decomposed contract elements are shown in vertical columns. For a design estimate, the decomposition of the project into footings, foundation walls and elevator pit is preferred since the designer can easily keep track of these design elements; however, for a bid estimate, the decomposition of the project into formwork, reinforcing bars and concrete may be preferred since the contractor can get quotations of such contract items more conveniently from specialty subcontractors. TABLE 5-5 Illustrative Decomposition of Building Foundation Costs Contract elements Design elements Formwork Rebars Concrete Total cost Footings $5,000 $10,000 $13,000 $28,000 Footings 15,000 18,000 28,000 61,000 Footings 9,000 15,000 16,000 40,000 Total cost $29,000 $43,000 $57,000 $129,000 Example 5-8: Cost estimate using labor, material and equipment rates. For the given quantities of work Qi for the concrete foundation of a building and the labor, material and equipment rates in Table 5-6, the cost estimate is computed on the basis of Equation (5.9). The result is tabulated in the last column of the same table. TABLE 5-6 Illustrative Cost Estimate Using Labor, Material and Equipment Rates Description Quantity Material Equipment Wage Labor Labor Direct 149
  19. Qi unit cost unit cost rate input unit cost cost Mi Ei Wi Li WiLi Yi Formwork 12,000 ft2 $0.4/ft2 $0.8/ft2 $15/hr 0.2 hr/ft2 $3.0/ft2 $50,400 Rebars 4,000 lb 0.2/lb 0.3/lb 15/hr 0.04 hr/lb 0.6/lb 4,440 Concrete 500 yd3 5.0/yd3 50/yd3 15/hr 0.8 hr/yd3 12.0/yd3 33,500 Total $88,300 Back to top 5.6 Methods for Allocation of Joint Costs The principle of allocating joint costs to various elements in a project is often used in cost estimating. Because of the difficulty in establishing casual relationship between each element and its associated cost, the joint costs are often prorated in proportion to the basic costs for various elements. One common application is found in the allocation of field supervision cost among the basic costs of various elements based on labor, material and equipment costs, and the allocation of the general overhead cost to various elements according to the basic and field supervision cost. Suppose that a project is decomposed into n tasks. Let y be the total basic cost for the project and yi be the total basic cost for task i. If F is the total field supervision cost and Fi is the proration of that cost to task i, then a typical proportional allocation is: (5.10) Similarly, let z be the total direct field cost which includes the total basic cost and the field supervision cost of the project, and zi be the direct field cost for task i. If G is the general office overhead for proration to all tasks, and Gi is the share for task i, then (5.11) Finally, let w be the grand total cost of the project which includes the direct field cost and the general office overhead cost charged to the project and wi be that attributable task i. Then, (5.12) 150
  20. and (5.13) Example 5-9: Prorated costs for field supervision and office overhead If the field supervision cost is $13,245 for the project in Table 5-6 (Example 5-8) with a total direct cost of $88,300, find the prorated field supervision costs for various elements of the project. Furthermore, if the general office overhead charged to the project is 4% of the direct field cost which is the sum of basic costs and field supervision cost, find the prorated general office overhead costs for various elements of the project. For the project, y = $88,300 and F = $13,245. Hence: z = 13,245 + 88,300 = $101,545 G = (0.04)(101,545) = $4,062 w = 101,545 + 4,062 = $105,607 The results of the proration of costs to various elements are shown in Table 5-7. TABLE 5-7 Proration of Field Supervision and Office Overhead Costs Allocated Total Allocated Description Basic cost field supervision cost field cost overhead cost Total cost yi Fi zi Gi Li Formwork $50,400 $7,560 $57,960 $2,319 $60,279 Rebars 4,400 660 5,060 202 5,262 Concrete 33,500 5,025 38,525 1,541 40,066 Total $88,300 $13,245 $101,545 $4,062 $105,607 Example 5-10: A standard cost report for allocating overhead The reliance on labor expenses as a means of allocating overhead burdens in typical management accounting systems can be illustrated by the example of a particular product's standard cost sheet. [5] Table 5-8 is an actual product's standard cost sheet of a company following the procedure of using overhead burden rates assessed per direct labor hour. The material and labor costs for manufacturing a type of valve were estimated from engineering studies and from current material and labor prices. These amounts are summarized in Columns 2 and 3 of Table 5-8. The overhead costs shown in Column 4 of Table 5-8 were obtained by allocating the expenses of several departments to the various products manufactured in these departments in proportion to the labor cost. As shown in the last line of the table, the material cost represents 29% of the total cost, while labor costs are 11% of the total 151
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