5. Cost Estimation

5.1 Costs Associated with Constructed Facilities

The capital cost for a construction project includes the expenses related to the inital establishment of the facility:

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.

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:

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

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

Source: Exxon Research and Engineering Company, Florham Park, NJ

5.2 Approaches to Cost Estimation

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 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.

5.3 Types of Construction Cost Estimates

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:
   Screening estimates (or order of magnitude estimates)
   Preliminary estimates (or conceptual estimates)
   Detailed estimates (or definitive estimates)
   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.
   Subcontractor quotations
   Quantity takeoffs
   Construction procedures.
3. 3. Control Estimates. For monitoring the project during construction, a control estimate is derived from available information to establish:
   Budget estimate for financing
   Budgeted cost after contracting but prior to construction
   Estimated cost to completion during the progress of construction.

Design Estimates

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.

Bid Estimates

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

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

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.

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

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

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.

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.

TABLE 5-2: Unit Prices in Two Contractors' Bids for Roadway Construction

5.4 Effects of Scale on Construction Cost

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.

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:

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

(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.

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 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

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

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.