5 Cost Estimation

Items	Unit	Quantity	Unit price
			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
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	100.00	80.00
Flagging	hr	20,000	8.25	12.50
Prestressed concrete member
type IV, 141’x4”	ea	7	12,000	16,000
132’x4”	ea	6	11,000	14,000
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
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

Treatment plant type	Exponent m	Capacity range (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:

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

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.

In contrast, an interesting NAC Executive Insight on Diseconomies of Scale is shared by Prieto et al (March 5, 2021).

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:

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.

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.

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.

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:

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.

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.

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 Q_i be the quantity of the i^th element and u_i be the corresponding unit cost. Then, the total cost of the project is given by:

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, u_i 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 C_i be the purchase cost of a major equipment component i and f_i 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:

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 C_i may be obtained by applying the exponential rule so the use of Equation (5.8) may involve a combination of cost estimation methods.

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 Q_i be the quantity of work for task i, M_i be the unit material cost of task i, E_i be the unit equipment rate for task i, L_i be the units of labor required per unit of Q_i, and W_i be the wage rate associated with L_i. In this case, the total cost y is:

Note that W_iL_i yields the labor cost per unit of Q_i, 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

Example 5-8: Cost estimate using labor, material and equipment rates.

For the given quantities of work Q_i 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

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 y_i be the total basic cost for task i. If F is the total field supervision cost and F_i is the proration of that cost to task i, then a typical proportional allocation is:

Similarly, let z be the total direct field cost which includes the total basic cost and the field supervision cost of the project, and z_i be the direct field cost for task i. If G is the general office overhead for proration to all tasks, and G_i is the share for task i, then

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 w_i be that attributable task i. Then,

and

 

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

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 cost. The allocated overhead cost constitutes 60% of the total cost. Even though material costs exceed labor costs, only the labor costs are used in allocating overhead. Although this type of allocation method is common in industry, the arbitrary allocation of joint costs introduces unintended cross subsidies among products and may produce adverse consequences on sales and profits. For example, a particular type of part may incur few overhead expenses in practice, but this phenomenon would not be reflected in the standard cost report.

TABLE 5-8  Standard Cost Report for a Type of Valve

5.8 Cost Indices

Since historical cost data are often used in making cost estimates, it is important to note the price level changes over time. Trends in price changes can also serve as a basis for forecasting future costs. The input price indices of labor and/or material reflect the price level changes of such input components of construction; the output price indices, where available, reflect the price level changes of the completed facilities, thus to some degree also measuring the productivity of construction.

A price index is a weighted aggregate measure of constant quantities of goods and services selected for the package. The price index at a subsequent year represents a proportionate change in the same weighted aggregate measure because of changes in prices. Let l_t be the price index in year t, and l_t+1 be the price index in the following year t+1. Then, the percent change in price index for year t+1 is:

If the price index at the base year t=0 is set at a value of 100, then the price indices l1, l2…ln for the subsequent years t=1,2…n can be computed successively from changes in the total price charged for the package of goods measured in the index.

The best-known indicators of general price changes are the Gross Domestic Product (GDP) deflators compiled periodically by the U.S. Department of Commerce, and the consumer price index (CPI) compiled periodically by the U.S. Department of Labor. They are widely used as broad gauges of the changes in production costs and in consumer prices for essential goods and services. Special price indices related to construction are also collected by industry sources since some input factors for construction and the outputs from construction may disproportionately outpace or fall behind the general price indices. Examples of special price indices for construction input factors are the wholesale Building Material Price and Building Trades Union Wages, both compiled by the U.S. Department of Labor. In addition, the construction cost index and the building cost index are reported periodically in the Engineering News-Record (ENR). Both ENR cost indices measure the effects of wage rate and material price trends, but they are not adjusted for productivity, efficiency, competitive conditions, or technology changes. Consequently, all these indices measure only the price changes of respective construction input factors (such as wood, steel, and concrete) as represented by constant quantities of material and/or labor. On the other hand, the price indices of various types of completed facilities reflect the price changes of construction output including all pertinent factors in the construction process. The building construction output indices compiled by Turner Construction Company and Handy-Whitman Utilities are compiled in the U.S. Statistical Abstracts published each year.

In Canada, by searching the Statistics Canada site Building construction price indexes, by type of building and division can be compiled, as illustrated in Figure 5-7.

Figure 5-7  Canadian Construction Price Index Data for Residential Buildings, 2020-2023

Table 5-9 shows a variety of United States indices from the same period, including the Gross Domestic Product (GDP) price deflator, the ENR building index, and the Turner Construction Company Building Cost Index from 1996 to 2007, using 2000 as the base year with an index of 100. Figure 5-8 illustrates more recent construction cost data.

TABLE 5-9  Summary of Input and Output Price Indices, 1996-2007

Note: Index = 100 in base year of 2000.

Figure 5-8  Turner Construction. (January 3, 2023). Construction cost index for non-residential buildings in the U.S. from 2005 to 2022 [Graph]. In Statista. Retrieved January 05, 2024, from https://www.statista.com/statistics/916054/us-nonresidential-building-construction-market-cost/ .

Since construction costs vary in different regions of the United States and in all parts of the world, locational indices showing the construction cost at a specific location relative to the national trend are useful for cost estimation. ENR publishes periodically the indices of local construction costs at the major cities in different regions of the United States as percentages of local to national costs.

When the inflation rate is relatively small, i.e., less than 10%, it is convenient to select a single price index to measure the inflationary conditions in construction and thus to deal only with a single set of price change rates in forecasting. Let j_t be the price change rate in year t+1 over the price in year t. If the base year is denoted as year 0 (t=0), then the price change rates at years 1,2,…t are j₁,j₂,…j_t, respectively. Let A_t be the cost in year t expressed in base-year dollars and A_t‘ be the cost in year t expressed in then-current dollars. Then:

If the prices of certain key items affecting the estimates of future benefits and costs are expected to escalate faster than the general price levels, it may become necessary to consider the differential price changes over and above the general inflation rate. For example, during the period between 1973 through 1979, it was customary to assume that fuel costs would escalate faster than the general price levels. With hindsight in 1983, the assumption for estimating costs over many years would have been different. During the pandemic, from 2020 to 2022, the price of lumber doubled and then it gave up almost all that increase in the next two years (Figure 5-8). Because of the uncertainty in the future, the use of differential inflation rates for special items should be judicious.

Figure 5-9  Bureau of Labor Statistics. (November 15, 2023). Producer price index (PPI) of softwood lumber in the United States from January 2020 to October 2023 [Graph]. In Statista. Retrieved January 05, 2024, from https://www.statista.com/statistics/195406/us-producer-price-index-of-softwood-lumber/

Future forecasts of costs will be uncertain: the actual expenses may be much lower or much 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. For the purpose of forecasting, it is often sufficient to project the trend of future prices by using a constant rate j for price changes in each year over a period of t years, then

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

A longer term perspective might use the average increase over a horizon of n past periods:

More sophisticated forecasting models to predict future cost increases include corrections for items such as economic cycles and technology changes.

Example 5-12: Changes in highway and building costs

Figure 5-10 shows the change of standard highway costs from 1992 to 2002, and Table 5-10 shows the change of residential building costs from 1970 to 1990.  

Figure 5-10  Producer Prices of Highway and Street Construction (Producer Price Index: Highways and Streets-monthly data).

TABLE 5-10  Comparison of Residential Building Costs, 1970-1990

5.9 Applications of Cost Indices to Estimating

In the screening estimate of a new facility, a single parameter is often used to describe a cost function. For example, the cost of a power plant is a function of electricity generating capacity expressed in megawatts, or the cost of a sewage treatment plant as a function of waste flow expressed in million gallons per day.

The general conditions for the application of the single parameter cost function for screening estimates are:

1. Exclude special local conditions in historical data
2. Determine new facility cost on basis of specified size or capacity (using the methods described in Sections 5.3 to 5.6)
3. Adjust for inflation index
4. Adjust for local index of construction costs
5. Adjust for different regulatory constraints
6. Adjust for local factors for the new facility

Some of these adjustments may be done using compiled indices, whereas others may require field investigation and considerable professional judgment to reflect differences between a given project and standard projects performed in the past.

Example 5-13: Screening estimate for a refinery

The total construction cost of a small refinery with a production capacity of 200,000 bbl/day in Gary, Indiana, completed in 2019 was $100 million. It is proposed that a similar refinery with a production capacity of 300,000 bbl/day be built in Los Angeles, California, for completion in 2023. For the additional information given below, make an order of magnitude estimate of the cost of the proposed plant.

1. 1. In the total construction cost for the Gary, Indiana, plant, there was an item of $5 million for site preparation which is not typical for other plants.
   2. The variation of sizes of the refineries can be approximated by the exponential rule, Equation (5.4), with m = 0.6.
   3. The inflation rate is expected to be 8% per year from 2019 to 2023.
   4. The location index was 0.92 for Gary, Indiana and 1.14 for Los Angeles in 2019. These indices are deemed to be appropriate for adjusting the costs between these two cities.
   5. New carbon scrubbing equipment for the LA plant costs $7 million in 2023 dollars (not required in the Gary plant).
   6. The contingency cost due to inclement weather delay will be reduced by the amount of 1% of total construction cost because of the favorable climate in LA (compared to Gary).

On the basis of the above conditions, the estimate for the new project may be obtained as follows:

1. 1. 1. Typical cost excluding special item at Gary, IN is

$100 million – $5 million = $ 95 million

1. 2. Adjustment for capacity based on the exponential law yields

($95)(300,000/200,000)^0.6 = (95)(1.5)^0.6 = $121.2 million

1. 3. Adjustment for inflation leads to the cost in 2023 dollars as

($121.2)(1.08)⁴ = $164.6 million

1. 4. Adjustment for location index gives

($164.6)(1.14/0.92) = $204.6 million

1. 5. Adjustment for new carbon scrubbing equipment at the LA plant gives

$204.6 + $7 = $211.6 million

1. 6. Reduction in contingency cost yields

($211.6)(1-0.01) = $209.5 million

Since there is no adjustment for the cost of construction financing, the order of magnitude estimate for the new project is $209.5 million.

Example 5-14: Conceptual estimate for a chemical processing plant

In making a preliminary estimate of a chemical processing plant, several major types of equipment are the most significant parameters in affecting the installation cost. The cost of piping and other ancillary items for each type of equipment can often be expressed as a percentage of that type of equipment for a given capacity. The standard costs for the major equipment types for two plants with different daily production capacities are as shown in Table 5-11. It has been established that the installation cost of all equipment for a plant with daily production capacity between 100,000 bbl and 400,000 bbl can best be estimated by using linear interpolation of the standard data.

TABLE 5-11  Cost Data for Equipment and Ancillary Items

A new chemical processing plant with a daily production capacity of 200,000 bbl is to be constructed in Memphis, TN in four years. Determine the total preliminary cost estimate of the plant including the building and the equipment on the following basis:

1. 1. The installation cost for equipment was based on linear interpolation from Table 5-11, and adjusted for inflation for the intervening four years. We expect inflation in the four years to be similar to the period 1990-1994 and we will use the GNP Deflator index.
   2. The location index for equipment installation is 0.95 for Memphis, TN, in comparison with the standard cost.
   3. An additional cost of $500,000 was required for the local conditions in Memphis, TN.

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

1. 1. The costs of the equipment and ancillary items for a plant with a capacity of 200,000 bbl can be estimated by linear interpolation of the data in Table 5-11 and the results are shown in Table 5-12.
      

TABLE 5-12  Results of Linear Interpolation for an Estimation Example

1. 2. Hence, the total project cost in thousands of current dollars is given by Equation (5.8) as:

($5,333)(1.37) + ($3,333)(1.42) +($2,667)(1.47) + ($2,000)(1.57) =
= $2,307 + $4,733 + $3,920 + $3,140 = $ 19,000

1. 3. The corresponding cost in thousands of four-years-in-the-future dollars using Equation (5.16) and Table 5-9 is:

($19,100)(105/94) = $21,335

1. 4. The total cost of the project after adjustment for location is

(0.95)($21,335,000) + $500,000   $20,800,000

5.10 Estimate Based on Engineer’s List of Quantities

The engineer’s estimate is based on a list of items and the associated quantities from which the total construction cost is derived. This same list is also made available to the bidders if unit prices of the items on the list are also solicited from the bidders. Thus, the itemized costs submitted by the winning contractor may be used as the starting point for budget control.

In general, the progress payments to the contractor are based on the units of work completed and the corresponding unit prices of the work items on the list. Hence, the estimate based on the engineers’ list of quantities for various work items essentially defines the level of detail to which subsequent measures of progress for the project will be made.

Example 5-15: Bid estimate based on engineer’s list of quantities

Using the unit prices in the bid of contractor 1 for the quantities specified by the engineer in Table 5-2 (Example 5-3), we can compute the total bid price of contractor 1 for the roadway project. The itemized costs for various work items as well as the total bid price are shown in Table 5-13.

TABLE 5-13: Bid Price of Contractor 1 in a Highway Project

 

5.10 Estimate Based on Engineer’s List of Quantities

The engineer’s estimate is based on a list of items and the associated quantities from which the total construction cost is derived. This same list is also made available to the bidders if unit prices of the items on the list are also solicited from the bidders. Thus, the itemized costs submitted by the winning contractor may be used as the starting point for budget control.

In general, the progress payments to the contractor are based on the units of work completed and the corresponding unit prices of the work items on the list. Hence, the estimate based on the engineers’ list of quantities for various work items essentially defines the level of detail to which subsequent measures of progress for the project will be made.

Example 5-15: Bid estimate based on engineer’s list of quantities

Using the unit prices in the bid of contractor 1 for the quantities specified by the engineer in Table 5-2 (Example 5-3), we can compute the total bid price of contractor 1 for the roadway project. The itemized costs for various work items as well as the total bid price are shown in Table 5-13.

TABLE 5-13: Bid Price of Contractor 1 in a Highway Project

5.11 Allocation of Construction Costs Over Time

Since construction costs are incurred over the entire construction phase of a project, it is often necessary to determine the amounts to be spent in various periods to derive the cash flow profile, especially for large projects with long durations. Consequently, it is important to examine the percentage of work expected to be completed at various time periods to which the costs would be charged. More accurate estimates may be accomplished once the project is scheduled as described in Chapter 10, but some rough estimate of the cash flow may be required prior to this time.

Consider the basic problem in determining the percentage of work completed during construction. One common method of estimating percentage of completion is based on the amount of money spent relative to the total amount budgeted for the entire project. This method has the obvious drawback in assuming that the amount of money spent has been used efficiently for production. A more reliable method is based on the concept of value of work completed which is defined as the product of the budgeted labor hours per unit of production and the actual number of production units completed, and is expressed in budgeted labor hours for the work completed. Then, the percentage of completion at any stage is the ratio of the value of work completed to date and the value of work to be completed for the entire project. Regardless of the method of measurement, it is informative to understand the trend of work progress during construction for evaluation and control. (Two other measures that will be covered later in the chapter on project controls are cost of work completed and earned value.)

In general, the work on a construction project progresses gradually from the time of mobilization until it reaches a plateau; then the work slows down gradually and finally stops at the time of completion. The rate of work done during various time periods (expressed in the percentage of project cost per unit time) is shown schematically in Figure 5-11 in which ten time periods have been assumed. The solid line A represents the case in which the rate of work is zero at time t = 0 and increases linearly to 12.5% of project cost at t = 2, while the rate begins to decrease from 12.5% at t = 8 to 0% at t = 10. The dotted line B represents the case of rapid mobilization by reaching 12.5% of project cost at t = 1 while beginning to decrease from 12.5% at t = 7 to 0% at t = 10. The dash line C represents the case of slow mobilization by reaching 12.5% of project cost at t = 3 while beginning to decrease from 12.5% at t = 9 to 0% at t = 10.

Figure 5-11:  Rate of Work Progress over Project Time

The value of work completed at a given time (expressed as a cumulative percentage of project cost) is shown schematically in Figure 5-12. In each case (A, B or C), the value of work completed can be represented by an “S-shaped” curve. You will see (or may have already seen) such curves on charts in the project manager’s office. The effects of rapid mobilization and slow mobilization are indicated by the positions of curves B and C relative to curve A, respectively.

Figure 5-12:  Value of Work Completed over Project Time

While the curves shown in Figures 5-11 and 5-12 represent highly idealized cases, they do suggest the latitude for adjusting the schedules for various activities in a project. While the rate of work progress may be changed quite drastically within a single period, such as the change from rapid mobilization to a slow mobilization in periods 1, 2 and 3 in Figure 5-11, the effect on the value of work completed over time will diminish in significance as indicated by the cumulative percentages for later periods in Figure 5-12. Thus, adjustment of the scheduling of some activities may improve the utilization of labor, material and equipment, and any delay caused by such adjustments for individual activities is not likely to cause problems for the eventual progress toward the completion of a project.

In addition to the speed of resource mobilization, another important consideration is the overall duration of a project and the amount of resources applied. Various strategies may be applied to shorten the overall duration of a project such as overlapping design and construction activities (as described in Chapter 2) or increasing the peak amounts of labor and equipment working on a site. However, spatial, managerial and technical factors will typically place a minimum limit on the project duration or cause costs to escalate with shorter durations.

Example 5-16: Calculation of Value of Work Completed

From the area of work progress in Figure 5-11, the value of work completed at any point in Figure 5-12 can be derived by noting the area under the curve up to that point in Figure 5-11. The result for t = 0 through t = 10 is shown in Table 5-14 and plotted in Figure 5-12.

TABLE 5-14  Calculation of Value of Work Completed

5.12 Computer Aided Cost Estimation

Numerous computer aided cost estimation software systems are now available. These range in sophistication from simple spreadsheet calculation software to integrated systems involving design and price negotiation over the Internet. While this software involves costs for purchase, maintenance, training and computer hardware, some significant efficiencies often result. In particular, cost estimates may be prepared more rapidly and with less effort.

Some of the common features of computer aided cost estimation software include:

• Databases for unit cost items such as worker wage rates, equipment rental or material prices. These databases can be used for any cost estimate required. If these rates change, cost estimates can be rapidly re-computed after the databases are updated.
• Databases of expected productivity for different component types, equipment and construction processes.
• Import utilities from design software for automatic quantity-take-off of components. Alternatively, special user interfaces may exist to enter geometric descriptions of components to allow automatic quantity-take-off.
• Export utilities to send estimates to cost control and scheduling software. This is very helpful to begin the management of costs during construction.
• Version control to allow simulation of different construction processes or design changes for the purpose of tracking changes in expected costs.
• Provisions for manual review, over-ride and editing of any cost element resulting from the cost estimation system
• Flexible reporting formats, including provisions for electronic reporting rather than simply printing cost estimates on paper.
• Archives of past projects to allow rapid cost-estimate updating or modification for similar designs.

A typical process for developing a cost estimate using one of these systems would include:

1. If a similar design has already been estimated or exists in the company archive, the old project information is retrieved.
2. A cost engineer modifies, adds or deletes components in the project information set. If a similar project exists, many of the components may have few or no updates, thereby saving time.
3. A cost estimate is calculated using the unit cost method of estimation. Productivities and unit prices are retrieved from the system databases. Thus, the latest price information is used for the cost estimate.
4. The cost estimation is summarized and reviewed for any errors.

5.13 Estimation of Operating Costs

In order to analyze the life cycle costs of a proposed facility, it is necessary to estimate the operation and maintenance costs over time after the start up of the facility. The stream of operating costs over the life of the facility depends upon subsequent maintenance policies and facility use. In particular, the magnitude of routine maintenance costs will be reduced if the facility undergoes periodic repairs and rehabilitation at periodic intervals.

Since the trade-off between the capital cost and the operating cost is an essential part of the 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. The techniques of estimating life cycle costs are similar to those used for estimating capital costs, including empirical cost functions and the unit cost method of estimating the labor, material and equipment costs. However, it is the interaction of the operating and capital costs which deserve special attention.

As suggested earlier in the discussion of the exponential rule for estimating, the value of the cost exponent may influence the decision whether extra capacity should be built to accommodate future growth. Similarly, the economy of scale may also influence the decision on rehabilitation at a given time. As the rehabilitation work becomes extensive, it becomes a capital project with all the implications of its own life cycle. Hence, the cost estimation of a rehabilitation project may also involve capital and operating costs.

While deferring the discussion of the economic evaluation of constructed facilities to Chapter 6, 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 with respect to the present. Consequently, the cost data at different time periods must be converted to a common baseline if meaningful comparison is desired.

Example 5-17: Maintenance cost on a roadway [6]

Maintenance costs for constructed roadways tend to increase with both age and use of the facility. As an example, the following empirical model was estimated for maintenance expenditures on sections of the Ohio Turnpike:

C = 596 + 0.0019 V + 21.7 A

where C is the annual cost of routine maintenance per lane-mile (in 1967 dollars), V is the volume of traffic on the roadway (measured in equivalent standard axle loads, ESAL, so that a heavy truck is represented as equivalent to many automobiles), and A is the age of the pavement in years since the last resurfacing. According to this model, routine maintenance costs will increase each year as the pavement service deteriorates. In addition, maintenance costs increase with additional pavement stress due to increased traffic or to heavier axle loads, as reflected in the variable V.

For example, for V = 500,300 ESAL and A = 5 years, the annual cost of routine maintenance per lane-mile is estimated to be:

C = 596 + (0.0019)(500,300) + (21.7)(5)
= 596 + 950.5 + 108.5 = 1,655 (in 1967 dollars)

Example 5-18: Time stream of costs over the life of a roadway [7]

The time stream of costs over the life of a roadway depends upon the intervals at which rehabilitation is carried out. If the rehabilitation strategy and the traffic are known, the time stream of costs can be estimated.

Using 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. For example, a time stream of costs and resurfacing projects for one pavement section is shown in Figure 5-13. As described in the previous example, the routine maintenance costs increase as the pavement ages, but decline after each new resurfacing. As the pavement continues to age, resurfacing becomes more frequent until the roadway is completely reconstructed at the end of 35 years.

Figure 5-13:  Time Stream of Costs over the Life of a Highway Pavement

5.14 References

1. Ahuja, H.N. and W.J. Campbell, Estimating: From Concept to Completion, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1987.
2. Clark, F.D., and A.B. Lorenzoni, Applied Cost Engineering, Marcel Dekker, Inc., New York, 1978.
3. Clark, J.E., Structural Concrete Cost Estimating, McGraw-Hill, Inc., New York, 1983.
4. Diekmann, J.R., “Probabilistic Estimating: Mathematics and Applications,” ASCE Journal of Construction Engineering and Management, Vol. 109, 1983, pp. 297-308.
5. Humphreys, K.K. (ed.) Project and Cost Engineers’ Handbook (sponsored by American Association of Cost Engineers), 2nd Ed., Marcel Dekker, Inc., New York, 1984.
6. Maevis, A.C., “Construction Cost Control by the Owners,” ASCE Journal of the Construction Division, Vol. 106, 1980, pp. 435-446.
7. Wohl, M. and C. Hendrickson, Transportation Investment and Pricing Principles, John Wiley & Sons, New York, 1984.

5.15 Problems

(1) Suppose that the grouting method described in Example 5-2 is used to provide a grouting seal beneath another landfill of 12 acres. The grout line is expected to be between 4.5 and 5.5 feet thickness. The voids in the soil layer are between 25% to 35%. Using the same unit cost data (in 1978 dollars), find the range of costs in a screening estimate for the grouting project.

(2) To avoid submerging part of U.S. Route 40 south and east of Salt Lake City due to the construction of the Jardinal Dam and Reservoir, 22 miles of highway were relocated to the west around the site of the future reservoir. Three separate contracts were let, including one covering 10 miles of the work which had an engineer’s estimate of $34,095,545. The bids were submitted on July 21, 1987 and the completion date of the project under the contract was August 15, 1989. (See ENR, October 8, 1987, p. 34). The three lowest bids were:

Find the percentage of each of these bidders below the engineer’s cost estimate.

(3) In making a screening estimate of an industrial plant for the production of batteries, an empirical formula based on data of a similar buildings completed before 1987 was proposed:

C = (16,000)(Q + 50,000)1/2

where Q is the daily production capacity of batteries and C is the cost of the building in 1987 dollars. If a similar plant is planned for a daily production capacity of 200,000 batteries, find the screening estimate of the building in 1987 dollars.

(4) For the cost factor K = $46,000 (in 1968 dollars) and m = 0.67 for an aerated lagoon basin of a water treatment plant in Table 5-4 (Example 5-6), find the estimated cost of a proposed new plant with a similar treatment process having a capacity of 480 million gallons (in 1968 dollars). If another new plant was estimated to cost $160,000 by using the same exponential rule, what would be the proposed capacity of that plant?

(5) Using the cost data in Figure 5-5 (Example 5-11), find the total cost including overhead and profit of excavating 90,000 cu yd of bulk material using a backhoe of 1.5 cu yd capacity for a detailed estimate. Assume that the excavated material will be loaded onto trucks for disposal.

(6) The basic costs (labor, material and equipment) for various elements of a construction project are given as follows:

Assuming that field supervision cost is 10% of the basic cost, and the general office overhead is 5% of the direct costs (sum of the basic costs and field supervision cost), find the prorated field supervision costs, general office overhead costs and total costs for the various elements of the project.

(7) In making a preliminary estimate of a chemical processing plant, several major types of equipment are the most significant components in affecting the installation cost. The cost of piping and other ancillary items for each type of equipment can often be expressed as a percentage of that type of equipment for a given capacity. The standard costs for the major equipment types for two plants with different daily production capacities are as shown in Table 5-15. It has been established that the installation cost of all equipment for a plant with daily production capacity between 150,000 bbl and 600,000 bbl can best be estimated by using liner interpolation of the standard data. A new chemical processing plant with a daily production capacity of 400,000 bbl is being planned. Assuming that all other factors remain the same, estimate the cost of the new plant.

(8) The total construction cost of a refinery with a production capacity of 100,000 bbl/day in Caracas, Venezuela, completed in 1977 was $40 million. It was proposed that a similar refinery with a production capacity of $160,000 bbl/day be built in New Orleans, LA for completion in 1980. For the additional information given below, make a screening estimate of the cost of the proposed plant.

1. In the total construction cost for the Caracus, Venezuela plant, there was an item of $2 million for site preparation and travel which is not typical for similar plants.
2. The variation of sizes of the refineries can be approximated by the exponential law with m = 0.6.
3. The inflation rate in U.S. dollars was approximately 9% per year from 1977 to 1980.
4. An adjustment factor of 1.40 was suggested for the project to account for the increase of labor cost from Caracas, Venezuela to New Orleans, LA.
5. New air pollution equipment for the New Orleans, LA plant cost $4 million in 1980 dollars (not required for the Caracas plant).
6. The site condition at New Orleans required special piling foundation which cost $2 million in 1980 dollars.

(9) The total cost of a sewage treatment plant with a capacity of 50 million gallons per day completed 1981 for a new town in Colorado was $4.5 million. It was proposed that a similar treatment plant with a capacity of 80 million gallons per day be built in another town in New Jersey for completion in 1985. For additional information given below, make a screening estimate of the cost of the proposed plant.

1. In the total construction cost in Colorado, an item of $300,000 for site preparation is not typical for similar plants.
2. The variation of sizes for this type of treatment plants can be approximated by the exponential law with m = 0.5.
3. The inflation rate was approximately 5% per year from 1981 to 1985.
4. The locational indices of Colorado and New Jersey areas are 0.95 and 1.10, respectively, against the national average of 1.00.
5. The installation of a special equipment to satisfy the new environmental standard cost an extra $200,000 in 1985 dollar for the New Jersey plant.
6. The site condition in New Jersey required special foundation which cost $500,000 in 1985 dollars.

(10) Using the ENR building cost index, estimate the 1985 cost of the grouting seal on a landfill described in Example 5-2, including the most likely estimate and the range of possible cost.

(11) Using the unit prices in the bid of contractor 2 for the quantities specified by the engineer in Table 5-2 (Example 5-3), compute the total bid price of contractor 2 for the roadway project including the expenditure on each item of work.

(12) The rate of work progress in percent of completion per period of a construction project is shown in Figure 5-14 in which 13 time periods have been assumed. The cases A, B and C represent the normal mobilization time, rapid mobilization and slow mobilization for the project, respectively. Calculate the value of work completed in cumulative percentage for periods 1 through 13 for each of the cases A, B and C. Also plot the volume of work completed versus time for these cases.

Figure 5-14

(13) The rate of work progress in percent of completion per period of a construction project is shown in Figure 5-15 in which 10 time periods have been assumed. The cases A, B and C represent the rapid mobilization time, normal mobilization and slow mobilization for the project, respectively. Calculate the value of work completed in cumulative percentage for periods 1 through 10 for each of the cases A, B and C. Also plot the volume of work completed versus time for these cases.

Figure 5-15

(14) Suppose that the empirical model for estimating annual cost of routine maintenance in Example 5-17 is applicable to sections of the Pennsylvania Turnpike in 1985 if the ENR building cost index is applied to inflate the 1967 dollars. Estimate the annual cost of maintenance per lane-mile of the tunrpike for which the traffic volume on the roadway is 750,000 ESAL and the age of the pavement is 4 years in 1985.

(15) The initial construction cost for a electric rower line is known to be a function of the cross-sectional area A (in cm2) and the length L (in kilometers). Let C1 be the unit cost of construction (in dollars per cm3). Then, the initial construction cost P (in dollars) is given by

P = C₁AL(10⁵)

The annual operating cost of the power line is assumed to be measured by the power loss. The power loss S (in kwh) is known to be

where J is the electric current in amperes, R is the resistivity in ohm-centimeters. Let C₂ be the unit operating cost (in dollars per kwh). Then, the annual operating cost U (in dollars) is given by

Suppose that the power line is expected to last n years and the life cycle cost T of the power line is equal to:

T = P + UK

where K is a discount factor depending on the useful life cycle n and the discount rate i (to be explained in Chapter 6). In designing the power line, all quantities are assumed to be known except A which is to be determined. If the owner wants to minimize the life cycle cost, find the best cross-sectional area A in terms of the known quantities.

5.16 Footnotes

1. This example was adapted with permission from a paper, “Forecasting Industry Resources,” presented by A.R. Crosby at the Institution of Chemical Engineers in London, November 4, 1981. (Back)
2. This example is adapted from a cost estimate in A.L. Tolman, A.P. Ballestero, W.W. Beck and G.H. Emrich, Guidance Manual for Minimizing Pollution from Waste Disposal Sites,Municipal Environmental Research Laboratory, U.S. Environmental Protection Agency, Cincinatti, Ohio, 1978. (Back)
3. See “Utah Interstate Forges On,” ENR, July 2, 1987, p. 39.(Back)
4. This and the next example have been adapted from P.M. Berthouex, “Evaluating Economy of Scale,” Journal of the Water Pollution Control Federation, Vol. 44, No. 11, November 1972, pp. 2111-2118. (Back)
5. See H.T. Johnson and R.S. Kaplan, Relevance Lost: The Rise and Fall of Management Accounting,Harvard Business School Press, Boston, MA 1987, p. 185. (Back)
6. This example is adapted from McNeil, S. and C. Hendrickson, “A Statistical Model of Pavement Maintenance Expenditure,” Transportation Research RecordNo. 846, 1982, pp. 71-76. (Back)
7. This example is adapted from S. McNeil, Three Statistical Models of Road Management Based on Turnpike Data,M.S. Thesis, Carnegie-Mellon University, Pittsburgh, PA, 1981. (Back)