COST INDEXES
A cost index is a number used to indicate change in magnitude as compared with the magnitude at some specified time usually taken as 100.
Cost indexes are produced by different procedures and different sources and published by several periodicals.
It is important to have a good knowledge of the procedures and sources utilized by the index editor before making use of the index.
Indexes are utilized when the cost of an article in the past is known. The following expression shows how to use a cost index.
NCC ={ Cost in the past } [ I(2) / I(1) ]
where, NCC = Needed current cost
I (1) = Index value at past time
I (2) = Index value at present time
INDEX LIMITATIONS
- 1. Indexes do not take local conditions into consideration.
- 2. Indexes do not make provision for technological advance.
- 3. Indexes are recommended within a 10 years range of known past cost only.
Example 1
A construction project was built at a cost of S.R. 15 million in 1986. The cost index for this kind of project at the construction time was 350. What would be the project cost in 1990, if the cost index for this year is 410 ?
The solution :
Project cost in 1990 = 15,000,000 * 410/350
Project cost in 1990 = S.R. 17,571,429
KNOWN COST INDEXES
ENGINEERING NEWS-RECORD CONSTRUCTION INDEX
The Engineering news-record construction Index shows variations of industrial construction cost due to variations in labor rates and material costs.
This index is based on an index value of 100 for the year 1949 and is developed upon a composite cost for 2,500 pounds of structural steel, 1,088 feet board measure of lumber, 6 bbl of cement and 200 hours of common labor.
MARSHALL AND SWIFT EQUIPMENT-COST INDEXES
The Marshall and Swift indexes are divided in two categories as follows:
- The all-industrial equipment index
- The process-industry equipment index
The former category is an arithmetic average of the individual indexes for 47 different types of industrial, commercial and housing equipment.
The process-industry equipment index is the weighted average of eight process-industry equipment, usually as follows :
Chemical 48
Petroleum 22
Paper 10
Rubber 8
Paint 5
Glass 3
Cement 2
Clay products 2
The above indexes are based on an index value of 100 for the year 1926.
The indexes include cost of machinery, major equipment, installation, fixtures, tools, office furniture and minor equipment.
COST FACTORS
Cost factors obtained by analysis of historical data of over 500 industrial capital projects are a handy tool for order of magnitude estimates.
After careful investigation the following factors are proposed :
Direct costs
- Purchased equipment cost 24%
- Installation 10%
- Instrument. & controls install 4%
- Piping installed 8%
- Electrical installed 4%
- Building including services 7%
- Services facilities installed 11%
- Land 2%
Total: 70%
Indirect costs
Engineering and supervision 10%
Construction expense 8%
Contractor's fee 6%
Contingency 6%
Total: 30%
The following example illustrates the utilization of cost factors to produce order of magnitude estimates.
Example 2.
Make an order of magnitude estimate for a factory, knowing that the cost of purchased equipment is $500,000.
The solution:
COST ASSIGNED
%
Direct costs
Equipment 500,000 24
Installation 208,000 10
Instrument /controls 83,000 4
Piping (installed) 166,400 8
Electrical (installed) 83,000 4
Buildings (services incl.) 145,600 7
Services facilities (inst.) 228,800 11
Land 41,600 2
Indirect costs
Engineering /Supervision 208,000 10
Construction expense 166,400 8
Contracting fee 124,800 6
TOTALS $ 2,080,400 100%
EQUIPMENT COST BY SCALING
When not enough cost data for a piece of equipment is available, the following mathematical expression, known as the six-tenth factor rule, provides the means of developing an order of magnitude estimate.
Cx = Cy ( Qx/Qy ) 0.6
where, Cx = Cost of equipment x
Cy = Cost of equipment y
Qx = Capacity of equipment x
Qy = Capacity of equipment y
Equation 1 is the equation of a straight line when drawn on log-log paper and the exponent 0.6 is the slope of that line.
Equation 1 should not be utilized beyond a tenfold range of capacity.
The utilization of 0.6 as the exponent for equation 1 is an oversimplification of the concept. The actual exponent value ranges between 0.2 and 1.0 for different kinds of equipment.
Furthermore, when the cost of the equipment at different capacities is known, the characteristic exponent for the equipment can be calculated by plotting the available information on Log-Log paper.
Example 3
A two hundred horse power air compressor costs $120,000. Estimate the cost of a 300 H.P. air compressor utilizing cost by scaling and knowing that the exponent value for this kind of equipment is 0.9.
By equation 1 :
Cx = 120,000 ( 300/200) 0.9
Cx = $ 172,847.60
Example 4
Estimate the cost by scaling of a plant producing 120,000 tons/year of Fertilizers, knowing the following information:
Capacity (tons/year) Cost ($)
20,000 870,000
50,000 1,830,000
75,000 2,640,000
100,000 3,370,000
Plotting the above information in log-log paper, the slope of the line can be calculated as follows:
slope = (log 3,370,000 - log 870,000) / (log 100,000 - log 20,000)
slope = 0.83
Utilizing equation 1:
Cost (120,000 tons/year plant) = 3,370,000 (120,000/100,000) 0.83
Cost (120,000 tons/year plant) = $ 3,920,580
TURNOVER RATIOS
Turnover ratios are the means to develop rapid order of magnitude cost estimates, utilizing the following mathematical expression:
TOR = Turnover ratio
TOR = GAS /Fixed capital investment (2)
where,
GAS = (Unit selling price)(annual production rate)
Turnover ratios are found to be in the range between 0.2 and 5.0 depending on the type of business establishment. For chemical industries the turnover ratio is usually in the range of 1.0 to 1.25.
Example 5
Estimate the fixed capital investment required for a chemical plant with an expected production of 30,000 tons per year of phosphate fertilizers that sell at $300 per ton.
The turnover ratio of this kind of industry is considered to be 1.1.
Utilizing the mathematical expression given by 2 above:
Fixed capital investment = 30,000(300)/1.1 = $8,181,000
CAPITAL RATIOS
Capital ratios are the reciprocal of turnover ratios or,
C R = Fixed capital investment / Gross annual sales (3)
As the turnover ratios, these are utilized for order of magnitude estimates.
THE LANG FACTORS METHOD
H.J. Lang suggests that a quick order of magnitude estimate for a process plant can be developed multiplying the delivered cost of equipment by the following factors:
- 3.10 For solid process plants
- 3.63 For solid-fluid process plants
- 4.74 For fluid process plants
Example 6
Make an order of magnitude estimate for a fluid process plant knowing that the delivered cost of the equipment is $ 4,000,000.
Utilizing the Lang factor for fluid plants:
Total plant cost = 4,000,000 (4.74) =$18,960,000
THE HAND FACTORS METHOD
Similar to the Lang factors method, W.E. Hand suggests that quick order of magnitude estimate for battery-limits process plants can be developed by multiplying the cost of different types of delivered equipment by the following factors:
- 4.0 For fractioning columns, pressure vessels, pumps and instruments
- 3.5 For heat exchangers
- 2.5 For compressors
- 2.0 For fired heaters
PARAMETRIC COST ESTIMATING
Parametric cost estimating is a technique for estimating costs from physical and/or performance characteristics of the subject under research, regardless of the magnitude of the aggregated systems involved.
Parametric estimating may be seen as the cost estimating of any system, made up of added components, by means of mathematical models containing parameters and derived from prior case histories.
Apparently, parametric cost estimating was an answer to the cost growth brought about in the 1960's due to rapidly changing technologies and performance standards.
Parametric cost estimating system building procedure.
This cost estimating procedure follows well known research techniques as follows:
Step Description
1 Problem definition
2 Data collection
3 Data normalization
4 Characteristics interdependence
5 Cost estimating relationships
6 Limitations
1 - Problem definition.
As in any Engineering endeavor, this first step determines the objectives and scope of the whole exercise.
2 - Data collection.
This step relates to historical cost information and how it may be collected.
Essential breakdown of cost collection usually refers to the project life cycle and its comprising phases.
Data collection must be planned according to specific needs and parametric definitions.
3 - Data normalization.
Data normalization means that all collected data must be adjusted for at least:
- Time;
- Size;
- Inflation;
- Technological advance;
- Learning process;
- Productivity; and
- Social activity.
All data gathered may be subject to consistent definitions to avoid redundant information or confusion.
4 - Cost drivers identification.
This includes identification of project characteristics which are most directly related to its cost. For instance: Size, complexity, density, fuel economy, speed etc.
5 - Cost estimating relationship.
Once all cost drivers are identified, a relationship or interdependence may be developed by means of statistical techniques such as regression analysis or the correlation coefficient.
6 - Limitations.
As it is well known all these statistical methods to arrive at a mathematical best representation of the system under study are subject to error since they are based on the development of the line or curve of best fit and are not an exact representation of the actual historical data.
- Forecasts must be subjected to professional interpretation.
- Time range for the derived relationship may be the most critical item.
- Sensitivity analysis should be carried out to test the results against the parameters influence.
- The most common difficulty in parametric estimating is to develop a comprehensive and sufficient data bank of historical costs.
- Records have to be collected from past projects, supplier quotations, price lists, and other sources.
Once the data has been normalized, a "curve-fit" procedure must be followed to find the best curve-fit for the data. Straight line, power curves, logarithmic curves, and exponential curves are tested and reliability measured to find the best curve fit.
Once the curve-fit procedure has taken place , the information is added to the data bank historical records to be utilized in future parametric estimating. The engineering input to the parametric estimating system is as essential as the data bank itself. The engineering goal should be to define and promote:
- The total design concept
- The individual tasks picture
- The component requirements
- A review by the cadre and
- A review by top management
There are five parametric estimating methods for utilization of the data bank in conjunction with the engineering information.
SYSTEM PARAMETERS (The sleeve of experience)
The average costs of a group of comparable projects, when equated or properly weighted and then plotted on log-log paper, dollars versus quantity, usually fall within a certain pattern similar to a sleeve in shape.
Each company has a unique sleeve of experience into which all of their experience data of completed programs will fall.
Learning curve techniques are then applied for the estimating of inexperienced but similar projects.
UNIT OF FUNCTION PARAMETERS
This method is based on the theory that anything can be estimated if one knows its weight and has a reliable cost per pound multiplier or any measurable function.
This method calls for developing constants from historical data and adjusting them for newness of components and techniques, inflation and state of the art.
PARAMETERS FOR BUDGETING MEN, MATERIALS AND MONEY
This method uses planning basic elements to set the estimate in perspective. This means spreading of the requirements (manpower, materials, money) for tasks for a project over the period of performance to provide costs for a co-ordinated plan to complete the project on schedule.
The estimate is based on:
- Establishing the required project activities;
- Finding activities precedence and time boundaries;
- Determining activities constraints; and
- Setting up activities manpower and material constraints.
PARAMETERS BY TYPE OF WORK AND/OR MATERIAL
Estimating standards (dollars per unit of output) can be developed and applied to each type of work to arrive at the estimated total cost for any project.
Standards may be as broad or as detailed as convenient.
PARAMETERS FOR MODULAR WORK MEASUREMENT
This method calls for a system procedure that uses historical data to develop monograms and formulas to be utilized in cost estimating new projects.
This method utilizes a data bank of essential production planning and estimating know-how of specialists for each type of work for developing modular historical data.
The example below shows the use of parametric cost estimating.
Example No.7
Develop a parametric cost estimate for a project with the following information.
The parameters are:
Parameter Parameter name Projected Quantity
code
1 Square feet of finished floor area 28,200
2 Linear feet of interior wall 23,700
3 Cross-sectional area of building 5,300
The work packages are:
Package name Parameter code Historical Unit cost
Excavation 3 0.40
Foundations 3 0.80
Exterior walls 1 0.95
Package name Parameter code Historical Unit cost
Interior walls 2 0.65
Finishes 2 0.70
Roof 3 0.29
Electrical 1 0.35
Mechanical 1 0.40
Plumbing 1 1.50
General conditions 1 0.34
The solution:
Estimated cost per trade:
Work package Code Unit cost Trade cost
Excavation 3 0.40 (5,300)0.40 = 2,120
Foundations 3 0.80 (5,300)0.80 = 4,240
Exterior walls 1 0.95 (28,200)0.95 =26,790
Interior walls 2 0.65 (23,700)0.65 = 15,405
Finishes 2 0.70 (23,700)0.70 = 16,590
Roof 3 0.29 (5,300)0.29 = 1,537
Electrical 1 0.35 (28,200)0.35 = 9,870
Mechanical 1 0.40 (28,200)0.40 = 11,280
Plumbing 1 1.50 (28,200)1.50 = 42,300
General cond. 1 0.34 (28,200)0.34 = 9,588
Total cost $ 139,720
RANGE ESTIMATING
Traditional estimating is an application of simple mathematics. All items of the estimate are represented by a number and to arrive to the total project estimate we add, subtract, multiply and divide these numbers assuming they are absolutes.
Real life tells us that cost estimates are affected by ranges of possibilities and not simple numbers frozen in time just waiting for us to count them.
Real life story is that we live in an uncertain world, a probabilistic one.
Range estimating is a decision tool that tells us the probability of having a cost overrun, how large it may be, and what should be done now to reduce risk.
Range estimating complements traditional estimating.
The basic assumptions of range estimating are:
- Only few elements of an estimate are critical (Pareto's rule application: the few significant and the many insignificant); and
- Measure uncertainty to manage it.(Montecarlo technique).
Range estimating breaks the problem down into its component parts. Critical elements of the estimate are identified, the uncertainty of each critical element is assessed and then by the use of the Montecarlo technique and a good computer the uncertainty at the bottom line may be measured.
The Range
Range estimating uses a range as the most effective measure of uncertainty.
The range is established by three parameters:
- The probability that the critical element's actual value is equal to or less than its target;
- The lowest estimate; and
- The highest estimate.
For instance, a critical element having a target of $5 and with the following range: probability of 75 percent, a lowest estimate of $3 and a highest estimate of $7, means:
- There are 75 percent chances out of 100 that the critical element's value will be equal to or less than $5.
- If the actual value is less than $5, it may be any value from $3 to $5.
- If the actual value is greater than $5, it may be any value between $5 and $7.
So the probability parameter measures the underrun probabilities, the lowest estimate measure the degree of potential under run and the highest estimate measure the degree of potential overrun.
Applying the Montecarlo technique one can come up with overrun, priority and contingency profiles that will give management a range cost estimate for the project at hand along with their probability of achieving a cost within that range.
The probability profile portrays the relationship of total cost to the chances of overrun.
The priority profile disclose those cost estimate elements contributing to larger risks and opportunities thereby presenting management with a chance to concentrate on them.
The contingency profile generated by this procedure is an excellent management tool to establish the confidence of not having an overrun by adding a contingency sum to the target estimate.
