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The main focus is the application of the cost-to-capacity method and scale factors in completing order-of magnitude cost estimates for entire industrial facilities and pieces of machinery and equipment. Basic methodology is discussed along with considerations that should be noted before applying the cost-to-capacity method and scale factors.

Examples are also presented to provide a better understanding of basic methodologies. While the concepts presented were originally developed more than a half century ago, they continue to be effective tools in developing reliable order-of-magnitude cost estimates. A fundamental understanding of the cost-to-capacity method and scale factors should be obtained by all professionals involved in the development of cost estimates. Introduction The cost-to-capacity method: What is it, and how is it applied?

The concepts and methodology behind the cost-to-capacity method are not overly complex. Yet, the method is often not fully understood, and thus it is applied in an inappropriate and inconsistent manner in various cost estimating analyses. In the early stages of nearly any project, cost estimates are needed in order to make educated decisions going forward. Specifically, the economic viability of a project must be sufficiently supported in order to move forward in the planning process.

Basic methodology and pertinent factors related to the application of the cost-to-capacity method in cost estimation modeling are presented, along with an example. The correct application of scale factors in the cost-to-capacity method is then discussed, along with applicable methodology and a scale factor derivation example.

Cost-to-Capacity Methodology The cost-to-capacity method is an order-of-magnitude cost estimation tool that uses historical costs and capacity in order to develop current cost estimates for an entire facility or a particular piece of machinery or equipment.

Both Class 5 and Class 4 estimates are preliminary in nature and are based on limited information, while a Class 1 estimate is highly detailed and based on a fully defined project scope. More specifically, cost is a function of size raised to an exponent or scale factor. A scale factor of less than 1 indicates that economies of scale exist and the incremental cost of the next added unit of capacity will be cheaper than the previous unit of capacity.

When the scale factor is greater than 1, economies of scale do not exist; rather, diseconomies of scale exist and the incremental cost becomes more expensive for every added unit of capacity. A scale factor of exactly 1 indicates that a linear relationship exists and there is no change in the incremental cost per unit of added capacity.

It can be applied to quickly develop reasonable order-of-magnitude cost estimates. Potentially even more useful is its capacity to allow sensitivity analyses to be quickly performed when high degrees of accuracy are not required. Differences in location would almost always require the application of a locational cost adjustment factor due to factors that include but are not limited to regional differences in skilled labor rates union vs.

Likewise, different configurations or unique design or site characteristics would require a cost adjustment prior to completing the cost-to-capacity analysis which could include construction material differences, atypical off-site assets, and government mandated environmental control and monitoring equipment which vary by state or region, to name a few.

For example, it may be required to develop a cost estimate for a piece of industrial equipment in current dollars but the known costs are based on dollars. In general terms, to appropriately account for the effects of cost inflation, the known historical cost must be escalated using cost indices applicable to the technology in question.

The older the historical costs are, the greater potential they have to diminish the accuracy of the estimate. Thus, historical cost estimates that are escalated using Equation 2 should be analyzed to determine whether the cost vintages are still relevant. Using historical costs that are as current as possible will typically yield more meaningful results. Research indicates that a combined cycle power plant with a capacity of MW with the same technology had construction completed in in the same regional area.

It is determined that, in addition to being located in the same region, the existing plant is almost identical to the proposed plant in terms of overall design, with the exception of having fewer units. Thus, it is concluded that the historical cost of this plant is a good reference for the required cost estimation. Because the existing plant is located in the same regional area, no locational adjustment is required; further, the almost identical design requires no additional cost adjustment for unique design characteristics.

The only adjustments that need to be taken into account in this cost estimation are cost inflation and size scaling. First, the dollars must be converted to dollars.

An applicable index related to costs associated with combined cycle power plants must be referenced. An appropriate index indicates a index value of 1. Thus, the historical cost must be escalated to dollars per the previously introduced Equation 2, as shown below: Next, the escalated cost must be scaled to account for the difference in size between the proposed plant and the existing plant.

The previously introduced Equation 1 can now be mathematically manipulated and solved as follows: As represented by the above cost estimate example, a size increase of 2 times results in a cost increase of approximately 1. This expresses the previously introduced concept of economies of scale inherent in applying a scale factor of less than 1. Similarly illustrated is the fact that as the capacity of the power plant in this example increases, it becomes incrementally cheaper for each additional unit of added capacity.

Scale Factor Derivation Methodology One of most crucial components when applying the cost-to-capacity method is an appropriate scale factor. The previously mentioned study performed by C. Chilton in derived a common scale factor for chemical facilities of approximately 0. However, the majority of scale factors that are published do not provide supporting industry data and derivations.

When using published scaled factors multiple sources should be referenced in order to make certain a reliable figure is applied in any cost-to-capacity analysis. The methodology for deriving a scale factor is not much more complex than the cost-to-capacity method and the previously presented Equation 1.

Equation 1 can be transformed by applying natural logarithms to the cost and capacity data on both sides of the equation to develop a linear relationship. It can then be further manipulated to solve for the scale factor, x. The below equations show this relationship. Refer to Equation 1 for variable definitions. The above relationship outlines the basic concept behind the development of a linear relationship and the derivation of a scale factor.

To accomplish this, natural logarithms can be applied to an entire set of cost and capacity data and then graphed. A linear regression analysis of the natural logarithm of the cost and capacity data can then be performed using graphing computer software. These are similar to the considerations of the cost-to-capacity method, as previously stated. Scale Factor Derivation Example The previously described scale factor derivation method using regression analysis is best illustrated by an example.

The example again involves combined cycle power plant technology, as introduced in the previous example of the basic cost-to-capacity method. Table 1 below shows the net plant capacity in megawatts and associated total cost and cost per net capacity in dollars for certain combined cycle power plants per GTW. This data set was developed by GTW in a consistent manner based on contractor pricing and basic manufacturer designs, in which the location basis, technology, configuration, and costs considered are the same.

Thus, it is a good source for deriving a scale factor for a combined cycle power plant. Table 1 — Combined Cycle Power Plant Capacities and Costs[11] Table 1 clearly illustrates a declining trend in the cost per net capacity as the size of the plant increases. This indicates that economies of scale exist when constructing larger combined cycle power plants. Figure 1 below shows the declining cost per net capacity relationship. Net Capacity[11] The relationship of economies of scale that exists for combined cycle power plants is what is captured when deriving the scale factor for the above data set.

As previously described, in order to derive a scale factor from the above data set, natural logarithms are applied to both the total cost and capacity data and then graphed. A linear regression analysis is then performed on the natural logarithm of the total cost and net capacity to derive a linear regression equation. Capacity Regression Analysis natural logarithm of the total cost and capacity data from Table 1, along with the resultant linear regression equation.

Capacity Regression Analysis Per the linear regression equation shown in Figure 2 above, the slope of the line is 0. As previously discussed, this slope is representative of the scale factor for the given set of analyzed data.

Thus, the scale factor for the combined cycle power plants analyzed is concluded to be approximately 0. By visual inspection, the linear regression equation appears to closely match the set of data. Scale Factor Considerations It should be noted that the previous scale factor derivation is a simplified example in that one scale factor was derived for a broad range of capacities for combined cycle power plants.

Likewise, the fact that scale factors may vary over ranges of capacity should warrant the same level of caution when applying a single scale factor in cost-to-capacity analyses for a broad range of facility or equipment sizes. Utilizing a scale factor that is too large or too small will lead to less reliable cost estimate results.

The accuracy of the scale factor has a direct impact on the accuracy of the cost estimation that is being developed by a cost-to-capacity analysis. Conclusion The cost-to-capacity method allows cost estimates to be developed on the basis of historical cost and capacity information for similar facilities.

It does not involve complex computation and is relatively easy to use. However, the cost-to-capacity analysis must be applied in a consistent and appropriate manner in order to produce meaningful cost estimate results.

Required inflationary adjustments and locational adjustments must also be considered. An appropriate scale factor that is representative of the technology in question must be applied in the cost-to-capacity analysis to yield reliable results.

When all the necessary factors are considered, the cost-to-capacity method can yield useful cost estimate results. Specifically, it can provide quick and reliable order-of-magnitude cost estimates when only a limited project scope is known, which can be critical in determining the economic feasibility of a project. Thus, the cost-to-capacity method is a highly effective tool in developing cost estimates both for entire facilities, and for individual pieces of industrial machinery and equipment.

Endnotes Chilton, C. Ellsworth, Richard K. Remer, Donald S. Humphreys, Kenneth K. Dysert, Larry R. Chase, David J.

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## Cost-to-Capacity Method: Applications and Considerations

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