## Estimate

A capacity factored estimate is one in which the cost of a new facility is derived from the cost of a similar facility of a known (but usually different) capacity. It relies on the nonlinear relationship between capacity and cost. In other words, the ratio of costs between two similar facilities of different capacities equals the ratio of the capacities multiplied by an exponent: \$B = (\$A) * (CapB / CapA) ^ e

where:

• \$B is the cost of the facility being estimated,

• \$A is the known cost of a similar facility,

• CapB is the capacity of the facility being estimated,

• CapA is the capacity of the similar facility, and

• “e” is the exponent or proration factor.

The exponent “e” typically lies between 0.5 and 0.85, depending on the type of facility, and must be analyzed carefully for
its applicability to each estimating situation. The exponent “e” used in the capacity factor equation is actually the slope
of the curve that has been drawn to reflect the change in the cost of a facility as it is made larger or smaller.

These curves are typically drawn from the data points of the known costs of completed facilities. The slope will usually
appear as a straight line when drawn on log-log paper. With an exponent value less than 1, scales of economy are achieved such that as facility capacity increases by a percentage (say, 20 percent), the costs to build the larger facility increase by less than 20 percent.

The methodology of using capacity factors is sometimes referred to as the “scale of operations” method or the “six
tenth’s factor” method due to the common reliance on an exponent value of 0.6 if no other information is available.
With an exponent of 0.6, doubling the capacity of a facility increases costs by approximately 50 percent, and tripling the
capacity of a facility increases costs by approximately 100 percent.

Capacity factored estimating can be quite accurate. If the capacity factor used in the estimating algorithm is relatively close to the actual value, and if the facility being estimated is relatively close in size to the similar facility of known cost, then the potential error from capacity factoring is quite small, and is certainly well within the level of accuracy that would be expected from such a conceptual estimating method.

Thus, if the facility size being estimated is reasonably close to the size of the known facility, and a realistic capacity factor exponent is used, error from the capacity factoring algorithm
is small. However, this error can be compounded by other assumptions we must make in an actual estimating situation. Typically, we must also adjust for differences in scope, location and time between the estimated facility and the known
facility. Each of these adjustments can also add to the level of error in the overall estimate.      The key steps in preparing a capacity factor estimate, therefore, are the following:
• Deduct costs from the known base case that are not applicable in the new plant being estimated;
• Apply location and escalation adjustments to normalize costs;
• Apply the capacity factor algorithm to adjust for plant size;
• Add any additional costs which are required for the new plant but which were not included in the known plant.

The capacity factor estimating method provides a relatively quick and sufficiently accurate means to prepare early estimates during the concept screening stage of a project. The method requires historical cost and capacity data for similar plants and processes. Although published data on capacity factors exists, the best data would be from our own organization and requires a level of commitment to maintain. When using this method, the new and existing known plant should be near duplicates, and reasonably close in size. We must account for differences in scope, location, and time. Each of the adjustments that we make adds additional uncertainty and potential error to the estimate. Despite this, capacity factor estimates can be quite accurate and are often used to support decision-making at the pre-design stage of a project.