This two-part series of articles has been abridged and adapted from the chapter “Analysis of Cost Behavior” by Elizabeth A. Eccher, Jeffrey H. Kinrich, and James H. Rosberg, in the book Lost Profits Damages: Principles, Methods, and Applications, edited by Everett P. Harry III and Jeffrey H. Kinrich (Valuation Products and Services, 2017).

In Part One of this series, we discussed concepts relevant to calculating avoided costs, a key step in calculating lost profits. In this article, we illustrate the use of these concepts in determining avoided costs.

Identifying the Cost Objects Comprising Lost Sales

The analysis of avoided costs logically follows, and depends on, an analysis of lost sales revenue, which is in turn a function of the quantity of products or services that were not sold and the price that would have been received if the sales had occurred. Therefore, for each cost object comprising the lost sales, the cost analysis requires consideration of the following questions:

• How many units of each product or service would have been sold?
• Over what time period(s) would the sales have occurred?
• At what prices would sales have occurred?

The total amount of any costs that are determined to be variable—and hence potentially avoided—will depend directly on the quantity of product that would have been manufactured and sold. In addition, because fixed costs may be fixed only with respect to a relevant range of time and activity, it is important to know whether the quantity of lost sales falls within or outside of that range. As discussed further below, the price of a lost sale may be relevant for certain incremental marketing costs, such as sales commissions.

Identifying Resources Involved in Producing the Product or Service

As discussed in Part 1, costs arise through the consumption of resources. Therefore, the analyst should gain an understanding of the resources and activities required to make the lost sales products or services. To gain this understanding, the analyst should consider the following:

• Are direct materials required?

These may include raw materials, such as steel or silicon, as well as components, such as batteries or circuit boards. Direct materials almost always result in variable, and thus incremental or avoidable, costs.

• Is direct labor required?

Labor costs depend on the nature of the contracts between employer and employees, which may affect the variability of these costs.

• Are productive assets (i.e., capital investments) used in the production process?

Machinery use, for example, can give rise to indirect costs, such as set-up, calibration, operating supplies, and routine maintenance. Similarly, the use of a factory or other building can give rise to indirect costs related to ongoing maintenance and other operating overhead costs, such as for electricity, other utilities, and security.

Identifying the Resources Involved in Selling and Delivering the Product or Service

In addition to production costs, the company may incur costs related to delivering and selling the product or service in question, as well as costs related to future obligations resulting from a sale. The following considerations will be relevant to this assessment:

• How are sales generated? Is there a direct sales force that receives a sales commission?
• Does the seller bear the cost of transporting the products to buyers? If so, the behavior of transportation/delivery costs should be analyzed.
• Is the product or service covered by a warranty or other contract that will give rise to expected costs in the future? Warranties obligate the seller to guarantee certain aspects of product performance after delivery.
• Is additional capital required to produce a good or service and, if so, at what cost? For example, the company may have accounts receivable or may purchase and hold relevant inventory. Whether the funds are provided by the company or sourced externally, the company is incurring a cost by using funds from which it could otherwise earn a return on investment.

Identifying the Cost Data Available for Analysis

For financial reporting under generally accepted accounting principles (GAAP), firms must calculate the cost of products they produce or purchase and transfer those costs from an inventory account to an expense called cost of goods sold (COGS) as the products are sold. COGS often include, however, both direct costs that can be traced to products and indirect costs, such as warehousing or depreciation costs, that may be unlikely to change as sales volume increases, at least within a relevant range. Nevertheless, the unit costs calculated under GAAP can provide a useful starting point, particularly if the underlying financial records allow the analyst to disaggregate unit costs into components (such as materials, labor, and various types of overhead) that can be further analyzed.

Beyond the cost systems used for financial reporting, firms sometimes maintain internal records and systems to support their own cost-management efforts.

Developing Hypotheses about Likely Cost Behaviors

When developing hypotheses about cost behavior, the central question is: What incremental costs must be incurred to develop, produce, and sell the good or service within the relevant time frame and range? In some cases, strong hypotheses about cost behavior exist at the outset of the analysis.

As mentioned in Part 1, though, expected cost behavior may not be as clear-cut for other resources. Consider direct labor costs in automobile manufacturing. Unlike direct materials, labor is not usually purchased by the unit (e.g., by the hour or even by the day). Rather, employees often have labor contracts that limit the firm’s ability to terminate employment over short periods. Thus, labor is one example of a cost for which it is important for an analyst to carefully assess cost behavior in order to determine whether the cost can be expected to vary (or not) with incremental sales volumes over specific periods.

Testing the Hypotheses

Two of the most common methods used to test cost behavior and estimate avoided costs are account analysis and regression analysis. We discuss and illustrate each in turn.

Account Analysis

Account analysis (sometimes called the direct assignment method) is a simple but often valuable method for identifying fixed and variable costs. The analyst reviews the historical income statements or a detailed general ledger and judges whether costs reflected in each account are fixed or variable based on experience, observation of the accounts’ behavior, review of the business’s contracts, and consultation with other sources of expertise. This background provides valuable information about how costs relate to activities and how both activities and costs behave with respect to changes in production or sales volumes.

Although account analysis can be a useful tool for analyzing cost behavior, accounting data are often “messy” due to changes in accounting practices over time, the presence of amortized or allocated costs, and end-of-quarter or end-of-year adjustments, among other issues. These data problems can lead to nonsensical results; thus, it is often informative to combine account analysis with other tools, such as regression analysis.

Regression Analysis

Regression analysis is a generally accepted statistical method used to measure the degree and nature of association between a dependent variable (the variable the analyst seeks to explain) and one or more independent variables (the variables hypothesized to cause the behavior of the dependent variable). That is, the analyst seeks to measure the association of the rate of change of a dependent variable with the rate of change of independent variables.

In the context of lost-profits analysis, costs are typically the dependent variable, whereas measures of activity (such as inputs to or from manufacturing processes or units sold) are typically among the independent variables. Analysts might use regression analysis when they have data for a dozen or more time periods for two or more particular costs or volumes and want to find a relation that can predict one value given the others.

Although the mathematics behind regression analysis may be complex, it is a powerful tool with which to measure the extent of the correlation between dependent and independent variables.

Developing Conclusions, Subjecting Them to “Sanity Checks,” and Revising

A common refrain in scientific analyses is that “correlation is not causation.” Regression analysis may yield spurious results, such as finding a statistically significant relationship between cost and sales (or production) that does not reflect a causal relationship, or failing to find a statistical relationship when a causal relationship does exist. Moreover, regression analysis may fail to identify an actual incremental cost when measures of cost are not recorded when they are incurred. For example, depreciation of capital equipment is typically recorded according to a preset formula, not according to the intensity of use of the machinery. Therefore, a regression analysis of depreciation cost will typically not find a statistically significant relationship with production even if machinery does wear out in proportion to its usage.

Given the potential for spurious results, the analyst must confirm any cost estimate, statistical or otherwise, as reasonable. Accepted testing methods include:

• Comparing the results of more than one estimation method. If the results are reasonable, both methods should yield approximately the same results; if results differ, reasonable explanations should exist for any discrepancy.
• Comparing the results to actual experience. For example, compare estimated costs at historical volumes to actual historical costs. Compare results at an assumed but for volume with historical results (at some other date) for roughly the same volume. The results need not be identical, but differences should be reasonable.
• Comparing the results to independent cost estimates. The company may have forecast costs as part of a business plan before the alleged misconduct. Industry statistics can also provide a useful baseline.
• Considering the intrinsic reasonableness of the results. Do costs increase with volume? Do they behave appropriately compared to changes in production capacity? In short, do the results make sense?
• Considering the insights and experience of company management, industry analysts, and experts on the particular production process.

Conclusion

Cost estimation is an important part of a lost-profits analysis. By understanding cost behaviors and using the tools of cost accounting, statistics, economics, and industrial engineering, the analyst can produce defensible estimates of incremental costs. If the tools are applied by rote or without sufficient consideration of the context, the results of the analysis will not be reliable.

Read Part One of this series.

Elizabeth A. Eccher is a principal in the Chicago office of Analysis Group, Inc.; Jeffrey H. Kinrich is a managing principal in the company’s Los Angeles office; and James H. Rosberg is a vice president in the San Francisco office.