TURN – THE PROFITS – OVER

Model Selection for Incremental Profit Margin
Estimation in Business Litigation

In business litigation, the amount of lost profits is what the parties fight over most typically when it comes to economic damages of a wrongful act. Lost profits represent how much more a firm could have earned but-for the alleged wrongful act.¹

When calculating such amounts, as forensic experts do, case specific factors and economic modeling techniques are used to identify the incremental profits that would have been earned during the damages period but-for the wrongful act.² Our scope in this whitepaper is to revisit how sensitive econometric and financial techniques can be to case specific income v. expense turnover cycle frequencies, i.e. the duration over which a sale-cycle reflects fully in the company’s books. 

There are two commonly accepted ways to calculate the incremental profit margin. First approach uses econometric models to study the relationship between additional (or, incremental) revenues and additional expenses, i.e. identifying how much expenses would go up if there were additional revenues but-for the alleged bad behavior. Second model is more subjective, and typically involves consulting with an accountant who is directly familiar with the generation of the underlying P&L data, in order to manually identify which cost items are to be variable vs fixed. In this white paper, we focus on the first method, i.e. the quantitative approach, although the same sensitivity to turnover cycle applies to the latter as well.

Econometrics is useful, but handle with care…

Econometrics is at the heart of data analysis in a broad range of fields and is extensively used in damages calculations. However, econometric models are only as powerful as how accurately the underlying hypothesis is formulated and how precisely it represents the actual finance-sales relationship for that firm. Historical data availability is another important dimension, as most econometric models are more reliable with more data. 

In most cases, econometric models would yield different results depending on the frequency of the underlying financial data, even when the data belongs to the same company. Monthly or quarterly data will provide advantages compared to annual data as they provide a higher number of data points, but performing estimations on higher data frequencies can have some disadvantages such as the mismatch between the timings of costs and revenues, i.e. the turnover cycle, for some industries. For example, most companies in the manufacturing sector pay for their inventory in advance, bearing high upfront costs of goods sold. However, they receive the respective revenues during the following two quarters, making monthly data insufficient for an econometric analysis to capture the relationship between incremental income and expenses. In this example, a bi-annual model could be more appropriate for capturing the relationship. Here we show an example of such mismatch, using a sample of synthetically generated profit and loss statements in monthly and quarterly frequencies:³

By definition, a firm’s “Expenses” include both fixed costs and variable costs, and the expert’s goal in this estimation is to isolate only the variable costs that would be incurred due to additional but-for revenues attributed to the alleged illegal behaviour. The observed fluctuations in the monthly expense to sales ratio compared to its relatively stable quarterly counterpart indicate the potential problem in this example. Month to month fluctuations are too high and the monthly frequency is too short to capture the expense v. revenues relationship. Of course, the exact nature of the expenses & sales relationship is hard to detect only using econometric techniques, and an economist does need to interview the particular firm’s accounting and sales personnel to identify the underlying process that generates such patterns carefully. 

Next, we plot sales and expense figures in scatter format, in which each dot is a point in time and sales are in horizontal axis while expenses are in vertical. Moreover, blue dots and white dots are used to show monthly and quarterly figures, respectively. We show linear regression fits as lines with respective colors. Slopes of these lines estimate the incremental cost that would be incurred when an additional dollar of revenues are added to the company books. Two unparallel lines are estimated for two different frequencies, which in turn lead to substantially different results in damages calculations.

In this example, we find that monthly estimation shows ~3 times lower incremental cost margin compared to the quarterly estimation, and could significantly overestimate the final damages figures. However, it should be noted using lower frequency might not be the solution to this problem even when the sample size is very rich, and the expert should definitely consider the totality of the case-specific evidence before finalizing her model selection.

… and with even more care!

Besides the frequency issue discussed above, there are other important factors that should be considered before selecting an econometric model for estimating incremental profits. One important issue is the difficulty of extrapolation when the application range (but-for revenues) is substantially different from the estimation range (actual revenues), but we have remedies available…

To be further addressed in our next post!