Among the few things I detest more than reality-based TV shows are denominators that approach zero. The former are insufferable; the latter are inscrutable. During the course of formulating or reviewing a disclosure statement or business plan, restructuring professionals invariably carry out some form of benchmarking analysis, typically in testing the reasonableness of a debtor's operating projections or capital structure relative to those of designated peers. Much of this effort boils down to ratio analysis—a useful tool because financial ratios are unaffected by size discrepancies among firms or across time.

Thanks to providers of financial statement data in electronic form, products such as Standard & Poor's Compustat allow the restructuring professional to download enormous amounts of financial and market-based data directly into spreadsheets within a matter of seconds. This empowers the analyst to choose dozens of peer companies from among hundreds of candidates based on user-specified selection criteria and to then perform relevant financial ratio benchmarking. Anyone who has ever done this work is no doubt familiar with those annoying, exceedingly large, approaching-infinity calculated values (resulting from extremely small, approaching-zero denominators) that wreak havoc on summary statistics. Furthermore, there are other mathematical oddities, such as ratios with negative values, ratios with positive values resulting from a negative numerator and denominator, or other calculated ratio values that have no obvious meaning or interpretation. The analyst must decide how to effectively deal with all these quirks without compromising the integrity of the analysis.

Near-zero Denominators

How should the analyst best deal with extreme ratio values caused by denominators approaching zero? Deleting the particular observation or company from the analysis is the obvious and most tempting option, but may produce summary statistics that are incomplete or non-representative of the peer group. In Exhibit 1, we calculated two coverage ratios, EBITDA-to-interest expense and EBIT-to-interest expense, for a swath of manufacturing companies with issuer credit ratings of single-A. Companies' DNA and COL have negligible interest expense, and consequently, pull up the average for the entire group—unfairly so. Removing these two companies from the data sets would result in coverage ratios of 13.4 and 9.2, respectively—certainly more realistic values than the unadjusted arithmetic means in Exhibit 1. However, by omitting these four extreme observations, we are effectively removing two companies from the group that choose to employ minimal leverage. This seems somewhat arbitrary, as we are depriving the group of two representative companies for no other reason than difficulty in interpreting their ratio values. Generally speaking, deleting an extreme observation is considered an appropriate measure only when it represents a true outlier—a value that is wholly inconsistent with other data points, is not representative of the underlying characteristic and cannot be explained in any logical way. Is there a meaningful way to include these minimally leveraged companies in the calculation of the group's coverage ratios without using their distorted (and distorting) calculated values?

Winsorizing

The analyst can "winsorize" these calculated values—that is, adjust the computed value of the four extreme observations to the next closest "reasonable value," thereby reining in these runaway values. For example, the analyst can use Microsoft Excel's If function to create a command that calculates a ratio but caps the ratio value at n if the calculated value exceeds n. In this instance, we could have specified that the calculated EBITDA coverage ratio not exceed, say, 25. This ensures that our two companies with extreme values are reasonably represented in the group. Lastly, we could have extended this command to companies in the group with no leverage at all—that is, zero interest expense. (There was one in our group, HDI, whose calculated coverage ratios in Exhibit 1—#DIV/0! due to the zero denominator—were omitted.) Whether to delete or winsorize, particularly in the last instance, is a judgment call by the analyst: To omit minimally leveraged and unleveraged companies from our ratio calculations (due to near-zero or zero denominators) would be to overlook those companies with the most conservative capital structures, but imposing a subjective adjustment to a calculated financial ratio whose computed value cannot be easily interpreted might appear too manipulative. (There are statistical software packages that winsorize a data set more rigidly, such as by taking those observations in the bottom and top deciles and changing their computed values to the decile values immediately above and below them, respectively.) If too many data points in a data set require winsorizing due to denominator issues, the analyst should consider an alternative ratio that measures a similar characteristic. In this case, EBITDAR-to-Fixed Charges would likely have been a fine substitute since broadening the definition of the denominator to include rent expense lessens the likelihood that it will contain a zero or near-zero value for any company.

Trimming the Data Set

An alternative to winsorizing individual data points in order to control the impact of extreme values is to trim the data set. Trimming a data set requires the omission of n percent of the calculated values and then computing the mean of the remaining (1-n) percent of the data set. For example, if the analyst decides an appropriate trim percentage (n) is 20 percent for a data set consisting of 200 data points, then 40 data points are omitted from the set—the top 20 and bottom 20 calculated ratio values—and the mean of the remaining 160 values is computed. The TRIMMEAN calculation is a standard Excel function. Trimming a data set with the TRIMMEAN function effectively removes the most extreme values at each end of a data set when calculating summary statistics. It spares the analyst the bother of having to explicitly scan data sets and delete individual data points or companies from the sets. If we apply the TRIMMEAN function to our two coverage ratios in Exhibit 1, we get ratio values of 17.2 and 12.5, respectively, for the group. Any time the analyst uses Excel's AVERAGE function, the TRIMMEAN function should be run on the data set as well, and the analyst should note the degree to which these two averages agree or diverge.

Medians

The median is probably the most common but simplistic summary statistic used to manage the impact of extreme values on a data set. It is simply the middle value in a data set and is completely unaffected by extreme values. The median may be a better indicator of central tendency than the arithmetic average, even if only a couple of extreme values remain in a data set. The median values of our two coverage ratios were 12.7 and 7.3, respectively, in each case smaller than the adjusted arithmetic average (after deleting the extreme values) and the trimmed mean. In its periodic reports on key industrial financial ratios, S&P only presents median ratio values for each debt-rating category.

Negative Ratios and Other Oddities

Another common problem encountered in ratio analysis is how to deal with negative value ratios. We see in Exhibit 2 that TXN's debt-to-EBIT ratio is a negative value. Deleting a negative data point is the most common remedy, but once again, this should not be done automatically. First, try to make sure the figure in question is "clean." In this instance, the difference between TXN's EBITDA and EBIT values is unusually large. Perhaps goodwill was deemed impaired and written-off, or some other non-cash, non-recurring charge hit the P&L. The analyst is encouraged to investigate these types of discrepancies and normalize the financial statement data if the information required to do so is available. Retrieving financial statement data for several surrounding quarters allows the analyst to eyeball numbers, establish some informal "range of normalcy" and quickly spot suspicious figures. However, this data-scrubbing might be impractical or overly time-consuming if a data set comprises dozens of companies. When using ratios that require income-statement data, it's best to use trailing four-quarter P&L data rather than quarterly data, so as to remove the impact of seasonality on the computed ratio values.

For certain ratios, a negative value may be an accurate (albeit undesirable) measurement of the characteristic of interest. For example, negative operating margins and subsequent negative returns on equity are not highly unusual observations for distressed companies or industries, and are perfectly explainable within the conceptual definition of the ratio. While negative values for these two ratios cannot persist indefinitely without eventually resulting in financial ruination, they can endure for several quarters and should be left intact within a data set if they are reflective of underlying business conditions during that time period. For other financial ratios, a negative value has no discernible meaning, and the data point should be deleted. If return on equity were negative due to negative shareholders' equity (as opposed to a net loss), then this ratio value would have no obvious interpretation and should be deleted from the data set. As with ratio values involving zero and near-zero denominators, it might be preferable to identify an alternative ratio that measures a related characteristic but avoids the math quirk, such as return on total assets instead of return on equity.

Unfortunately, it isn't always obvious whether a negative value is an acceptable value for a particular ratio. The analyst must first discern whether a negative value is consistent or inconsistent with the natural direction of the ratio. For example, the larger the debt-to-EBIT ratio, the more leveraged a firm is considered to be. However, by including a company with negative EBIT, as we did with TXN in Exhibit 2, we (improperly) reduced the group's average leverage ratio. By this logic, a group that contains some firms with operating losses would have a lower debt-to-EBIT ratio than if those firms had operating income ceteris paribus. This conclusion is counterintuitive and nonsensical. Therefore, any negative value data points should be excluded from the group for this particular ratio. (Winsorizing these negative data points would be a large and subjective adjustment here.) Conversely, the analyst might decide to include a negative value data point for the coverage ratio EBIT-to-interest expense, since such a reading is not inconsistent with the normal direction of the ratio (i.e., smaller is "worse" and negative means smaller). In Exhibit 1, leaving TXN's negative EBIT-to-interest expense ratio value in the data set does not distort the group average as its negative debt-to-EBIT ratio value does in Exhibit 2.

Another mathematical subtlety is a positive ratio caused by two negative numbers, such as a positive return on equity resulting from a net loss and negative shareholders' equity. Without question, it would be improper to allow this calculation to remain in the group. The trick here is simply to identify these instances, which are easy to miss if the data service provider's software calculates the ratio directly. As a general rule, it's best to download the raw financial statement data that underlie a ratio and scan them to ensure that two negatives don't inadvertently produce a positive value ratio that stays in the data set. Excel's MAX and MIN functions are extremely helpful in quickly locating oddball numbers within a large data series.

Hopefully it is clear by now that ratio analysis, when carried out thoughtfully, can be tedious work that requires lots of attention to detail. The second-worst sin the analyst could commit in this exercise (first place goes to deliberate selection bias—that is, picking a sample that will produce a desired outcome) is to ignore the insidious subtleties of working with fractions. With ratio analysis, the formulas may all be fine, strictly speaking, but the conclusions can still be way off the mark.