To illustrate the valuation dilemma, consider the following scenario: a company which manufactures and sells skin care products receives the result of laboratory testing which indicates the extensive use of its products renders users more susceptible to sunburn, resulting in a higher incidence of various forms of skin cancer. As a result of these issues, a class action lawsuit has been initiated by users of the company’s products. The litigation is ongoing and the outcome is unknown at the date the company files for bankruptcy protection. If the company is ultimately found liable for the full amount of the plaintiffs' claims, the company's assets would be insufficient to pay the claims and the company could potentially be forced into liquidation.
In this scenario, both the ultimate financial impact to the company, as well as the probability of an adverse outcome of the litigation, are uncertain as of the date of the bankruptcy filing. How then can a bankruptcy trustee or their appraiser determine the value of this contingent liability? The remainder of this article discusses the methodologies and guidance that exist relating to the valuation of contingent liabilities.
Valuation Theory
In general, valuation theory states that the present value of an asset is “the value of future economic benefits and/or proceeds from sale, calculated using an appropriate discount rate.” International Glossary of Business Valuation Terms, 2001. In other words, an asset has value to the extent the owner will receive a benefit––generally in the form of a single or recurring cash payments––from owning the asset, discounted to the present value at the proper rate of return.
When applied to a liability, the converse also holds true: The value of a liability is the present value of the cash payments, or economic sacrifices that would be required to satisfy or transfer the obligation, discounted at a rate of return that reflects the risk of that liability.
In addition to the concept of present value presented above, a contingent liability also incorporates additional uncertainty regarding the likelihood or probability that the event that would give rise to the liability may not in fact take place. This additional uncertainty must also be taken into consideration in determining the liability’s value.
Consider the example presented earlier involving the company embroiled in a classaction lawsuit resulting from its products. The contingent liability relating to the lawsuit has two components: the likelihood (probability) that the company will be found liable to the claimants and the total amount of the payments the company will be required to pay if it is found liable. Based on these factors, the value of the contingent liability could be stated based on the following:
probability of outcome × present value of cash flows resulting from outcome = value of contingency
Application of Valuation Theory
Using the above formula as a guide, a valuation professional may chose to value a contingent liability using one of two approaches: a singlescenario model or a multiplescenario model. As the name implies, under a singlescenario model, the valuation professional performs a single analysis, which is used to determine the value of the contingent liability. Using the skincarecompany example, the valuation professional may prepare an analysis in which it is assumed there is a 50 percent probability the company will be required to pay class action claimants (in total) $10 million per year for 10 years. These cash flows are discounted back to present value using a 15 percent discount rate, which the appraiser has determined properly captures the uncertainty relating to the amount of the cash flows (payments) that the company will make to the classaction plaintiffs. In addition, the appraiser––based on discussions with company management and legal counsel––has also applied a 50 percent probability of adverse ruling to capture the uncertainty relating to the ultimate outcome of the litigation.
Presented in a table, the valuation of the contingency using a singlescenario model would look like this:

Year 1

Year 2

Year 3 …

… Year 10






Annual Payment

$ 10,000,000

$ 10,000,000

$ 10,000,000

$ 10,000,000

× Discount Factor (15%)

.9325

.8109

.7051

.2651

Present Value

9,325,000

8,109,000

7,051,000

2,651,000






Sum of Present Values

$ 52,820,000




× Probability of Adverse Ruling

50%




Value of Contingency

$ 26,910,000




Singlescenario models are frequently used by valuation professionals due to the relative ease to prepare such a model as well as the ease by which the model can be explained to a bankruptcy judge. However, the model is extremely sensitive to the inputs that are used. In this case, the annual cash payment, the discount rate applied and the probability of adverse outcome, and the model may not adequately capture the various possible outcomes relating to the contingent liability.
It should be noted the appraiser must pay particular attention to the development of the discount rate used in the analysis. Generally, appraisers develop discount rates by first identifying a “riskfree” rate of return as of the valuation date, generally using U.S. Treasury bond rates as a proxy for a riskfree rate of return due to the fact the United States has never defaulted on its debt or interest payments.
Once a riskfree rate is determined, various additional risk premia are added to reflect the additional risk in the asset (or, in this case, the liability) being valued. These risk premia are typically based on public company rates of return and reflect such items as the additional risk in an equity versus debt security, additional risk due to the size of the company, etc. As the majority of data used by appraisers to develop discount rates is based on public company rates of return, the discount rate developed from this data may tend to understate the risk associated with a contingent liability. As such, the appraiser must pay particular attention to the specific facts and circumstances surrounding the contingent liability to help ensure that the uncertainty embedded in the liability has been adequately addressed and incorporated into the discount rate applied.
To address the shortcomings of the singlescenario model, a valuation professional may choose to instead use a multiplescenario model. Using such an analysis, the valuation professional will either prepare multiple singlescenario models and then assign a probability factor to each outcome to arrive at a probabilityweighted value, or may use computeraided simulation techniques such as a “Monte Carlo” simulation.
Under a Monte Carlo simulation, key variables in the model are identified, and then a range for each of the variables is determined based on a statistical probability model. In the example above, the significant assumptions include the annual cash payment, the discount rate, and the probability of adverse outcome. Incorporating changes into the significant assumptions included in the model, the value for the liability is recalculated a specified number of times (in this case, 1,000 recalculations were performed), which results in a minimum and maximum value for the liability, as well as a statistical “mode,” which represents the most likely outcome (value) for the liability.
Applying a Monte Carlo simulation to the valuation of the contingency above resulted in the following ranges for the assumptions being tested:
Description

Low

Median

High





Annual Payment

$ 8,355,000

$ 10,000,000

$ 11,645,000

Discount Rate

12.5%

15.0%

17.5%

Probability of Adverse Ruling

41.8%

50.0%

58.2%





Calculated Value of Contingent Liability

$ 16,564,000

$ 26,965,000

$ 40,935,000

Unlike the singlescenario model, the multiplescenario model produces a range of values for the contingent liability that a bankruptcy trustee or its business valuation advisor can use to assess the potential impact to the solvency of the company being evaluated. For example, if the company in question has assets for which the fair value is $20 million more than the fair value of its liabilities, and the Monte Carlo simulation indicates there is a 95 percent probability, based on the inputs, that the value of the contingent liability is more than $20 million, the bankruptcy trustee can conclude with a reasonable amount of certainty that the company was insolvent as of the date of the bankruptcy filing.
While the strength of a multiplescenario model lies in its ability to incorporate a wider range of potential outcomes, as well as the ability to provide a range of values based on changes to the significant assumptions used, the difficulty inherent in using such an analysis relates both to the complexity of the model––which makes it more difficult to explain to a bankruptcy judge or opposing parties––as well as the requirement that multiple forecasts and the related probabilities be developed and defended by the appraiser.
In light of the strengths and weaknesses of both the single and multiplescenario models, the valuation professional must carefully consider the facts and circumstances of his or her situation, and the intended audience of the analysis, in deciding the most appropriate model to use.
Summary
Valuing contingent liabilities presents a unique challenge to business appraisers and bankruptcy trustees. Although financial reporting guidance exists relating to the timing and manner in which contingent liabilities exist, the valuation of contingent liabilities remains an evolving area for valuation professionals, with best practices continuously being challenged and revised.
The final article in this series will revisit the quandary frequently faced by a bankruptcy trustee when faced with the possibility of a company with contingent liabilities. In addition, the final article will synthesize the financial reporting and valuation guidance available relating to this complicated and complex issue.