Evaluation of claims on distressed firms. A conceptual framework based on structural models

Master's Thesis, 2017

246 Pages, Grade: 12/12


Table of contents

0 Executive summary

1 Introduction
1.1 Problem definition
1.2 Delimitations
1.3 Structure

2 Methodology
2.1 Research design
2.2 Development of the framework
2.3 Case study

3 Distress and bankruptcy
3.1 Definition of financial and economic distress
3.2 Default and bankruptcy
3.3 Characteristics of firms in distress or bankruptcy
3.4 Proceedings in financial distress and bankruptcy
3.5 Scope of this study

4 Option theory
4.1 Nature of an option
4.1.1 Generic option payoffs
4.1.2 Put-call-parity
4.1.3 Bull spread option strategy
4.2 Option pricing theory
4.2.1 Black- Scholes model in continuous time

5 Structural models
5.1 Firm value as a portfolio of options
5.2 Contingent claim pricing
5.3 Probability of default and credit risk assessment
5.4 Extended default-claim pricing

6 Framework
6.1 Discussion of valuation approaches
6.1.1 Income models
6.1.2 Liquidation models
6.2 Valuation uncertainty arising from distress
6.2.1 Structural uncertainty
6.2.2 Strategic uncertainty
6.3 Superiority of contingent claim pricing models
6.4 Estimation of model input variables
6.4.1 Risk-free rate
6.4.2 Default barrier
6.4.3 Debt maturity
6.4.4 Asset value
6.4.5 Asset volatility
6.5 Presentation

7 Case study
7.1 Company description
7.2 Framework applicability assessment
7.3 Macro and industry analysis
7.4 Strategic company analysis
7.5 Financial statement analysis
7.6 Capital structure analysis
7.7 Estimation of input variables
7.8 Contingent claim pricing
7.9 Probability of default
7.10 Discussion of model outputs I

8 Limitations and future research

9 Conclusion

10 References

11 List of abbreviations

12 Appendix

0 Executive summary

Within this thesis, we develop and apply a comprehensive, yet tractable framework comprising 10 sequential steps for the evaluation of claims on corporations suffering from distress.

While traditional industry approaches yield consistent and unbiased valuations for claims on a healthy firm’s assets, we find encumbering evidence that results may be distorted if the valuation object experiences severe financial or economic difficulties. Standard present value, multiple, or accrual based equity valuation methods are deterministic in nature and hence, fail to properly account for the elevated idiosyncratic uncertainties surrounding distress.

Initiated by Merton (1974), on the other hand, asset pricing research has suggested structural models as a theoretically superior alternative explicitly incorporating the optionality features and asymmetric payoff-profiles of limited liability claims. However, these models have been rarely adopted by industry professionals for their proclaimed complexity, lack of transparency and stylized assumptions on the valuation object’s capital structure.

Accordingly, the proposed framework aims to overcome the above shortcomings of the original Merton (1974) model and eventually allows for an intuitive, seamless pricing of multiple claims with diverse maturity and coupon profiles based on their absolute priority ranking in bankruptcy.

First, we provide a thorough characterization of both economic and financial distress and accompanying (firm) characteristics based on which a framework applicability assessment can be performed. Besides, we stress a comprehensive discussion how model input parameters can be estimated reliably.

Subsequently, we perform a holistic application of the framework to the distressed Gemían air carrier Air Berlin. Model outputs imply a current market undervaluation of common equity by 52%. While our analysis demonstrates remarkable upsides of the framework compared to traditional valuation procedures, we conclude that a separate estimation of a going concern- and a liquidation value only partially circumvents frictions associated with the computation of a distressed firm’s overall asset value.

Moreover, we find that model results are highly sensitive to changes in input factors in general and the expected asset drift rate in particular, implying a considerably low robustness to estimation errors. The latter deficiency may mitigate a broad adoption of our framework going forward.


First and foremost, we express our gratitude to our supervisor, Domenico Tripodi, CFA, Senior Investment Manager at PKA AIP, for his continuous guidance and support throughout the master thesis process.

Domenico’s scientific curiosity paired with a hands-on perspective and his participation in many fruitful discussions eventually helped US develop a framework for the evaluation of claims on distressed firms that we consider both useful and relevant to a target group outside of academia as well.

Moreover, we would like to thank Björn Imbierowicz, Assistant Professor at Copenhagen Business School, for insightful explanations of the seniority and covenant profiles of claims on distressed firms observed in the cross-section. Next, we would like thank Peter Raahauge, Visiting Associate Professor at Copenhagen Business School for sharing his experiences and advice on the development and implementation of quantitative, yet intuitive financial models.

We are deeply indebted to our proof-readers Marissa Blank, Master’s candidate at Erasmus University/ Rotterdam School of Management, Licia Bobzien, PhD candidate at Hertie School of Governance, Heike Bockius, Master’s candidate at the University of St. Gallen, Felix Brandt, Bachelor’s candidate at the Technical University of Darmstadt and Susan Xiao, MBA candidate at Duke University/ Fuqua School of Business. Their valuable comments and suggestions both enhanced the quality of and accelerated the journey to the finishing line of our research endeavor.

Lastly, we appreciate assistance in the design of our title page by Hannah Marie Dean and Kasia Sznajder, Master’s candidates at Copenhagen Business School.

All remaining errors are our own.

1 Introduction

The accurate valuation of a firm is one of the most crucial disciplines in the field of finance. Common income models range from cash flow based to accrual based to relative valuation based procedures (Petersen and Plenborg, 2012, Imam et ah, 2008). In practice, these techniques are usually used in combination when estimating the fair value of a company (Imam et al., 2008).

While these valuation techniques yield economically sound and internally consistent results for firm values when carefully implemented for healthy companies under both stable and predictable conditions (Koller et al., 2005, Petersen and Plenborg, 2012), their application to firms in financial or economic distress and bankruptcy has resulted in a very wide dispersion of valuation errors (Gilson et al., 2000). These findings can be attributed to the substantial shortcomings of traditional valuation techniques for firms in distress or bankruptcy (Damodaran, 2009). Nevertheless, these techniques have generally been used for the valuation of troubled firms by professionals in the field of distressed investing without much consideration of the special uncertainties and distortions arising from distress (Scarberry et ah, 1996, Houlihan Lokey, 2011).

Indeed, already Wruck (1990) notes that ״the number of investors buying and selling the securities of distressed firms and the capital available for such investments has grown spectacularly” (Wruck, 1990, p. 420). Vulture investors may have different objectives but often seek profits by identifying and investing into undervalued claims of distressed companies (Hotchkiss and Mooradian, 1997, Moyer et ah, 2012). Thus, Crystal and Mokal (2006) correctly highlight the necessity of a thorough claim valuation before an investment decision is made.

In more recent years, there has been a clear trend of traditional buyout funds to acquire distressed companies with the ultimate goal of value creation (Kucher and Meitner, 2004, Roland Berger, 2017a). On top, banks currently sell their non-perfomiing loans (NPL) in an effort to restructure their balance sheet to comply with increasing stricter regulations (Roland Berger, 2017b, Debtwire, 2017). Also Financial Times (2015) finds attractive market opportunities for distressed investors willing to move beyond standard products and valuation techniques.

Yet, financial or economic distress is a versatile and complex process characterized by increased uncertainty both of structural and strategic nature (Wruck, 1990, Gilson et ah, 2000). Despite its great importance for distressed investment professionals, existing research on distress and bankruptcy has only been remotely connected to other fields in financial economics. Likewise, Hrdý and Simek (2012) chide that no directly applicable valuation model reflecting the special characteristics of real- life distressed firms has been assessed in detail so far.

Since the seminal work of Black and Scholes (1973) and Merton (1973, 1974), structural models have emerged as a prominent tool for the stylized valuation of corporate liabilities. Based on option pricing theory, these models may (i) mitigate many of the shortcomings of traditional static valuation approaches, (ii) arguably incorporate more flexibility, and (iii) overcome the bargaining problem between different claimholders inherent in the bankruptcy process, which results in the elevated strategic uncertainty named above (Damodaran, 2009, Sundaresan, 2013).

The application of structural models requires the estimation of various model input parameters, a process often described as too complicated for the model to be of practical use (Hrdý and Simek, 2012). Contrarily, Damodaran (2002, 2009) suggests to price equity in a distressed firm characterized by negative cash flows as a call option on the firm’s assets and thus ultimately advocates the use of structural models to account for the value of flexibility. Yet, the original Merton model is based on a single zero-coupon debt - a setup not applicable to handle real-life firms’ capital structure consisting of multiple debt instruments with different maturities and coupon features.

Consequently, this thesis develops and presents a hands-on framework for the evaluation of claims in distressed firms by consolidating state of the art research findings in the field of financial economics and corporate distress. Thereunder, a considerable part of this thesis investigates how structural models achieve the advantages introduced above. Subsequently, to prove its practical applicability, the developed framework will be applied to a real-life case company, the German network carrier Air Berlin, in a step-by-step process.

1.1 Problem definition

Consequently, this thesis investigates the following research question:

How should a framework for the evaluation of claims in distressedfirms be designed to (i) overcome the shortcomings of traditional valuation methods, (ii) ensure a practical applicability, and (iii) be consistent with paradigms of modern scientific financial economics?

How does the framework perform once applied to a real-life distressed company?

In order to answer the above research question, this thesis examines the following sub-questions:

- What are common characteristics of firms facing financial or economic distress and eventually bankruptcy? What are possible proceedings to overcome financial distress or bankruptcy?
- What is the rationale behind applying contingent claim pricing to the valuation of debt and equity in a firm? Which structural models have been proposed in academia?
- What are the shortcomings of traditional valuation techniques when applied to firms facing distress and bankruptcy and which factors contribute to the elevated uncertainty arising in a distressed environment?
- How would a framework need to be designed to implement contingent claim analysis in the valuation of distressed firms? In particular, how does the framework overcome the shortcomings of traditional valuation approaches? How can users of the framework estimate the necessary model input variables?
- For which prerequisites does the framework proposed above yield superior results in comparison to traditional valuation methods, and hence justifies its application?
- What are the fair values of the various debt and equity claims on Air Berlin using the proposed framework? What potential caveats accompany an application to a real-life company?

1.2 Delimitations

Due to the complexity of this thesis, several delimitations and assumptions have been made to ensure a focused, yet comprehensive investigation of the main research question. Thus, emphasis is put on factors that impose the greatest impact and relevance in regard to both the evaluation of claims in distressed firms based on structural models and the case study implementation.

1.2.1 Bankruptcy code

This thesis is based on stylized proceedings in financial distress and bankruptcy derived from the u.s. bankruptcy code Chapter 7 and Chapter 11 (see chapter 3.4). While we acknowledge that bankruptcy is a legal procedure and therefore highly dependent on country specific legislation (Pindado and Rodrigues, 2004, 2005, Brealey et ah, 2010), insolvency acts across nations pursue similar overarching goals (Jones Day, 2007). Besides, the majority of structural models and academic research in the field of financial distress and bankruptcy is ultimately founded on and derived from the U.S. bankruptcy code. Finally, as the assessment of specific legal aspects is outside our area of competence, this work shall rather be seen as a contribution to the field of finance and economics.

1.2.2 Option Theory

The contingent claim pricing approach based on structural models can be implemented both in a continuous time setting using the Black-Scholes-Merton (BSM) model or in a discrete time environment employing lattices. On the one hand, lattice analysis allows for easier model-adjustments to reflect characteristics and circumstances of real life firms. In contrast, once carefully set up, the BSM closed forni model significantly enhances the traceability and scalability of the outlined procedure ultimately enabling the pricing of a great number of different claims. Moreover, to ensure a fast and convenient implementation of the BSM model, we provide the necessary VBA code as part of the framework (see Appendix 6.4.4-A.l).

1.2.3 Convertibility and callability feature of debt instruments

The underlying framework for the evaluation of claims in distressed firms does not take potential convertibility or callability provisions of debt instruments into account. This delimitation, however, does not imply noteworthy restrictions since such features only play a subordinated role for firms facing financial distress or bankruptcy. First, distressed firms usually experience a substantial drop in market capitalization which makes it highly unattractive to convert debt into equity claims (see Crosbie and Bohn, 2003). Second, companies in distress commonly face cash constraints, and hence do not often have the financial resources for an earlier repayment of their debt instruments. Further, given the severe situation it is unlikely that a distressed firm will be able to refinance itself with better terms.

In addition, the framework refrains from directly considering potential put provisions, which are sometimes part of bond indentures. These features permit investors to request the repayment of the outstanding face value prior to maturity. However, if the framework user finds the exercise of the early redemption option to be optimal, we heuristically suggest to replace the contractual maturity of the respective instrument with the period length until the exercise date when calculating the firm's aggregated debt maturity (see chapter 6.4.3).

A number of authors has developed various complex extensions to the original structural Merton model to account for the debt instrument features mentioned above. Yet, Hull et al. (2004a) note that “none [of these] has emerged as clearly superior” (Hull, 2004a, p. 4). Accordingly, the framework builds on the initial structural model by Merton (1974).

1.2.4 Absolute priority rule

Fixed bankruptcy proceedings and compliancy with the absolute priority rule form the basis of contingent claim pricing. Therefore, in line with existing academic literature, this thesis does not model deviations from the absolute priority rule in case of bankruptcy or liquidation. However, various empirical studies (e.g. Warner, 1977, Baldwin and Mason, 1983, Franks and Torous, 1989) have shown that the absolute priority rule in bankruptcy is seldom honored fully in real life.

1.2.5 Case study: case company

The practical application of the developed framework and the concluding discussion of results are exclusively based on the case of the Gemían airline Air Berlin PLC. Therefore, this allows for a detailed and holistic analysis of the fimi but is not yet generalizable to the cross-section of distressed firms.

1.2.6 Case study: time frame

This work undertakes the evaluation of various claims on Air Berlin’s assets as of December 31, 2016. Consequently, major subsequent events are not taken into account for the strategy assessment and financial valuation perfomied within the case study.

1.2.7 Case study: publication of the annual report 2016

According to Air Berlin’s financial calendar, the company publishes its annual report 2016 on April 27, 2017 (Air Berlin, 2017). Given the short time left the official thesis submission deadline set by CBS, we base our calculations partly on Q3 2016 and otherwise carefully estimated figures.

Further, the company’s restructuring of its operating model together with the effects of economic and financial distress impede an ordinary forecast of Air Berlin’s income statement and balance sheet. While relevant future income statement items are modelled based on a comprehensive peer group benchmarking study, a forecast of the balance sheet is omitted. Yet, this approach shall not significantly influence the overall valuation results obtained.

1.3 structure

Exhibit 1.3-1 illustrates the structure of the underlying work. The current introduction is followed by a methodology section. Subsequently, chapter 3 is dedicated to a formal characterization of distress and bankruptcy. Along with chapter 4 on option theory, these parts form the basis for the understanding of structural models and the contingent claim pricing approach outlined in section 5. The main part of this thesis motivates, develops, and outlines a framework for the evaluation of claims in distressed firms using the structural Merton model. Section 7 applies the outlined framework to a case company. Finally, the work closes with a discussion of model outputs and limitations, recommendations for future research and lastly a concluding remarks and limitations

Exhibit 1.3-1: Structure of the thesis

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Source: Own production

2 Methodology

Bryrnan et al. (2011) stress a clear understanding of the research design is crucial for any academic endeavor. In particular, a thorough assessment of the underlying assumptions about the philosophy of science and resulting paradigms guiding the research is considered pivotal to apprehend how results can be achieved, which inferences can be drawn based upon it and, more generally, which research gaps can/ cannot be closed by the chosen research method. Accordingly, the following sections will outline the research philosophy, approach and strategy selected for this thesis. Moreover, we cast light on how the framework for the evaluation of claims on distressed firms has been developed and how the case study has been implemented.

To ensure that the analysis conducted within this thesis can also be understood and applied by a general audience without experience in financial economics and business administration, the major theoretical financial and strategic concepts underling our work have been summarized in Appendix 2-A. 1 and Appendix 2-A.2, respectively.

2.1 Research design

For Gupta and Lincoln (1994), the evaluation of appropriate paradigms, i.e. “basic belief system[s] or world view[s] that guide[s] the investigation” (Gupta and Lincoln, 1994, p. 105), ranks the highest within the research process. Saunders et al. (2009) point out that different paradigms or research priorities can be characterized based on their ontological, epistemological and axiological positioning.[1]

Within this thesis, a positivistic paradigm is chosen: Remenyi et al. (1998) and Saunders et al. (2009) clarify that reality is perceived as objective (with regard to ontology) and observable (with regard to epistemology) so that research findings often culminate into “law-like generalizations” (Saunders et ah, 2009, p. 113). Accordingly, Bryrnan et al. (2011) remark that scientific knowledge is developed through a logical processing of theorems or empirical data. With regard to axiology, Saunders et al. (2009) point out that research ought to be carried out as value-free as possible way.

We follow Schophuus and Stefanac (2008) and exclusively rely on one single paradigm to ensure that all assumptions, methods and inferences part of this thesis are mutually aligned. On top, building on the idea that knowledge is objective, most theories used in this thesis are considered factually valid across their specific contexts.

According to Saunders et al. (2009), a positivistic research philosophy is typically accompanied by a deductive research approach. Snieder and Lamer (2009) conclude that deductive reasoning tracks the standard path of logic most closely, while Wilson (2014) clarifies that existing theories are often used or combined to first craft a research question or hypothesis that is assessed subsequently. The inductive approach, on the other hand, typically starts with (specific) observations and aims to identify generalizable patterns within them (Babbie, 2007).

Since the individual academic fields relevant for the development of our framework (see section 2.2 for a more detailed discussion) have generally been broadly covered on a stand-alone basis, we mostly deduce insights from existing research. While we abstain from articulating fomial hypotheses, the research question is addressed by the consolidation of various connected research strands, finally leading to a framework tailored to distressed firms.

Exhibit 2.1-1: The research onion

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Source: Saunders et al. (2009), own production

Subsequently, a case study has been chosen as the most appropriate research strategy to demonstrate both the validity and applicability of the step-by-step process outlined in the framework (see section 2.3). Since Saunders et al. (2009) point out that case study research is necessarily context-specific, the interferences drawn from this section involve inductive elements as well.

2.2 Development of the framework

The framework developed in this thesis builds on a broad review of existing literature and solely relies on secondary data such as peer-reviewed academic publications or, if not possible otherwise, so far unpublished working papers. This is in line with a positivistic philosophy and the deductive approach outlined in section 2.1. More concretely, our analysis consolidates previous academic work devoted to both theoretical and empirical research within asset pricing, corporate finance as well as the investigation of financial/ economic distress and bankruptcy.

Whenever possible, rigorous quality-filters have been applied to ensure high validity and relevance of the research fomling the base for this thesis. Hence, predominantly research printed in leading academic journals or well recognized publishing houses has been considered. Moreover, we broadly follow the generic requirements articulated by Schophuus and Stefanac (2008) how to identify theories and empirical results relevant for the compilation of our framework: first, the research has to focus on one of the academic fields listed above. In addition, the results obtained need to be generalizable beyond the specific context of their genesis. Eventually, research contributions considered for our framework ought to represent the contemporary state of knowledge and should be considered valid. Again, the last requirement is ensured through a stringent focus on journals or publishing houses with a strict editorial process and a generally high impact factor.

2.3 Case study

Damodaran (2002) and Damodaran (2009) argue that the valuation of (claims of distressed) firms is inevitably dependent on the idiosyncratic characteristics of the valuation object. Likewise, Yin (2003) and Saunders et al. (2009) correctly remark that case-studies, i.e. “empirical investigation[s] of a particular contemporary phenomenon within its real-life context” (Robson, 2002, p. 178), are domain­dependent and typically yield detailed insights into the specific scenario considered. On the other hand, broader quantitative studies seem inappropriate for our research question since claim (e)valuation typically involves a detailed investigation of a single company and requires a considerable degree of model adjustments to reflect idiosyncratic circumstances.

In view of the space requirements set by CBS and for the sake of a (i) profound application of our framework and (ii) rigorous discussion of the model outputs, the examination of a single case study was chosen. Nonetheless, Flyvbjerg (2006) argues that despite the context dependent nature, careful analysis may actually allow to extrapolate selected case study findings to a broader population.

Our case study exclusively builds on secondary data and hence, includes company disclosures, press articles and market research studies complied by broker analysts or independent industry experts as well as security and claim prices provided by leading financial database providers. By abstaining from sourcing primary data, we ensure that the framework is applied in a setting similar to the outside­in perspective on the valuation object often faced by industry professionals.

Finally, we consider the financial data used for the application of our framework to be of high quality: financial statements have been audited and should thus comply with the applicable accounting standards. On the other hand, figures obtained from database providers were often provided by organized exchanges subject to strict regulations of security law.

3 Distress and bankruptcy

The development of a tailored framework for the evaluation of claims in distressed companies undeniably requires a holistic understanding of the special environment such firms operate in. Given the remark of Hamoto and Correia (2012) that analogous notions and theories used in academia are often overlapping but ultimately lack coherence, we will carefully derive a differentiation between economic and financial distress. On top, default and bankruptcy, two conmion outcomes of distress with pivotal importance for contingent claim pricing models, will be conceptualized.

Exhibit 3-1: Structure of the distress and bankruptcy chapter

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Source: Own production

Next, we portray common characteristics of firms in financial distress or bankruptcy and provide an overview on measures to overcome distress or handle bankruptcy processes. The chapter closes with a delimitation of concepts and assumptions we will incorporate in our own model and thus sets the boundaries for further analysis.

3.1 Definition of financial and economic distress

A clear and precise definition and conceptual distinction between economic and financial distress is the key for understanding the various contingent claim pricing models and their underlying default trigger. While some authors note that economic and financial distress might be mutually dependent,[2] the great majority of literature separates both concepts.

The definition of financial distress can effectively be reduced to a firm’s inability to honor its debt obligations, most commonly related to an ultimate cash flow insolvency (Wruck, 1990, Shobhana and Deepa, 2012). In other words, Davydenko (2007, p. 1) summarizes more precisely:

“The finn is financially distressed when it has difficulties honoring its financial obligations. Even when the business is fundamentally sound, temporary declines in cash flows may result in the inability of highly-leveredfirms to make promised debt payments. ”

Following Outecheva (2007), financial distress is a complex and broad economic concept, whose definitions can be clustered into three different categories.

Exhibit 3.1-1: Definitions of financial distress

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Source: Outecheva (2007), own production

The first group of event-oriented delimitations relates financial distress to failure, default or bankruptcy. Accordingly, financial distress can be defined as “the inability of a fimi to pay its financial obligations as they mature” (Beaver, 1966, p. 71). Further on, the following events may trigger a firm’s failure: “bankruptcy, bond default, an overdrawn bank account, or nonpayment of a preferred stock dividend” (Beaver, 1966, p. 71). Congruent definitions of financial distress are made by Baldwin and Mason (1983), Brown et al. (1993), Dennis and Dennis (1995), Andrade and Kaplan (1998), and Kahl (2001). These authors define financial distress as an event separating the time of financial health from the period of financial difficulties and ultimately triggering measures of restructuring and reorganization (Outecheva, 2007).

Secondly, early contributions to define the term financial distress as a process have been made by Gordon (1971) who characterizes financial distress to precede failure and reorganization. Under his definition, financial distress is triggered by the deterioration of a firm’s earnings trajectory resulting in a higher probability to default on upcoming interest payments and hence, a higher bond yield. Similarly, Van Gestel et al. (2006) characterize financial distress and failure as a result of recurring substantial losses essentially leading to insolvency as the firm’s liabilities exceed its assets. Moreover, Turetsky and McEwen (2001) explicitly postulate “financial distress as a series of financial events that reflect varied stages of corporate adversity” (Turetsky and McEwen, 2001, p.323). Pumanandam (2008) characterizes financial distress as an intermediate low-cash flow state between solvency an insolvency.[3] Similar to the original Merton model, “insolvency occurs on the maturity date if [the] temiinal firm value is below the face value of debt” (Pumanandam, 2008, p. 707).[4]

Thirdly, a large group of academics has defined financial distress in technical temis through the deployment of financial ratios as the main indicator. Most popular within this category are contributions by Altman ( 1968) and Ohlson (1980) who use a combination of different financial ratios to predict financial distress. More specifically, Asquith et al. (1994) characterize a fimi in financial distress using solely the interest coverage ratio, whereupon a fimi is declared distressed if its EBITDA is less than 80% of its interest expenses in two consecutive years. Whitaker (1999) combines accounting based and market based detemiinants to classify financial distress. According to his definition, a fimi is financially distressed if, first, its cash flow is less than the due amount of outstanding debt and, second, the fimi suffers from a substantial drop in market value.

Finally, financial distress may be caused by a broad variety of factors comprising but not limited to economic distress, poor management, operating difficulties and fimi perfomiance relative to the industry, decline of firm’s industry, technological or social change or regulatory restrictions (Bibeault, 1982, Wruck, 1990, Denis and Denis, 1990, Whitaker, 1999, Hrdý and Simek, 2012, Van Gestel et ak, 2006). In addition, Opier and Titman (1994) as well as Andrade and Kaplan (1998) find that the higher the firm’s level of debt, the higher is the probability of financial distress.

While there are various different approaches to the definition of financial distress, economic distress is rather homogenously characterized and consistently used in existing literature. Its diagnosis is independent of the presence of debt or pending interest payments but, on the contrary, builds on the economic viability of the firm’s business activity (Davydenko, 2007). Further, as the company’s future ability to generate positive cash flows worsens, its business model is no longer viable, economic distress prevails, and ultimately the fimi value expressed as the market value of its productive assets will decrease (Davydenko, 2007). In other words, “economically distressed firms can be identified by declining asset values, even though [the fimi] may have no immediate difficulty making ongoing debt payments” (Davydenko, 2007, p. 2).

In addition, Crystal and Mokal (2006) argue that a business is economically distressed, if “the net present worth of the business as a going concern is less that the total value of its assets” (Crystal and Mokal, 2006, p. 1). Thus, the firm’s assets would be more valuable in the hand of another owner and hence, should be sold to avoid further deterioration to the firm’s claimants (Crystal and Mokal, 2006).

3.2 Default and bankruptcy

Both economic and financial distress can eventually lead the company into default. Generally speaking, a fimi is considered to be in default if it fails to honor one of its debt payments as they come due (Meckling, 1977, Pastena and Rulând, 1986, Hamoto and Correia, 2012). For 2015, the credit rating agency Moody’s found that 29.4% of all corporate defaults are related to payment defaults (Moody’s, 2016). Additionally, a fimi is in technical default if it violates any of the contractually specified debt covenants not related to principal and interest payments, e.g. minimum-net-worth requirements or working capital constraints (Wmck, 1990).[5] In the case of a violation of minimum- net-worth requirements, technical default is essentially caused by economic distress. Finally, according to Moody’s delimitation, a fimi is also found to be in default if it files for “bankruptcy, administration, legal receivership, or other legal blocks” (Moody’s, 2007, p. 1).

Systematically, triggers of default can be clustered based on whether they are related to financial (liquidity shortage) or economic distress (low market value of assets, Davydenko, 2007). However, empirically analyzing reasons for firms to default, Davydenko (2007) reports that most firms in default are insolvent both economically and financially.[6]

The vast majority of theoretical structural models specifies fimi default to be driven by economic distress, i.e. in temis of the market value of the firm’s assets vt and liabilities D. The default boundary can both be specified exogenously or defined endogenously by stakeholders (Davydenko, 2007).

Exhibit 3.2-1: Exogenous and endogenous default trigger

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Source: Own production

Even if market value ranks among the best univariate default predictors, “there is no pronounced boundary separating defaulting and non-defaulting firms” (Davydenko, 2007, p. 4). First, some firms continue to operate and service their debt although their asset value reaches the book value of total liabilities. Those firms might potentially default at a later point in time (Crosbie and Bohn, 2003, Davydenko, 2007). Secondly, given the long-temi nature of some debt instmments, Crosbie and Bohn (2003) note that generally the default barrier, the asset value at or below which the fimi will default, lays between the firm’s short-term and total liabilities. Likewise, Davydenko (2007) finds that a default boundary of 68% of the face value of the firm’s debt has the highest discriminatory power to differentiate between failing and surviving firms. These findings confimi similar results derived by Leland (2004).

Although most often used, the market value of assets is not the only default trigger deployed in academic literature. Other authors have developed structural models reflecting the nature of financial distress whereupon the firm defaults due to a shortage in instantaneous cash flow to cover its current debt obligations (Davydenko, 2007). The most prominent contributions in this field have been made by Kim et al. (1993), Anderson and Sundaresan (1996) and Ross (2005). Since these models usually prevent external financing and assume the absence of cash reserves, Davydenko (2007) notes “in most such models the market value of assets is always proportional to the current cash flow. As a result, the default trigger specified in terms of a threshold cash flow [i.e. financial distress] is equivalent to one that uses the boundary market value of assets [i.e. economic distress]” (Davydenko, 2007, p. 6). More information will be provided in section 3.5 and 5.4 of this work.

While Meckling (1977) states that default and bankruptcy should be considered alternative outcomes, Hamoto and Correia (2012) note that in most cases they are sequential events with bankruptcy following from default. Likewise, Brealey et al. (2010) note that bankruptcy commonly can be viewed as a result of default triggered from declining asset values.

Bankruptcy has very different characteristics than has financial distress (Gilbert et ak, 1990) and should essentially be understood as only one possible outcome of financial distress (Giroux and Wiggins, 1984, Ward and Foster, 1997, Pindado and Rodrigues, 2005). In particular, different from financial distress, bankruptcy is merely a legal mechanism with no economic significance and hence, depends of the legal procedure of the relevant country (Pindado and Rodrigues, 2004, 2005, Brealey et al., 2010). It essentially provides the institutional platform to organize a potential “transfer of ownership from one security holder to another” (Haugen and Senbet, 1988, p.32) and thereby to resolve the problem of insolvency (Meckling, 1977, Berkovitch et ak, 1998).

3.3 Characteristics of firms in distress or bankruptcy

Hrdý and Simek (2012) point out that firms in distress or bankruptcy differ from healthy, stable firms along a broad array of dimensions. Hence, an understanding of their special and distinguishable characteristics contributes to an applicability assessment of the framework (step 1) developed in chapter 6 of this thesis.

While Platt and Platt (2002) recall the absence of a single measure valid in isolation to identify when a company can be considered distressed, academic research has often used the candidate’s past earnings trajectory as a main indicator (see Exhibit 3.3-1 for an overview on this and alternative metrics). Davydenko (2007) finds that more than 90% of all failing firms have a negative accounting income (with a median profit margin below -20%) in the year of default, almost 60% of these firms exhibit a negative book equity (compared to less than 15% in the non-defaulting control sample).

Exhibit 3.3-1: Characteristics of firms in distress or bankruptcy

illustration not visible in this excerpt

Source: Own production

An additional phenomenon common among distressed firms is a decline of asset values. This may either indicate industry-wide decline or recessions (Shleifer and Vishny, 1992) or reflect that alternative users could employ the firm’s resources more effectively (Crystal and Mokal, 2006). Moreover, the balance sheet total may also decline since distressed firms often conduct asset sales to ensure short-term liquidity despite low operational profitability (see section 3.4 for a more detailed discussion).

As a direct consequence, firms in financial distress often experience a significantly negative equity return momentum. For example, Davydenko (2007) observes that a firm’s share price typically starts to decline about 3.5 years before default, while debt yields tend to widen approximately two years in advance. Since equity absorbs most of the decline in asset value, increasing leverage ratios can be observed for almost all firms in distress. This effect is exacerbated by the tendency of distressed firms to issue additional debt to fund operations or to meet existing short-term obligations. This move is often required since cash flows from operations are negative and interest coverage ratios insufficient to honor interest or principal repayments with the money generated by the firm itself (see e.g. Asquith etai, 1994).

Further, common characteristics among firms in distress or bankruptcy include the cut or overall suspension of dividends (DeAngelo and DeAngelo, 1990, Platt and Platt, 2002, Franks and Sanzhar, 2003), the reduction of capital expenditures (Asquith et ah, 1994), a declining workforce, most likely due to layoffs (e.g., Hotchkiss, 1995, and Agarwal and Matsa, 2013) as well as the initiation of operational or financial restructuring programs (see section 3.4).

Alternatively, it has been popular to heuristically rely on other market participants’ aggregate beliefs or rating agencies’ expert opinions to identify distressed firms. For example, Moyer (2005) reports that within the financial community, issuers with credit spread of 1,000 basis points or more above the corresponding government bond yield are classified as such. On the other hand, Moyer (2005) and Prasetyo (2009) list a low credit rating, i.e. ccc and below (on the Standard & Poor’s/ Fitch scale), as well as rating downgrades into the speculative array by at least two rating buckets as additional characteristics. Similarly, Brown and Matsa (2016) use credit default swap spreads (relative to industry peers) required to insure corporate debt against losses to assess the extent to which a company is in distress.

3.4 Proceedings in financial distress and bankruptcy

In contrast to the stylized assumptions of many contingent claim models, the default of a distressed firm does neither immediately induce the transfer of control nor does it automatically trigger liquidation (Galai et al., 2007). Instead, Berkovitch et al. (1998) clarify that once the debtor files for bankruptcy, a rule based, organized and neutrally overseen bargaining process about the firm’s assets is onset among all accredited claimants. Ayotte and Skeel (2009, p. 474) describe the central societal function of the institution of bankruptcy as

“[T]o separate out the financially distressedfirms from the economically distressed ones, allowing those with financial distress to continue in business, and liquidating the economically distressed ones. ”

In line with the above paradigm, LaPorta et al. (1998) find that most modem jurisdictions have established bankruptcy laws that ensure a fair treatment of each claimant and aim to preserve as much fimi value as possible. In the U.S., two general bankruptcy protection guidelines are prevalent (Gilson et ah, 1990): if it becomes clear that the single parts of the fimi are worth more if marketed separately (i.e. economic distress cannot be resolved), a liquidation process following Chapter 7 is triggered. As summarized by Berk and DeMarzo (2014), an appointed tmstee will organize an auction-process during which the firm’s assets are sold off. The collected proceeds are used to pay off the firm’s creditors per their ranking in the bankruptcy hierarchy and the fimi goes out of business. In view of the limited liability provision of equity (which will be discussed in detail in chapter 5), Gilson (2010) points out that shareholders can even simply abandon the business, i.e. walk away without taking care of the liquidation, if the proceeds from the auction are not high enough to justify their efforts.

If, on the other hand, equity-owners or the management assess that the firm is worth more if it stays in business, bankruptcy proceedings are governed by Chapter 11 and officially referred to as corporate reorganizations (Gilson et ah, 1990). Typically, the firm’s incumbent management team stays in charge of the ongoing operations and proposes a reorganization plan in which the treatment of each claimant group is specified.[7] Claimants are sorted into clusters based on the seniority of their pre-petition liabilities.[8] Each cluster that would receive less than the complete face value of its claim under the proposed plan is awarded the right to vote on it and, where applicable, to propose changes to the court (Gilson et ah, 1990, Hamoto and Correia, 2012, Berk and DeMarzo, 2014). Moreover, note that the maturity of all pre-petition debt is automatically suspended during the bankruptcy process until the bankruptcy court has ruled on the proceedings (Shobhana and Deepa, 2012). While Bris et al. (2006) report that there are only comparatively few Chapter 7-driven complete firm liquidations, Asquith et al. (1994), Brown et al. (1994), Ofek (1993) as well as Shleifer and Vishny (1992) and Pulvino (1998) all present evidence for the strong popularity of asset sales both before the actual Chapter 11 filing but also as part of the reorganization plan. Moreover, Gilson (2010) and Sundaresan (2013) list debt renegotiations and distressed exchanges as popular measures to overcome distress. While renegotiations involve the adjustment of contractual features for outstanding securities, a distressed change implies that debt-owners swap their original securities for a package of new claims which is often worth less.[9]

On the other hand, Gilson et al. (1990) advocate a private re-contracting of claims if the expected costs for doing so are substantially lower than for a formal, courtroom based bankruptcy process. Empirically, Asquith et al. (1994) find out-of-court restructurings to be particularly popular if a firm has comparatively few secured or collateralized claims and if the structure of public debt is relatively simple, i.e. does not involve many different instruments.

Eventually, Berk and DeMarzo (2014) present pre-packaged bankruptcies as a hybrid version of private workouts and formal bankruptcies: hereunder, distressed firms negotiate a reorganization plan first and, once the approval of major claimholders is ensured, officially file for Chapter 11, which, is typically resolved promptly. Exhibit 3.4-1 summarizes the different proceedings discussed above.

Exhibit 3.4-1: Proceedings in financial distress and bankruptcy

illustration not visible in this excerpt

Source: Gilson (2010), own production

3.5 Scope of this study

In line with the original Merton (1974) approach and the vast majority of structural models, the underlying work will deploy the concept of economic distress with an exogenously defined default barrier. In other words, the fimi is assumed to default if its market value of assets vt falls below its total obligations D at maturity T. Further on, this work will not model any deviations from the absolute priority rule in bankruptcy.

This approach is most appropriate given the earlier outlined similarity between (restricted) cash flow and value based default boundary models and the fact that most often financial and economic distress go hand in hand (see Davydenko, 2007). Furthermore, assuming that a fimi with an economically viable business model is able to raise financing to overcome temporary cash flow shortages, purely financial distress shall not trigger default if not accompanied by persistent economic distress.

Thus, we will not deploy cash flow based endogenous contingent claim models. However, we account for different claim priorities and intemiediate coupon payments until debt maturity. This procedure will be explained in more detail in the framework section 6.4.2.

4 Option theory

Financial options are not only one of the most actively traded securities in modem financial markets.[10] Their intuition and terminology has also contributed enormously to both the understanding and subsequent modeling of different financial instruments, including the various equity and debt instruments corporations nowadays fund their operations with.

Thus, a sound knowledge of related payoff and price dynamics will, next to an understanding of the (i) nature of distress and (ii) various default triggers discussed in the previous section, help understand the overall idea of contingent claim pricing models in the context of stmggling or failing firms.

Mandelbrot and Hudson (2010) as well as Read (2012) document that it took until the postulation of a rigorous, scientific pricing framework in the 1970’s to establish the broad use of call and puts in the financial community outside of famling markets. Much of these achievements can be attributed to seminal work conducted by Black and Scholes (1973), Merton (1973) as well as Cox et al. (1979) who proposed tractable and easily implementable solutions for the fair valuation of different options.

4.1 Nature of an option

Broadly speaking and as conceptualized by Hillier et al. (2008), financial options are derivative products, i.e. their future payoff and hence, present value is entirely detemiined by the value of another asset, referred to as the underlying. More specifically, Brealey et al. (2010, p. 542) propose the following definition:

“A financiai option is a right, but not the obligation, of its owner to buy or sell an underlying financiai asset at a predetermined price on or before a predetermined date. ”

In a generic forni, two kinds of options exist: a call represents the right to buy a financial asset for a pre-specified price, commonly referred to as the option’s strike, whereas a put entails the right to sell the underlying for a pre-specified price. A call (put) is said to be in-the-money if the value of the underlying is above (below) the strike price. The opposite scenario is referred to as out-of-the-money while an underlying value equal to the strike price is denoted as at-the-money.

Further on, Hull et al. (2004a) defines an option’s moneyness к as the quotient of “the option strike price to the forward equity price” (Hull et al, 2004a, p. 8). While a European option provides its holder with the right to buy/ sell the underlying at the maturity date of the option, an American option, on the other hand, also allows an exercise at any time prior to maturity. Hull (2014) points out that while most options traded nowadays are of American type, European exercise provisions are typically easier to analyze based on closed-form (i.e. non-numerical) solutions.

4.1.1 Generic option payoffs

At the maturity t = T of an European option, its holder must decide whether to exercise the option or not. If exercised, the payoff of a call is represented by its intrinsic value, i.e.

illustration not visible in this excerpt

Accordingly, the payoff of a European put at maturity equals

illustration not visible in this excerpt

It can easily be seen that a call (put) will be exercised if the value of the underlying is above (below) the option strike price к. Exhibit 4.1.1 -1 plots the option’s payoff to its owner at maturity as a function of the value of the underlying. To assess the resulting profit or loss, the payoff must be reduced by the option premium, i.e. the price to acquire the right to buy/ sell the underlying.

Exhibit 4.1.1-1: Payoff diagram of a call/ put option at maturity

illustration not visible in this excerpt

Source: Hull (2014)

4.1.2 Put-call-parity

Financial engineering, as defined by Kaur et al. (2015), describes the combination of already existing financial products to create/ replicate new instruments. As a basic underlying paradigm, the law of one price states – for the absence of arbitrage to hold and an economy to be in equilibrium following Arrow and Debreu (1954) - that two securities with equal payoffs must trade at the same value. Subsequently, using this line of arguments, it can be shown that the payoff of a put-option at maturity can be replicated by the combination of a long-position in a call with the same strike price and maturity, a risk-free zero-coupon bond with a notional equal to the options’ strike price and a short- position in the underlying asset, cf. Exhibit 4.1.2-1.

Exhibit 4.1.2-1: Derivation of the put-call-parity via payoff-diagrams

illustration not visible in this excerpt

Source: Hull (2014)

Further, it can be shown analytically that both portfolios lead to the same payoff at maturity.

illustration not visible in this excerpt

Recalling the law of one price, the following pricing relationship must hold during the overall life of a European option:[11]

Equation 4.1.2-1: Put-call-parity pricing relationship for European options

illustration not visible in this excerpt

Source: Hull (2014)

As we will demonstrate in chapter 5 of this thesis, a congeneric argument can be used to establish a relationship between a firm’s enterprise value as well as the price of its equity and debt instruments.

4.1.3 Bull spread option strategy

Following Hull (2014), the payoff of a security that participates in the upside of the underlying if a lower strike price кг is surpassed but whose payoff is capped as soon as the underlying trades above a higher strike price K2 can be constructed as a combined long and short position in two calls on the underlying. Exhibit 4.1.3-1 depicts the resulting profit profile.

Exhibit 4.1.3-1: Replication of a Bull-spread using two call options

illustration not visible in this excerpt

Source: Hull (2014)

Exhibit 4.1.3-2 summarizes the potential payoffs depending on the value of the underlying.

Exhibit 4.1.3-2: Payoff profile of a bull spread using two call options

illustration not visible in this excerpt

Source: Hull (2014)

In chapter 5 of this thesis, we will demonstrate that a bull-spread represents the pay-off profile of a corporate security that holds an intermediate priority claim on a firm’s asset in the bankruptcy hierarchy – such as junior debt whose owners rank above equity holders but are subordinated to senior or secured debt. We will subsequently incorporate this option portfolio into our valuation framework for distressed firms to account for the remark of Sundaresan (2013) that – while most contingent claim based models assume a single class of debt – firms indeed have multiple types outstanding.

4.2 Option pricing theory

Financial economists have proposed theoretical models for the fair valuation of options both in a continuous and discrete time setting. As outlined by Hull (2014), continuous set-ups assume a constant, uninterrupted passage of time. Further, asset prices can take any value within a pre-specified range. On the other hand, Hull (2014) notes that discrete time models divide the time flow in blocks with equal lengths. On top, asset prices may only take certain distinct values.

While the first advanced approach to the valuation of financial options dates to Bachelier (1900) already, it took until the groundbreaking contribution of Black and Scholes (1973) and Merton (1973) to establish rigorous and coherent closed-form solutions.

4.2.1 Black- Scholes model in continuous time

In their seminal (stock) option pricing paper, Black and Scholes (1973) and Merton (1973) assume[12] that stock prices follow a lognormal distribution, i.e. are nomial after taking the natural logarithm. In particular, their stochastic continuous time diffusion process and the corresponding differential equation are depicted in Equation 4.2.1-1/ 2.

Equation 4.2.1-1/ 2: Stochastic differential equation for an asset following a log-normal distribution

illustration not visible in this excerpt[13]

Source: Black and Scholes (1973), Merton (1973)

Building on stochastic calculus tools, Black and Scholes (1973) as well as Merton (1973) demonstrate that - for a marginally short time interval - it is possible to perfectly replicate the final payoff (under all possible price evolution scenarios) of an option through a dynamic combination of a fractional investment in the underlying itself as well as lending/ borrowing at the risk-free interest rate. In a next step, Merton (1973) proposes to build a portfolio consisting of a short-position in the derivative and a long-position in the synthetic replicating portfolio. Since the payoffs of both portfolio constituents exactly neutralize each other, the return of the portfolio becomes locally deterministic and hence, must equal the risk-free interest rate.[14]

Indeed, it is possible to define a (“risk-neutral”) probability-measure Q under which the overall market price for risk stays unchanged but the drift rate of the underlying itself becomes the risk-free interest rate (Hull, 2014). This insight finally resolved the dispute about which rate is appropriate to discount expected option payoffs. Now, the fair price of an option can be written as w0 = e_r('r_^£'f(/(yt)). Building on the properties of the log-normal distribution, the fair value of a European call eventually can be expressed by Equation 4.2.1-3.[15]

Equation 4.2.1-3: Value of a European call option

illustration not visible in this excerpt

Source: Black and Scholes (1973), Merton (1973)

A valuation formula of a European put option can be derived based on the put-call-parity and will be presented in Appendix 4.2.1-A.5.

Next to exact valuation output, the closed form solutions developed by Black and Scholes (1973) and Merton (1973) provide also guidance how the fair price of an option qualitatively (and, for concrete applications also quantitatively) depends on the relevant input parameters. Exhibit 4.2.1-ldepicts this sensitivity analysis as, for example, summarized in Taleb (1997).

Exhibit 4.2.1-1: Price sensitivities of call and put options

illustration not visible in this excerpt[16]

Source: Taleb (1997)[17]

An awareness of an option’s sensitivities may not only help to understand its pricing dynamics but also educate about the different incentives that the various stakeholders of an asset whose payoff resembles a financial option may have (see chapter 5.2).

Since seminal work conducted by Cox et al. (1979), binomial lattice based pricing approaches have become a powerful alternative for the closed-form solutions discussed above. For the arguments developed in section 1.2.2, our framework does not incorporate such techniques. Nonetheless, Appendix 4.2.1-A.6 will provide an overview on binomial lattice analysis in discrete time setting.

5 Structural models

The subsequent part on structural models and contingent claim pricing lays the theoretical foundation for the later development of the framework. The chapter is subdivided into four segments:

Exhibit 5-1 : Structure of structural models chapter

illustration not visible in this excerpt

Source: Own production

Generally, structural models use modem option pricing theory to value corporate securities by proving an explicit relationship between default risk and capital structure (Wang, 2009). More precisely, in their seminal options pricing paper Black and Scholes (1973) propose how to apply their approach to the valuation of warrants and other corporate liabilities such as credit-risky debt. Given that any option can be seen as a simple contingent-claim asset, Merton (1973) argues that all “securities can be expressed as combinations of basic option contracts, and, as such, a theory of option pricing constitutes a theory of contingent-claim pricing” (Merton, 1973, p. 141), also referred to as contingent-claim analysis (CCA) by Jones et al. (1984) or default-claim pricing by Uhrig-Homburg (2002).

In 1974, Merton is the first to reveal a rigorous option based theory on the pricing of corporate debt, thereby laying the basis for a broad strand of research summarized under structural models (Wang, 2009). These structural models are very important in a variety of fields within finance. For instance, they are used to understand firm’s financing decisions and classical issues in corporate finance such as the firm’s optimal capital stmcture (Uhrig-Homburg, 2002, Hamoto and Correia, 2012). Secondly, they can be applied for the credit-risk assessment of debt products as for example by the rating agency Moody’s to assign credit ratings and probabilities of default (Crosbie and Bohn, 2003) or in the assessment of the temi and risk stmcture of interest rates (Duffie and Lando, 2001). Thirdly, stmctural models have emerged as a prominent tool to price capital market products such as credit derivatives or stmctured products like collateralized debt obligations (Hull and White, 2010). In addition, Merton (1977) has deployed modem option pricing theory and CCA to analytically derive the cost of deposit insurance and loan guarantees, whereas Myers (1977) recognizes that option pricing theory could be applied to real assets and non-financial investments such as corporate growth opportunities.[18]

Most relevant for the underlying work, CCA is used to price the equity of firms in special situations or with particular characteristics, i.e. high growth or financially distressed firms with negative earnings (Damodaran, 2009). Similarly, Jones et al. (1984) argue that given the stmcture of the CCA model, it is fairly easy to “infer fimi values and other security values from the values of traded claims, and to price different covenant structures” (Jones et ah, 1984, p. 611). Moreover, contributing to the last area of application, Anderson and Sundaresan (1996) analyze the design and valuation of debt contracts, in particular a variety of debt covenants.

5.1 Firm value as a portfolio of options

Generally, a fimi can finance its operations by issuing debt or equity. Assume an equity-financed fimi issues only one homogenous type of debt, a risky zero-coupon bond with a face value D and a maturity T. Both sources of financing have different claims on the firm’s assets. Equity in a fimi is a residual claim, i.e. equity holders have a claim on the firm’s cash flows remaining after all other financial claimholders, e.g. debtholders or preferred stock, have been paid-off according to the absolute priority of claims outlined earlier (Crosbie and Bohn, 2003, Damodaran, 2009). The same reasoning applies if the fimi is liquidated at time t. Based on the absolute priority mie, equity holders receive the remainder of the firm’s assets after all other claimants are satisfied (see chapter 3.4).

In most listed firms, equity has two important features, which forni the necessary basis of the contingent-claim pricing approach. First, equity holders own the fimi and can chose to liquidate its assets and pay off other claim holders at any time. Secondly, in publicly traded firms (PLC) and some private companies (LLC), the liability of equity is restricted to their equity investments in these companies (Glassemian, 2003, Damodaran, 2009).

Let vt denote the market value of the firm’s assets at time t. “In reality, the market value is an abstract quantity representing the present value of all future cash flows that the fimi will generate” (Lando, 2016, p. 1, see also Appendix 2-A. 1). Based on the above, the payoff to equity holders in a liquidation reads as defined in Exhibit 5.1-1. Consequently, with limited liability, if the firm’s assets at time t are less than the value of the outstanding debt and other claims, i.e. the fimi is bankrupt, equity holders will simply choose to walk away with their loss being equal to their initial investment (Crosbie and Bohn, 2003, Glassemian, 2003, Damodaran, 2002). In that case, equity holders will lose ownership of the firm’s assets, which are handed over to debt holders according to predetemiined debt covenants in case of default. Crosbie and Bohn (2003, p. 8) summarize:

“The limited liability feature of equity means that the equity holders have the right, but not the obligation, to pay off the debt holders and take over the remaining assets of the firm. ”

Combining (i) the option to liquidate and (ii) limited liability, “equity can thus be viewed as a call option on the fimi, where exercising the option requires that the fimi be liquidated and the face value of the debt be paid off’ (Damodaran, 2002, chapter 30, p. 2).

Exhibit 5.1-1: Payoff on equity as option in a firm

illustration not visible in this excerpt

Source: Damodaran (2009)

The firm’s asset value VT corresponds to the option’s underlying, while the face value of outstanding debt D is equivalent to the option’s strike price. The option expires at the maturity T of the outstanding debt. Therefore, this call option is not equivalent to a financial option as outlined in section 4 of this work, “since it is an option on a real underlying asset - an operating firm” (Hamoto and Correia, 2012, p. 1). In summary, equity payoff as a function of debt principal and fimi asset value at time T, denoted ST (S for stock), is given as:

Equation 5.1-1: Equity as call option payoff

illustration not visible in this excerpt

Source: Merton (1974)

However, in many private companies, owners have unlimited liability, i.e. are fully liable with all their assets including personal wealth and thus their liability is not capped to the initial investment in case the fimi mns into bankruptcy. Under the lack of limited liability, the firm’s equity can hence not be valued as a call option (Damodaran, 2002).

Complementarity, at maturity T bondholders are entitled to receive the face value of debt D if the fimi value exceeds the amount of debt outstanding, i.e. if VT > D. Alternatively, bondholders immediately take over the fimi (and shareholders receive nothing), if the fimi value is lower than the outstanding debt obligations, i.e. if Tty < D and hence, the fimi is technically in default.

Note that the basic Merton model (1974) assumes the absence of frictions such as transaction costs, taxes and any potential distress costs, thus in case of default creditors realize the full amount of vt (see also Sundaresan, 2013). Equivalently, debt as a function of firm asset value, denoted BT (B for bond) can be expressed as:

Equation 5.1-2: Bond value as option payoff

BT Bond value

illustration not visible in this excerpt

Source: Merton (1974)

Exhibit 5.1-2: Bondholder payoff as portfolio of risk-free bond and put option

illustration not visible in this excerpt

Source: Own production

Apparent from the above, the payoff to bondholders corresponds to a portfolio composed of a risk­free zero-coupon bond with a face value of D and a short European put option on the fimi’s assets (Löffler and Posch, 2007, Sundaresan, 2013). In other words, Merton (1974) notes that the difference between credit-risky debt and otherwise identical risk-free debt is simply equal to the value of this European put option (see also Sundaresan, 2013). Similarly, “debt is risky because [the] asset value may not be sufficient to meet the promised debt payments” (Gapen et ak, 2004, p. 6) and hence, the put option is consistent with “the expected loss associated with default when the assets are insufficient to meet the promised payments on the debt” (Gapen et ak, 2004, p. 6). Thus, both Merton (1974) and Black and Scholes (1973) suggest a model of the fimi that relates credit risk to the capital stmcture of the company (Hull et ak, 2004a, Wang, 2009).

Inserting the above derived option pricing relationship for equity (equation 5.1-1) and debt (equation 5.1-2) into the balance sheet relationship summarizes the fact that firm value can be expressed as a portfolio of options:

Equation 5.1-3: Firm as portfolio of options

illustration not visible in this excerpt

Source: Gapen et al. (2004)

Exhibit 5.1-3: Payoff to equity and bond holders at maturity T

illustration not visible in this excerpt

Source: Löffler and Posch (2007)

In line with the latter, it becomes obvious that equity and bond holders always hold the respective offsetting stakes in the different option positions. In other words, if bond holders are long a risk-free bond and short a put option on the firm’s assets, equity holders are necessarily short, i.e. borrow, a risk-free bond and hold a long position in the put option.

“Once we recognize that the borrower (equity holders in Merton’s model), (i) owns the fimi, (ii) borrowed the amount D at t = 0, and (iii) owns a put option on the assets of the fimi with a strike price equal to D, it is immediate, by a put-call parity relationship that equity is a call option on the assets of the borrowing fimi with a strike price equal to D, the face value of debt” (Sundaresan, 2013, p. 5-3, see also Bharath and Shumway, 2008).

Exhibit 5.1-4: Equity as portfolio of risk-free bond, put option and underlying

illustration not visible in this excerpt

Source: Own production

Finally, given the above, Petersen and Plenborg (2012) correctly point out that understanding equity as a call option of the firm’s assets under the umbrella of contingent claim pricing is equivalent to the real option valuation approach. Different from static present value models, real option valuation incorporates the value of flexibility for equity, here in forni of the long position in the put option with a strike price equal to the level of outstanding debt. Subsequently, the contingent claim approach combines present value models with a flexibility feature by adding the value of an option, here the equity holder’s option to abandon the firm’s assets.

5.2 Contingent claim pricing

The key underlying assumptions of Merton’s (1974) structural model are that the firm’s assets V follow a lognormal stochastic diffusion process with constant volatility (Merton, 1974, Hull et ah, 2004a, Sundaresan, 2013) and default is triggered if the asset value ends up below the value of the outstanding debt at maturity T. More specifically, as previously outlined in chapter 4.2.1, the value of the underlying asset is assumed to follow a Geometric Brownian Motion (GBM), which reads as follows (assumption A.8 in the original Merton (1974) model):

Equation 5.2-1: Geometric Brownian Motion model

illustration not visible in this excerpt

Source: Merton (1974), Black and Cox (1976)

In addition, Merton (1974) defines a series of underlying model assumptions, which can be found in Appendix 5.2-A. 1. Building on the above and the option pricing theory by Black and Scholes (1973) outlined in section 4.2 of this work, the various claims on the firm’s assets can be priced as follows:

Equation 5.2-2: Debt and equity in BS option pricing setup[19]

illustration not visible in this excerpt

Source: Sundaresan (2013), Lando (2016)

Note that the valuation can be done at any point in time prior to reaching debt maturity T and the theoretical liquidation of the firm’s assets. Moreover, in line with chapter 4.2.1, the value of equity in the Black and Scholes (1973) setting can be written as follows:

Equation 5.2-3: Pricing equity with Black and Scholes

illustration not visible in this excerpt

Source: Sundaresan (2013), Lando (2016)


[1] Following Saunders et al. (2011), the philosophical term ontology characterizes how the nature of reality/ being is perceived while epistemology relates to the question what composes acceptable knowledge and how such knowledge is created. Lastly, axiology is concerned about the role (personal) values should assume in the research process.

[2] Both Wruck (1990) and Davydenko (2007) find financial distress to follow from (persistent) economic distress. Similarly, Kahl (2002) postulates that financial distress is an imperfect indicator of economic viability. Further on, Asquith et al. (1994) note the difficulty of studying financial distress in isolation since firms may be in economic distress simultaneously.

[3] A similar definition of distress has been deployed by Titman (1984).

[4] The definition of insolvency based on assets and liabilities by Pumanandam (2008) is equivalent to the stock based classification of insolvency by Wruck (1990). On the other hand, a firm is insolvent on a flow basis if it is unable to meet current cash obligations.

[5] Note that default may also be triggered by cross-default provisions, i.e. “default on one debt security is a condition for technical default in another” (Wmck, 1990, p. 421).

[6] In his sample Davydenko (2007) finds that ,,‘the average market value of assets at default is only 60% of the face value of debt, and liquidity ratios are below the industry median for 80% of defaulting firms’’ (Davydenko, 2007, p. 2).

[7] A large sample of reorganization in the u.s. includes a violation of the absolute priority mie, i.e. holders of junior liabilities or even common stock are awarded with cash/equity in the reorganized unit even if the claims of senior liability holders have not been folly satisfied yet. This convention may be justified if it incentivizes junior claimants for smoother coordination with senior counterparts, eventually leading to a faster resolution of the bankruptcy process (see, e.g. Franks and Torous, 1989, Eberhardt et al., 1990, or Weiss, 1990, for a comprehensive discussion).

[8] Gilson et al. (2015) observe a recent rise in merger and acquisition activities involving firms currently in Chapter 11 and consternate that this trend has blurred the distinction between liquidations and reorganizations of distressed firms.

[9] Note that debt renegotiation is not only a phenomenon common for distressed companies. In an empirical study entailing listed U.S. companies, Roberts and Sufi (2009) find that more than 90% of all long-term debt contracts are renegotiated diuing their life-time. Contractual changes include, but are not limited to, principal outstanding, matiuity and pricing featiues.

[10] Survey data collected by the Bank for International Settlements (2016a) and Bank for International Settlements (2016b) shows that nowadays financial options achieve an average daily turnover above $3tn and a notional amount close to $50tn, a figure similar in magnitude to the aggregated output of the world’s largest economies.

[11] For American options, Hull (2014) shows that the put-call-parity can be expressed as a relationship were two boimdary conditions for the upper and lower value must hold: [illustration not visible in this excerpt]

[12] A complete overview on the assumptions underlying the BSM model is provided in Appendix 4.2.1 -A. 1.

[13] A standard Brownian motion/Wiener process represents a continuous time stochastic process with normally distributed and independent increments so that [illustration not visible in this excerpt] see Merton (1990) for a more detailed discussion of its properties.

[14] A formal hedging based derivation of the Black-Scholes-Merton equation, which is the backbone for arbitrage-free pricing of every derivative security, is presented in Appendix 4.2.1 -A.3.

[15] A formal proof for this is provided in Appendix 4.2.1-A.4.

[16] The standard normal Gaussian distribution is represented by [illustration not visible in this excerpt]

[17] Hull (2014) correctly points out that the depicted sensitivity of an option’s price towards the option’s time to maturity T only holds in the absence of dividends. Consider two European call options differing only in their remaining life. Under the absence of dividends, the option with the later maturity date should be worth more since there is more time left to benefit from the asymmetric participation in price changes of the underlying. If, however, the underlying is expected to pay substantial dividends over the remaining life of the options, ultimately lowering the price of the underlying, a rational investor may find it optimal to exercise a call option as early as possible. As a result, under such a scenario, a European call option with a shorter maturity should trade at the higher price. The reverse reasoning applies for Einopean puts.

[18] For examples on the valuation of strategic options the interested reader may also refer to McDonald and Siegel (1986), Majd and Pindyck (1987), Myers and Majd (1990), and Ingersoll and Ross (1992).

[19] Note that the standard Merton (1974) model assumes a simple default boundary equal to the face value of the firm’s single homogenous zero-coupon debt with a maturity of г = 1.

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Evaluation of claims on distressed firms. A conceptual framework based on structural models
Copenhagen Business School  (Department of Finance)
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Structural Models, Option Valuation, Distress, Framework, Merton Model, Claim valuation, Bankruptcy, Contingent claim pricing, Case study
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Elias Fiebig (Author)Alexander Brandt (Author), 2017, Evaluation of claims on distressed firms. A conceptual framework based on structural models, Munich, GRIN Verlag, https://www.grin.com/document/377663


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