2.1 CA and continuous auditing

The existing approach to auditing corporate financial statements contains two inherent flaws that have raised concerns in both academia and practice. The nature of the traditional attestation framework hinders timely and relevant assurance reporting (Vasarhelyi & Halper, Reference Vasarhelyi and Halper1991). Performing an audit only once a year may result in fraudulent activity going undetected for up to a year or more and key stakeholders must wait an entire audit cycle to determine if the financial numbers released by an organization are correct in all material respects and that appropriate internal controls are in place to detect financial fraud. Critical decisions by investors, creditors, management, and others therefore may be determined from out-of-date information and conjecture rather than current, audited facts. This situation raises the risk of making less than optimal decisions.

Concerns over this weakness, in combination with the corporate frauds of the early part of this millennium, fostered the CA movement that many consider a viable approach to help identify potential audit concerns earlier in the process. The current SEC initiative for mandated continuous reporting of financial information and the focus of SOX on tighter internal controls over financial reporting and more transparency create an even stronger impetus to develop and implement CA functionality. CA can provide the external auditor a method of providing a more comprehensive, efficient, and effective audit by automating the testing of the full population of transactions for specific audit areas rather than evaluating only smaller samples due to the time constraints of manual processing. Boundless opportunities exist for researchers and practitioners alike to determine the optimal design, implementation approaches, and aftereffects of CA system use.

The environment in which organizations operate has become increasingly complex. Internal and external parties interact with one another creating a dynamic, connected network where the actions of one individual or organization can significantly affect the livelihood and behavior of others regardless of time and space dimensions. Auditors must be cognizant of this fact and consider the implications of external forces on their clients’ operations. The remainder of this essay introduces the theories of complexity and CAS then discusses the techniques of simulation and agent-based modeling designed to analyze complex, organizational phenomena.

2.2 Complexity

Complexity, what does it truly mean? It depends on who you ask. The Merriam-Webster Online Dictionary defines the word as ‘a whole made up of complicated or interrelated parts’ (Merriam-Webster Inc., 2008). This understanding held true until about 15 years ago (Laurent & Koch, Reference Laurent and Koch1999) when a new, deeper interpretation emerged distinguishing complexity from complicated (Mikulecky, Reference Mikulecky1999; Reitsma, Reference Reitsma2003). A complicated system (and the original view of complexity) can be completely and accurately described regardless of the number of individual components (Reitsma, Reference Reitsma2003); ‘complication is a quantitative escalation of that which is theoretically reducible’ (Chapman, Reference Chapman1985). A complex system, on the other hand, cannot be fully understood by analyzing the components (Cilliers, Reference Cilliers1998); the whole is greater than the sum of its parts where the dynamics of real systems arise from traits of the individuals and their environment (Siebers & Aickelin, Reference Siebers and Aickelin2007). The core of complexity science lies in understanding the indirect effects that arise from the interactions of system components.

Collectively, complexity science and research have adopted the ‘anti-reductionist’ approach to analyzing phenomena as the dominant lens. Chapman (Reference Chapman1985) argued that if the world can be explained in a reductionist manner then complexity is not qualitatively different from simplicity but merely quantitatively different. The main task for complexity science is to explain how relatively stable, aggregated, macroscopic patterns emerge from local interactions of numerous lower level entities (Srbljinovic & Skunca, Reference Srbljinovic and Skunca2003). This notion of aggregate complexity underlies the theory of CAS that lies at the heart of this particular study. The next section delves further into CAS.

2.3 CAS

The theory of CAS arose from the complexity theories spawned in the natural sciences to develop mathematical models of systems in nature. Although considered one stream of complexity research, many variations of the definition and key premises of CAS exist. A quote from John H. Holland included in Waldrop (Reference Waldrop1993), one of the original researchers in the area, best depicts the general principles underlying CAS:

CAS examples include economies, social systems, ecologies, cultures, politics, technologies, traffic, weather, etc. (Dooley, Reference Dooley1997). In order to adequately comprehend and utilize a theory that spans such a wide array of disciplines with varied interpretations, Choi et al. (Reference Choi, Dooley and Rungtusanatham2001) developed a comprehensive framework of CAS elements and attributes depicted in Figure 1. The framework consists of three interacting and intertwined main foci each with a subset of additional components: (1) internal mechanisms, (2) co-evolution, and (3) environment. The remainder of this section on CAS briefly reviews these foundational concepts and principles in more depth as they represent the supporting lens for this study.

Figure 1 Underlying principles of complex adaptive systems. Adapted from Choi et al. (Reference Choi, Dooley and Rungtusanatham2001)

Agents represent the building blocks of CAS and are semi-autonomous units that seek to maximize some measure of goodness, or fitness, by evolving over time where fitness corresponds to the general well-being of the system. Giddens (Reference Giddens1984) defined agency as the ability to intervene meaningfully in the course of events. Therefore, by definition, a system must include agents that can impact the state of the system by their actions in order to be considered a CAS—a definitive characteristic differentiating CAS from other types of systems. Examples of agents in a social CAS include individuals inside organizations, organizations comprising a profession, or even a profession operating in a global marketplace. The latter two illustrate a network of multiple CASs functioning in concert. Defining agents and CASs thus depends entirely upon the perspective of the observer.

CAS agents interact with other agents, both within their own system as well as with the environment which may include other CASs and their respective agents, commonly referred to as meta-agents (Benbya & McKelvey, Reference Benbya and McKelvey2006). The exchange of information and resources between agents facilitate the generation of schema (Schein, Reference Schein1992) defined as the norms, values, beliefs, and assumptions shared among the collective that dictate the manner in which agents interpret information and perform actions. Organizational leaders often declare formalized mission statements, create codes of conduct, ethics statements, etc. that represent core values and guide the behavior of agents, in particular, the interaction between employees and other stakeholders (e.g. customers, vendors, and other related parties).

Within the bounds of these ‘rules of behavior’ and shared values, agents strive to increase the fitness of their system, both locally and globally, by self-organization—the emergence of a pattern of order from a simple set of rules governing agent behavior in a connected network without the intervention of a central controller (Anderson, Reference Anderson1999; Luoma, Reference Luoma2006; Mason, Reference Mason2007). The actions of agents can result in nonlinear impacts to the local system and network of systems depending on the connectedness of the system(s); a more connected system will generally experience larger ripple effects throughout as agents interact in a dynamic fashion. This symbiotic relationship facilitates co-evolution where multiple systems and/or sub-systems emerge together because ‘there is feedback among the systems in terms of competition or co-operation and utilization of the same limited resources’ (Zimmerman et al., Reference Zimmerman, Lindberg and Plsek1998). The environment imposes changes on its members who react thus changing themselves and consequently changing the environment. Therefore, co-evolution occurs when system members are forced to adapt continually to the changing context wrought by others’ strategies in order to remain relatively fit (Van Valen, Reference Van Valen1973; Kim & Kaplan, Reference Kim and Kaplan2006).

Although the nature of a CAS prevents exact prediction of future actions and outcomes, distinct patterns of behavior exist underneath apparent randomness allowing examination and general predictive ability of most likely system states. In some cases small changes may lead to drastically different future paths; however, the same characteristic pattern of behavior emerges despite the change (Choi et al., Reference Choi, Dooley and Rungtusanatham2001). Now that we have discussed the elements of the CAS theoretical foundation, the remainder of the section will describe ABM simulation, the primary research approach used to analyze CAS in the social sciences.

2.4 Simulation and agent-based modeling

As discussed previously, certain phenomena in nature and society are complex, dynamic, and impossible to break down into deterministic cause and effect relationships; no definable end point or optimal solution exists to problems in such contexts. Gaining insight, understanding, and knowledge of these events or happenings requires robust tools and technologies. Analytical models fail to adequately account for the indirect effects of CAS agent interactions. Computer-based simulation, on the other hand, offers the capacity and power to mimic real-world system behavior and observe changes in system states at any time rather than merely predicting the output of a system based on a set of inputs (Siebers & Aickelin, Reference Siebers and Aickelin2007). The purpose of simulation is to better understand the inner workings of a system and/or to predict performance. Siebers and Aickelin (Reference Siebers and Aickelin2007) compared simulation to an artificial white-room that allows one to gain insight but also to test new theories and practices without disrupting the actual system's operation. Troitzsch (Reference Troitzsch2000) stated that if the theory framed for a particular system holds and the theory has been adequately translated into a computer model, then the simulation can assist in determining (1) what kind of behavior a target system will display in the future and (2) which state the target system will reach in the future. Such predictions involve analyzing trends rather than generating precise and absolute predictions of system performance (Siebers & Aickelin, Reference Siebers and Aickelin2007); Keen and Sol (Reference Keen and Sol2007) referred to this as ‘rehearsing the future’. Simulation, therefore, should be viewed as a decision support tool that requires consideration of the context of the real system before moving forward to implement steps intended to alter the system's direction and influence future state changes.

Agent-based modeling represents one type of stochastic simulation modeling that facilitates exploration of the nonlinear, adaptive interactions inherent to a CAS (Srbljinovic & Skunca, Reference Srbljinovic and Skunca2003; Siebers & Aickelin, Reference Siebers and Aickelin2007). The researcher specifies the rules of behavior at the micro-level for the individual agents and the interactions between agents. Structures then emerge at the macro-level due to the actions of these agents and their interactions with each other and the environment. The consequences at the macro-level that result from ABM many times are not obvious or expected. This discovered knowledge allows the interested party to identify potential system states that may not have been considered otherwise, thus enhancing the effectiveness of the decision making process. Cederman (Reference Cederman1997) noted the following as some advantages of ABM: (1) the possibility of modeling fluid or turbulent social conditions when modeled agents and their identities are not fixed or given, but susceptible to changes that may include birth or death of individual agents, as well as adaptation of their behavior; (2) the possibility of modeling boundedly rational agents, making decisions and acting in conditions of incomplete knowledge and information; and (3) the possibility of modeling processes out of equilibrium.

Complexity researchers began using ABM in earnest in the 1990s (Epstein & Axtell, Reference Epstein and Axtell1996) and the approach has become a well-established simulation modeling tool in academia (Siebers & Aickelin, Reference Siebers and Aickelin2007; Sklar & Richards, Reference Sklar and Richards2010). As an example, an entire specialty in economics called Agent-Based Computational Economics (ACE) developed from the CAS movement to computationally study economies modeled as evolving systems of autonomous interacting agents (Tesfatsion, 2001). ACE attempts to understand why certain global regularities evolved and continue on in decentralized market economies despite the absence of a central controller (e.g. trade networks, currencies, and market protocols) and to examine the effects of alternative socio-economic structures on individual behavior and social welfare. Additional, related agent-based work continues by examining the evolutionary selection of forecasting heuristics (Anufriev & Hommes, Reference Anufriev and Hommes2009) and knowledge encapsulation and discovery in market exchanges (Greenwood, Reference Greenwood2007). As the gap between multi-agent system analysis/design and system implementation narrows, ABM is quickly becoming more commonplace in practice to solve real business problems such as examining customer behavior in a supermarket based on differing configurations of products in the store layout (Casti, Reference Casti1997; Dastani & Gomez-Sanz, Reference Dastani and Gomez-Sanz2005) and stakeholder (investors, market makers, and issuers) reactions to proposed changes to the tick size on the NASDAQ stock exchange (Bonabeau, Reference Bonabeau2002).

The underlying concepts of complexity science, CAS, and ABM hold true for ABM itself as a scientific tool. As current ABM researchers model complex phenomena, present their findings, and solve real world problems, more individuals will be convinced of the merits of ABM and begin to incorporate the approach in their own work which will increase exposure exponentially through a myriad of academic and professional networks. We fully expect ABM to continue a pattern of emergent behavior and growth for the foreseeable future. As Courtney et al. (2008) note, the need exists for a complex view of organizations and the stage is set for such a paradigm shift: ‘… the science is there; the systems are there; the computational capacity is there. All that is lacking is the consciousness to apply them’.

In this background section, we present the supporting base for this study. First, the discussion on CA sets the stage for the practical setting of the study by detailing the origins and progression of the continuous audit movement. Next, the explanation of complexity science and CAS provides the theoretical foundation upon which the study relies. Finally, the discussion on simulation and agent-based modeling introduces the technical approach that will be applied. The next section integrates the key tenets of CAS with Churchman's SIS to develop the theory of CAIO.

3.1 Churchman's SIS

Organizations must learn, adapt, and manage knowledge in order to succeed in today's dynamic environment (Richardson et al., Reference Richardson, Courtney and Paradice2001). To accomplish that, organizations must be inquisitive. Churchman (Reference Churchman1971) defined inquiry as an activity that produces knowledge and stated one must have the capacity and ability to adjust behavior to changing circumstances in order to be considered knowledgeable. In his seminal text The Design of Inquiring Systems, Churchman examined the epistemologies of five schools of philosophy from a general systems theory perspective to determine their suitability as the foundation for the design of inquiring computer systems. These inquiring systems have been proposed as theoretical models for the creation of learning or inquiring organizations (Courtney et al., Reference Courtney, Croasdell and Paradice1998; Courtney, Reference Courtney2001; Linden et al., Reference Linden, Kuhn, Parrish, Richardson, Adams, Elgarah and Courtney2007). As such, Linden et al. (Reference Linden, Kuhn, Parrish, Richardson, Adams, Elgarah and Courtney2007) in their review of Churchman's inquiring systems believed that the inquirers can form the basis for the design of organizational KMS and encouraged their use to further develop IS as a discipline. This study answers that call.

Churchman named one of the inquiring systems after the philosophical beliefs of his mentor, Edgar Singer. The SIS is above all teleological, a grand teleology with an ethical base (Churchman, Reference Churchman1971). The SIS aspires to reach a highly idealistic purpose, the creation of exoteric knowledge for everyone as opposed to esoteric scientific knowledge that becomes relevant to an increasingly smaller audience as it is refined. The system seeks this knowledge in such a way as to take human and environmental considerations into account by choosing the right means for a broad spectrum of society. The SIS views the world as a holistic system in which everything is connected to everything else. Complex social and managerial problems must be analyzed as wholes (Mitroff & Linstone, Reference Mitroff and Linstone1993) and may require knowledge from any domain, discipline, or profession to solve; reductionism inhibits the solution to such problems.

The SIS is based upon metrology, the science of measurement. Measuring in the system requires cooperation concerning the rules for measuring and agreement on units and standards in order to ensure the ability to replicate—the results agree within an acceptable level of refinement. The refinement process continues by partitioning the measurement process until the readings disagree (i.e. pushing back the decimal places), at which point progress can be made. Variables are ‘swept in’ to explain the discrepancy. By bringing in information from any source to improve its image of the world including varied perspectives or worldviews of a problem, this process represents one of the most holistic aspects of the SIS (Richardson et al., Reference Richardson, Courtney and Paradice2001). Mitroff and Linstone (Reference Mitroff and Linstone1993) stated these perspectives bring to the forefront human beings collectively and individually in all their complexity. Because of the need for cooperation and a holistic view, the SIS has no primary authority built into the system. Every participant possesses authority, no single executive exists.

Refinement alone does not necessarily induce change and adaptation. The most dramatic changes occur when the need arises to revise assumptions. Churchman referred to this as the ‘heroic mood’ necessary to slay the ‘status quo dragon’. To achieve such a state, the SIS uses a Hegelian dialectic process where the thesis and antithesis work simultaneously to determine the truth. The thesis defends the status quo of an existing paradigm while the antithesis proposes radical change questioning the quality of the status quo. Members of the community are both the observers of the debate as well as the participants. Ultimately, the community reaches a synthesis and the process of seeking new knowledge then continues on. Analyzing this process, Richardson et al. (Reference Richardson, Courtney and Paradice2001) stated revolutionary change cannot be measured quantitatively and some of the most important measures in the SIS (exoteric knowledge, cooperation, diffusion of authority, and ethical purpose) may only be measurable qualitatively. Overall progress of an SIS should be measured by the extent to which the client, decision maker and designer become the same, that is, involves all of humanity, perhaps even those humans who are no longer living or are yet to be born (Linden et al., Reference Linden, Kuhn, Parrish, Richardson, Adams, Elgarah and Courtney2007).

Early in the book Churchman (Reference Churchman1971: 43) lays out nine characteristics deemed necessary for something to be called a system. Later (p. 200) he applies these to Singerian inquirers Here we describe these and illustrate them with Wikipedia, which demonstrates many of an SIS's elements.

1. 1. The system has the purpose of creating knowledge, which means creating the capability of choosing the right means (in the moral sense of right) for one's desired ends. Wikipedia does not create knowledge directly, but fosters knowledge-sharing and enables knowledge creation. Contributors are ethically bound to enter only knowledge that has been scientifically validated or at least to indicate its level of known validity.

2. 2. The system's measure of performance is the ‘level’ of scientific and educational excellence of all society. Studies that compare the educational systems of various countries attempt to measure this.

3. 3. The client is humankind, that is, all human teleological beings. Wikipedia exhibits this characteristic to the degree that it tries to make scientific knowledge available in many languages to anyone with a computer and internet connection.

4. 4. The components of the system have traditionally been disciplines unless the goal is exoteric knowledge that is relevant to everyone in every society. Wikipedia makes knowledge from many and diverse disciplines available to all who can access it.

5. 5. The system has a cooperative environment with fuzzy boundaries necessary for cooperation. Cooperation is of paramount concern in Wikipedia and is evidenced by all who contribute and maintain it.

6. 6. The decision makers are ideally everyone, the most important of which are the heroes. The heroes are those who are not satisfied with the status quo, but who dare to ask such questions as whether the earth is the center of the universe or whether gravity may not only cause the apple to fall to the ground but may also affect the relationship between celestial objects. Such heroes abandon the known world and wander off into the perhaps chaotic unknown but may make major contributions to knowledge as a result of their quest. Jimmy Wales, the founder of Wikipedia, exhibited this characteristic to a degree when he envisioned how the internet could be harnessed to share the knowledge of the world.

7. 7. The designers are ideally everyone. Progress can be measured in terms of the degree to which the client, decision maker, and designer are the same. Anyone who access or might access Wikipedia is its client; anyone who contributes decides what to contribute and designs that contribution.

8. 8. The designer's intention is to change the system so as to maximize its value to the client (everyone). Wales’ intent seems to have been maximizing the value of knowledge to curiosity seekers across the glove.

9. 9. There is a built-in guarantor that gives a sense of optimism. The Wikipedia community seems optimistic that it can maintain the truth of knowledge in the system even though some bits of ‘knowledge’ have been untrue on occasion.

A smattering of KMS and decision support research has incorporated Churchman's inquiring systems into system design and decision-making frameworks. Hall et al. (Reference Hall, Paradice and Courtney2003) and Hall and Paradice (Reference Hall and Paradice2005) described the architecture of a learning-oriented KMS developed through the integration of the inquiring systems with Simon's (Reference Simon1996) decision-making model. Richardson et al. (Reference Richardson, Courtney and Haynes2006) presented design principles for KMS based on an integration of SIS with Habermas's theory of communicative action. From a decision-making standpoint, Hall and Davis (Reference Hall and Davis2007) extended Mitroff and Linstone's (Reference Mitroff and Linstone1993) technical, organizational, and personal perspective (TOP) model and Courtney's (Reference Courtney2001) DSS paradigm in the development of a value-based decision-making model that encourages multiple value-based perspectives and mediates value conflicts. As Linden et al. (Reference Linden, Kuhn, Parrish, Richardson, Adams, Elgarah and Courtney2007) propose, these efforts show the beginnings or, more appropriately, a revitalization of Churchman's inquirers as kernel theories for the design of organizational KMS. We now continue Churchman's legacy by integrating the core concepts of SIS and CAS theory to present the design principles for a CAIO.

3.2 Design principles for a continuous auditing system to support a CAIO

As can be seen in the previous discussions, CAS theory and Churchman's (Reference Churchman1971) SIS share many characteristics. This section delves further by comparing and contrasting the two types of systems (summarized in Table 1) then discusses how they can inform one another to offer a new, enlightened theoretical approach to the design of organizational KMS and DSS. The design principles developed and presented in Table 2 adhere to Churchman's (Reference Churchman1971) conditions for a system and are intended to support decision making in a complex, connected organization facing complex, wicked problems.

Table 1 Characteristics of the complex adaptive inquiring organization

Table 2 Design Principles for a continuous auditing system to support a CAIO

CAIO = Complex Adaptive Inquiring Organizations

4.1 Design science

The CAIO system design principles developed in this study fall under the design science paradigm. Design science research is intended to both further the academic field and be relevant to practitioners through the rigorous creation of IS artifacts in the form of theories, constructs, methods, frameworks, or instantiations (Parrish, Reference Parrish2008) and is fundamentally a problem-solving paradigm (Hevner et al., Reference Hevner, March, Park and Ram2004). Benbasat and Zmud (Reference Benbasat and Zmud1999) argue that the relevance of IS research directly ties to the ability of practice to implement theories. This study adheres to the design science requirements of rigorousness and relevance by testing the CAIO organizational learning and KMS theory through the creation of an agent-based simulation model in the context of the auditor's going concern opinion. The simulation model represents an instantiation of the theory.

4.2 The research problem

Accounting regulation mandates that auditors assess the ongoing viability of every client's business operations and report any substantial doubt about a company's ability to continue as a going concern for a reasonable period of time in the issued audit report that accompanies the financial statements. The Statement on Auditing Standards No. 59 The Auditor's Consideration of An Entity's Ability to Continue As a Going Concern (SAS 59) requires auditors to gain an understanding and assess existing conditions that affect an organization, including those of others in the industry and the economy in generalFootnote ². With the push by the SEC for continuous reporting, associated need for CA, and the quickness by which the state of an organization can change in today's environment, auditors will need to assess continuing operations on a more frequent basis than once a year.

Although not explicitly expected to predict future conditions or events, auditors historically have relied upon bankruptcy prediction models, most commonly the Altman (Reference Altman1968) Z-score model (Dugan & Zavgren, Reference Dugan and Zavgren1988; Grice & Dugan, Reference Grice and Dugan2001; Grice & Ingram, Reference Grice and Ingram2001; McKee, Reference McKee2003). Bankruptcy prediction poses a challenge to auditors as the identification of cause and effect relationships between factors that may cause or be related to bankruptcy and the actual occurrence of bankruptcy can be difficult (McKee, Reference McKee2003), if not impossible in a complex and connected business environment. McKee (Reference McKee2003) examined 146 US public companies that filed bankruptcy during 1991–1997. Of those, the auditors only reported a going concern problem in 54% of the cases. Further confounding the situation, the models auditors employ contain inherent faults and rely on restrictive assumptions such as linearity, normality, and independence among predictor variables (Zhang et al., Reference Zhang, Hu, Patuwo and Indro1999). Grice and Ingram (Reference Grice and Ingram2001) examined the accuracy of the Altman Z-score and Grice and Dugan (Reference Grice and Dugan2001) reviewed the same for the Zmijewski (Reference Zmijewski1984) and Ohlson (Reference Ohlson1980) models. Both studies determined all three models failed to transcend generalizability to industries and time periods outside those of the original samples when manufacturing firms dominated the landscape. The environment most definitely has changed and now consists of knowledge-based organizations and economies that require more holistic research approaches.

Not all auditors employ statistical modeling techniques to the going concern assessment. Some perform analytical procedures such as historical trend analyses on operating losses, working capital deficiencies, negative operating cash flow, and adverse key financial ratios. They augment these financial reviews with examination of operational factors (e.g. labor work stoppages and dependence on the success of particular projects) and external circumstances (legal proceedings, changes in legislation, loss of a principal customer or supplier, or a natural disaster). Through discussions with three partners from an international public accounting firm, each elaborated on the general firm guidance by stating that every client is unique and therefore factors may be weighted differently in their assessments from client to client. However, all three agreed the primary indicator of potential business distress relates to the ability to pay short-term debt so the level of working capital (current assets—current liabilities), operating losses, and cash from operations receive the most attention.

The next section applies the CAIO theory to develop an agent-based simulation model for the auditor's going concern opinion that takes into account external conditions and can be executed on a regular basis to obtain a more timely sense of the direction an organization may head (i.e. a CA application). The model is based on the operations and financial condition for Frontier Airlines, a low-fare airline that recently filed for bankruptcy protection.

4.3 Construction of the model

4.3.2 Design specifications

Hevner et al. (Reference Hevner, March, Park and Ram2004) asserted that IS design theory should guide both researchers and practitioners. These ‘kernel theories’ are applied, tested, modified, and extended through experience, creativity, intuition, and problem solving capabilities of the researcher (Walls et al., Reference Walls, Widmeyer and El Sawy1992; Markus et al., Reference Markus, Majchrzak and Gasser2002). As such, this study proceeds from the theory building stage to theory testing and refinement through construction of a simulation model, the IS artifact. The CAIO theory informs the design specifications for the model as summarized in Table 3.

Table 3 Design specifications

4.3.4 Types of agents and agent behavior

4.3.4.1 Consumer agent properties

Harris and Uncles (Reference Harris and Uncles2007) empirically examine a myriad of potential factors that affect airline consumer patronage—including behavioral, performance, promotional, and structural. The results indicate that past purchasing behavior (i.e. frequency of travel with a specific airline) and perception of airline performance (i.e. view of last experience) ranked highest in predictive ability for future purchases. Suzuki (Reference Suzuki2000) examines the relationship of airline on-time performance to market share noting that the level of satisfaction with the most recent experience can significantly affect future purchases, even for frequent flyers. Adhering to the minimalist abductive approach, the consumer agents in the model represent airline passengers that base their future purchases on past purchasing behavior and related experiences. For example, a consumer who has traveled Frontier Airlines seven times over the past 3 months is more likely to choose Frontier on the next purchase than a consumer who flew Frontier only once during that same timeframe. Furthermore, customers who encounter a low quality experience on their last Frontier flight will be more likely to switch airlines, particularly if the last prior experience with another airline was positive. Thus, frequent travel and high quality experiences act as anchors in consumer memory for future purchases. Consumer choice behavior in the model is therefore a function of four consumer agent properties that must be populated before executing the market simulation (i.e. Time 0):

1. 1. Strength of Memory (1–9 rating).

2. 2. Frequency of Travel (% chance to travel).

3. 3. Last Airline Chosen (Frontier, United, Other, None).

4. 4. Last Trip Experience (Good, Bad, None) for each airline (Frontier, United, and Other).

The incorporation of Strength of Memory (SOM) and Frequency of Travel was facilitated by access to data from a recent study on airline consumer travel frequency conducted by the Cornell University School of Hotel Administration. We classified the SOM for consumer agents (as a percentage of total agents) as a 1–9 rating where 1 represents consumers who traveled only once in the past 3 months and 9 for those that traveled nine times or more over the same period. So, for example, in a model run consisting of 1000 consumer agents, the SOM property for 717 agents contained a value of 1, 165 with a value of 2, and so forth. These ratings will affect consumer behavior as discussed in the next section. As for the frequency property, consumers in the simulation determine whether or not to travel each week in the 52-week simulation (note: a single ‘tick’ in the model represents time passage of 1 week). The chance for each consumer to travel is also derived from the data in the Cornell study. For instance, consumers with a SOM rating of 1 only traveled once during the past 3 months (i.e. 12 weeks); therefore, the chance to travel in any individual week is 8% (1/12). Table 4 presents the nine SOM ratings and the associated chance to travel each week.

Table 4 Consumer travel frequencies

To determine the value of the last airline chosen property for each consumer agent, the model first calculates a random number from 0 to 100 then a random number for new travelers (i.e. no last airline), Frontier, and United to ‘divvy up’ the chances that the consumer agent will have flown a specific airline or not flown at all; the Other Airline category receives the remainder. In order to infuse some variability to avoid a deterministic model, the second calculation consists of a 10-point range around the 2006 market share percentage for the two airlines obtained from the collection of online databases administered by the Bureau of Transportation Statistics (BTS) with a −2% adjustment to accommodate for the consideration of new travelers. For example, Frontier earned the business of 18% of the travelers during 2006 for routes the airline serviced (Bureau of Transportation Statistics, 2008); therefore, the range for the chance that a specific consumer will have flown Frontier on the last trip randomly falls between 11% and 21% (16% +5/−5). For new travelers, the random number calculation falls between 0% and 10%. As an illustration of the process, assume the following occurs for the first consumer in the model: Last Airline random number = 75, New Traveler = 5, Frontier = 15, and United Airline = 25. The if/then logic of the model to assign an airline (or none) as the last airline flown occurs in a sequence ending once a value has been assigned. The pseudo-code for this scenario would look like the following:

• • If Last Airline rand num < 5 Then Last Airline = 0 else

• • If Last Airline rand num < 20 Then Last Airline = 1 else

• • If Last Airline rand num < 45 Then Last Airline = 2 else

• • Last Airline = 3

• • End If

In this particular instance, the random number 75 causes an assignment of 3 for the last airline flown by this consumer agent.

Following assignment of the Last Airline property, the model determines whether the consumer agent experienced a good (value 0) or bad trip (value 1) by calculating a random number from 0 to 100 then comparing to the bad trip likelihood percentage (also a random number from 70 to 100). For instance, assume the model determines 75% of all travelers will experience a bad trip and then calculates a 60 as the random number used to determine the value for the Last Experience property. In this scenario, the consumer will have experienced a good trip with the last airline and thus, the value for Last Experience will be 0. Subsequently, the identical process occurs in order to set an experience value for the remaining two airlines. This holds true even if the consumer has not actually flown one or both of the airlines as the person may have predetermined opinions based on interaction with others in their personal network (i.e. friends, family, etc.). The visual editor and JAVA programming code can be viewed and downloaded from the publications list on the Repast website (http://repast.sourceforge.net/papers/papers_main.html). Now, on to consumer agent behavior.

4.3.4.2 Consumer agent behavior

Once consumers (and other agent types: airlines, environmental factors) receive the property assignments discussed in the previous section, the model simulation can commence. At Time 1 and each subsequent ‘tick’ representing the next week, the consumer ‘decides’ whether or not to travel based on the probabilities assigned to each consumer's Frequency of Travel property. Since new travelers have no previous flight experience they follow the same procedure for the assignment of Last Airline and Last Experience that existing travelers (i.e. they have flown before) encountered at Time 0; this occurs only when a new traveler chooses to travel for the first time. Existing travelers, after deciding to fly, the model reads whether Last Experience was good or bad. If good, then the traveler flies with the same airline and the Last Experience is updated for the current trip based on a random number compared against the bad trip likelihood percentage. On the other hand, if the Last Experience was bad, the model first identifies the SOM property value then continues on one of three distinct paths depending upon that value and will now be discussed.

We divided consumers into three groups based on the SOM: (1) 7, 8, 9 (very frequent travelers), (2) 4, 5, 6 (fly fairly often), and (3) 1, 2, 3 (fly less often). Consumers who fly very frequently typically are most likely to be enrolled in frequent flyer programs and have a stronger commitment to that specific airline; thus, they are not likely to switch airlines. The second group flies, on average, 1.3–2 times per month. Therefore, they too are very likely to be enrolled in frequent flyer programs and have a strong commitment to that specific airline but may be persuaded to switch airlines if the last trip was bad and/or they are exposed to airline promotional efforts (more detail provided in discussion of airline agents). For the final group, the model first looks at whether or not the Last Airline for the consumer advertised high during this week. If so, there is a greater likelihood that the consumer will have been exposed and persuaded to stay with the airline. If not, then the model examines the Last Experience for the other two airlines. If the consumer experienced positive trips for both other airlines, then the model randomly assigns one of the two as the airline the consumer now chooses to fly. If both past experiences on the other two airlines were not good, then the model will check to see if one was and the consumer will choose to fly that airline if true. If the consumer experienced bad trips for all three airlines, then the model will randomly choose to stay with the current airline or switch to one of the other two. The following discussion details airline agent properties and behavior.

4.3.4.3 Airline agents

The Airport Council International ranked DIA as the fifth busiest airport in the United States and 10th in the world serving 47 million passengers annually through 29 airline carriers, as obtained from the 2006 report provided by the Denver International Business Center (City and County of Denver, Colorado Municipal Airport System, 2006). United dominates the regional market with a 56.4% share of 2006 passengers and Frontier, as a distant second, services 20.7%. Twenty-seven airlines attract the remaining 22.9% with no single carrier serving more than 4.1%. In this simulation, the airline agents consist of United, Frontier, and Others.

Due to the dependence on the DIA market as the sole hub and intense competition at that airport (and others) with United and other carriers, Frontier cannot raise prices to any significant degree to increase profit levels or offset unexpected and/or rising costs. Frontier management state in the 2006 annual report, ‘Business and leisure travelers continue to reevaluate their travel budgets and remain highly price sensitive’ (Frontier Airlines Holdings, 2006). For the 4-year period 2004–2007, the average fare ranged from a low of $102.31 in 2005 to a high of $103.54 in 2004, only a maximum swing of 1.2% over 4 years. Therefore, Frontier and other airline agents must entice consumers primarily through advertising efforts. The following excerpt from the 2006 annual report emphasizes the importance Frontier management places on advertising and brand awareness:

‘Our sales efforts target value conscious leisure and business travelers. Value conscious customers are price-sensitive; however, we believe their travel decisions are also balanced with other aspects of our product offering such as our frequent flyer program, non-stop service, advanced seat assignments, service level and live television entertainment. In the leisure market, we offer discounted fares marketed through the Internet, newspaper, radio and television advertising along with special promotions and travel packages. In May 2003, we launched a new brand strategy and advertising campaign designed to identify Frontier as “A Whole Different Animal” and to set us apart from our competition. The campaign includes television, print and radio components that began running in the Denver market and have since expanded to additional markets along our routes. We have gathered extensive customer and employee feedback that has allowed us to identify elements of service that are important to our customers who have the potential to fly with us more often’. (Frontier Airlines Holdings, 2006)

In addition to the new branding campaign, Frontier also engaged in various sponsorship agreements including, but not limited to: the Colorado Avalanche hockey team, the Denver Nuggets basketball team, Colorado Rockies baseball team, etc. Advertising and promotions constituted 9% of total operating expenses in 2006. Clearly, advertising plays a large role in the success or failure of Frontier Airlines.

United Airlines entered bankruptcy proceedings on December 9, 2002 and eventually emerged on February 1, 2006. As expected, companies operating under the court's oversight must focus on managing costs. As a component of overall 2006 operating costs, advertising and promotion only comprised 6% (United Air Lines, 2006). The report contained no specific income statement line item for these costs or any discussion of related expenses. Based on this lack of information, we assume United focuses their primary efforts on other areas and relies on their size, extensive flight availability, networks within the industry (e.g. partnership agreements with other airlines and travel agencies), and brand name to attract and retain customers. Therefore, the model places less emphasis on advertising for United.

As for the Other airlines category, the model contains no specific agent per se with. This category of airlines places a modicum of value on advertising levels in the consumer purchasing process and remains static. Only the Frontier and United agents evaluate environmental conditions (discussed later) and market share in order to adjust advertising levels.

The Frontier and United agents determine overall advertising levels initially at Time 0 then re-evaluate every 2 weeks (before the start of consumer purchases). Both agents first identify the environmental agent values: Fuel Cost (high/low), Regulation (high/low), and Credit Availability (high/low). As these conditions affect the availability to fund advertising efforts, high Fuel Cost, high Regulation, and low Credit Availability represents the worst case scenario. The agents next determine the advertising level to set based on the values of the environmental agents. Frontier relies heavily on advertising so the model allows them to set the property Advertising to high if two out of the three values are favorable. United, on the other hand, requires all three values to be favorable in order to set Advertising to high.

Starting at beginning of Week 12 of the simulation (i.e. end of the first quarter) and reoccurring every 12 weeks thereafter, the Frontier and United agents calculate the current market share to date in the simulation and compare to a predetermined minimum desired level (Frontier = 16%, United = 21%). We arbitrarily selected these amounts based on historic market share percentages. Should the current market share fall below the threshold, the airline agent re-evaluates the advertising level based on the environmental agent values at that time (same procedure as at Time 0). No action happens if the market share remains above threshold. The environmental factors affecting the airline advertising decisions will now be examined.

4.3.4.4 Environmental factors

Several critical economic and environmental factors severely impact the ongoing operations and financial stability of Frontier as well as all carriers in the airline industry and therefore, have been included in the model. First, fuel costs represent the single largest individual operating expense item for Frontier (29.0% in 2007 and 27.9% in 2006) (Frontier Airlines Holdings, 2006, 2007). Over the 4-year period 2004–2007, fuel costs rose 103.8% and the trend is expected to continue with little ability to pass cost on to consumers. Second, subjection to heavy federal regulation has resulted in operating cost increases in the past and may do so in the future. For example, President Bush signed the Stabilization Act in to law in 2001 that federalizes most civil aviation security and requires the implementation of certain security measures by airlines and airports such as screening all passenger baggage by the Transportation Security Administration (TSA). Funding for these security activities comes from a $2.50 per enplanement ticket tax and the TSA can impose additional fees on air carriers as the agency deems necessary (Frontier Airlines Holdings, 2006). In the ‘Risk Factors’ section of their respective 2006 annual reports, both airlines acknowledge extensive government regulation could increase operating costs and affect the ability to conduct business. To the extent costs of measures such as the Stabilization Act cannot be passed on to consumers, airlines face significant financial challenges. Finally, availability of credit in the broader economic market or lack thereof poses a great risk to airlines in several respects. When credit is scarce and the economy suffers, consumers tend to tighten their purse strings and travel less. Creditors also become more stringent and wary of extending additional credit. As noted in their 2006 annual reports, both Frontier and United suffer from very little available credit and must rely on existing cash and generation of operating cash flows to support operating activities. Another potential consequence of tighter credit markets, commonly referred to as the ‘credit-card holdback’, affects the airline industry specifically. Airlines contract with one or more (usually no more than three) credit card companies to process their customers’ credit purchases. Typically, credit card processors immediately pass along the majority of proceeds to airlines with the remainder held back until the passenger completes the flight. However, processors have the right at any time to raise the amount held until completion of service should they feel at risk of an airline discontinuing service thus transferring responsibility to them for the money (Atlanta Journal-Constitution, 2008). This sort of event could adversely affect the cash flow position of an airline, particularly those dependent on operating cash to survive.

Accordingly, the simulation model contains external agents that represent fuel costs, federal regulation, and credit availability. In actuality, the agents are proto-agents rather than full-fledge agents. The behavior of proto-agents affect other agents but do not act and react to changes to or made by other agents. The environmental agents in this study randomly start with either a high or low value then have the potential to adjust (randomly) on a predetermined schedule: Fuel Cost has a 60% chance of being set to high at Time 0 and every 4 weeks, Regulation 60% chance at Time 0 and every 12 weeks, and Credit Availability 50% at Time 0 and every 4 weeks.

4.3.4.5 Design specifications and model functionality

Using the design principles derived from the CAIO theory presented earlier, we developed an ABM of the Frontier Airlines market as an illustration of the type of continuous auditing application an auditor can realistically develop as a tool in the analysis of a client's ongoing financial viability. We strived to maintain simplicity in the model by focusing on the factors that provide the greatest impact. The model contains agents representing consumers, airlines, and environmental factors that act and react to the behaviors of each other in a simulated economy.

Midgley et al. (Reference Midgley, Marks and Kunchamwar2007) recommend (1) publishing detailed specifications and programming code, (2) enlisting the assistance of programming experts to inspect and correct code implementation of the specifications, (3) subjecting the model to destructive testing, and (4) empirically validating the model against real data. In this vein, Table 3 proposes a set of design specifications for the ABM and Table 5 compares the functionality built into the model to these specifications. As previously noted, we enlisted the assistance of an ABM programming expert to evaluate the correctness of the coding as well as the implementation of design specifications and intended functionality. During initial model testing both we and the external expert executed the model numerous times to assess the robustness of the model to extreme parameter values. The next section presents the results of the model simulation and subsequent financial statement analysis of projected 2007 operating results for Frontier Airlines to the actual 2007 results.

Table 5 Model functionality

4.4 Simulation results and financial statement analysis

4.4.2 Simulation results

Across the three consumer levels (i.e. 1000, 10 000, and 100 000) with 30 runs each, Frontier's anticipated 2007 market share in the unconstrained model averaged 17.64% (range 15.74–19.33%) with United at 24.99% and Other at 57.37%. Consumers switched airlines 39.69% of the time. Frontier gained 29.38% of these ‘switchers’ and lost 28.95%, a slight net gain. Of the total Frontier trips, consumers switching to Frontier comprised 66.10%, repeat passengers 33.14% (i.e. non-switchers), and new flyers 0.74%.

Under the worst case scenario with both Fuel Cost and Regulation set at high and Credit Availability set at low, Frontier earned 16.03% (range 14.57–17.51%) of the market with United at 24.84% and Other at 59.13%. Consumers switched airlines 41.22% of the time. Frontier gained 27.36% of these ‘switchers’ and lost 27.76%, a slight net loss. Of the total Frontier trips, consumers switching to Frontier comprised 70.35%, repeat passengers 28.81% (i.e. non-switchers), and new flyers 0.84%. Further analysis shows Frontier attracted 2.02% less switchers and retained 20.93% fewer repeat passengers in the ‘bad’ environment. To determine if the difference in Frontier's market share is different between the unconstrained model and the bad model, we performed an independent-samples t-test comparison of mean values for the two sets (three batches each with 30 records for a total n = 90 per model). The test revealed the two sample means are statistically different (t = 14.782, p < 0.01) indicating the inability to advertise due to poor environmental factors severely affected Frontier's ability to attract and retain consumers.

Under the best case scenario with both Fuel Cost and Regulation set at low and Credit Availability set at high, Frontier earned 21.25% (range 20.35–22.63%) of the market with United at 20.91% and Other at 57.84%. Consumers switched airlines 39.74% of the time. Frontier gained 32.43% of these ‘switchers’ and lost 30.81%, a weighty net gain. Of the total Frontier trips, consumers switching to Frontier comprised 60.66%, repeat passengers 38.68% (i.e. non-switchers), and new flyers 0.66%. Further analysis shows Frontier attracted 3.06% more switchers and retained 40.88% more repeat passengers in the ‘good’ environment. To determine if the difference in Frontier's market share is different between the unconstrained model and the good model, we performed an independent-samples t-test comparison of mean values for the two sets (three batches each with 30 records for a total n = 90 per model). The test revealed the two sample means are statistically different (t = −35.388, p < 0.01) indicating the ability to advertise due to better environmental factors positively affected Frontier's ability to attract and retain consumers.

The Bureau of Transportation Statistics reported that Frontier earned 17.46% of the market share for the routes the company serviced during 2007 with United at 32.20% and Other at 50.34% (Bureau of Transportation Statistics, 2008). After three batches and 90 runs, the model estimated only 0.18% higher than Frontier's actual but underestimated United by 7.21% and overestimated Other by 7.03%. United's activity on these routes fluctuates significantly rising from a 23% market share in 2006 to 32% in 2007 then falling again to 25% in 2008 as the company acquires/sells gates and adds/subtracts flights. Given the focus of the model is to estimate Frontier's status in the marketplace, these results seem reasonable.

Table 6 highlights the results of the three models. Using the estimated market share from the unconstrained model, we will now create a prospective income statement to estimate operating income and operating cash flow in order to conduct a mock going concern analysis.

Table 6 Comparison of model simulation results

As discussed previously, some auditors use statistical models (e.g. Altman Z-score) while others perform analytical procedures of key financial numbers to assess the ongoing viability of audit clients per SAS 59 requirements (i.e. the going concern opinion). Inherent problems arise with the structure and use of the more common statistical models hence the application of the alternative method that allows greater auditor judgment and reliance on expertise. Analytical procedures are comparisons of unaudited financial data with expected results (Glover et al., Reference Glover, Jiambalvo and Kennedy2000). These procedures occur primarily at the beginning of an audit to plan the nature, timing, and extent of testing (American Institute of Public Accountants, 1998). Significant fluctuations between client data and auditor expectations signal increased risk of material error for a particular accounting area (e.g. valuation of accounts receivable and estimated bad debts). Auditors perform essentially the same process at the end of the audit to develop expectations of the financial statements for the upcoming year, also known as prospective financial statement forecasts. The prospective information (most notably the estimated operating income and operating cash flow) form the basis for the auditor's going concern opinion. Drawing on results from the ABM developed in this study and historical trend analyses, we briefly discuss the comparison of prospective statements we prepared for 2007 to Frontier's audited financial results.

The process to create prospective financial statements consists of first identifying the key account balances and financial statement line items that comprise the majority of each statement. Once determined, the auditor develops expectations of each item then assembles them together in the appropriate financial statement format. Expectations result from analysis of historical financial data, anticipated actions by management, industry factors that may affect the major financial statement line items. For this exercise, we chose to analyze key income statement line items to project Frontier's 2007 operating income and operating cash flow. Revenues represent the most important and most difficult component of the income statement to anticipate. So many interrelated factors come in to play that potentially could affect the business a company earns that the human mind has a difficult time assimilating the interactions. Enter the computer simulation.

The Frontier ABM produces the key driver of revenue for the airline as consumer passenger volume represents 97% of Frontier's 2006 revenue. Therefore, estimation of two components is needed: (1) number of passengers and (2) the revenue generated per passenger. To develop the estimate of 2007 passenger revenue, we first calculated a total market that Frontier competed in by utilizing the data reported by BTS of the total number of passengers traveling the routes Frontier serviced in 2006, an estimated 50.75 million travelers. After estimating a total market we determined a proportion to assign to Frontier. The unconstrained model of the ABM generated a 17.64% Frontier market share. Multiplying the simulated market share percentage times the projected total market results in an estimated 8.95 million passengers for Frontier. However, a discrepancy exists between the amount of passengers BTS reports for Frontier in 2006 and the amount reported in the financial statements. Of the 40.78 million passengers traveling Frontier routes in 2006, Frontier earned the business of 7.47 million (18.32%) according to BTS. The 2006 financial statements reported 8.68 million revenue passengers carried. The discrepancy lies in the various agreements with other airlines such as code-sharing and outsourcing of certain routes. BTS reports these passengers under the airline actually operating the flight, not the company whose financial statements include these passengers. To reflect the difference, we adjusted the 8.95 million passengers estimated using BTS figures by +16% (the amount BTS differed from the financial statements in 2006) resulting in a projection of 10.38 million Frontier passengers. To estimate the second component necessary to project passenger revenue, we calculated the revenue per passenger for the years 2003–2006. Using the average change from year-to-year for the period (−0.35%), we calculated $111.58 of revenue to be generated by each of the 10.38 million passengers. Projected passenger revenue for 2007 is $1.16 billion. For the other key items in the model we used more linear analysis based on historical relationships as those components, particularly costs and expenses, typically have direct relationships to the amount of revenue earned. The first numerical column in Appendix C presents the projected operating income statement and operating cash flow.

So, how well did the prospective financial statements developed using the ABM simulation compare to Frontier's actual, audited financial data for 2007? As previously noted, the ABM derived a 17.64% market share for Frontier whereas the actual was 17.46%. Frontier reported 10.04 million passengers carried (3.33% less than prospective) and $1.17 billion revenue (2.19% less). However, the revenue generated per passenger of $112.71 exceeded that in the prospective financial statements by 1.01%. Furthermore, actual operating expenses were $1.18 billion (2.27% less) providing a higher actual operating income (a net loss of $9.83 million). Frontier appears to have further streamlined expenses to become even more efficient. Frontier generated positive operating cash flow of $23.23 million which is 5.14% less than prospective and a higher percentage relative to operating revenues (−236.19%) meaning the company squeezed out more cash per revenue dollar than previous years. Based on actual operating income and the 3-year average factor of −205.15% included in the prospective financial statements, the expectation would be the generation of $20.18 million of free cash. On the key figures of operating income and operating cash flow, Frontier slightly outperformed the prospective financial statements. Overall, the ABM helped produce prospective financial statements fairly close to actual 2007 operations. Appendix C provides a comparison of prospective financial information to actuals.

This section presented an instantiation of the CAIO theory through an agent-based simulation model to assist with the auditor's going concern opinion for Frontier Airlines. The design of the model adhered to prescribed guidelines and best practices for design science, simulation, and agent-based modeling. The design specifications presented were based on CAIO design principles and acted as the guide for developing the types of agents, their behavior, and interaction with other agents. Multiple executions of the simulation model produced an expected market share for Frontier Airlines used to develop prospective financial information for 2007 necessary to issue a going concern opinion for the viability of Frontier during the next year. The ABM built from the underlying theories of complexity science and SIS helped develop prospective financial information that estimated actual results fairly well and showed Frontier consistently produces positive operating cash in spite of continued net operating losses. The final section of this study summarizes the study as a whole and discusses the implications of continuous auditing in a complex business environment.