The unexpected value of litigation: a real options perspective.

AuthorGrundfest, Joseph A.

INTRODUCTION I. REFRAMING THE ECONOMIC DESCRIPTION OF LITIGATION A. Real Options, Investments, and Litigation B. Summary of Our Model C. Analytic Implications of a Real Options Approach to Litigation D. Normative Implications of a Real Options Approach to Litigation II. A REAL OPTIONS MODEL OF LITIGATION THAT INCORPORATES BARGAINING A. An Example of Real Options Analysis Applied to a Research and Development Project B. The Formal Definition of Our Model C. Related Literature III. INTUITION AND EXAMPLES A. Positive Expected Value Litigation B. An Online Calculator and Graphing Tool C. Negative Expected Value Litigation 1. Recapitulating Bebchuk's example: The pure divisibility value of NEV litigation 2. An example of a learning option that reduces settlement value 3. An example of a real option with a dead zone 4. NEV litigation with a point discontinuity IV. ANALYTIC RESULTS A. Credibility Conditions B. Option Settlement Value, Divisibility Value, and Expected Value C. Comparative Statics V. DISCUSSION AND EXTENSIONS A. Analytic Implications B. Normative Implications C. Extensions APPENDIX: PROPOSITIONS AND PROOFS INTRODUCTION

Lawsuits and investment projects have much in common. (1) Indeed, every lawsuit forces litigants to make current expenditures in order to influence future outcomes. That is the essence of investment. Lawsuits bear a particularly strong resemblance to commercial research and development projects because both involve the discovery of new information in an environment in which managers can adjust their strategies in response to those disclosures. We therefore suggest that, by modeling lawsuits as investments in competitive research and development projects, it is possible to generate valuable insights about the operation of the litigation process that are difficult or impossible to derive through the application of more traditional modeling techniques.

Commercial research and development projects involve uncertainty about whether they can be completed on budget and on schedule and about the profits, if any, that will be generated if the project succeeds. Researchers modify their strategies while they conduct their projects, and they increase, decrease, accelerate, defer, or terminate expenditures in response to new information. Because firms often race to introduce products that target similar markets, complex competitive interactions can arise as each firm's strategies and expenditures influence its competitor's strategies and expenditures. The ability to respond to new information in a strategic manner is therefore central to the research and development process. In addition, new information may indicate that the firm should terminate its project early, which incurs shutdown costs and thereby benefits competitors who continue with their own research and development efforts.

Lawsuits can be described in essentially identical terms. They involve uncertainty about the facts underlying the plaintiff's claim and about the interpretation of the law to be applied to those facts. There is also uncertainty about the damages, if any, that will be awarded if the plaintiff's claim prevails. Litigants modify their strategies during the lawsuit and increase, decrease, accelerate, defer, or terminate litigation expenditures in response to new information. Defendants may make settlement payments to plaintiffs in order to terminate a lawsuit. Thus, just as a shutdown decision imposes costs on the exiting firm and generates benefits for its competitors, a settlement imposes costs on the defendant and benefits the plaintiff. (2)

Litigation also raises complex competitive interactions because each litigant's strategies and expenditures can influence an opponent's strategies and expenditures. The ability to respond to new information in a strategic manner is evidently central to the litigation process. Put another way, litigants and their lawyers are not "potted plants" who adopt a strategy at a lawsuit's inception and then watch passively as new information spills out and opponents alter their tactics. (3)

From an investment perspective, lawsuits are therefore largely indistinguishable from research and development projects, and it follows that the tools applied to the economic analysis of research and development projects might also be profitably applied to the economic analysis of litigation. The literature, however, reveals a rather remarkable gap between the two fields of study. Over the last two decades or so, real options analysis has emerged as the state-of-the-art technique for the economic analysis of research and development and has generated insights that are difficult or impossible to obtain through the application of more traditional discounted cash flow or net present value techniques. (4) Real options analysis has, however, had very little influence on the economic analysis of litigation. (5)

This Article seeks to narrow that gap. We present a real options model of litigation in which parties bargain over the allocation of litigation expenditures that are avoided when a case settles early. Ours is not the first real options model of litigation, (6) but it is the first to incorporate bargaining behavior and the first to generate closed form solutions that define a lawsuit's settlement value with precision. (7) Our model's bargaining component also differentiates it from standard real options models that typically involve a single decisionmaker seeking to optimize value over exogenously determined states of nature. (8) Our model is not, however, a "complete" model of litigation because it assumes that the parties' litigation expenditures are exogenously determined. (9)

Thus, at one level, this Article constitutes a straightforward intellectual arbitrage in which we transplant insights that are well understood by students of real options theory from the world of investment analysis to the world of litigation analysis where those insights are not as broadly appreciated. This arbitrage is of more than narrow, technical interest because it generates novel insights that are difficult or impossible to derive through more traditional modes of analysis. Moreover, these insights have significant analytic and normative implications for the economic analysis of litigation. The rather simple model presented in this Article also suggests that more complex applications of real options theory offer a particularly promising paradigm for further study of litigation behavior.

In Part I, we expand on the suggestion that litigation can be reframed as a real option, summarize our model, and outline the analytic and normative implications of our findings. Part II offers a simple example of real options analysis as applied to a research and development project, formally defines our model, and describes our model in the context of prior literature. Part III provides several intuitions regarding the model's equilibrium concept and offers examples of how to generate equilibrium solutions. This Part also introduces an online calculator and graphics tool that allows readers to solve for our model's equilibrium real option settlement values for any set of parameters input. Part IV summarizes a series of formal propositions about the model's equilibrium properties. (Proofs for these propositions are presented in the Appendix.) Part V expands on our model's analytic and normative implications and describes potential extensions.

  1. REFRAMING THE ECONOMIC DESCRIPTION OF LITIGATION

    1. Real Options, Investments, and Litigation

      The most common economic model applied to both investment and litigation decisions involves expected value analysis based upon a discount factor that reflects the risk inherent in the project or lawsuit. (10) In these models, an investment project's expected value is described as the probability of its success multiplied by the likely payoff in the event of success. The effects of risk or uncertainty (11) are reflected through changes in the relevant discount rate, or cost of capital, with riskier projects bearing a higher discount rate or capital cost and therefore having a lower discounted expected value. (12) These models are commonly described as discounted cash flow (DCF) or net present value (NPV) models. (13) When NPV analysis is applied to litigation, the lawsuit's expected value is typically described as the probability that the plaintiff will prevail multiplied by the likely award. (14) The effects of risk or uncertainty are again expressed through changes in the relevant discount rate, with riskier lawsuits bearing a higher discount rate and therefore having a lower expected value. (15)

      In the investment world, this expected value analysis has recently been supplemented by a "real options" approach that has "had a huge impact on academic research." (16) The interest in real options theory arises, in part, because "traditional discounted cash flow (DCF) approaches to the appraisal of capital-investment projects, such as the standard net-present-value (NPV) rule, cannot properly capture management's flexibility to adapt ... to unexpected market developments." (17) Real options analysis solves this problem by integrating the investment manager's ability to adapt to new information into the model itself. While the traditional DCF and NPV approaches assume a fixed commitment to full investment at the outset, real option theory models the investment process as a series of decision points at which investors have the option of adjusting their investments in response to new information. (18) This perspective supports the insight that investment "[p]rojects that can easily be modified ... are more valuable than those that do not provide such flexibility. The more uncertain the outlook, the more valuable this flexibility becomes." (19)

      Because of these advantages, the real options approach has "influenced research in virtually every business discipline[,] ... promoting better understanding of...

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