Sunk Costs

At our June 23, 2021 webinar on decision tree analysis, we discussed that after calculating the expected value (EV) of a lawsuit using a decision tree in connection with settlement negotiations or a mediation, plaintiffs should subtract the anticipated future costs of continuing to litigate (e.g., attorney and expert fees) from the EV, while defendants should add anticipated future costs to the EV.

For example, assume that during mediation of a commercial litigation, the mediator reaches a consensus with the parties on the structure of a decision tree showing the remaining material uncertainties to be resolved at trial with respect to liability and damages. After hearing arguments from both sides concerning the probabilities of how these uncertainties will resolve, the mediator concludes that the EV of the lawsuit is approximately $2M if the case were to go to trial (which the parties agree to accept for purposes of further negotiation).

The mediator further learns through caucus that the plaintiff anticipates it would spend another $200K on attorney and expert fees through trial, while the defendant anticipates it would spend another $350K in fees. The mediator should then subtract $200K from the $2M to generate an adjusted EV of $1.8M for the plaintiff, and add $350K to the $2M to generate an adjusted EV of $2.35M for the defendant.

By adjusting the EV for future costs that are avoidable if the case settles — i.e., costs that neither party would have to pay if they settled — the mediator creates a bargaining zone of $550K within which the parties should settle (since the plaintiff should be willing to settle for any amount over $1.8M, while the defendant should be willing to settle for any amount below $2.35M).  That is, any number between $1.8M and $2.35M represents a sure outcome that is worth more than the gamble that either party would take by going to trial, and thus unless either party elects to act in a risky manner (i.e., choose a gamble that is worth less than a sure outcome), the case should settle (perhaps via a mediator’s proposal at the midpoint between $1.8M and $2.35M, or $2.075M).

Some webinar attendees had asked why only future avoidable costs, and not also past costs (a/k/a “sunk” costs), are relevant to calculating the EV of a lawsuit using a decision tree. The simple answer is that “sunk” costs are, by definition, not recoverable regardless of whether the parties decide to settle or continue litigating, and thus as a matter of simple mathematics have zero impact on the decision about whether to settle or continue litigating. In contrast, future costs can be avoided if a party choses to settle, and thus have an impact on the value of settling (costs not paid) versus continuing to litigate (costs paid). Let’s unpack that.

Consider the following hypothetical. A plaintiff spends $600K on attorney’s fees (which it cannot recover since there is no fee shifting), and then gets an offer to settle the case for $400K prior to trial. The plaintiff wants to reject the offer on the ground that it has already spent $600K on fees and won’t settle for less than $600K so it can at least break even.

Further assume, however, that a rigorous decision tree analysis of the value of the case indicates that its adjusted EV for the plaintiff is only $300K (e.g., the EV of the probabilities of how all the material uncertainties may resolve through trial is $325K, minus anticipated future costs of $25K).

So $400K is actually a good deal given the current value of the case. If the plaintiff accepts, its loss on the case will only be $200K ($600K fees -$400K sure recovery). But if it rejects, its expected loss on the case is $300K ($600K fees – $300K EV of gamble) — $100K greater than the loss from settling. In effect, because the past fees cannot be recovered, they cancel out on each side of the equation, and the plaintiff is left with $400K settle > $300K litigate. So it’s economically rational to ignore sunk costs, accept the offer, cut losses, and stop throwing good money after bad (or to quote other maxims — “let bygones be bygones;” “don’t cry over spilt milk,” and “it’s water under the bridge.”).

Of course, we don’t know what the outcome of continuing to litigate would be. The plaintiff could be surprised and recover far more than $400K even after accounting for future costs. But the plaintiff could also recover $0. That’s the whole point of a decision tree analysis — decision making under conditions of uncertainty that takes into account the probabilities of all of the potential outcomes of taking the gamble, and calculates the average of all those possible outcomes (in this case, $300K after adjusting for costs). That is to say, neither lawyers nor their clients are prophets who can predict the future; the best we can do is undertake a disciplined risk analysis that weighs the probabilities of all the possible outcomes.

As a result, if the plaintiff rejects the $400K offer and continues litigating, it’s acting in a “risky” manner — i.e., rejecting a sure outcome ($400K) worth more than the gamble ($300K) just because it’s annoyed at having already spent $600K on fees on what turned out to be a bad case. That’s an emotional response, not a rational response; a psychological trap referred to as the “sunk cost” fallacy that causes bad decision making.

Decision tree analysis is a risk-neutral, objective method designed to remove emotion like that from the analysis and facilitate good decision making by showing a party when it’s economically rational to settle at a certain point in time (of course, we discussed at the webinar that certain (typically “wealthy”) parties may decide to act in a “risky” manner and pursue gambles worth less than sure outcomes for completely legitimate reasons, but doing so solely because a party is annoyed at all the money it has already spent on legal fees is not a legitimate reason).

In closing, to accentuate the point, let’s consider a common “everyday” hypothetical. You pay $100 for movie tickets, decide the movie is horrible, but force yourself (and your family) to watch until the end because you already paid for the tickets, and there are no refunds. But that’s irrational. Instead, the logical choice would be to leave early and engage in a family activity that is more enjoyable than suffering through a terrible movie. The idea is to cut your losses once it’s apparent the value isn’t what you expected.

Same thing with sunk costs. A litigant involved in a case where settling is now clearly worth more than the gamble of continuing to litigate should logically choose to cut losses rather than increasing them (absent other legitimate considerations that logically support “risky” behavior).

We hope the above explanation is helpful; we encourage comments below.

For those who missed the June 23 webinar on decision tree analysis, click here to register to watch a recorded replay (PDF of slides available upon request).

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