# Cost of Capital Profiling

## Explore

### Introduction

Litigant capital costs can have a profound, complex and sometimes counterintuitive influence on rational settlement bargaining strategies. These effects go beyond the mere discounting of the expected value of trial to influence the optimal settlement offer, expected wealth from the bargaining process and the probability of settlement. Quantitative modelling of litigation settlement bargaining can illuminate this complex issue and give litigants a bargaining advantage.

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Litigants can intuitively imagine how the capital costs of parties to a dispute can affect the economics of the settlement-versus-trial decision and in particular the level of offers each litigant might consider rational or attractive. If trial is expected to occur three or four years hence, each litigant will have an intuitive sense for the diminished value of the future potential cash flows in present value terms, and it is relatively straightforward to derive an appropriately discounted expected value of trial. But this simple intuition very likely fails to capture the more complex effect of capital cost differentials on claim valuation and settlement bargaining optimisation.

### Complex Relationship

Capital costs in general serve to discount the value of future litigation cash flows and accordingly they serve to lower the overall level at which a settlement bargain can be achieved. This comes as no surprise. However, the impact of capital costs in the context of settlement bargaining is more complex than this simple statement suggests. In the bargaining context, the discounting effect only acts upon future cash flows to the extent that there is a failure to settle. Therefore the influence of discounting itself turns also on how attractive a settlement offer is and how likely it is that a settlement agreement is reached. This has several complex consequences which are not obvious without quantitative modelling.

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For example as a defendant increases his settlement offer, trial obviously becomes less probable. But as trial becomes less probable, the role of discounting of future cash flows becomes less significant which in turn will have an impact on the merits of the offer. It is not difficult to see how bargaining intuition (or a heuristic approach to “pricing” settlement) would struggle to reflect this real economic complexity in the formulation an optimal settlement strategy.

An example will help to illustrate this complexity.

### Counter-Intuition

Our Settlement Dynamics Chart application below illustrates the importance of the relative differential of capital cost on settlement bargaining optimization. Here we examine a typical $10 million lawsuit with fairly typical cost structure and about four years before a trial date. The chart shows the result of a game theoretic analysis which examines the relationship between the plaintiff’s expected wealth and her settlement demand.

### Legal Dynamics Chart

#### Cost of funds differential

Cost of funds differential: -27 %

The chart illustrates the significant effect that the cost of capital differential between the defendant and the plaintiff can have on settlement optimization. Moving the chart control button (just below the chart) from left to right alters the cost of capital differential between the defendant and plaintiff from -30% to +30%.

Notice first how sensitive the wealth function is to this capital cost differential. This analysis first underscores how important it is to be alert to the influence of both litigants’ costs of capital on the bargaining dynamics. You will also notice how counter-intuitive the effect of this variable can be as the defendant’s cost of capital begins to significantly exceed that of the plaintiff. For example, as the defendant’s cost of capital goes from 15% over to 21% over that of the plaintiff, you will notice an inversion in the plaintiff’s optimal settlement offer (an example of a tipping point). Essentially, here, the defendant has so severely discounted the future trial cash flows as to make settlement now generally unattractive to the plaintiff. With a significantly lower cost of capital the plaintiff’s only rational settlement offer is now so high (in the receiving defendant’s reference frame) as to virtually guarantee a bargaining impasse.

Here we can see how capital cost differentials can have a polarising effect on settlement bargaining and in the extreme can make trial a virtual certainty.

### Capital Cost Taxonomy

Given this complexity, we can think of cost of capital effects as having a taxonomy: the Absolute Effect and the Relative Effect.

**Absolute Effect:**The combined overall impact of capital costs is relatively simple to understand and reflects our common intuition of discounted cash flow. Equal and parallel shifts in the discount rates of both litigants will have a predictable effect on settlement: higher rates will depress expected settlement values and lower rates will increase settlement values. We will call this the “Absolute Capital Cost Effect”.

**Relative Effect:**But in addition to the absolute level of discount rates, there is a more important and subtle relationship in the relative difference between the defendant and plaintiff capital costs. It is here that we can find the most complex and sometimes counterintuitive effects of discount rates.

In certain cases, shifts in the relative cost of capital differential between litigants can:

- Alter the overall location of the settlement bargaining space
- Narrow or expand the rational range of potential settlements
- Non-linearly alter the expected wealth from bargaining
- Have an inverse effect on the optimal settlement offer

### Capital Cost Profiling

In the example presented above, our analysis examines an exaggerated range of capital cost differentials to illustrate a point. However, irrespective of the actual assumptions, the point is that litigants would be well advised to understand the quantitative influence of capital costs on their own dispute and settlement bargaining process.

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The results of these analyses suggests that certain litigant combinations can be expected to generate different settlement bargaining behaviours and outcomes. For example:

- Disputes involving high growth, high cost of capital corporate defendants versus wealthy low cost of capital plaintiffs would be particularly prone to lengthy disputes, reluctant settlement agreements and more frequent bargaining impasses.
- Whereas disputes involving slow growth, low cost of capital institutional defendants versus high cost of capital plaintiffs would be more apt to see shorter disputes, rapid settlements and less frequent recourse to adjudication.

Given the complex sensitivity of settlement bargaining to capital costs, we can see how “capital cost profiling” of disputes could help to add insight into potential obstacles to settlement. Forewarned being forearmed, we believe it would be good routine practice for mediators, legal counsel and institutional litigants to examine cost of capital effects.

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There are many other interesting insights that can be gained from the correct analysis of capital costs in the context of settlement bargaining. Suffice it to say that litigants should accurately assess and measure their impact on settlement bargaining before approaching negotiations.

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Correctly analyzing capital cost effects can help litigants formulate optimal settlement offers, avoid costly bargaining errors and provide an early warning of a potential bargaining impasse. Armed with the correct analytics, better decisions become possible.