Should the Discount Rate for Contingent/Unliquidated Liabilities be Low, Medium, or High?

Valuing Liabilities Differs from Valuing Assets

Valuing contingent/unliquidated liabilities raises some interesting questions. Do contingent/unliquidated liabilities have liability-specific risk? If yes, does liability-specific risk result in lower or higher obligations? Why do contingent/unliquidated liabilities related to lawsuits tend to settle as opposed to go through verdict and appeals? This article addresses these questions.

Valuing contingent/unliquidated liabilities raises some interesting questions. Do contingent/unliquidated liabilities have liability-specific risk? If yes, does liability-specific risk result in lower or higher obligations? Why do contingent/unliquidated liabilities related to lawsuits tend to settle as opposed to go through verdict and appeals? This article addresses these questions.

Discount Rate for Assets

Determining the discount rate for assets is very simple in one important aspect: investors are risk averse. Holding everything else constant, investors will pay more for an asset with lesser risk and pay less for an asset with greater risk. Higher risk leads to a higher discount rate and lower value when holding everything else constant.

It is also possible to incorporate checks-and-balances. Practitioners can debate many discount rate-related issues. However, a market value-based analysis requires the valuation to take both a buyer’s and seller’s perspective into account.

Discount Rate for Debt Instruments

Determining the discount rate for debt instruments can be straightforward. The key drivers are (a) overall interest rates and (b) credit quality.

Change in Interest Rates

We will use an example to introduce this topic. Consider a previously issued bond that pays interest at 6 percent per year. Now assume the debtor’s credit quality remained the same and interest rates for a comparable bond issued today would pay interest at 8 percent per year.

The value of this bond decreased from both the borrower’s and lender’s perspective due to the change in interest rates. The increase in interest rates was good for the borrower (the value of the liability declined) and bad for the lender (the value of the asset declined). There is asset-liability symmetry because the decrease in asset value was exactly matched by the decrease in liability value.

Change in Credit Quality

We will use a revised version of the previous example. Assume the increase in interest rates from 6 percent to 8 percent was due to a change in the debtor’s credit quality instead of a change in overall interest rates.

Mathematically, the results are the same. The bond decreased in value from the borrower’s and lender’s perspective by the same amount as the previous example.

However, there is one important difference: it may be harder to incorporate the reduction in the value of the bond from the borrower’s perspective into the liability valuation. For example, solvency analyses for fraudulent transfer lawsuits typically do not allow reductions in the borrower’s creditworthiness to factor into the analysis. The reason is logical: reducing the value of a debtor’s obligation(s) due to a decline in the debtor’s creditworthiness can paradoxically cause a debtor’s insolvency to be the driving factor for a determination that the debtor is solvent.

What Makes the Discount Rate for Contingent/Unliquidated Liabilities Interesting?

The amount owed on a contingent or unliquidated liability is unknown on the valuation date. The variance in the potential obligation (perhaps from zero to a lot) differentiates contingent and unliquidated liabilities from debt instruments with known obligation amounts.

A contingent liability (e.g., a debt guaranty) is a liability that is only incurred if something specific happens in the future (e.g., the guaranteed debt is not repaid). An unliquidated liability (e.g., a lawsuit) is a liability whose incurrence is not contingent upon subsequent events, but the amount is unknown as of the valuation date.

Are Investors Risk Averse when Evaluating Liabilities?

Investors are clearly risk averse when evaluating assets. As previously mentioned, higher risk leads to a higher discount rate and a lower asset value when holding everything else constant.

But what about liabilities? Perhaps the answer is: it depends.

Incorporate Credit Risk

It may not be difficult to think of an example where investors would embrace liability-specific risk when a debtor’s credit risk can be factored into the equation. Consider a company with $20 million in assets that has only two liabilities. The first liability is a $10 million debt obligation (with no interest payments) due in five years. The second liability is a lawsuit with a 90% probability of owing nothing and a 10% probability of owing $100 million (inclusive of prejudgment interest) also expected to be due in five years. Both liabilities have $10 million of expected cash outflows due in five years.[1] If given a choice to eliminate one of these liabilities for free, the owner of this company may logically choose to eliminate the less risky debt obligation.

The choice may be easy because this company only has $20 million in assets and could never fulfill the $100 million judgement if that scenario came to be. As a practical matter, the expected cash outflow for the lawsuit is only $1 million[2] because this company cannot pay more than $20 million on the debt obligation and lawsuit claims. Thus, the marginal exposure associated with the lawsuit (which has a 10% probability of being incurred) is capped at $10 million. The owner of this company would have a logical basis to choose to eliminate the debt obligation because it has a much higher expected cash outflow ($10 million vs. $1 million) after taking the company’s credit risk into account.

No Credit Risk

To get around the debtor’s credit risk issue, we will assume this company has the wherewithal to pay any judgment. Now the investor is faced with two choices that each truly have an expected cash outflow of $10 million due in five years. What will the investor choose?

The answer depends on whether the investor is risk averse, risk seeking, or risk neutral when evaluating liabilities. A risk averse investor would eliminate the risky lawsuit. A risk seeking investor would eliminate the less risky debt obligation. A risk neutral investor is indifferent.

Notably, many valuations of contingent or unliquidated liabilities appear to assume investors are risk neutral when it comes to evaluating liability-specific risks. That is the implied assumption when obligations with liability-specific risk are discounted at the debtor’s (or industry participant’s) cost of debt. No incorporation of liability-specific risk (in either direction) implicitly assumes that investors are risk neutral as it pertains to liability-specific risk.

Is There Asset-Liability Symmetry for Contingent/Unliquidated Liabilities?

One investor’s liability can be another investor’s asset. For example, consider a lawsuit, which is an asset to the plaintiff and a liability to the defendant.

Intuitively, the value of this lawsuit should not change if we are thinking about it from the plaintiff’s perspective or the defendant’s perspective. The expected cash flows and associated risk should be the same whether the lawsuit is valued as an asset or a liability. This concept is like the previously mentioned debt instrument that has the same value from the asset and liability perspective.

However, asset-liability symmetry can only be achieved if investors are risk averse when valuing assets, and risk seeking when assessing liability-specific risk. Said differently, the detrimental effect of asset/liability-specific risk on asset values must have the equal and opposite (i.e., beneficial) effect on liability values. This would be a valuation version of Newton’s third law of motion, which states every action has an equal and opposite reaction.

What Happens if There is No Asset-Liability Symmetry for Contingent/Unliquidated Liabilities?

There typically are checks-and-balances within the valuation process. The market value of an asset is dependent on the competing interests of buyers and sellers. A debt obligation is often valued the same from the asset (creditor’s) and liability (debtor’s) perspective.

The system of checks-and-balances breaks down if there is no asset-liability symmetry and there is no market for offloading liability exposure. One cannot use asset values as a proxy for liability values, or vice versa, if increased asset/liability-specific risk results in lower asset values and higher liability values.

Can Contingent Liabilities be Very Risky?

Yes. It is axiomatic in ”bet the company litigation” that there is a lot of risk associated with the litigation. Win and the company survives; lose and the company does not survive (at least in its current form).

The litigation finance industry provides some additional insight. Some litigation funders seek returns consistent with private equity and venture capital funds. High required rates of return on the litigation funding front (assuming they can get them) presumably implies that the underlying cash flows are risky (or that the litigation funding market is very inefficient).

Should Some Contingent/Unliquidated Liabilities be Very Risky?

That is a more nuanced question. On the one hand, the answer should be no. The beta (excluding its role in determining the defendant’s credit risk) for a lawsuit based on something that happened in the past is zero because future changes in market conditions play no role in expected cash flows. The zero to low (when including the defendant’s credit risk) beta suggests very low risk. On the other hand, there can be a lot variability in the expected cash flows that is difficult to diversify away because the market for litigation claims (particularly on the liability side) is not as efficient as the market for stocks and bonds. The inability to diversify this exposure in some instances can result in very high levels of risk.

Do Some Contingent/Unliquidated Liabilities Have Low Risk?

Delaware appraisal lawsuits are an example of relatively low risk litigation-related liabilities. Plaintiffs are shareholders who allege the company was sold too cheaply. These shareholders seek to get their shares appraised at a value that (greatly) exceeds the sale price. The risk is relatively low because the downside is very limited: they will get paid something for their shares (presumably close to the unaffected stock price) even in the worst-case scenario. The downside risk was even lower a few years ago (prior to decisions such as Dell) when it was more likely that plaintiffs would get their shares appraised at the deal price or higher. The combination of relatively low risk combined with relatively high interest rates (plaintiffs receive prejudgment interest at 5 percent over the federal discount rate) explains why commenters used to view appraisal lawsuits as an interest rate arbitrage opportunity.

Do Risky Liabilities Require Bizarro World Discount Rates?

Fans of Superman or Seinfeld are familiar with the bizarro world, where everything is the opposite from the real world. The same concept might apply to discount rates when one pivots from valuing assets to valuing liabilities. This is the case if investors are risk averse when evaluating both assets and liabilities.

Discount rates must be lowered (not increased) to arrive at a higher value for the obligation due to increased liability-specific risk. Therefore, discount rates for liability-specific risk (which is different from a debtor’s credit risk) can be characterized as a bizarro world: down is up (need to lower discount rates to reflect increased risk) and up is down (need to raise discount rates to reflect decreased risk).

To avoid the bizarro world, one can adjust cash flows as an alternative. Instead of lowering the discount rate, a practitioner can increase expected cash outflows to directly reflect the risk premium. This cash flow could be viewed as compensation that a hypothetical party would require to take on the liability.

Does Lack of Asset-Liability Symmetry Lead to Settlements?

Most lawsuits settle. There can be a variety of reasons for this outcome. For example, settling results in lower costs for both sides. However, a leading explanation may be the lack of asset-liability symmetry, if it exists.

There is a very strong incentive to settle if there is a lack of asset-liability symmetry due to risk aversion adversely affecting the value of both assets and liabilities. Any reduction in risk via a settlement reduces risk from both the plaintiff’s (asset’s) and defendant’s (liability’s) perspective. This is a win/win proposition, as opposed to a zero-sum game where one side’s gain is the other side’s loss.

Conclusion

Valuing contingent/unliquidated liabilities raises a series of interesting questions. We tend to only focus on discount rate-related risk in the context of assets (which includes equity and debt claims on a company) or debt-like obligations. The amount and direction of incremental liability-specific risk associated with contingent/unliquidated liabilities is not addressed as often and might be more nuanced.

[1] Debt obligation: $10 million * 100% = $10 million. Lawsuit: ($0 * 90%) + ($100 million * 10%) = $10 million.

[2] Lawsuit: ($0 * 90%) + ($10 million * 10%) = $1 million.

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Michael Vitti, CFA, joined Duff & Phelps in 2005. Mr. Vitti is a managing director in the Morristown, NJ office and is a member of the Disputes Consulting practice. He focuses on issues related to valuation and credit analyses across a variety of contested matters and industries. This article represents the views of the author and is not the official position of Duff & Phelps, LLC.

Mr. Vitti can be contacted at (973) 775-8250 or by e-mail to michael.vitti@duffandphelps.com.