This guest post on methods of testing solvency was contributed to the Bankruptcy Blog by David Tabak of NERA Economic Consulting.
Questions of solvency often arise in bankruptcy and related matters such as claims of fraudulent conveyance.  One would hope that such an important concept would have a single, clear definition along with a single test.  Unfortunately, that is not the case.  In fact, there are two standard definitions of solvency used in the courts along with associated tests.  This post discusses the relationships between those tests and addresses the question of what to do if different tests yield apparently divergent results either in terms of the ultimate solvency question or even on the degree to which a company is said to be either solvent or insolvent.
Insolvency is often characterized as potentially encompassing “legal insolvency,” meaning that the value of the subject’s assets are less than its debts, and “equitable insolvency,” meaning that the subject will not be able to pay its debts as they come due.  The test associated with legal insolvency is the “balance-sheet test,” which asks if assets exceed liabilities while the test associated with equitable insolvency is the “cash-flow test,” which seeks to determine if future assets, including future cash flows to the subject, will allow it to satisfy any cash flows out.
From the point of view of financial economics, the distinction between these two sets of definitions and tests may at first seem a bit peculiar and strained.  If a company’s assets, including the value of future assets, properly discounted for risk and the time value of money, exceed its liabilities, then the company has a positive net value that one would typically expect could be allocated over time to cover all of its debts, with something left over.  That is, under the baseline scenario in which assets can be freely transferred over time, the balance-sheet and cash-flow tests should give identical results.
If that is the baseline case, when can we have a divergence between the tests?  There are two broad sets of possible answers.  The first is that when the tests were conducted, they were not based on the same underlying assumptions.  That is, there was an inconsistency in the analysis.  For example, suppose that a company had an immediately upcoming debt of $100 and expected to receive $110 in cash flow next year.  If the discount rate on that cash flow is ten percent or less, that cash flow is worth at least $100 and the company passes the balance-sheet test, while if the discount rate is greater than ten percent, the company fails the balance-sheet test.  Similarly, if the company can roll over the debt, whether that means rolling over the same debt or obtaining alternative financing, at a borrowing rate of ten percent or less, its obligations in one year will be less than or equal to $110 and it will pass the cash-flow test, while if the borrowing rate is greater than ten percent, it will fail the cash-flow test.
In our example, all that is necessary for the tests to yield the same results is for the discount rate on future cash flows to equal the borrowing rate.  In fact, in this simple example, that must be the case.  If not, there is a “free lunch.”  For example, if one argues that the discount rate is larger than the borrowing rate, then the company could be said to have a negative value (if the discount rate is above ten percent) even if it can operate in a manner in which it pays off its debt and has money left over (if the borrowing rate is less than ten percent).  Even without going as far as to have a positive result for one test and a negative result in the other, we can say that if the two tests do not yield the same result, there is still a free lunch.  In the example where the discount rate is greater than the borrowing rate, an investor could buy the company at its present value, have the company borrow money to pay off its future debt, and wind up with a profit.  In the situation in which the discount rate is less than the borrowing rate, the company could make a profit by selling the claim on its future cash flow and prepaying the debt today to avoid the higher borrowing costs.
While the equivalence between the tests is relatively clear in this example, that equivalence should hold, in the absence of certain conditions, more broadly.  What that means is that when confronting analyses that yield different results, either in direction or even those that differ materially in the magnitude by which a company is said to be solvent or insolvent, there is either an error in the analysis or else there needs to be an explanation for the difference.  Often errors in the analysis are due to underlying inconsistencies in assumptions that may occur if one is not careful in dealing with more complicated capital structures with multiple borrowing rates for different liabilities and different time periods.  Other times there may be inconsistencies in how future cash flows or terminal values are estimated, leading to differences in the valuation analyses.
As alluded to above, there are certain conditions that can in fact lead to different results for the solvency tests.  For example, borrowing and discount rates could be different because of asymmetries in information.  The company under consideration may know that its future cash flows are relatively secure, but the lender may not share the same view.  While this works in theory, it leads to an important question: why should anyone evaluating solvency be convinced by the company’s arguments if those arguments did not or could not have convinced a lender?  That is, if lenders turned down or would have turned down the opportunity to lend to the company at a rate close to what the company claims is the proper borrowing/discount rate, why should we now find the company’s arguments about the legitimacy of a lower borrowing rate convincing? 
As a first pass, it seems that if the lending market is competitive, the proper borrowing and discount rate is the best that the company could have received in that market, not a rate based on its own position.  Thus, to support a difference between the discount rate and the available borrowing rate, one has to show that the appraiser is using information that would not have been available to lenders at the time.  Of course, this sounds like an immediate red flag about an improper appraisal, and one certainly has to be careful in this area.  One possible answer may be if there is a reason to believe that the appraiser is now able to use company information that would not have been available to lenders even under proper confidentiality agreements or similar arrangements.  Consequently, establishing this distinction may be a mixed question of finance and law.  Another possible answer is that borrowing was not possible because the mere act of borrowing would have revealed information to the public or to competitors that would have reduced the value of the company.  Again, this is a tricky situation that does not lend itself to a boilerplate or unsupported claim that there can simply be differences between the borrowing and discount rates, and thus between the balance-sheet and cash-flow tests.
In fact, probably all of the conditions that allow for a difference between the balance-sheet and cash-flow tests share the feature that they rely on relatively strong or unusual assumptions about what is possible.  That is not surprising because differences between the two tests imply a possible arbitrage opportunity for some party, so it should be the case that profit-minded individuals would find a way around any weak barriers to such arbitrage.  The moral of the story is to be careful when you encounter differences in the results of the solvency tests, whether those differences are actual differences in conclusions or even material differences in the degree to which an entity is said to be solvent or insolvent.  There may be reasons for the difference in results, but they should be well-identified and satisfy rigorous examination about why they actually hold.  Moreover, the explanations should correspond to the underlying differences in the analyses, such as borrowing difficulties primarily or wholly corresponding to higher borrowing rates to borrowing limits affecting the size of potential loans.  And if the explanations are weak or there is no explanation, then it may be worth investigating the analyses to see whether they contain inconsistent assumptions that undermine at least one of the solvency tests.

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