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When Black Scholes Falls Short

April 25, 2011 at 3:28 pm Gunther Hofmann 2 comments

Every now and then, the SEC lets the world know their interpretation of generally accepted accounting principles. More often than not, this happens in speeches by SEC employees, and the resulting guidance is referred to as “Speech-GAAP”.

An interesting speech during the annual AICPA National Conference on Current SEC and PCAOB Developments in December 2010 picks up on some of the issues surrounding derivative accounting for ASC 815 (aka FASB 133). For a good summary of the conference, see KPMG’s Issues In-Depth or Grant Thornton’s New Development Summary.

Amongst other tidbits, the SEC commented on the analysis and valuation of embedded conversion options and freestanding warrants. Similar comments can be observed at this SEC presentation dated November 2010.

The SEC admits that it is indeed a complicated path to determine the appropriate accounting for such instruments. It makes several observations:

1. They continue to encounter registrants who fail to appropriately apply the guidance relating to derivative accounting. This may not be surprising given the complexity of the subject matter, but this failure may lead to comment letters from the SEC and embarrassing re-statements of financial information.

2. More specifically, the SEC remarks cite a failure to consider all the different settlement provisions and features contained in such instruments and their impact on the accounting treatment (i.e., “down-round protection” – a rather common feature that has been explicitly mentioned in FASB’s EITF 07-5, making the instrument “not indexed to an entity’s own stock” and hence should be presented as a derivative liability at fair value with changes in fair value periodically flowing through the income statement.)

3. Often, such instruments are erroneously valued using the Black Scholes formula. The Black Scholes formula is not designed to accurately value the embedded features of the derivative, such as down-round protection or performance provisions etc. More appropriate valuation methods would be a lattice model or a Monte Carlo simulation.

The Black Scholes model is known as a “close form” model, providing a deterministic outcome for a limited number of inputs. All inputs are observable, explaining the popularity that the Black Scholes model enjoys with the audit community. It is relatively easy to implement, in turn explaining its popularity with financial statement preparers. However, the Black Scholes model is limited to valuing “plain vanilla” options or warrants: options with no additional features. There are closed-form solutions for some of the more “exotic” options, such as barrier options or Asian options, but the features embedded in warrants seldom map to any of these.

A lattice model or Monte Carlo simulation by itself does not necessarily value these embedded features. Rather, these “open form” models allow the user to insert conditions and varying assumptions depending on stock price movements or other, additional inputs. They will need to be tailored to the specific embedded features of the derivative, and hence are more complex to set up. Most issuers shy away from implementing these models in favor of valuation firms with specialized expertise.

The Brenner Group regularly values companies with complex capital structures, including multiple levels of preferred shares, convertible debt, and warrants. We have seen a considerable increase in the need to provide support for the valuation of warrants and embedded features for ASC 815, especially after the latest guidance of EITF 07-5, and more specifically the stated preference of the SEC for issuers to use the proper valuation method to value complex features.

Gunther Hofmann is a Vice President of The Brenner Group and has done extensive work in valuations, M&A, venture capital, and corporate finance with significant international experience in small firms as well as global corporations. Gunther earned a Masters Degree in Electrical Engineering and Business Administration from Darmstadt University of Technology in Germany, and was a Visiting Scholar at UC Berkeley. He is a holder of the Chartered Financial Analyst designation, and a member of the National Association of Certified Valuation Analysts. Gunther is Chairman of the Software/IT Industry Group of the German American Business Association (GABA).

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