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When FASB required the valuation of earnouts, I was tasked with developing a framework for producing reliable and consistent valuations. To promote consistency of practice, I published the results of my work as, “Valuing Contingent Consideration Using Option Pricing,” in the Business Valuation Review. While there have been refinements of the ideas in that article, it is fair to say it describes what has become the industry standard for valuing complex earnouts. Please refer to the "Earnouts" page.

Convertible Debt

There are at least three alternative models to use when valuing convertible debt and its embedded derivatives. In a recent article, “Comparing Three Convertible Bond Valuation Models,” Business Valuation Review, 36, 1, (2017), 32 – 41, I explored the performance characteristics of those models.  Please refer to the "Convertible Debt" page.


Valuing plain vanilla warrants is a relatively straightforward  application of the Black-Scholes-Merton formula for the valuation of a call option. The crucial contribution of an appraiser is the choice of a volatility. However, warrant pricing becomes much more complex if the warrants convert into more than 5 to 10% of the common stock, if they have different terms to maturity, if they have special terms such as exercise price reset provisions and if they are written on preferred stock in a complex capital structure of a private company. I describe how to address those complexities in Valuing Warrants: Dilution, Multiple Exercise Prices, Down-Round Price Protection, published in the Business Valuation Review and "Valuing Warrants with Multiple Exercise Prices, and Warrants on Convertible Preferred Stock". Please refer to the "Warrants" page.

Interest Rate Derivatives

Valuing interest rate derivatives is often more complex than valuing equity derivatives, because interest rates are more complex to model than equity prices. The more complex models of interest rate movements mean that we often cannot use closed-form solution such as the Black-Scholes-Merton formulas. Instead we use numerical methods such as lattices or Monte Carlo simulation and interest rate lattices and simulations are much more complex than equity price lattices and simulations. I have spent a lot of time on this subject as evidenced by the four interest rate research papers I published while a professor. You can find those papers in "Interest Rate Derivatives" as well as a short piece on how to value interest rate floors with a 0% exercise price. Please refer to the "Interest Rate Derivatives" page.

Complex Capital Structures

I have performed or reviewed hundreds of valuations of securities in complex capital structures. Most used an option pricing approach, because it is very effective. That method uses the Black-Scholes-Merton formulas and thus implicitly relies on the assumption that equity value is lognormally distributed. Many early stage companies have a more limited ranges of outcomes including, in the limit, two outcomes, success or failure. I developed a way to apply option pricing in those cases and compared it to the standard models. Please refer to the "Complex Capital Structures" page.

Tranche Financing

Firms sometimes enter into multi-tranche equity financing agreements. The issuance of future tranches can be certain or contingent on future events, such as the achievement of business targets. When the issuance of future tranches is certain, the initial contract is a sale of shares and forward contracts on the shares. When the issuance of future tranches is contingent, the initial contract is a sale of shares and call options on the shares. In both cases the value received in the first round is for the purchase of the common shares in the first round and for the derivatives related to future rounds. When confronted with this valuation challenge, I developed a valuation method that uses basic option pricing principles and requires a modest level of data input from management. Please refer to the "Tranche Financing" page.

Hedge Effectiveness

When FASB introduced FAS 133, now ASC 815, I worked with PwC to develop and test valuation models and hedge effectiveness models. John Finnerty and I then published two articles to explain how we thought effectiveness should be tested.  “Testing Hedge Effectiveness Under SFAS 133,” The CPA Journal LXXIII No. 4 (April 2003) 40 – 47 and “Alternative Approaches To Testing Hedge Effectiveness Under SFAS 133,” Accounting Horizons 16 (June 2002), 94 – 108.

Our suggested approaches have been widely adopted. Please refer to the "Hedge Effectiveness" page.


Discounts for Lack of Marketability (DLOM)

There is a rich empirical literature on DLOMs based on, typically, the differences in transaction prices between traded securities and their corresponding 144A-restricted securities. Appraisers can use these results, the indications of put models, and their judgment to conclude the appropriate values for DLOMs. I wrote an article to clarify how one can calculate security specific DLOMs for securities in complex capital structures and how to calculate DLOMs relative to the prices paid for non-marketable securities. “Thoughts on Calculating DLOMs,” Business Valuation Review, 33, 2, (2014), 102 – 112. Please refer to the "Discount for Lack of Marketabilty" page.

The FedEx Cup for Golf and Numbers Lovers

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