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Signs You Are Misapplying Black-Scholes

Signs You Are Misapplying Black-Scholes

The reality is that private companies must meet a higher standard than public companies in the valuation of share-based payments as compensation for both financial reporting (ASC Topic 718) and tax purposes (IRC Section 409A). Beyond the issue of valuing private company’s stock, we generally see two big challenge areas: Volatility estimation and model selection. Selecting the appropriate volatility, which should be guidance based, is a subject for a later article. The following is an abridged discussion.

Model selection errors are more obvious to call-out and, for my money, constitute the biggest mistake we see companies making and unqualified professionals advising companies to use. People are quick to use the Black-Scholes Model (BSM) because it’s free and fundamentally easy to populate. A number of conditions exist, especially for small start-ups, where the BSM output is not a reliable indication of value. The BSM only works for “plain vanilla” options.

Smaller, privately-held companies pay folks with share-based compensation all the time. Growing companies also raise money in the form of equity or convertible securities to pay for growth or maintenance capital expenditures. Out of fairness to its employees, companies often include provisions in the compensation agreements that limit or negate the impact of raising more equity capital on the total compensation amount. These provisions are almost standard at this point.

Some of the terms that seriously challenge or negate the effectiveness and appropriateness of using a BSM to value share-based compensation are as follows:

  • Anti-Dilution Considerations – Whereas participation dilution measures how diluted the equity pool gets when additional equity is sold, anti-dilution provisions offer full or partial protection to existing share or share-option holders.
  • Down Round Provisions – Popular with earlier stage companies and often embedded in financing packages, down round provisions lower the strike price of an option if the underlying shares are issued in the future at a lower value than preceding rounds
  • Longer Term Options – Using a longer term assumption in the BSM will tend to result in overstating the option’s value, since logically impossible scenarios are more frequently implied in the distribution.
  • Knock-In Options – These options have a strike price below the price at which they can exercise. A simple BSM cannot account for the non-linear payout.
  • Changing Volatility – The BSM only allows consideration of a single volatility estimate. A high volatility number can result in a significantly different distribution of future expected prices.
  • Lumpy Dividend Payments – If the historical dividend payments have been lumpy, or are expected to be lumpy going forward or event based, then again (as above) the BSM’s ability to properly draw the distribution of future stock prices is negated.

In each of the above cases, the company or practitioner advising the company should consider using open-form, option pricing models like the Binary Option Pricing Model (BOPM) or a Monte Carlo simulation. While costlier in initial set-up, efficiencies may be applied quarterly going forward. More importantly, these open-form models can account for all the challenges in a supportable and proven manner avoiding more costly penalties or issues down the road.  For more detailed information on misapplying Black-Scholes please view the attached PDF containing specific challenges for each consideration.

To ensure compliance with U.S. Treasury rules, unless expressly stated otherwise, any U.S. tax advice contained in this communication is not intended or written to be used, and cannot be used, by the recipient for the purpose of avoiding penalties that may be imposed under the Internal Revenue Code.

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