Binomial Creep

Although most companies still use Black-Scholes to value their stock options, a small but growing number are finding good reason to employ a more complicated valuation model.

When CFOs willingly take on a heavier workload, something’s up.

Between 1995 and 2004, a grand total of just 68 companies that offered stock options to their employees switched from the traditional Black-Scholes model to a more complicated binomial valuation method. Black-Scholes is still far more prevalent; according to Aon Consulting, only 308 companies now use a binomial methodology, out of some 17,000 U.S. public companies in all. Aon observes, however, that last year alone, 134 companies switched from Black-Scholes to binomial, and so far this year, another 106 have made the transition.

The binomial method is being embraced thanks, in part, to a search for lower stock-option valuations, says Charlie Stryker, a managing director with Trenwith Valuation. In 2004, the Financial Accounting Standards Board issued FAS 123R, which requires most public companies to expense stock options. Once those pro forma figures were slated for the balance sheet, many companies began looking into spending additional time and money on a model that would yield a lower stock-option valuation — and less of a hit to earnings.

The basic mathematics of the Black-Scholes and binomial valuation methodologies are identical; both were developed for valuing exchange-traded stock options. However, the binomial and its sibling methodologies (yes, there’s a trinomial version) allow companies to insert additional assumptions into Black-Scholes, providing a more accurate valuation, according to Aon vice president Terry Adamson.

To be sure, Black-Scholes is useful for estimating the value of exchange-traded options. The model assumes that options are exercised at the end of the option’s contractual term and that expected volatility, dividends, and Treasury interest rates remain constant.

The behavior of employees who hold options is less predictable, however. Just when those options are actually exercised is affected by demographic factors such as age, gender, pay level, and years of service to the company as well as variables such as share-price movement, expected stock volatility, expected holding period, vesting period, and company-specific exercise rules. In fact, says Adamson, there is “no way Black-Scholes can value more exotic [options]” that are based on market triggers. FASB agrees; the board now requires companies to use the binomial method when valuing employee options that are tied to market events.

MakeMusic, a music education technology company, began using the binomial method this year for just that reason — but only for the roughly 25 percent of its 670,000 outstanding options that have market triggers, says chief financial officer Alan Shuler. “I don’t know if the binomial method does a better job; you still have to take an educated guess as to when vesting takes place,” maintains Shuler, who uses Black-Scholes to value the remaining 75 percent of outstanding options. Both valuation approaches are “flawed,” he adds, but “they’re the best that we’ve come up with so far.”

For his part, Big Lots treasurer Jared Poff has found that the binomial method produces valuations that are “a lot more accurate” than Black-Scholes. The Fortune 500 discount retailer made the switch in 2005, after the Securities and Exchange Commission signaled a preference for such a methodology (the SEC later pulled back from that recommendation); about 10 million options are outstanding, according to its latest 10-K. Poff says that auditors Deloitte and Touche conducted “very in-depth reviews” of the Aon binomial model, “challenging the assumptions we used.” Poff concluded that going binomial “was the right way to depict our grants — better than the more generic Black-Scholes model.”


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