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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.
Marie Leone, | US
May 19, 2006

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."

The Society of Actuaries hopes to help more companies improve their valuation models. An SoA task force is developing tables that depict option-exercise behavior, so companies will not need to rely solely on their own exercise history when they make valuation-model assumptions. Task force leader Sean Scrol, the president of actuarial consultancy Valtrinsic, also muses that by using the SoA's tables, companies would provide investors with more comparability between financial statements.

Six large brokerages, which together handle 85 percent of employee stock option trades, have agreed to share their exercise data with the SoA; the group is also eliciting comment and advice from the Big Four accounting firms regarding assumptions and model technology.

Scrol suggests that smaller companies could work directly from the tables' assumptions, which likely will include data categorized by employee demographics, company size and age, and industry. Larger, older companies, which have more extensive exercise data of their own, could layer it on top of the table's assumptions. A likely completion date for the tables is year-end 2007, says Scrol.

Meanwhile, companies will increasingly adopt the binomial model as they and their auditors become more comfortable with it, predicts Adamson of Aon, whose clients tend to be Fortune 500 companies. Many that have already gone binomial, he notes, weren't necessarily looking for a lower valuation, though all of them welcomed one.

However, "the floodgates are not opening," observes Trenwith's Stryker; "I don't see much movement toward the binomial method." Trenwith, an affiliate of BDO Seidman, provides the audit firm with valuation guidance, mainly for midsize corporations. Moving to the binomial method is "fine," he maintains, quickly adding that "from a cash-flow perspective it doesn't matter what methodology companies use. Recognition of the expense doesn't change cash flow."

Every vendor has its own take on the binomial method, says Adamson, and companies and their auditors are still looking for their comfort zone. Another factor that companies should consider carefully, he says, is that once a company goes binomial, its auditor generally won't allow the company to reverse course. For CFOs who might someday find themselves longing for the simple days of Black-Scholes, some further thought might be in order.

Going Binomial
Companies of all sizes seem equally likely to make the switch from the Black-Scholes to the binomial model.
Year Small
(Less than $100m)*
(More than $5b)*
1995 5 7 3 1 16
1996 0 1 1 0 2
1997 0 0 0 0 0
1998 1 0 0 0 1
1999 0 1 1 1 3
2000 0 3 0 0 3
2001 1 0 1 1 3
2002 2 3 1 0 6
2003 1 4 0 3 8
2004 7 4 6 9 26
2005 37 44 26 27 134
2006 18 25 40 23 106
Total 72 92 79 65 308
*Annual revenue
Source: Aon Consulting