Option Models: Cos. Prefer Black-Scholes; Volatility Drops

Companies seem to be making assumptions about stock option valuations roughly in step with market reality when it comes to interest rates and stock volatility, even as many take the easy route to calculate options’ value—and their effect on the corporate balance sheets.

Those are the findings gleaned from a Compliance Week analysis of 50 companies with revenues exceeding $20 billion that filed their 2005 annual reports recently. This spring is the first proxy season where companies must comply with Financial Accounting Statement 123R, requiring them to deduct the value of stock options from corporate earnings. FAS No. 123R does, however, give companies the choice of several accepted valuation methods to establish a fair market value for the illiquid securities.

80 percent of the companies in Compliance Week’s study sample chose the faster, more straightforward Black-Scholes model to value their options. Still, debate rages about whether Black-Scholes is preferred because it provides a more accurate figure, a more earnings-friendly figure, or just a simpler, easy-to-audit equation.

Ma

Cindy Ma, a vice president at NERA Economic Consulting and proponent of the more detailed analysis that comes with a binomial model, says auditors are steering clients toward Black-Scholes. “They like Black-Scholes because it’s a simple equation, only five inputs, so it’s easy to audit,” she explains. “The binomial model requires historical exercise data and a statistical, economic approach. That’s beyond the capability of most auditors.”

Sean Dineen, a principal at Deloitte Financial Advisory Services and leader of its option valuation practice, says in-house capability is a key factor for companies deciding which model to use; he reports anecdotal evidence that Deloitte is seeing about a 60/40 split between Black-Scholes and binomial models.

But Dineen’s 60/40 anecdotal split seems extremely high to Equilar president Tim Ranzetta. “I was even surprised that 20 percent of companies [in the Compliance Week report] were using a binomial model, as most surveys seemed to indicate that only 5 percent to 10 percent of companies were using such a model.” According to Ranzetta, the figure may skew higher for the large-cap companies included in the Compliance Week report, as they have the resources to run such a model, “and also the large potential option expense that makes binomial easier to justify.”

Dineen at Deloitte agrees, noting that, “Most larger companies are better suited to conduct the analysis in-house.”

Larger companies have more experience with the models as well, says Sean Scrol, president of Valtrinsic, an actuarial firm focused on stock compensation consulting, because they voluntarily adopted FAS No. 123R in larger numbers and earlier than smaller companies did. Thanks to their larger employee populations that required more detailed analysis, “larger companies have spent more time and effort looking into this,” he says.

Making Assumptions

Whatever the chosen model, companies must make some assumptions about stock options that become critical elements to equations that determine their value. Volatility (the change in a company’s stock price) and interest rates are chief among them.

In the Compliance Week analysis, companies reported a median 13.1 percent decline in expected volatility from 2003 to 2005, along with a median 32.1 percent increase in interest rates for the same period (view spreadsheet in box above, right, for details on each companies’ model assumptions). Both of those aggregate assumptions are consistent with what’s happening in the market, experts say.

Angel

“Volatility has actually dropped in the U.S. equity market,” and that does reduce the value of stock options, says James Angel, a finance professor at Georgetown University. Volatility in the Standard & Poor 500 index, he notes, dropped from 16 percent in 2003 to 11 percent in 2004 to 10.3 percent in 2005. “That’s extraordinarily low, so I would not be surprised to see corporations would be reporting lower volatility numbers.”

Scrol agrees that volatility is heading down. He said most companies’ volatility figures likely go back as far as 1999 and 2000, “the worst and the best years in the market bubble,” he says. “The fact that volatility is trending down is not surprising.”

Ranzetta concurs. “With the stock market at historically low levels of volatility, it is not surprising to see the sharp reduction in expected volatility that companies are incorporating into their option pricing models,” he says.

Dineen also cites the idea of “implied volatility” that reflects projected future volatility, versus actual historical volatility. Current guidance from regulators lets companies choose between the two.

Dineen

“The option for companies to use implied volatility or combine implied with historic volatility under 123R, coupled with the fact that companies in general are at a historic low with regard to volatility, may have contributed to a general decline in volatility over the recent past,” he says.

The overall rise in the interest rate assumptions is also consistent with the market, Scrol says. The 50 companies in Compliance Week’s analysis reported a median 3.4 percent assumed interest rate in 2004 and a 3.96 percent assumed rate in 2005; the average five-year Treasury rate was 3.4 percent in 2004 and 4 percent in 2005, Scrol notes. “That’s almost exactly what we see here.”

“The interest rate assumption in Black-Scholes is usually tied to the interest on a risk-free investment—Treasury bonds tend to be the proxy,” Ranzetta adds. “Since interest rates have climbed quite significantly as the Fed has raised the discount rate, it is not surprising that companies are increasing the interest rate assumptions that they use in their models.”

Less consistent are companies’ assumptions about the expected life of outstanding stock options—which is also difficult to assess, since the data is too young. As a group, Compliance Week’s study sample assumed an expected term of 5.5 years in 2003, a 5-year term in 2004, and then an increased 5.5 year-term in 2005.

EXCERPT

Below is an excerpt from FAS No. 123R, Share-Based Payment, outlining how stock options should be valued.

The measurement objective for equity instruments awarded to employees is to estimate the fair value at the grant date of the equity instruments that the entity is obligated to issue when employees have rendered the requisite service and satisfied any other conditions necessary to earn the right to benefit from the instruments (for example, to exercise share options). That estimate is based on the share price and other pertinent factors, such as expected volatility, at the grant date.

To satisfy the measurement objective in the above paragraph, the restrictions and conditions inherent in equity instruments awarded to employees are treated differently depending on whether they continue in effect after the requisite service period. A restriction that continues in effect after an entity has issued instruments to employees, such as the inability to transfer vested equity share options to third parties or the inability to sell vested shares for a period of time, is considered in estimating the fair value of the instruments at the grant date. For equity share options and similar instruments, the effect of nontransferability (and nonhedgeability, which has a similar effect) is taken into account by reflecting the effects of employees’ expected exercise and post-vesting employment termination behavior in estimating fair value (referred to as an option’s expected term).

In contrast, a restriction that stems from the forfeitability of instruments to which employees have not yet earned the right, such as the inability either to exercise a nonvested equity share option or to sell nonvested shares, is not reflected in estimating the fair value of the related instruments at the grant date. Instead, those restrictions are taken into account by recognizing compensation cost only for awards for which employees render the requisite service.

Awards of share-based employee compensation ordinarily specify a performance condition or a service condition (or both) that must be satisfied for an employee to earn the right to benefit from the award. No compensation cost is recognized for instruments that employees forfeit because a service condition or a performance condition is not satisfied (that is, instruments for which the requisite service is not rendered). Some awards contain a market condition. The effect of a market condition is reflected in the grant-date fair value of an award. Compensation cost thus is recognized for an award with a market condition provided that the requisite service is rendered, regardless of when, if ever, the market condition is satisfied.

The fair-value-based method described in the above paragraphs uses fair value measurement techniques, and the grant-date share price and other pertinent factors are used in applying those techniques. However, the effects on the grant-date fair value of service and performance conditions that apply only during the requisite service period are reflected based on the outcomes of those conditions.

Source

Financial Accounting Standards Board (December 2004)

Individually, most companies reported little or no change in their term assumptions, although some did assume significantly longer or shorter life spans. Insurance business St. Paul Travelers, for example, doubled its expected term from three years in 2004 to six years in 2005. Citigroup increased its expected term by about half from 2003 to 2005.

A shorter expected term has the effect of establishing a lower value for an outstanding option, but only six of the 50 companies assumed a shorter term. CBS Corp. increased its expected term from 6.8 years in 2003 to 7.3 years in 2004, but trimmed it back to 5.5 years in 2005. DuPont scaled back its expected life from 6.2 years in 2003 to 4.5 years in 2004 and 2005.

Taking The Short Cut

Experts say the expected terms companies report now are not always based on reliable historic data, because many companies haven’t kept the detailed records necessary to predict adequately when employees might exercise their options. Dineen says companies may be making reasonable guesses based on whatever data they may have or may be taking advantage of a short-cut provided by the Securities and Exchange Commission in its Staff Accounting Bulletin No. 107.

The shortcut allows companies to add the average vest term and the contract term and then simply divide the result by two to establish an expected term for use in the valuation model. The method is expected to be phased out after 2007, by which point companies are expected to have established some more complete exercise data of their own, Dineen says.

The Society of Actuaries and the American Academy of Actuaries are in the midst of a comprehensive “experience study” to create exercise data that will be useful to companies in valuing stock options. Scrol chairs the study, which he says is intended to produce industry-specific data about employees’ patterns of exercising stock options. The study will examine several factors that relate to when employees exercise their rights, including the specifics of the option grant, employee demographics, industry factors, stock price and more.

Scrol

“We’re looking at tens of millions of exercise records from thousands of companies,” he says. “This public study will be a starting point for companies that have no data. We’re looking to create tables that will serve as a standard starting point.”

Dineen argues that FAS 123R raised the bar on the quality of the input assumptions companies use to value options. “Companies need to provide support for their assumptions,” he says. “Now companies have to do a deeper dive on expected life in general. This is the most time-consuming assumption to calculate.”

The figures seen so far would suggest companies are starting to apply greater analysis, Scrol says. “Of all the assumptions that get used in the valuation, expected term got the least time and attention,” before stock options became a mandatory expense, he contends. “It used to be that companies just reported whole numbers, five, six or seven years. Now you’re seeing some numbers that show some analysis is being put into them.”

The Compliance Week report, available in Microsoft Excel spreadsheet format, can be downloaded from the box above, right. Also available is related guidance and coverage.