Forget Black-Scholes?

Let the mudslinging begin — again. No, we're not talking about the Presidential campaign. We're talking about the latest battle over the Financial Accounting Standards Board's plan to require companies to treat employee stock options as an expense. Now that the long-awaited proposal is out, corporate and political opponents are reviving their oft-heard arguments against the idea in an effort to get the board to reverse course.

But while opponents of expensing have forced FASB to back down in the past, their efforts appear less likely to succeed this time around, in large part because the unrestrained granting of stock options has been widely blamed for fueling the excesses of the 1990s' stock-market bubble.

The critics have at least one legitimate complaint about the rule — valuation. It is difficult to estimate the actual expense of employee options. But FASB has not let this problem (which also applies to many other items used to calculate earnings) derail its proposal. The board's view is that subtracting even a rough estimate of options expense from earnings will produce more-transparent financial results than simply footnoting the extent of dilution caused by options, as the current rule allows. Moreover, the board's view on how to value options may take an important step forward.

At this point, the traditional method for valuing options, the Black-Scholes model, seems likely to be eclipsed for purposes of expensing employee grants by an alternative known as the binomial method (also known as the Cox, Ross, Rubinstein model). While the alternative may be easier to adopt than some experts warn, it requires more assumptions than Black-Scholes to be used effectively. Because of the potential that creates for abuse, auditors and regulators may require more documentation before they accept a company's financial statements.

The Black-Scholes Problem
The reason the Black-Scholes formula may not be appropriate for purposes of expensing employee grants is that it is widely considered to overstate their value by an unacceptable margin. That's because the model does not take into account the essential differences between traditional exchange-traded stock options and those granted to employees.

Unlike conventional options, employee options are subject to vesting schedules and forfeiture conditions, and cannot be transferred. As a result, they are invariably exercised before their usual 10-year term expires. These characteristics reduce the value of an option.

To properly value an option grant, a company must be able to estimate the effects these variables have on an employee's ability and inclination to exercise the option. "You can't do that with Black-Scholes," explains Ron Rudkin, a vice president of Boston-based consultancy Analysis Group. "It just doesn't have the flexibility."

The most widely used alternative, the binomial method, is more flexible than Black-Scholes because it uses a lattice framework (see "Up the Lattice," at the end of this article). The framework divides the time from an option's grant date to its expiration date into small increments. That enables the model to take into account many more assumptions about a grant's features, and better estimate employees' likely behavior regarding investments.

That difference hasn't been lost on FASB. As proposed, the new rule recommends use of a lattice-based model unless a company lacks sufficient historical data.

Troublesome Variables
Thanks to its additional flexibility, the binomial model tends to produce a lower estimate of option value than Black-Scholes. A study by Analysis Group found that the Black-Scholes model overstated the value of some grants by anywhere from 28 percent to 56 percent.

But some critics worry that the flexibility of the binomial model could help unscrupulous executives manipulate their financial results. The fear is that they will take advantage of the model's flexibility to underestimate their compensation costs and overstate their earnings. "My concern is that people will use the more-powerful models in the wrong ways," says Mark Rubinstein, a finance professor at the University of California at Berkeley who helped create the binomial model. Rubinstein says the first question he gets from managers is, "Can you tell me how I can get lower numbers?"

For better or worse, small changes in the assumptions concerning an option grant's features can produce wildly different estimates of its value, and that's obviously a bigger problem under the binomial method than under Black-Scholes, notes Chris Kruse, a consultant with New York­based CFX Inc. who studied under Rubinstein. "You can incorporate a lot of things in the binomial model that will significantly reduce the value of the option," warns Kruse.

Forfeiture assumptions represent a particularly troublesome variable, he says, since they are something of "a random element." That's because at least some option recipients quit before their options vest, and thereby relinquish the right to exercise them. In those cases, of course, a company would not incur any expense at all. So simply by projecting a higher-than-likely rate of employee attrition, explains Kruse, a company could artificially deflate the expense it reports for its grants. It may be easy enough to convince auditors to go along, he contends, since the probability of forfeiture is related to such difficult-to-quantify factors as an employee's opportunities elsewhere. "This is probably highly variable, especially when moving up the food chain to the executive suite," says Kruse. "It is also highly idiosyncratic, since a firm's outlook may affect employee attrition." This variable alone, he cautions, gives companies tremendous leeway in estimating option values.

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