In the 29 years since Fisher Black and Myron Scholes published "The Pricing of Options and Corporate Liabilities", the valuation of company-stock options has emerged as a central issue in equity analysis. The greater focus on such valuation reflects both the increased reliance on options by public companies and the increased concern of investors regarding financial-statement transparency in the wake of ongoing accounting scandals.

Ironically, the most publicized of these scandals, concerning Enron Corp., was driven by malfeasance which had essentially nothing to do with the proper valuation of stock options — nevertheless, the backlash against the fraudulent accounting which precipitated the collapse of this and other companies, exacerbated by the poor performance of the equity markets in general, has created a momentum for sweeping reform (similar to the widespread support for change in the wake of systemically unethical practices in the 1920s and the subsequent decade's bear market). The current environment for accounting reform contrasts sharply with the circumstances in the mid-1990s, when the movement towards more accurate valuation of company-stock options initiated by the FASB was detoured from the income statement to the financial footnotes, the result of effective political lobbying by public corporations, particularly those in the technology sector.

Warren Buffett, Chairman of Berkshire Hathaway, has framed the valuation issue in three simple questions: If company-stock options aren't compensation, then what are they? And if compensation isn't an expense, then what is it? And if an expense doesn't belong on the income statement, then where does it?

Add to these questions a fourth: If the cost of options belongs on the income statement, then how should this expense be measured? These four questions are interrelated — the accuracy and logical consistency of the valuation methodology influences the case for including the valuation of options on the income statement.

Company-stock options (which are warrants in every respect except name) are rewarded to employees each year as annual compensation, yet options provide the recipients with contingent claims on a stream of cash into the indeterminate future. The dilutive impact of those claims, if not offset by share repurchases*, can become significant.

* Although stock-option dilution can be mitigated by share repurchases, the shareholder is still footing the bill. Mr. Buffett has highlighted the implicit cost of "…repurchasing shares to offset the shares issued when stock options granted at much lower prices are exercised. This 'buy high, sell low' strategy is one many unfortunate investors have employed — but never intentionally! Managements, however, seem to follow this perverse activity very cheerfully."

Dilution of only 1% annually will reduce the relative claim of shareholders in a corporation by almost 26% after three decades. Dilution of 2% will reduce that claim by almost 45% — in effect, shareholders will have seen their proportional ownership nearly halved without selling a single share.

The Black-Scholes Model

To comply with SFAS 123, companies provide the components for measuring option expense relying on the Black-Scholes model. Most companies present both the assumptions (risk-free interest rate, expected life of the options granted and expected volatility of the underlying stock) and the resulting option values in the Notes to the Financial Statements. Many companies choose to list only the assumptions in their footnotes, while a rare few (only Boeing and Winn Dixie among the S&P 500) are willing to treat the cost of options as an expense on their income statement.

Black-Scholes is not without limitations, however, beginning with the first two assumptions underlying the valuation formula as outlined in the 1973 article:

1. The short-term interest rate is known and is constant through time.
2. The stock price follows a random walk in continuous time with a variance rate proportional to the square of the stock price. Thus the distribution of possible stock prices at the end of any finite interval is log-normal. The variance rate of the return on the stock is constant.

Note the comments in the 2001 10-Ks for Intel Corp. and Symantec Corp. (identical wording in the two documents): "The Black-Scholes option valuation model was developed for use in estimating the fair value of traded options that have no vesting restrictions and are fully transferable. In addition, option valuation models require the input of highly subjective assumptions, including the expected stock price volatility. Because the company's stock options have characteristics significantly different from those of traded options, and because changes in the subjective input assumptions can materially affect the fair value estimate, in the opinion of management, the existing models do not necessarily provide a reliable measure of the fair value of employee stock options."*

* The criticisms by Intel and Symantec of the Black-Scholes model are not without vested interest: in the 1998-2001 period, the Black-Scholes model valued options granted by Intel, net of cancellations, at $6.05 billion or 18% of adjusted pretax earnings (goodwill amortization added back). For Symantec, in the fiscal (March) 1999-2001 period, the Black-Scholes valuation of options was nearly one-half of the adjusted pretax earnings (amortization, in-process R&D and restructuring charges added back). Nonetheless, the comments stand on their merits.

While the objections quoted above are rational, it would be irrational to argue them in favor of the status quo. The number and percentage of individuals who directly or indirectly own equities is at an all-time high, and this constituency has every right to review financial statements which reflect the economic reality of the underlying corporations as accurately as possible. The challenge is in providing a valuation methodology which most effectively serves the needs of shareholders.

To an investor in the long-term future of a company, the principal variable in determining the cost of options is the growth rate of the stock price, not its volatility. The cost to offset the dilutive impact of options will be less to a company whose stock is rising x% annually than that of a 2x% grower, regardless of volatility.

When a stock provides an average annual return of zero, for example, the expected cost of options will be close to zero over a timeframe relevant to investors, irrespective of the volatility of the shares. Certainly, the only times these options will be exercised will be when the stock price exceeds the strike price. If the company chooses to repurchase offsetting shares immediately, the cost will be greater than zero (for the option holders as well since they will suffer future capital losses if they don't sell their shares immediately). In the more likely scenario that the company does not act concurrently with the exercises, however, the net cost can be less than zero. (This scenario would be consistent with a company choosing to offset option dilution at the end of its fiscal year — the average stock price at that time would be the exercise price, implying no net cost, while the company would accrue the tax benefits from the earlier exercise.)

In the case of U.S. Steel, the value of the 3.1 million options granted, net of cancellations, during the 1998-2001 period was $22.6 million based on the Black-Scholes model. (At the present time, more than two-thirds of these options are out-of-the-money and the remainder are only slightly in the money.) During this same four-year period, 233,785 options were exercised — if the company had repurchased shares at the end of each fiscal year to offset dilution, the results would have aggregated to a net benefit to shareholders in excess of $1 million.

Volatility is considered risk in an investment context; to shareholders, however, true risk is "the permanent loss of capital". The value of equities — the present value of future dividends; the claim on a stream of cash into the future in exchange for a fixed amount of cash at the time of purchase — is not reduced by volatility. To the contrary, volatility benefits investors since shareholders who invest discretionary funds without margin are neither required to sell when prices decline nor forced to buy when prices rise.

In a time-limited speculation, volatility does create value. An option buyer will pay more when the underlying stock price is more volatile, raising what seems to be a contradiction: if volatility increases the option price to a buyer, why wouldn't it increase the cost to a seller — in this case, the company which grants options to employees?

In the case of an option which expires in nine months or less, the limitations of time significantly affect the probabilities that the option will expire worthless. Company-stock options, by contrast, generally do not expire for 7-10 years, and time is less of a constraint.

A company which is growing its earnings per share (EPS) by 7% annually will see its stock price rise by more than 50% in seven years and nearly double in ten years, assuming that the price-earnings multiple (M) at the end of the period is similar to that at the beginning. Once an option is firmly "in-the-money" there is no conclusive argument that volatility will necessarily benefit the option holder. Given the relative unreliability of short-term stock-price forecasting and the influence of fear and greed on stockholder decisions, the option is as likely to be exercised when the volatility is on the downside (the option holder wants to sell the underlying shares in fear of a further decline) as when it is on the upside.

Ignoring volatility, however, contradicts the Black-Scholes model, which is based on arbitrages between hedged positions and a risk-less interest rate and in which variance is a component. This theoretical arbitrage is unattainable in practice, however, given the absence of public trading of company-stock options and the assumption that variance is a constant.

The Black-Scholes model is arguably not the most-useful tool in quantifying the cost of company options to shareholders. The limitations of the model, however, should not be used as a rationale for excluding option expense from the income statement.

Cost of Exercised Options

A different approach suggested by UPI Editor Martin Hutchinson, among others, ignores the options which are granted and cancelled, focusing instead on those which are converted into shares:

C = cost of exercised options
EO = number of options exercised
SP = stock price (average or year-end)
EP = average strike price of options exercised
t = tax rate

The most obvious drawback of this approach is that the income statement will reflect an expense which was effectively incurred years earlier when the options were granted. Yet, a similar argument can be made about depreciation and both approaches have the advantages of simplicity, objectivity and measurability.

Another concern is that this cost-of-exercise valuation would create greater volatility in net income. Most managements try to avoid "lumpy" results which create uncertainty among investors, speculators and analysts. Of course, options are made available at the discretion of managements and large variations in option expense can be mitigated by less-generous option grants. If nothing else, accounting for the impact of options on a quarterly basis, as recommended by Standard & Poor's ("Measures of Corporate Earnings" — May 14, 2002), would spread out the annual impact and would provide investors with more timely information than is currently offered through the 10-K disclosures.

Given the lag effect of valuing options based on exercise period and the trend of rising stock-option grants, a reasonable assumption would be that the cost to shareholders in recent years determined by the cost-of-exercise approach would have been understated relative to the results of the Black-Scholes model. This assumption might not stand up to analysis, however — for example, all of the companies cited as examples in this discussion incurred higher costs using the cost-of-exercise approach. Evidently, the strength in stock prices during the 1996-2001 period more than offset the lag effect and the rising trend of option grants.

Cost of Granted Options

An approach which more accurately reflects the current-period cost of options to shareholders focuses on the estimated cost incurred in offsetting future dilution. This cost is determined by the # net options granted and the estimated stock price at the time these options are projected to be exercised. The future after-tax cost is then discounted back to the present:

For example, assuming a growth rate of 6%, an effective life of 7 years and a terminal price-earnings multiple of 15x, the estimated cost to offset 2% annual dilution would average 6.5% of earnings. (Increases or decreases in the dilution percentage will have a proportional impact on the option cost relative to earnings.) With growth of 8% and a terminal multiple of 20x, the estimated cost would be 13.6%. (If the effective life were reduced to 5 years, the estimated cost would drop to 10.4%; if the effective life were increased to 9 years, the estimated cost would rise to 16.2%.) With 12% growth, an effective life of 7 years and a terminal multiple of 35x,* the estimated cost would be 25% of earnings.

* The assumption in this example of a terminal multiple of 35x for 12% growth, more than twice the assumed multiple of 15x for a 6% grower, is not aggressive. Over a 25-year period, 12% growth will increase earnings sixteen-fold, almost four times the increase in earnings from 6% growth.

Equation (4) does not require a present-value calculation (assuming g is constant) or a tax-benefit adjustment (the denominator uses net income rather than pre-tax income). Note that the assumption of stock-price growth as a constant is not undermined by the uncertain expected life of a given company's options since these options are granted on an ongoing basis over time.

Equations (2), (3) and (4) are simplistic in assuming that the variables which determine C will not, in turn, be affected by the result. Once calculated, the cost of options would reduce a company's income and stock price unless the equity markets are efficient in the semi-strong form. If such efficiency exists, the methodology for valuing options would be an important academic exercise but one without incremental value to investors since the cost of options would already be reflected in stock prices.

The Question of Market Efficiency

The new accounting rules for the treatment of goodwill amortization, SFAS 141 and 142, will provide some guidance on the efficiency or inefficiency of the equity markets in valuing expenses which have been improperly reflected on the income statement. In the case of company-stock options, a valid expense has been excluded from the calculation of net income; with goodwill, an irrelevant expense had been included prior to 2002. It is too early, however, to draw any conclusions on the market's reaction to the new amortization standards.

An argument can be made that the equity markets are neither efficient nor entirely inefficient in adjusting a company's financials for the off-income-statement expense of options. For example, were Cisco Systems required to reduce its reported earnings by approximately 75% to reflect the Black-Scholes valuation, the shares of Cisco would likely be impacted but not to one-quarter of their previous prices.

A more striking example is provided by Siebel Systems. In the 1996-2001 period, options granted net of cancellations were valued by the Black-Scholes model at $3.26b (the cost-of-exercise value was approximately $3.5b), considerably higher than the cumulative pretax income of $1.07b.

At the extreme, if a company was committed to a compensation strategy whereby option values would exceed pretax income each year, an efficient market should price the underlying shares close to zero. (Regardless of the extent to which option values exceed pretax income, the shares must sell at a positive value since options are a contingent liability which, at worst, can only dilute existing shareholders by some percentage less than 100%.) The anecdotal evidence suggests that the equity markets either expect option values to decline below pretax income on a sustainable basis or, more likely, that the true costs of options are not adequately discounted in stock prices.

Support for semi-strong inefficiency is provided by two studies — one highlighting contrarian strategy; the other, fundamental analysis. In a study conducted by Investars, a "ROSS (Rate of Success System)" ranking was developed for the performance of the equity ratings of various brokerage firms:

"Of the 19 brokerages that Investars shows to have issued ratings on at least 500 stocks since Jan. 1, 1997, only four — Credit Suisse First Boston, A.G. Edwards, Salomon Smith Barney and Merrill Lynch — showed a portfolio return in positive territory as of May 29, 2001, according to Investars' ROSS calculations*…ROSS takes brokerages at their word on stock recommendations, hypothetically investing or withdrawing money on a fixed scale depending on the recommendation type. A 'Buy' recommendation, for example, generates a $300,000 investment; an upgrade to 'Strong Buy' raises the investment to $450,000, while a downgrade to 'Outperform' reduces it to $200,000.

"Among boutique brokerages — those that have covered more than 100 but fewer than 500 stocks since Jan. 1, 1997 — eight showed positive portfolio returns…It should be noted, however, that the proportion of boutique firms in positive territory (8 out of 34, or 21.0%) is comparable to the proportion of larger firms in positive territory (4 out of 19, or 23.5%)."

By contrast, the S&P 500 Index rose 71.2% in the 1/1/97-5/29/01 time period.

* "Here are the overall ROSS rankings, as of May 29, 2001, of the top 10 firms among the 19 that have covered at least 500 stocks since Jan 1, 1997:

WSJ Partners (Walter J. Schloss) provided an 18.8% annual compounded return from 1/1/84 through 12/31/01 — after fees, the limited partners received a 14.3% return compared with 13.9% for the S&P 500. For the 45 years ended 12/31/00, the limited partners received a 15.7% compounded annual return vs. 11.2% for the S&P.

TBK Partners (Tweedy, Browne Company LLC) provided a 14.4% compounded annual return from 9/30/83 through 12/31/01 — after fees, the limited partners received a 12.6% return compared with 14.4% for the S&P 500. For the 43 years ended 12/31/2001, the partnership provided a 19.3% compounded annual return vs. 11.3% for the S&P. For the 34 years ended 12/31/2001, the partnership provided a 17.5% return and the limited partners received a 14.7% return vs. 11.7% for the S&P.

The book value of Berkshire Hathaway (Warren Buffett, chairman since 1964; Charles Munger, vice-chairman since 1978) grew at a 22.5% compounded annual return from 12/31/83 through 12/31/01. For the 37 ¼ years ended 12/31/2001, the compounded growth in book value was 22.6% annually vs. 11.0% for the S&P, despite the relative tax disadvantage of Berkshire's corporate structure — during this same period, the stock price rose at a compounded rate of approximately 25.5%.

Sequoia Fund (Ruane, Cunniff & Co., Inc.) provided a 16.6% compounded annual return from 1/1/84 through 3/31/02 compared with 14.3% for the S&P 500. For the 31.6 years ended 3/31/02, the fund provided a 17.0% compounded annual return vs. 12.7% for the S&P.

Recommendations

An assumption of market inefficiency suggests that the valuation of options is a worthwhile calculation for investors, whether the valuation methodology is Black-Scholes, cost-of-exercise or cost-of-grant.

In the cost-of-grant equations, C is best determined by iteration since the variables used in determining C are not entirely independent of the result. Companies and investors could simplify the process by averaging the first two iterations of equation (3)* — these first two results will set the upper and lower boundaries of C. The same process can be used to estimate the percentage cost of options (C%) in an inefficient market, using equation (4).**

* In computing the second result, reduce EP by some or all of the % impact on EPS from the first iteration, consistent with the earlier argument that an inefficient market will reduce stock prices to some extent as a result of option-related reductions in earnings.

C% = (G-T)((NI(1+g^n))M)-EP)/((PTI(1+g^n))

C% can also be used to determine the option-adjusted price-earnings multiple (M') for any company which does not deduct the cost of options on its income statement:

As a first step in projecting stock-price appreciation, companies would best serve their shareholders by providing an estimated earnings growth rate based on hurdle rates of return on retained capital and on expected retention ratios. If a company projects an overly optimistic growth rate, its income statement will incur an excessive expense. If the projection is too conservative, the company will need to justify its pessimism to its owners and to the financial community.

In estimating the cost of options, companies would have considerable discretion in projecting an earnings growth rate, the expected life of the options and a terminal P-E multiple at that time. Comparing the assumed rate of stock-price appreciation to historical results over the previous 5, 10 and even 15 years would offer a frame of reference.

Companies might choose to use an average of the three-period returns as a proxy for g — this average will give greater weight to more recent results. Since historical returns implicitly incorporate the impact of options, the case can be made for valuing options based on the initial result of equation (3), rather than on the average of the first two iterations. (Investors and shareholders might prefer to skip the second iteration, regardless — for most, ease of use will outweigh the minor loss of accuracy.)

Even more practical in valuing company-stock options would be to follow a variation of William Sharpe's suggestion more than two decades ago to let the financial markets have their say. If companies which granted stock options were required to sell (or permitted employees to sell) a small percentage of these grants to the public markets, another estimate of option values — one which takes into account any variable which any equity-market participant deems relevant — would be available to companies and their stockholders.*

* In theory, a public-market valuation would be the most accurate of all. In practice, however, it would be vulnerable to manipulation by large-scale arbitrageurs who could short the underlying shares, hedge their positions by buying and bidding up the price of the options and then benefiting from any declines in the share price due to the "higher" expense of the options and the lower resulting net income. (Again, a concern such as this would be irrelevant to those who believe in semi-strong efficiency.)

For the equity markets as a whole, the inclusion of options as an operating expense would likely have an impact on stock prices, with some prices less affected than others. There could be both income effects (on market averages, as "new" information on income statements is assimilated) and substitution effects (on individual stocks, as the widely varying impacts are reported by companies).

While companies should have considerable discretion in determining the underlying assumptions, managements should be required to adjust the compensation charges if these assumptions are proven in time to be inaccurate. This process would be similar to the reserve adjustments made by insurance companies.

Companies would have a temptation towards optimism in their assumptions about expected life.* In contrast to the observation by Fisher Black and Myron Scholes that "a rational investor will not exercise a call option before maturity," companies routinely assume expected lives of company-stock options which are considerably shorter than the stated lives. Whether this assumes irrational behavior or rational behavior in irrational markets doesn't undermine the value of the methodology. (The fact that most reserve adjustments in the insurance industry involve additional charges — reflecting a pattern of under-reserving — is not a credible argument to ignore these expenses on the income statement.)

* As noted earlier, companies would have more incentive to be as accurate as possible in their assumptions concerning the expected growth rate of earnings. The greater the growth rate, the greater the value of the stock options, including those which have been granted to senior executives.

Certainly, there is no groundswell of support to change the current method of pension accounting, which is based on assumed, rather than actual, returns on assets. These assumed ROAs, usually in the optimistic 9-10% range, have allowed companies to report pension-related expenses which are lower than would be the case if actual ROAs were used.

Conclusion

The recognition of stock price as a component of company-stock-option valuation would assist investors in determining the intrinsic value of the underlying equities. If corporations provided their own projections for stock-price appreciation based on internal assumptions for return-on-invested-capital and retention ratios, current and prospective shareholders would have additional useful inputs on which to make their decisions.

The reality that assumptions about future stock prices are subjective (as with assumptions regarding variance in the Black-Scholes model) does not make them irrelevant.** Certainly, investors are already discounting a variety of important but uncertain factors in valuing equities.

** Nor should it be assumed that, given the differing components of the Black-Scholes model and the cost-of-grant model, that the results will differ widely. For example, Johnson & Johnson has produced perhaps the most predictable long-term growth of any company growing faster than 10% annually and therefore conceptually provides an ideal candidate for divergence between the Black-Scholes model and the cost-of-grant equations — low volatility / high growth. Yet, for the 1996-2001 period, the results are similar: using Black-Scholes, the aggregate cost was $1.1 billion or 4.5% of reported income; using equation (3) with two iterations, the cost was $1.5b or 6.2% (a 12% rate was assumed for g, below the fifty-year average of 14%). A much greater divergence was found between the results of the cost-of-exercise model (10.1%) and those of the other two models, which is not surprising given the strength in equity prices during the six-year period.

Practicality is not dependent on certainty; as John Maynard Keynes noted, it's preferable to be "vaguely right than precisely wrong". Option valuation models which incorporate assumptions about stock-price performance, though inexact in their results, provide the foundation for reasonably quantifying the cost of company-stock options to shareholders and for improving the transparency of financial statements.

The goal of improving the quality of equity analysis argues in favor of including option expense on the income statement and of providing projections of stock-price changes. Perhaps one positive legacy of the abuses in the financial markets will be a willingness to acknowledge that financial statements should seek to reflect, not recast, the health of Corporate America.

BIBLIOGRAPHY

Black, Fisher and Scholes, Myron S., 1973, "The Pricing of Options and Corporate Liabilities", Journal of Political Economy 81

Buffett, Warren E., 1984, "The Superinvestors of Graham-and-Doddsville", Hermes, Magazine of Columbia Business School; Appendix to "The Intelligent Investor", Harper & Row, Publishers

Buffett, Warren E., 2000, "Chairman's Letter", Berkshire Hathaway Annual Report

Investars, 2001, "Batting Averages for Brokers", www.investars.com/pr_may29.asp

Samuelson, Paul A., 1965, "Rational Theory of Warrant Pricing", Industrial Management Review 6

Sharpe, William F., 1978, "Investments", Prentice-Hall, Inc.