1	Standard & Poor’s Core Earnings Timothy A. Luehrman, Ph.D. Corporate Value Consulting October 23, 2002
2	Determining the Value of Stock Options Introduction: SFAS 123 Questions Does SFAS 123 require an option pricing model? If option value changes after being booked, can the company make an adjustment? Does the Black-Scholes model really work for non-traded employee stock options? What’s the difference between Black-Scholes and the Binomial model? What about non-transferability and vesting requirements? What about dilution? How should expected volatility be measured? What about American options?
3	SFAS 123 Issued October, 1995 Covers options, restricted stock, phantom stock, etc. Allows an election for “fixed” stock option plans: Fair value at grant date is expensed over the service period (usually the same as the vesting period), or Intrinsic value (generally zero) is expensed at grant date according to APB 25, with further expense to be recognized upon exercise. Companies electing to follow APB 25 must disclose: Pertinent details about plan and outstanding options Pro forma net income and EPS, as if fair value accounting had been adopted
4	Determining the Value of Stock Options è Simple answer: YES “The fair value of a stock option (or its equivalent) granted by a public entity shall be estimated using an option-pricing model (for example, the Black-Scholes or a binomial model) that takes into account as of the grant date the exercise price and the expected life of the option, the current price of the underlying stock and its expected volatility, expected dividends on the stock…” - SFAS 123 paragraph 19 What about market-based mechanisms such as Coca-Cola’s proposed “auction” mechanism? Auditors probably will require an “active” market Not clear that auction idea will benefit very many companies
5	Determining the Value of Stock Options è Simple answer: NO “The fair value of an option at the grant date shall not be subsequently adjusted for changes in the price of the underlying stock or its volatility, the life of the option, dividends on the stock, or the risk-free interest rate.” - SFAS 123 paragraph 19
6	Determining the Value of Stock Options The fundamental Black-Scholes insight is still very powerful: The option’s payoffs look like a leveraged position in the underlying stock If we can estimate “fair value” for untraded assets generally, we should be able to estimate “fair value” for untraded options When the underlying shares will be restricted following exercise, it may be legitimate to consider applying a discount to the share price used in the the pricing model “The fair value of a share of restricted stock awarded to an employee… is the same amount as a share of similarly restricted stock issued to a non-employee.” - SFAS 123 paragraph 18
7	Determining the Value of Stock Options There are some (economic) red flags that suggest alternatives to Black-Scholes should be considered: Event risk (litigation, R&D outcomes, etc.) Calls into question the standard log-normality assumption High dividends Increase the likelihood of early exercise Path-dependence or formula-driven exercise prices Black-Scholes assumes a fixed exercise price Onerous restrictions on trading Reduces confidence in input values (e.g. stock price) and in the model’s output
8	Determining the Value of Stock Options To a first approximation: Almost none. They are exploiting the same replicating strategy and “no-arbitrage” condition The most common versions of the Binomial Model are programmed to give same answer as Black-Scholes for European call However, a binomial lattice is more flexible than Black-Scholes Can handle American options Can handle discrete dividends Easy to include a term structure in interest rates or volatility Possible to program formulaic, path-dependent exercise prices
9	Determining the Value of Stock Options Employee Stock Options are generally non-transferable Liquidity can be obtained only by exercising the option Consequently, employee stock options tend to be exercised early SFAS 123 stipulates that this phenomenon should be treated by inputting expected life rather than contractual term in a model such as Black-Scholes Hence, a 10-year option might be valued under SFAS 123 using its “expected” life of, say, 5 years The resulting lower value is deemed to reflect an appropriate discount for non-transferability
10	Determining the Value of Stock Options Companies must support their estimates of expected life based on actual experience with a plan, if such data are available SFAS 123’s Appendix B contains guidance and illustrative calculations of expected life No additional discount is allowed under SFAS 123, either for lack of marketability or vesting requirements
11	Determining the Value of Stock Options Employee stock options are technically warrants, not calls When they are exercised, the company issues new shares and receives the exercise price In theory, this dilution effect makes warrant worth less than an otherwise identical call Most finance texts suggest: Warrant Value = [Call Value] – [Adjustment for Dilution] SFAS 123 does not mention any adjustment, nor do any of the worked examples include adjustments I infer that SFAS 123 does not permit a dilution adjustment
12	Determining the Value of Stock Options Expected volatility (s) is the standard deviation per period of future returns on underlying shares Estimates should be forward-looking, and period must match the unit of measurement for expected life SFAS 123 recommends use of historical volatility over the most recent period equal in length to the expected life See SFAS 123 Appendix F for sample calculations Historical volatility is not always reliable. In general, volatility is not constant over long periods Major changes in strategy, structure, etc. may cause permanent shifts in s Evolutionary (life cycle) change is common. It implies a term structure in volatility. Volatility changes that are correlated with market movements tend to be mean-reverting
13	Determining the Value of Stock Options Implied volatilities can be informative Use observed market values of traded options + an option pricing model to solve for implied volatility Note, however, that most traded options are short-term Finally, examine historical and implied volatilities for comparable companies Beware of differences in leverage Beware of company-specific, sources of volatility (e.g., litigation, control contests, publicity, etc.) Non-public companies are allowed to set s = 0. This gives a so-called “minimum value”. There is no good reason for such companies not to avail themselves of this right
14	Determining the Value of Stock Options In general, American options are worth more than similar European options if expected dividends are positive. The Binomial Model will pick up this extra value; Black-Scholes will not. However, SFAS 123 permits companies to value long-lived American options as if they were shorter-lived European options An example in SFAS 123 Appendix A (paragraph 170) values a 10-year American call with a 1% dividend yield, as if it were a European option with a 5-year expected life and 1% dividend yield The example doesn’t state which model was used, but the value given is clearly Black-Scholes, not Binomial
15	Determining the Value of Stock Options