Valuation Techniques: Discounted Cash Flow, Earnings Quality, Measures of Value Added, and Real Options

NOTES

1. A lattice model divides time between grant and option expiration into N discrete periods. At each time n, possible changes in the underlying stock price between times n and n + 1 are captured by two (or three) branches. This process is iterated until every possible path between n = 0 and n = N is mapped. Probabilities are then estimated along every stock price path. The stock option payoff outcomes and probabilities flow backward through the tree until a fair value of the option today is calculated. A simple lattice model for options is the binomial option-pricing model.

2. Statement of Financial Accounting Standards No. 123 (revised), Share-Based Payment (FAS 123R), makes compulsory the expensing of ESOs in the United States as of fiscal years commencing after June 15, 2005. Similar rules have been implemented by the International Accounting Standards Board and the Canadian Accounting Standards Board. FAS 123R permits the use of modified Black–Scholes methodologies but also envisages the use of lattice models; the standard specifically cites the HW model and illustrates its use with numerical examples. U.S. SEC Staff Accounting Bulletin No. 107 also refers to the HW model.

3. See Huddart (1994); Carpenter (1998); Detemple and Sundaresan (1999).

4. Some practitioners using a Black–Scholes approach do not distinguish between voluntary early exercise and termination-related exercise or forfeiture. Rather, they combine these factors into a single expected-life estimate. We ...