Valuing employee stock options

26Figure 3.6 Impact of suboptimal exercise behavior and stock price on option value in the binomial model.. Table 3.1 Effects of Changing Risk-Free Rates on Table 3.2 Effects of Changing

Valuing Employee

Stock Options

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to e-commerce, risk management, financial engineering, valuation, and nancial instrument analysis, as well as much more

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Copyright © 2004 by Johnathan Mun All rights reserved.

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An Executive Summary of the FAS 123 Valuation Implications 5

Technical Justification of Methodology Employed 22Options with Vesting and Suboptimal Behavior 26

Options Where Risk-Free Rate Changes over Time 29

v

Options Where Volatility Changes over Time 32Options Where Dividend Yield Changes over Time 32

CHAPTER 4

Haircuts on Nonmarketability, Modified Black-Scholes with

Applying Monte Carlo Simulation to Obtain

Applying Monte Carlo Simulation for Statistical

CHAPTER 6

ESO Expense Attribution Schedule as Minigrants 65

Binomial Lattices 80

CHAPTER 8

A Stock Option Provides Value in the Face of Uncertainty 92Binomial Lattices as a Discrete Simulation of Uncertainty 94Solving a Simple European Call Option Using

Solving American and European Options

Appendix 8A—Binomial, Trinomial, and

CHAPTER 9

PART THREE

A Sample Case Study Applying FAS 123

CHAPTER 10

Appendix 10A—Introduction to the Software 158

Thirty-Five Percent Volatility and 3-Year Maturity ESOs withVarying Stock Price, Suboptimal Behavior, Vesting Period,

Seventy Percent Volatility and 3-Year Maturity ESOs with Varying Stock Price, Suboptimal Behavior, Vesting Period,

Thirty-Five Percent Volatility and 5-Year Maturity ESOs withVarying Stock Price, Suboptimal Behavior, Vesting Period,

Seventy Percent Volatility and 5-Year Maturity ESOs with Varying Stock Price, Suboptimal Behavior, Vesting Period,

Thirty-Five Percent Volatility and 7-Year Maturity ESOs withVarying Stock Price, Suboptimal Behavior, Vesting Period,

Seventy Percent Volatility and 7-Year Maturity ESOs with Varying Stock Price, Suboptimal Behavior, Vesting Period,

Thirty-Five Percent Volatility and 10-Year Maturity ESOs withVarying Stock Price, Suboptimal Behavior, Vesting Period,

Seventy Percent Volatility and 10-Year Maturity ESOs with Varying Stock Price, Suboptimal Behavior, Vesting Period,

List of Figures and Tables

FIGURES

Figure 3.1 Tornado chart listing the critical input factors of a

Figure 3.2 Tornado chart listing the critical input factors of

Figure 3.3 Spider chart showing the nonlinear effects of input

Figure 3.4 Dynamic sensitivity with simultaneously changing

input factors in the binomial model 25Figure 3.5 Impact of suboptimal exercise behavior and vesting

on option value in the binomial model 26Figure 3.6 Impact of suboptimal exercise behavior and stock

price on option value in the binomial model 27Figure 3.7 Impact of suboptimal exercise behavior and volatility

on option value in the binomial model 28Figure 3.8 Impact of forfeiture rates and vesting on option

Figure 5.2 Distributional-fitting using historical, comparable,

Figure 5.5 Statistical confidence restrictions and

xi

Figure 8.5 Twenty percent volatility stock 91

Figure 8.7 Monte Carlo probability distributions of

Figure 8.10 The binomial lattice as a discrete simulation 96Figure 8.11 Lattice views with different volatilities 98Figure 8.12 European call option solved using the BSM and

dependent simulation techniques 135Figure 10.2 Results of stock price forecast using Monte

Figure 10A.7 Using ESO functions in existing

Table 3.1 Effects of Changing Risk-Free Rates on

Table 3.2 Effects of Changing Risk-Free Rates with Exotic

Table 3.3 Effects of Changing Volatilities on Option Value 33

Table 3.6 Effects of Changing Dividends over Time 35Table 3.7 Effects of Blackout Periods on Option Value 36Table 3.8 Effects of Significant Blackouts (Different Forfeiture

Table 3.9 Effects of Significant Blackouts (Different Dividend

Table 3.10 Effects of Significant Blackouts (Different Dividend

Yields and Suboptimal Exercise Behaviors) 38Table 4.1 Customized Binomial Lattice Valuation Results 43Table 4.2 Nonmarketability and Nontransferability Discount 44Table 4.3 Imputing the Expected Life for the BSM Using the

Table 4.4 Imputing the Expected Life for the BSM Using the

Binomial Lattice Results under Nonzero

Table 5.1(a–d) The Three Approaches’ Comparison Results 56Table 5.2 Single-Point Result Using a Customized

Table 6.3 Monthly Graded-Vesting Grants Allocation 72

Table 8.2 Higher Lattice Steps Equals Higher Granularity

Table 8.3 Comparing the Application of Forfeiture Rates 113Table 8A.1 Binomial and Trinomial Results (Basic Inputs) 118Table 8A.2 Binomial and Trinomial Results (Exotic Inputs) 118Table 10.1 Stock Price Forecast from Investor Relations 134Table 10.2 U.S Treasuries Risk-Free Spot Rates 137Table 10.3 Forward Risk-Free Rates Resulting from

Table 10.4 Generalized Autoregressive Conditional

Heteroskedasticity for Forecasting Volatility 139

Table 10.6 Estimating Suboptimal Exercise Behavior

Table 10.7 Estimating Suboptimal Exercise Behavior Multiples

with Statistical Hypothesis Tests 145

Table 10.9 Convergence of the Customized Binomial Lattice 148Table 10.10 Analytical Customized Binomial Lattice Results 149

Table 10.12 Contribution to Options Valuation Reduction 155

Table 10.15 Expense Allocation (Customized Binomial Lattice) 157Table 10.16 Dollar and Percentage Difference in Expenses 157Table A.1 Scenario Analysis on the Option Results Tables

This book was written after FASB released its proposed FAS 123 revision

in March 2004 As one of the valuation consultants and FASB advisors

on the FAS 123 initiative in 2003 and 2004, I would like to illustrate tothe finance and accounting world that what FASB has proposed is actuallypragmatic and applicable I am neither for nor against the expensing ofemployee stock options and would recuse myself from the philosophicaland sometimes emotional debate on whether employee stock optionsshould be expensed (that they are a part of an employee’s total compensa-tion, paid in part for the exchange of services, and are an economic oppor-tunity cost to the firm just like restricted stocks or other contingent claimsissued by the company) or should not be expensed (that they simply dilutethe holdings of existing shareholders, are a cashless expense, and if ex-pensed, provide no additional valuable information to the general investor

as to the financial health of the company but rather reduce the company’sprofitability and hence the ability to continue issuing more options to itsemployees) Rather, as an academic and valuation expert, my concern iswith creating a universal standard of understanding on how FAS 123 can

be uniformly applied to avoid ambiguity, and not whether employee stockoptions should be expensed Therefore, let it not be said that the new rul-ing is abandoned because it is not pragmatic This book is also my re-sponse to FASB board member Katherine Schipper’s direct request to me atthe FASB public panel roundtable meeting (Palo Alto, California, June2004) for assistance in providing more guidance on the overall valuationaspects of FAS 123

Hopefully the contents of this book will subdue some of the criticisms

on how binomial lattices can be used and applied in the real world The sults, tables, graphics, and sample cases illustrated throughout the bookwere calculated using customized binomial lattice software algorithms I de-veloped to assist FASB in its deliberations, and were based on actual real-life consulting and advisory experience on applying FAS 123 Inexperiencedcritics will be surprised at some of the findings in the book For instance,criticisms on the difficulty of finding the highly critical volatility may be un-founded because when real-life scenarios such as vesting, forfeitures, and

re-xv

suboptimal exercise behavior are added to the model, volatility plays amuch smaller and less prominent role In addition, the book illustrates howMonte Carlo simulation with correlations can be added (to simulatevolatility, suboptimal exercise behavior multiple, forfeiture rates, as well asother variables for thousands and even hundreds of thousands of simula-tion scenarios and trials) to provide a precision of up to $0.01 at a 99.9percent statistical confidence; coupled with a convergence test of the latticesteps, this provides a highly robust modeling methodology Future editions

of this book will include any and all changes to the FAS 123 requirementssince the March 2004 proposal

Parts One and Four are written specifically for the chief financial cer and finance directors, who are interested in understanding what are theimpacts and implications of using a binomial lattice versus a Black-Scholesmodel Parts Two and Three are targeted more toward the analysts, con-sultants, and accountants who require the technical knowledge and exam-ple cases to execute the analysis

offi-JOHNATHANMUN

San Francisco, California

JohnathanMun@cs.com

August 2004

The author is greatly indebted to Winny van Veeren of Veritas SoftwareCorporation for her great insights in ESO valuation In addition, a spe-cial word of thanks goes to Bill Falloon, senior editor at John Wiley &Sons, Inc., for his support and encouragement Finally, many thanks toMike Tovey, FAS 123 project manager, and members of the board of direc-tors at FASB for graciously allowing me to assist in their deliberations

J M

xvii

About the Author

Dr Johnathan C Mun is the author of several other well-known books,

including Real Options Analysis: Tools and Techniques (Wiley, 2002),

Real Options Analysis Course: Business Cases (Wiley, 2003), Faith Journey

(Xulon Press, 2003), and Applied Risk Analysis: Moving Beyond

Uncer-tainty (Wiley, 2003) He is also the creator of the Real Options Analysis

Toolkit software His books and software have been adopted by major versities in the United States and around the world, and are used widely at

uni-a vuni-ariety of Fortune 500 compuni-anies Dr Mun huni-as tuni-aught seminuni-ars uni-andworkshops worldwide on the topics of options valuation, risk analysis, sim-ulation, forecasting, financial analysis, and real options analysis This book

is the result of analytical work he did for the Financial Accounting dards Board in 2003 and 2004, as well as FAS 123 employee stock optionsvaluation advisory and consulting work he has performed at dozens of For-tune 500 firms

Stan-He is currently the Vice President of Analytics at Decisioneering, Inc.,

the makers of Real Options Analysis Toolkit and the Crystal Ball suite of

products, including applications of Monte Carlo simulation, optimization,options analysis, and forecasting He heads up the development of real op-tions analysis and financial analytics software products, analytical consult-ing, training, and technical support He is also a Visiting and AdjunctProfessor and has taught courses in financial management, investments, fi-nancial options, real options, economics, and statistics at the undergradu-ate and graduate MBA levels, as well as chairing several graduate Master’stheses committees He has taught at universities all over the world, fromthe University of Applied Sciences (Germany and Switzerland) to GoldenGate University (California), St Mary’s College (California), and others.Prior to joining Decisioneering, he was Consulting Manager and FinancialEconomist in the Valuation Services and Global Financial Services practice

of KPMG Consulting and a manager with the Economic Consulting vices practice at KPMG LLP He has extensive experience in econometricmodeling, financial options analysis, real options, economic analysis, andstatistics During his tenure both at Decisioneering and at KPMG Consult-ing, he consulted with, advised, and trained others in the areas of optionsanalysis, risk analysis, economic forecasting, and financial valuation for

Ser-xix

many Fortune 500 firms His experience prior to joining KPMG includedbeing Department Head of Financial Planning and Analysis at Viking, Inc.

of FedEx, responsible for performing financial forecasting, economicanalysis, and market research Prior to that, he had also performed some fi-nancial planning and freelance financial consulting work

Dr Mun received a Ph.D in Finance and Economics from Lehigh versity, where his research and academic interests were in the areas of In-vestment Finance, Econometric Modeling, Financial Options, CorporateFinance, and Microeconomic Theory He also has an MBA from NovaSoutheastern University and a BS in biology and physics from the Univer-sity of Miami He is certified in Financial Risk Management (FRM), a Cer-tified Financial Consultant (CFC), and a Certified Risk Analyst (CRA), and

Uni-is currently a third-level candidate for the Chartered Financial Analyst(CFA) He is a member of American Mensa, Phi Beta Kappa Honor Soci-ety, and Golden Key Honor Society as well as several other professional or-ganizations, including the Eastern and Southern Finance Associations,American Economic Association, and Global Association of Risk Profes-sionals Finally, he has written many academic articles published in the

Journal of the Advances in Quantitative Accounting and Finance, Global Finance Journal, International Financial Review, Journal of Applied Finan- cial Economics, Journal of International Financial Markets, Institutions and Money, Financial Engineering News, Journal of the Society of Petro- leum Engineers, and Journal of Financial Analysis.

He currently resides in California and can be reached via e-mail atJohnathanMun@cs.com

Valuing Employee

Stock Options

One

Impacts of the New FAS 123 Methodology

CHAPTER 1

Implications of the New FAS 123 Requirements

A BRIEF INTRODUCTION

In what the Wall Street Journal calls “among the most far-reaching steps

that the Financial Accounting Standards Board (FASB) has made in its 30year history,”1on March 31, 2004, FASB released a Proposed Statement ofFinancial Accounting Standards (FAS) on Share-based Payment amendingthe old FAS Statements 123 and 95 issued in October 1995.2

The original 1995 statements required that all share-based paymentarrangements with parties other than employees be accounted for in value.The revised 2004 statement retains the principle established in FAS 123(1995) that a public entity should measure the cost of employee services re-ceived in exchange for awards of equity instruments based on the fair value

of the instruments at the grant date In addition, the FASB has reaffirmedthe conclusion in the 2004 proposed Statement 123 revision that employeeservices received in exchange for equity instruments give rise to recogniz-able compensation cost as the services are used in the issuing entity’s opera-tions Based on that conclusion, this proposed Statement requires that suchcompensation cost be recognized in the financial statements

The FASB states in its proposal that it wants to maximize the

conver-gence of U.S and international accounting standards for employee stock

options (ESOs), and as such, the proposed 2004 FAS 123 revisions are

con-sistent with the International Accounting Standards Board’s share-based

payment (IFRS 2, issued February 19, 2004) At the date of writing, the

proposed Statement will be effective for new awards and portions of ing awards that have not yet vested at the beginning of the first fiscal yearstarting from December 15, 2004, with a possible delay in effective date toallow corporations to better prepare for the transition In anticipation ofthe Standard, many companies such as GE and Coca-Cola have already

exist-3

voluntarily expensed their ESOs at the time of writing This need for moretransparency is in line with the 2002 Sarbanes-Oxley Act, which requiresthat public companies develop and comply with accepted standards of fi-nancial and managerial prudence.

One of the areas of concern is the fair-market valuation of these ESOs.The binomial lattice is the preferred method in the proposed FAS 123 re-quirements, and critics argue that companies do not necessarily have theresources in-house or the data availability to perform complex valuationsthat not only are consistent with these new requirements but will pass anaudit as well

The goal of this book is to provide you with a better understanding ofthe valuation applications of a customized binomial lattice through a sys-tematic and objective assessment of the methodology This book is con-cerned only with the valuation of ESOs, and not the management of theseoptions.3The analyses performed in this book use my own proprietary cus-tomized binomial lattice computer algorithms and my software, the RealOptions Analysis Toolkit, and Decisioneering, Inc.’s Crystal Ball MonteCarlo simulation software This book was written based on my advisorywork with FASB in 2003 and 2004, graduate research work in the area ofoptions analysis, actual FAS 123 consulting projects with several Fortune

500 firms, and options software development experience, as well as myprior three books

This book is divided into four parts In Part One, the impacts of the

2004 FAS 123 are reviewed In Chapter 1, the implications of the new FAS

123 requirements with respect to the valuation of ESOs are introduced.Chapter 2 reviews the FAS 123 requirements in more detail, focusing onthe methodological requirements Chapter 3 illustrates the impacts to thevaluation results of using a customized binomial lattice versus a traditional

tradi-tional BSM described throughout this book is the original model withnạve assumptions without any modifications to include more exotic in-puts, which can be very mathematically complex.) The chapter also re-views the selection and justification of the customized binomial lattice, aswell as the effects of incorporating vesting, employee suboptimal exercisebehavior, forfeiture rates, changing risk-free rates, changing dividends, andchanging volatilities over time Chapter 4 reviews some of the other modi-fications to value such as nonmarketability, expected life analysis, and dilu-tion Chapter 5 provides an introduction to using Monte Carlo simulationcoupled with binomial lattices to obtain a robust and statistically valid set

of option valuation results Chapter 6 illustrates an example of how theoption valuation’s fair-market value can be allocated and expensed overthe vesting period of the option

In Part Two, the technical background required to run the BSM andcustomized binomial lattices are provided Chapter 7 provides a brief tech-nical background of the BSM and binomial lattice Chapter 8 providesmore detailed technical background on the use of a simple binomial lattice,complete with step-by-step valuation examples The customized binomiallattice algorithms are briefly explained Chapter 8’s appendix explores inmore detail the uses of binomial, trinomial, and multinomial lattices.Chapter 9 deals with how to obtain the model inputs, and their financial,statistical, and analytical justifications.

Chapter 10 in Part Three shows an example ESO fair-market valuationthat is based on several real-life cases.5 Chapter 10’s appendix provides a

“Getting Started Guide” in using the demo software in the accompanyingCD-ROM

Finally, Part Four provides multiple options valuation results that willprove valuable from the perspective of the analyst all the way to the chieffinancial officer when it comes to valuing the impact of using the binomiallattice versus BSM These tables provide a first-pass rough estimate of thefair-market value of the option using a customized binomial lattice, provid-ing management with valuable insights into the possible expenses beforehaving to delve into more detailed, complex, and protracted analyses Inthe face of implementing a challenging and potentially complex valuationsystem, firms need to first obtain a benchmark to understand if these moresophisticated models will provide comparable, lower, or higher values thanthe BSM

AN EXECUTIVE SUMMARY OF THE

FAS 123 VALUATION IMPLICATIONS

This book broaches the subject of fair-market valuation through an cal assessment of the three mainstream approaches used in option pricing,and provides guidance on using them, coupled with the mathematical back-ground, sample case study, and demo software to help the reader get startedwith ESO valuation The first approach is a set of closed-form models,6in-cluding the BSM for option pricing and the American option approxima-tion pricing models The second approach is the use of Monte Carlopath-dependent simulation, including its applications in option pricing aswell as its use in simulating the option model’s uncertain and probabilisticinputs The third and final approach is the use of lattices and the customizedbinomial lattices applied throughout this book These three sets of method-ologies are reviewed based on several criteria, including method applicabil-ity, underlying assumptions, robustness of analytical results, and ease of use.7

analyti-Based on the results illustrated throughout the book, it can be cluded that the BSM, albeit theoretically correct and elegant, is insufficientand inappropriately applied when it comes to quantifying the fair-marketvalue of an ESO This is because the BSM is applicable only to Europeanoptions without dividends, where the holder of the option can exercise theoption only on its maturity date and the underlying stock does not pay anydividends However, in reality, most ESOs are American-type options withdividends, where the option holder can execute the option at any time up

con-to (after the vesting period and except blackout dates) and including thematurity date while the underlying stock pays dividends A stock’s pricedrops by approximately the amount of the dividend on the ex-dividenddate, which means that the value of an American stock option (with itsability for early exercise) is greater than that of a European-type option.However, for fairness of comparison, the Generalized Black-Scholes model(GBM) is used—the GBM allows for the inclusion of dividends albeit it isapplicable only for valuing European options The terms BSM and GBMwill be used interchangeably throughout this book, which describes theoriginal models developed by Black and Scholes without any modifications(the correct model will be used whenever appropriate)

In addition, under real-world conditions, ESOs have blackout datesand a time to vesting before the employee can execute the option, which isalso contingent on the firm and/or the individual employee attaining aspecific performance level (e.g., profitability, growth rate, or stock pricehitting a minimum barrier before the options become live), and subject toforfeitures when the employee leaves the firm or is terminated prematurelybefore reaching the vested period Also, certain options follow a tranching

or graduated scale, where a certain percentage of the stock option grantsbecomes exercisable every year, and if the firm underperforms, it may berequired to repurchase the options at a specific termination price Just asimportant, the GBM assumes that all employees execute their options op-timally—that is, the model assumes that every employee is intelligentenough to execute the option whenever it becomes optimal to do so In re-ality, employees tend to execute their stock options prematurely and oftensuboptimally The GBM or BSM do not adequately account for this sub-optimal early exercise behavior and subsequently overvalue the option(sometimes significantly) The firm may undergo some corporate restruc-turing (e.g., divestitures, or mergers and acquisitions that may require astock swap that changes the volatility of the underlying stock) and henceits underlying stock’s volatility may change over time In addition, risk-free rates change over time (both U.S Treasury spot rates and forwardrates fluctuate) and will impact the value of the option The same applies

to dividend policy, where dividend payout ratios can change over the life

of an ESO In addition, ESOs cannot be executed during blackout periods(typically weeks before and afer earnings announcements), and the ESOs

in general are nonmarketable and nontransferable (cannot be freelybought or sold in an open market) Finally, options that are granted maysometimes be forfeited by employees when they leave or are terminatedduring the vesting period (alternatively, employees have a limited time,typically 30 to 90 days, to exercise the portion of the options that havevested, after they leave the firm) All these real-life scenarios make theGBM and BSM insufficient and inappropriate when used to place a fair-market value on the option grant In summary, firms can implement a va-riety of provisions that affect the fair value of the options whereas theabove list is only a few examples

Generally speaking, the BSM and GBM typically overstate the

fair-market value of ESOs where there is suboptimal early exercise behaviorcoupled with vesting requirements and where employee forfeitures occur,

or when the risk-free rates, dividends, and volatilities change over the life

of the option In fact, firms using the BSM and GBM to value and expenseESOs may be significantly overstating their true expense, typically incur-ring hundreds of thousands to tens of millions of dollars in excess expensesper year.8

The analyses in this book illustrate that under very specific tions (European options with and without dividends) the binomial lat-tice and Monte Carlo simulation approaches yield identical values to theGBM, indicating that the two former approaches are robust and exact atthe limit When American options with dividends are analyzed, the tra-ditional BSM and GBM undervalue the options, whereas binomial lat-tices and American options approximation models are more exact.However, when specific real-life business conditions are modeled (i.e.,forfeiture rates, probability that the employee leaves or is terminated,time-vesting, blackout dates, tranching, employee suboptimal exercisebehavior, changing risk-free rates, and so forth), the American approxi-mation models or Monte Carlo simulation by themselves are also insuffi-cient to capture all of the real-life nuances Only when the binomiallattice (which is highly flexible in its modeling capabilities) is used willthe true fair-market value of the stock option be captured—Monte Carlosimulation can be applied to further simulate the uncertain inputs that

condi-go into the binomial lattices That is, the binomial lattice is used to culate the American stock option with dividend while the inputs into thebinomial lattice can be simulated to capture the uncertainty and proba-bilistic effects of the real-life conditions mentioned Basic binomial lat-tices are extremely easy to use and apply as compared with the othermethods However, in the case of FAS 123, more complex customized

cal-binomial lattices are required, but their analytics are based on the simplebinomial lattice In addition, a comparison of other lattices (trinomialsand multinomials) indicates that the binomial lattice is still the preferredmethod (all lattices provide similar results at the limit, while binomiallattices are the easiest and most convenient to compute).

Binomial lattices can be customized to account for exotic events such asstock price barriers (a barrier option exists when the stock option becomes ei-ther in-the-money or out-of-the-money only when it hits a stock price bar-rier), vesting tranches (a specific percent of the options granted becomesvested or exercisable each year), changing volatilities, dividends, and risk-freerates over time (changing business and economic conditions or corporate re-structuring), employee suboptimal exercise behaviors (early execution by em-ployees who require liquidity or are risk-averse), forfeitures (employeesleaving or terminated during and after the vesting period), and so forth—thesame conditions where the BSM and GBM fail miserably Monte Carlo simu-lation then can be applied to simulate the probabilities of forfeitures and em-ployee suboptimal behavior, and these simulated values can be used as the

inputs into the binomial lattices Without the use of binomial lattices, firms

may be significantly overvaluing ESOs and could potentially end up pensing millions of dollars per year.

overex-In using the highly flexible binomial lattices with Monte Carlo tion, firms can now create exotic ESOs with different flavors such as perfor-mance-based options (i.e., a percentage of ESOs that come into-the-money

simula-if the firm hits a particular earnings level, and this percentage may increasebased on some graded scale) and value them accordingly

This book provides a comprehensive review of all the necessary stepsand methodologies required to value ESOs No matter which direction thefinal requirements lean toward, the methodologies described here can bemixed and matched accordingly

SUMMARY AND KEY POINTS

■ It has been over 30 years since Fischer Black and Myron Scholes rived their option pricing model and significant advancements havebeen made; therefore, do not restrict stock option pricing to one spe-cific model (the BSM) where a plethora of other models and applica-tions can be explored

de-■ The three mainstream approaches to valuing stock options are form models (e.g., BSM, GBM, and American option approximationmodels), Monte Carlo simulation, and binomial lattices

closed-■ The BSM and GBM will typically overstate the fair value of ESOs

where there is suboptimal early exercise behavior coupled with vesting

requirements and option forfeitures In fact, firms using the BSM and

GBM to value and expense ESOs may be significantly overstating their true expense.

■ The BSM requires many underlying assumptions before it works, and

as such, has significant limitations, including being applicable only forEuropean options without dividends In addition, American option ap-proximation models are very complex and difficult to create in aspreadsheet.9The BSM cannot account for American options, options

based on stocks that pay dividends (the GBM can, however, accountfor dividends in a European option), forfeitures, underperformance,stock price barriers, vesting periods, blackout dates, changing businessenvironments and volatilities, suboptimal early exercise, and a slew ofother conditions

■ Monte Carlo simulation when used alone is another option valuationapproach, but is restricted only to European options Simulation can

be used in two different ways: solving the option’s fair-market valuethrough path simulations of stock prices, or in conjunction with otherapproaches (e.g., binomial lattices and closed-form models) to capturemultiple sources of uncertainty in the model.10

■ Binomial lattices are flexible and easy to implement They are capable

of valuing American-type stock options with dividends but requirecomputational power Software applications should be used to facili-tate this computation Binomial lattices can be used to calculate Amer-ican options paying dividends and can be easily adapted to solveoptions with stock price barriers and used in conjunction with MonteCarlo simulation to account for the uncertain input assumptions (e.g.,probabilities of forfeiture, suboptimal exercise behavior, vesting,blackout periods, underperformance, and so forth)

■ Based on the analyses throughout the book, it is recommended that theuse of a model that assumes an ESO is European style, when in fact theoption is an exotic American style option with vesting, should not bepermitted as this substantially overstates compensation expense Manyfactors (e.g., vesting, suboptimal exercise behavior, performance-basedoptions, blackout dates, and forfeitures) influence the fair value ofESOs, and a binomial lattice approach to valuation that considersthese factors should be used Option valuations using BSM, GBM, orother closed-form models should not be permitted when the require-ments for those models are not met Binomial lattice valuation modelsshould be used instead

CHAPTER 2

The 2004 Proposed FAS 123 Requirements

FAS 123 BACKGROUND

The proposed 2004 FAS 123 revision explains that a better estimate of the

fair value of an employee share option may be obtained by using a

bino-mial lattice model that incorporates employees’ expected exercise and

ex-pected post-vesting employment termination behavior than by using a

closed-form model (such as the Black-Scholes-Merton or BSM formula)

with a single weighted-average expected option term as an input Further,this revised statement does not permit the use of the minimum valuemethod as a substitute for the fair-value-based method.1

In addition, the 1995 FAS 123 provided alternative methods of suring and recognizing compensation cost for awards with graded vest-ing—that is, awards for which different parts vest at different times Therevised 2004 FAS 123 requires a single method under which those differentparts are treated as separate awards in estimating fair value and attributingcompensation cost

mea-The 1995 FAS 123 permitted enterprises the option of continuing touse Opinion 25’s intrinsic-value method of accounting for share-based pay-ments to employees provided those enterprises supplementally disclosedpro forma net income and related pro forma earnings-per-share informa-tion (if earnings per share is presented) as if the fair-value-based method ofaccounting had been used For the reasons described in paragraphs C26through C30 of the proposed 2004 FAS 123 revision, the FASB concludedthat such pro forma disclosures are not an appropriate substitute for recog-nition of compensation cost in the financial statements The FASB Board ofDirectors believes fair value is the relevant measurement attribute and grantdate is the relevant measurement date

11

Further, the FASB has determined that the BSM formula and similarclosed-form models do not produce reasonable estimates of fair value be-cause they do not adequately take into account the unique characteristics

of employee share options The FASB recognizes that closed-form modelsmay not necessarily be the best available technique for estimating the fairvalue of employee share options—they believe that a lattice model (as de-fined in paragraph E1 of the 2004 FAS 123) is preferable because it offersthe greater flexibility needed to reflect the unique characteristics of em-ployee share options and similar instruments This provides support for theanalyses performed throughout the book, which applies the customized bi-nomial lattice

In addition, the 2004 FAS 123 also suggests that information otherthan historical volatility should be used in estimating expected volatility,and explicitly notes that defaulting to historical volatility as the estimate ofexpected volatility without taking into consideration other available infor-mation is not appropriate

The FASB concluded that the 2004 proposed FAS 123 would require asingle method of accruing compensation cost for awards with a graded vest-ing schedule This statement considers an award with a graded vestingschedule to be in substance separate awards, each with a different fair valuemeasurement and requisite service period, and would require that they beaccounted for separately That treatment results in a recognition patternthat attributes more compensation cost to earlier portions of the combinedvesting period of an award and less compensation cost to later portions.This statement would require the modified prospective method of transitionfor public companies and would not permit retroactive application

The estimated fair value of an equity instrument on the date it isgranted should not reflect the effects of vesting conditions or other restric-tions that apply only during the vesting period Those effects are reflected

by recognizing compensation cost only for awards that actually vest cause the requisite service is provided

be-If observable market prices of identical or similar equity or liability struments of the entity are not available, the fair value of equity and liabil-ity instruments awarded to employees shall be estimated by using avaluation technique that (1) is applied in a manner consistent with the fairvalue measurement objective and the other requirements of Statement 123,(2) is based on established principles of financial economic theory and gen-erally accepted by experts in that field (paragraph B9 of the 2004 FAS123), and (3) reflects any and all substantive characteristics of the instru-ment (except for those characteristics explicitly excluded, such as vestingconditions and reload features)

in-In estimating the fair value of employee share options at the grantdate, the determination of the amount at which the instruments being val-ued would be exchanged would factor in expectations of the probabilitythat the options would vest (that is, that the service or performance vestingconditions would be satisfied) The estimated fair value of the equity in-struments at grant date does not take into account the effect on fair value

of vesting conditions and other restrictions prior to vesting

Several valuation techniques, including a lattice model (an example ofwhich is a binomial model) and a closed-form model (an example of which

is the BSM) meet the criteria required by Statement 123 for estimating thefair values of employee share options and similar instruments Those valu-

ation techniques or models, sometimes referred to as option-pricing

mod-els, are based on well-established financial economic theory Those models

are used by valuation professionals, dealers in derivative instruments, andother experts to estimate the fair values of options and similar instrumentsrelated to equity securities, currencies, interest rates, and commodities.Those models are used to establish trade prices for derivative instruments,

to establish fair market values for U.S tax purposes, and to establish ues in adjudications Both a lattice model and a closed-form model can beadjusted to account for the characteristics of share options and similar in-struments granted to employees

val-The selection of a valuation model will depend on the substantive acteristics of each arrangement and the availability of data necessary to usethe model A valuation model that is more fully able to capture and betterreflects those characteristics is preferable and should be used if it is practica-ble to do so For example, the BSM formula, a closed-form model, assumesthat option exercises occur at the end of an option’s contractual term, andthat volatility, dividends, and risk-free interest rates are constant over theoption’s term If used to estimate the fair value of employee share optionsand similar instruments, the BSM formula must be adjusted to take account

char-of certain characteristics char-of employee share options and similar instrumentsthat are not consistent with the assumptions of the model (e.g., exerciseprior to the end of the option’s contractual term, and changing volatilityand dividends) Because of the nature of the formula, those adjustmentstake the form of weighted-average assumptions about those characteristics

In contrast, a lattice model can be designed to incorporate certain istics of employee share options and similar instruments; it can accommo-date changes in dividends and volatility over the option’s contractual term,estimates of expected option exercise patterns during the option’s contrac-tual term, and blackout periods A lattice model, therefore, is more fullyable to capture and better reflects the characteristics of a particular em-ployee share option or similar instrument in the estimate of fair value

character-Entities that do not have reasonable access to the data required by alattice model may conclude that a closed-form model provides a reason-able estimate of fair value; those entities subsequently may obtain rea-sonable access to the data and decide to use a lattice model Further,entities for which compensation cost is not a significant element of the fi-nancial statements may conclude that a closed-form model produces es-timates of fair value that are not materially different from thoseproduced by a lattice model and that this pattern can be reasonably as-sumed to persist Those entities may conclude that a closed-form modelprovides reasonable estimates of fair value Public entities for whichcompensation cost from share option arrangements is a significant ele-ment of the financial statements may conclude, when inputs are avail-able, that a lattice model would provide a better estimate of fair valuebecause of its ability to more fully capture and better reflect the charac-teristics of a particular employee share option or similar instrument inthe estimate of fair value.

A U.S entity issuing an option on its own shares must use as the free interest rates the implied yields from the U.S Treasury zero-couponyield curve over the expected term of the option if the entity is using a lat-tice model incorporating the option’s contractual term If the entity is using

risk-a closed-form model, the risk-free interest rrisk-ate is the implied yield currentlyavailable on U.S Treasury zero-coupon issues with a remaining term equal

to the expected term used as the input to the model

There is likely to be a range of reasonable estimates for expectedvolatility, dividends, and option term If no amount within the range ismore or less likely than any other amount, an average of the range (its

expected value) should be used That entity might base expectations

about future volatility on the average volatilities of similar entities for

an appropriate period following their going public Data and tions used to estimate the fair value of equity and liability instrumentsgranted to employees should be determined in a consistent manner fromperiod to period

assump-For employee share options and similar instruments, a lattice model ispreferable to a closed-form model and, therefore, is preferable for justify-ing a change in accounting principle Once an entity changes its valuationtechnique for employee share options and similar instruments to a latticemodel, it may not change to a less preferable valuation technique

An entity should not estimate share option fair values based on ical average share option lives, historical share price volatility, or historicaldividends (whether stated as a yield or a dollar amount) without consider-ing the extent to which future experience is reasonably expected to differfrom historical experience

histor-Expected term is an input to a closed-form model However, if an tity uses a lattice model that has been modified to take into account an op-tion’s contractual term and employees’ expected exercise and post-vestingemployment termination behavior, the expected term is estimated based onthe resulting output of the lattice For example, an entity’s experiencemight indicate that option holders tend to exercise those options when theshare price reaches 200 percent of the exercise price If so, that entity mightuse a lattice model that assumes exercise of the option at each node alongeach share price path in a lattice at which the early exercise expectation ismet, provided that the option is vested and exercisable at that point More-over, such a model would assume exercise at the end of the contractualterm on price paths along which the exercise expectation is not met but theoptions are in-the-money at the end of the contractual term That methodrecognizes that employees’ exercise behavior is correlated with the price ofthe underlying share Employees’ expected post-vesting employment termi-nation behavior also would be factored in Expected term then could be es-timated based on the output of the resulting lattice.

en-Other factors that may affect expectations about employees’ exerciseand postvesting employment termination behavior include the following:

■ The vesting period of the award An option’s expected term must atleast include the vesting period

■ Employees’ past exercise and postvesting employment termination havior for similar grants

be-■ Expected volatility of the price of the underlying share

■ Blackout periods and other coexisting arrangements such as ments that allow for exercise

agree-Option value is not a linear function of option term; value increases at adecreasing rate as the term lengthens For example, a two-year option isworth less than twice as much as a one-year option, other things beingequal Accordingly, estimating the fair value of an option based on a singleexpected term that effectively averages the widely differing exercise andpost-vesting employment termination behaviors of identifiable groups ofemployees will potentially misstate the value of the entire award

FAS 123 also provides guidance on how volatility can be computed:

■ The term structure of the volatility of the share price over the most cent period that is generally commensurate with (1) the contractualterm of the option if a lattice model is being used to estimate fairvalue or (2) the expected term of the option if a closed-form model isbeing used