Tax Valuation Insights

Valuing Stock Options in Compliance with Section 409A Reid Chanon

Internal Revenue Code Section 409A provides the income tax provisions related to deferred compensation—including employee stock options. Section 409A does not prescribe a universal methodology to value employee stock options. However, many analysts apply pricing models—such as the Black-Scholes option pricing model (“Black-Scholes”) or a binomial model—to value employee stock options. This discussion provides (1) a summary of Section 409A and (2) an overview of common option pricing models.

ntroduction Therefore, it is common for analysts to apply I an option pricing model to value employee stock Internal Revenue Code Section 409A applies to the options. This is because option pricing models allow compensation that is earned by an employee in one analysts to assign probabilistic assumptions to ana- year but is paid in a future year, such as a nonquali- lyze contingent events. fied deferred compensation plan. The value of employee stock options is contin- A nonqualified deferred compensation plan is an gent on the economic circumstances that will exist arrangement between an employer and an employee in the future when the employee has the right to to pay the employee compensation in the future. receive the shares. Such arrangements include the following: 1. Nonqualified retirement plans Section 409A Overview 2. Elective deferrals of compensation Section 409A requires that all compensation deferred 3. Severance and separation programs for the taxable year and all preceding taxable years 4. Post-employment payments provided for in be included in gross income for the taxable year an employment agreement unless there is a substantial risk of forfeiture. 5. Equity incentive programs, such as stock Section 409A applies to all deferred compensa- options tion that an employee earns for the taxable year and imposes severe tax penalties on noncompliant deferred compensation arrangements. According to Section 409A, every time a corpo- In order to avoid noncompliant arrangements, ration issues a stock option to an employee, there company managements and their analysts should should be a valuation of the corporation’s common understand how to establish (1) the value of the stock. However, Section 409A does not provide a shares that underlie the option and (2) the universally accepted valuation method to value price for the stock option. employee stock options. Noncompliant arrangements may include the For this reason, it is up to the employer and its following: advisers to elect a practical valuation method, or 1. Stock options and stock appreciation rights application, to estimate the fair market value of the that are granted with an exercise price employee stock options. below fair market value at the time of grant

64 INSIGHTS • AUTUMN 2016 www .willamette .com 2. Stock options or stock appreciation rights 1. The value of tangible and intangible assets that are not affiliated with the common of the company less its liabilities (an asset- stock of the company the employee works based approach valuation analysis) for or its parent company 2. The present value of expected future cash- 3. Rights that are added later to further defer cash flow of the company (an income the stock option or stock appreciation approach valuation analysis) rights1 3. Recent arm’s-length transactions involving the sale or transfer of the subject stock (a According to Section 409A, stock options and market approach valuation analysis) stock appreciation rights that are noncompliant 4. The market value of stock or equity interest may result in significant unfavorable tax conse- in similar companies (a market approach quences for the employee and the employer. valuation analysis), based on: For example, the nonqualified deferred compen- a. observable trading prices on an repu- sation in question will be fully taxable as soon as the table securities market or employee has a vested right to receive it. In addi- b. an amount paid in a recent arm’s-length tion, a tax penalty of 20 percent may be applied.2 private transaction 5. A method that is regularly used for other purposes that have a material economic Valuing Public and Private effect on the company, its stockholders, or its creditors (which may include relevant Corporation Stock factors such as ownership control price To avoid unfavorable tax consequences under premiums or discounts for lack of market- Section 409A, the exercise price of the stock option ability)4 must not be less than the fair market value of the underlying stock as of the date of the grant. A valuation method is not considered to be rea- The following valuation guidelines are appropri- sonable if: ate for both public and private corporation stock. 1. it fails to reflect important information that is known or knowable as of the grant date Determining Fair Market Value of that may materially affect the value of the Public Company Stock corporation’s stock such as: a. the resolution of material litigation or The fair market value of stock that is actively traded on an organized securities market may be based b. the issuance of a patent, or upon: 2. the valuation date was more than 12 months prior to the date for which the valuation is 1. the most recent sale price before the grant, being used.5 2. the closing price on the trading day before the grant, 3. the arithmetic mean of the high and low Valuation Safe Harbors for prices on the trading day before or the trad- ing day of the grant, or Private Company Stock 4. another reasonable basis using actual The Internal Revenue Service (the “Service”) may transactions in the stock as reported by rebut this presumption by showing that the con- the market.3 cluded value of company stock was “grossly unrea- sonable” by the improper use of the valuation Determining the Fair Market Value of method.6 A private company’s use of a valuation method Private Company Stock is presumed to be reasonable under the following The fair market value as of the date of the grant of three safe harbor provisions. stock that is not traded on a reputable securities market is to be established by reasonable applica- tion of a recognized valuation method. Safe Harbor I The fair market value of the private company stock A reasonable valuation method may include one is estimated by a qualified independent appraiser or more of the following considerations: that has:

www .willamette .com INSIGHTS • AUTUMN 2016 65 1. met educational and 2. A is fundamentally a for- “Stock options in experience requirements ward contract. But, future contracts differ or from forward contracts in that futures:8 the public market 2. a professional designa- a. are standardized and traded on orga- differ from a stock tion recognized by the nized exchanges whereas the terms Secretary of Treasury. of a can be privately option issued by a negotiated, b. are highly regulated compared to for- closely held compa- Such requirements must wards, and ny because they are be met 12 months prior to the date for which the valu- c. are backed by the clearinghouse. issued by a third ation of employee stock 3. A is equivalent to a series of forward party rather than options is being used. contracts. A swap is simply defined as an agreement between one party to pay the the public company floating rate of interest on a determined Safe Harbor II itself.” amount of principle, and the counterparty The fair market value is agrees to pay a fixed rate of interest in based on a formula (e.g., return.9 multiple of book value or 4. A credit is a contract that pro- multiple of earnings or a combination of both) that vides protection for the lender against is regularly used for other purposes that have a default by the borrower. material economic effect on the company, its stock- holders, or its creditors. Stock options in the public market differ from a stock option issued by a closely held company Safe Harbor III because they are issued by a third party rather than The fair market value is estimated by a qualified the public company itself. individual who is not independent of the company. A “” gives its holder the right, but However, this safe harbor provision usually applies not the obligation, to buy the underlying asset at a only to illiquid stock of a start-up company. predetermined price within a specific time period. A “” gives its holder the right, but not n mployee tock ption s a the obligation, to sell the underlying asset at a pre- A E S O I determined price within a specific time period. Derivative Security The “” is the stated price per share An is a derivative security for which underlying stock may be purchased or whose value is contingent on the price of the com- sold by the option holder upon exercise of the pany stock. A stock option gives the holder the option contract. In other words, the “strike price” right, but not the obligation, to acquire stock in a represents the exercise price specified in the option company within a specific time period. contract. In addition, a stock option typically includes an An “ date” is the last day for the holder exercise price and a stated expiration date. Unlike to exercise their right. futures and forward contracts, options do not have An “American option” allows the owner to exer- an obligation where final purchases are required. cise the option at any time before or at expiration. The following discussion presents a brief descrip- A “European option” can be exercised only on tion of other common derivatives. the expiration date. Thus, an “American option” has 1. A forward contract is an agreement between more flexibility than the “European option,” so it is one party to buy, and the other to sell, an worth at least as much and typically more. asset at a predetermined price. The price If the value of the underlying asset is greater at which the exchange occurs is set at the than the exercise price, the option is referred to time of the initial contracting. as being “in the money.” Being “in the money” If the value of the asset decreases provides a positive payoff if the option is exercised. between the time the contract is entered Conversely, if the value of the underlying asset is into and the time it is executed, then the below the exercise price, the option is referred to as seller has a gain and the buyer has a loss.7 being “out of the money.”

66 INSIGHTS • AUTUMN 2016 www .willamette .com If the value of the underlying asset equals the 6. The effect of expected dividends on the strike price, then the option is referred to as being underlying asset. “at the money.” Thus, the amount that is in the In general, an option holder is not entitled money or the difference between the current price to receive the dividend that is paid to the of the underlying asset that is above its strike price holder of the underlying asset. is referred to as its “intrinsic value” of the option, When an investor holds an underlying and zero otherwise. asset on the ex-dividend date, the underlying The difference between the price of an option asset will usually depreciate in value by the and its intrinsic value is referred to as being the amount of dividends paid per share. “time value” of the option on a certain date. This is primarily because of the compa- A “stock ” is of a longer duration than a ny’s retained earnings that could have been stock option and is issued by the company rather reinvested into the company are now being than by third parties. The pricing of a warrant must paid out as a dividend—usually as a cash take into consideration the potential dilution effect or a stock dividend—to the shareholder, on earnings. which theoretically should reflect an overall decrease in the company’s market cap. As a result, call options are usually more valuable when dividends are zero or mini- Factors Involved with Valuing mal. Stock Options Conversely, after the ex-dividend has Many option pricing models incorporate the follow- been declared, put options are typically ing six factors: more valuable. 1. The current price of the underlying asset. Call options increase in value when the price of the underlying asset appreciates Important Dates relative to the strike price. Conversely, put Employee stock option values are usually sensi- options increase in value when the price of tive to various dates. Therefore, an analyst should the underlying asset depreciates relative to understand the following types of dates when valu- the strike price. ing stock options: 2. The strike price. A call option is in the money when the Grant Date strike price is below the price of the under- The grant date is the date when a company issues lying asset. Conversely, a put option is in stock options to the employee. In other words, it is the money when the strike price is above the date when the company and the employee agree the price of the underlying asset. to the terms of the employee stock options. 3. The time to expiration. A call or put option is more valuable when the time to expiration is longer and are Vesting Period less valuable as their time to expiration The vesting period is a restricted time period dur- decreases. ing which the employee does not yet own the stock options. Cliff vesting is when an employee owns the 4. The of the underlying asset. stock options at an agreed upon date. Volatility is the annualized standard devia- Equal annual vesting is when an employee tion of returns. A high standard devia- 10 receives an annual right to own a fixed percentage tion in the pricing of the underlying asset of their stock options. increases the probability that it will be higher than the strike price on the expira- Similarly, variable annual vesting is when an tion date. Put and call options become more employee receives an annual right to own their valuable as the volatility of the pricing of stock option based on a formula. the underlying asset increases. 5. The risk-free rate. Exercise Date As the risk-free rate increases, call options The exercise date is the date on which an employee become more valuable and put options may exercise his or her stock options. Under become less valuable. Section 409A, an employees can only exercise their

www .willamette .com INSIGHTS • AUTUMN 2016 67 stock options under the follow- dom movements of microscopic particles suspended “Many analysts ing circumstances: in a liquid or a gas. 1. An employee separates The Black-Scholes model is primarily based on consider using from service the assumption that an investor could create a per- option pricing 2. Employee disability fectly hedged position to eliminate risk by buying an models such as 3. Employee death option and selling the underlying stock. 4. An agreed upon future date Therefore, any movement in price would be off- the Black-Scholes set by a position in the option and the underlying 5. A change in control of the stock. The value of the call option is equal to the model or a binomi- business present value, discounted at the risk-free rate, of al model to value 6. The occurrence of an the expected net proceeds received after closing the unforeseeable emergency employee stock 11 hedge at the option’s expiration date.12 Thus, an option is priced correctly when the options.” Expiration Date perfect hedge yields the risk-free rate. The expiration date is the last Some of the other assumptions underlying the day an employee’s options may be exercised and is Black-Scholes model include the following: provided in the terms of the contract. 1. There are no commissions or other transac- tion costs in buying or selling the stock or the option. ption ricing odels O P M 2. The short-term risk-free interest rate is Section 409A does not prescribe a universal meth- known and is constant through time. odology to value employee stock options. Many analysts consider using option pricing models such 3. Trading is continuous through time follow- as the Black-Scholes model or a binomial model to ing a geometric Brownian motion. value employee stock options. 4. The underlying stock pays no dividends and The Black-Scholes model effectively treats the makes no other distributions. time between the current time and the expiration 5. There is unrestricted access to credit, of the options as one time period divided into an and the securities are perfectly divisible. infinite number of discrete periods. However, it is possible to borrow any frac- The binomial option pricing model, on the other tion of the price of a security to buy, or to hand, divides the time period between the current hold it, at the short-term risk-free rate. time and the expiration of the options into discrete periods—most often one year. 6. The stock price follows a random walk with a log normal distribution. The binomial model is sometimes used to esti- mate the effect on the value of employee stock 7. The volatility of the stock is constant over options of factors such as the following: the life of the option. 1. Vesting periods 8. The option can be exercised only at matu- 2. Employee turnover rity. 3. Blackout periods 9. A seller who does not own a security (a 4. Change in risk-free rates short seller) will simply accept a future date by paying for an amount equal to the price 5. Volatility of the security on that date. While this short sale is outstanding, the short seller will have The following discussion gives a brief overview of the use of, or interest on, the proceeds of the Black-Scholes model and the binomial models. the sale. 10. The tax rate, if any, is identical for all trans- Black-Scholes Option Pricing Model actions and all market participants.13 In 1973, Fisher Black and Myron Scholes developed an option pricing model for the valuation of publicly The Black-Scholes formulas for the prices at traded options on non-dividend-paying stocks. time 0 of a European call option on a non-dividend- The model was derived from Robert Brown’s paying stock and a European put option on a non- “Brownian Motion model,” which describes the ran- dividend-paying stock are as follows:14

68 INSIGHTS • AUTUMN 2016 www .willamette .com Page 7

Black Scholes Option Pricing Model In 1973, Fisher Black and Myron Scholes, developed an option pricing model for the valuation of publicly traded options on non-dividend paying stocks. The model was derived from Robert Brown’s, Brownian Motion model, which describes the random movements of microscopic particles suspended in a liquid or a gas.

The Black Scholes model is primarily based on the assumption that an investor could create a perfectly hedged position to eliminate risk by buying an option and selling the underlying stock. Therefore, any movement in price would be offset by a position in the option and the underlying stock. The value of the call option is equal to the present value, discounted at the risk-free rate, of the expected net proceeds received after closing the hedge at the option’s expiration date. Thus, an option is priced correctly when the perfect hedge yields the risk-free rate.

Other assumptions underlying the Black Scholes model are as follows:12

1. There are no commissions or other transaction costs in buying or selling the stock or the option. 2. The short-term risk-free interest rate is known and is constant through time. 3. Trading is continuous through time following a geometric Brownian motion. 4. The underlying stock pays no dividends and makes no other distributions. 5. There is unrestricted access to credit, and the securities are perfectly divisible. However, it is possible to borrow any fraction of the price of a security to buy, or to hold it, at the short-term risk-free rate. 6. The stock price follows a random walk with a log normal distribution. 7. The volatility of the stock is constant over the life of the option. 8. The option can be exercised only at maturity. 9. A seller who does not own a security (a short seller) will simply accept a future date by paying for an amount equal to the price of the security on that date. While this short sale is outstanding, the short seller will have the use of, or interest on, the proceeds of the sale. 10. The tax rate, if any, is identical for all transactions and all market participants.

The Black-Scholes formulas for the prices at time 0 of a European call option on a non-dividend paying stock and a European put option on a non-dividend paying stock are as follows:

-rT Call Value = S0 × N(d1) ‒ Ke × N(d2) -rT Call Value = S0 × N(d1) – Ke × N(d2) fied Black-Scholes model. Fisher Black’s model val- and ues an option for the possibility of early exercise. and This is simply done by valuing an option to each ex-dividend day and choosing the maximum of the Put Value = Ke-rT Put Value = Ke-rT× × N N(–d2)(‒d2) ‒ –S S0 × ×N (N(–d‒d1) ) estimated call values.18 0 1 Dividends are adjusted for both the exercise where:Where: price and the stock price. The procedures in the method are as follows: Page 8 1. Compute the adjusted market price of the � ����� / ����� � ���� �� stock by deducting the present value, using �� � �√� the risk-free rate, of the future dividends

payable during the remaining life of the 12 Ibid, Page 589-590 � = option. ����� / ����� ‒ ���� �� � Incomplete Work Product Prepared2. for For Discussion each pseudo-option Purposes Onlyassumed to expire � � �√� ��1 ‒ σ√� The function N(x) is the cumulative probability distributionon a dividend function date, for deduct a standardized from the exernormal- Thedistribution. function13 N(x) In otheris the words, cumulative it is probabilitythe probability that a cisevariable price with of the a standardoption the normal dividend distribution, pay- distribution function for a standardized normal dis- able on the dividend date and the present φ (0, 1), will be less than x.14 S is the stock price at time zero, K is the strike price, e is the base of natural tribution.15 0 value, using the risk-free rate, of all the logarithms, ln is the natural logarithm, r is the continuouslyremaining compounded dividends risk-free to be rate, paid σ afteris the the stock In other words, it is the probability that a vari- 15 price volatility, and T is the time to maturity of the option. dividend date during the term of the option. able with a standard normal distribution, φ (0, 1), will be less than x.16 3. Using the Black-Scholes model, compute There are many assumptions and computations that need to be made to derive the option value using the the value of the actual option as well, using SBlack-Scholes0 is the stock priceformula. at time In the zero, model K is (1)the dividendsstrike are ignored and (2) fluctuations in the geopolitical and price, e is the base of natural logarithms, ln is the the adjusted market price and the unad- macro-economic environment preclude coherent acceptancejusted of the exercise assumption price. that investors can borrow naturalor lend logarithm, at a constant r is the continuouslyrisk free rate. compound Robert -Merton added an additional computation to account for ed risk-free rate, is the stock price volatility, and 4. The value of the American option is the dividends in theσ Black Scholes Model (“Black-Scholes-Merton model”). T is the time to maturity of the option.17 European option with the highest value.19

ThereThe Black-Scholes-Merton are many assumptions model and computations essentially assumes that dividends are paid continuously over the life thatof need the optionto be asmade a percentage to derive of the the option underlying value stock price.Some analysts prefer to use the pseudo-American using the Black-Scholes formula. In the model (1) call option model to determine if early exercise of an dividends are ignored and (2) fluctuations in the geo- Pseudo-American Call Option Model American call option has value. If it does, then the political and macroeconomic environment preclude investor would use a different model to determine coherentUnlike acceptance the Black-Scholes of the assumption model, whichthat investors only values the Eu Americanropean options call option’s on non-dividend price, such paying as a binomial stocks, the can borrow or lend at a constant risk free rate. pseudo-American call option model values Americanmodel. options or employee stock options that can be Robertexercised Merton anytime added during an additional the life of computation the option. The Pseudo-American Call Option Model was developed to accountby Fisher for dividendsBlack and in is the essentially Black-Scholes a modified model BlacBinomialk-Scholes Modelmodel. Fisher Black’s model values an (referredoption to for herein the possibility as the “BSM of model”).early exercise. This is simply done by valuing an option to each ex-dividend In 1978, John16 C. Cox, Stephen Ross, and Mark Theday BSMand choosingmodel essentially the maximum assumes of thatthe estimateddivi- Rubinstein call values. published Dividends a paper are adjustedentitled for“Option both the 17 dendsexercise are paid price continuously and the stock over price. the The life steps of thein the methodPricing: are A Simplified as follows: Approach.” option as a percentage of the underlying stock price. The binomial model discussed in this paper con- 1. Compute the adjusted market price of the stocktains by the deducting Black-Scholes the present option value, pricing using formula. the risk-free It rate, of the future dividends payable during isthe considered remaining as life a ofpractical the option. application for valuing 2. For each pseudo-option assumed to expire specialon a dividend cases of date,American deduct options, from suchthe exercise as employee price of Pseudo-American Call Option stock options. the option the dividend payable on the dividend date and the present value, using the risk free Modelrate, of all the remaining dividends to be paidThe after binomial the dividend model separates date during the theprice term move of- the Unlike the Black-Scholesoption. model, which only values ment in the underlying stock into time intervals, or European options on non-dividend-paying stocks, steps. It is based on the probability that the share the pseudo-American3. Using the Blackcall option Scholes model model, values Compute price the ofvalue the common of the actualstock canoption only asmove well, to oneusing of the American optionsadjusted or market employee price stock and theoptions unadjusted that exercisetwo possible price. prices in the following time period. can be 4.exercisedThe value anytime of the duringAmerican the optionlife of is thethe EuropeanThe optionprobability with the of highest moving value. these prices or option. “nodes” should total 100 percent.20 The amount of TheSome pseudo-American analysts prefer tocall use optionthe pseudo-American model was upcall or option down modelmovement to determine in the underlying if early stockexercise price of an developedAmerican by Fisher call option Black hasand value. is essentially If it does a modi then- the isinvestor determined would by use its avolatility different and model the option’sto determine time the American call option’s price, such as a binomial model.

69 www .willamette . com INSIGHTS • AUTUMN 2016 13 Ibid. 14 Ibid. 15 Ibid. Page 291-292. 16 http://people.stern.nyu.edu/adamodar/pdfiles/valn2ed/ch5.pdf, Page 18. 17 “Valuing a Business Fifth Edition” by Shannon Pratt, Page 593.

Incomplete Work Product Prepared for Discussion Purposes Only

Page 9

Binomial Model In 1978, John C. Cox, Stephen Ross, and Mark Rubinstein published a paper entitled “Option Pricing: A simplified Approach”. The binomial model discussed in this paper, contains the Black-Scholes option pricing formula, and is considered as a practical application for valuing special cases of American options, such as employee stock options.

to Theexpiration. Binomial The model possible separates movements the price at each movement step inceeding the underlying step, otherwise stock into the time option intervals, is held or tosteps the formsand abased binomial on the tree probability or “lattice.” of the share price of the commonnext step. stock can only move to one of two possible prices in the following time period. The probability of moving these prices or “nodes” must total 100 pricesGiven inthe18 the stock following price lattice,time period. the method The probability then of Theremoving are these many prices assumptions or “nodes” and must computations total 100 percent.18 The amount of up or down movement in the underlying stock price is determined by its calculatespercent. the The individual amount ofoption up orat downeach movementnode of inthat the needunderlying to be madestock toprice derive is determined the option by value its volatility and the options time to expiration. The possible movements at each step forms a binomial tree thevolatility stock price and lattice.the options21 The time value to expiration.of the option The is possibleusing movements either the Black-Scholes at each step forms or the a binomialbinomial mod tree- theor present “lattice”. value Given, of theall thestock individual price lattice, option the metandhod thenels. Analystscalculates need the individualto consider option the atassumptions each node ofof 19 ex-dividendthe stock pricedate valueslattice. at Theeach value node ofof the optionlattice, is thethe present option value pricing of allmodel the individualwhen deciding option on and which ex- 20 weighteddividend by date its probability values at each of occurrence. node of the22 lattice, weightedmodel by itsto useprobability to value of specific occurrence. stock20 options.

The binomial model formulas for the prices at For example, time to expiration, early exercise of timeThe 0 Binomialof a American model callformulas option for on the a pricesdividend- at time the0 of option, a American dividends, call optionvolatility, on aand dividend the economic paying stock are the following:21 payingstock stock are the are following: the following: 23 environment should be considered when valuing employee stock options. (-r(t/step)) C = Max ((P × Cu + (1 ‒ P) × Cd) (-r(t/step))× e(-r(t/step)), S ‒ E) C =C Max = Max ((P ×(( PC u× + C (1u + – (1 P) ‒ × P C) d×) C×d e) × e , ,S S – ‒E E) ) It is noteworthy that there is no universally

accepted model for an option pricing valuation. Thus, two analysts valuing the same company may ௧� ሺ௜ିௗ௜௩ሻሺ�������� ௧ ሻ� arrive at different valuations for their stock options. ሺ௜ିௗ௜௩ሻሺ௦௧௘௣����ሻ ௦௧௘௣ However, when the valuation methodology is con- ݁� െܦ�� ܲൌ�� sistent across analysts, the results may be closer to ܲൌ ��� ܷെܦ one another. ഑� ඥ�௧Ȁ௦௧௘௣������ ඥ௧Ȁ௦௧௘௣ Publicly traded call options do not need to be ܷൌ݁���Where C is the call price at current step, P is the probability of upward movement in the succeeding step, (1 ‒ P) is the probability of downward movement inexercised the succeeding to realize step, profitsC is thefrom value the of underlying call after (1 ‒ P) is the probability of downward movement in the succeeding step, Cu is the value of call after upward movement in the succeeding step, C is thestock. value This of callis becauseafter downward the option movement can be soldin the to upward movement in the succeeding step, Cd is theanother value investorof call after who downwardreceives the movement rights associated in the succeeding 1 step, e is the base of natural logarithms, r is the continuously compounded risk-free rate, t is succeeding� �� step, e is the base of natural logarithms, rwith is the the continuously option contract. compounded risk-free rate, t is where:time to� expiration in years, step is the number of steps or time periods, S is the stock price at the same stepWhere, E Cis isthe the exercise call price price at currentat the same step, step,P is thei is probability the annualizedDeferred of upward and compensation con movementtinuously plans incompounded the that succeeding include risk-free stockstep, C = Call price at current step options do not have this advantage. This is primarily interest(1 ‒ P) rateis the for probability the same timeof downward as the remaining movement life in ofthe the succeeding option, div step, is theCu isdividend the value yield, of callU is after the Pupward = movementProbability inof theupward succeeding movement step, in Ctheis thebecause value ofthey call are after usually downward nonmarketable. movement However, in the upward movementsucceeding during step a step, D is the downwardd movement during a step, and σ is the stock price volatility.succeeding22 step, e is the base of natural logarithms, rthe is theassumptions continuously to value compounded publicly tradedrisk-free options rate, tare is (1volatility. – P) = Probability of downward movement in relevant to most employee stock option contracts. time to expiration in years, step is the number of steps or time periods, S is the stock price at the same the succeeding step Thestep ,option E is the may exercise be exercised price at if the the samedifference step, ibetween is the annualized the stock priceand con andtinuously the exercise compounded price, at therisk-free same CThe = optionValue may of be call exercised after upward if the differencemovement between in the stock price and the exercise price, at the same step,interestu is greaterrate for than the the same value time of theas thesucceeding remaining step life, otherwise of the option, the option div isis heldthe todividend the next yield, step. U is the step, is greaterthe succeeding than the value step of the succeeding step, otherwise the option is held to the next step. upward movement during a step, D is the downwardT movementhe Black during-S choa step,l andes Mσ isode the stockl v erprice- 22 CTherevolatility.d = areV aluemany of assumptionscall after downward and computations movement that need to be made to derive the option value using There arein manythe succeeding assumptions step and computations that needsus to tbehe made Binomia to derive lthe M optionode valuel using Black-Scholes or Binomial models. Analyst need to consider the assumptions of the option when deciding eThe = optionBase may of naturalbe exercised logarithms if the difference betweenWhether the stock Black-Scholes price and the orexercise binomial, price, both at the of samethese on a model to use when valuing stock options. For modelsexample, come time fromto expiration, the probabilistic early exercise assumptions of the rstep, = is greaterContinuously than the compounded value of the succeedingrisk-free rate step, otherwise the option is held to the next step. option, dividends, volatility, and the economic environmentabout shouldthe financial be considered world. Both when models valuing are employee derived t = Time to expiration in years stock options. from the Wiener process or Brownian motion where step = Number of steps or time periods the underlying stock follows continuous paths in a S = Stock price at the same step stochastic process with stationary independent nor- 18 E18 = Ibid, PageExercise 597. price at the same step mally distributed increments. 19 i 19= Ibid. Annualized and continuously com- In fact, the binomial model converges with 20 20 Ibid. pounded risk-free interest rate for the the Black-Scholes model as the number of steps 21 21 Ibid, Pagesame 600. time as the remaining life of the increase in the binomial model. Therefore, the 22 22 Ibid. option binomial model provides discrete approximations to div = Dividend yield the continuous process of the Black-Scholes model. Incomplete Work Product Prepared for Discussion Purposes Only U = Upward movement during a step As a result, a European option or an employee

D = Downward movement during a step stock option can be valued with either model. σ = Stock price volatility24 For example, let’s assume the following scenario: Asset Price $30.00 The option may be exercised if the difference Strike Price $30.00 between the stock price and the exercise price, at Years to Maturity 4 the same step, is greater than the value of the suc- Risk-Free Rate 2.25%

70 INSIGHTS • AUTUMN 2016 www .willamette .com Dividend Yield 2% Summary Volatility 30% There is no universally accepted analytical method Number of Shares 5,000 for valuing stock options under Section 409A. The most often used option pricing methods were sum- Applying these assumptions in the Black-Scholes marized in this discussion. model, we arrive at a value of $6.58 per share, and In the employee stock option price is derived conclude a fair market value of the 5,000 options of by applying one of the safe harbor methods, the $32,906. valuation burden of proof will shift to the Service to For illustration purposes, we use five steps for determine that the valuation method or its applica- our binomial model. Exhibit 1 presents a stock price tion was “grossly unreasonable.” of $30 and will move up or down based on the 30 Employee stock options are issued by an employ- percent volatility. er who provides the terms. For the employee stock As a result, we arrive at a value of $7.07 per option to have no tax consequence to the employee share, and conclude a fair market value of the on the date of the grant, the strike price for the options of $35,338. employee stock options is typically equal to or higher than the fair market value of the stock.

Exhibit 1 The Binomial Model Illustrative Example

Input Values: Current Stock Price 30 S Exercise Price 30 E Divdend Rate 2% Div_Rate Dividend 0 Divdend Present Value of Expected Dividend $0.00 PV_Dividend Option Life in Years 4 t Annuual Risk-Free Rate 2.25% i Volatility 30% Std_dev Number of Steps 5 Step

Calculated Values: Current Stock Prices less Dividend S Adjustment $30.00 = S - PV_Dividend Up Movement U 1.308 = Exp(Std_dev)^(SQRT(t/Step)) Down Movement D 0.765 = 1/U Risk Neutral Up Movement Probability P 0.437 = (EXP((i-Div_Rate)*(t/Step))-d)/(U-d) Risk Neutral Down Movement Probability (1-P) 0.563 = 1-P

Stock Price Lattice: X/Y 012345 0 30.00 39.23 51.31 67.10 87.75 114.76 1 22.94 30.00 39.23 51.31 67.10 2 17.54 22.94 30.00 39.23 3 13.41 17.54 22.94 4 10.26 13.41 5 7.84

Call Option Price Lattice: X/Y 012345 0 7.07 12.74 22.19 37.10 57.75 84.76 1 2.90 5.81 11.34 21.31 37.10 2 0.73 1.70 3.96 9.23 3 4 5

Source: Shannon P. Pratt, Valuing a Business, 5th ed. (New York: McGraw-Hill, 2008).

www .willamette .com INSIGHTS • AUTUMN 2016 71 The Black-Scholes model is commonly used in practice Measuring Equity Volatility for Closely when valuing employee stock options. Held Company Securities However, one may argue that the binomial model may Continued from page 46 be more practical to value employee stock options. This is because an analyst can include assumptions such as early exercise, blackout periods, employee turnover, and vesting Fundamentally, esti- provisions in the model. mating stock option “A higher required volatility for a closely held business is subjec- return for closely Notes: tive. A higher required held businesses 1. “A Question and Answer Guide to Code Section return for closely held 409A” found at http://www.sandw.com/assets/html- businesses compared compared with documents/CLIENT_ADV._-_A_Question_and_Answer_ with GPTCs commonly Guide_409A_(B0778012).PDF reinforces a higher level GPTCs commonly 2. Ibid. of . reinforces a higher 3. “Income Tax Regulation Including Proposed Regulations However, lower vola- §1.301-1–§1.483-4” (Winter 2016), 33,815. tility tends to materi- level of implied alize when additional 4. Ibid. volatility.” factors, which have a 5. Ibid. lesser impact on close- 6. Ibid. ly held companies, are 7. Robert W. Kolb, Futures, Options, and Swaps, 4th ed. introduced. (London, U.K.: Pearson Prentice Hall, 2003), 3. Once the valuation analyst determines an acceptable 8. Ibid. GPTC estimate for implied volatility, the analyst applies the estimate in the BSM for the closely held business stock 9. Ibid., 5. option. 10. Paul Wilmott, Frequently Asked Questions in Quantitative Finance, 2d ed. (London, U.K.: John Wiley However, given the fundamental differences between & Sons, 2009), 162. GPTCs and closely held businesses, the analyst should apply professional judgment when considering the final 11. “A Question and Answer Guide to Code Section implied volatility estimate. 409A” found at http://www.sandw.com/assets/html- documents/CLIENT_ADV._-_A_Question_and_Answer_ An analyst may consider the closely held company Guide_409A_(B0778012).pdf. geographic footprint in the market it serves, the reactive- 12. Shannon P. Pratt, Valuing a Business, 5th ed. (New ness to macroeconomic news events, and access to capital York: McGraw-Hill, 2008), 589. compared to the GPTCs. 13. Ibid., 589–590. This is by no means an exhaustive list—many other factors may change the implied volatility estimate. The 14. John C. Hull, Options, Futures, and Other Derivatives, analyst should be aware of these potential influential fac- 7th ed. (Upper Saddle River, NJ: Pearson Education, 2009), 291. tors and apply them on a case by case basis. 15. Ibid. Essentially, when selecting a closely held implied vola- tility estimate, valuation analysts apply 16. Ibid. professional judgment in relying on 17. Ibid., 291–292. GPTC implied volatility data. 18. http://people.stern.nyu.edu/adamodar/pdfiles/valn2ed/ ch5.pdf, 18. Note: 19. Pratt, Valuing a Business, 593. 1. Aaron M. Rotkowski, “Estimating 20. Ibid., 597. Stock Price Volatility in the Black- Scholes-Merton Model,“ The Value 21. Ibid. Examiner (November/December 22. Ibid. 2011). 23. Ibid., 600. 24. Ibid. Patrick Van Dyke and Benjamin Groya are associates in our Chicago practice office. Patrick can be reached at (773) 399-4338 or Reid Chanon is an associate in our Chicago at [email protected]. Ben can be practice office. He can be reached at (773) reached at (773) 399-4312 or at bhgroya@ 399-4339 or at [email protected]. willamette.com.

72 INSIGHTS • AUTUMN 2016 www .willamette .com