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Expected life after SAB 107 and SAB 110: one approach to estimating the expected term of stock options.

The safe harbor rule of SEC Staff Accounting Bulletin 107 (SAB 107) allows companies to use the simplified method to estimate the expected term for employee stock options. Released in March 2005, SAB 107 was slated to sunset on December 31, 2007. Companies with no historical data to estimate the expected term expressed concern about what they would do after the expiration of SAB 107. On December 21,2007, the SEC released SAB 110, which enables eligible companies--both publicly traded and privately held--to continue to use the simplified method. The SEC, however, has tightened the rules by permitting the use of the SAB 107 simplified method only if the company does not have sufficient historical exercise data to provide a reasonable basis for an estimate of the expected term.

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The SEC explained that at the time SAB 107 was released, it had expected that historical information about employee exercise behavior from other companies, such as actuarial studies, would soon be readily available. This was the basis for the statement in SAB 107 that the staff would not expect a company to use the simplified method after December 31, 2007. Because such information was not yet available, the staff removed the deadline. It is likely that once the data is available, the SEC may again prohibit the use of the SAB 107 simplified method.

In most instances, the expected term estimated using the simplified method tends to be higher than the expected term estimated using actual historical option exercise data. The higher the expected term, the higher the value of the employee stock option. Therefore, even for companies with little or no historical data, it may make economic sense to explore other viable estimating alternatives instead of simply relying on the safe harbor rule. The objective of this article is to propose alternative approaches to estimating the expected term of employee stock options for companies that have previously relied on the safe harbor rule.

Impact on Employee Stock Options

Statement of Financial Accounting Standards 123, revised in 2004, [SFAS 123(R)], Share-Based Payment, requires the expensing of the share-based payment transactions including restricted share plans, performance-based awards, and employee stock options (ESOs). SFAS 123 (R) paragraph A27 defines the expected term of an employee option as "the period of time for which the instrument is expected to be outstanding {that is, the period of time from the service inception date to the date of expected exercise or other expected settlement)."

The expected term, while not particularly relevant in the context of freely traded stock options, is an important concept relative to ESOs. Like conventional stock options, ESOs have contractual terms, measured as the time between the grant date and the maturity date of the option.

Unlike freely traded options, holders of ESOs cannot sell or hedge their options--they can only exercise them. This lack of liquidity, marketability, and transferability often triggers suboptimal behavior, including voluntary early exercise, involuntary early exercise, and forfeiture of options by employees departing the company--all of which translate into an effective term that is shorter than the contractual term. These sub-optimal exercise behaviors not only create uncertainty around the expected term, but also reduce the fair value of the ESOs. Consequently, SFAS 123(R) paragraphs A3 and A18 require that the fair value of an ESO be based on the expected term rather than the contractual term.

Lattice Versus Black-Scholes

While SFAS 123(R) requires fair value-based reporting, it does not prescribe a specific methodology for arriving at the related valuation, stating instead that "the grant-date fair value of employee share options and similar instruments will be estimated using option-pricing models adjusted for the unique characteristics of those instruments."

Either the Black-Scholes or the lattice option pricing model is acceptable under the standard, but most companies choose the former due to its ease of implementation, despite having theoretically sufficient data to support a more rigorous lattice model analysis. This choice of simplicity should be evaluated against a number of deficiencies inherent in the Black-Scholes model.

The Black-Scholes model's principal drawback lies in its inability to price options with American-style exercise; it calculates option price only at expiration and does not consider prior potential exercise opportunities. This issue becomes particularly significant in the context of ESOs, which, unlike traditional options, are illiquid and subject to forfeiture conditions--and therefore almost inevitably exercised before the expiration of their term. The Black-Scholes model, when applied to ESOs, summarizes all behavioral information with a single number--the expected term--which arguably places disproportionate emphasis on an assumption that is difficult to estimate in the first place.

On the other hand, the lattice model is better suited to the unique and restrictive characteristics of ESOs. A key advantage of the binomial model lies in its flexibility, which allows companies to incorporate detailed market-based information on a more incremental basis, as well as to capture the impact of characteristics unique to ESOs, such as vesting restrictions and early or suboptimal exercise. The most important advantage is that the lattice model generates as output the expected term value that users of the Black-Scholes model must meticulously derive. The expected term is a necessary input to the Black-Scholes model, while it is an output of a lattice model.

The Simplified Method Under SAB 107

Designed to grant companies substantial latitude in estimating the fair value of share-based compensation, SAB 107 also lays out a simplified methodology as a temporary solution for determining the expected term. This methodology has effectively allowed companies using the Black-Scholes model in valuing plain vanilla options to assume the midpoint of the vesting term and the contractual term as the expected life for related awards. For example, an option with a four-year graded vesting schedule (i.e., 25% of options will vest at the end of the first year, with another 25% vesting at the end of the second year, and so on) and a seven-year contractual term would have an expected term assumption of {[(l+2+3+4)/4]+7}/2 = 4.75 years.

Companies using the safe harbor rule generally fall under one of three categories:

* Those with no historical option data,

* Those with limited historical option data that is insufficient for rigorous analysis to estimate the expected term, and

* Those that have substantial historical option data but have not implemented the binomial model.

With the issuance of SAB 110, companies that fall under the third category would not be allowed to use the simplified method, except under certain circumstances (i.e., in the event of significant changes to share option grant programs or structural business changes that render historical exercise data an impractical basis from which to determine expected term), because they should be suitably equipped to transition from the Black-Scholes model to the more rigorous lattice approach. Should these companies decide to continue to use the Black-Scholes model, however, they must keep in mind that, because Black-Scholes summarizes all employee behavioral information into a single expected term assumption, it is critical that the estimate be rigorous, defensible, and supported.

Companies in the second category cannot for a similar transition or conduct more in-depth analysis on their limited historical option data to arrive at a more precise expected option term. As of today, companies in the first category are still allowed to use the simplified method initially outlined in SAB 107 until further notice from the SEC. In the absence of the SAB 107 method, however, this group of companies would face perhaps the most formidable hurdle; with no historical option information, no obvious alternatives exist to determine the expected term.

Houlihan Lokey Approach

The Houlihan Lokey Approach (HL approach) can be deployed by any company in estimating the expected term. The HL approach entails a detailed and rigorous analysis of the historical option exercise data by taking into consideration the historical exercise time, vesting restrictions, and contractual life, and can be can be modified to adapt to situations where limited or no historical option data is available.

Many companies with years of historical option activity data have yet to make the switch from Black-Scholes to the more rigorous binomial model and have instead relied on historical average terms for input estimates. Under SFAS 123(R), the use of historical averages as an indication of prospective behavior requires more rigorous support.

The expected term should not be confused with the average historical time to exercise, because the latter ignores the terms of options that 1) are still outstanding; 2) expire worthless at the option maturity; and 3) become forfeited out-of-the-money as an employee leaves the company. Not capturing these three categories will lead to an inaccurate estimate of the historical term--and, needless to say, relying on average historical exercise time would not constitute a reliable method for estimating expected term.

Another key limitation associated with average historical time to exercise is that it does not necessarily take into account significant structural variables across option grants. While some companies use the same vesting schedule and contractual term for all their option grants over the year, others modify the design and structure due to changes in market conditions and the economic environment. Given that vesting restrictions and contractual terms impact timing of exercise, it is difficult to extract meaningful conclusions about historical exercise behavior across multiple grants without normalizing for those factors.

It is worth noting that in the case of companies with limited to no historical grants, data from comparable companies can also be applied using a normalization factor. Normalizing exercise data also addresses the issue of limited disclosure in public filings. For example, a company may disclose that its options will vest over a four-year period. Very often, however, the disclosure will not be specific enough to inform the market participants whether the options are vested under a four-year graded or four-year cliff vesting schedule. This makes the prospect of identifying comparable grants with identical terms challenging at best.

In a similar vein, applying historical data to new option grants also makes more sense on a normalized basis. From a theoretical valuation standpoint, holding all the other inputs constant, the longer the contractual term, the higher the expected term, and the more expensive an ESO. Similarly, the expected term will be higher if it takes longer for an ESO to be vested and, hence, the higher the ESO value. Because differences in the design and structure of an option grant have an impact on the theoretical expected term and the theoretical value of an ESO, applying historical exercise data on a non-normalized basis could distort the value of the new grant.

Step 1: Calculating normalized expected term factor from historical data. For companies with substantial historical data, the first step in implementing the HL approach consists of calculating a normalized expected term factor (NETF) for each historical option grant by adjusting the contractual option term for vesting restrictions and early exercise (see the Sidebar for a glossary of the terms used here and below).
GLOSSARY

[AR.sub.i]      Adjusting Ratio for tranche i, calculated as
                ([TE.sub.i] - [TV.sub.i])/([OT - [TV.sub.i])

ANETF           Average of the NETFs for several grants.

[CET.sub.i]     Contribution of tranche i to the expected term of a
                new option grant.

Cliff Vesting   A vesting schedule in which 100% of the option
                grant shares vest on a particular date.

[ET.sub.i]      Expected Term of tranche i in the context of a new
                option grant

Expected Term   The period of time for which an instrument is
                expected to be outstanding, as measured by date of
                service inception to date of expected exercise or
                other expected settlement.

Graded Vesting  A vesting schedule in which the option grant
                consists of several tranches of shares that vest on
                different dates.

NETF            Weighted average of the AR of each tranche within
                an option grant

OT              The contractual term of an option grant in years.

P[Vest.sub.i]   Percentage of option grant shares allotted to
                tranche i in accordance with the contractual
                vesting schedule.

[TE.sub.i]      The actual exercise time from the grant date in
                years.

[TR.sub.i,j]    Contribution of tranche i to the NETF of Grant j.

[TV.sub.i]      The time period between grant date and the
                contractual vesting date for tranche i options in
                years.


As an example, for an option Grant j with a four-year graded vesting schedule (i.e., 25% of the options slated to vest at each anniversary date of the grant for four years), given the differences in the length of the vesting period for the four tranches, it is necessary to adjust each tranche individually to arrive at an NETF for the entire Grant j, as shown below:

[TR.sub.ij] = [PVest.sub.1] x [AR.sub.j] = [PVest.sub.i] x [([TE.sub.i] - [TV.sub.i])/(OT - [TV.sub.i])]

Here, [TR.sub.ij] = contribution of tranche i to the normalized expected term factor of Grant j; P[Vest.sub.i] = percentage of options for tranche i in accordance with the contractual vesting schedule of Grant j; and [AR.sub.j] = adjusting ratio for tranche i, calculated as the difference between [TE.sub.i] (the actual exercise time from the grant date) and TV; (the time period between the grant date and the contractual vesting date for tranche i options), divided by the difference between OT (the contractual term) and [TV.sub.i]. ([TE.sub.i], [TV.sub.i], and OT are expressed in units of years.)

If the granted option turns out to be out-of-the-money (i.e., the strike price is above the prevailing stock price) throughout the entire contractual term, the option will be unexercised and expire worthless. The term TE will equal OT, implying that the actual historical life equals the contractual term of this option, and the adjusting ratio will be one.

All tranche contributions are then aggregated, resulting in a weighted average NETF for the entire option Grant j.

As an example, Company Bluechip issued N different option grants in the past 10 years. Options issued under Grant k have a 10-year contractual term and a two-year graded vesting schedule: 50% of the options vested at the end of the first year and the remaining 50% vested at the end of the second year. In addition, historical data shows that the first tranche has typically been exercised at the end of the third year, with the second tranche typically exercised at the end of the fourth year.

The calculation of the NETF for Grant k first involves determining the individual tranche contribution.

First tranche:

[TR.sub.1] = 50% x ([3 - 1]/[10 - 1]) = 11.11%

Second tranche:

[TR.sub.2] = 50% x ([4 - 2]/[10 - 2]) = 12.5%

The NETF of Grant k is the sum of the two tranches:

11.1% + 12.5% = 23.6%

This process is repeated for the N option grants that Company Bluechip issued, and the aggregate NETF (ANETF) is an average of the NETFs terms across the N grants. For the sake of simplicity, it is assumed that Company Bluechip has only issued one grant in the past (N = 1) and the ANETF is the same as the NETF for Grant k of 23.6%.

Step 2: Estimating the expected term of future grants. The next step involves applying the ANETF estimated from historical data to approximate the expected term of Company Bluechip's newly issued grant. Assume that the new option grant has a seven-year contractual term and a four-year graded vesting schedule (i.e., 25% of the options slated to vest at each anniversary date of the grant for four years). The expected term is first calculated for each of the four tranches using the following formula:

[ET.sub.i] = [ANETF x (OT - [TV.sub.i]) + [TV.sub.i]]

Here, [ET.sub.i] = expected term of tranche i of the new grant; ANETF = aggregate normalized expected term factor; OT = contractual option term (in years); and [TV.sub.i] = vested time of that particular tranche (in years).

A weighted average expected term for the entire new option grant is then determined by calculating and aggregating the contribution to the expected term of each of the four tranches. The contribution of a tranche is calculated using the following formula:

[CET.sub.i] = P[Vest.sub.i] x [ET.sub.i]

Here, [CET.sub.i] = contribution of tranche i to the expected term of the new grant; and P[Vest.sub.i] = percentage of options for tranche i in accordance with the contractual vesting schedule of Grant j.

Using the ANETF of 23.6% calculated above, as illustrated in Exhibit I, the estimated expected term for the new grant is calculated to be 3.56 years.
EXHIBIT 1
Estimated Expected Term Calculation

Tranche  Percent of Options  Aggregate Normalized  Option Term (Years)
               Vested            Expected Term
  (1)            (2)                    (3)                 (4)

1                25%                   23.6%                 7
2                25%                   23.6%                 7
3                25%                   23.6%                 7
4                25%                   23.6%                 7

Tranche  Time at Which  Estimated Term of  Contribution to Estimated
         Options Vest     Each Tranche                 Term
            (Years)          (Years)
  (1)         (5)              (6)                      (7)

                        (3)x[(4)-(5)]+(5)             (2)x(6)
1              1               2.42                    0.60
2              2               3.18                    0.80
3              3               3.94                    0.99
4              4               4.71                    1.18
                               Total                   3.56


Had Company Bluechip not applied the HL approach and simply calculated the estimated term using the simplified method under SAB 107, it would have used an expected term of 4.75 years ([[(l+2+3+4)/4]+7]/2) in valuing its ESOs. Lowering the expected term by 1.19 years (4.75 versus 3.56) should substantially reduce the value of the ESOs. Depending on the number of options issued, it might have a significant impact on the company's financial statements.

Modified Houlihan Lokey Approach

A challenge arises when a company has limited historical option data, or worse, no data at all (i.e., if this is the first time the company is issuing employee stock options). In such cases, a company can no longer rely on historical data to estimate the expected term of a future grant. These companies can consider the modified HL approach, which uses publicly available information on comparable companies to estimate the expected term.

In the absence of historical data, key input assumptions (such as the vesting period, expected term, and contractual term of an option) can be obtained from public filings of companies designated as suitable com-parables for the target company. These key assumptions can be used to solve for the ANETF of each comparable company's option grant. (Recall the generalized formula for the estimated term used above, CE[T.sub.i] = P[Vest.sub.i] x [ANETF x (OT - [TV.sub.i]) + [TV.sub.i].)

The ANETF variable can be calculated either by applying available precise information on vesting schedules, time of exercise, and contractual term, or, in the case of imperfect information, using the solver function in Microsoft Excel.

Columns 6, 7, and 8 of Exhibit 2, for example, illustrate the derived ANETF for three different vesting scenarios generated from Excel's solver function. This process is repeated for other comparable companies, and the distribution of the outcomes is analyzed to derive the final ANETF for a company that has no historical option exercise data, such as hypothetical Company Techcom. Only companies that have applied quantitative methodology (other than SAB 107) to arrive at an expected term assumption should be considered as suitable for comparison.
EXHIBIT 2
Comparable Company Analysis of Aggregate Normalized Expected Term
Factor

                              Comparable Company

Ticker  Company Name  Vesting Years   Expected Life  Contractual Life
                                      in 10K (Year)     10K (Year)
(1)         (2)            (3)         (4)                (5)

J           AAA             3             5.4              10
2           BBB             3             6.3              10
5           CCC             4             4.7               7
4           DDD             3             5.0              10
5           EEE             4             5.2              10

                Aggregate Normalized Expected Term

Ticker  Hypo. Vesting   Hypo. Vesting     Hypo. Vesting
        Schedule: CGH  Schedule:Yearly  Schedule: Monthly
           Vesting     Graded Vesting    Graded Vesting
(1)          (6)             (7)               (8)

J          34.29%          42.50%            45.62%
2          47.14%          53.75%            56.26%
5          23.33%          48.89%            53.61%
4          28.57%          37.50%            40.89%
5          20.00%          36.00%            39.69%


Not surprisingly, the level of disclosure of share-based compensation information in public filings can leave some ambiguity with respect to the assumptions on contractual life or vesting schedules. For example, sentences such as "the term of a nonqualified option is usually five to 10 years" or phrases like "typically a four-year vesting period" are commonplace in a company's 10-K submission. A "four-year vesting period" could mean that the option grant follows a graded annual vesting schedule, or could imply that 100% of the option grant vests at the end of the four years (cliff vesting). It could also signify various alternatives in between.

In such situations, assumptions on the option's contractual term and vesting schedule must be made before the information can be analyzed. In most cases, information provided on the vesting schedule will drive assumptions on the contractual term. For example, an option grant with a four-year vesting period is more likely to be characterized by a seven-year or 10-year contractual term than by a five-year term. The vesting schedule assumption involves a more rigorous analysis, however, comparing various scenarios under which, for example, a "four-year vesting period" can be interpreted. The least and most conservative scenarios serve as boundaries for the range from which the final ANETF value is ultimately derived.

Following up on the "four-year vesting period" example highlighted above, it can be assumed that the most conservative scenario consists of a cliff-vesting schedule where 100% of options vest at the end of the fourth year, and that the most aggressive scenario consists of a schedule characterized by monthly vesting of equal grant increments starting one month after the option inception date. The neutral scenario can consist of the annual graded vesting schedule, where 25% of the grant vests at the end of each year.

Exhibit 2 illustrates an analysis in which the above methodology is performed for each of Company Techcom's comparable companies to help arrive at the selected ANETF. The ANETFs derived under the cliff-vesting scenario in column 6 form the lower bound, the ANETFs from the monthly vesting scenario in column 8 form the upper bound, and the neutral scenario in column 7--based on annual graded vesting--produces numbers that fall in between. Because the mean and median statistics are similar in this particular analysis, Company Techcom's selected ANETF reflects the average of the mean statistics;

(40.54% = 30.67% + 43.73% + 47.21% /3)

Using Selected Normalized Expected Term Factor

Once the selected ANETF is determined, it should be applied together with other parameters from Company Techcom's newly issued grant to arrive at an estimate of the expected term. Using the generalized formula discussed above to each tranche of the new option grant:

[CET.sub.i] = P[Vest.sub.i] x [ANETF x (OT-[TV.sub.j]) + [TV.sub.j]]

In this case, suppose that Company Techcom is issuing an option grant for the very first time with the following structure: a 10-year contractual term, with a four-year graded vesting schedule effective on the second anniversary of the grant's issuance. Applying these values, along with the ANETF of 40.54% as determined above, the estimated expected term for the new grant is 6.13 years (Exhibit 3).
EXHIBIT 3
Estimating Expected Term of New Option Grant

Tranche     Percent of      Aggregate   Option Term (Years)
         Options Vested    Normalized
                         Expected Term
(1)            (2)             (3)              (4)

1              25%           40.54%              10
2              25%           40.54%              10
3              25%           40.54%              10
4              25%           40.54%              10

Tranche  Time at  Estimate  Contribution
          Which   Term of   to Estimated
         (Years)    Each        Term
                  Tranche
                  (Years)
(1)        (5)      (6)         (7)

1           2       5.24        1.31
2           3       5.84        1.46
3           4       6.43        1.61
4           5       7.03        1.76
                   Total        6.13


Had Company Techcom not applied the modified HL Approach and simply calculated the estimated term using the simplified method under SAB 107, it would have used an expected term of 6.75 years ({[(2+3+4+5)/4]+10}/2) in valuing its ESOs. Lowering the expected term by 0.62 years (6.75 versus 6.13) would reduce the ESO's value. Depending on the number of options issued, this could have a significant impact on the company's financial statements.

Implementing a Better Approach

In the aftermath of the safe harbor rule, companies that have historically relied on the simplified method to value their plain vanilla options will have two basic choices: 1) transition to the binomial model; or 2) adopt of a more rigorous methodology for the determination of expected life of stock option grants. It is likely that, given the relative ease of implementation associated with Black-Scholes, many companies will opt for the latter. Such companies should consider adopting the HL approach or modified HL approach to estimate the expected term of options. Not only are the approaches statistically based, economically sound, and empirically supported by a company's own or comparable historical data, but they may also produce a shorter expected term than the simplified method under SAB 107.

Cindy W. Ma, PhD, CPA, CFA, is a managing director of Houlihan Lokey Howard & Zukin. She was also a member of FASB's ad-hoc option valuation group for SFAS 123(R).
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Title Annotation:accounting; employee stock options
Author:Ma, Cindy W.
Publication:The CPA Journal
Geographic Code:1USA
Date:May 1, 2009
Words:4232
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