Expected Term Input for Re-Valuing Options for the Purposes of Pay vs. Performance

Written By: CJ Van Ostenbridge

As part of the new Pay vs. Performance (PvP) disclosure requirement, companies must estimate the fair value of outstanding and unvested stock options held by Named Executive Officers (NEOs) as of the end of each fiscal year, as well as upon each vest date. The process and best practices for estimating the fair value of options as of the grant date are well defined, but the process for estimating fair value for Pay vs. Performance is less clear, especially given somewhat conflicting guidance provided by the SEC:

  • Item 402(v)(2)(iii)(C)(3) of the final disclosure requirements state that “fair value amounts must be computed in a manner consistent with the fair value methodology used to account for share-based payments in the registrant’s financial statements under generally accepted accounting principles”. In other words, companies should use the same valuation methodologies that were used to estimate the grant-date fair values.
    • Later, the SEC would clarify in a Question 128D.20 of the C&DI’s released on September 27, 2023 that registrants could “satisfy this requirement by using a valuation technique that differs from the one used to determine the grant date fair value” as long as the new valuation technique would be permitted under ASC Topic 718. However, the change in valuation technique would need to be disclosed as an assumption that differs materially from the assumptions disclosed as of the grant date, as required by Item 402(v)(4). 
  • Question 128D.21 of the September 27, 2023 C&DI’s states that “the fair value of stock awards and option awards must be computed using a methodology and assumptions consistent with FASB ASC Topic 718”. This question also goes on to define two approaches for estimating the expected term of an option as non-compliant:
    • An approach that simply subtracts the elapsed time from the original expected term as of the grant date, as this does not reflect changes in factors like volatility and exercise behavior between the grant date and remeasurement date.
    • The “simplified” method for options that are no longer at-the-money, and therefore no longer “plain vanilla” as of the remeasurement date.
  • In the Costs section of the final disclosure requirements, the SEC states that they “believe that, given that the disclosures require the collection of minimal new information, the overall compliance costs of the final rules should be modest. In particular, while some of the computations involved are more complex than simple arithmetic, existing models and established methodologies should aid in making the required calculations.”
    • The SEC goes on to say that “the annual revaluation of options (as well as any stock with market-based conditions) can generally be accomplished by reevaluating the appropriate inputs and entering these into the existing valuation models used to calculate currently disclosed values”.
    • The SEC also says that they “agree with several commenters who indicated that annual computations of fair value of outstanding equity awards would not be overly burdensome”.

Taken together, the guidance points towards using existing models and methodologies for the revaluation of equity awards, even though it does not preclude the use of new valuation techniques. However, companies should update the inputs to the valuation models to reflect the facts and circumstances as of the remeasurement date, especially with consideration to the moneyness of options. Finally, the SEC believes this new disclosure process should not be overly burdensome, incur modest cost, and require minimal new information. 

A Balanced Approach

For companies that estimate the grant date fair value of employee options using the Black-Scholes model, it is logical to use the Black-Scholes model to revalue the options for PvP purposes. The SEC noted that they believe existing models can be used, provided inputs are updated appropriately. Additionally, Black-Scholes is well understood by investors and transparent. Most inputs to the Black-Scholes model needed for PvP purposes as of a given remeasurement date are easily obtained:

  • Stock price can be observed directly from market traded shares
  • Strike price is defined in the option agreement
  • Risk-free rate can be pulled from public sources in a manner consistent with grant date valuation
  • The same volatility methodology used for grant date valuation can be applied
  • Dividend yield is easily observed and/or calculated 

Only the expected life input requires more judgement as of the remeasurement date. Infinite Equity believes companies can construct simple tables to estimate the expected of life of options remeasured for PvP based on three key data points, as well as commonly accepted theory that expected life increases as an option gets further out-of-they money, while expected life decreases as an option gets further in-the-money. The three key data points we need to populate are:

  • At what S/K ratio1 will the expected life equal the full contractual term (also equal to 100% of the remaining exercisable window2)?
  • What is the expected life assumption if the option is still at-the-money?
  • At what S/K ratio will the employee exercise immediately (expected life of 0.00 years)?
S/K RatioExercise % (as function of exercisable Window)
X%100%
100%Y%
Z% and Above0%

Expected Life When Option is At-the-Money

Most companies have a well-established process for estimating the fair value of options as of the grant date, which are almost always at-the-money. A large majority of companies use the Black-Scholes model, and estimate expected life based on either i) historical employee exercise behavior, or ii) the “simplified” method defined in SAB 107 (the midpoint of the weighted average time-to-vest and the full contractual term of the option). Let’s look at 2 example companies, assuming a 3-year cliff vesting period and 10-year contractual term.

As of Grant Date: 

Company using “Simplified”Company using Employee Data
Time to Vest3.00 years3.00 years
Time to Expiration10.00 years10.00 years
Exercisable Window7.00 years7.00 years
Expected Life as %
of Exercisable Window
50.0%28.6%
Expected Life6.50 years5.00 years

The expected life as a percentage of the exercisable window can be applied for remeasurement directly if the award is still at-the-money:

1-year into Vesting Schedule:

Company using “Simplified”Company using Employee Data
Time to Vest2.00 years2.00 years
Remaining Contractual Term9.00 years9.00 years
Exercisable Window7.00 years7.00 years
Expected Life as %
of Exercisable Window
50.0%30.0%3
Expected Life5.50 years4.10 years

As of Vest Date:

Company using “Simplified”Company using Employee Data
Time to Vest0.00 years0.00 years
Remaining Contractual Term7.00 years0.00 years
Exercisable Window7.00 years7.00 years
Expected Life as %
of Exercisable Window
50.0%35.0%4
Expected Life3.50 years2.45 years

One might ask if this approach is simply the “elapsed time” approach that the SEC noted was non-compliant, as it “does not reflect changes in factors like volatility and exercise behavior between the grant date and remeasurement date”. This problem can easily be solved by using the percentage exercise factor from the year of remeasurement, as opposed to from the year of grant. The expected life percentage disclosed in the year of remeasurement already accounts for changes in volatility and exercise behavior and has been audited and deemed appropriate for valuing at-the-money options. 

When Would Expected Life Equal the Full Contractual Term?

ASC Topic 718 allows for the use of an expected life (as opposed to the full contractual term) when estimating the fair value of employee options for two reasons:

  1. Employees have been observed to exercise sub-optimally (i.e., prior to full contractual term)
    a. Employees are not financial institutions. Sometimes, employees need to recognize value of their options to pay for college tuition or a new house, even if financial theory would suggest they are not maximizing the value of their holdings. 
  2. Most employee options have a shortened window to exercise (e.g., 90 days) when employment ends. 

Therefore, in order for the expected life to equal the full contractual term, the probability of termination would have to go to 0% and the stock price would have to go to $0. For any non-zero price, there is a change the option returns to the money and is exercised sub-optimally. For any non-zero termination probability, there is a change the employee will be forced into a post-vesting cancellation upon termination. These facts, combined with our guiding principle that expected life increases as an option gets further out-of-the-money suggests that the expected life only equals the contractual term when stock price reaches $0. This will serve as one endpoint for our expected life estimation. 

When Would Options be Exercised Immediately?

It is well known that employees tend to exercise their options suboptimally, either voluntarily or upon termination. Academics have studied the S/K ratio at which employees tend to exercise and have observed that exercise tends to occur when the stock price reaches an S/K ratio of 200% to 350%5. Another way to estimate when an employee would exercise an option immediately is a sensitivity-based approach; at what point does the intrinsic value of an option (the value recognized upon exercise) get significantly close to the theoretical fair value of an option that it is reasonable to assume the employee will exercise immediately? 6

Infinite Equity believes that 10% is an appropriate threshold to examine when comparing the Black-Scholes value to the intrinsic value. Once the difference is less than 10%, it is reasonable to assume an employee would place more importance on immediate, guaranteed value as opposed to waiting multiple years to recognize minimally more expected value. 

Assuming a 0% dividend yield, the following table can be constructed:

VolatilityStock PriceS/K RatioBlack-Scholes Fair ValueIntrinsic
Value
Percent Difference
10.00%$281.27281%$199.40 $181.27 10.00%
20.00%$281.84 282%$200.02 $192.33 10.00%
30.00%$292.33 292%$211.56 $218.89 10.00%
40.00%$318.89 319%$240.78 $256.68 10.00%
50.00%$356.68 357%$282.35 $302.16 10.00%
60.00%$402.16 402%$332.38 $353.28 10.00%
70.00%$453.28 453%$388.60 $408.46 10.00%
80.00%$508.46 508%$449.31 $466.23 10.00%
90.00%$566.23 566%$512.86 $466.23 10.00%
100.00%$625.09 625%$577.60 $525.09 10.00%

The S/K ratios where the difference between the Black-Scholes value of an option with a 5.00-year expected life and the intrinsic value of the option is less than 10% range from ~280% to ~625%. 

The following table was constructed if assuming a 1.5% dividend yield.

VolatilityStock PriceS/K RatioBlack-Scholes Fair ValueIntrinsic
Value
Percent Difference
10.00%$163.41 163%$69.75 $63.41 10.00%
20.00%$171.98 172%$79.18 $71.98 10.00%
30.00%$191.21 191%$100.34 $91.21 10.00%
40.00%$215.45 215%$126.99 $115.45 10.00%
50.00%$242.94 243%$157.23 $142.94 10.00%
60.00%$272.87 273%$190.16 $172.87 10.00%
70.00%$304.56 305%$225.01 $204.56 10.00%
80.00%$337.31 337%$261.04 $237.31 10.00%
90.00%$370.40 370%$297.44 $270.40 10.00%
100.00%$403.07 403%$333.38 $303.07 10.00%

The S/K ratios now range from about ~160% to ~400% depending on the volatility assumption. These are lower due to the fact that, when a company pays a dividend, exercising earlier entitles the option holder to more dividend payments, compared to waiting to exercise the option until a later date.  

The S/K ratios above for when employees would exercise immediately align with the academic research in that they are centered around 200% to 350% when considering a range of expected volatility and dividend assumptions. 

Putting It Together

Using the analysis above, companies that use the Black-Scholes model to value employee options as of the grant date can quickly and simply construct a table that can be used to estimate the expected life for options that need to be remeasured during the year for Pay vs. Performance purposes. For example, a company that uses the simplified method to estimate expected life at grant date with 40% volatility and 0% dividend yield could construct the table below. 

S/K RatioExercise % (as function of
exercisable Window)
Commentary
0%100%Assume full contractual term
exercise when stock price goes to $0
100%50%Assume midpoint exercise for
options at-the-money
319% and Above0%Assume immediate exercise when
S/K ratio gets to 319%

A company that uses the historical exercise behavior (30% of exercisable window) with 60% volatility and a 1.50% dividend yield could construct the table below to estimate expected life:

S/K RatioExercise % (as function of
exercisable Window)
Commentary
0%100%Assume full contractual term
exercise when stock price goes to $0
100%30%Assume 30% exercise for options
at-the-money. 30% is consistent with
grant-date valuation for at-the-money
options in year of re-valuation.
273% and Above0%Assume immediate exercise when
S/K ratio gets to 350%

The expected life for each tranche of options can be easily interpolated between the points above, and the resulting value will consider both changes in volatility and employee behavior (through the use of the current year’s expected life for at-the-money options) and moneyness. The methodology is consistent with grant date practices but considers inputs that reflect the current circumstances of the option award. It is transparent and easy to apply to a large population of options without being overly burdensome or expensive.  

Next Steps 

Infinite Equity continues to examine the Pay vs. Performance disclosures and how they will impact public companies. For more information on the Pay vs. Performance regulations or assistance navigating these changes, reach out to us at Infinite Equity for help. 

  1. The S/K ratio is the ratio of the current stock price (S) to the strike price (K). An “at-the-money” option has an S/K ratio of 100%. Options that are “in-the-money” have an S/K ratio greater than 100%, while options that are “out-of-the-money” have an S/K ratio below 100%. 
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  2. The Exercisable Window is the time between the vest date and the full contractual term. 
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  3. Reflects employee exercise behavior from year of remeasurement, as opposed to grant date
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  4. Reflects employee exercise behavior from year of remeasurement, as opposed to grant date
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  5. See page 5 of https://ecommons.cornell.edu/server/api/core/bitstreams/e238cc5a-71a1-4b39-8932-9b9f3bcfccc3/content
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  6. For this exercise, the theoretical fair value of an option will be based on the following assumptions: strike price of $100, risk-free rate of 4.00%, expected life of 5.00 years. 
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