BE IN A POSITION OF STRENGTH SM withum.com VALUATION SERVICES The reality is that private companies must meet a higher standard than public companies in the valuation of share-based payments as compensation for both financial reporting (ASC 718) and tax purposes (IRC 409A). Share-based payments can come in the form of shares or options to purchase shares. Both ASC Topic 718 and IRC Section 409A require companies to estimate the fair (market) value of its shares—which can be especially challenging for private companies. For instance, estimating the fair value of the common stock is difficult if the private company has little revenue or is an emerging stage company. If the share-based compensation is in the form of options, then additional, unobservable assumptions have to be made in order to arrive at an appropriate value. Let’s say the company has a decent handle on its share price. We then generally observe two big challenge areas: Volatility estimation and model selection. Selecting the appropriate volatility, which should be guidance based, is a subject for a later article. Model selection errors are more obvious to identify and, for my money, constitute the biggest mistake we see companies making. This is also where we see unqualified professionals wrongly advising companies to use an inappropriate model. People are quick to use the Black-Scholes Model (BSM) because it’s free and fundamentally easy to populate. A number of conditions exist, especially for small start-ups, where the BSM output is not a reliable indication of value. The BSM only works for “plain vanilla” options. In fact, from a December 2010 speech by Wayne Carnall, the chief accountant at the time in the SEC’s Division of Corporation Finance, to the American Institute of Certified Public Accounts, “There may be multiple embedded features or the features of the bifurcated derivatives may be so complex that a Black- Scholes valuation does not consider all of the terms of the instrument. Therefore, the fair value may not be appropriately captured by simple models.” ASC Topic 718 Financial Accounting Standards Board Accounting Standards Codification Topic 718, Stock Compensation (formerly Statement of Financial Accounting Standards No. 123R), requires a fair value to be estimated for share-based payments—restricted shares and share options. Privately held companies will generally find it more challenging than public companies to develop the fair value of its share-based compensation given that there is no active market to observe a fair value for its stock. Share price being arguably the most critical component of the valuation. By Howard Krieger and Jason Kunkel, CFA, FRM Share-based Compensation Valuation: Signs You Are Misapplying Black-Scholes - ASC Topic 718 and IRC Section 409A 1. SAB 110, https://www.sec.gov/interps/account/sab110.htm Howard Krieger Valuation Specialist T (201) 265 2800 [email protected]Jason Kunkel, CFA, FRM T (609) 520 1188 [email protected]
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BE IN A POSITION OF STRENGTHSM withum.com
VALUATION SERVICES
The reality is that private companies must meet a higher standard than public companies in the valuation of share-based payments as compensation for both financial reporting (ASC 718) and tax purposes (IRC 409A). Share-based payments can come in the form of shares or options to purchase shares.
Both ASC Topic 718 and IRC Section 409A require companies to estimate the fair (market) value of its shares—which can be especially challenging for private companies. For instance, estimating the fair value of the common stock is difficult if the private company has little revenue or is an emerging stage company. If the share-based compensation is in the form of options, then additional, unobservable assumptions have to be made in order to arrive at an appropriate value.
Let’s say the company has a decent handle on its share price. We then generally observe two big challenge areas: Volatility estimation and model selection. Selecting the appropriate volatility, which should be guidance based, is a subject for a later article.
Model selection errors are more obvious to identify and, for my money, constitute the biggest mistake we see companies making. This is also where we see unqualified professionals wrongly advising companies to use an inappropriate model. People are quick to use the Black-Scholes Model (BSM) because it’s free and fundamentally easy to populate. A number of conditions exist, especially for small start-ups, where the BSM output is not a reliable indication of value. The BSM only works for “plain vanilla” options.
In fact, from a December 2010 speech by Wayne Carnall, the chief accountant at the time in the SEC’s Division of Corporation Finance, to the American Institute of Certified Public Accounts, “There may be multiple embedded features or the features of the bifurcated derivatives may be so complex that a Black-Scholes valuation does not consider all of the terms of the instrument. Therefore, the fair value may not be appropriately captured by simple models.”
ASC Topic 718Financial Accounting Standards Board Accounting Standards Codification Topic 718, Stock Compensation (formerly Statement of Financial Accounting Standards No. 123R), requires a fair value to be estimated for share-based payments—restricted shares and share options. Privately held companies will generally find it more challenging than public companies to develop the fair value of its share-based compensation given that there is no active market to observe a fair value for its stock. Share price being arguably the most critical component of the valuation.
By Howard Krieger and Jason Kunkel, CFA, FRM
Share-based Compensation Valuation:Signs You Are Misapplying Black-Scholes - ASC Topic 718 and IRC Section 409A
1. SAB 110, https://www.sec.gov/interps/account/sab110.htm
While not suggesting a specific method to value privately-held stock, the guidance provides for a few of the approaches used to estimate this one input, including:
• Recent sales to an unrelated party of common stock• Recent sales to an unrelated party of preferred stock• Independent third-party appraiser valuation• Internally prepared valuation analysis
A third-party valuation is generally considered objective and should rely on sound economic theory. Internal analysis of fair value is considered to be the least objective of the alternatives and may not follow accepted valuation techniques depending on the background and experience of the preparer. These statements are true for the entire share-based compensation valuation and not just the valuation behind the share price.
IRC Section 409ASection 409A set rules regarding deferred compensation arrangements. The final regulations, which began as part of the American Jobs Creation Act of 2004 under Section 409A were issued in 2007 and became effective on January 1, 2009. There are significant adverse tax consequences for noncompliance. Section 409A applies whenever there is a “deferral of compensation,” a term with far reaching effects, which occurs whenever the service provider has a, “…legally binding right during a taxable year to compensation that … is or may be payable to (or on behalf of) the service provider in a later taxable year.” If the deferred compensation plan does not follow the various rules regarding deferral elections, funding methods, timing and type of payment, all amounts deferred under the plan for this year and previous years become taxable once vested. Additionally, a 20 percent tax and interest-based tax may apply.
The ChallengeSmaller, privately-held companies pay folks with share-based compensation all the time. Growing companies also raise money in the form of equity or convertible securities to pay for growth or maintenance capital expenditures. Out of fairness to its employees, companies often include provisions in the compensation agreements that limit or negate the impact of raising more equity capital on the total compensation amount. These provisions are almost standard at this point.
In seeking guidance on how to value the share-based compensation, leadership will generally turn to their first outside point of contact, often its attorneys or auditors, for a recommendation on how to proceed. These service providers often refer clients to free, online BSM calculators and spreadsheets to come up with a value. The surprise then comes down the road when the regulators, well-versed in the BSM’s limitations, review the share-based compensation agreements and throw out the prior recorded values as incorrect.
We describe some of the terms below that seriously challenge or negate the effectiveness and appropriateness of using a BSM to value share-based compensation. Additionally, we provide some suggestions on other methods which address the BSM’s limitations.
Black-Scholes Model OverviewAt a very high, non-technical level, the BSM calculates an option value by averaging all the positive differences between the single exercise price of the option and all the possible future prices of the underlying stock. The BSM assumes that the future prices of a stock are tied to the current price of the stock. The pattern of possible future prices is a classic bell-curve adjusted so that no value can be less than zero. The peak of the distribution is the current price grown by a risk free rate over the expected term of the option. The fatness or thinness of the distribution is driven by two factors: time and volatility.
The following is an example of the relationship between the current price of a stock (S0), the assumed median future price (Sn) and the strike price (Xn) of an equity-based option. The distribution of all future possible stock prices is commonly called a lognormal distribution. This is a point-in-time distribution; specifically, this is the assumed distribution of possible stock prices ON the exercise date. Everything that can occur between now and the term (n) is not considered in the Black-Scholes formula.
Every point to the right of the line (Xn) represents those instances where the option has a positive value. Some of the terms that we see when assessing the value of an option based on the current stock price and the exercise price are:
• In-the-money, where the S0 is greater than Xn
• At-the-money, where the S0 is equal to Xn
• Out-of-the-money, where the S0 is less than Xn
We will be basing a lot of the discussion on a simple share-based compensation option where the stock price is currently $1.00 and the employee can exercise
Diagram I:
Simplified
Illustration of the
BSM Logic
Prob
abili
ty (%
)
Dollar ($)
Zero Value Positive Value
(Sn)(So)
(xn)
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Example II: BSM – Vanilla Call Option with Dilution
The issue with using the BSM is that certain anti-dilution clauses are often built into share-based compensation, making the BSM’s applicability suspect. We have seen instances where upon issuance of additional equity, usually defined as a capital raise or recapitalization beyond general operating capital needs, partial dilution protection exists. This partial dilution protection has the effect of increasing the number of share-based compensation shares available when an additional capital raise takes place.
In essence, the expected price per share distribution becomes unpredictable and the number of shares the option holder would receive (not pictured here) becomes probability-based considering such factors as the amount and timing of additional funds being raised:
its option in a number of years to purchase the company’s stock for $1.00. If the term for this option was 5 years, below is how that “plain vanilla” share-based compensation option could be valued:
As an added bonus, I’ve included the N(d2) or a measure of the probability that this particular option will end “in-the-money”. This is the percentage of the distribution that falls to the right of the line (Xn).
Below are generally those conditions observed related to share-based compensation and why the BSM fails to adequately capture the impact on the value.
Anti-Dilution ConsiderationsShare-based compensation as options are issued directly by companies, as opposed to being traded on public exchanges. Exercising the share-based compensation generally results in the issuance of additional shares, which then allows the option holder to purchase these new shares at the agreed upon (i.e. strike) price.
Example II now assumes that there were 1,000,000 shares outstanding, and the warrant creates an additional 500,000 shares.
Share Option Value =
(Old Number of Shares[N] + Number of New Shares[M])
Call Option Value
Old Number of Shares[N]
Symbol Description Amount
S Stock Price $1.00
X Exercise Price $1.00
Return (Annual) 1.25%
r Return (Continuously Compounded) 1.24%
(T - t) Total Time (Years) 5.00
σ Volatility 60.0%
Dividend Yield (Annual) 0.00%
Dividend Yield (Continuously Compounded) 0.00%
Call Option $0.51
Components of the Formula:
N(d1) 0.7633
N(d2) 0.2661
Example I: Black-Scholes Option Pricing Model – Vanilla Call Option
Symbol Description Amount
S Stock Price $1.00
X Exercise Price $1.00
Return (Annual) 1.25%
r Return (Continuously Compounded) 1.24%
(T - t) Total Time (Years) 5.00
σ Volatility 60.0%
Dividend Yield (Annual) 0.00%
Dividend Yield (Continuously Compounded) 0.00%
Call Option $0.51
w dilution $0.34
Components of the Formula:
N(d1) 0.7633
N(d2) 0.2661
N Shares Outstanding 1,000,000
M New Shares 500,000
Diagram II:
Simplified
Illustration
of Future
Stock Price
Uncertainty
and BSM
Prob
abili
ty (%
)
Dollar ($)
Zero Value Positive Value
(Sn)(So)
(xn)
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the probability that the subject equity will be worth more than the entire world’s economy. Increasing the term or time assumption shifts the distribution to the right, which increases the influence of time value (versus today’s intrinsic value) on the conclusion.
The following diagram illustrates the effect of the distribution as time increases:
As far as we know, there is no specific guidance as to what contractual term classifies an option as a longer term option. However, one generally does not see qualified practitioners using terms greater than 4 or 5 years in a BSM framework.
Diagram III:
Simplified
Illustration
of Dividend
Impact on BSM
logic
Prob
abili
ty (%
)
Dollar ($)
Zero Value Positive Value
(Sn)(So)
(xn)
To illustrate another way, I’ve laid out a table showing simple participation dilution alongside a table assuming some sort of anti-dilution protection were in place. In this example, the anti-dilution protection increases as the number of additional shares associated with a capital raise increases. The field shows the value of the share-based compensation option for various combinations of current stock price and amount of new shares issued as part of the additional capital raise.
Applying the BSM will most certainly not capture the relationship either. As a result, using an open form model, like a Binomial Option Pricing Model (BOPM) or Monte Carlo simulation would more accurately reflect the value of the share-based compensation.
Current Stock Price (S0)
Down Round ProvisionsPopular with earlier stage companies and often embedded in financing packages, down round provisions lower the strike price of a warrant if the underlying share is issued in the future at a lower value than preceding rounds. Common terminology when describing the amount the share-based compensation strike price changes depending on the price at which the new equity is offered includes partial or full ratchet.
The use of a BSM is discouraged by the SEC when valuing options with this type of provision, since there is no way for the BSM to incorporate the value of this protection in its simplified math. As a result, one should consider using a BOPM, probability weighted expected return model (PWERM) or Monte Carlo simulation when valuing warrants with down round provisions.
For visualization purposes, for warrants with down round provisions, not only does the future share price vary, but now the exercise price location on the diagram could be somewhere significantly left of where it started.
Longer Term OptionsThe BSM makes very simplistic assumptions regarding the distribution of future stock prices in relation to the company’s current stock price. Longer term assumptions tend to result in overstating the option’s value, since logically impossible scenarios are more frequently implied in the distribution, such as
0.25 0.50 1.00 1.25 1.50
NEW SHARES (M)
200,000 0.04 0.14 0.43 0.59 0.76
350,000 0.04 0.13 0.38 0.53 0.68
500,000 0.03 0.11 0.34 0.47 0.61
650,000 0.03 0.10 0.31 0.43 0.56
800,000 0.03 0.09 0.29 0.39 0.51
0.25 0.50 1.00 1.25 1.50
0.04 0.16 0.47 0.65 0.84
0.04 0.15 0.45 0.62 0.80
0.03 0.14 0.43 0.59 0.76
0.03 0.14 0.41 0.57 0.74
0.03 0.13 0.40 0.55 0.71
0.25 0.50 1.00 1.25 1.50
0.00 0.01 0.04 0.06 0.08
0.01 0.02 0.07 0.09 0.12
0.01 0.03 0.09 0.12 0.15
0.01 0.03 0.10 0.14 0.18
0.01 0.04 0.11 0.16 0.20
New Distribution assuming longer time to expiration
TABLE 1: Vanilla Call Option Value (w full dilution)
TABLE 2: Call Option Value with Non-Linear Anti-Dilution Provision
The following table illustrates the impact of time on the value of the share-based compensation assuming all else (i.e. risk-free rate, volatility, dividend yield, etc.) remain equal. The necessary changes in those assumptions would further exacerbate the issue. An open form model like the BOPM would allow the appraiser to temper the impact of time on the longer termed securities or increase the risk associated with those far off payouts.
It’s interesting to note that for deep out-the-money options, the impact of the time value is much greater as a percentage of the shortest term option value, than those options at- or out-of-the money.
Knock-In OptionsKnock-in options are a type of breaking option, which are exercisable when the underlying share price rises above a certain amount greater than the option’s strike price. For example, an option which “knocks-in” at a stock price of $7.50/shr, but with a strike price of $5.00/shr means that when the share price is between $5.01/shr and $7.49/shr, there is no value. However, once the stock hits $7.50/shr, the option holder can realize $2.50/shr gain along with any value above the $7.50 price per share. This diagram illustrates the range of prices and associated probability by which the BSM will overstate the option value.
There are ways to use combinations of BSMs to get to a better value estimate. However, we’d recommend just going with a BOPM, PWERM or Monte Carlo and avoid the number of limitations afforded by the BSM in these cases.
Changing VolatilityVolatility tends to be greater for emerging and growing companies. As companies mature, volatility may decrease significantly. The companies that are more apt to offer share-based compensation are emerging companies that wish to preserve capital by offering alternative compensation to its employees. The BSM only allows consideration of a single volatility estimate. A high volatility number can result in a significantly different distribution of future expected prices:
Relying on the initial high volatility number for the life of the share-based compensation option will overstate the value if the company is expected to mature during the term of the share-based compensation.
One should consider using an open-form model or PWERM when valuing these options so that the assumptions regarding volatility and up-side/down-side potential may be adjusted over the life of the share option.
Most folks are aware of the impact that volatility has on option prices, but here’s a table using our running vanilla call option example at varying current stock prices and volatility amounts. Were volatility to change over time, the BSM could not capture such period-by-period adjustment, and the values below would be unpredictably different.
TABLE 4: Vanilla Call Option and Term
[Current Stock Price (S0)]
0.25 0.50 1.00 1.25 1.50
TERM (N)
5 0.05 0.17 0.51 0.71 0.92
7 0.07 0.22 0.59 0.80 1.01
10 0.11 0.28 0.68 0.89 1.11
15 0.15 0.34 0.78 1.00 1.23
20 0.17 0.39 0.84 1.07 1.31
Prob
abili
ty (%
)
Dollar ($)
Zero Value Positive Value
(Sn)(So)
(xn)
Diagram V:
Simplified
Illustration of
Volatility on
BSM logic
High Volatility Curve
(Xn)
Prob
abili
ty (%
)
Dollar ($)
Zero Value Positive Value
(Sn)(So)
(xn)
Diagram IV:
Simplified
Illustration
of Knock-In
Option Value
and BSM Logic
Value that should not be ascribed to the share options that the BSM alone cannot account
(Xn)
Knock-in-Price
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The following table illustrates the simple, yet significant, impact of assuming the share-based compensation issuer pays a steady dividend over the life of the share-based compensation. Using a BSM, once cannot calculate a reasonable value assuming a lumpy dividend payment and clearly consideration of dividend payments is important.
ConclusionThe reality is that private companies must meet a higher standard than public companies in the valuation of share-based payments as compensation for both financial reporting and tax purposes. Using a BSM will not work to produce a reliable value if the inputs make no sense and key terms must be ignored to fit a square peg in a round hole. If you are in a situation where share-based compensation values are required, and you are not sure if any of the above matter applies, discuss with a qualified valuation professional. A quick read-through of the agreement and a brief conversation regarding the business model should be enough to understand the risks of using one valuation method versus another.
About WithumSmith+Brown, PCWithumSmith+Brown, PC (Withum) professionals offer valuation services to help companies comply with ASC Topic 718 and IRC Section 409A (Section 409A). With a well-established track record in the venture capital/private equity community, our professionals have the technical and industry knowledge to effectively support the valuation requirements of venture-backed companies. We can also involve our tax and accounting advisory colleagues if needed.
TABLE 5: Vanilla Call Option Value and Dividend
[Current Stock Price (S0)]
0.25 0.50 1.00 1.25 1.50
DIVIDEND
1.0% 0.04 0.16 0.48 0.66 0.86
2.5% 0.04 0.14 0.43 0.59 0.77
5.0% 0.03 0.11 0.35 0.50 0.65
7.5% 0.02 0.09 0.29 0.42 0.55
10.0% 0.02 0.07 0.24 1.35 0.46
Lumpy Dividend PaymentsThe BSM’s future stock price distribution is based, in part, on the expected growth in equity value for the company as a whole. Dividend payments reduce the equity value. The BSM will accept a dividend yield input which shifts the area under the future stock price distribution to the left, as illustrated below:
If the historical dividend payments have been lumpy, or are expected to be lumpy going forward or event based, then again (as above) the BSM’s ability to properly draw the distribution of future stock prices is negated. Additionally, if the option is exercisable before a large dividend payment, the holder may be incentivized to exercise the option immediately prior to the dividend payment which cannot be captured by the BSM.
