Are Your ESO Values on Target?






Employee stock options (ESOs) more closely resemble warrants than traditional options in that they result in the issuance of additional shares of stock. Like warrants, ESOs impact stock values because they are dilutive.

To determine the value of ESOs for a closely held company, first determine the fair value of common equity then allocate that value between the common stock and the ESOs .

The value of the options and the value of the common stock cannot be determined independently, with the remainder simply being allocated to the other. Because the value of each instrument is a function of the other, their values must be determined simultaneously.

The value of each of a company’s potentially dilutive instruments, including outstanding ESOs, warrants or convertible debt, must be included in the valuation of any new ESOs being granted.

Because closely held companies do not have historical volatility data, special rules apply when estimating expected volatility for these companies.

Keith Sellers, CPA/ABV, CVA, DBA, Yingping Huang, Ph.D., OCP, CISSP, and Brett A. King, Ph.D., serve on the faculty of the College of Business, University of North Alabama. Their e-mail addresses are, and, respectively.

Until recently, non-public companies that granted options, warrants or other types of stock-based compensation to their employees were not typically required to determine values for these complex derivative instruments. Current financial reporting standards such as FASB Statement no. 123(R), Share-Based Payment, as well as recent federal tax law changes (IRC § 409A) are compelling companies to value these financial instruments using stock option valuation models developed for publicly traded stock options.

But several issues are unique to the valuation of employee stock options (ESOs) for closely held companies. Even well-designed option valuation models will yield incorrect values if they are not modified to address these unique issues. These problems are not only a concern when the ultimate objective is to value ESOs. The failure to correctly value employee stock options can result in a material error in the appraisal of the underlying common shares.

Statement no. 123(R) does not prescribe a specific option valuation model. Rather, it states that “a lattice model (for example, a binomial model) and a closed-form model (for example, the Black-Scholes-Merton formula) are among the valuation techniques that meet the criteria required by this Statement for estimating the fair values of employee share options.”

However, the standard clearly states that the appropriate method to use depends on the “substantive characteristics of the instrument being valued.” Since ESOs include characteristics such as vesting schedules, anticipated employee turnover and the possible early/suboptimal exercise of the option, it is clearly more appropriate to use a lattice model that can incorporate these features.

The Hull-White approach is a lattice model that can be customized to fit virtually any option feature including the early exercise of options by employees, turnover and employee exit rates both before and after vesting, which can vary over the life of the option.

The model can incorporate suboptimal exercise assumptions (the conditions under which employees are expected to exercise their options in terms of the stock price reaching a specified multiple of the exercise price). Users can also incorporate historical or projected turnover and employee exit rate information into the model. Specifically, given an employee turnover rate, each node on the lattice contains a probability that the employee will exercise a vested option or forfeit an unvested option, depending on its probability of being “in the money” at that time.

When a publicly traded call option is exercised, the owner of the call option receives an existing share from an assigned call writer. The writing and exercising of such options have no effect on the value of the underlying shares. All basic option valuation models, including lattice models, were “constructed” to value these non-dilutive, publicly traded options.

When valuing employee stock options, it is critical to understand that ESOs are more correctly identified as warrants than options. Consistent with the financial literature, warrants are similar to call options, but the money (exercise price) goes to the issuer, not an option underwriter. When a warrant is exercised, the company issues new shares of stock, so the number of outstanding shares increases. In short, exercise of an ESO results in the issuance of new shares. Since by definition that issuance takes place at a price that is below fair value, ESOs dilute the value of common stock.

This dilution impacts the value of both the common shares of the company and its ESOs. For publicly traded companies, the dilutive effects are incorporated into observed market prices. However, this mechanism is not available for closely held companies that issue ESOs.

When valuing ESOs for a closely held company, CPAs must rely on an appraised value of common equity rather than an observed market-determined price. However, if the company has issued ESOs, this appraised value cannot merely be attributed to common shares. Rather, it must be allocated to both existing shares and all outstanding ESOs. Through dilution, the issuance of ESOs will directly impact the value of existing common shares. Since the value of the underlying shares is a direct input in the valuation of any ESO, any change in the value of the underlying common shares will impact ESO values. Thus, the dilution simultaneously affects the value of both the common shares and ESOs. The interrelationship between stock and ESO value was addressed by FASB in paragraph A38 of Statement no. 123(R):

“[E]xercise of employee share options results in the issuance of new shares by the entity that wrote the option (the employer), which increases the number of shares outstanding. That dilution might reduce the fair value of the underlying shares, which in turn might reduce the benefit realized from option exercise.”

To correctly account for these interrelationships, all new and existing ESOs and the common stock must be valued simultaneously. Since most option valuation models require stock value as an input (as opposed to an output), these models should be modified to let both stock value and ESO value be determined simultaneously, with fair value of equity being provided as an input.

The effects of these interrelationships on value can be demonstrated with the following examples. Assume that the value of common equity for a non-public company has been independently appraised at $5 million and there are 100,000 common shares outstanding. In the absence of any ESOs, the stock would be worth $50 per share.

Now assume that the company grants 10,000 ESOs with an exercise price of $50 each. The options have a maturity of 10 years and the typical attributes and assumptions shown in Exhibit 1 are used to value the options.

Based on this information, the use of a typical Hull-White lattice model with 1,000 time steps yields an option value of $27.75 per option. However, this value does not reflect the dilutive effect of the ESOs. Modifying the option valuation model to use a bisection method (see sidebar “ A Method for Partitioning Value”) that simultaneously determines the optimal stock price and option value yields the results shown in Exhibit 2.

As can be seen, dilution materially reduced the per-share or per-option value of both the stock and the ESOs. For this reason, the value of both the stock and the options can only be determined simultaneously. This interrelationship of values extends to any additional ESOs, warrants or other dilutive instruments. For example, now assume the same company already has an additional 10,000 ESOs outstanding, which were issued five years ago with an exercise price of $30. The appraised value of equity would be allocated as shown in Exhibit 3.

In summary, unless your option valuation model can simultaneously allocate values to stocks and all ESOs, it will yield incorrect ESO values for closely held companies. This, in turn, will result in incorrect stock valuations. Statement no. 123(R) states that “employee share options and similar instruments will be estimated using option-pricing models adjusted for the unique characteristics of those instruments” (italics added). Clearly, any “off-the-shelf” option valuation model must be adjusted to incorporate the dilutive effects of ESOs.

A Method for Partitioning Value

When valuing the common stock and ESOs of a closely held company, the appraised total value of common equity must first be determined using traditional business valuation methods.

This value must then be allocated between the various components of common equity, in this case common stock and ESOs. While this process is complicated by the fact that the value of each component is a function of the other component’s value, one can assume that the correct value of the company’s stock can be no less than zero and no more than the total value of common equity.

Using this information, the bisection method determines the midpoint of this interval and uses this midpoint as the stock price to calculate a value for the options. If the resulting sum of the option and stock values exceeds the total value of equity, the model understands that the midpoint value is too high. The model then discards values above the original midpoint, making the midpoint the top of the remaining interval of potentially correct stock prices. The model then uses the midpoint of the remaining possible stock prices and performs this procedure again.

Thus, with each iteration, half of the possible solutions are rejected. This process is repeated until the total value of the options and stock equals the total value of equity (within a specified tolerance, such as $0.01).

The authors have developed a software package called the BVR/DVA 123R Compliance Calculator that uses the method described above. For more information, visit

A final relationship between employee stock options and stock values should be mentioned. While the appraised value of equity was held constant in the preceding examples, the existence of ESOs may very likely influence the appraised value of common equity. A primary purpose of ESOs is to help attract, reward and retain valuable employees. The use of ESOs may allow the issuing company to pay below-market cash compensation while reducing employee turnover and improving productivity. In other words, while the issuance of ESOs will directly reduce stock values through dilution, the business appraiser should consider their potential impact on the amount, timing and uncertainty of future cash flows and other key variables affecting firm value.

The need to partition value between shares and ESOs is not the only issue when valuing private vs. public companies. Volatility is a critical input in any option valuation model because a relatively small change in this estimate can result in a large change in the value of the option. Unfortunately, volatility can also be one of the more difficult variables to estimate since it requires a combination of empirical data, advanced statistical techniques and the use of professional judgment. The appropriate measure of volatility, referred to as “expected volatility” in Statement no. 123(R), is that which is expected during the remaining life of the option. Expected volatility is most often estimated using historical price data. In fact, Statement no. 123(R), paragraph A21, states that “Historical experience is generally the starting point for developing expectations about the future.”

However, non-public companies have no historical price volatility by which to estimate expected volatility. For these companies, the standard provides two alternative sources of volatility information:

  1. Identify similar public companies. If a company can identify similar public companies, it should consider the historical, expected or implied volatility of those public companies’ shares to help estimate expected volatility.
  2. Identify an appropriate index. If no similar public companies can be identified, one should identify and use the volatility of an appropriate industry or subindustry index (see example at paragraph A139 of Statement no. 123(R)).

In either case, one must exercise judgment in identifying either appropriate similar companies or an appropriate index. FASB has determined that the choice of estimating future volatility requires professional judgment that cannot be prescribed, so it is up to the individual performing the valuation to determine (and support) which data and approach is most appropriate for the specific options he or she is valuing. In all cases, Statement no. 123(R) cautions that companies should be consistent in this and all critical inputs.


JofA article
How to ‘Excel’ at Options Valuation,” Dec. 05, page 57

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“Accounting for Employee Stock Options: A Practical Approach to Handling the Valuation Issues,” Journal of Derivatives Accounting, Vol. 1, No. 1 (2004), page 3
“How to Value Employee Stock Options,” Financial Analysts Journal, Vol. 60, No. 1 (Jan./Feb. 2004), page 114


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