By John Summa, CTA, PhD, Founder of HedgeMyOptions.com and OptionsNerd.com

Valuation of ESOs is a complex issue but can be simplified for practical understanding so that holders of ESOs can make informed choices about management of equity compensation.

Valuation
Any option will have more or less value on it depending on the following main determinants of value: volatility, time remaining, risk free rate of interest, strike price and stock price. When an option grantee is awarded an ESO giving the right (when vested) to buy 1,000 shares of the company stock at a strike price of $50, for example, typically the grant date price of the stock is the same as the strike price. Looking at the table below, we have produced some valuations based on the well known and widely used Black-Scholes model for options pricing. We have plugged in the key variables cited above while holding some other variables (i.e. price change, interest rates) fixed to isolate the impact of changes in ESO value from time-value decay and changes in volatility alone.

First of all, when you get an ESO grant, as seen in the table below, even though these options are not yet in the money, they are not worthless. They do have significant value known as time or extrinsic value. While time to expiration specifications in actual cases can be discounted on the grounds that employees may not remain with the company the full 10 years (assumed below is 10 years for simplification), or because a grantee may conduct a premature exercise, some fair value assumptions are presented below using a Black-Scholes model. (To learn more, read What Is Option Moneyness? and How To Avoid Closing Options Below Instrinsic Value.)

Assuming you hold your ESOs until expiration, the following table provides an accurate account of values for an ESO with a $50 exercise price with 10 years to expiration and if at the money (stock price equals strike price). For example, with an assumed volatility of 30% (another assumption that is commonly used, but which may understate value if the actual volatility across time turns out to be higher), we see that upon grant the options are worth $23,080 ($23.08 x 1,000 = $23,080). As time passes, however, let's say from 10 years to just three years to expiration, the ESOs lose value (again assuming price of stock remains the same), falling from $23,080 to $12,100. This is loss of time value.

Theoretical Value of ESO Across Time - 30% Assumed Volatility
Stock Price $50 $50 $50 $50
Volatility 30% 30% 30% 30%
Time Remaining 10 Years five years three years two years
Risk-Free Rate 3% 3% 3% 3%
Strike Price $50 $50 $50 $50
Fair Value $23.08 $15.99 $12.10 $9.69
Total Value $23,080 $15,990 $12,100 $9,690
Figure 3: Valuation of an ESO, assuming at the money, while varying time remaining. Assumes non-dividend paying stock.




Figure 4: Fair value prices for an at-the-money ESO with exercise price of $50 under different assumptions about time remaining and volatility.

Figure 4 shows the same schedule of prices given time remaining until expiration, but here we add a higher assumed level of volatility - now 60%, up from 30%. The yellow plot represents the lower assumed volatility of 30%, which shows reduced fair values at all time points. The red plot, meanwhile, shows values with higher assumed volatility (60%) and different time remaining on the ESOs. Clearly, at any higher level of volatility, you are showing greater ESO value. For example, at three years remaining, instead of just $12,000 as in the previous case at 30% volatility, we have $21,000 in value at 60% volatility. So volatility assumptions can have a big impact on theoretical or fair value, and should be factored decisions about managing your ESOs. The table below shows the same data in table format for the 60% assumed levels of volatility. (Learn more about the calculation of options values in ESOs: Using the Black-Scholes Model.)

Theoretical Value of ESO Across Time – 60% Assumed Volatility
Stock Price $50 $50 $50 $50
Volatility 60% 60% 60% 60%
Time Remaining 10 Years five years three years two years
Risk-Free Rate 3% 3% 3% 3%
Strike Price $50 $50 $50 $50
Fair Value $35.34 $26.76 $21.20 17.45
Total Value $35,340 $26,760 $21,200 $17,450
Figure 5: Valuation of an ESO, assuming at the money, while varying volatility



Next: Employee Stock Options: Risk and Reward Associated with Owning ESOs »



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