Valuing Employee Share Options-ESOP

Valuing an employee share option plan using black Scholes

Employee stock options (ESOPs) are a form of compensation that gives employees the right to buy a certain amount of company shares at a predetermined price for a specific period of time. ESOPs are intended to align the interests of employees and shareholders, as well as to attract and retain talent.

However, ESOPs also have a cost for the company that grants them, as they represent a liability that is yet to be settled. Therefore, it is important to measure and report the fair value of ESOPs in the financial statements, as required by accounting standards.

One of the most common methods to estimate the fair value of ESOPs is the Black-Scholes model, which is based on a formula that was originally developed for valuing options on stocks that do not pay dividends. The Black-Scholes model can be adapted to value ESOPs by taking into account the specific features and assumptions of the plan.

The Black-Scholes formula for valuing an ESOP option is:

C = S * N(d1) - K * e^(-rT) * N(d2)

where:

- C is the fair value of the option

- S is the current market price of the underlying stock

- K is the exercise price of the option

- T is the expected life of the option

- r is the risk-free interest rate for the duration of the option's expected life

- N(d) is the cumulative standard normal distribution function

- d1 = (ln(S/K) + (r + sigma^2/2) * T) / (sigma * sqrt(T))

- d2 = d1 - sigma * sqrt(T)

- sigma is the expected volatility of the stock price over the option's expected life

The Black-Scholes model requires some inputs that are observable in the market, such as S, K, r, and T, and some inputs that are not directly observable, such as sigma and N(d). Therefore, some estimation and judgment are needed to determine these inputs.

The expected life of the option is not necessarily equal to the contractual term of the option, as employees may exercise their options before they expire or forfeit them if they leave the company. The expected life can be estimated based on historical or expected exercise and forfeiture patterns or by using a simplified method such as dividing the contractual term by two.

The expected volatility of the stock price reflects how much the stock price fluctuates over time. The higher the volatility, the higher the value of the option, as it increases the probability of making a profit from exercising the option. The expected volatility can be estimated based on the historical or implied volatility of similar publicly traded options or stocks or using industry or peer group averages.

The expected dividend yield is another factor that affects the value of an ESOP option, as it reduces the value of holding the stock. The higher the dividend yield, the lower the value of the option, as it decreases the expected growth rate of the stock price. The expected dividend yield can be estimated based on historical or projected dividends paid by the company.

The Black-Scholes model has some advantages and disadvantages for valuing ESOPs. The main advantage is its simplicity and wide acceptance, as it can be easily calculated once the inputs are known. The main disadvantage is that it may not capture some complex features of ESOPs, such as vesting conditions, performance criteria, early exercise behavior, marketability discounts or dilution effects. For these cases, more sophisticated models such as binomial or Monte Carlo models may be more appropriate.

The following is an example of how to use the Black-Scholes model to value an ESOP:

Assume that a company grants 1000 options to an employee on January 1, 2023. The options have an exercise price of $50 and vest over four years (25% each year). The options expire after 10 years. The current stock price is $60. The risk-free interest rate for 10 years is 3%. The expected dividend yield is 2%. The expected volatility is 30%.

Using these inputs, we can calculate d1 and d2 as follows:

d1 = (ln(60/50) + (0.03 + 0.3^2/2) * 10) / (0.3 * sqrt(10)) = 1.32

d2 = 1.32 - 0.3 * sqrt(10) = 0.42

Then we can use a standard normal distribution table or calculator to find N(d1) and N(d2):

N(d1) = 0.9066

N(d2) = 0.6628

Finally, we can plug these values into the Black-Scholes formula to get the fair value of one option:

C = 60 * 0.9066 - 50 * e^(-0.03*10) * 0.6628 = $34.67

Therefore, the fair value of 1000 options is $34,670.

In conclusion, valuing an ESOP option using black scholes is a common and simple method that requires some assumptions and inputs that may not be directly observable in the market. The accuracy and reliability of this method depend on how well these assumptions and inputs reflect the reality and expectations of the plan.