Thu, Sep 1, 2016

Introduction to Valuation of Employee Incentive Schemes: Options

Employee incentive schemes embed optionality linked to performance indicators of the company.

Accounting rules are imposed to determinate fair value and costs associated to such schemes. The complexity of the scheme, and the optionality involved, can make this task quite challenging.

Employee incentive schemes are commonly used by companies to remunerate their employees and to give them a stake in the performance of the company as a whole. These schemes often involve granting employees instruments whose value is linked to the performance of the company, assessed by financial metrics such as EPS or ROCE, or by market metrics such as the share price of the company itself. 

Accounting rules such as IFRS 2 and ASC 718 require that the fair value of grants made under these schemes is determined, and that corresponding charges are booked in financial statements. Under IFRS 2, this calculation of fair value is required to incorporate the impact of ‘market-based conditions’, which are aspects of the scheme dependent on market variables, such as the company’s share price. Similarly, ASC 718 requires that fair value of ‘market conditions’ is reflected in the fair value of awards.

In practice, incorporating these market-based conditions when estimating the fair value of the grants requires an option-pricing model for a large proportion of schemes that do not have a very simple dependence on the behavior of the share price. Examples of such schemes include standard stock options, as well as more complex schemes, such as those where the amount received by participants varies according to a set of tiered share price targets, or where share price performance is assessed relative to the performance of a group of peer companies.

Option Pricing Models
Option pricing models are mathematical models which aim to capture the uncertainty of future stock performance by treating the future share price as random, and applying a probabilistic approach. These models typically incorporate parameters such as the average return on the shares and the expected variation of future returns. By specifying these parameters, a probability distribution of the return on the shares can be calculated.

Once appropriate parameters for the model have been estimated, the amount received by grant recipients for each level of the share price can be calculated, and from this the expected amount received can be determined. Discounting this to the time of the grant gives the present value of the grant.

The Black-Scholes Model
One common option pricing model is the Black-Scholes model. This model assumes that returns on the company’s shares follow a normal distribution. The standard deviation of this distribution (known as the volatility) provides a measure of the amount of uncertainty over future share price returns. This model also depends on the risk-free interest rate and the dividends paid by the company to its shareholders.

The Black-Scholes formulae provide a means of calculating the value of call and put options under the Black-Scholes model. The call option formula is the most common of these in employee incentive schemes, and gives the value of an instrument which provides the holder the right, but not the obligation, to purchase shares for a fixed amount at a single future date.

By specifying the values of the Black-Scholes model parameters, such as the volatility and risk-free interest rate, as well as the features of the option itself, such as its strike price (the price at which the shares can be purchased) and the time to the final date at which the underlying shares can be purchased (its maturity date), the present value of the option can be calculated.

Dealing with Complexity
However, the Black Scholes formula does not apply to instruments that are more complex than the simple options described above. Whilst there are alternative formulae for calculating the present values of other option-like instruments under the Black-Scholes model, these cannot cover the variation and complexity of real-world share-option schemes. In practice, the complexity of these schemes means that other methods must be used to estimate their fair value.

Binomial Trees
One common approach for determining the present value of more complex employee incentive schemes is the Binomial tree approach. This approach involves approximating the behavior of the shares by splitting the time until the final maturity of the grant into a large number of time steps. The share price is allowed to move either up or down by a fixed amount over each time step, and a probability is assigned to each of these two possibilities. By using a large number of these time steps, a large number of possibilities for the future share price can be considered, and by choosing appropriate values for the sizes of the up and down steps and their associated probabilities, the model can match the expected return and volatility under the Black-Scholes model.

The simplified share-price behavior assumed by this approach allows the value of the instruments at their maturity to be determined, and then tracked backwards by probability-weighting the values received under the ‘up’ and ‘down’ cases at each time step. This approach gives approximate values for the instrument throughout the time from grant to maturity, allowing the modelling of early exercise conditions, such as options that allow the holder to purchase shares between the grant date and the final maturity date, rather than just at a single date in the future.

Monte Carlo
Another common approach for estimating the fair value of employee incentive schemes is the Monte Carlo approach. Under this approach, random numbers following a normal distribution are used to produce a random share price path. If the share price at times before maturity is required to determine the value of the grant, multiple random numbers are used and the share price path is split into several time steps, with a random number being used to determine the price movement over each of the time steps. The value of the grant under that share price path can then be determined easily by calculating the value of any underlying performance hurdles or payoffs, and the resulting cashflows to the holder.

However, calculating the value of the scheme under a single share price path does not correspond to its value at the grant date, since many other share price paths would be possible in practice. The Monte Carlo approach deals with this by considering a very large number of different share price paths, with the present value determined as the average (discounted) value across all of the different paths considered. Each share price path will correspond to one possible outcome, and as the number of paths increases, more of the possible future outcomes will be considered in the analysis, and the average of the present values of the payoffs will approach the present value of the instrument.

The Monte Carlo approach allows the estimation of the fair value of schemes whose value depends on the share price at multiple dates, such as schemes where the amount received by the holder depends on the level of a trigger or hurdle at an earlier date.

In addition, Monte Carlo analysis allows the modelling of schemes where the payoff to the holder depends on performance relative to a peer group. In this case, a correlation matrix is used to generate a share price path for the company and for each peer, allowing the performance of the company relative to its peers to be assessed according to the terms of the scheme. This is then repeated for a large number of sets of share price paths for the company and its peers, allowing the present value of the grants to be determined in a similar manner to schemes depending only on the performance of the company itself.

Implementing Option Pricing Models
In practice, the level of variation in the schemes implemented by different companies, together with the complex mathematical modelling required and the steps involved in determining appropriate valuation assumptions (such as estimating the future share price volatility) can make the determination of the fair value of employee incentive schemes a challenging task.

Kroll performs fair value analysis of employee incentive schemes for a wide range of clients across industries and geographies, reporting under both IFRS and US GAAP. Our experience with modelling these schemes, together with the transparent and detailed analysis that we provide allows our clients to meet their fair value calculation requirements for even the most complicated employee incentive programs.


Valuation of businesses, assets and alternative investments for financial reporting, tax and other purposes.

Financial Instruments and Technology

The Kroll Financial Instruments and Technology practice is a leading solutions provider for asset managers, hedge funds, fund administrators, banks, insurers, private equity firms, commodity trading and investment firms, and corporations.