Valuing performance rights – LTIP

• Fixed salary
• Short term incentives
• Long term incentives.

Short term incentives typically result in the payment of cash bonuses based on achievement of near-term controllable objectives such as sales outcomes, retention of key staff, gross profit margins, average length of contracted customer revenues, etc.

Long-term incentives aim to align executive performance to expectations of shareholders and are typically structured by remuneration committees as performance rights (shares which issue for nil consideration if particular performance hurdles are met by the executives).

As a consequence, the CFOs need to comply with AASB 2: Share based payments. The performance rights (and ultimately the shares) that are issued under long-term incentive plans (LTIP) are treated as an expense under AASB 2.

It is the long-term incentives which are the subject of this article.

The critical question for the CFO and remuneration committee is the value of the shares expected to be issued under an LTIP at grant date and each successive vesting date.

Most performance rights are issued under LTIPs which specify performance hurdles which are either absolute performance or relative performance.

Commonly, a total shareholder return [“TSR”], return on assets [“ROA”] or return on equity [“ROE”] or growth in earnings per share [“EPS”] hurdle is employed as the vesting condition. Often the return measures and vesting occur over three years and have a retention clause (i.e. the executive is still in the employ of the company at the vesting date) and an escrow condition restricting disposal of the shares for a period of twelve months.

ASX300 Historical Total Shareholders Return (%)

The challenge for the CFO (and auditors) is the assessment of the value of the performance rights granted to the executive at the beginning of each plan year.

The expense under AASB2 requires an assessment of the likely achievement of the performance hurdles which – in the case of relative TSR performance – requires consideration of the likely returns (share price and dividends) of the company compared against a universe of peer companies (often an index such as ASX300 or Small Cap Companies). This requires a very robust ‘crystal ball’ which forecasts the returns of each of the peer companies and the issuing company.

Many CFOs have assumed that the Black-Scholes Option Pricing Model [“BSOPM”] can accurately assess the likely value of performance rights. Performance rights exhibit some characteristics of a zero-exercise price option which is not entitled to dividends.

We have demonstrated time and again that the BSOPM was neither intended nor capable of accurately assessing the value of performance rights as it does not consider specific conditions of vesting of those performance rights. Our LTIP survey of 2017 sets out the technical reasons why the BSOPM fails to reliably value performance rights.

Working with capital market experts, auditors and academics, Peloton Corporate has developed a proprietary approach to the valuation of performance rights which rely on TSR and other hurdles. The approach is based on Monte Carlo analysis (our models assess value across the various input variables in 500,000 iterations) and has been audited by all of the major accounting firms in application to listed and unlisted companies.

This article outlines some of the technical issues which need to be considered in the valuation process and also some recent experiences of Peloton Corporate in valuing performance rights.

If you are a CFO or a remuneration committee member here are two key reasons to read on:

1. To reduce potential auditor ‘friction’
2. Remove the possibility of over-expensing the share-based payment that inevitably occurs through the use of BSOPM¹.

1. AASB2: Para no. 23 prohibits any adjustment to the equity after vesting date. For example, the entity shall not subsequently reverse the amount recognised for services received from an employee if the vested equity instruments are later forfeited or, in the case of share options, the options are not exercised.

The basics: Black-Scholes option pricing model & Monte Carlo methods

The science of option valuation relies heavily on the calculation of key probabilities and expected values.

For a Black-Scholes-style European call option, the valuer needs to estimate the probability that the option will finish in-the-money (i.e., that the share price will exceed the exercise price), and the expected payoff to the option in that case. The Black-Scholes scenario is sufficiently simple that a closed-form formula can be derived (the celebrated Black-Scholes equation).

Unfortunately, the characteristics of an option need not depart too far from the Black-Scholes world to significantly complicate the valuation. Even moving from a European-style option to an American-style option (which can be exercised prior to expiry), we cannot obtain closed-form solutions. Hence, numerical procedures (such as Monte Carlo simulation or the Binomial approach) are required.

The Monte Carlo approach simulates many time-series paths of the underlying asset assuming that the share price evolves according to the geometric Brownian motion model. The simulated price paths are calibrated to historical data (e.g. stock volatility and dividend payments) so that they are a plausible representation of possible future paths. For any given simulated path, one can estimate if the option will be in the money, whether the employee will exercise it, and what the payoff will be. The options are valued for that particular path by discounting the option payoff to present value.

The entire simulation/valuation process described above is repeated many times. Each simulation represents a plausible, yet different, outcome. By simulating many possible paths, the valuer is able to estimate the probabilities and expected values mentioned above. The value of the option is calculated as the average over all simulation runs. Valuations of performance rights are usually conducted using 500,000 Monte Carlo simulations, which is more than sufficient to obtain a precise estimate.

It is important to understand that Monte Carlo simulation is not an attempt to predict the future share price – this is impossible. Rather, the Monte Carlo approach simulates plausible future share-price paths. By repeating the simulation process many times, the valuer quantifies the probabilities and expected payoffs highlighted above.

Suitability of application: Black- Scholes vs. Monte Carlo methods

Black-Scholes option pricing model values the option under a set of well-defined rules. This model assumes that the option can only be exercised at the end of its tenor (i.e. European style options). BSOPM relies on the following five key inputs:

• Current underlying price
• Strike or exercise price
• Risk-free interest rate
• Time until expiration, expressed as a percent of a year
• Implied volatility.

As a general rule, the above parameters will impact options valuation estimated using BSOPM as follows:

It is important to highlight that the option value may react differently due to the various levels of inputs for each of underlying security price, strike price and implied volatility.

The Black-Scholes model cannot be accommodated to value options with some unique conditions (vesting conditions or performance hurdles). As stated earlier, these conditions may include differing vesting periods for multiple performance hurdles and performance conditions covering a range of outcomes of ROA, ROE, EPS, margins, or any of their variants over a given period of time. If Black-Scholes model is applied where any of these limiting conditions apply, then it tends to overprice the option valuation.

Monte Carlo methods offer a resolution to the shortcomings which limit the application of Black-Scholes model, as discussed above. As mentioned earlier that these performance conditions can either be market-based or non-market-based. It is important to highlight that, in theory, in the absence of any performance hurdles both of these valuation methods should produce virtually the same valuation result.8

The chart on the following page illustrates one instance where Monte Carlo methods should be preferred over Black-Scholes option pricing model to value performance offered under a long-term incentive plan.

For example, if a company awards its senior executive 50,000 performance rights if the company would achieve an EPS growth of 5% Compound Annual Growth Rate (CAGR) over the next three years. This three year period is also called the ‘performance period’. Each performance right would entitle the executive to receive a share in the company for nil consideration. First, we will value these performance rights using the Black-Scholes model and the Monte Carlo method; and, then, compare these valuations with some plausible explanations.

In order to apply the Black-Scholes model, the following assumptions will be used:

• Underlying security price of $10.00
• Option strike price of ‘nil’
• Maturity period of three years
• Risk-free rate of 3% per annum
• Security price volatility of 50% (implied volatility).

Using the above inputs, we estimate the value of $10.00 for each performance right. The Black-Scholes model cannot capture the probability of that company achieving the EPS CAGR of 5.0%. Our starting point under application of the Black- Scholes model is the assumption that the company has achieved the EPS CAGR of 5.0% by the end of the performance period.

Whereas under the Monte Carlo methods, our starting point is the expected budget EPS growth over the performance period and its historical & forecast volatility. Let’s suppose that the company has budgeted for an EPS growth of 4.0% over the performance period. We have performed 50,000 iterations to simulate the outcomes based on the following parameters:

• Underlying stock price of $10.00
• Options strike price of ‘nil’
• Maturity period of three years
• Volatility of 50% in the EPS CAGR.

Based on the above parameters, our iterations reveal an average vesting percentage of 38.6% which is then multiplied by the underlying stock price of $10.00 to estimate the value of $3.86 for each performance right.

Analysis of Valuations using Black-Scholes & Monte Carlo Methods

Black-Scholes model assumes 100% probability of vesting as the model is incapable of estimating and capturing a vesting probability into the option valuation.

In contrast, Monte Carlo method considers all the possible outcomes based on the terms of the offer and simulates real life outcomes over the performance period. The following probability distribution of EPS CAGR, assuming normal distribution, has been developed with 4.0% mean EPS CAGR over the performance period with a standard deviation of 50.0% over the performance period. The area which is of interest to us is the right-hand side of this probability distribution with the EPS CAGR outcomes of 5.0% or above. We note a 38.6% probability of the company achieving an EPS CAGR of 5.0% or above. For the sake of simplicity, we have assumed, the executive of the company will either be awarded 100% performance rights if the company achieves an EPS CAGR of 5.0% or above, or nil performance rights if the EPS CAGR falls below 5.0%. Generally, companies will set a minimum threshold to qualify for a certain percentage of performance rights, aka vesting percentage. The vesting percentage will usually increase in line with the achievement of the performance threshold.

EPS CAGR Probability Distribution

There are three key parameters which impact the valuation under the Monte Carlo methods:

• Budget performance of the EPS growth
• Minimum threshold of a performance hurdle
• The standard deviation of the EPS growth.

We have examined each of these parameters with their possible impact on the valuation below.

Expected Budget Performance

It is generally assumed that the EPS growth will be normally distributed with its mean equal to the expected budget performance. That ‘mid-point’ becomes our reference point to estimate the vesting percentage. In our case, the budget EPS CAGR of 4.0% is below the minimum threshold of 5.0% to achieve 100% vesting of the performance rights.

In our example, we estimated the 38.5% probability of meeting the performance hurdle. If the budgeted EPS CAGR is, say, 4.9% instead of 4.0%, we can demonstrate that the expected vesting percentage will be marginally higher than 38.5% assuming everything else is unchanged. We have re-run the simulation with budgeted EPS CAGR of 4.9% and estimated a 39.6% probability of achieving an EPS CAGR of at least 5.0%.

EPS CAGR Probability Distribution

Minimum Threshold of a Performance Hurdle

The minimum threshold of a performance hurdle and its variance from the budgeted performance is another key determinant of the value of performance rights. If the minimum threshold is significantly higher than the budgeted performance then, as a general rule, the value of performance rights will be lower. In order to illustrate this point, we have increased the minimum threshold of 5.0% to 10.0% with the following EPS CAGR probability distribution:

EPS CAGR Probability Distribution

We can observe from the above distribution that the vesting percentage reduced from 38.6% to 32.6% as a result of increasing the minimum threshold from 5.0% to 10.0%.

Standard Deviation of the EPS Growth

Standard deviation plays a critical role in development of future EPS growth iterations. A higher standard deviation of the EPS growth will have two inter-related implications for the vesting percentage.

First, the EPS growth iterations would have a wider set of outcomes. We know the following from three sigma rule that:

• 3% of the random outcomes lie within one standard deviation on either side of the mean;
• 5% of the random outcomes lie within two standard deviations on either side of the mean; and,
• 7% of the random outcomes lie within three standard deviations on either side of the mean.

Secondly, given the above relationship between a mean and a standard deviation, a higher standard deviation will ‘bridge’ the gap between a minimum threshold of a performance hurdle and a budgeted performance, and will increase the value of performance rights.

In our example, the budgeted performance of the EPS CAGR is at 4.0% with the standard deviation of 50% and the minimum threshold of 5.0%. Let’s consider an extreme position and assume that the standard deviation of the EPS CAGR is 1.0% instead of 50.0%. The vesting will reduce significantly to 4.1% assuming no other change in other variables. The rationale is that the EPS CAGR is not volatile enough to meet the minimum threshold over the performance period.

The following graph reflects the probability distribution of the EPS CAGR with 1.0% standard deviation.

EPS CAGR Probability Distribution

Benefits of using an independent adviser

In our view, the following are the key benefits of an independent adviser.