September 01, 2010

Companies continue to employ creative and unique financial instruments to incentivize management in an effort to align their compensation with shareholder return. Commonly employed financial instruments such as stock options and restricted stock awards have advantages and disadvantages as contemplated by equity investors and employees. One of the more recent developments in this regard relates to the introduction of performance units with total shareholder return requirements. Given the recent volatility in the global capital markets, performance units with total shareholder return components are being designed such that executive compensation is aligned with shareholder return *relative to a peer group*, as opposed to being solely based on equity appreciation. (The concept being that management “outperforming” the industry even in a downturn when everyone’s stock price is declining should be rewarded.)

The introduction of these securities has presented unique valuation issues as it pertains to computing compensation expense for financial reporting purposes. An accurate assessment of the value of such securities is obviously critical as the compensation cost is reflected from an income statement perspective and thus impacts earnings per share.

As a general overview, performance units are a form of compensation issued to an employee only after the achievement of certain pre-determined performance thresholds. Commonly, corporations issue performance units based on the total shareholder return (“TSR”) of the company’s stock relative to a defined group of “peer” companies or an index. In the valuation work that SRR has performed in this regard, TSR is typically defined as follows:

A valuation challenge arises when measuring the cost of the units to be granted. This article addresses the methodologies utilized to value performance units, as well as the associated value drivers.

Pursuant to Financial Accounting Standards Board (“FASB”) Accounting Standards Codification (“ASC”) Topic 718, *Compensation – Stock Compensation *(“FASB ASC 718”), the cost of performance units is determined upfront upon grant, as the cost of the units is measured at Fair Value based on the expected probability that the performance thresholds are achieved. FASB ASC 718 defines Fair Value as the amount at which an asset (or liability) could be bought (or incurred) or sold (or settled) in a current transaction between willing parties, that is, other than in a forced or liquidation sale. The cost is recognized over the period during which an employee is required to provide service in exchange for the award. FASB 718 requires an entity to measure the cost of employee services received in exchange for an award of equity instruments based on the Fair Value of the award as of the grant date.^{1} While the guidance associated with FASB ASC 718 centers around the application of a binomial pricing model to determine the value of option like securities – it is more common to employ a Monte Carlo simulation to value this type of a security.

A Monte Carlo analysis is a simulation of a specified future outcome based on a class of computational algorithms that rely on repeated random sampling. Through this analysis, the outcome of a specific unknown quantity (i.e., the Fair Value of future performance unit grants) is determined based on random variation, within a given probability distribution, in certain specified underlying variables.

In the valuation of performance units with total shareholder return requirements, the typical key inputs necessary to derive Fair Value are volatility of the subject company as well as the comparable companies (or index), the respective dividend yields, and market correlation. To illustrate the concepts, we have performed a sample analysis to demonstrate the change in Fair Value of the financial instrument given changes in each of these economic drivers. It should be noted that the following case study is hypothetical in nature and may contain different facts and circumstances of individual plans. However, while the magnitude in the change of Fair Value may differ based on the change in assumptions, it is likely that the directional impact would remain the same.

Consider the following example:

- The board of directors of ABC Company (“ABC”), a publically traded company, issued performance units to its executive management team on December 31, 2009 (the “Award”).
- The performance awards are based on the TSR of ABC’s stock (trading at $10.00 per share on December 31, 2009) relative to the stocks that make up the Dow Jones Industrial Average (“DJIA”) over a three-year period ending December 31, 2012 (the “Term”).
- The number of awards to be granted is predicated on a comparison of the TSR of ABC to the companies comprised of the DJIA. A base award is increased or decreased according to the following schedule:

In this case study, a TSR return in the 60th percentile of the peer group would yield an award equal to 125% of the base number of awarded units, while a TSR return in the 40th percentile would yield an award equal to 75% of the base number of awarded units.

To properly measure the cost of the grant at Fair Value, a Monte Carlo analysis is used to determine the most likely total shareholder return of ABC’s stock relative to the companies included in the DJIA over the Term. To determine the TSR of ABC’s stock as well as the 30 individual DJIA stocks, an analyst must estimate the ending stock price and any dividends to be paid over the Term. The mean expected ending stock price for each of the companies, including ABC, is calculated utilizing a risk-free rate of return of 1.70%, which is the three-year U.S. Treasury bond rate as of December 31, 2009. The risk-free rate is used to increase the beginning stock prices for each of the companies over a three-year period, resulting in the mean estimated stock price at the end of the Term for each of the comparable companies, as well as ABC. The mean estimated ending stock price is then utilized to estimate the lognormal distribution of expected stock prices for each of the comparable companies. A volatility factor is utilized to estimate the standard deviation from the mean ending stock price (i.e., the probability weighted distribution of all possible outcomes of the company’s ending stock price). Finally, the dollar value of the expected dividends to be paid over the Term is added to the ending stock price to determine the stock’s return. The TSR of ABC is compared to the TSRs of all 30 DJIA companies to determine ABC’s expected TSR percentile and the associated vesting percentage of the Award.

A Monte Carlo simulation is then utilized to simulate the above methodology (30,000 times in this example), with variation in the TSR of every stock based on a probability weighted (i.e., lognormal) distribution pattern. Further, to incorporate the interconnectedness of the index and the market as a whole, a correlation coefficient is applied to the simulation of each TSR relative to the DJIA.

Based upon these assumptions and fact pattern, we further examined the sensitivity of the value conclusion given changing assumptions in volatility, dividend yield, and market correlation.

Volatility is a measure of the risk associated with a stock. Specifically, volatility is a measure of the variation in the returns of a stock. Generally speaking, a stock with low volatility yields relatively consistent returns, while a stock with high volatility would likely yield inconsistent and less predictable returns. As such, a high volatility indicates a riskier stock.

The volatility utilized to calculate the lognormal distribution of expected stock prices for each comparable company was based upon the observed historical volatility over the three-year period ending December 31, 2009.^{2}

It is important to consider the impact of the assumed volatility in the analysis of performance units. In the instant case, the value of the Award is based on an asymmetrical vesting schedule. For any TSR percentile under 30%, the recipient receives 50% of the total number of shares available to be granted. As such, a low ABC volatility relative to the DJIA implies that it is less likely that ABC will outperform the benchmark companies. As such, a low volatility assumption decreases the likelihood that ABC’s TSR will be at the high end of the range observed as compared to the comparable companies, thereby resulting in a lower expected number of Awards in the instant case. Conversely, a higher volatility, relative to the comparable companies, would likely result in a greater number of Awards. The following table illustrates the Award value per share sensitivity to changes in the assumed volatility of ABC’s stock.

As illustrated in the chart, a 50% increase in ABC’s volatility results in a 5% change in the Fair Value of the award. In this case study, the award payout was not highly sensitive to changes in volatility largely due to the minimum and maximum range associated with the payout schedule.

The second key input in this analysis is the dividend yield. Once the ending stock prices have been projected via the Monte Carlo simulation, the applicable dividends to be paid over the time period are calculated. In the instant case, the dividend yield assumption for each comparable company was based upon the three-year period prior to December 31, 2009.^{3}

As with volatility, it is important to consider the impact of the assumed dividend yield in the valuation analysis. As a direct component of TSR, the dividends paid over the Term have a significant impact on the TSR percentile. As the assumed dividend yield of the subject company increases relative to the comparable companies, so too will the mean TSR (holding volatility constant) and, correspondingly, the Fair Value of the Awards.

All else held constant, a greater dividend yield will result in a greater TSR, and thus a greater award value. In practice, however, it is important to consider how changes in dividend yield would impact a security’s share price, as this would also impact a company’s TSR.

The final key input in the analysis is the correlation coefficient of the individual companies. A correlation coefficient is a measure of the degree of which one security moves in sync with another. Because a performance unit is commonly based on a comparison of a company’s stock to a group of its peers, a correlation coefficient is an important input because it captures the fact that certain macroeconomic and industry-specific factors will influence the TSR of all the stocks in a given index or industry. In the instant case, the correlation coefficient of each comparable company and ABC to the stock market as a whole^{4} was included in the simulation of the expected results. We applied a correlation coefficient applicable to each company specifically, as calculated using the daily returns implied by the company’s stock price, compared to the same return calculation for the market over the three year period ended December 31, 2009.^{5}

Finally, an analyst must consider the impact of the assumed correlation coefficient between the subject company and the market. A low correlation coefficient indicates that ABC’s TSR is not strongly tied to that of the DJIA. In this respect, it is more likely that ABC’s TSR will deviate from that of the companies included in the DJIA, thereby increasing the likelihood that ABC’s TSR will exceed that of the DJIA companies. Conversely, it should be noted that the opposite is also true; there is an increased likelihood in the instant case that ABC’s TSR will be lower when the DJIA’s TSR is high. The following table illustrates the sensitivity of the Award value to changes in ABC’s assumed market correlation.

As shown in the chart, a lower correlation coefficient results in an increased chance that the subject company’s TSR will move independent of its peer group. As such, a lower correlation coefficient (or a negative change in correlation per the graph) would yield a greater award in this case.

As corporations implement performance units to tie management compensation with *relative* performance, it is important for boards and financial management to consider the cost of the award in their planning. Traditional valuation models (such as discounted cash flow analysis, binomial option pricing) may not be robust enough to handle the statistical analysis required with performance units. As such, Monte Carlo simulations have become the preferred methodology in this context. Correspondingly, as each plan has unique characteristics associated with the total shareholder return requirements, it is critical that management consider the potential Fair Value implication as the structure is developed. Thus, it is useful that management understands how changing variables in the structure of awards impact the ultimate Fair Value conclusion via the application of a Monte Carlo simulation.

^{1} FASB ASC 718

^{2} Ideally, the volatility of each company should be based on observable inputs specific to each company. Please refer to the SRR article, “Market Collapse and Option Modifications” (published Summer 2009), which can be found in the “Resource Center” section.

^{3} Ideally, the dividend yield of each company should be based on observable inputs specific to the company.

^{4} As a proxy for the stock market as a whole, we utilized the DJIA.

^{5} Ideally, the correlation coefficient of a company should be based on observable inputs specific to the company.