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Performance Share Plans: Valuation and Empirical Tests

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Craig W. Holden & Daniel S. Kim (김성연) — Journal of Corporate Finance, Vol. 44 (2017), pp. 99–125. doi:10.1016/j.jcorpfin.2017.03.004

Research Question

Performance share plans (PSPs) are equity-based long-term incentive plans in which the number of shares awarded depends on achieving a pre-specified performance goal over a fixed period. They have grown from 26% of Forbes 250 firms in 2003 to 81% in 2014, surpassing stock options as the dominant incentive vehicle. Despite their scale — PSPs carry an average grant date value of $2.53 million and represent 14.0% of total CEO compensation — their fair value is poorly understood and inconsistently measured.

The central question is: can we derive theoretically grounded, closed-form valuation formulas for PSPs that outperform the heuristic rule of thumb currently used by most firms? And do these formulas actually track realized payouts better? The policy stakes are high: FASB requires grant date fair value disclosure for stock options but applies a less rigorous standard to PSPs, permitting many firms to report heuristic values based on the closing stock price times the target number of shares.

Data and Methodology

The empirical sample covers S&P 500 firms from fiscal years ending December 15, 2006 to December 31, 2012. The authors hand-collect plan design parameters from 2,881 firm-year proxy statements, identifying 1,435 firm-years with performance share plans carrying a mean target award of $2.53 million and a median of $1.80 million.

Three stochastic process models are developed to accommodate the variety of performance measures used in practice:

  • Arithmetic Brownian Motion (ABM) — for non-traded measures that can be negative, such as earnings per share (EPS) and free cash flow.
  • Geometric Brownian Motion (GBM) — for always-positive non-traded measures such as revenue.
  • Rank-order tournament of traded asset returns — for relative performance measures such as percentile of ranked stock returns vs. a peer group, modelled under Black-Scholes no-arbitrage conditions.

Under each model, closed-form propositions are derived for the date-0 value of a PSP with threshold goal L, target goal M, stretch goal H, and corresponding share allocations. The resulting formula values are compared to (1) reported proxy statement values, (2) heuristic values (NM × S0), and (3) realized actual payouts for a subset of 421 firm-years where maturity-date outcomes are observable.

Key Results

Performance measure landscape: The most common performance measures among the 2,881 firm-years are stock returns (24.7%), earnings per share (18.1%), EBIT (16.0%), and revenue (10.2%), with a wide variety of other measures comprising the remainder.

Formula vs. heuristic — ex ante: Table 5 compares formula values, reported values, and heuristic values for EPS, revenue, and stock return percentile plans. For EPS-based plans (198 firm-years), formula values average $2.85M vs. reported $2.81M and heuristic $2.70M — differences that are small and largely insignificant. For stock return percentile plans (420 firm-years), however, formula values average $1.98M vs. reported $2.36M and heuristic $2.22M — significantly lower, with formula-vs-reported differences of −16.0% (mean) and −17.3% (median) at the 1% significance level. This suggests that firms systematically overstate PSP values when performance is measured as relative stock return rankings, potentially for tax minimization under IRS §162(m).

Formula vs. actual payout — ex post: For plans where realized outcomes are available, the accuracy comparison depends critically on the method used to forecast future performance. When the prior five-year historical average is used as the performance forecast (Table 6), the formula produces larger errors than reported or heuristic values. But when analyst consensus prior to the grant date is used as the forecast (Table 7), formula values for EPS-based PSPs achieve valuation accuracy comparable to — or better than — reported and heuristic values. Specifically, the formula generates a dif-in-absolute-dif advantage of −0.29% (formula vs. reported) and −3.36% (formula vs. heuristic) for mean EPS plans, both directionally favorable though not always statistically significant.

Pre-grant analyst consensus (Table 8): Restricting the sample to firms with analyst consensus issued before the grant date produces the sharpest results. For EPS-based performance-vested share plans (14 observations), the formula generates a 30.25% mean improvement in absolute valuation error relative to heuristic values (significant at 5%). The result underscores that the efficiency of any formula is constrained by the quality of the performance forecast embedded in it.

Heuristic dominates reported values: Across all tables and plan types, reported values and heuristic values are statistically indistinguishable in the majority of cases, providing strong evidence that heuristic value is the predominant basis for firms' reported grant date fair values on proxy statements — not formula-based models.

Implications for Institutional Investors

For stewardship teams and proxy advisors assessing executive compensation proposals, this paper raises several important considerations. First, reported grant date fair values for PSPs — particularly those with relative stock return performance metrics — cannot be taken at face value. Firms appear to systematically report values above formula-based fair values for these plans, suggesting disclosure inflation that understates the true accounting cost of executive compensation. Investors engaging on pay-for-performance alignment should apply scrutiny to the valuation methodology underpinning reported PSP fair values.

Second, the paper demonstrates that heuristic valuation (NM × S0) — while simple — ignores the true probability distribution of performance outcomes, the time value of options, and correlation between performance and stock price. This matters for evaluating whether reported compensation expense correctly reflects the economic cost of incentive grants. Compensation committees and their advisors who rely on heuristic values may be systematically underestimating or overestimating plan costs depending on the performance measure used.

Third, the finding that formula accuracy depends heavily on the forecast method used for future firm performance is practically important. Proxy advisors who estimate "expected" PSP payouts using historical averages — a common approach — may generate less accurate value assessments than those who incorporate forward-looking analyst consensus. This has implications for say-on-pay analysis and the modelling of long-term incentive plan costs in compensation benchmarking.

Finally, the policy implication is that FASB should consider extending the fair value accounting requirement — currently applied rigorously to stock options — to PSPs. Better disclosure would give shareholders, stewardship teams, and analysts a more accurate picture of executive compensation costs, supporting more informed engagement and voting on say-on-pay proposals.

Selected References

  1. Hall, B.J., & Murphy, K.J. (2003). The trouble with stock options. Journal of Economic Perspectives, 17(3), 49–70.
  2. Bettis, J.C., Bizjak, J.M., Coles, J.L., & Kalpathy, S. (2010). Stock and option grants with performance-based vesting provisions. Review of Financial Studies, 23(10), 3849–3888.
  3. Cox, J.C., & Ross, S.A. (1976). The valuation of options for alternative stochastic processes. Journal of Financial Economics, 3(1–2), 145–166.
  4. Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81(3), 637–654.
  5. Holden, C.W., & Kim, D.S. (2017). Performance share plans: Valuation and empirical tests. Journal of Corporate Finance, 44, 99–125.