Performance Share Plans: Valuation and Optimal Design

Abstract

Performance share plans are an increasingly important component of executive compensation. A performance share plan is an equity-based, long-term incentive plan where the number of shares to be awarded is a quasi-linear function of a performance result over a fixed time period. A special case is a performance-vested share plan, which provides a fixed number of shares whenever a performance result exceeds a threshold goal. We begin by documenting the size and importance of performance share plans and performance-vested share plans. Next, we derive closed-form formulas for the value of a performance share plan or performance-vested share plan when the performance measure is: (1) a non-traded measure following an Arithmetic Brownian Motion (e.g., earnings per share), (2) a non-traded measure following a Geometric Brownian Motion (e.g., revenue), or (3) a rank-order tournament of traded asset returns that are following Arithmetic Brownian Motions (e.g., percentile of ranked stock returns). Finally, we compare the actual payout of plans to our new valuation formulas, the reported values on proxy statements, and heuristic values. We find that our valuation formulas do significantly better or at least tie reported value and heuristic value in matching the magnitude of actual payout in all subsamples. We also find that our valuation formulas are more accurate or tie in all subsamples. The policy implication is that FASB should consider requiring that grant date fair value be estimated using valuation formulas such as ours.