Maximizing the probability of realizing profit targets versus maximizing expected profits: A reconciliation to resolve an agency problem

It is generally accepted in the operations literature that a firm should strive to maximize its expected profit. However, in practice it is not uncommon for a firm to offer a bonus to managers for achieving some pre-established target profit, possibly yielding managerial actions that differ from the profit-maximizing approach (given a profit target, we assume managers will maximize the probability of reaching that target). We use the Newsvendor framework to illustrate how the firm's shareholders (e.g., through its board of directors) can align these two seemingly different decision approaches: maximizing expected profit versus maximizing the probability of reaching a target profit. Alignment is achieved by setting what we call an “aligned profit target” (APT) – a target profit that yields the same managerial action namely, the same stocking quantity, across both decision approaches. We find that the APT should typically be an aggressive profit target, one that is significantly higher than the maximum expected profit, with a corresponding low probability of achievement – this result is consistent across demand distributions with light tails (uniform), moderate tails (normal) and heavy tails (lognormal). Notably, the aggressive APT target should be distinguished from any target that the firm might set to signal future profit expectations to financial analysts.