Extending the Profit Elasticity Measure of Operating Leverage in Managerial Economics Texts

ABSTRACT The authors suggest recasting operating leverage (DOL) treatments in managerial textbooks. They extend the profit elasticity form of DOL used by firms to other than competitive markets by introducing nonlinear cost and revenue functions. From their results, the authors urge text writers to highlight four key issues: the role and limitations of 1) management--long run versus short run operating leverage decisions, 2) engineering--variable cost changes associated with fixed cost changes, 3) economic forces--competitive versus non-competitive markets and 4) mathematical results--DOL equals zero at the maximum profit output level, regardless of the level of fixed cost. INTRODUCTION Operating leverage is important to firm management for one reason, additions to operating fixed costs affect a firm's value by increasing risk as measured by the variability of returns (Lev, 1974, and Berner, 2002). Operating leverage discussions often follow as a natural extension to linear breakeven analysis in managerial economics textbooks. Application of the generally received profit sensitivity formula, the degree of operating leverage (DOL), is limited both theoretically and practically. Most textual treatments ignore the role DOL variables other than fixed costs play. Most authors assume overly restrictive linear cost and revenue functions, while subsequent chapters develop standard non-linear economic cost and revenue functions. The roles of management, engineering and economic markets along with the measure's inherent mathematical limitations are left unstated. This article reviews unstated aspects of the DOL measure and offers a more theoretically complete framework for operating leverage textual discussions aimed at the practicing corporate managerial specialist. Aspects of DOL we consider important include a) consistency with orthodox economic theory, b) recognizing the larger business risk context within which the DOL measure is applied, c) a clearer view of management's role in influencing certain DOL parameters as business risk components and d) some important analytical limitations inherent to the measure's form. Business risk is a central determinant of a firm's value, the risk-adjusted present value of future profit. Several important parameters affect a firm's business risk position. Among them are price, variable costs, operating fixed costs, the output rate and the stability of demand. The DOL measure contains variables that capture four of these parameters. The fifth, demand stability, is a through-time assessment while DOL is a point in time measure. The level of operating fixed cost, the parameter of greatest attention in textual DOL discussions, is only one business risk parameter. A change in a single business risk parameter in the DOL expression also affects the remaining parameters. For example, increases in operating fixed cost without a compensating reduction in unit variable cost may require increases in output to sustain a desired profit level. A meaningful discussion of DOL should at least mention the distinction between management-led choices addressing the firm's business risk posture versus market forces and engineering-based limits. Finally, other than for expository simplicity, we question the use of restrictive linear cost functions in the DOL formula application, when textual narrative in the same text stresses non-linear relationships. Discussion in Section 2 confirms the mathematical equivalence between various DOL measures and presents works by Dran (1991), Long (1992) and shows that DOL is sensitive not only to changes in the firm's operating fixed cost but also to short run output. That section suggests that narrative treatments indicating which DOL parameters management can directly influence would help place the measure into a useful operational context. Section 3 extends the DOL expression to include a cubic variable (and total) cost function and parabolic total revenue function to demonstrate that DOL equals zero at the theoretically optimized output, regardless of the level of fixed cost. …