Chapter 18: Decision Analysis: Degree of Operating Leverage

The degree of operating leverage (DOL) is a crucial concept in cost-volume-profit (CVP) analysis, as it helps assess how changes in sales volume will impact a company’s income. Here’s a breakdown of the DOL, how it’s calculated, and its implications for sales changes using the Rydell Company as an example. Understanding the Degree of Operating Leverage (DOL) 1. Definition: DOL measures a company's sensitivity to changes in sales volume in relation to its fixed and variable costs. It shows how much operating income (or contribution margin) will change with a change in sales. A higher DOL indicates that a company has a greater proportion of fixed costs relative to variable costs, which means income will be more sensitive to changes in sales volume. 2. Formula: The DOL at a certain sales level can be calculated using the formula: DOL=Contribution MarginOperating Income\text{DOL} = \frac{\text{Contribution Margin}}{\text{Operating Income}}DOL=Operating IncomeContribution Margin where: o o Contribution Margin = Sales - Variable Costs Operating Income = Contribution Margin - Fixed Costs Example: Rydell Company Assuming Rydell sells 1,200 footballs, let’s calculate its DOL and analyze the effect of a 10% change in sales. Step 1: Calculate Contribution Margin and Operating Income • • • Selling Price per Football: $100 Variable Cost per Football: $70 Fixed Costs: $24,000 1. Contribution Margin per Unit: Contribution Margin=Selling Price−Variable Cost=100−70=30 2. Total Contribution Margin: Total Contribution Margin=Contribution Margin per Unit×Number of Units Sold=30×1200=36,000 3. Operating Income: Operating Income=Total Contribution Margin−Fixed Costs=36,000−24,000 =12,000 Step 2: Calculate DOL DOL=Contribution MarginOperating Income=36,00012,000=3 Step 3: Predict Changes in Income with DOL Assuming a 10% change in sales, we can predict how Rydell's income will change using the DOL. 1. Sales Increase by 10%: o New Sales Volume: 1,200×1.10=1,3201,200 \times 1.10 = 1,3201,200×1.10=1,320 footballs o New Contribution Margin: New Contribution Margin=30×1,320=39,600 o New Operating Income: New Operating Income=39,600−24,000=15,600 o Change in Income: Change in Income=15,600−12,000=3,600 2. Sales Decrease by 10%: o New Sales Volume: 1,200×0.90=1,0801,200 \times 0.90 = 1,0801,200×0.90=1,080 footballs o New Contribution Margin: New Contribution Margin=30×1,080=32,400 o New Operating Income: New Operating Income=32,400−24,000=8,400 o Change in Income: Change in Income=8,400−12,000=−3,600 Summary of Findings • • • DOL of 3: A DOL of 3 means that for every 1% change in sales volume, operating income changes by 3%. 10% Increase in Sales: Results in a $3,600 increase in income, raising it from $12,000 to $15,600. 10% Decrease in Sales: Results in a $3,600 decrease in income, lowering it from $12,000 to $8,400. Conclusion The degree of operating leverage is a powerful indicator for managers, as it highlights how sensitive operating income is to changes in sales volume. Companies with a higher DOL must be cautious about their fixed costs, as significant changes in sales can lead to larger swings in income.