# Degree of Operating Leverage

Operating leverage is the extent to which a business can increase its operating income by increasing sales. Degree of operating leverage (DOL) is the multiple by which operating income changes in response to a change in sales.

Net operating income of businesses with high operating leverage is more sensitive to change in sales and vice versa. Degree of operating leverage depends on a business’ cost structure i.e. the relative proportion of fixed costs and variable costs. When fixed costs are high, degree of operating leverage is high too and changes in sales have relatively more pronounced effect on operating income. When variable costs are relatively high, degree of operating leverage is low and change in sales results in slower increase in operating income.

Degree of operating leverage is a measure of business risk. Businesses with high fixed costs are prone to large fluctuations in operating profit in response to small changes in sales. DOL is closely linked with degree of financial leverage, which measures the interest burden; and degree of total leverage, which measures the combined burden of fixed costs and interest costs.

## Formula

Degree of operating leverage is defined as percentage change in operating income that occurs in response to percentage change in sales:

$$\text{DOL}\ =\ \frac{\text{%\ Change in Operating Income}}{\text{%\ Change in Sales}}$$

After some mathematical manipulation, we can come with some alternate formula for DOL:

$$\text{DOL}\ =\ \frac{\text{Q}\times(\text{P}\ -\ \text{V})}{\text{Q}\times(\text{P}\ -\ \text{V})\ -\ \text{FC}}$$

Where Q is the quantity, P is price, V is variable cost per unit and FC is fixed cost.

$$\text{DOL}\ =\ \frac{\text{Contribution Margin}}{\text{Operating Income}}$$

$$\text{DOL}\ =\frac{\text{Contribution Margin Ratio}}{\text{%\ Operating Margin}}$$

## Example

Calculate degree of operating leverage in the following cases and identify which company will experience largest increase in operating income in response to a 15% increase in sales.

Company A: Operating income increases by 15% if sales increase by 10%.

Company B: Sales are $2,000,000, contribution margin ratio is 40% and fixed costs are$400,000

Company C: Management wants to determine how changes in output level affects its operating leverage. It is considering three output levels: 10,000 units, 15,000 units and 20,000 units. The company’s sales price is $120, variable cost pe unit is$60 and fixed costs are $300,000. ### Solution Company A: Degree of operating leverage = % change in operating income/% change in sales = 15%/10% = 1.5 In response to a 15% increase sales, operating income will increase by 22.5% [=1.5 × 15%] Company B: Operating margin = ($2,000,000 × 0.4 − $400,000) ÷$2,000,000 = 20%

Degree of operating leverage = contribution margin ratio/operating margin = \$40% ÷ 20% = 2

Increase in operating income in response to 15% increase in sales = 2 × 15% = 30%

Company C:

The following table shows calculation of degree of operating leverage at different output levels:

Sales in units Q 10,000 15,000 20,000
Sales revenue @ 120 per unit S = Q × P 1,200,000 1,800,000 2,400,000
Variable costs @ 60 per unit VC = Q × V (600,000) (900,000) (1,200,000)
Contribution margin CM = S - VC 600,000 900,000 1,200,000
Fixed costs FC (300,000) (300,000) (300,000)
Operating income OI = CM - FC 300,000 600,000 900,000
DOL DOL = CM/OI 2.00 1.50 1.33
Change in OI 30% 23% 20%

Company C’s case shows that degree of operating leverage is not a constant, but it depends on the output level.

Company B and Company C (at output level of 10,000 units) have DOL of 2 which shows that 15% change in sales will result in 30% increase in operating income.