Operating leverage should not be confused with financial leverage. Whereas operating leverage deals with the operating cost structure of the business, in contrast financial leverage deals with the capital structure of the business.
Operating leverage, sometimes referred to as fixed cost leverage, shows what percentage of the total costs of a business are fixed costs. Specifically it is calculated by dividing fixed costs by total costs.
Operating Leverage Formula
As can be seen below the leverage ratio formula can be stated as follows:
To illustrate for example if fixed costs are 40,000 and total costs are 75,000, then the operating leverage is 40,000/75,000 = 0.533, alternatively if fixed costs are 55,000 and total costs are still 75,000, then the leverage is 55,000/75,000 = 0.733. As can be seen the higher the fixed costs as a proportion of total costs, the higher the leverage.
Calculating Operating Leverage
Consider the following information for two very different businesses, the first a low leverage business, and the second a high leverage business.
| Low | High | |
|---|---|---|
| Units | 1,000 | 1,000 |
| Selling price per unit | 165.00 | 165.00 |
| Cost price per unit | 135.00 | 10.00 |
| Contribution per unit | 30.00 | 155.00 |
| Low | High | |
|---|---|---|
| Revenue | 165,000 | 165,000 |
| Variable costs | 135,000 | 10,000 |
| Contribution margin | 30,000 | 155,000 |
| Fixed costs | 12,000 | 135,000 |
| Operating income | 18,000 | 20,000 |
Accordingly using this information and the leverage ratio formula, we can calculate the leverage as follows:
Low operating leverage business OL = Fixed costs / Total costs OL = 12,000 / (12,000 + 135,000) = 8.163% High operating leverage business OL = Fixed costs / Total costs OL = 135,000 / (135,000 + 10,000)= 93.103%
As can be seen the operating leverage ratio is an indicator of the level of leverage. Consequently it can be used like any ratio to spot trends and for comparison with other businesses. However. it does not tell us the effect on operating income of the level of leverage, this is done by the degree of operating leverage (DOL) calculation discussed below.
Degree of Operating Leverage Calculation
If we consider now what happens to the business when the number of units sold is increased by one percent. We currently sell 1,000 units so a one percent increase is 1% x 1,000 = 10 units, and the contribution margin statement would be as follows:
| Low | High | |
|---|---|---|
| Units | 1,010 | 1,010 |
| Selling price per unit | 165.00 | 165.00 |
| Cost price per unit | 135.00 | 10.00 |
| Contribution per unit | 30.00 | 155.00 |
| Low | High | |
|---|---|---|
| Revenue | 166,650 | 166,650 |
| Variable costs | 136,350 | 10,100 |
| Contribution margin | 30,300 | 156,550 |
| Fixed costs | 12,000 | 135,000 |
| Operating income | 18,300 | 21,550 |
Changes in Operating Income
As shown above by increasing the number of units, the operating income has changed for both businesses, this change is summarized in the table below.
| Low | High | |
|---|---|---|
| Operating income after the 1% increase in units | 18,300 | 21,550 |
| Operating income before the increase in units | 18,000 | 20,000 |
| Change in operating income | 300 | 1,550 |
| % Change in operating income | 1.667% | 7.750% |
As can be seen the 1% change in the number of units sold has resulted in a 1.667% change in operating income for the low operative leverage business, and a 7.750% change for the high leverage business. This is the effect of fixed cost leverage, the higher the fixed cost proportion, the lower the variable cost proportion, and the greater the effect on contribution margin and operating income for each unit sold.
The percentage change in operating income as a result of a percentage change in revenue is referred to as the degree of operating leverage.
It should be noted that, the change in operating income is in fact the contribution margin for the product multiplied by the increase in the number of units. Consequently for the low operating leverage business this was 10 x 30.00 = 300, and for the high operating leverage business this was 10 x 155 = 1,550.
Degree of Operating Leverage Formula
The degree of operating leverage formula is the percentage change in operating income for each percentage change in the number of units sold.
DOL = % Operating income change / % Units change
To illustrate using the information in the example above the degree of operating leverage is computed as:
Low operating leverage business DOL = % Operating income change / % Units change DOL = (300/18,000) / (10/1,000) = 1.667 High operating leverage business DOL = % Operating income change / % Units change DOL = (1,550/20,000) / (10/1,000) = 7.750
Other Versions of the Degree of Operating Leverage Formula
Additionally the DOL formula can be rearranged in a number of ways each of which will give the same answer. If the quantity of units sold is Q, then the formula becomes
DOL = Q x Unit contribution / (Q x Unit contribution - Fixed costs)
To illustrate, using the information in the example above we have:
Low operating leverage business DOL = Q x Unit contribution / (Q x Unit contribution - Fixed costs) DOL = 1,000 x 30.00 / (1,000 x 30.00 - 12,000) = 1.667 High operating leverage business DOL = Q x Unit contribution / (Q x Unit contribution - Fixed costs) DOL = 1,000 x 155.00 / (1,000 x 155.00 - 135,000) = 7.750
or alternatively
DOL = Contribution / Operating income
In the example above the DOL is calculated as follows:
Low operating leverage business DOL = Contribution / Operating income DOL = 30,000 / 18,000 = 1.667 High operating leverage business DOL = Contribution / Operating income DOL = 155,000 / 20,000 = 7.750
Summary
The operating leverage shows the level of leverage within a business, and the degree of operating leverage shows the impact of the cost structure on the operating income of the business. Both are dependent on the number of units sold and will change as the number of units sold changes.
The operating income for a business with high leverage can change dramatically for a given change in the number of units sold, and its earnings are said to be more volatile and therefore more risky.
Furthermore the effect of leverage is to amplify (leverage) the effect of any changes in the number of units sold, the higher the leverage the higher the change in operating income for a given change in the number of units sold.
Additionally this effect can be positive if the business is above break-even and profitable, as any change in the number of units sold substantially increases profit. However, the reverse is also true, if the business is below break-even and loss making, the effect of high leverage is to amplifying the losses as the number of units sold falls.
Our DOL calculator is available for download in Excel format, and calculates both the operating leverage and the DOL by entering details of the quantity of units sold, unit selling price and cost price, and fixed costs of a business.
About the Author
Chartered accountant Michael Brown is the founder and CEO of Double Entry Bookkeeping. He has worked as an accountant and consultant for more than 25 years and has built financial models for all types of industries. He has been the CFO or controller of both small and medium sized companies and has run small businesses of his own. He has been a manager and an auditor with Deloitte, a big 4 accountancy firm, and holds a degree from Loughborough University.