Operating leverage should not be confused with financial leverage. Operating leverage deals with the operating cost structure of the business, whereas financial leverage deals with the capital structure of the business.

The operating leverage, sometimes referred to as fixed cost leverage, shows what percentage of the total costs of a business are fixed costs. It is calculated by dividing fixed costs by total costs.

## Operating Leverage Formula

The leverage formula can be stated as follows:

For example is 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 operating leverage is 55,000/75,000 = 0.733. 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 operating 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 |

Using this information and the operating leverage formula, we can calculate the leverage as follows:

Low operating leverage businessOL = Fixed costs / Total costs OL = 12,000 / (12,000 + 135,000) = 8.163%High operating leverage businessOL = Fixed costs / Total costs OL = 135,000 / (135,000 + 10,000)= 93.103%

The operating leverage ratio is an indicator of the level of leverage. 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

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% |

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 operative 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. 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 equation is the percentage change in operating income for each percentage change in the number of units sold.

DOL = % Operating income change / % Units change

Using the information in the example above the degree of operating leverage is computed as:

Low operating leverage businessDOL = % Operating income change / % Units change DOL = (300/18,000) / (10/1,000) = 1.667High operating leverage businessDOL = % Operating income change / % Units change DOL = (1,550/20,000) / (10/1,000) = 7.750

## Other Versions of the Degree of Operating Leverage Formula

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)

Using the information in the example above we have:

Low operating leverage businessDOL = Q x Unit contribution / (Q x Unit contribution - Fixed costs) DOL = 1,000 x 30.00 / (1,000 x 30.00 - 12,000) = 1.667High operating leverage businessDOL = 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 businessDOL = Contribution / Operating income DOL = 30,000 / 18,000 = 1.667High operating leverage businessDOL = 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.

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.

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, 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.