Operating Leverage

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 operating leverage formula can be stated as follows:

`Operating leverage = Fixed costs / Total costs`

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.

Unit Information
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
Contribution Margin Income Statement
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 business
Operating leverage = Fixed costs / Total costs
Operating leverage = 12,000 / (12,000 + 135,000) = 8.163%
Operating leverage = Fixed costs / Total costs
Operating leverage = 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 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:

Unit Information
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
Contribution Margin Income Statement
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

By increasing the number of units, the operating income has changed for both businesses, this change is summarized in the table below.

Changes in Operating Income
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.

`Degree of operating leverage = % Operating income change / % Units change`

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

```Low operating leverage business
Degree of operating leverage = % Operating income change / % Units change
Degree of operating leverage = (300/18,000) / (10/1,000) = 1.667
Degree of operating leverage = % Operating income change / % Units change
Degree of operating leverage = (1,550/20,000) / (10/1,000) = 7.750
```

Other Versions of the Degree of Operating Leverage Formula

The degree of operating leverage (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 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
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

`Degree of operating leverage = Contribution / Operating income`

In the example above the degree of operating leverage is calculated as follows:

```Low operating leverage business
Degree of operating leverage = Contribution / Operating income
Degree of operating leverage = 30,000 / 18,000 = 1.667
Degree of operating leverage = Contribution / Operating income
Degree of operating leverage = 155,000 / 20,000 = 7.750
```

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 degree of operating leverage calculator is available for download, and calculates both the operating leverage and the degree of operating leverage by entering details of the quantity of units sold, unit selling price and cost price, and fixed costs of a business.

Operating Leverage November 6th, 2016

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