# Operating leverage

Sachin Jadhav explained the Definition of Operating Levarage as, The operating leverage is a measure of how revenue growth translates into growth in operating income. It is a measure of leverage, and of how risky (volatile) a company's operating income is.

## Definition

There are various measures of operating leverage,[1] which can be interpreted analogously to financial leverage.

### Costs

One analogy is "fixed costs + variable costs = total costs ..similar to.. debt + equity = assets". This analogy is partly motivated because (for a given amount of debt) debt servicing is a fixed cost. This leads to two measures of operating leverage:

One measure is fixed costs to total costs:

$\frac{\text{FC}}{\text{TC}}=\frac{\text{FC}}{\text{FC}+\text{VC}}$

Compare to debt to value, which is

$\frac{\text{Debt}}{\text{Assets}}=\frac{\text{Debt}}{\text{Debt}+\text{Equity}}$

Another measure is fixed costs to variable costs:

$\frac{\text{FC}}{\text{VC}}$

Compare to debt to equity ratio:

$\frac{\text{Debt}}{\text{Equity}}$

Both of these measures depend on sales: if the unit variable cost is constant, then as sales increase, operating leverage (as measured by fixed costs to total costs or variable costs) decreases.

### Contribution

Contribution margin is a measure of operating leverage: the higher the contribution margin is (the lower variable costs are as a percentage of total costs), the faster the profits increase with sales. Note that unlike other measures of operating leverage, in the linear Cost-Volume-Profit Analysis Model, contribution margin is a fixed quantity, and does not change with Sales. Contribution = Sales - Variable Cost

### DOL and Operating income

Operating leverage can also be measured in terms of change in operating income for a given change in sales (revenue).

The Degree of Operating Leverage (DOL) can be computed in a number of equivalent ways; one way it is defined as the ratio of the percentage change in Operating Income for a given percentage change in Sales (Brigham 1995, p. 426):

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

This can also be computed as Total Contribution Margin over Operating Income:

$\text{DOL} = \frac{\text{Total Contribution}}{\text{Operating Income}} = \frac{\text{Total Contribution}}{\text{Total Contribution} - \text{Fixed Costs}} = \frac{(\text{P}-\text{V})\times \text{X}}{(\text{P}-\text{V})\times \text{X} - \text{FC}}$

Alternatively, as Contribution Margin Ratio over Operating Margin:

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

For instance, if a company has sales of 1,000,000 units, at price $50, unit variable cost of$10, and fixed costs of $10,000,000, then its unit contribution is$40, its Total Contribution is $40m, and its Operating Income is$30m, so its DOL is

$\frac{\\text{40m}}{\\text{30m}} = 1 \frac{1}{3} \approx 1.33$

This could also be computed as 80%=$40m/$50m Contribution Margin Ratio divided by 60%=$30m/$50m Operating Margin.

It currently has Sales of $50m and Operating Income of$30m, so additional Unit Sales (say of 100,000 units) yield $5m more Sales and$4m more Operating Income: a 10% increase in Sales and a 10% $\times 1 \frac{1}{3}=$ 13 1/3% increase in Operating Income.

Assuming the model, for a given level of sales and profit, the DOL is higher the higher fixed costs are (an example): for a given level of sales and profit, a company with higher fixed costs has a higher contribution margin, and hence its Operating Income increases more rapidly with Sales than a company with lower fixed costs (and correspondingly lower contribution margin).

If a company has no fixed costs (and hence breaks even at zero), then its DOL equals 1: a 10% increase in Sales yields a 10% increase in Operating Income, and its operating margin equals its contribution margin:

$\frac{\text{Operating Income}}{\text{Sales}}=\frac{\text{Unit Price} - \text{Unit Variable Cost}}{\text{Unit Price}}$

DOL is highest near the break-even point; in fact, at the break-even point, DOL is undefined, because it is infinite: an increase of 10% in sales, say, increases Operating Income for 0 to some positive number (say, $10), which is an infinite (or undefined) percentage change; in terms of margins, its Operating Margin is zero, so its DOL is undefined. Similarly, for a very small positive Operating Income (say,$.1), a 10% increase in sales may increase Operating Income to \$10, a 100x (or 9,900%) increase, for a DOL of 990; in terms of margins, its Operating Margin is very small, so its DOL is very large.

DOL is closely related to the rate of increase in the operating margin: as sales increase past the break-even point, operating margin rapidly increases from 0% (reflected in a high DOL), and as sales increase, asymptotically approaches the contribution margin: thus the rate of change in operating margin decreases, as does the DOL, which asymptotically approaches 1.

## Industry-specific

Examples of companies with high operating leverage include companies with high R&D costs, such as pharmaceuticals: it can cost billions to develop a drug, but then pennies to produce it. Hence from a life cycle cost analysis perspective, the ratio of preproduction costs (e.g. design widgets) versus incremental production costs (e.g. produce a widget) is a useful measure of operating leverage.

### Outsourcing

Outsourcing a product or service is a method used to change the ratio of fixed costs to variable costs in a business. Outsourcing can be used to change the balance of this ratio by offering a move from fixed to variable cost and also by making variable costs more predictable.

## References

Brigham, Eugene F. (1995), Fundamentals of Financial Management

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