science

Operating leverage

Operating leverage is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Operating leverage rather than just read about it. In short: 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, or volatile, a company's operating income is.

Key takeaways

Operating leverage belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Operating leverage to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Operating leverage from memory before moving on to harder problems.

Reference excerpt

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, or volatile, a company's operating income is.

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

Costs One analogy is "fixed costs + variable costs = total costs . . . is 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:

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

Compare to debt to value, which is

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

Another measure is fixed costs to variable costs:

FC VC {\displaystyle {\frac {\text{FC}}{\text{VC}}}}

Compare to debt to equity ratio:

Debt Equity {\displaystyle {\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):

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

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

DOL = Total Contribution Operating Income = Total Contribution Total Contribution − Fixed Costs = ( P − V ) ⋅ X ( P − V ) ⋅ X − FC {\displaystyle {\text{DOL}}={\frac {\text{Total Contribution}}{\text{Operating Income}}}={\frac {\text{Total Contribution}}{{\text{Total Contribution}}-{\text{Fixed Costs}}}}={\frac {({\text{P}}-{\text{V}})\cdot {\text{X}}}{({\text{P}}-{\text{V}})\cdot {\text{X}}-{\text{FC}}}}}

The above equivalence follows as the relative change in operating income with one more unit dX equals the contribution margin divided by operating income while the relative change in sales with one more unit dX equals price divided by revenue (or, in other words, 1 / X with X being the quantity). Alternatively, as Contribution Margin Ratio over Operating Margin:

DOL = Contribution Margin Ratio Operating Margin {\displaystyle {\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

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

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Operating leverage

Start with the simplest possible case. Write down what Operating leverage claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Operating leverage before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Operating leverage ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Operating leverage

In research: Operating leverage appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Operating leverage in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Operating leverage is common in secondary-school and first-year university syllabi. It links to neighbouring topics Financial ratios, Management accounting, so understanding it makes those chapters shorter.
In everyday life: Look for Operating leverage outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Operating leverage in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Operating leverage means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Operating leverage out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Operating leverage in simple terms?

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, or volatile, a company's operating income is.

Why does Operating leverage matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Operating leverage?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Operating leverage.