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<title>Operating leverage</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Operating leverage</span></span>

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<p><b>Operating leverage</b> is a measure of how revenue growth translates into growth in <a href="Operating_income" class="mw-redirect" title="Operating income">operating income</a>. It is a measure of <a href="Leverage_(finance)" title="Leverage (finance)">leverage</a>, and of how risky, or volatile, a company's operating income is.

</p>

<div class="mw-heading mw-heading2"><h2 id="Definition">Definition</h2></div>

<p>There are various measures of operating leverage,<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>

which can be interpreted analogously to <a href="Financial_leverage" class="mw-redirect" title="Financial leverage">financial leverage</a>.

</p>

<div class="mw-heading mw-heading3"><h3 id="Costs">Costs</h3></div>

<p>One analogy is <b>"fixed costs + variable costs = total costs . . . is similar to . . . debt + equity = assets".</b> 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:

</p><p>One measure is <a href="Fixed_costs" class="mw-redirect" title="Fixed costs">fixed costs</a> to <a href="Total_costs" class="mw-redirect" title="Total costs">total costs</a>:

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<mfrac>

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<annotation encoding="application/x-tex">{\displaystyle {\frac {\text{FC}}{\text{TC}}}={\frac {\text{FC}}{{\text{FC}}+{\text{VC}}}}}</annotation>

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</math></span><img src="./b0254fe7c0666c0f6e0d501e2ea2ec6eee788a02.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:17.584ex; height:5.676ex;" alt="{\displaystyle {\frac {\text{FC}}{\text{TC}}}={\frac {\text{FC}}{{\text{FC}}+{\text{VC}}}}}" loading="lazy"></span></dd></dl>

<p>Compare to <a href="Debt_to_equity_ratio" class="mw-redirect" title="Debt to equity ratio">debt to value</a>, which is

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<mfrac>

<mtext>Assets</mtext>

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<mfrac>

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<mtext>Equity</mtext>

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<annotation encoding="application/x-tex">{\displaystyle {\frac {\text{Debt}}{\text{Assets}}}={\frac {\text{Debt}}{{\text{Debt}}+{\text{Equity}}}}}</annotation>

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</math></span><img src="./f55a4e4ebc7200ffec98b41e3409608701c3d7f6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:25.927ex; height:5.843ex;" alt="{\displaystyle {\frac {\text{Debt}}{\text{Assets}}}={\frac {\text{Debt}}{{\text{Debt}}+{\text{Equity}}}}}" loading="lazy"></span></dd></dl>

<p>Another measure is <a href="Fixed_costs" class="mw-redirect" title="Fixed costs">fixed costs</a> to <a href="Variable_costs" class="mw-redirect" title="Variable costs">variable costs</a>:

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<mfrac>

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<annotation encoding="application/x-tex">{\displaystyle {\frac {\text{FC}}{\text{VC}}}}</annotation>

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</math></span><img src="./2f443a9f0b15b409934e1666b0d0807fd2445ced.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:4.257ex; height:5.509ex;" alt="{\displaystyle {\frac {\text{FC}}{\text{VC}}}}" loading="lazy"></span></dd></dl>

<p>Compare to <a href="Debt_to_equity_ratio" class="mw-redirect" title="Debt to equity ratio">debt to equity ratio</a>:

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<mfrac>

<mtext>Equity</mtext>

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<annotation encoding="application/x-tex">{\displaystyle {\frac {\text{Debt}}{\text{Equity}}}}</annotation>

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</math></span><img src="./e7e653640b4a157e2dddb5d7c388b1d2d4c08a2c.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:7.718ex; height:5.843ex;" alt="{\displaystyle {\frac {\text{Debt}}{\text{Equity}}}}" loading="lazy"></span></dd></dl>

<p>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.

</p>

<div class="mw-heading mw-heading3"><h3 id="Contribution">Contribution</h3></div>

<p><a href="Contribution_margin" title="Contribution margin">Contribution Margin</a> 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 <a href="Cost-Volume-Profit_Analysis" class="mw-redirect" title="Cost-Volume-Profit Analysis">Cost-Volume-Profit Analysis</a> Model, contribution margin is a fixed quantity, and does not change with Sales.

Contribution = Sales - Variable Cost

</p>

<div class="mw-heading mw-heading3"><h3 id="DOL_and_Operating_income">DOL and Operating income</h3></div>

<p>Operating leverage can also be measured in terms of change in <a href="Operating_income" class="mw-redirect" title="Operating income">operating income</a> for a given change in sales (revenue).

</p><p>The <b>Degree of Operating Leverage</b> (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 (<a href="#CITEREFBrigham1995">Brigham 1995</a>, p. 426):

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<mtext> change in Operating Income</mtext>

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<mtext> change in Sales</mtext>

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<annotation encoding="application/x-tex">{\displaystyle {\text{DOL}}={\frac {\%{\text{ change in Operating Income}}}{\%{\text{ change in Sales}}}}}</annotation>

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</math></span><img src="./45bb1219b16d99feedd8b4e17a65c4f417b934f1.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:39.653ex; height:6.176ex;" alt="{\displaystyle {\text{DOL}}={\frac {\%{\text{ change in Operating Income}}}{\%{\text{ change in Sales}}}}}" loading="lazy"></span></dd></dl>

<p>This can also be computed as Total <a href="Contribution_Margin" class="mw-redirect" title="Contribution Margin">Contribution Margin</a> over <a href="Operating_Income" class="mw-redirect" title="Operating Income">Operating Income</a>:

</p>

</mrow>

<mfrac>

<mtext>Total Contribution</mtext>

<mtext>Operating Income</mtext>

</mfrac>

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<mfrac>

<mtext>Total Contribution</mtext>

<mrow>

<mtext>Total Contribution</mtext>

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<mtext>Fixed Costs</mtext>

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<annotation encoding="application/x-tex">{\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}}}}}</annotation>

</semantics>

</math></span><img src="./f030326f41b83a38eeb7db1a34d2d53be18b8851.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:87.636ex; height:6.509ex;" alt="{\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}}}}}" loading="lazy"></span></dd></dl>

<p>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).

</p><p>Alternatively, as Contribution Margin Ratio over <a href="Operating_Margin" class="mw-redirect" title="Operating Margin">Operating Margin</a>:

</p>

</mrow>

<mfrac>

<mtext>Contribution Margin Ratio</mtext>

<mtext>Operating Margin</mtext>

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<annotation encoding="application/x-tex">{\displaystyle {\text{DOL}}={\frac {\text{Contribution Margin Ratio}}{\text{Operating Margin}}}}</annotation>

</semantics>

</math></span><img src="./5d4c72bff52bbc78a20e7ca582c67c1bd6440ec1.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:36.214ex; height:5.843ex;" alt="{\displaystyle {\text{DOL}}={\frac {\text{Contribution Margin Ratio}}{\text{Operating Margin}}}}" loading="lazy"></span></dd></dl>

<p>For instance, if a company has sales of 1,000,000 units, at price <span style="white-space: nowrap">$50</span>, unit variable cost of <span style="white-space: nowrap">$10</span>, and fixed costs of <span style="white-space: nowrap">$10,000,000</span>, then its unit contribution is <span style="white-space: nowrap">$40</span>, its Total Contribution is <span style="white-space: nowrap">$40m</span>, and its Operating Income is <span style="white-space: nowrap">$30m</span>, so its DOL is

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<annotation encoding="application/x-tex">{\displaystyle {\frac {\${\text{40m}}}{\${\text{30m}}}}=1{\frac {1}{3}}\approx 1.33}</annotation>

</semantics>

</math></span><img src="./915f43567799b60dcb2fb8440767cbb12069f1af.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:19.752ex; height:5.676ex;" alt="{\displaystyle {\frac {\${\text{40m}}}{\${\text{30m}}}}=1{\frac {1}{3}}\approx 1.33}" loading="lazy"></span></dd></dl>

<p>This could also be computed as 80% = <style data-mw-deduplicate="TemplateStyles:r1214402035">

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</style><span class="sfrac">⁠<span class="tion"><span class="num">$40m</span><span class="sr-only">/</span><span class="den">$50m</span></span>⁠</span> Contribution Margin Ratio divided by 60% = <span class="sfrac">⁠<span class="tion"><span class="num">$30m</span><span class="sr-only">/</span><span class="den">$50m</span></span>⁠</span> Operating Margin.

</p><p>It currently has Sales of <span style="white-space: nowrap">$50m</span> and Operating Income of <span style="white-space: nowrap">$30m</span>, 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 <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 10\%\times 1{\frac {1}{3}}=13{\frac {1}{3}}\%}">

<mfrac>

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<annotation encoding="application/x-tex">{\displaystyle 10\%\times 1{\frac {1}{3}}=13{\frac {1}{3}}\%}</annotation>

</semantics>

</math></span><img src="./275c961c68646efdfe5b6f45d2636587cb420b3f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:19.62ex; height:5.176ex;" alt="{\displaystyle 10\%\times 1{\frac {1}{3}}=13{\frac {1}{3}}\%}" loading="lazy"></span> increase in Operating Income.

</p><p>Assuming the model, for a given level of sales, the DOL is higher the higher fixed costs are (<a rel="nofollow" class="external text" href="http://moneyterms.co.uk/operational_gearing/">an example</a>): for a given level of sales and profit, a company with higher fixed costs has a lower Operating Income, and hence its Operating Income increases more rapidly with Sales than a company with lower fixed costs (and correspondingly lower contribution margin and higher Operating Income).

</p><p>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 <a href="Operating_margin" title="Operating margin">operating margin</a> equals its <a href="Contribution_margin" title="Contribution margin">contribution margin</a>:

</p>

<mfrac>

<mtext>Operating Income</mtext>

<mtext>Sales</mtext>

</mfrac>

</mrow>

<mfrac>

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<mtext>Unit Price</mtext>

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<mtext>Unit Variable Cost</mtext>

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<mtext>Unit Price</mtext>

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<annotation encoding="application/x-tex">{\displaystyle {\frac {\text{Operating Income}}{\text{Sales}}}={\frac {{\text{Unit Price}}-{\text{Unit Variable Cost}}}{\text{Unit Price}}}}</annotation>

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</math></span><img src="./3fb72246af3202f251cea7cc27148dcd6716aee8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:55.083ex; height:5.509ex;" alt="{\displaystyle {\frac {\text{Operating Income}}{\text{Sales}}}={\frac {{\text{Unit Price}}-{\text{Unit Variable Cost}}}{\text{Unit Price}}}}" loading="lazy"></span></dd></dl>

<p>DOL is highest near the <a href="Break-even_point" title="Break-even point">break-even point</a>; 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, <span style="white-space: nowrap">$10</span>), 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, <span style="white-space: nowrap">$.1</span>), a 10% increase in sales may increase Operating Income to <span style="white-space: nowrap">$10</span>, 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.

</p><p>DOL is closely related to the rate of increase in the <a href="Operating_margin" title="Operating margin">operating margin</a>: 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.

</p>

<div class="mw-heading mw-heading2"><h2 id="Industry-specific">Industry-specific</h2></div>

<p>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 <a href="Whole-life_cost" title="Whole-life cost">life cycle cost analysis</a> 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.

</p>

<div class="mw-heading mw-heading3"><h3 id="Outsourcing">Outsourcing</h3></div>

<p><a href="Outsourcing" title="Outsourcing">Outsourcing</a> a product or service is a method used to change the ratio of <a href="Fixed_costs" class="mw-redirect" title="Fixed costs">fixed costs</a> to <a href="Variable_costs" class="mw-redirect" title="Variable costs">variable costs</a> 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.

</p>

<ul><li><a href="Cost_accounting" title="Cost accounting">Cost accounting</a></li>

<li><a href="Efficiency_ratio" title="Efficiency ratio">Efficiency ratio</a></li>

<li><a href="Operating_margin" title="Operating margin">Operating margin</a></li>

<li><a href="Financial_leverage" class="mw-redirect" title="Financial leverage">Financial leverage</a></li>

<li><a href="Contribution_margin" title="Contribution margin">Contribution margin</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

<li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.westga.edu/~bquest/1998/leverage.html">Operating and Financial leverage</a></span>

</li>

</ol></div>

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</style><cite id="CITEREFBrigham1995" class="citation cs2">Brigham, Eugene F. (1995), <i>Fundamentals of Financial Management</i></cite>

</p>

<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

<ul><li><a rel="nofollow" class="external text" href="http://www.investorwords.com/3462/operating_leverage.html">operating leverage Definition</a></li>

<li><a rel="nofollow" class="external text" href="http://www.investopedia.com/terms/o/operatingleverage.asp">Operating Leverage</a></li></ul></div><div><div class="zim-footer">

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