This is “Leverage”, section 15.2 from the book Finance for Managers (v. 0.1).

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- Explain the effects of leverage on variability of returns.
- Define and calculate degree of operating leverage and degree of financial leverage.

*Little Jamie wants to put out a lemonade stand, to take advantage of the hot weather. She has $5 in her piggy bank with which to buy supplies. She expects to be able to sell that amount of lemonade for $10, for a nice $5 profit. But she knows that she could sell even more lemonade if she could afford to buy more supplies, so she asks her mother for a loan of $5. Now, with $10 of supplies, she can generate $20 worth of sales! After paying back her mother, she’ll have $15 left, for a profit of $10!*

*Unfortunately, little Jamie has terrible luck, and a summer thunderstorm roars through the neighborhood, scattering her supplies and ruining her product. She had only sold $2 worth of lemonade before the storm. In tears, she offers the $2 to her mother, knowing that she has lost her own $5 and can’t even return what she borrowed. The loving mother consoles her daughter, and tells her that she can try again when the weather turns better.*

Little Jamie has learned some important lessons from this experience (and, thankfully, her mother is more generous than most banks would be!). The first is that, by borrowing money, she has the potential for a larger reward for her invested capital ($10 profit vs. $5 profit). The second lesson is that not everything goes exactly to plan, leading to the third lesson: when the business was in trouble, she lost more money because she borrowed. If she had only used her own money, she would have only lost $3 (her $5 investment less the $2 she took in before the storm). Since she borrowed, she lost her entire investment, plus most of her mother’s to boot (debt holders, barring maternal love, have claims to the money before the equity holders)! This effect, in which debt increases the variability of potential returns, we call leverageThe effect in which debt increases the variability of potential returns..

Leverage isn’t only caused by debt: any time we take on fixed costs, we increase our risk. If we purchase a new machine that is able to make our product more cheaply, we need to be certain that we’ll sell enough product to make the purchase worthwhile. If we sell more, then the added efficiency will increase our potential for profit. Or we might choose to build our own warehouse rather than pay for storage space. If business drops, we’ll be stuck with an empty warehouse, but still have the warehouse payments. Typically we call this leverage caused by fixed costs of operations operating leverageLeverage caused by fixed costs of operations. (as opposed to leverage caused by borrowing, which we call financial leverageLeverage caused by borrowing.). The firm’s total leverage is a combination of the two.

Equation 15.1 Degree of Operating Leverage

$$DegreeofOperatingLeverage=\frac{\%changeinEBIT}{\%changeinRevenues}$$Equation 15.2 Degree of Financial Leverage

$$DegreeofFinancialLeverage=\frac{\%changeinNetIncome}{\%changeinEBIT}$$Equation 15.3 Degree of Total Leverage

$$\begin{array}{ccc}DegreeofTotalLeverage& =& \frac{\%changeinNetIncome}{\%changeinRevenues}\\ & =& DegreeofOperatingLeverage\times DegreeofFinancialLeverage\end{array}$$- Leverage increases potential gains and potential losses.
- Operating leverage is caused by large fixed costs.
- Financial leverage is caused by interest payments due to debt.

- A manager believes that her company will do extremely well in the upcoming year, surpassing others’ expectations. Should she increase or decrease her leverage?
- A firm believes that if sales increase by 2%, their EBIT will increase by 3%. What is their degree of operating leverage?
- A firm believes that if sales increase by 3%, their Net Income will increase by 5%. What is there degree of total leverage?