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CHAPTER 4
MEASURES OF LEVERAGE
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1. INTRODUCTION
Leverage is the use of fixed costs in a company’s cost structure.
- Operating leverage relates to the company’s operating cost structure.
- Financial leverage relates to the company’s capital structure.
Fixed
Costs
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Fixed
Costs
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WHY WORRY ABOUT LEVERAGE?
1. A company’s use of leverage affects its risk and return.
2. Operating leverage and financial leverage provide insight into a company’s
business and its future.
3. Leverage helps us understand a company’s future cash flows and the risk
associated with those cash flows and, hence, its valuation.
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2. LEVERAGE
• Leverage increases the volatility of earnings and cash flows → hence, it
increases risk to suppliers of capital (creditors and owners).
• Consider two companies, Company One and Company Two, with the following
information:
Company Company
One
Two
Number of units produced and sold
Sales price per unit
Variable cost per unit
Fixed operating cost
Fixed financing expense
Debt
Equity
Total assets
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1,000
€250
€125
€50,000
€5,000
1,000
€250
€25
€100,000
€55,000
€50,000
€700,000
€750,000
€550,000
€200,000
€750,000
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WHAT DOES LEVERAGE DO EXACTLY?
Company Two uses more operating and financial leverage than Company One.
Company One
Company Two
€ 200,000
€ 150,000
€ 100,000
Net
Income
€ 50,000
€0
-€ 50,000
-€ 100,000
-€ 150,000
Number of Units Produced and Sold
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3. BUSINESS RISK AND FINANCIAL RISK
• Business risk is the risk associated with the volatility in operating earnings.
- Business risk is composed of both operating and sales risk.
• Sales risk is the uncertainty associated with the number of units produced and
sold, as well as the sales price.
Operating
Risk
Sales Risk
Business
Risk
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OPERATING RISK
• Operating risk is the risk associated with the mix of variable and fixed
operating expenses.
- Operating risk is the sensitivity (i.e., elasticity) of operating earnings to
changes in unit sales.
• The degree of operating leverage (DOL) is the ratio of the percentage
change in operating income to the percentage change in units sold.
• The per unit contribution margin is the difference between the sales price
and the variable cost per unit. This difference is available to cover fixed
operating costs.
- Overall, for all units sold, the contribution margin is the difference between
total revenues and variable operating costs.
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DOL
The DOL is at Q units produced and sold:
DOL=
Q (P − V)
Q P−V −F
(4-2)
where
Q is the number of units
P is the price per unit
V is the variable operating cost per unit and
F is the fixed operating cost
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EXAMPLE: COMPANY ONE AND COMPANY TWO
COMPANY ONE
DOL1,000 =
1,000(€250 − €125)
1,000 €250 − €125 − €50,000
€125,000
DOL1,000 =
€75,000
DOL1,000 = 1.667%
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COMPANY TWO
DOL1,000 =
1,000 (€250 − €25)
1,000 €250 − €25 −€100,000
DOL1,000 =
€225,000
€125,000
DOL1,000 = 1.800
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FINANCIAL RISK
• Financial risk is the risk associated with the choice of financing the business.
- The greater the reliance on fixed-cost obligations, such as debt, the greater
the financial risk.
- Similar to operating risk, financial risk elasticity is the sensitivity of income
available to owners to a change in operating earnings.
• The degree of financial leverage (DFL) is the ratio of the percentage change
in net income to the percentage change in operating income.
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DFL
At a specific level of operating earnings (and, therefore, Q):
DFL=
Q(P − V) − F
QP−V −F−C
(4-4)
where Q, P, V, and F are as before, and C is the fixed financial cost.
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Company Two
Company One
EXAMPLE: COMPANY ONE AND COMPANY TWO
1,000(€250 − €125) − €50,000
DFL1,000 =
1,000 €250 − €125 − €50,000 − €5,000
€75,000
DFL1,000 =
€70,000
DFL1,000 = 1.071%
1,000(€250 − €25) − €100,000
DFL1,000 =
1,000 €250 − €25 − €100,000 − €55,000
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€125,000
DFL1,000 =
€70,000
DFL1,000 = 1.786%
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RETURN ON EQUITY AND THE DFL
• The greater the degree of financial leverage, the greater the financial risk.
• We can see the leveraging effect by looking at the return on equity (ROE) for
different levels of units produced and sold.
• The greater the DFL, the more sensitive the ROE is to changes in the units
produced and sold.
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EXAMPLE: RETURN ON EQUITY
Consider the example of Company One and Company Two:
100%
80%
60%
40%
Return on 20%
Equity
0%
-20%
-40%
-60%
-80%
Company One
Company Two
Units Produced and Sold
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DEGREE OF TOTAL LEVERAGE
• Total leverage is the combined effect of operating leverage and financial
leverage.
• The degree of total leverage (DTL) is the product of the degree of operating
leverage and the degree of financial leverage:
DTL =
Q(P − V)
QP−V −F−C
(4-6)
Or, equivalently:
DTL = DOL × DTL
• If DOL is 3 and DFL is 2, DTL = 2 × 3 = 6.
- So, a 1% change in the units produced and sold results in a 6% change in
the earnings to owners.
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Company Two
Company One
EXAMPLE: COMPANY ONE AND COMPANY TWO
1,000(€250 − €125)
DTL1,000 =
1,000 €250 − €125 − €50,000 − €5,000
€125,000
DFL1,000 =
€70,000
DFL1,000 = 1.786
1,000(€250 − €25)
DTL1,000 =
1,000 €250 − €25 − €100,000 − €55,000
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€225,000
DFL1,000 =
€70,000
DFL1,000 = 3.214
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BREAKEVEN QUANTITY
• The breakeven point (QBE) is the level of units produced and sold at which the
costs (both variable and fixed) are just covered—that is, net income is zero.
• The breakeven point is
𝑄𝐵𝐸 =
𝐹+𝐶
𝑃−𝑉
(4-7)
• The operating breakeven point (QOBE) is the level of units produced and sold
at which the operating costs are covered.
𝐹
𝑄𝑂𝐵𝐸 =
𝑃−𝑉
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Company Two Company One
EXAMPLE: COMPANY ONE AND COMPANY TWO
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Breakeven=
€55,000
= 440 units
€250 − €125
Operating breakeven=
Breakeven=
€50,000
= 400 units
€250 − €125
€155,000
= 689 units
€250 − €25
Operating breakeven=
€100,000
= 444 units
€250 − €25
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RISKS TO CREDITORS AND OWNERS
• Business risk is affected by demand uncertainty, output price uncertainty, and
cost uncertainty.
• Financial risk adds to the company’s business risk, increasing the risk to
creditors and owners.
• The creditor claims are fixed, whereas the equity claims are residual.
• In the event that creditor claims cannot be satisfied, there may be legal
statuses that help sort out the claims:
- Reorganization is the restructuring of claims, with the expectation that the
company will be able to continue, in some form, as a going concern.
- Liquidation is the situation in which assets are sold and then the proceeds
distributed to claimants.
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4. SUMMARY
• Leverage is the use of fixed costs in a company’s cost structure.
• Business risk is the risk associated with operating earnings and reflects
- sales risk (uncertainty with respect to the price and quantity of sales) and
- operating risk (the risk related to the use of fixed costs in operations).
• Financial risk is the risk associated with how a company finances its operations
(i.e., the split between equity and debt financing of the business).
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SUMMARY (CONTINUED)
• The degree of operating leverage (DOL) is the sensitivity of operating earnings
to changes in units produced and sold.
• The degree of financial leverage (DFL) is the sensitivity of cash flows to
owners to changes in operating earnings.
• The degree of total leverage (DTL) is the sensitivity of the cash flows to owners
to changes in unit sales.
• The breakeven point, QBE, is the number of units produced and sold at which
the company’s net income is zero.
• The operating breakeven point, QOBE, is the number of units produced and sold
at which the company’s operating income is zero.
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