Presenter’s name
Presenter’s title dd Month yyyy

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
Copyright © 2013 CFA Institute
Fixed
Costs
2

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.
Copyright © 2013 CFA Institute 3

• 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
One
Company
Two
Number of units produced and sold
Sales price per unit
Variable cost per unit
Fixed operating cost
Fixed financing expense
1,000
€250
€125
1,000
€250
€25
€50,000 €100,000
€5,000 €55,000
Debt
Equity
Total assets
Copyright © 2013 CFA Institute
€50,000 €550,000
€700,000 €200,000
€750,000 €750,000
4

Company Two uses more operating and financial leverage than Company One.
Company One Company Two
€ 200 000
€ 150 000
Net
Income
€ 100 000
€ 50 000
€ 0
€ 50 000
€ 100 000
-
€ 150 000
Number of Units Produced and Sold
Copyright © 2013 CFA Institute 5

• 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.
Sales Risk
Business
Risk
Operating
Risk
Copyright © 2013 CFA Institute 6

• 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.
Copyright © 2013 CFA Institute 7

Q
Q
P
V
Q P
V
F 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
(4-2)
Copyright © 2013 CFA Institute 8

C OMPANY O NE
DOL1,000=
1,000( € 250 − € 125)
1,000 € 250 − € 125 − € 50,000
DOL1,000=
€125,000
€75,000
DOL1,000= 1.667%
C OMPANY T WO
DOL1,000=
1,000 ( € 250 − € 25)
1,000 € 250 − € 25 − €10 0,000
DOL1,000=
€225,000
€125,000
DOL1,000= 1.800
Copyright © 2013 CFA Institute 9

• 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.
Copyright © 2013 CFA Institute 10

At a specific level of operating earnings (and, therefore, Q):
DFL=
Q ( P − V ) − F
Q P − V − F − C
(4-4) where Q , P , V, and F are as before, and C is the fixed financial cost.
Copyright © 2013 CFA Institute 11

DFL1,000=
1,000( € 250 − €125) − € 50,000
1,000 € 250 − €125 − € 50,000 − € 5,000
DFL1,000=
€75,000
€70,000
DFL1,000= 1.071%
DFL1,000=
1,000(€250 − €25) − €100,000
1,000 €250 − €25 − €100,000 − €55,000
DFL1,000=
€125,000
€70,000
DFL1,000= 1.786%
Copyright © 2013 CFA Institute 12

• 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.
Copyright © 2013 CFA Institute 13

Consider the example of Company One and Company Two:
100%
80%
60%
Return on
Equity
40%
20%
0%
-20%
-40%
-60%
-80%
Company One Company Two
Units Produced and Sold
Copyright © 2013 CFA Institute 14

• 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 )
Q P − 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.
Copyright © 2013 CFA Institute 15

DTL1,000 =
1,000( € 250 − € 125)
1,000 € 250 − € 125 − € 50,000 − € 5,000
DFL1,000 =
€125,000
€70,000
DFL1,000 = 1.786
DTL1,000 =
1,000(€250 − € 25)
1,000 €250 − € 25 − €100,000 − €55,000
DFL1,000 =
€225,000
€70,000
DFL1,000 = 3.214
Copyright © 2013 CFA Institute 16

• The breakeven point ( Q
BE
) 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
𝑄
𝐵𝐸
=
𝐹 + 𝐶
𝑃 − 𝑉
(4-7)
• The operating breakeven point ( Q
OBE
) is the level of units produced and sold at which the operating costs are covered.
𝐹
𝑄
𝑂𝐵𝐸
=
𝑃 − 𝑉
Copyright © 2013 CFA Institute 17

Breakeven=
€55,000
€250 − €125
= 440 units
Operating b reakeven=
€50,000
€250 − €125 = 400 units
Breakeven=
€155,000
€250 − €25
= 689 units
Operating b reakeven=
€100,000
€250 − €25 = 444 units
Copyright © 2013 CFA Institute 18

• 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.
Copyright © 2013 CFA Institute 19

• 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).
Copyright © 2013 CFA Institute 20

• 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, Q
BE
, is the number of units produced and sold at which the company’s net income is zero.
• The operating breakeven point, Q
OBE
, is the number of units produced and sold at which the company’s operating income is zero.
Copyright © 2013 CFA Institute 21