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Foundations of FinancialManagement

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5Chapter

Operating and Financial

Leverage

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Chapter 5 - Outline

What is Leverage?

Operating Leverage

Financial Leverage

Leverage Means Risk

Combined or Total Leverage

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What is Leverage?

Leverage is using fixed costs to magnify

the potential return to a firm

2 types of fixed costs:

f ixed operating costs= rent,

depreciation

f ixed f inancial costs= interest costs

from debt

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Operating Leverage

Measure of the amount of fixed operating

costs used by a firm

Degree of Operating Leverage (DOL) =

%age in EBIT (or OI) / %age in Sales

a in Sales a larger in EBIT (or OI)

Operating Leverage measures the sensitivity

of a firms operating income to a in sales

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T 5-1

Figure 5-1Break-even chart: LeveragedfirmPage 114

Revenues and costs ($ thousands)

200

160

120

100

80

6040

20 40 50 60 80 100 120

TotalRevenue

Totalcosts

Variable costs

Fixedcosts

Profit

BE

Loss

Units produced and sold (thousands)

Fixed costs ($60,000) Price ($2) Variable costs per unit ($0.80)

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We use Equation 5-1 to

calculate the break-even (BE)pointPage 115

1-5VC-P

FC

unitpercostVariable-Price

costsFixed

marginonContributi

costsFixedBE

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Table 5-2Volume-cost-profit analysis: Leveraged

firmPage 115Total Operating

Units Variable Fixed Total Total Income

Sold Costs Costs Costs Revenue (loss)

0 0 60,000 60,000 0 (60,000)

20,000 16,000 60,000 76,000 40,000 (36,000)

40,000 32,000 60,000 92,000 80,000 (12,000)

50,000 40,000 60,000 100,000 100,000 0

60,000 48,000 60,000 108,000 120,000 12,000

80,000 64,000 60,000 124,000 160,000 36,000

100,000 80,000 60,000 140,000 200,000 60,000

$ $ $

$$

T 5-2

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T 5-3

Figure 5-2Break-even chart: Conservative firmPage 116


200

160

120

80

40

20 40 60 80 100 120

TotalRevenue

Totalcosts

Variable costs

Fixedcosts

Profit

BE

Loss

Units produced and sold (thousands)Fixed costs ($12,000) Price ($2) Variable costs per unit ($1.60)

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Table 5-3Volume-cost-profit analysis: Conservative

firmPage 117

0 0 12,000 12,000 0 (12,000.

)20,000 32,000 12,000 44,000 40,000 (4,000 .)

30,000 48,000 12,000 60,000 60,000 0

40,000 64,000 12,000 76,000 80,000 4,000

60,000 96,000 12,000 108,000 120,000 12,000

80,000 128,000 12,000 140,000 160,000 20,000100,000 160,000 12,000 172,000 200,000 28,000

$ $ $$$

Total Operating

Units Variable Fixed Total Total Income

Sold Costs Costs Costs Revenue (loss)

T 5-4

d i f i i l

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Equation 5-3 gives another

method of computing DOL

3-5FC-VC)-Q(P

VC)-Q(PDOL

F d i f Fi i l

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0 $(60,000) $(12,000)

20,000 (36,000) (4,000)

40,000 (12,000) 4,000

60,000 12,000 12,000

80,000 36,000 20,000100,000 60,000 28,000

. . .

. . .

. . .

. . .

. . .

. . .

Leveraged ConservativeFirm Firm

Units (Table 5-2) (Table 5-3)

T 5-5

Table 5-4Operating income or lossPage 118

F d i f Fi i l

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T 5-6

Units (thousands)


200

120

80

40

20 40 60 80 100 120

Revenueweakness

Totalcosts

Valid area

160

Totalrevenue

Costoverruns

Figure 5-3Nonlinear break-even analysisPage 120

F d i f Fi i l

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Financial Leverage

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Financial Leveragemeasures the

sensitivity of a firmsearnings per share to a

in operating income

F d ti f Fi i l

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Financial Leverage

is a measure of theamount of debt

used by a firm

F d ti f Fi i l

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Degree of F inancialLeverage

(DFL) =%age in EPS /

%age in EBIT (orOI)

F d ti f Fi i l

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A in EBIT (or OI)a larger in EPS

Fo ndations of Financial

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1. EBIT (0)Earnings before interest and taxes (EBIT) 0 0Interest (I) $(12,000.) $ (4,000.)Earnings before taxes (EBT) (12,000 .) (4,000.)Taxes (T) * (6,000.) (2,000.)

Earnings after taxes (EAT) $ (6,000 .) $ (2,000.)Shares 8,000 24,000Earnings per share (EPS) $ (0.75) $ (0.08)

2. EBIT ($12,000)Earnings before interest and taxes (EBIT) $12,000 $12,000Interest (I) 12,000 4,000Earnings before taxes (EBT) 0 8,000Taxes (T) 0 4,000Earnings after taxes (EAT) $ 0 $ 4,000Shares 8,000 24,000 Earnings per share (EPS)

0 $0.17

Plan A Plan B(leveraged) (conservative)

* The assumption is that large losses can be written off against other income, perhaps in other years, thusproviding the firm with a tax savings benefit. The tax rate is 50 percent for ease of computation.

T 5-7

Table 5-5Impact of financing plan onearnings per sharePage 122

Foundations of Financial

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3. EBIT ($16,000)

Earnings before interest and taxes (EBIT) $ 16,000 $ 16,000

Interest (I) 12,000 4,000

Earnings before taxes (EBT) 4,000 12,000

Taxes (T) 2,000 6,000Earnings after taxes (EAT) $ 2,000 $ 6,000

Shares 8,000 24,000

Earnings per share (EPS) $0.25 $0.25

4. EBIT ($36,000)

Earnings before interest and taxes (EBIT) $ 36,000 $ 36,000Interest (I) 12,000 4,000

Earnings before taxes (EBT) 24,000 32,000

Taxes (T) 12,000 16,000

Earnings after taxes (EAT) $ 12,000 $ 16,000

Shares 8,000 24,000

Earnings per share (EPS) $1.50 $0.67


T 5-7

Table 5-5 (continued)--Impact of financing plan onearnings per sharePage 122


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5. EBIT ($60,000)

Earnings before interest and taxes (EBIT) $ 60,000 $ 60,000

Interest (I) 12,000 4,000Earnings before taxes (EBT) 48,000 56,000

Taxes (T) 24,000 28,000

Earnings after taxes (EAT) $ 24,000 $ 28,000

Shares 8,000 24,000

Earnings per share (EPS) $3.00 $ 1.17


T 5-7

Table 5-5 (continued)Impact of financing plan onearnings per sharePage 122


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T 5-8

EPS ($)

4

3

2

1

0

-1

-2

0 12 25 50 75 100

Plan A

16 EBIT (thousands)

.25

Plan B

Figure 5-4Financing plans and earnings per sharePage

121


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Financial

LeverageBreak-Evenpoint


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In the previousfigure (5-4), the pointwhere Plans A and Bcross is a financialbreak-even point.


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Financial break-

even occurs whenEBIT = borrowing

rate X total assets


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If EBIT is to bebelow this BE point,

we would preferPlan B, with a

conservative, lowlevel of debt.


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If EBIT is to beabove this BE point,

we would preferPlan A, with an

aggressive, high levelof debt.


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One way to measure the

relative level of debt is tocompute the Degree ofFinancial Leverage

(Equations 5-4 and 5-5).


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Degree of Financial Leverage(Equations 5-4 and 5-5)

I-EBIT

EBIT

EBITinchangePercent

EPSinchangePercentDFL

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About DOLand DFL

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Note that DOL isnever less than 1.

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A DOL of 1 meansthere is no fixed

cost in the firm.

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Note that DFL isnever less than 1.

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A DFL of 1

means there isno debt in thefirm.

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Degree of

combinedleverage = DCL

= DOL X DFL.

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DCL isnever lessthan 1.

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DCL = 1 means

the firm has nofixed costs andno debt.

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If a firm hasinherent business

risk, then it shoulduse debt and fixed

costs sparingly toreduce overall risk.

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Leverage Means Risk

Leverage is a double-edged sword

It magnifies profits as well as losses

An aggressive or highly leveraged firm has

a relatively high break-even point (and high

fixed costs)

A conservative or non-leveraged firm has a

relatively low break-even point (and low

fixed costs)

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Sales (total revenue) (80,000 units @ $2) $160,000

Fixed costs 60,000

Variable costs ($0.80 per unit) 64,000

Operating income $ 36,000

Earnings before interest and taxes $ 36,000

Interest 12,000

Earnings before taxes 24,000

Taxes 12,000

Earnings after taxes $ 12,000Shares 8,000

Earnings per share $1.50

Operating

leverage

Financial

leverage

T 5-9

Table 5-6Income statementPage 124

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T 5 10

Figure 5-5Combining operating and financial leveragePage 125

$ Earnings generated EPS =$1.50

Operating income = EBIT

$36,000

Operating

leverage

Sales =

$160,000

Financialleverage

$36,000

Leverage impact

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Combined or Total Leverage

Represents maximum use of leverage

Degree of Combined or Total Leverage

(DCL or DTL) = %age in EPS /%age in Sales

a in Sales a larger in EPS

Short-cut formula:

DCL or DTL = DOL x DFL

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T 5 11

Table 5-7--Operating and financial leverage

Page 126Sales$2 per unit $160,000 $200,000

Fixed costs 60,000 60,000

Variable costs ($0.80 per unit) 64,000 80,000

Operating income (EBIT) 36,000 60,000Interest 12,000 12,000

Earnings before taxes 24,000 48,000

Taxes 12,000 24,000

Earnings after taxes $ 12,000 $ 24,000

Shares 8,000 8,000Earnings per share $1.50 $3.00

Note than unit sales increased by 25%; EBIT increased by 67% (operating

leverage); and EPS increased by 100% (financial leverage).

(80,000 units) (100,000 units)

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THE END

805 Chapter 05

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