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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
$ $ $
$$
T 5-2
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T 5-3
Figure 5-2Break-even chart: Conservative firmPage 116
Revenues and costs ($ thousands)
200
160
120
80
40
20 40 60 80 100 120
TotalRevenue
Totalcosts
Variable costs
Fixedcosts
Profit
BE
Loss
Units produced and sold (thousands)Fixed costs ($12,000) Price ($2) Variable costs per unit ($1.60)
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Table 5-3Volume-cost-profit analysis: Conservative
firmPage 117
0 0 12,000 12,000 0 (12,000.
)20,000 32,000 12,000 44,000 40,000 (4,000 .)
30,000 48,000 12,000 60,000 60,000 0
40,000 64,000 12,000 76,000 80,000 4,000
60,000 96,000 12,000 108,000 120,000 12,000
80,000 128,000 12,000 140,000 160,000 20,000100,000 160,000 12,000 172,000 200,000 28,000
$ $ $$$
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) $(12,000)
20,000 (36,000) (4,000)
40,000 (12,000) 4,000
60,000 12,000 12,000
80,000 36,000 20,000100,000 60,000 28,000
. . .
. . .
. . .
. . .
. . .
. . .
Leveraged ConservativeFirm Firm
Units (Table 5-2) (Table 5-3)
T 5-5
Table 5-4Operating income or lossPage 118
F d i f Fi i l
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T 5-6
Units (thousands)
Revenues and costs ($ 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
F d ti f Fi i l
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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
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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
Plan A Plan B(leveraged) (conservative)
T 5-7
Table 5-5 (continued)--Impact of financing plan onearnings per sharePage 122
Foundations of Financial
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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
Plan A Plan B(leveraged) (conservative)
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
Foundations of Financial
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In the previousfigure (5-4), the pointwhere Plans A and Bcross is a financialbreak-even point.
Foundations of Financial
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Financial break-
even occurs whenEBIT = borrowing
rate X total assets
Foundations of Financial
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If EBIT is to bebelow this BE point,
we would preferPlan B, with a
conservative, lowlevel of debt.
Foundations of Financial
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If EBIT is to beabove this BE point,
we would preferPlan A, with an
aggressive, high levelof debt.
Foundations of Financial
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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).
Foundations of Financial
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Degree of Financial Leverage(Equations 5-4 and 5-5)
I-EBIT
EBIT
EBITinchangePercent
EPSinchangePercentDFL
h
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About DOLand DFL
h
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Note that DOL isnever less than 1.
h
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A DOL of 1 meansthere is no fixed
cost in the firm.
h
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Note that DFL isnever less than 1.
h
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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.
th
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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.
th
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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)
th
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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
th
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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
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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
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