Financial Management Slides Ch 16

6-1
Chapter 16Chapter 16
Operating andOperating and
Financial LeverageFinancial Leverage
Instructor: Ajab Khan Burki

6-2
Operating andOperating and
Operating Leverage
Financial Leverage
Total Leverage
Cash-Flow Ability to Service Debt
Other Methods of Analysis
Combination of Methods

6-3
Operating LeverageOperating Leverage
One potential “effect” caused by the
presence of operating leverage is
that a change in the volume of sales
results in a “more than proportional”
change in operating profit (or loss).
Operating LeverageOperating Leverage -- The use of-- The use of
fixed operating costs by the firm.fixed operating costs by the firm.

6-4
Impact of OperatingImpact of Operating
Leverage on ProfitsLeverage on Profits
Firm F Firm V Firm 2FFirm F Firm V Firm 2F
Sales $10 $11 $19.5
Operating Costs
Fixed 7 2 14
Variable 2 7 3
Operating Profit $$ 11 $ 2$ 2 $ 2.5$ 2.5
FC/total costs .78 .22 .82
FC/sales .70 .18 .72
(in thousands)(in thousands)

6-5
Now, subject each firm to a 50%50%
increase in salesincrease in sales for next year.
Which firm do you think will be more
“sensitive”“sensitive” to the change in sales (i.e.,
show the largest percentage change in
operating profit, EBIT)?
[ ] Firm FFirm F; [ ] Firm VFirm V; [ ] Firm 2FFirm 2F.

6-6
Firm F Firm V Firm 2FFirm F Firm V Firm 2F
Sales $15 $16.5 $29.25
Operating Costs
Fixed 7 2 14
Variable 3 10.5 4.5
Operating Profit $$ 55 $ 4$ 4 $10.75$10.75
PercentagePercentage
Change in EBITChange in EBIT* 400% 100% 330%400% 100% 330%
(in thousands)(in thousands)
* (EBITt - EBIT t-1) / EBIT t-1

6-7
Firm FFirm F is the most “sensitive” firmis the most “sensitive” firm -- for it, a 50%
increase in sales leads to a 400% increase in400% increase in
EBITEBIT.
Our example reveals that it is a mistake to
assume that the firm with the largest absolute or
relative amount of fixed costs automatically
shows the most dramatic effects of operating
leverage.
Later, we will come up with an easy way to spot
the firm that is most sensitive to the presence of
operating leverage.

6-8
Break-Even AnalysisBreak-Even Analysis
When studying operating leverage,
“profits” refers to operating profits
before taxes (i.e., EBIT) and excludes
debt interest and dividend payments.
Break-Even AnalysisBreak-Even Analysis -- A technique for
studying the relationship among fixed
costs, variable costs, profitsprofits, and sales
volume.

6-9
Break-Even ChartBreak-Even Chart
QUANTITY PRODUCED AND SOLDQUANTITY PRODUCED AND SOLD
0 1,000 2,000 3,000 4,0004,000 5,000 6,000 7,000
Total RevenuesTotal Revenues
ProfitsProfits
Fixed CostsFixed Costs
Variable CostsVariable Costs
LossesLosses
REVENUESANDCOSTSREVENUESANDCOSTS
($thousands)($thousands)
175175
250
100
50
Total CostsTotal Costs

6-10
Break-EvenBreak-Even
(Quantity) Point(Quantity) Point
How to find the quantity break-even point:
EBIT = PP(QQ) - VV(QQ) - FCFC
EBIT = QQ(PP - VV) - FCFC
P = Price per unitP = Price per unit V = Variable costs per unitV = Variable costs per unit
FC = Fixed costsFC = Fixed costs Q = Quantity (units)Q = Quantity (units)
produced and soldproduced and sold
Break-Even PointBreak-Even Point -- The sales volume required-- The sales volume required
so that total revenues and total costs areso that total revenues and total costs are
equal; may be in units or in sales dollars.equal; may be in units or in sales dollars.

6-11
(Quantity) Point(Quantity) Point
Breakeven occurs when EBIT = 0
QQ (PP - VV) - FCFC = EBIT
QQBEBE (PP - VV) - FCFC = 0
QQBEBE (PP - VV) = FCFC
QQBEBE = FCFC / (PP - VV)

6-12
Break-Even (Sales) PointBreak-Even (Sales) Point
How to find the sales break-even point:
SSBEBE =FCFC + (VCVCBEBE)
SSBEBE =FCFC + (QQBEBE )(VV)
or
SSBEBE
**
=FCFC / [1 - (VCVC / S) ]
* Refer to text for derivation of the formula

6-13
Point ExamplePoint Example
Basket Wonders (BW) wants to
determine both the quantity and salesquantity and sales
break-even pointsbreak-even points when:
Fixed costsFixed costs are $100,000$100,000
Baskets are sold for $43.75$43.75 eacheach
Variable costs are $18.75 per basket$18.75 per basket

6-14
Break-Even Point (s)Break-Even Point (s)
Breakeven occurs when:
QQBEBE = FCFC / (PP - VV)
QQBEBE = $100,000$100,000 / ($43.75$43.75 - $18.75$18.75)
QQBEBE = 4,000 Units4,000 Units
SSBEBE =(QQBEBE )(VV) + FCFC
SSBEBE =(4,0004,000 )($18.75$18.75) + $100,000$100,000
SSBEBE = $175,000$175,000

6-15
Break-Even ChartBreak-Even Chart
0 1,000 2,000 3,000 4,0004,000 5,000 6,000 7,000
Total RevenuesTotal Revenues
ProfitsProfits
Fixed CostsFixed Costs
Variable CostsVariable Costs
LossesLosses
REVENUESANDCOSTSREVENUESANDCOSTS
($thousands)($thousands)
175175
250
100
50
Total CostsTotal Costs

6-16
Degree of OperatingDegree of Operating
Leverage (DOL)Leverage (DOL)
DOLDOL at Q
units of
output
(or sales)
Degree of Operating LeverageDegree of Operating Leverage -- The
percentage change in a firm’s operating
profit (EBIT) resulting from a 1 percent
change in output (sales).
=
Percentage change in
operating profit (EBIT)
output (or sales)

6-17
Computing the DOLComputing the DOL
DOLDOLQ unitsQ units
Calculating the DOL for a single productCalculating the DOL for a single product
or a single-product firm.or a single-product firm.
=
QQ (PP - VV)
QQ (PP - VV) - FCFC
= QQ
QQ - QQBEBE

6-18
Computing the DOLComputing the DOL
DOLDOLS dollars of salesS dollars of sales
Calculating the DOL for aCalculating the DOL for a
multiproduct firm.multiproduct firm.
=
SS - VCVC
SS - VCVC - FCFC
=
EBIT + FCFC
EBIT

6-19
Point ExamplePoint Example
Lisa Miller wants to determine the degreedegree
of operating leverageof operating leverage at sales levels ofsales levels of
6,000 and 8,000 units6,000 and 8,000 units. As we did earlier,
we will assume that:

6-20
Computing BW’s DOLComputing BW’s DOL
DOLDOL6,000 units6,000 units
Computation based on the previouslyComputation based on the previously
calculated break-even point of 4,000 unitscalculated break-even point of 4,000 units
=
6,0006,000
6,0006,000 - 4,0004,000
=
= 33
DOLDOL8,000 units8,000 units
8,0008,000
8,0008,000 - 4,0004,000
= 22

6-21
Interpretation of the DOLInterpretation of the DOL
A 1% increase in sales above the 8,000A 1% increase in sales above the 8,000
unit level increases EBIT by 2%unit level increases EBIT by 2%
because of the existing operatingbecause of the existing operating
leverage of the firm.leverage of the firm.
=DOLDOL8,000 units8,000 units
8,0008,000
8,0008,000 - 4,0004,000
= 22

6-22
2,0002,000 4,0004,000 6,000 8,0006,000 8,000
11
22
33
44
55
00
-1-1
-2-2
-3-3
-4-4
-5-5
DEGREEOFOPERATINGDEGREEOFOPERATING
LEVERAGE(DOL)LEVERAGE(DOL)
QQBEBE

6-23
DOL is a quantitative measure of the “sensitivity”
of a firm’s operating profit to a change in the
firm’s sales.
The closer that a firm operates to its break-even
point, the higher is the absolute value of its DOL.
When comparing firms, the firm with the highest
DOL is the firm that will be most “sensitive” to a
change in sales.
Key Conclusions to be Drawn from SlideKey Conclusions to be Drawn from Slide
16-22 and our Discussion of DOL16-22 and our Discussion of DOL

6-24
DOL and Business RiskDOL and Business Risk
DOL is only one componentone component of business risk
and becomes “active” only in the presenceonly in the presence
of sales and production cost variabilityof sales and production cost variability.
DOL magnifiesmagnifies the variability of operating
profits and, hence, business risk.
Business RiskBusiness Risk -- The inherent uncertainty-- The inherent uncertainty
in the physical operations of the firm. Itsin the physical operations of the firm. Its
impact is shown in the variability of theimpact is shown in the variability of the
firm’s operating income (EBIT).firm’s operating income (EBIT).

6-25
Application of DOL forApplication of DOL for
Our Three Firm ExampleOur Three Firm Example
Use the data in Slide 16-4 and theUse the data in Slide 16-4 and the
following formula forfollowing formula for Firm FFirm F::
DOLDOL = [(= [(EBITEBIT ++ FCFC)/)/EBITEBIT]]
=DOLDOL$10,000 sales$10,000 sales
1,0001,000 ++ 7,0007,000
1,0001,000
= 8.08.0

6-26
Our Three Firm ExampleOur Three Firm Example
following formula forfollowing formula for Firm VFirm V::
2,0002,000 ++ 2,0002,000
2,0002,000
= 2.02.0

6-27
Our Three-Firm ExampleOur Three-Firm Example
following formula forfollowing formula for Firm 2FFirm 2F::
2,5002,500 ++ 14,00014,000
2,5002,500
= 6.66.6

6-28
Our Three-Firm ExampleOur Three-Firm Example
The ranked results indicate that the firm mostThe ranked results indicate that the firm most
sensitive to the presence of operating leveragesensitive to the presence of operating leverage
isis Firm FFirm F.
Firm FFirm F DOLDOL == 8.08.0
Firm VFirm V DOLDOL == 6.66.6
Firm 2FFirm 2F DOLDOL == 2.02.0
Firm FFirm F will expect awill expect a 400% increase in profit400% increase in profit from afrom a 50%50%
increase in salesincrease in sales (see Slide 16-6 results).(see Slide 16-6 results).

6-29
Financial leverage is acquired by
choice.
Used as a means of increasing the
return to common shareholders.
Financial LeverageFinancial Leverage -- The use of-- The use of
fixed financing costs by the firm.fixed financing costs by the firm.
The British expression isThe British expression is gearinggearing..

6-30
EBIT-EPS Break-Even,EBIT-EPS Break-Even,
or Indifference, Analysisor Indifference, Analysis
Calculate EPSEPS for a given level of EBITEBIT at a
given financing structure.
EBIT-EPS Break-Even AnalysisEBIT-EPS Break-Even Analysis -- Analysis-- Analysis
of the effect of financing alternatives onof the effect of financing alternatives on
earnings per share. The break-even point isearnings per share. The break-even point is
the EBIT level where EPS is the same forthe EBIT level where EPS is the same for
two (or more) alternatives.two (or more) alternatives.
(EBITEBIT - I) (1 - t) - Pref. Div.
# of Common Shares
EPSEPS =

6-31
EBIT-EPS ChartEBIT-EPS Chart
Current common equity shares = 50,000Current common equity shares = 50,000
$1 million in new financing of either:$1 million in new financing of either:
All C.S. sold at $20/share (50,000 shares)
All debt with a coupon rate of 10%
All P.S. with a dividend rate of 9%
Expected EBIT = $500,000Expected EBIT = $500,000
Income tax rate is 30%Income tax rate is 30%
Basket WondersBasket Wonders has $2 million in LT financinghas $2 million in LT financing
(100% common stock equity).(100% common stock equity).

6-32
EBIT-EPS Calculation withEBIT-EPS Calculation with
New Equity FinancingNew Equity Financing
EBITEBIT $500,000$500,000 $150,000$150,000*
Interest 0 0
EBT $500,000 $150,000
Taxes (30% x EBT) 150,000 45,000
EAT $350,000 $105,000
Preferred Dividends 0 0
EACSEACS $350,000$350,000 $105,000$105,000
# of Shares 100,000 100,000
EPSEPS $3.50$3.50 $1.05$1.05
Common Stock Equity AlternativeCommon Stock Equity Alternative
* A second analysis using $150,000 EBIT rather than the expected EBIT.

6-33
0 100 200 300 400 500 600 7000 100 200 300 400 500 600 700
EBIT ($ thousands)EBIT ($ thousands)
EarningsperShare($)EarningsperShare($)
00
11
22
33
44
55
66
CommonCommon

6-34
New Debt FinancingNew Debt Financing
EBITEBIT $500,000$500,000 $150,000$150,000*
Interest 100,000 100,000
EBT $400,000 $ 50,000
Taxes (30% x EBT) 120,000 15,000
EAT $280,000 $ 35,000
Preferred Dividends 0 0
EACSEACS $280,000$280,000 $ 35,000$ 35,000
# of Shares 50,000 50,000
EPSEPS $5.60$5.60 $0.70$0.70
Long-term Debt AlternativeLong-term Debt Alternative

6-35
0 100 200 300 400 500 600 7000 100 200 300 400 500 600 700
00
11
22
33
44
55
66
CommonCommon
DebtDebt
Indifference point
between debtdebt and
common stockcommon stock
financing

6-36
New Preferred FinancingNew Preferred Financing
EBITEBIT $500,000$500,000 $150,000$150,000*
Interest 0 0
EBT $500,000 $150,000
Taxes (30% x EBT) 150,000 45,000
EAT $350,000 $105,000
Preferred Dividends 90,000 90,000
EACSEACS $260,000$260,000 $ 15,000$ 15,000
# of Shares 50,000 50,000
EPSEPS $5.20$5.20 $0.30$0.30
Preferred Stock AlternativePreferred Stock Alternative

6-37
0 100 200 300 400 500 600 7000 100 200 300 400 500 600 700
00
11
22
33
44
55
66
CommonCommon
DebtDebt
Indifference point
between preferredpreferred
stockstock and commoncommon
stockstock financing
PreferredPreferred

6-38
What About Risk?What About Risk?
0 100 200 300 400 500 600 7000 100 200 300 400 500 600 700
00
11
22
33
44
55
66
CommonCommon
DebtDebt
Lower riskLower risk. Only a small
probability that EPS will
be less if the debt
alternative is chosen.
ProbabilityofOccurrenceProbabilityofOccurrence
(fortheprobabilitydistribution)(fortheprobabilitydistribution)

6-39
What About Risk?What About Risk?
0 100 200 300 400 500 600 7000 100 200 300 400 500 600 700
00
11
22
33
44
55
66
CommonCommon
DebtDebt
Higher riskHigher risk. A much larger
probability that EPS will
be less if the debt
alternative is chosen.
ProbabilityofOccurrenceProbabilityofOccurrence
(fortheprobabilitydistribution)(fortheprobabilitydistribution)

6-40
Degree of FinancialDegree of Financial
Leverage (DFL)Leverage (DFL)
DFLDFL at
EBIT of
X dollars
Degree of Financial LeverageDegree of Financial Leverage -- The
percentage change in a firm’s earnings
per share (EPS) resulting from a 1
percent change in operating profit.
=
earnings per share (EPS)
operating profit (EBIT)

6-41
Computing the DFLComputing the DFL
DFLDFLEBIT of $X
Calculating the DFLCalculating the DFL
=
EBITEBIT
EBITEBIT - II - [ PDPD / (1 - tt) ]
EBITEBIT = Earnings before interest and taxes= Earnings before interest and taxes
II = Interest= Interest
PDPD = Preferred dividends= Preferred dividends
tt = Corporate tax rate= Corporate tax rate

6-42
What is the DFL for EachWhat is the DFL for Each
of the Financing Choices?of the Financing Choices?
DFLDFL$500,000$500,000
Calculating the DFL forCalculating the DFL for NEWNEW equityequity* alternativealternative
=
$500,000$500,000
$500,000$500,000 - 00 - [00 / (1 - 00)]
* The calculation is based on the expected EBIT
= 1.001.00

6-43
DFLDFL$500,000$500,000
Calculating the DFL forCalculating the DFL for NEWNEW debtdebt * alternativealternative
=
$500,000$500,000
{{ $500,000$500,000 - 100,000100,000
- [00 / (1 - 00)] }
= $500,000$500,000 / $400,000
1.251.25=

6-44
DFLDFL$500,000$500,000
Calculating the DFL forCalculating the DFL for NEWNEW preferredpreferred * alternativealternative
=
$500,000$500,000
{{ $500,000$500,000 - 00
- [90,00090,000 / (1 - .30.30)] }
= $500,000$500,000 / $400,000
1.351.35=

6-45
Variability of EPSVariability of EPS
Preferred stockPreferred stock financing will lead to
the greatest variability in earnings per
share based on the DFL.
This is due to the tax deductibility of
interest on debt financing.
DFLDFLEquityEquity = 1.00= 1.00
DFLDFLDebtDebt = 1.25= 1.25
DFLDFLPreferredPreferred == 1.351.35
Which financing
method will have
the greatest relativegreatest relative
variability in EPS?variability in EPS?

6-46
Financial RiskFinancial Risk
Debt increases the probability of cash
insolvency over an all-equity-financed firm. For
example, our example firm must have EBIT of at
least $100,000 to cover the interest payment.
Debt also increased the variability in EPS as the
DFL increased from 1.00 to 1.25.
Financial RiskFinancial Risk -- The added variability in-- The added variability in
earnings per share (EPS) -- plus the risk ofearnings per share (EPS) -- plus the risk of
possible insolvency -- that is induced by thepossible insolvency -- that is induced by the
use of financial leverage.use of financial leverage.

6-47
Total Firm RiskTotal Firm Risk
CVCVEPSEPS is a measure of relative total firm risktotal firm risk
CVCVEBITEBIT is a measure of relative business riskbusiness risk
The difference, CVCVEPSEPS - CV- CVEBITEBIT, is a measure of
relative financial riskfinancial risk
Total Firm RiskTotal Firm Risk -- The variability in earnings per-- The variability in earnings per
share (EPS). It is the sum of business plusshare (EPS). It is the sum of business plus
financial risk.financial risk.
Total firm riskTotal firm risk = business riskbusiness risk + financial riskfinancial risk

6-48
Degree of TotalDegree of Total
Leverage (DTL)Leverage (DTL)
DTLDTL at Q units
(or S dollars)
of output (or
sales)
Degree of Total LeverageDegree of Total Leverage -- The
percentage change in a firm’s earnings
per share (EPS) resulting from a 1
percent change in output (sales).
=
earnings per share (EPS)
output (or sales)

6-49
Computing the DTLComputing the DTL
DTLDTLS dollars
of sales
DTLDTL Q units (or S dollars)Q units (or S dollars) = ( DOLDOL Q units (or S dollars)Q units (or S dollars) )
x ( DFLDFL EBIT of X dollarsEBIT of X dollars )
=
EBITEBIT + FC
EBITEBIT - II - [ PDPD / (1 - tt) ]
DTLDTL Q units
QQ (PP -- VV)
QQ (PP -- VV) - FC - II - [ PDPD / (1 - tt) ]
=

6-50
DTL ExampleDTL Example
Lisa Miller wants to determine the
Degree of Total LeverageDegree of Total Leverage at
EBIT=$500,000.EBIT=$500,000. As we did earlier, we
will assume that:

6-51
for All-Equity Financingfor All-Equity Financing
DTLDTLS dollars
of sales
=
$500,000$500,000 + $100,000
$500,000$500,000 - 00 - [ 00 / (1 - .3.3) ]
DTLDTLS dollarsS dollars = (DOLDOL S dollarsS dollars) x (DFLDFLEBIT of $SEBIT of $S )
DTLDTLS dollarsS dollars = (1.21.2 ) x ( 1.01.0* ) = 1.201.20
= 1.201.20
*Note: No financial leverage.

6-52
for Debt Financingfor Debt Financing
DTLDTLS dollars
of sales
=
$500,000$500,000 + $100,000
{ $500,000$500,000 - $100,000$100,000
- [ 00 / (1 - .3.3) ] }
DTLDTLS dollarsS dollars = (DOLDOL S dollarsS dollars) x (DFLDFLEBIT of $SEBIT of $S )
DTLDTLS dollarsS dollars = (1.21.2 ) x ( 1.251.25* ) = 1.501.50
= 1.501.50
*Note: Calculated on Slide 43.

6-53
Risk versus ReturnRisk versus Return
Compare the expected EPS to the DTL for
the common stock equity financing
approach to the debt financing approach.
FinancingFinancing E(EPS)E(EPS) DTLDTL
EquityEquity $3.50$3.50 1.201.20
DebtDebt $5.60$5.60 1.501.50
Greater expected return (higher EPS) comes atGreater expected return (higher EPS) comes at
the expense of greater potential risk (higher DTL)!the expense of greater potential risk (higher DTL)!

6-54
What is an AppropriateWhat is an Appropriate
Amount of Financial Leverage?Amount of Financial Leverage?
Firms must first analyze their expected futureexpected future
cash flows.cash flows.
The greatergreater and more stablemore stable the expected future
cash flows, the greater the debt capacity.the greater the debt capacity.
Fixed charges includeFixed charges include: debt principal and
interest payments, lease payments, and
preferred stock dividends.
Debt CapacityDebt Capacity -- The maximum amount of debt-- The maximum amount of debt
(and other fixed-charge financing) that a firm(and other fixed-charge financing) that a firm
can adequately service.can adequately service.

6-55
Coverage RatiosCoverage Ratios
Interest CoverageInterest Coverage
EBITEBIT
Interest expensesInterest expenses
Indicates a firm’s
ability to cover
interest charges.
Income Statement
Ratios
Coverage Ratios
A ratio value equal to 1
indicates that earnings
are just sufficient to
cover interest charges.

6-56
Coverage RatiosCoverage Ratios
Debt-service CoverageDebt-service Coverage
EBITEBIT
{ Interest expensesInterest expenses +
[Principal payments / (1-t)Principal payments / (1-t) ] }
Indicates a firm’s
ability to cover
interest expenses and
principal payments.
Income Statement
Ratios
Coverage Ratios
Allows us to examine the
ability of the firm to meet
all of its debt payments.
Failure to make principal
payments is also default.

6-57
Coverage ExampleCoverage Example
Make an examination of the coveragecoverage
ratiosratios for Basket Wonders when
EBIT=$500,000.EBIT=$500,000. Compare the equity
and the debt financing alternatives.
Assume thatAssume that:
Interest expensesInterest expenses remain at $100,000$100,000
Principal payments of $100,000Principal payments of $100,000 are
made yearly for 10 years

6-58
Compare the interest coverage and debt
burden ratios for equity and debt financing.
InterestInterest Debt-serviceDebt-service
FinancingFinancing CoverageCoverage CoverageCoverage
EquityEquity InfiniteInfinite InfiniteInfinite
DebtDebt 5.005.00 2.502.50
The firm actually has greater risk than the interestThe firm actually has greater risk than the interest
coverage ratio initially suggests.coverage ratio initially suggests.

6-59
-250 0 250 500 750 1,000 1,250-250 0 250 500 750 1,000 1,250
Firm B has a much
smaller probability
of failing to meet its
obligations than Firm A.
Firm BFirm B
Firm AFirm A
Debt-service burdenDebt-service burden
= $200,000= $200,000
PROBABILITYOFOCCURRENCEPROBABILITYOFOCCURRENCE

6-60
Summary of the CoverageSummary of the Coverage
Ratio DiscussionRatio Discussion
A single ratio value cannot be interpreted
identically for all firms as some firms have
greater debt capacity.
Annual financial lease payments should be
added to both the numerator and
denominator of the debt-service coverage
ratio as financial leases are similar to debt.
The debt-service coverage ratio accounts
for required annual principal payments.

6-61
Other Methods of AnalysisOther Methods of Analysis
Often, firms are compared to peer institutions in the
same industry.
Large deviations from norms must be justified.
For example, an industry’s median debt-to-net-worth
ratio might be used as a benchmark for financial
leverage comparisons.
Capital StructureCapital Structure -- The mix (or proportion) of a-- The mix (or proportion) of a
firm’s permanent long-term financingfirm’s permanent long-term financing
represented by debt, preferred stock, andrepresented by debt, preferred stock, and
common stock equity.common stock equity.

6-62
Firms may gain insight into the financial
markets’ evaluation of their firm by
talking with:
Investment bankers
Institutional investors
Investment analysts
Lenders
Surveying Investment Analysts and LendersSurveying Investment Analysts and Lenders

6-63
Firms must consider the impact
of any financing decision on the
firm’s security rating(s).
Security RatingsSecurity Ratings

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