Financial Liverage

7/27/2019 Financial Liverage

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Chapter Five

Leverage and Capital Structure

Allen BFIN241 1


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Learning Goals1. Discuss role ofbreakeven analysis in leverage study,

determine operating breakeven point (OBEP), andeffect of changing production/sales on breakeven

point.2. Understand 3Leverages

Degree of Operating Leverage (DOL)

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egree o nanc a everage Degree of Combined Leverage (DCL/DTL/DGL)

3. Able to calculate DOL, DFL and DCL (DTL or DGL)as well as to implement sensitivity (indifferencepoint of EBITs) and risk analysis.

4. Understand the implications of different leverages.


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1. Breakeven Concept Breakeven Analysis is used by firms:

To determine the level of operations necessary to cover all operating

costs, variable cost and fixed cost, and

To evaluate the profitability associated with various levels of sales. Operating Break-Even Point (BE) at different points,

Economic Breakeven: EBIT = 0

Financial Breakeven: EBT = 0 Questions #1 and #2

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Accounting Breakeven: NITA = 0 Why do we start with Breakeven Analysis?

Business Risk: how is cost structured, variable and fixed costs

Financial Risk: how business is financed, debt or equity

Operating leverage: how capital assets are employed

Financial leverage: how the amount of debts are utilized


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Total

Cost

Revenue

Breakeven point

$

At breakeven point Q*:Total revenue S* = total cost(TC) = TFC + TVC.

Because the slope of Revenue > the slope

of Total Cost, therefore total cost

increases at slower speed when revenue

increases,,

S

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Variable Cost

Fixed Cost

QQ*

S*

Q

cost (TC) which is a sum of TFCand TVC. S > TC = TFC+TVC

Time


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Breakeven Output

Operating Profit = (P Q) (VC Q) FC

PQ = ? VC

Q = ? FC= ?

To determine operating breakeven point at quantity Q*:

Operating Profit = 0 = (P Q*) (VC Q*) FC*

> 0= 0

< 0

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FC = fixed operating cost per period

VC = variable operating cost per unit

P = sales price per unit

PFT = $0.00Q* is quantity at BE point, Profit = 0 .

EBIT = earnings before interest and taxes = Operating Profit

Questions #3 p140


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Aggressively Leveraged/Capital-intensive firm

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Conservatively Leveraged/Labor-Intensive Production Firm

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Re-visit Income Statement

Operating Section $ billionSales revenue (Price multiplies units produced): $20

Less: Cost Of Good Sold as (Variable Cost) $11

Cross margin $9

Total operating expenses as (Fixed Cost) $5

Operating (income/profit) earnings (EBIT) $4

Financial (Non-Operating) Section

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Other income $0Less interest expenses (Financial cost) $0.8

Earning (income) before tax $3.2

Owner Section

Less taxes (rate 40%) $1.28

Net income after tax (NIAT) $1.92


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Income Statement

Sales Revenue S = (P Q) Less: Variable operating cost (VC Q) Gross margin Q(P VC)

Less: Fixed operating cost (FC) EBIT (operating margin) Q(P-VC) - FC Less: Interest expense

Operating

Leverage

Total

CostStructure

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Less: Taxes NIAT (profit margin) Less: Preferred share dividends

Earnings available for commonshareholders (EAC) Earnings per share (EPS)

FinancialLeverage

FinancialStructure

Income Statement with VC and FC


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Measuring the Degree of Operating Leverage Degree of Operating Leverage (DOL) is the numerical

measure of a firms operating leverage at abase level

(year) of sales.

FCVCQQP

VCQQPQ

=

)()(

)()(levelbase@DOL

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The equation can be simplified (from income statement)

as the ratio of the dollar value of gross margin over

EBIT. DOL at base level (year) of Q is

EBIT

GM

TFCTVCSales

TVCSales

FCTVCTR

TVCTR $

Revenue

RevenueDOL =

=

=


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3. Financial Leverage

Financial Leverage is the useof fixedfinancialcosts tomagnify the effects ofchanges in EBIT on the firmsearnings per share, EPS.

Two fixed financial costs can

Sales Revenue (P * Q)

Less: COGS (VC * Q)

Gross margin

Less: Operating cost (FC)EBIT (operating margin)

Less: Interest exp. & Taxes

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be identified in the incomestatement are:

Interest on long-term debt,and

Preferred share dividends.

What about taxes?

pro marg n

Less: Preferred share divid.

EAC

Earnings per share (EPS)

Financial

Leverage


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Measuring the Degree of Financial Leverage

Degree of Financial Leverage (DFL) is the

numerical measure of the firms financial

leverage.

=

PD

EBITEBITlevelbase@DFL

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whereI = interest on debt

PD = preferred shares dividends

T = corporate tax rate in percentage

T1

1

PD

T

= converts after-tax preferred share dividends into before-

tax amount to keep consistency with the other terms.


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4. Degree of Combined Leverage Degree of Total Leverage is the application of fixed

costs, bothoperating and financial costs, to magnify thedirect effect from changes in sales to/on the firms earningsavailable for common shareholders (EAC) or earnings pershare (EPS).

Degree of Total Leverage (DOL) is acombinedeffect of

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pera ng everage an nanc ng everage

Degree of Total Leverage is total impact of the fixedcosts in the firms operating structure and financialstructure on EPS.

Degree of Total Leverage gives youdirect answer fromchange of sales to change of EPS.

Question # 9 of page 141 and #11 of page 142


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Operating Leverage Operating leverage is the use offixed

operating costs (as a leverage) tomagnify the effects of changes in

sales (production, Q) on the firmsearnings before interest and taxes(EBIT).

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,the more you produce, the higherEBIT you obtain, assuming the priceand VC/unit remain unchanged. Seenext slide, from EBIT

0to EBIT

1and

then EBIT2 at different outputs of Q

Change with quantity, Q*, produced


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Breakeven Analysis

TVC* = $2,500

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11

11111

TFC = $2,500

TC* = $5,000


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Sensitivity Analysis

EBIT2

Questions #5

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1

VariableCost

, EBIT*

Q* Q1 Q2


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Question

1. Should DOL be greater than 1 or equal to 1 or

EBIT

GM

TFCTVCSales

TVCSales

FCTVCTR

TVCTR $DOL =

=

=

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2. What does it mean when DOL = 1?

3. Can DOL equal to zero, DOL = 0?

4. What happens if DOL is zero?


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Example of DOL XYZ has fixed operating costs of $86,000, variable

operating costs of $5.48/unit, and a selling price of$8.98/unit. (use your calculator).

A) Calculate the operating breakeven point in units B) Compute the DOL for the following unit sales:

25,000; 30,000; and 40,000

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C) Graph the DOL figures that you computed in B)(on the y axis) against sales levels (on x axis).

D) Compute the degree of operating leverage at the

point of breakeven units; add this point to your graph. E) what principle is illustrated by your graph and

figure? DOL Example


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FV $86,000

Price $8.98

VC $5.48Breakeven Point $24,571

Answers to Example of DOL

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Units DOLDOL at 25,000 25,000 58.3.0

DOL at 30,000 30,000 5.50

DOL at 40,000 40,000 2.60

DOL at breakeven 24,571


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30

25

50

40

DOL curve

DOL

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15,000 20,000 25,000 30,000 40,00035,000

0

15

10

5

Breakeven point Output


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Operating Section $ billionSales revenue (Price multiplies units produced): $20

Less: Cost Of Good Sold as (Variable Cost) $11

Cross margin $9

Total operating expenses as (Fixed Cost) $5

Operating (income/profit) earnings (EBIT) $4

Financial (Non-Operating) Section

Predict EBIT from base level/year

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Other income $0Less interest expenses (Financial cost) $0.8

Earning (income) before tax $3.2

Owner Section

Less taxes (rate 40%) $1.28

Net income after tax (NIAT) $1.92

What are DOL and DFL? If POS = 15%, what is EBIT and Net Income in next year


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Nonlinear break-even analysis

Profit

Limitation s of DOL1. Revenue and cost are

linear function of volume

changes.2. Focusing on limited time

period.

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Loss

.

timing of cash flows;4. Limited by Opportunity cost

of an investment;5. Without considering

changes in marketplaceand new products


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DOL is Double-Edged Sword

A leveraged firm (highly leveraged in capital

assets) has high fixed costs, a high Break-Even

point and high DOL.

A conservative (non-leveraged or less

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everage rm as ow xe cos s, a owBreak-Even point and low DOL.

Leverage is adouble-edged sword. It magnifies

losses as well as profits implications. Relationship between risk and returns.


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Summary of Measuring DOL1. Degree of Operating Leverage (DOL): For any given level

of fixed assets, Any changes () in sales will produceMagnifiedchanges () in EBIT. Sales change by apercentage, EBIT will change by a greater percentage.

2. Normally DOL > 1. As long as DOL > 1, there isoperating leverage. At breakeven point, DOL =

3. The higher the firms fixed operating cost relative to

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,

greater the degree of operating leverage.4. In application, DOL can be used in current year and/or as

base year to identify futures EBIT if sales revenue ispredicted DOL can be used in conjunction with sales

forecasting and Pro Forma statements5. The higher DOL, the greater the impacts that sales change

have on EBIT. but higher levels of DOL also implygreater operating risk Why?


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3. Financial Leverage

Financial Leverage is the useof fixedfinancialcosts tomagnify the effects of

changes in EBIT on the firmsearnings per share, EPS.

Two fixed financial costs can

Sales Revenue (P * Q)

Less: COGS (VC * Q)

Gross margin

Less: Operating cost (FC)EBIT (operating margin)

Less: Interest exp. & Taxes

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be identified in the incomestatement are:

Interest on long-term debt,and

Preferred share dividends. What about taxes?

pro marg n

Less: Preferred share divid.

EAC

Earnings per share (EPS)

Financial

Leverage


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Measuring the Degree of Financial Leverage

Degree of Financial Leverage (DFL) is the

numerical measure of the firms financial

leverage.

=

PD

EBITEBITlevelbase@DFL

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whereI = interest on debt

PD = preferred shares dividends

T = corporate tax rate in percentage

T1

1

PD

T

= converts after-tax preferred share dividends into before-

tax amount to keep consistency with the other terms.


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4. Degree of Combined Leverage Degree of Total Leverage is the application of

fixed costs, bothoperating and financial costs,to magnify the direct effect from changes in sales

to/on the firms earnings available for commonshareholders (EAC) or earnings per share (EPS).

Degree of Total Leverage (DOL) is acombined

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e ec o pera ng everage an nanc ngLeverage

Degree of Total Leverage is total impact of thefixed costs in the firms operating structure and

financial structure on EPS. Degree of Total Leverage gives youdirect answer

from change of sales to change of EPS.


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Combining operating and financial leverage

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DCL implications

T

PDI

GMQ

=

1

EBIT

$levelbase@DCL

GMQ =

$levelbase@DCL

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> 1 ? Why and what does that imply ?

= 1 ? Why and what does that imply ?

< 1 ? Why and what does that imply ?

Should DCL be

T 1EBT


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Example of DCL

Firm X has sales of 100,000 units at $2/unit, VOC of$1.70/unit, and FOC of $6,000. Interest cost is$10,000/year. Firm Y has sales of 100,000 units at

$2.5/unit, VOC of $1/unit. FOC of $62,500. Interest costis $17,500/year. Assume the both firms are in the 40%tax bracket.

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, .

Explain the implications of your answers.

B) Compute the DOL, DFL and DCL for Firm Y.Explain the implications of your answers.

C) Compare the relative risks of the two firms D) Discuss the principles of leverage illustrated in your

answers.


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Summary of Information

VOC FOC Price Q S I TaxX $1.70 $6,000 $2.00 100,000 $200,000 $10,000 40%

Y $1.00 $62,500 $2.50 100,000 $250,000 $17,500 40%

X YSales Revenue $200,000 $250,000

Total variable cost (TVC) $170,000 $100,000

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Gross Margin in dollars $ $30,000 $150,000

Total fixed cost (TFC) $6,000 $62,500

EBIT $24,000 $87,500

Interest payment I $10,000 $17,500

Earning before Taxes (EBT) $14,000 $70,000

Taxes amount @ 40% $5,600 $28,000

EAC $8,400 $42,000


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Answer

DOL DFL DCL

X 1.25 1.71 2.14

Y 1.71 1.25 2.14

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financial risk than Firm Y.D) Two firms with differing operating and financial

structures may be equally leveraged. Since total

leverage is the product of operating and financialleverages, each firm may structure itself differently and

still has the same amount of total risk.


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Example of application of leverages

XYZ Inc. sold it products at $6/unit. VOC is $3.50/unit andFOC is $50,000/year. Interest cost is $13,000 and $7,000 ofpreferred share dividends each year. At this point, XYZ Inc.is selling 30,000 units/year and is taxed at 40%.

A) Calculate XYZ Inc.s Operating breakeven point in unitsand sales dollars;

B) Based on the XYZ Inc.s current sales of 30,000 units

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,

Calculate its EBIT and EAC; C) Calculate XYZ Inc.s DOL, DFL and DCL. Explain your

answers.

D) XYZ Inc. has entered into a contract to produce and sell

an additional 15,000 units in the coming year. Use the DOL,DFL and DCL to predict and calculate the changes in EBITand EAC.


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Answers A) and B)

A) Breakeven Units and RevenueQ* = FC (P - VC) = $50,000 ($6 - $3.50) = 20,000 unitsS* = Breakeven quantity price/unit = 20,000 $6 = $120,000

B) EBIT and EACSales ($6 30,000) $180,000

Less: Variable costs ($3.50 30,000) 105,000

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xe costs ,

EBIT 25,000 Less interest expense 13,000

EBT 12,000

Less taxes (40%) 4,800

NIAT $7,200 Less: Referred Dividends $7,000

EAC $200


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Answers C)

C) DOL DFL DCL

30,000 units 3.0 75.08 225.24

45,000 units 1.8 1.65 2.97

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Answer D)

1) % Change in EBIT

= % Change in sales DOL

= 50% 3 = 150% New EBIT = $25,000 + ($25,000 150%) = $62,500

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ange n

= % Change in sales DCL

= 50% 225.24 = 11,262%

New EAC = $200 + ($200 11,262%)= $200 + $22,524 = $22,724 (vs. $22,700)


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D: another way to present

Sales (in units): 30,000 45,000

Sales revenue: $180,000 $270,000

Less: Variable operating costs $105,000 $157,500

Less: Fixed operating costs $50,000 $50,000

EBIT: $25,000 $62,500

+50%

+150%

Cost structure

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, ,

EBT $12,000 $49,500

Less: Taxes (40%) $4,800 $19,800

NIAT $$7,200 $29,700

Preferred Dividends $7,000 $7,000

EAC $200 $22,700

+11,250%

financial structure


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Answer D

B) Sales ($6 45,000) $270,000

Less: Variable costs ($3.50 45,000) 157,500

Fixed costs 50,000EBIT 62,500

Less interest ex ense 13 000

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EBT 49,500Less taxes (40%) 19,800

NIAT $29,700

Less: Referred Dividends $7,000EAC $22,700

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