Analysis and Impact of Leverage

1

Analysis and Impact Analysis and Impact of Leverageof Leverage

Chapter 15Chapter 15

3Goal of a firmGoal of a firm

Managers' objective is to maximize stockholders' wealth--maximize the price of the firm's stock. We noted in an earlier chapter that the capital structure that produces the lowest WACC (risk) is also the one that maximizes share price.

4RiskRisk

Variability of the expected net income (EPS)Variability of the expected net income (EPS)

5RiskRisk

Variability of revenues from expectedVariability of revenues from expectedTwo types of Risk: Business Risk & Financial RiskTwo types of Risk: Business Risk & Financial Risk

6RiskRisk


RevenueRevenue-Variable Cost -Variable Cost Contribution marginContribution margin-Fixed cost-Fixed cost=EBIT/operating profits=EBIT/operating profits--InterestInterest=NI=NI

7RiskRisk


Business RiskBusiness RiskRisk Due to Operations

8RiskRisk


Business RiskBusiness RiskRisk Due to Operations

Measured by variability of EBIT (earnings before interest and taxes)

9RiskRisk


Business RiskBusiness RiskRisk Due to OperationsMeasured by variability of EBIT (earnings before

interest and taxes)Coefficient of Variation of EBIT

=Standard Deviation of EBIT

Expected EBIT

10RiskRisk


Financial RiskFinancial RiskRisk due to raising money with fixed income securities

11Business RiskBusiness Risk

Major determinants of business risk

1. Demand Variability2. Sales Price Variability3. Input Price variability.4. Inability to adjust output prices for a change in input prices-a utility can

transfer costs more easily5. Operating Leverage--the extent to which costs are 'fixed' (the ratio of

fixed cost to total cost).

Business risk not only varies from industry to industry, it varies among firms in a given industry.

Business risk of a firm can change over time.

12RiskRisk

Financial RiskFinancial RiskRisk due to raising money with fixed income securitiesFinancial risk is high with high levels of debt financing

13RiskRisk

Financial RiskFinancial RiskRisk due to raising money with fixed income securitiesFinancial risk is high with high levels of debt financingFinancial leverage - the use of fixed income securities

to finance a portion of assets

14RiskRisk


to finance a portion of assetsExample

Firm A is an all equity firm -- it has no financial leverage

15RiskRisk


to finance a portion of assetsExample

Firm A is an all equity firm -- it has no financial leverageFirm B is financed by 50% debt and 50% equity -- it uses

financial leverage

16RiskRisk

Notes:

1. Business risk is largely determined by technology and by industry/market conditions, although management decisions, to some extent, do matter.

2. Financial risk is largely management determined.

3. If business risk is high, financial risk (leverage) should be restrained.

17Break-even AnalysisBreak-even Analysis

The point of sales where operating profits are zero. The point of sales where operating profits are zero. The point where revenues barely cover all costs.The point where revenues barely cover all costs.

Steps to SolutionSteps to SolutionDetermine the quantity of output which results in an

EBIT = $0



EBIT = $0Shows output necessary to cover operating (not

financial) costs




financial) costsCalculate EBIT at various output levels




financial) costsCalculate EBIT at various output levelsApplications

Capital Expenditure Analysis




financial) costsCalculate EBIT at various output levelsApplications

Capital Expenditure AnalysisDetermining PricesEvaluating Fixed vs. Variable Costs


AssumptionsAssumptionsFixed costs remain constant as quantity changes

Fixed Costs Includes:Salaries, Depreciation, Rent






Variable Costs Includes:Materials, Labor, Commissions


Variable costs vary as quantity of output changes: they are constant per unit of output

Drop Semivariable costs




Quantity Sold

Costs$

Fixed Costs

Variable Costs








Revenues are quantity sold times price per unit


Calculation of Break-even QuantityCalculation of Break-even Quantity

EBIT = Sales – Variable Costs - Fixed Costs

Find Quantity which results in EBIT = $0Find Quantity which results in EBIT = $0


Calculation of Break-even QuantityCalculation of Break-even QuantityTrial and Error Method

Choose arbitrary output levelCalculate EBITIf EBIT < 0, choose a larger output levelIf EBIT > 0, choose a lower output levelContinue until find a level of output which results in EBIT

= $0



QB =

Algebraic AnalysisAlgebraic Analysis

F P – V

Where:QB = Break-even QuantityP = Price per UnitF = Total Fixed CostsV = Variable Costs per Unit



QB =

Example:Example:

F P – V

Fixed Costs = $1,000,000 per yearPrice = $800/unitVariable Costs = $400/unit



QB =

Example:Example:

F P – V


QB = $1,000,000 $800 – $400



QB =

Example:Example:

F P – V


QB = $1,000,000 $800 – $400

= 2,500 Units


Calculation of Break-even Sales Level (S*)Calculation of Break-even Sales Level (S*)

S* = QB x P

To Find S* for a single product use Break-even Quantity (QTo Find S* for a single product use Break-even Quantity (QBB):):



S* = QB x P

S* = 2,500 units x $800




S* = QB x P


S* = 2,500 units x $800

= $2,000,000


Calculation of Break-even Sales Level (S*)Calculation of Break-even Sales Level (S*)May want to Calculate the Break-even Sales Level (S*)

for the entire firm with many products



for the entire firm with many productsCalculate from Income Statement data at a particular

Sales Level



for the entire firm with many productsCalculate for Income Statement at one Sales Level

S* = F 1 - VC

SS = Dollar Level of SalesVC = Total Dollar Variable Costs




S* =

S* =$3,000,000

F 1 - VC

SS = Dollar Level of Sales = $3,000,000VC = Total Dollar Variable Costs = $1,500,000

Example:Example:

$1,000,000 1 – $1,500,000




S* =

S* =$3,000,000

F 1 - VC

SS = Dollar Level of Sales = $3,000,000VC = Total Dollar Variable Costs = $1,500,000

Example:Example:

$1,000,000 1 – $1,500,000 = $2,000,000


Graphical Analysis of Break-even PointGraphical Analysis of Break-even Point

Quantity of Units

Sales &

Costs$

Fixed Costs$1,000,000



Quantity of Units

Sales &

Costs$


Variable Costs



Quantity of Units

Sales &

Costs$


Variable Costs

Total Costs



Quantity of Units

Sales &

Costs$

Fixed Costs

Variable Costs

$1,000,000

Total Costs

Sales



Quantity of Units

Sales &

Costs$

Fixed Costs

Variable Costs

$1,000,000

Total Costs

Sales

QB = 2,500

$2,000,000


Limitations:Limitations:1.1. The sales-volume-cost-profit relationship is The sales-volume-cost-profit relationship is

assumed to be linear—it may not be. In the real assumed to be linear—it may not be. In the real world It is not, except for a small range of sales.world It is not, except for a small range of sales.

2.2. Cost-price structure of the firm is assumed to Cost-price structure of the firm is assumed to remains constant. It generally does not.remains constant. It generally does not.

3.3. Sales price per unit is assumed to be constant Sales price per unit is assumed to be constant regardless of the output. This is not the case in the regardless of the output. This is not the case in the real world—you have to ? Price if you want to sell real world—you have to ? Price if you want to sell more.more.

46Operating LeverageOperating Leverage

Degree of Operating LeverageDegree of Operating Leverage

• With With FIXEDFIXED operating costs, there will be operating operating costs, there will be operating leverageleverage

• DOL measures the sensitivity of EBIT to changes in sales. DOL of a company is different at different levels of sales.

• High DOL implies that a relatively small change in sales will result in large change in the operating income (EBIT)


Degree of Operating LeverageDegree of Operating LeverageOperating Leverage is responsiveness of a firm’s EBIT

to fluctuations in Sales



to fluctuations in SalesDegree of Operating Leverage (DOL)

Measurement of Operating LeverageFor a unique level of sales, DOL changes as sales

change.



to fluctuations in SalesDegree of Operating Leverage (DOL)

Measurement of Operating LeverageFor a unique level of sales, DOL changes as sales

change.

DOLS = % Change in EBIT % Change in Sales

Unique Level of SalesUnique Level of Sales


Measurement of DOLMeasurement of DOLCalculation using per unit information:

DOLS = Q(P – V)

Q(P – V) – F



DOLS = Q(P – V)

Q(P – V) – F

Q = 3,750 unitsPrice = $800 per unit

Variable costs = $400 per unit Fixed Costs = $1,000,000 per year.

Example:Example:



DOLS = Q(P – V)

Q(P – V) – F



Example:Example:

DOL3,750 units = 3,750(800 – 400) 3,750(800 – 400) – 1,000,000



DOLS = Q(P – V)

Q(P – V) – F



Example:Example:

DOL3,750 units = 3,750(800 – 400) 3,750(800 – 400) – 1,000,000

= 3 times



DOLS = Q(P – V)

Q(P – V) – F



Example:Example:

DOL3,750 units = 3,750(800 – 400) 3,750(800 – 400) – 1,000,000

= 3 times Interpretation: If sales change 1%, then EBIT will change 3% in the same direction.

Interpretation: If sales change 1%, then EBIT will change 3% in the same direction.


Measurement of DOLMeasurement of DOLCalculation using Income Statement Information

DOLS = S – VC

S – VC – F



DOLS = S – VC

S – VC – F



Example:Example:



DOLS = S – VC

S – VC – F



Example:Example: SalesSales$3,000,000

SalesSales$3,000,000x



DOLS = S – VC

S – VC – F



Example:Example:

Variable CostsVariable Costs$1,500,000

Variable CostsVariable Costs$1,500,000x



DOLS = S – VC

S – VC – F



Example:Example:

DOL3,750 units = 3,000,000 – 1,500,00 3,000,000 – 1,500,000 – 1,000,000



DOLS = S – VC

S – VC – F



Example:Example:

DOL3,750 units = 3,000,000 – 1,500,00 3,000,000 – 1,500,000 – 1,000,000

= 3 times



DOLS = S – VC

S – VC – F



Example:Example:

DOL3,750 units = 3,000,000 – 1,500,00 3,000,000 – 1,500,000 – 1,000,000

= 3 times Same Answer as beforeSame Answer as before


Degree of Operating LeverageDegree of Operating LeverageDegree of Operating Leverage is highest when the firm

is closest to break-even point--DOL falls as sales rise

Quantity DOL2,500 (QB) Undefined3,250 4.333,750 35,000 2



is closest to break-even point--DOL falls as sales riseQuantity DOL2,500 (QB) Undefined3,250 4.333,750 35,000 2

The higher the sales level above break-even, the less EBIT (in %) changes as sales change



is closest to break-even point--DOL falls as sales riseQuantity DOL2,500 (QB) Undefined3,250 4.333,750 35,000 2

The higher the sales level above break-even, the less EBIT(in %) changes as sales change

If Fixed Costs = $0, Degree of Operating Leverage = 1

65Financial LeverageFinancial Leverage

Degree of Financial LeverageDegree of Financial LeverageFinance a portion of the firm’s assets with securities

that have fixed financial costsDebtPreferred Stock




Financial Leverage measures changes in earnings per share (NI) as EBIT changes.




Financial Leverage measures changes in earnings per share as EBIT changes.

Degree of Financial Leverage (DFL) at one level of EBIT:

DFLEBIT = % Change in EPS % Change in EBIT

Unique Level of EBITUnique Level of EBIT


DFLEBIT = EBIT EBIT – I

Measurement of DFLMeasurement of DFL




Total Fixed FinancingCosts

Total Fixed FinancingCosts



EBIT = $500,000Interest Charges = $200,000

Example:Example:





Example:Example:

DFLEBIT=500,000 = 500,000 500,000 – 200,000





Example:Example:

DFLEBIT=500,000 = 500,000 500,000 – 200,000

= 1.67 times





Example:Example:

DFLEBIT=500,000 = 500,000 500,000 – 200,000

= 1.67 times


Interpretation: For 1% change in EBIT (from an existing level of $500,000) Earnings Per Share will change 1.67%

Interpretation: For 1% change in EBIT (from an existing level of $500,000) Earnings Per Share will change 1.67%

74DFLDFL

S - VC - FS - VC - FDFL = ---------------------DFL = --------------------- S - VC - F - IS - VC - F - I

75Combined LeverageCombined Leverage

Degree of Combined LeverageDegree of Combined LeverageMeasures changes in Earnings Per Share given

changes in Sales



changes in SalesCombines both Operating and Financial Leverage



changes in SalesCombines both Operating and Financial LeverageComputed for a specific level of sales


DCLS = % Change in EPS % Change in Sales


changes in SalesCombines both Operating and Financial LeverageComputed for a specific level of sales

Unique Level of SalesUnique Level of Sales


DCLS = DOLS x DFLEBIT

Measurement of DCLMeasurement of DCL



DFLEBIT = 1.67 DOLS = 3.0

Example:Example:





Example:Example:


DCL3,750 = 3.0 x 1.67




Example:Example:

= 5.0 times


DCL3,750 = 3.0 x 1.67




Example:Example:

= 5.0 times


Interpretation: When sales change 1%, Earnings Per Share (NI) will change 5.0%

Interpretation: When sales change 1%, Earnings Per Share (NI) will change 5.0%

DCL3,750 = 3.0 x 1.67


DCLS =

Measurement of DCL--Alternative ComputationMeasurement of DCL--Alternative Computation

Q(P – V) Q(P – V) – F – I


DCLS =


Q(P – V) Q(P – V) – F – I


Variable costs = $400 per unit Fixed Costs = $1,000,000 per year

Interest = $200,000 per year

Example:Example:


DCLS =


Q(P – V) Q(P – V) – F – I




Example:Example:

DCLS = 3,750(800 – 400) 3,750(800 – 400) – 1,000,000 – 200,000


DCLS =


Q(P – V) Q(P – V) – F – I




Example:Example:

DCLS = 3,750(800 – 400) 3,750(800 – 400) – 1,000,000 – 200,000

= 5 times


DCLS =


Interpretation: When sales change 1%, Earnings Per Share will change 5.0%

Interpretation: When sales change 1%, Earnings Per Share will change 5.0%

Q(P – V) Q(P – V) – F – I




Example:Example:

DCLS = 3,750(800 – 400) 3,750(800 – 400) – 1,000,000 – 200,000

= 5 times

89

S - VC - FS - VC - FDCLDCLSS = --------------------- = ---------------------

S - VC - F - IS - VC - F - I

Combined Leverage

Measurement of DCL--Alternative Computation-Measurement of DCL--Alternative Computation- Using income statement.Using income statement.

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Analysis and Impact of Leverage