break even&leverageanalysis

8/2/2019 Break Even&LeverageAnalysis

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Break-even & Leverage Analysis

Timothy R. Mayes, Ph.D.

FIN 330: Chapter 12


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Types of Costs

Essentially, there are two types of costs that abusiness faces: Variable costs which vary proportionally with sales

hourly wages

utility costs

raw materials

etc.

Fixed costs which are constant over a relevant range of sales

executive salaries

lease payments

depreciation

etc.


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Types of Costs Grapically

Unit Sales Unit Sales

TotalVariableCost

Unit Sales

FixedCostper

Unit

Unit SalesVariableCostpe

rUnit

Total

Per Unit


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Operating (Accounting) Break-even

The operating break-even point is defined as thatlevel of sales (either units or dollars) at which EBIT isequal to zero:

Sales VC FC 0

Q P v FC 0Or

Where VC is total variable costs, FC is total fixedcosts, Q is the quantity, p is the price per unit, and vis the variable cost per unit


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The Operating Break-even in Units

We can find the operating break-even point in unitsby simply solving for Q:

Q FCp v

FCCM$ unit

*

/

Where CM$/unit is the contribution margin per unitsold (i.e., CM$/unit = p - v)

The contribution margin per unit is the amount thateach unit sold contributes to paying off the fixedcosts


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The Operating Break-even in Dollars

We can calculate the operating break-even point insales dollars by simply multiplying the break-evenpoint in units by the price per unit:

BE Q p$ *

Note that we can substitute the previous definition ofQ* into this equation:

BE FC

p vp FC

p vp

FCCM

$%

Where CM% is the contribution margin as a % of theselling price


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Operating Break-even: an Example

Suppose that a company has fixed costs of $100,000and variable costs of $5 per unit. What is the break-even point if the selling price is $10 per unit?

Q units*,

,

100 000

10 520 000

OrBE$ , $200, 20 000 10 000

Or

BE$

100 000

10 510

000,

$200,


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Targeting EBIT

We can use break-even analysis to find the salesrequired to reach a target level of EBIT

Q FC EBITp v

T et

T et

arg

* arg

Note that the only difference is that we have definedthe break-even point as EBIT being equal to

something other than zero


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Targeting EBIT: an Example

Suppose that we wish to know how many units thecompany (from the previous example) needs to sellsuch that EBIT is equal to $500,000:

Q units*, ,

,

100 000 500 000

10 5120 000

OrBE$ , $1, , 120 000 10 200 000

Or

BE$

, ,$1, ,

100 000 500 000

10 510

200 000


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Cash Break-even Points

Note that if we subtract the depreciation expense (anon-cash expense) from fixed cost, we can calculatethe break-even point on a cash flow basis:

QFC Depreciation

p vT etarg

*


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Leverage Analysis

In physics, leverage refers to a multiplcation of aforce into even larger forces

In finance, it is similar, but we are refering to amultiplication of %changes in sales into even largerchanges in profitability measures

Force InForce Out

Leverage in physics

% Sales% Profits

Leverage in finance


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Types of Risk

There are two main types of risk that a companyfaces: Business risk - the variability in a firms EBIT. This type of

risk is a function of the firms regulatory environment, laborrelations, competitive position, etc. Note that business riskis, to a large degree, outside of the control of managers

Financial risk - the variability of the firms earnings beforetaxes (or earnings per share). This type of risk is a direct

result of management decisions regarding the relativeamounts of debt and equity in the capital structure


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The Degree of Operating Leverage (DOL)

The degree of operating leverage is directlyproportional to a firms level of business risk, andtherefore it serves as a proxy for business risk

Operating leverage refers to a multiplication ofchanges in sales into even larger changes in EBIT

Note that operating leverage results from thepresence of fixed costs in the firms cost structure


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Calculating the DOL

The degree of operating leverage can be calculatedas:

DOL

EBIT

Sales

%

%

This approach is intuitive, but it requires two incomestatements to calculate

We can also calculate DOL with one income

statement:

DOLQ p v

Q p v FC

Sales VC

EBIT


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The Degree of Financial Leverage (DFL)

The degree of financial leverage is a measure of the %changes in EBT that result from changes in EBIT, it iscalculated as:

DFLEBT

EBIT

%

%

This approach is intuitive, but it requires two incomestatements to calculate

We can also calculate DFL with one incomestatement:

DFLEBIT

EBT


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The Degree of Combined Leverage (DCL)

The degree of combined leverage is a measure of thetotal leverage (both operating and financial leverage)that a company is using:

DCLEBT

Sales

EBIT

Sales

EBT

EBITDOL DFL

%

%

%

%

%

%

It is important to note that DCL is the product (not

the sum) of both DOL and DFL


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Calculating Leverage MeasuresBase Case Sales Down 10% Sales up 10%

Sales 1000 900 1100Variable Costs 450 405 495

Fixed Costs 300 300 300

Depreciation 100 100 100

EBIT 150 95 205

Interest Expense 30 30 30

EBT 120 65 175

Percentage Changes Relative to the Base Case

Sales -10.000% 10.000%

EBIT -36.667% 36.667%

EBT -45.833% 45.833%

Leverage Measures

Using a single income statement:

DOL 3.67 5.21 2.95DFL 1.25 1.46 1.17

DCL 4.58 7.62 3.46

Using two income statements:

DOL 3.67

DFL 1.25

DCL 4.58

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