Break Even&LeverageAnalysis
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Transcript of 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