1. Breakeven and Leverage
Byers

2. Risk Two types of Risk: Business Risk & Financial Risk Business Risk
Risk Due to Operations
Measured by variability of EBIT (earnings before interest and taxes)

3. Risk Two types of Risk: Business Risk & Financial Risk Financial Risk
Risk due to raising money with fixed income securities
Financial risk is high with high levels of debt financing
Financial leverage - the use of fixed income securities to finance a portion of assets

4. EBIT = Sales – Variable Costs - Fixed Costs
Break-even Analysis
Calculation of Break-even Quantity
EBIT = Sales – Variable Costs - Fixed Costs
Find Quantity which results in EBIT = $0

5. Break-even Analysis Calculation of Break-even Quantity F QB = P – V
Where:
QB = Break-even Quantity
P = Price per Unit
F = Total Fixed Costs
V = Variable Costs per Unit

6. Break-even Analysis Calculation of Break-even Quantity F QB = P – V
Example:
Calculation of Break-even Quantity F
P – V
QB =
Fixed Costs = $1,000,000 per year
Price = $800/unit
Variable Costs = $400/unit

7. Break-even Analysis Calculation of Break-even Quantity F QB = P – V
Example:
Calculation of Break-even Quantity F
P – V
QB =
Fixed Costs = $1,000,000 per year
Price = $800/unit
Variable Costs = $400/unit
$1,000,000
$800 – $400
QB =
= 2,500 Units

8. Break-even Analysis Calculation of Break-even Sales Level (S*)
To Find S* for a single product use Break-even Quantity (QB):
Calculation of Break-even Sales Level (S*)
S* = QB x P
S* = 2,500 units x $800
= $2,000,000

9. Break-even Analysis Calculation of Break-even Sales Level (S*)
May want to Calculate the Break-even Sales Level (S*) for the entire firm with many products
Calculate for Income Statement at one Sales Level

10. Break-even Analysis F S* = 1 - VC S
Calculation of Break-even Sales Level (S*) F
1 - VC
S* = S
S = Dollar Level of Sales
VC = Total Dollar Variable Costs

11. Break-even Analysis F S* = 1 - VC S
Calculation of Break-even Sales Level (S*) F
1 - VC
S* = S
Example:
S = Dollar Level of Sales = $3,000,000
VC = Total Dollar Variable Costs = $1,500,000

12. Break-even Analysis F S* = 1 - VC S
Calculation of Break-even Sales Level (S*) F
1 - VC
S* = S
Example:
S = Dollar Level of Sales = $3,000,000
VC = Total Dollar Variable Costs = $1,500,000
$1,000,000
1 – $1,500,000
S* =
= $2,000,000
$3,000,000

13. Break-even Analysis Graphical Analysis of Break-even Point Sales &
Costs $
Fixed Costs
$1,000,000
Quantity of Units

14. Break-even Analysis Graphical Analysis of Break-even Point Sales &
Costs $
Variable Costs
Fixed Costs
$1,000,000
Quantity of Units

15. Break-even Analysis Graphical Analysis of Break-even Point Sales &
Costs $
Total Costs
Variable Costs
Fixed Costs
$1,000,000
Quantity of Units

16. Break-even Analysis Graphical Analysis of Break-even Point Sales &
Costs $
Sales
Total Costs
Variable Costs
Fixed Costs
$1,000,000
Quantity of Units

17. Break-even Analysis Graphical Analysis of Break-even Point Sales &
Costs $
Sales
Total Costs
Variable Costs
$2,000,000
Fixed Costs
$1,000,000
QB = 2,500
Quantity of Units

18. Operating Leverage
With FIXED operating costs, there will be operating leverage
Operating Leverage is responsiveness of a firm’s EBIT to fluctuations in Sales
Degree of Operating Leverage (DOL)
Measurement of Operating Leverage
For a unique level of sales, DOL changes as sales change.
% Change in EBIT
% Change in Sales
DOLS =
Unique Level of Sales

19. Operating Leverage Measurement of DOL
Calculation using per unit information:
Q(P – V)
Q(P – V) – F
DOLS =
Example:
Q = 3,750 units
Price = $800 per unit
Variable costs = $400 per unit
Fixed Costs = $1,000,000 per year.

20. Operating Leverage Measurement of DOL
Calculation using per unit information:
Q(P – V)
Q(P – V) – F
DOLS =
Example:
Q = 3,750 units
Price = $800 per unit
Variable costs = $400 per unit
Fixed Costs = $1,000,000 per year.
3,750(800 – 400)
3,750(800 – 400) – 1,000,000
DOL3,750 units =
= 3 times

21. Operating Leverage Measurement of DOL
Calculation using per unit information:
Q(P – V)
Q(P – V) – F
DOLS =
Example:
Q = 3,750 units
Price = $800 per unit
Variable costs = $400 per unit
Fixed Costs = $1,000,000 per year.
3,750(800 – 400)
3,750(800 – 400) – 1,000,000
DOL3,750 units =
Interpretation: If sales change 1%, then EBIT will change 3% in the same direction.
= 3 times

22. Operating Leverage Measurement of DOL
Calculation using Income Statement Information
S – VC
S – VC – F
DOLS =
Example:
Q = 3,750 units
Price = $800 per unit
Variable costs = $400 per unit
Fixed Costs = $1,000,000 per year.

23. Operating Leverage Measurement of DOL
Calculation using Income Statement Information
S – VC
S – VC – F
DOLS =
Example:
Q = 3,750 units
Price = $800 per unit
Variable costs = $400 per unit
Fixed Costs = $1,000,000 per year.
Sales
$3,000,000 x

24. Operating Leverage Measurement of DOL
Calculation using Income Statement Information
S – VC
S – VC – F
DOLS =
Example:
Q = 3,750 units
Price = $800 per unit
Variable costs = $400 per unit
Fixed Costs = $1,000,000 per year.
Variable Costs
$1,500,000 x

25. Operating Leverage Measurement of DOL
Calculation using Income Statement Information
S – VC
S – VC – F
DOLS =
Example:
Q = 3,750 units
Price = $800 per unit
Variable costs = $400 per unit
Fixed Costs = $1,000,000 per year.
3,000,000 – 1,500,00
3,000,000 – 1,500,000 – 1,000,000
DOL3,750 units =
= 3 times

26. Operating Leverage Measurement of DOL
Calculation using Income Statement Information
S – VC
S – VC – F
DOLS =
Example:
Q = 3,750 units
Price = $800 per unit
Variable costs = $400 per unit
Fixed Costs = $1,000,000 per year.
3,000,000 – 1,500,00
3,000,000 – 1,500,000 – 1,000,000
DOL3,750 units =
= 3 times
Same Answer as before

27. Operating Leverage Degree of Operating Leverage
Degree of Operating Leverage falls as sales rise
Quantity DOL
2,500 (QB) Undefined 3,
3,750 3
5,000 2
The higher the sales level above break-even, the less EBIT changes as sales change
If Fixed Costs = $0, Degree of Operating Leverage = 1

28. Financial Leverage Degree of Financial Leverage
Finance a portion of the firm’s assets with securities that have fixed financial costs
Debt
Preferred Stock
Financial Leverage measures changes in earnings per share as EBIT changes.
Degree of Financial Leverage (DFL) at one level of EBIT:
% Change in EPS
% Change in EBIT
DFLEBIT =
Unique Level of EBIT

29. Financial Leverage Measurement of DFL EBIT DFLEBIT = EBIT – I Example:
Total Fixed Financing
Costs
Example:
EBIT = $500,000
Interest Charges = $200,000

30. Financial Leverage Measurement of DFL EBIT DFLEBIT = EBIT – I Example:
Interest Charges = $200,000
500,000
500,000 – 200,000
DFLEBIT=500,000 =
= 1.67 times
Interpretation: When EBIT changes 1% (from an existing level of $500,000) Earnings Per Share will change 1.67%

31. Combined Leverage % Change in EPS DCLS = % Change in Sales
Degree of Combined Leverage
Measures changes in Earnings Per Share given changes in Sales
Combines both Operating and Financial Leverage
Computed for a specific level of sales
% Change in EPS
% Change in Sales
DCLS =
Unique Level of Sales

32. Combined Leverage
Measurement of DCL
DCLS = DOLS x DFLEBIT

33. Combined Leverage Measurement of DCL DCLS = DOLS x DFLEBIT Example:

34. Combined Leverage Measurement of DCL DCLS = DOLS x DFLEBIT Example:
DCL3,750 = 3.0 x 1.67
= 5.0 times
Interpretation: When sales change 1%, Earnings Per Share will change 5.0%

35. Combined Leverage Measurement of DCL--Alternative Computation Q(P – V)
Q(P – V) – F – I
DCLS =

36. Combined Leverage Measurement of DCL--Alternative Computation Q(P – V)
Q(P – V) – F – I
DCLS =
Example:
Q = 3,750 units
Price = $800 per unit
Variable costs = $400 per unit
Fixed Costs = $1,000,000 per year
Interest = $200,000 per year

37. Combined Leverage Measurement of DCL--Alternative Computation Q(P – V)
Q(P – V) – F – I
DCLS =
Example:
Q = 3,750 units
Price = $800 per unit
Variable costs = $400 per unit
Fixed Costs = $1,000,000 per year
Interest = $200,000 per year
3,750(800 – 400)
3,750(800 – 400) – 1,000,000 – 200,000
DCLS =
= 5 times
Interpretation: When sales change 1%, Earnings Per Share will change 5.0%