Impact and Analysis of Leverage
Impact and Analysis
Impact and Analysis
of Leverage of Leverage
Impact and Analysis
Impact and Analysis
of Leverage
of Leverage
What is What is
Leverage?
Leverage?
What is What is
Leverage?
Leverage?
Two concepts that Two concepts that enhance our enhance our understanding of risk... understanding of risk...
1) Operating Leverage - affects
a firm’s business risk .2) Financial Leverage - affects a firm’s financial risk .
Business Risk Business Risk
The variability or uncertainty of a firm’s operating income (EBIT).
Analytical Income Statement
Analytical Income Statement
sales - variable costs - fixed costs operating income (EBIT) - interest EBT - taxes net incomeBusiness Risk Business Risk
Affected by:
Sales volume variability
Competition
Product diversification
Operating leverage
Growth prospects
Size
Operating Leverage Operating Leverage
The use of fixed operating costs as opposed to variable operating costs
A firm with relatively high fixed operating costs will experience
more variable operating income if
sales change.
EBIT
EBIT Operating Leverage
Operating Leverage Operating Leverage
Operating Leverage -- The use of
- -- Operating Leverage The use of fixed operating costs by the firm .
fixed operating costs by the firm .
One potential “effect” caused by the presence of operating leverage is that a change in the volume of sales results in a “more than proportional” change in operating profit (or loss).
Impact of Operating
Impact of OperatingLeverage on Profits Leverage on Profits
Firm F Firm V Firm 2F Sales $10 $11 $19.5 Operating Costs
(in thousands) (in thousands)
Firm F Firm V Firm 2F
7
3 Operating Profit $
$
2
1
$ 2
$ 2
$ 2.5
$ 2.5
FC/total costs .78 .22 .82 FC/sales .70 .18 .72
Fixed 7 2 14 Variable
1
Impact of Operating Impact of Operating
Leverage on Profits Leverage on Profits
50%
Now, subject each firm to a 50% increase in sales for next year. increase in sales
Which firm do you think will be more
“sensitive” to the change in sales (i.e.,
“sensitive” show the largest percentage change in operating profit, EBIT)? Firm F Firm V Firm 2F . [ ] Firm F ; [ ] Firm V ; [ ] Firm 2F
Firm F Firm V Firm 2F
5
400% 100% 330% (in thousands) (in thousands)
Change in EBIT
Change in EBIT
Percentage
Percentage
$10.75
$10.75
$ 4
$ 4
5
Impact of Operating Impact of Operating
$
4.5 Operating Profit $
10.5
3
14 Variable
2
7
Fixed
Firm F Firm V Firm 2F
Sales $15 $16.5 $29.25
Operating CostsLeverage on Profits Leverage on Profits
- * 400% 100% 330%
- * (EBIT t - EBIT t-1 ) / EBIT t-1
Impact of Operating
Impact of Operating
Leverage on Profits Leverage on Profits
Firm F is the most “sensitive” firm -- for it, a 50%
Firm F is the most “sensitive” firm 400% increase in EBIT . increase in sales leads to a 400% increase in EBIT Our example reveals that it is a mistake to assume
that the firm with the largest absolute or relative
amount of fixed costs automatically shows the most dramatic effects of operating leverage.Later, we will come up with an easy way to spot the firm that is most sensitive to the presence of operating leverage.
Break-Even Analysis Break-Even Analysis
Break-Even Analysis -- A technique for
Break-Even Analysis studying the relationship among fixed costs, variable costs, sales volume, and
profits . Also called cost/volume/profit
profits (C/V/P) analysis.
When studying operating leverage, “profits” refers to operating profits before taxes (i.e., EBIT) and excludes debt interest and dividend payments.
Total Revenue TOTAL REVENUE
Quantity $
Total Revenue Total Cost FC
TOTAL REVENUE VC TC
Quantity { $
Total Revenue Total Cost FC
Quantity { $
1 + - } EBIT TOTAL REVENUE
Quantity { $
1 + - } EBIT TOTAL REVENUE
Operating Leverage
Operating Leverage
What happens if the firm
increases its fixed operating
costs and reduces (or eliminates) its variable costs?Total Revenue
Total Cost FC Break- even point Q
Quantity { $
1 + - } EBIT
Total Revenue
Total Cost = Fixed FC Break-even point } Q
1 + - EBIT
Quantity { $
Total Revenue
Trade-off: Trade-off: the firm has the firm has a higher breakeven a higher breakeven $
point. If sales are not EBIT point. If sales are not high enough, the firm } + high enough, the firm will not meet its fixed will not meet its fixed Total Cost - expenses! expenses! FC
= Fixed { Quantity
1 Break- Q even point
Break-Even Chart
Break-Even Chart
QUANTITY PRODUCED AND SOLD 0 1,000 2,000 3,000 4,000 4,000 5,000 6,000 7,000 Total Revenues Total Revenues Profits Profits Fixed Costs Fixed Costs Variable Costs Variable Costs Losses Losses R E V E N U E S A N D C O S T S R E V E N U E S A N D C O S T S ($ t h o u sa n d s) ($ t h o u sa n d s) 175 175 250 100 50 Total Costs Total Costs
Break-Even Break-Even
(Quantity) Point (Quantity) Point
Break-Even Point -- The sales volume required Break-Even Point -- The sales volume required so that total revenues and total costs are so that total revenues and total costs are equal; may be in units or in sales dollars. equal; may be in units or in sales dollars.
How to find the quantity break-even point:
P Q
V Q FC
EBIT = P (Q ) - V (Q ) - FC
Q P
V FC
EBIT = Q (P - V ) - FC
P = Price per unit V = Variable costs per unit P = Price per unit V = Variable costs per unit FC = Fixed costs Q = Quantity (units) FC = Fixed costs Q = Quantity (units) produced and sold produced and sold
Break-Even Break-Even
(Quantity) Point (Quantity) Point
Breakeven occurs when EBIT = 0
QQ (P P - V
V ) - FC FC = EBIT Q Q BE BE (P P - V
V ) - FC FC = 0 Q Q BE BE (P P - V V ) = FC FC Q Q BE BE = FC FC / (P P - V V ) a.k.a. Unit Contribution Margin
Break-Even (Sales) Point Break-Even (Sales) Point
How to find the sales break-even point:
S S BE BE = FC FC + (VC
BE
BE
) S S BE BE = FC FC + (Q Q BE BE )(V V )or
S S BE BE * * = FC FC / [1 - (VC
VC / S) ]
Break-Even Break-Even
Point Example Point Example
Basket Wonders (BW) wants to determine both the quantity and sales
quantity and sales
break-even points
break-even points when: Fixed costs Fixed costs are $100,000 $100,000
Baskets are sold for $43.75 $43.75 each each Variable costs are $18.75 per basket $18.75 per basket
- - V
- - $18.75
= (4,000
Q BE BE
)(V
V
) + FC
FC
S
S BE BE
4,000
S BE BE
)($18.75
$18.75
) + $100,000
$100,000
S
S BE BE
= $175,000
= (Q
S
Break-Even Point (s)
Break-Even Point (s)
Q
Breakeven occurs when: Q
Q BE BE
= FC
FC
/ (P
P
V )
Q BE BE
4,000 Units
= $100,000
$100,000
/ ($43.75
$43.75
$18.75 )
Q
Q BE BE
= 4,000 Units
$175,000
Break-Even Chart
Break-Even Chart
QUANTITY PRODUCED AND SOLD 0 1,000 2,000 3,000 4,000 4,000 5,000 6,000 7,000 Total Revenues Total Revenues Profits Profits Fixed Costs Fixed Costs Variable Costs Variable Costs Losses Losses R E V E N U E S A N D C O S T S R E V E N U E S A N D C O S T S ($ t h o u sa n d s) ($ t h o u sa n d s) 175 175 250 100 50 Total Costs Total Costs
Degree of Operating Degree of Operating
Leverage (DOL) Leverage (DOL)
DOL
DOL at Q
units of output (or sales) Degree of Operating Leverage
Degree of Operating Leverage -- The
percentage change in a firm’s operating profit (EBIT) resulting from a 1 percent change in output (sales). = Percentage change in operating profit (EBIT) Percentage change in output (or sales)
- - V
- - V
- - Q
Q
Q
Q
Q
= Q
FC
) - FC
V
P
(P
Q
Computing the DOL Computing the DOL
V )
P
(P
Q
= Q
Calculating the DOL for a single product
or a single-product firm. or a single-product firm.Calculating the DOL for a single product
DOL Q units Q units
DOL
Q BE BE
Computing the DOL Computing the DOL
- - VC
- - VC
- - FC
DOL
DOL S dollars of sales S dollars of sales
Calculating the DOL for a
Calculating the DOL for a multiproduct firm. multiproduct firm.
= S
S
VC
S
S
VC
FC
= EBIT + FC
FC
EBIT
Break-Even Break-Even
Point Example Point Example
degree
Lisa Miller wants to determine the degree
of operating leverage
of operating leverage
at sales levels of
sales levels of
6,000 and 8,000 units
6,000 and 8,000 units . As we did earlier,
we will assume that:
Fixed costs Fixed costs are $100,000 $100,000 Baskets are sold for $43.75 $43.75 each each
Variable costs are $18.75 per basket $18.75 per basket
Computing BW’s DOL
Computing BW’s DOL
Computation based on the previously
Computation based on the previously
calculated break-even point of 4,000 units
calculated break-even point of 4,000 units
6,0006,000
3
3 DOL DOL 6,000 units 6,000 units =
=
6,000 4,000
- - 4,000 6,000
8,000
8,000
2
2 =
DOL
DOL 8,000 units 8,000 units =
8,000 4,000
- - 4,000 8,000
Interpretation of the DOL Interpretation of the DOL
A 1% increase in sales above the 8,000
A 1% increase in sales above the 8,000
unit level increases EBIT by 2%
unit level increases EBIT by 2%
because of the existing operating
because of the existing operating
leverage of the firm.leverage of the firm.
8,000
8,000
2
2 =
DOL
DOL 8,000 units 8,000 units =
8,000 4,000
- - 4,000 8,000
Interpretation of the DOL
Interpretation of the DOL G
IN T IN T G ) ) 4
5 3 3 4 5 R A E P A R P E O E O L ( ( L D D 2 1 1 2 O F O -1 F O O G A A E R R G -1 2,000 4,000 6,000 8,000 2,000 4,000 6,000 8,000 E -2 E G R E G R E E L E V V L E E -2 -3 -3 Q D E D -4 E -5 -5 -4
Q BE BE QUANTITY PRODUCED AND SOLD QUANTITY PRODUCED AND SOLD
Interpretation of the DOL Interpretation of the DOL
Key Conclusions to be Drawn from the
Key Conclusions to be Drawn from the
previous slide and our Discussion of DOL
previous slide and our Discussion of DOL
DOL is a quantitative measure of the “sensitivity” of a firm’s operating profit to a change in the firm’s sales.
The closer that a firm operates to its break-even point, the higher is the absolute value of its DOL.
When comparing firms, the firm with the highest DOL is the firm that will be most “sensitive” to a change in sales.
DOL and Business Risk DOL and Business Risk
Business Risk -- The inherent uncertainty
Business Risk -- The inherent uncertainty in the physical operations of the firm. Its
in the physical operations of the firm. Its
impact is shown in the variability of the
impact is shown in the variability of the
firm’s operating income (EBIT). firm’s operating income (EBIT).
one component of business risk DOL is only one component only in the presenceand becomes “active” only in the presence
of sales and production cost variability . of sales and production cost variability magnifies the variability of operating DOL magnifies profits and, hence, business risk.- + 7,000
1,000
8.0
=
1,000
1,000
7,000
1,000 +
DOL $10,000 sales $10,000 sales
Application of DOL for Application of DOL for
] = DOL
DOL = [( = [(EBIT EBIT + + FC FC )/ )/EBIT EBIT ]
: DOL
following formula for following formula for Firm F
Firm F :Use the data in Slide 16-12 and the
Use the data in Slide 16-12 and the
Our Three Firm Example Our Three Firm Example
8.0
- + 2,000
2,000
2.0
=
2,000
2,000
2,000
2,000 +
DOL $11,000 sales $11,000 sales
Application of DOL for Application of DOL for
] = DOL
DOL = [( = [(EBIT EBIT + + FC FC )/ )/EBIT EBIT ]
: DOL
following formula for following formula for Firm V
Firm V :Use the data in Slide 16-12 and the
Use the data in Slide 16-12 and the
Our Three Firm Example Our Three Firm Example
2.0
- + 14,000
2,500
6.6
=
2,500
2,500
14,000
2,500 +
DOL $19,500 sales $19,500 sales
Application of DOL for Application of DOL for
] = DOL
DOL = [( = [(EBIT EBIT + + FC FC )/ )/EBIT EBIT ]
: DOL
following formula for following formula for Firm 2F
Firm 2F :Use the data in Slide 16-12 and the
Use the data in Slide 16-12 and the
Our Three-Firm Example Our Three-Firm Example
6.6
Application of DOL for Application of DOL for
Our Three-Firm Example Our Three-Firm Example
The ranked results indicate that the firm most
The ranked results indicate that the firm most
sensitive to the presence of operating leverage
sensitive to the presence of operating leverage
is is Firm F Firm F . Firm F Firm F DOL DOL = = 8.08.0 Firm V Firm V DOL DOL = = 6.6
6.6 Firm 2F Firm 2F DOL DOL = = 2.0
2.0 Firm F Firm F will expect a will expect a 400% increase in profit 400% increase in profit from a from a 50% 50% increase in sales increase in sales (see Slide 16-14 results). (see Slide 16-14 results).
What does this tell us? What does this tell us?
If DOL = 8, then a 1% increase in
sales will result in a 8% increase in operating income (EBIT). Stock- EPS Sales EBIT holdersWhat does this tell us? What does this tell us?
If DOL = 8, then a 1% increase in
sales will result in a 8% increase in operating income (EBIT). Stock- EPS Sales EBIT holders