Leverages
The ability to influence a system, or an
environment, in a way that multiplies the
outcome of one's efforts without a corresponding
increase in the consumption of resources. In
other words, leverage is the advantageous
condition of having a relatively small amount of
cost yield a relatively high level of returns.
What is Leverage?
Leverage is the use of fixed costs to
magnify the potential return to a firm.
Types of fixed costs:
 fixed operating costs = rent, amortization of equipment
and other long-lived assets.
 fixed financial costs = interest costs from debt.
What is Leverage?
 3 types of leverage:
-- Operating Leverage = the extent to which capital assets and associated
fixed costs are utilized
-- Financial Leverage = the amount of debt used in the capital structure
(debt/equity mix)
--Composite Leverage = the entire income of the concern.
Balance Sheet___________________
Assets
Liabilities and Equity
Current Assets
Debt (Loans, bonds, leases)
operating
(interest charges) financial
leverage Capital Assets
leverage
(fixed charges)
Equity (Shares)
Operating Leverage
Operating Leverage -- The use of 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
Leverage on Profits
(in thousands)
Sales
Operating Costs
Fixed
Variable
Operating Profit
FC/total costs
FC/sales
Firm F Firm V Firm 2F
10
11
19.5
7
2
2
7
1
2
14
3
2.5
.78
.70
.22
.18
.82
.72
Impact of Operating
Leverage on Profits
 Now, subject each firm to a 50% increase in
sales for next year.
 Which firm do you think will be more
“sensitive” to the change in sales (i.e., show
the largest percentage change in operating
profit, EBIT)?
[ ] Firm F; [ ] Firm V; [ ] Firm 2F.
Impact of Operating
Leverage on Profits
(in thousands)
Firm F Firm V Firm 2F
15
16.5
29.25
Sales
Operating Costs
Fixed
7
Variable
3
Operating Profit
5
Percentage Change 400%
in EBIT*
* (EBITt - EBIT t-1) / EBIT t-1
2
10.5
4
100%
14
4.5
10.75
330%
Impact of Operating
Leverage on Profits



Firm F is the most “sensitive” firm -- for it, a 50%
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 -- A technique for
studying the relationship among fixed costs,
variable costs, sales volume, and profits.
Also called cost/volume/profit (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.
Break-Even Chart
REVENUES AND COSTS
($ thousands)
Total Revenues
Profits
250
Total Costs
175
Fixed Costs
100
Losses
50
0
Variable Costs
1,000 2,000 3,000 4,000 5,000 6,000 7,000
QUANTITY PRODUCED AND SOLD
Break-Even (Quantity)
Point
Break-Even Point -- The sales volume required so
that total revenues and total costs are equal; may be
in units or in sales dollars.
How to find the quantity break-even point:
EBIT = P(Q) - V(Q) - FC
EBIT = Q(P - V) - FC
P = Price per unit
FC = Fixed costs
V = Variable costs per unit
Q = Quantity (units)
produced and sold
Degree of Operating
Leverage (DOL)
Degree of Operating Leverage -- The
percentage change in a firm’s operating profit
(EBIT) resulting from a 1 percent change in
output (sales).
DOL at Q
units of
output
(or sales)
=
Percentage change in
operating profit (EBIT)
Percentage change in
output (or sales)
Computing the DOL
Calculating the DOL for a single product or a
single-product firm.
DOLQ units
=
=
Q (P - V)
Q (P - V) - FC
Q
Q - QBE
Computing the DOL
Calculating the DOL for a
multiproduct firm.
DOLS dollars of sales
=
S - VC
S - VC - FC
=
EBIT + FC
EBIT
Financial Leverage
Financial Leverage -- The use of fixed
financing costs by the firm. The
British expression is gearing.
 Financial leverage is acquired by choice.
 Used as a means of increasing the return
to common shareholders.
EBIT-EPS Break-Even, or
Indifference, Analysis
EBIT-EPS Break-Even Analysis -- Analysis of the
effect of financing alternatives on earnings per
share. The break-even point is the EBIT level
where EPS is the same for two (or more)
alternatives.
Calculate EPS for a given level of EBIT at a given
financing structure.
EPS
=
(EBIT - I) (1 - t) - Pref. Div.
# of Common Shares
Financial Leverage
Financial Leverage -- The use of fixed
financing costs by the firm. The
British expression is gearing.
 Financial leverage is acquired by choice.
 Used as a means of increasing the return
to common shareholders.
Impact of Financial Leverage
 A firm is considering two plans with a view to examining
their impact on earnings per share (EPS) the total funds
required in assets are Rs 5,00,000.
Financial plans
Debt (Interest @ 10% p.a)
4,00,000
1,00,000
Equity Shares(Rs 10 each)
1,oo,ooo
4,00,000
Total Finances required
5,oo,000
5,00,000
No. of equity shares
10,000
40,000
The earnings before interest and tax are assumed as Rs.
50,000 , Rs. 75,000 , Rs. 1,25,000 .
The rate of tax be taken at 50% .
(1) When earnings before interest and
tax (EBIT) are Rs. 50,000
plan (1)
Earnings before interest and
tax (EBIT )
Less : Interest on debt
Earnings before tax (EBT)
Less : Tax @ 50%
Earnings after Interest and tax
No. of equity shares
Earning per share (EPS)
50,000
40,000
10,000
5,000
5,000
10,000
5,000
10,000
=0.50 Paisa
plan (2)
50,000
10,000
40,000
20,000
20,000
40,000
20,000
40,000
=0.50 Paisa
(2) When earnings before interest and
tax (EBIT) are Rs. 75,000
PLAN (1)
Earnings before interest
and tax (EBIT )
Less : Interest on debt
Earnings before tax (EBT)
Less : Tax @ 50%
Earnings after Interest
and tax
No. of equity shares
Earning per share (EPS)
PLAN(2)
75,000
40,000
35,000
17,500
17,500
75,000
10,000
65,000
32,500
32,500
10,000
40,000
=1.75
=0.81
(3) When earnings before interest
and tax (EBIT) are Rs. 1,25,000
PLAN(1)
Earnings before interest and
tax (EBIT )
Less : Interest on debt
Earnings before tax (EBT)
Less : Tax @ 50%
Earnings after Interest and
tax
No. of equity shares
Earning per share (EPS)
PLAN(2)
1,25,000
(40,000)
85,000
(42,500)
1,25,000
(10,000)
1,15,000
(57,500)
42,500
10,000
57,500
40,000
=4.25
=1.438
Impact of Financial Leverage
 The financial leverage is used to magnify the shareholders




earnings. It us based on the assumption that the fixed charges or
cost funds can be obtained at a cost lower than the firm’s rate of
return on its assets .
When the difference between the assets financed by fixed cost funds
and the cost of these funds are distributed to the equity stockholders
, they will get additional earnings without increasing their own
investment .
Consequently , the Earning per share (EPS) and the rate of return on
equity share capital will go up .
The situation in which Earning per share (EPS) and the rate of return
on equity share capital will go up , may also be reverse sometimes.
if the firm acquires fixed cost funds at a higher cost than the
Earnings from those assets .
Degree of Financial
Leverage (DFL)
Degree of Financial Leverage -- The
percentage change in a firm’s earnings per
share (EPS) resulting from a 1 percent change
in operating profit.
Percentage change in
DFL at
earnings per share (EPS)
EBIT of X
=
dollars
Percentage change in
operating profit (EBIT)
Computing the DFL
Calculating the DFL
DFL EBIT of $X
EBIT
I
PD
t
=
EBIT
EBIT - I - [ PD / (1 - t) ]
= Earnings before interest and taxes
= Interest
= Preferred dividends
= Corporate tax rate
Variability of EPS
DFLEquity
= 1.00
Which financing
method
will
have
the
DFLDebt
= 1.25
greatest relative
DFLPreferred = 1.35
variability in EPS?
 Preferred stock financing will lead to the
greatest variability in earnings per share
based on the DFL.
 This is due to the tax deductibility of
interest on debt financing.
Importance of financial leverage
 PLANNING OF CAPITAL STRUCTURE :
A financial manager has to decide about the ratio
between fixed costs funds and equity share capital.
 PROFIT PLANNING:
EPS is effected by degree of financial leverage . If the
profitability of the concern is increasing than fixed costs
funds will help in increasing the availability of profits for
the equity stockholders . Therefore , financial leverage
is important for profit planning .
Limitations of financial leverage
 DOUBLE- EDGED WEAPON .
 BENEICIAL ONLY TO COMPANIES HAVING
STABILITY OF EARNINGS .
 INCREASES RISK AND RATE OF RETURN .
 RESTRICTIONS FROM FINANCIAL INSTITUIONS .
Both financial and operating leverage magnify the revenue of
the firm. Operating leverage affects the income which is result
of production. On the other hand, the financial leverage is the
result of financial decisions. The composite leverage focuses
attention on the entire income of the concern. The risk factor
should be properly assessed by the management before using
the composite leverage. The high financial leverage may be
offset against low operating leverage or vice-versa.
The degree of composite leverage can be calculated as follows:
Degree of composite leverage (DCL) = Percentage change in EPS
Percentage Change in Sales
Or,
Composite leverage = Operating leverage * Financial leverage
Financial Risk
Financial Risk -- The added variability in earnings
per share (EPS) -- plus the risk of possible insolvency
-- that is induced by the use of financial leverage.
 Debt increases the probability of cash insolvency
over an all-equity-financed firm. For example, our
example firm must have EBIT of at least $100,000 to
cover the interest payment.
 Debt also increased the variability in EPS as the DFL
increased from 1.00 to 1.25.
Total Firm Risk
Total Firm Risk -- The variability in earnings per
share (EPS). It is the sum of business plus financial
risk.
Total firm risk = business risk + financial risk
 CVEPS is a measure of relative total firm risk
 CVEBIT is a measure of relative business risk
 The difference, CVEPS - CVEBIT, is a measure of
relative financial risk
Degree of Total Leverage
(DTL)
Degree of Total Leverage -- The percentage
change in a firm’s earnings per share (EPS)
resulting from a 1 percent change in output
(sales).
DTL at Q units Percentage change in
(or S dollars) of earnings per share (EPS)
=
output (or sales)
Percentage change in
output (or sales)
Computing the DTL
DTL Q units (or S dollars) = ( DOL Q units (or S dollars) )
x ( DFL EBIT of X dollars )
DTL S dollars =
of sales
DTL Q units
EBIT + FC
EBIT - I - [ PD / (1 - t) ]
Q (P - V)
=
Q (P - V) - FC - I - [ PD / (1 - t) ]
Summary and Conclusions
 Leverage refers to the use of fixed costs to magnify the
profits (or losses) of a firm.
 Management must be aware of the level of risk assumed.
 Operating leverage refers to using fixed operating
costs, such as lease or amortization expense. Asset
side related.
 Financial leverage refers to the fixed financing charge
such as interest cost on debt. Liability side related.
 Composite leverage refers to the combination of both
financial and operating leverage.