This document summarizes a lecture on leverage given by Dr. Mahmoud Otaify. It defines leverage and differentiates between operating and financial leverage. It provides examples to calculate the degree of operating leverage and degree of financial leverage. The document discusses how leverage increases both business risk and financial risk for a company. It also examines how leverage impacts earnings per share and the relationship between earnings before interest and taxes and earnings per share under different capital structures.

1. 10/20/2022
Leverage
Financial management and control systems (Lecture 2)
Dr. Mahmoud Otaify
Assistant Professor of Finance
Define
leverage
1
Differentiate
between
operating and
financial
leverage
2
Calculate
degree of
operating
leverage
3
Calculate
degree of
financial
leverage
4
Measure
Impact of
Financial
leverage
5
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What is Leverage?
Operating
Leverage
Sales Revenues
Less: Cost of Goods Sold (COGS)
Gross Profit
Less: Operating Exp.
Earnings Before Interest & Taxes (EBIT)
Financial
Leverage
EBIT
Less: interest
EBT
Less: taxes
Net income after tax
Less: Preferred Stock Dividends
Earnings Available for Common stocks (EACS)
Divide: Number of Shares
Earnings Per shares
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Total
Leverage
What is Leverage?
Leverage
Depreciation, rents,
wages for salaried
employees
Operating Leverage
Interest on bank
loans/bonds, preferred
stock dividends
Financial Leverage
the use of fixed
costs in a
company’s cost
structure.
Regardless sales
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𝐷𝑂𝐿
=
%∆ in EBIT
% ∆ 𝑖𝑛 𝑆𝑎𝑙𝑒𝑠
Sales Revenues
Less: Cost of Goods Sold (COGS)
Gross Profit
Less: Operating Exp.
Earnings Before Interest & Taxes (EBIT)
𝐷𝑭𝐿
=
%∆ in 𝐄𝐏𝐒
% ∆ 𝑖𝑛 𝑬𝑩𝑰𝑻
EBIT
Less: interest
EBT
Less: taxes
Net income after tax
Less: Preferred Stock Dividends
Earnings Available for Common stocks (EACS)
Divide: Number of Shares
Earnings Per shares
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𝐷𝑻𝐿
=
%∆ in 𝐄𝐏𝐒
% ∆ 𝑖𝑛 𝑺𝒂𝒍𝒆𝒔
How to Calculate Degree of Leverage?
Example on Operating Leverage
Using the data for ALEX (sales, 1000 units, sale price, P
= $10 per unit; variable operating cost, VC = $5 per
unit; fixed operating cost, FC = $2,500).
Calculate the degree of operating leverage under the
following cases:
Case 1: an increase in the firm’s sales increase from
1,000 to 1,500 units
Case 2: a decrease in the firm's sales from 1,000 to 500
units
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Base Case Case 1 Case 2
Sales (in units) 1000 1,500 500
Sales revenue 1000*10=10,000 1,500*10=15000 500*10=5000
Less: Variable
operating costs
1000*5=5000 1500*5=7,500 500*5=2,500
Less: Fixed
operating costs
2,500 2,500 2,500
Earnings before
interest and
taxes (EBIT)
2,500 5,000 $0
% ∆ 𝒊𝒏 𝑺𝒂𝒍𝒆𝒔 1500-1000/1000 = 0.5 = 50% 500-1000/1000 = -0.5
=-50%
%∆ 𝐢𝐧 𝐄𝐁𝐈𝐓 5000-2,500/2,500 = 1 =100% 0 – 2,500/2500 = -1
= -100%
𝑫𝑶𝑳 =
%∆ 𝐢𝐧 𝐄𝐁𝐈𝐓
% ∆ 𝒊𝒏 𝑺𝒂𝒍𝒆𝒔
𝐷𝑂𝐿 =
100
50
= 2 𝐷𝑂𝐿 =
−100
−50
= 2
comment A 50% increase in sales (from
1,000 to 1,500 units) results in a
100% increase in earnings before
interest and taxes (from $2,500
to $5,000).
A 50% decrease in sales (from 1,000 to
500 units) results in a 100% decrease
in earnings before interest and taxes
(from $2,500 to $0).
Example on Financial Leverage
Borg Foods, a small food company, expects EBIT of
$10,000 in the current year. It has a $20,000 bond with
a 10% (annual) coupon rate of interest and an issue of
600 shares of $4 (annual dividend per share) preferred
stock outstanding. It also has 1,000 shares of common
stock outstanding. Assume that the firm is in the 40%
tax bracket. Calculate the degree of financial leverage
under the following cases:
Case 1 An increase in EBIT to 14,000
Case 2 A decrease in EBIT to 6,000
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Base Case Case 1 Case 2
EBIT 10,000 14,000 6,000
Less Interest 0.1*20,000 =2000 2000 2000
EBT 8,000 12,000 4,000
Taxes (40%) 8000*0.4
=3,200
12,000*0.4 = 4,800 4000*0.4 = 1600
Net profit after taxes 4,800 7,200 2,400
Less preferred stock
dividends
4*600
=2,400
2,400 2,400
Earnings available for
common (EAC)
2,400 4,800 0
Earnings per share
(EPS)
2,400/1000
=2.4
4,800/1000 = 4.8 0/1000 = $0
% ∆ 𝒊𝒏 𝑬𝑩𝑰𝑻 14,000-10,000/10,000 = 40% 6000-10,000/10000 = -40%
%∆ 𝒊𝒏 𝑬𝑷𝑺 4.8-2.4/2.4 = 1 = 100% 0-2.4/2.4 = -1 = -100%
Comment A 40% increase in EBIT (from
$10,000 to $14,000) results in
a 100% increase in earnings
per share (from $2.40 to
$4.80).
A 40% decrease in EBIT (from $10,000 to
$6,000) results in a 100% decrease in
earnings per share (from $2.40 to $0).
𝑫𝑭𝑳 =
%∆ 𝒊𝒏 𝑬𝑷𝑺
% ∆ 𝒊𝒏 𝑬𝑩𝑰𝑻
𝑫𝑭𝑳 =
𝟏𝟎𝟎
𝟒𝟎
= 𝟐. 𝟓 𝑫𝑭𝑳 =
−𝟏𝟎𝟎
−𝟒𝟎
= 𝟐.𝟓
What is risk of
Leverage?
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The greater the firm’s fixed
operating costs (operating
leverage)
The higher its business risk
The risk to the firm of being
unable to cover its operating
costs
The more fixed financing—debt
(including financial leases) and
preferred stock—a firm has in its
capital structure
the greater its financial risk
The risk to the firm of being
unable to cover its financing
costs
Greater probability of bankruptcy
Breakeven Point
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Operating Breakeven Point Breakeven Point
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Q
Item Value
Fc 2500
Price 10
Vc 5
Q= = = 500
Item Value
Interest 2000
Q
Q= = = 900
How many units to achieve profits
and pay preferred dividends
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Q
𝟏
𝟏 𝑻𝑪
Q = 1700
Item Value
Fc 2500
Price 10
Vc 5
Interest 2000
Preferred Dividends (PD) 2,400
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Equity
capital
Percentage of
equity used to
fund the firm’s
assets
E/V
Debt
capital
Percentage of
debt used to
fund the firm’s
assets
D/V
Capital
Structure
Percentage of
debt and equity
used to fund the
firm’s assets
D/E
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Financial Leverage
Capital Structure Decision
D/E
Financial Leverage
RD RE WACC
EPS P0 V0
Capital Structure Decision
(Debt/Equity Ratio)
Increase Debt
To purchase Assets
D increase and E is
constant, D/E increase
Capital Raising Decision
Increase Debt
To buyback portion of
common shares outstanding
D increase and E decrease,
D/E increase
Capital Restructuring
Decision
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The Impact of Financial Leverage
financial leverage can dramatically alter the payoffs to shareholders in the firm
When we increase the amount of debt financing, we
increase the fixed interest expense
If we have a really good year, we pay our fixed costs and
we have more left over for our shareholders
If we have a really bad year, we still have to pay our fixed
costs and we have less left over for our shareholders.
we describe the impact of leverage in terms of its effects
on earnings per share, EPS, and return on equity, ROE.
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EBIT–EPS approach to Capital
Structure
The EBIT–EPS approach to capital structure involves
selecting the capital structure that maximizes EPS over the
expected range of earnings before interest and taxes (EBIT).
To analyze the effects of a firm’s capital structure on the
owners’ returns, we consider the relationship between
earnings before interest and taxes (EBIT) and earnings per
share (EPS).
In other words, we want to see how changes in EBIT lead to
changes in EPS under different capital structures.
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 The Trans Corporation currently has
no debt in its capital structure. The
CFO, Ms. Morris, is considering a
restructuring that would involve
issuing debt and using the proceeds
to buy back some of the outstanding
equity. Table presents both the
current and proposed capital
structures.
 As shown, the firm’s assets have a
market value of $8 million. Because
Trans is an all-equity firm and the
price per share is $20, there are
400,000 shares outstanding.
Capital Structure
Current Proposed
Assets $8000,000 $8000,000
Debt $0 $4000,000
Equity
Debt-equity ratio
Share price $20 $20
Shares
outstanding
Interest rate % 10% 10%
Interest $
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Table 13.1
Current Proposed
Assets $8,000,000 $8,000,000
Debt $0 $4,000,000
Equity $8,000,000 $4,000,000
Debt/Equity Ratio 0.0 1.0
Share Price $20 $20
Shares Outstanding 400,000 200,000
Interest rate 10% 10%
 To investigate the impact of the
proposed restructuring, Ms. Morris has
prepared Table 13.2, which compares
the firm’s current capital structure to
the proposed capital structure under
three scenarios. The scenarios reflect
different assumptions about the firm’s
EBIT.
 Under the expected scenario, EBIT is
$1 million.
 In the recession scenario, EBIT falls
to $500,000.
 In the expansion scenario, it rises to
$1.5 million.
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Ignore the effect of taxes, What happens to EPS
when we issue debt and buy back shares?
CURRENT CAPITAL STRUCTURE: NO DEBT
Recession Expected Expansion
EBIT 500,000 1000000 1,500,000
Interest 0 0 0
Net
income
500,000 1,000,000 1,500,000
EPS $1.25 $2.5 $3.75
Variability EPS ranges from $1.25 to $3.75
Proposed CAPITAL STRUCTURE: With DEBT
Recession Expected Expansion
EBIT 500,000 1000000 1,500,000
Interest 400,000 400,000 400,000
Net
income
100,000 600,000 1,100,000
EPS $0.5 $3.00 $5.5
Variability EPS ranges from $0.50 to $5.50
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Choosing Capital Structure
In the no-debt case
 𝑬𝑷𝑺 =
𝑬𝑩𝑰𝑻
# 𝒔𝒉𝒂𝒓𝒆𝒔
, 𝑬𝑷𝑺 =
𝑬𝑩𝑰𝑻
𝟒𝟎𝟎,𝟎𝟎𝟎
In the with-debt case
 𝑬𝑷𝑺 =
𝑬𝑩𝑰𝑻 𝒊𝒏𝒕𝒆𝒓𝒆𝒔𝒕
# 𝒔𝒉𝒂𝒓𝒆𝒔
, 𝑬𝑷𝑺 =
𝑬𝑩𝑰𝑻 𝟒𝟎𝟎,𝟎𝟎𝟎
𝟐𝟎𝟎,𝟎𝟎𝟎
Level of EBIT EPS
Current CS
(No Debt)
Proposed CS
(with debt)
$0 0 -2
$400,000 1 0
$800,000 2 2
$1,200,000 3 4
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In the no-debt case
𝑬𝑷𝑺 =
𝑬𝑩𝑰𝑻
# 𝒔𝒉𝒂𝒓𝒆𝒔
𝑬𝑷𝑺 =
𝑬𝑩𝑰𝑻
𝟒𝟎𝟎,𝟎𝟎𝟎
In the with-debt case
𝑬𝑷𝑺 =
𝑬𝑩𝑰𝑻 𝒊𝒏𝒕𝒆𝒓𝒆𝒔𝒕
# 𝒔𝒉𝒂𝒓𝒆𝒔
𝑬𝑷𝑺 =
𝑬𝑩𝑰𝑻 𝟒𝟎𝟎,𝟎𝟎𝟎
𝟐𝟎𝟎,𝟎𝟎𝟎
 
$2.00
400,000
800,000
EPS
$800,000
EBIT
800,000
EBIT
2
EBIT
400,000
EBIT
200,000
400,000
EBIT
200,000
400,000
EBIT
400,000
EBIT
















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If EBIT is above this level, leverage is
beneficial;
if EBIT is below this point, it is not.
 https://www.youtube.com/watch?v=kadnjTgBmbA
 https://www.youtube.com/watch?v=Pz34ptgO5Bc
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