Bor

1. Financial Management
Dr : Samira Allam

3.  Learning Goals
By Completing This lecture, you should be able to :
 Define and explain leverage
 Know the main three relationship inside income
Statement
 Differentiate among three types of Leverage
 Calculate and interpret each of these Three types of
leverage
 Degree Of Operating Leverage (DOL).
 Degree Of Financial Leverage ( DFL) .

4.  At First what do we mean by leverage ?
 Leverage, refers to the effects that fixed costs have on the returns
that shareholders earn. By “fixed costs” we mean costs that does not
rise or fall with changes in a firm’s sales.
 Firms must pay these fixed costs whether business conditions are
good or bad.
 These fixed costs may be Operating Costs, such as the costs incurred
by purchasing raw materials and equipment , or may be Financial
Costs, such as the fixed costs of making debt payments.
 A firm with more leverage may earn higher returns on average than a
firm with less leverage, but the returns on the more leveraged firm will
also be more volatile.

5.  Leverage, in the sense we use it here, refers to the amount of
a firm has.
 These fixed costs may be , such
as building or equipment leases, or
, such as interest payments on debt.

6. Income Statement :
Sales ( revenues )
(-) Cost of Good Sold ( COGS )
= Gross Profit
(-) expenses ( operating , General and administrative , lease, and Depreciation )
=
Operating Profit ( Earning before interest and Tax ) EBIT
(-) Interest expenses ( $)
= Net profit before Tax ( EBT )
(-) Tax expenses ( $)
= Net profit After Tax
(-) Dividends for preferred Stocks
= Net Profit ( Available to Common Stockholders ) ÷No . Of Common Shares
outstanding
Earning Per share

7. Table 13.1 uses an income statement to highlight where different sources of leverage come
from.

8. 1) The Degree of Operating Leverage (DOL):
 Operating leverage is defined as the percentage change in
Operating income (EBIT) that results from a given percentage
change in Sales.
 is concerned with the relationship between the firm’s sales
revenue and its earnings before interest and taxes (EBIT) or
operating profits. When costs of operations (such as cost of
goods sold and operating expenses) are largely fixed, small
changes in revenue will lead to much larger changes in EBIT.
We can define it by using :
DOL =
𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝐸𝐵𝐼𝑇
𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑠𝑎𝑙𝑒𝑠

9. 1) The degree of operating leverage (DOL):
 To calculate a firm's DOL for a particular level of unit sales, Q,
DOL is:
DOL =
𝑸(𝑷−𝑽)
𝑸 𝑷−𝑽 −𝑭
where:
Q = quantity of units sold , P = price Per unit , V = variable cost Per
unit , F = fixed costs.
Another way to calculate DOL
DOL =
𝑺−𝑻𝑽𝑪
𝑺−𝑻𝑽𝑪−𝑭
: S = Sales , TVC = Total variable costs , F = Total fixed
costs

10. EXAMPLE: Degree of operating leverage Atom Company produced 5,000 units
last year that it sold for $75 each. Atom’s fixed costs were $70,000, and its variable
cost per unit was $50. Calculate and interpret Atom’s degree of operating leverage
at this level of production. Determine what will happen if Sales increase by 3% .
Answer: DOL =
𝑸(𝑷−𝑽)
𝑸 𝑷−𝑽 −𝑭
=
5,000($75−$50)
5,000 $75−$50 −$70,000
= 2.2727 °
a change by 1 % in sales will lead to change in EBIT by 2.2727 °
The result indicates that if Atom Company has a 3% increase in sales, its EBIT will
increase by 2.2727 × 3% = 6.82%.
the degree of operating leverage for a company depends on the level of sales

11.  For example :
if Atom Company sells 10,000 units, the DOL is
decreased:
DOL (Atom) =
𝑄(𝑃−𝑉)
[𝑄 𝑃−𝑉 −𝐹]
=
10,000($75−$50)
[(10,000 $75−$50 −$70,000]
=
250,000
180,000
= 1.39°

12. 2) Degree of Financial leverage ( DFL ) :
 is interpreted as the ratio of the percentage change in net income
(or EPS) to the percentage change in EBIT.
 is concerned with the relationship between the firm’s EBIT
and its common stock earnings per share (EPS).
 small changes in EBIT produce larger changes in EPS.
DFL =
𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝐸𝐵𝑆
𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝐸𝐵𝐼𝑇
For a particular level of operating earnings, DFL is calculated as:
DFL =
𝐸𝐵𝐼𝑇
𝐸𝐵𝐼𝑇−𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑒𝑥𝑝𝑒𝑛𝑠𝑒

13. Example : Degree of financial leverage ( DFL ) :
From the previous example, Atom Company’s operating income from
selling 5,000 units is $55,000. Assume that Atom has an annual interest
expense of $20,000. Calculate and interpret Atom’s degree of financial
leverage.
Answer:
DFL =
𝐸𝐵𝐼𝑇
𝐸𝐵𝐼𝑇−𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡
=
$55,000
$55,000−$20,000
= 1.5714°
That means : percentage change in net income (or EPS) to the percentage change
in EBIT equal 1.5714 .
So :
if EBIT increased by 10 % EPS has to increased by (10 % * 1.5714) = 15.714 %

14. 3) The Degree of Total Leverage (DTL) :
combines the degree of Operating leverage and Financial
leverage.
 DTL measures the sensitivity of EPS to change in sales.
 is the combined effect of operating and financial leverage. It is concerned with
the relationship between the firm’s sales revenue and EPS.
DTL is computed as:
DTL = DOL × DFL
DTL =
𝑄(𝑃−𝑉)
𝑄 𝑃−𝑉 −𝐹−𝐼
DTL =
𝑆−𝑇𝑉𝐶
𝑆−𝑇𝑉𝐶−𝐹−𝐼

15. The Degree of Total Leverage (DTL) :
EXAMPLE: Degree of total leverage
Continuing with our previous example, calculate Atom Company’s degree of total
leverage and determine how much Atom’s EPS will increase if its sales increase by
10%.
Answer:
DTL = DOL × DFL = 2.2727° × 1.5714 ° = 3.5713 °
 The result indicates that if Atom Company has a 10% increase in sales,
Earnings Per Share will increase by 3.5714 × 10% = 35.714%.