Financial Leverage Final

1.  Financing Decision: Leverage
 The term leverage may be defined as the employment of an asset or source
of funds for which the firm has to pay a fixed cost or fixed return.
Consequently, the earnings available to the shareholders as also the risk are
affected. If earnings less the variable costs exceed the fixed cost, or
earnings before interest and taxes(EBIT) exceed the fixed return
requirement, the leverage is called favorable. When they do not, the result
is unfavorable leverage.
 Types of Leverage: There are two types of leverage- Operating and
Financial. The leverage associated with investment (asset acquisition)
activities is referred to as operating leverage, while leverage associated
with financing activities is called financial leverage.
 The two types of leverage are closely related due to while we are basically
concerned with financial leverage for purpose of the financing decision of
the firm, the discussion of operating leverage is to serve as a background to
the understanding of financial leverage.
 Operating Leverage: is determined by the relationship between the firm’s
sales revenues and its earnings before interest and taxes(EBIT). EBIT are
also generally called as operating leverage.[ EBIT= Operating profits]

2. Financial Leverage: represents the relationship between the
firms earnings before interest and taxes (operating
profits) and the earnings available for ordinary
shareholders.
The operating profits (EBIT) are, thus used as the pivotal point
in defining operating and financial leverage represent two
stages in the process of determining the earnings
available to the equity holders.
Operating Leverage: The operating costs of a firm fall into
three categories:
i) Fixed costs which may be defined as those which do not
vary with sales volumes they are a function of time and
are typically contractual; they must be paid regardless of
the amount of revenues available;

3. ii) Variable costs which vary directly with the sales volume;
iii) semi-variable or semi-fixed costs are those which are partly
fixed and partly variable.
They are fixed over a certain range of sales volume and increase
to higher levels for higher sales volumes. Since the last
category of costs can be broken down into fixed and
variable components, the costs of a firm in operational
terms can be divided in to (i) fixed and (ii) variable
Definition of Operative leverage: The operating leverage may be
defined as the firm’s ability to use fixed operating costs to
magnify the effects of changes in sales on its earnings
before interest and taxes.
Operating leverage occurs any time, a firm has fixed costs that
must be met regardless of volume, we comply assets with
fixed cost in the hope that volume will produce revenue
more than sufficient to cover all fixed and variable costs.

4. In other words, with fixed costs, the percentage changes in profits
accompanying a change in volume is greater than the percentage change
in volume. This occurrence is known as operating leverage.
Example:10.1: A firm sells its products for Tk. 100 per unit, has variable
operating costs of Tk. 50 per unit and fixed operating costs of Tk.
50,000 per year. Show the various levels of EBIT that would result from
sale of (1) 1,000 units (2) 2000 units and (3) 3,000 units.
Solution: In sales level of 2,000 units are used as a basis for comparison, the
operating leverage is shown below:
EBIT for various Sales
Case -2
-50%
Base Case-1
+50%
1. Sales in units 1,000 2,000 3,000
2. Sales revenues (Tk.) 1,00,000 2,00,000 3,00,000
3. Less variable operating cost (Tk.) 50,000 1,00,000 1,50,000
Total contribution margin (TCM) 50,000 1,00,000 1,50,000
4. Less fixed operating cost (Tk.) 50,000 50,000 50,000
EBIT (Tk.) Zero 50,000 1,00,000
-100% +100%

5. From the above results, certain generalizations follows:
(i) Case 1 : A 50% increase in sales (from 2,000 to 3,000 units)
results in a 100% increase in EBIT (from Tk. 50,000 to Tk.
1,00,000).
(ii) Case 2 : A 50% decrease in sales (from Tk. 2,000 to 1,000
units), results in a 100% decrease in EBIT (from Tk.
50,000 to zero).
Example: 10.2: A firm sells its products for Tk. 50 per unit has
variable operating costs of Tk. 30 per unit and fixed
operating costs Tk. 50,00 per year. Its current level of sales
is 300 units. We wish to ascertain the firm’s degree of
operating leverage. What will happen to EBIT if sales
change? Let us suppose that the sales level (a) rises to 350
units and (b) decreases to 250 units.

6. EBIT at various sales levels
In the case-2, 16.7% decrease in sales volume (from 300 units to
250 units) leads to 100% decline in the EBIT( from Tk.
1,000 to Zero). On the other hand, a 16.7% increase in the
sales level in case- 1 (from 300 units to 350 units) results in
100% increase in EBIT (from Tk. 1000 to Tk. 2,000).
Case -2
-16.7%
Base Case-1
+16.7%
1. Sales in units 2,50 3,00 3,50
2. Sales revenues (Tk. 50 per unit) 12,500 15,000 17,500
3. Less variable operating cost (Tk. 30 per unit) 7,500 9,000 10,500
Total contribution margin (TCM) 5000 6000 7,000
4. Less fixed operating cost (Tk.) 5000 5000 5000
EBIT (Tk.) Zero 1,000 2,000
-100% +100%

7. Mentioned two illustration clearly shown that when a firm has
fixed operating costs, an increase in sales volume results in a
more than proportionate increase in EBIT. Similarly, a
decrease in the level of sales has an exactly opposite effect.
This is operating leverage; the former being known as
favorable leverage, while the letter is known as unfavorable.
Thus leverage works in both directions.
Alternative Definition of Operating Leverage (DOL):
Operating leverage can also be defined and illustrated in other
way. This is more precise measurement in terms of degree of
operating leverage(DOL). The DOL measures in quantitative
terms the extent or degree of operating leverage.
Symbolically
DOL= (%change in EBIT / %change in sales) >1-(10.1)
if DOL 1 it is favourable and when DOL = 1 unfavourable
Alternatively, DOL =
DOL=

8. EBIT= Q(S-V)-F, EBIT= Q(S-V)
Where, Q=Sales quantity in units
S= Selling price per unit
V= variable cost per unit
F= Total fixed cost
EBIT=Q(S-V)/Q(S-V)-F x Q/Q= S-V/S-V-F= Total contribution(at base
level)/EBIT(at base level)
Appling Equation 10.1 and 10.2 to example we get ,
DOL= +100%/+50%=2(case1), -100%/-50%=2(case2)
Or, = Tk. 100000/50000=2
Similarly, in example 10.2
DOL= +100%/+16.7%=6 (case1), -100%/-16.7%=6(case2)
OR= Tk.6,000/Tk.1,000= Tk.6
Since the DOL exceeds 1 in both the illustrations, operating leverage exits.
However, the degree of operating leverage is higher (3 times) in example
10.2 as compared to example 10.2, the respective quotients being 6 and 2.

9. The quotients mean that for every 1% change in sales, there
will be 6%(example10.2) and 2% (example10.2) changes in
EBIT in the same direction in which the sales change.
However, operating leverage exists only when there are
fixed operating costs. If there are no fixed operating costs,
there will be no operating leverage.
Particulars Base level New level
1. Unit: sold 1000 1100
1. Sales price per unit TK.10 Tk.10
1. Variable cost per unit 6 6
1. Fixed operating cost Nill Nill

10. Particulars Base
level
New
level
1. Sales revenue 10,000 11,000
1. Less: Variable costs 6000 6600
1. Fixed operating cost ---- ----
1. EBIT 4000 4400
Since DOL=1(10%/10%) , there is no operating leverage.
No fixed operating cost, no operating leverage of a firm.
The relavant computations are given below:

11. Financial leverage relates to the financing
activities of a firm. The sources from
which funds can be raised by a firm, from
the point of view of the cost, can be
categorized into-
(1) those which carry a fixed financial
charge, and
2) those which do not involve any fixed
charge.
(

12. The sources of funds in the first category consist of various
types of long-term debt, including bounds, debentures, and
preference shares. .
*The long- term debts carry a fixed rate of interest which is a
contractual obligation for the firm. Although the dividend on
preference shares is not a contractual obligation, it is a the
ordinary shareholders. .
*The equity holders are entitled to the remainder of the
operating profits of the firm after the prior obligations are
met. We assume in the discussions in this chapter that all
preference dividends are paid. This assumption is necessary
in order to ascertain the operating profits available for
distribution to ordinary shareholders. .

13. Example: The financial manager of the Hypothetical Ltd experts that its earnings
before interest and taxes (EBIT) in the current year would amount to Tk. 10,000.
The firm has 5 per cent aggregating Tk 40,000, while the 10 per cent preference
shares amount to Tk 20,000. What would be the earnings per share (EPS)?
Assuming the EBIT being (1) Tk 6,000 and (2) 14,000 how would the EPS be
affected? The firm can be assumed to be in the 35 per cent tax bracket. The number
of outstanding ordinary shares is 1,000.
Solution:
Case2 Base Case1
-40% +40%
EBIT Tk 6,000 10,000 14,000
Less: Interest on bonds 2,000 2,000 2,000
EBT 4,000 8,000 12,000
Less: Taxes(35%) 1,400 2,800 4,200
EAT 2,600 5,200 7,800
Less: Preference dividend 2,000 2,000 2,000
EAOS 600 3,200 5,800
EPS 0.6 3.2 5.8
-81.25% +81.25%

14. Case 1: A 40 percent increase in EBIT (from Tk
10,000 to 14,000) results in 81.25 per cent increase
in EPS (from Tk 3.2 to Tk5.8)
Case 2: A 40 percent decrease in EBIT (from Tk
10,000 to 6,000) leads to 81.25 per cent decrease in
EPS (from Tk 3.2 to Tk0.6)
The financial risk refers to the risk of neither the
firm nor being able to cover its fixed its financial
costs. With the increase in financial charges, the firm
also required to raise the level of EBIT necessary to
meet financial charges.

15. Alternative definition of Financial
Leverage:
DFL =
DFL =
=
(1.3)
Alternatively, DFL =
=
= 2.03
Case 2 =
= 2.03
=

16. Applying equations to case 1 and case 2 in example 1.4
case 1:
+81.25% / +40% = 2.03
-81.25 / -40% = 2.03
Or, 1000-2000-/(2000-(1-0.35))= 2.03
In another example
case 1:
+50% / +40% = 1.25
-50% / -40% = 1.25
Or, 50000/(50000-10000)= 1.25

17. exclusively use equity capital
exclusively use debt
exclusively use preference
capital,
use a combination of (1) and (2)
a different proportions,
a combination of (1), (2),and (3)
in different proportions,
The EBIT-EPS analysis, as a method to study the effect
of leverage, essentially involves the comparison of
alternative methods of financing under various
assumptions of EBIT. A firm has the choice to raise funds
for financing its investment proposals from different
sources in different proportions. For instance, it can

18. Example: 18.6
Suppose a firm has a capital exclusively comprising of ordinary
shares amounting to Rs. 1000000. The firm now wishes to raise
additional Rs. 1000000 for expansion. The firm has four alternative
financial planes:
•It can raise the entire amount in the form of equity capital.
•It can raise 50 per cent as equity capital and 50 per cent as 5%
debentures.
•It can raise the entire amount as 6% debentures.
•It can raise 50 per cent as equity capital and 50 per cent as 5%
preference capital.
Further assume that the existing EBIT are Rs. 120000, the tax rate
is 35 per cent, outstanding ordinary shares 10000 and the market
per share is Rs. 100 under all the four alternatives.
Which financial plan should the firm select?

19. Particulars Financing plans
A B C
D
EBIT 120000 120000 120000 120000
Less: interest ---- 25000 60000 ----
Earnings before taxes 120000 95000 60000 120000
Taxes : 42000 33 250 21000 42000
Earnings after taxes 78000 61750 39000 78000
Less: preference dividend ---- ---- ---- 25000
Earnings available to ordinary
shareholders
78000 61750 39000 53000
Numbers of shares 20000 15000 10000 15000
EPS 3.9 4.1 3.9 3.5

20. Example: 18.7
The financial manager of a company has formulated various
financial plans to finance Rs. 3000000 required to implement
various capital budgeting projects:
•Either equity capital of Rs. 3000000 or Rs. 1500000 10%
debentures and Rs. 1500000 equity;
•Either equity capital of Rs. 3000000 or 13%preference shares
of Rs. 1000000 and Rs. 2000000 equity;
•Either equity capital of Rs. 3000000 or 13%preference capital
of Rs. 1000000, (subject to dividend tax of 10 per cent), Rs.
1000000 10% debentures and Rs 1000000 equity; and
•Either equity share capital of Rs. 2000000, 10% debentures
of Rs. 1000000 or 13% preference capital of Rs. 1000000,
10% debentures of Rs. 800000 and Rs. 12000 equity.
You are required to determine the indifference point for each
financial plan, assuming 35 per cent corporate tax rate and the
face value of equity shares as Rs. 100.

21. 2
1
)
1
)(
(
)
1
(
N
t
I
X
N
t
X 



15000
)
150000
(
30000
)
35
.
0
1
( 

 X
X
15000
97000
65
.
0
30000
65
.
0 

X
X
Or,
Or,
Or, 0.65X = 1.3X-195000
Or, X = 1950000/0.65 = 300000
Particulars 15%
Debt
issue
Equity
issue
EBIT 300000 300000
Less: Interest ----- 150000
Earnings before Taxes 300000 150000
Less: Taxes 105000 52500
Earnings for equity holders 195000 97500
Number of Equity shares 30000 15000
EPS 6.5 6.5
Conformation Table

22. 3
1
)
1
(
)
1
(
N
D
t
X
N
t
X p




20000
130000
)
35
.
0
1
(
30000
)
35
.
0
1
( 


 X
X
20000
130000
65
.
0
30000
65
.
0 

X
X
Or,
Or,
Or, X = 600000
Particulars Equity
Financing
Equity +
preference
share
EBIT 600000 600000
Less: Taxes
210000
210000
Earnings after Taxes 390000 390000
Dividends on preference share ---- 130000
Earnings for equity holders 390000 260000
Number of Equity shares 30000 20000
EPS 13 13
Conformation Table

23. 6
1
)
1
(
)
1
)(
(
)
1
(
N
Dt
D
t
I
X
N
t
X p 





10000
)
1
.
0
1
(
130000
)
35
.
0
1
)(
100000
(
30000
)
1
( 




 X
t
X
10000
143000
65000
65
.
0
30000
65
.
0 


X
X
Or,
Or,
Or, X = Tk. 480000
Particulars Equity
financing
Equity +
Preference
+ Debenture
financing
EBIT 480000 480000
Less: Interest ----- 100000
Earnings after interest 480000 380000
Less: Taxes 168000 133000
Earnings after taxes 312000 247000
Less: dividends including dividend tax on
preference share
---- 143000
Earnings available for equity holders 312000 104000
Number of equity holders 30000 10000
EPS 18.4 18.4

24. 6
1
)
1
)(
(
)
1
)(
(
N
D
t
I
X
N
t
I
X p






12000
130000
)
35
.
0
1
)(
80000
(
20000
)
35
.
0
1
)(
100000
( 




 X
X
(3)
Or,
Or, X = Tk. 550000
Particulars Equity
financing
Equity +
Preference
+
Debenture
financing
EBIT 550000 550000
Less: Interest ----- 80000
Earnings after interest 450000 470000
Less: Taxes 157000 164500
Earnings after taxes 292500 305500
Less: dividends on preference
share
---- 130000
Earnings available for equity
holders
292500 175500
Number of equity holders 20000 12000
EPS 14.6 14.6

25. 1





 
1
)
1
(
N
t
X
2 




 


2
)
1
)(
(
N
D
t
I
X P
The indifference point may be computed in another way he using
market value as the basis. Since the operational objective of financial
management is the maximization of share prices, the market price of a
firm with two different financial plans should be identical.
The indifference point can be symbolically compounded by this
equation:
PE =
Where ,P/E is ratio of unlevered plan and P/E is ratio of levered plan.
P/E =
2

26. Example 18.8: determine the indifference point at which
market price of equity share of a corporate firm will be
the same from the following data:
•funds require, Rs 50000
•existing number of equity share outstanding 5000 @ 10
per share
•existing 10% debt, Rs 20000
•funds required can be raised either by (a) issue of 2000
equity shares, netting Rs 25 per share or (b) new 15 per
cent debt.
•The P/E ratio will be 7 times in equity alternative and 6
times in debt alternative.
•corporate tax, 35 per cent

27. 1





 

1
1 )
1
)(
(
N
t
I
X
2





 


2
2
1 )
1
)(
(
N
t
I
I
x
P/E
= P/E





 
7000
65
.
0
)
2000
(x





 
5000
65
.
0
)
9500
(x
Or, 7 = = 6
7000
1300
65
.
0 
x
5000
6175
65
.
0 
x
Or =
Conformation table
Or, 5(4.55x-9100) = 7(3.9x × 37050)
Or, x = 47000
Particulars 15%
Debt
issue
Equity
issue
EBIT 47000 47000
Less: Interest
9500
2000
Earnings before Taxes 37500 45000
Less: Taxes 13125 15750
Earnings after taxes 24375 29250
Number of Equity shares 5000 7000
EPS 4.875 4.18
P/E ratio 6 7
Market price of the share 29.25 29.25

28. EBIT
on
Contributi
I
EBIT
EBIT

Combined leverage : Total Risk
Combined leverage is the product of operating leverage and financial
leverage. Total risk is the risk associate with combined leverage. The
result of combined leverage and the risk associate with combined
leverage is known as total risk. Symbolically
DCL = DOL×DFL (18.11)
Substituting the value of DOL and DFL, we have:
DCL = × ×
×
=
(
EBIT
on
Contributi
I
EBIT
on
Contributi

I
EBIT
on
Contributi


29. A firm sells, variable cost, fixed cost is Tk. 7500000 Tk.
4200000 and 600000 respectively it has borrowed tk.
4500000 at 9% and its equal capitals totals Tk.
5500000
•What is the firms ROI?
•Does it have favorable financial leverage?
•If the firm belongs to an industry whose asset turnover
is 3, does it have a high or low asset leverage?
•What are the operating, financial and combined
leverage of the firm?
•If sales drop to Tk. 5000000 what will be new EBIT?
•At what level will the EBIT of the firm equal to zero?

30. Sales 7500000
(-) variable cost 4200000
Total contribution margin 3300000
Fixed cost 600000
EBIT 2700000
Interest on loan 9% 405000
EBT 2295000
Solution:
Necessary calculations:
Investment
EBIT
10000000
2700000
=
=
•ROI = = = 27%
•27% > 9% ROI > Interest rate (favorable)

31. c) Here, (4500000*3)/ 100 = 1500000
So, (10000000-1500000) = 8500000
And turnover 8500000/ 10000000 = 0.85
Previous asset turnover = 7500000/10000000 = 0.75
We get 0.85 > 0.75
d)DOL = =
3300000/2700000 = 1.22 times
DFL= = 2700000/ 2295000 = 1.18
times.
DCL = DOL * DFL =1.22 * 1.88 = 1.44 times
EBIT
TC
VC
Sales )
(

EBT
EBIT

32. Sales revenue 5000000
(-)VC (5000000*0.56) 2800000
(-)FC 2200000
EBIT 6000000
EBIT at ales level of tk. 5000000
f) The level of sales where EBIT is zero. EBIT zero means no
profit level of sales in BEP
Break-even analysis: The break-even point that
point of sale volume at which total revenue is equal
to total costs.

33. BEP sales =
)
arg
( inratio
onm
contributi
CMR
FC
100

sales
CM
100
7500000
3300000

Where CMR =
=
=
= 44%
Note, Interest also FC
FC = 600000+ 405000 = 1005000
BEP Sales = 1005000/ 0.44= 2284091
Conformation table:
Sales Revenue 2284091
VC(0.56) 1279091
1005000
FC (operating) 600000
405000
interest 405000
0
EBT

34.  Figure: BEP Chart