Description
This is a presentation explaining what is operating leverage, financial leverage and combined leverage with the help of detailed examples.
Chapter 3
Operating, Financial And
Combined Leverage
OPERATING, FINANCIAL AND
COMBINED LEVERAGE
Operating Leverage
Financial Leverage
Combined Leverage : Total Risk
Solved Problem
Mini Case
Leverage refers to the use of an asset or source
of funds which involves fixed costs or fixed
returns. As a result, the earnings available to
the shareholders/owners are affected as also
their risk. There are three types of leverage,
namely,
1) Operating
2) Financial
3) Combined
Operating Leverage
Leverage associated with asset acquisition or investment
activities is referred to as the operating leverage. It refers to
the firm’s ability to use fixed operating costs to magnify the
effect of changes in sales on its operating profits (EBIT) and
results in more than a proportionate change (±) in EBIT with
change in the sales revenue.
Degree of operating leverage (DOL) is computed in two
ways:
1) Percentage change in EBIT/Percentage change in sales
and
2) (Sales – Variable costs)/EBIT.
The operating leverage is favourable when increase in sales
volume has a positive magnifying effect on EBIT. It is
unfavourable when a decrease in sales volume has a negative
magnifying effect on EBIT. Therefore, high DOL is good when
sales revenues are rising and bad when they are falling.
The DOL is a measure of the business/operating risk of the firm.
Operating risk is the risk of the firm not being able to cover its
fixed operating costs. The larger is the magnitude of such costs,
the larger is the volume of sales required to recover them. Thus,
the DOL depends on fixed operating costs.
Example 1
A firm sells products for Rs 100 per unit, has variable operating costs of Rs 50 per unit and fixed
operating costs of Rs 50,000 per year. Show the various levels of EBIT that would result from sale
of (i) 1,000 units (ii) 2,000 units and (iii) 3,000 units.
Solution
If sales level of 2,000 units are used as a base for comparison, the operating leverage is illustrated
in Table 1
Table 1 EBIT for Various Sales Levels
Case 2
– 50%
Base Case 1
+ 50%
1. Sales in units 1,000 2,000 3,000
2. Sales revenue Rs 1,00,000 Rs 2,00,000 Rs 3,00,000
3. Less: Variable operating cost 50,000 1,00,000 1,50,000
4. Contribution 50,000 1,00,000 1,50,000
5. Less: Fixed operating cost 50,000 50,000 50,000
6. EBIT Zero 50,000 1,00,000
–100% +100%
From the results contained in Table 1, certain generalizations follow:
1) Case 1: A 50 per cent increase in sales (from 2,000 to 3,000
units) results in a 100 per cent increase in EBIT (from Rs 50,000
to Rs 1,00,000).
2) Case 2: A 50 per cent decrease in sales (from 2,000 to 1,000
units) results in a 100 per cent decrease in EBIT (from Rs 50,000
to zero).
Example 2
A firm sells its products for Rs 50 per unit, has variable operating costs of
Rs 30 per unit and fixed operating costs of Rs 5,000 per year. Its current
level of sales is 300 units. Determine the degree of operating leverage. What
will happen to EBIT if sales change: (a) rise to 350 units, and (b) decrease to
250 units?
Solution: The EBIT for various sales levels is computed in Table 2.
Table 2: EBIT at Various Sales Levels
Case 2
–16.7%
Base Case 1
+16.7%
1. Sales in units 250 300 350
2. Sales revenue Rs 12,500 Rs 15,000 Rs 17,500
3. Less: Variable cost 7,500 9,000 10,500
4. Contribution 5,000 6,000 7,000
5. Less: Fixed operating
cost
5,000 5,000 5,000
6. EBIT Zero 1,000 2,000
– 100% + 100%
Interpretation
In case 2, 16.7 per cent decrease in sales volume (from 300 units to 250 units)
leads to 100 per cent decline in the EBIT (from Rs 1,000 to zero). On the other
hand, a 16.7 per cent increase in the sales level in case 1 (from 300 units to
350 units) results in 100 per cent increase in EBIT (from Rs 1,000 to Rs 2,000).
The two illustrations (Tables 1 and 2) clearly show 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
favorable leverage, while the latter is unfavorable. Leverage, thus, works in
both directions.
Alternative definition of Operating Leverage
When proportionate change in EBIT as a result of a given change in sales is
more than the proportionate change in sales, operating leverage exists. The
greater the DOL, the higher is the operating leverage. Symbolically,
2)
level) base (at EBIT
level) base (at on Contributi Total
F V) Q(S
V) Q(S
?Q
Q
F - V) - Q(S
V) - Q(S ?
DOL
costs. fixed Total F
unit per cost Variable V
unit per price Selling S
units in quantity Sales Q
Where
V) - Q(S ? EBIT ? F, V) Q(S EBIT
Q ?Q
EBIT ?EBIT
DOL ely, Alternativ
1) 1
sales in change Percentage
EBIT in change Percentage
DOL
(
(
=
÷ ÷
÷
= × =
=
=
=
=
= ÷ ÷ =
÷
÷
=
> =
Since the DOL exceeds 1 in both the illustrations, operating leverage exists. However, the degree of
operating leverage is higher (3 times) in the case of the firm in Example 2 as compared to the firm in
Example 1, the respective quotients being 6 and 2. The quotients mean that for every 1 per cent
change in sales, there will be 6 per cent (Examples 2) and 2 per cent (Example 1) change in EBIT in
the direction the sales change.
2
50,000 Rs
1,00,000 Rs
2) (Case 2
50%
100%
1), (Case 2
50%
100%
DOL
get, we 1 Example to 2 and 1 Equations Applying
= =
=
÷
÷
=
+
+
=
6
1,000 Rs
6,000 Rs
2) (Case 6
16.7% -
100% -
1), (Case 6
16.7%
100%
DOL
2, Example in Similarly,
= =
= =
+
+
=
Operating leverage exists only when there are fixed operating costs. If there are no
fixed operating costs, there will be no operating leverage. Consider Example 3.
Example 3
Particulars Base Level New Level
1. Units sold 1,000 1,100
2. Sales price per unit Rs 10 Rs 10
3. Variable cost per unit 6 6
4. Fixed operating cost Nil Nil
Solution The relevant computations are given in Table 3.
TABLE 3 EBIT for Various Sales Volume
Particulars Base Level New Level
1. Sales revenues Rs 10,000 Rs 11,000
2. Less: Variable costs 6,000 6,600
3. Less: Fixed costs — —
4. EBIT 4,000 4,400
Applying Equation 1, DOL = 1. Since the quotient is 1, there is no operating
leverage.
Financial Leverage
Financial leverage is related to the financing
activities of a firm. It results from the presence of
fixed financial charges (such as interest on debt and
dividend on preference shares). Since such financial
expenses do not vary with the operating profits,
financial leverage is concerned with the effect of
changes in EBIT on the earnings available to equity-
holders. It is defined as the ability of a firm to use
fixed financial charges to magnify the effect of
changes in EBIT on the earnings per share (EPS).
Example 4
The financial manager of the Hypothetical Ltd expects that its earnings before
interest and taxes (EBIT) in the current year would amount to Rs 10,000. The firm
has 5 per cent bonds aggregating Rs 40,000, while the 10 per cent preference
shares amount to Rs 20,000. What would be the earnings per share (EPS)?
Assuming the EBIT being (i) Rs 6,000, and (ii) Rs 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
TABLE 4 EPS for Various EBIT Levels
Case 2 Base Case 1
–40% +40%
EBIT
Less: Interest on bonds
Earnings before taxes (EBT)
Less: Taxes (35%)
Earning after taxes (EAT)
Less: Preference dividend
Earnings available for ordinary
shareholders
Earnings per share (EPS)
Rs 6,000
2,000
4,000
1,400
2,600
2,000
600
0.6
Rs 10,000
2,000
8,000
2,800
5,200
2,000
3,200
3.2
Rs 14,000
2,000
12,000
4,200
7,800
2,000
5,800
5.8
– 81.25%
+81.25%
The interpretation of Table 4 is as follows:
Case 1:
A 40 per cent increase in EBIT (from Rs 10,000 to Rs 14,000)
results in 81.25 per cent increase in EPS (from Rs 3.2 to Rs
5.8).
Case 2:
A 40 per cent decrease in EBIT (from Rs 10,000 to Rs 6,000)
leads to 81.25 per cent decrease in EPS (from Rs 3.2 to Re
0.6).
Example 5
A company has Rs 1,00,000, 10% debentures and 5,000 equity shares
outstanding. It is in the 35 per cent tax-bracket. Assuming three levels of EBIT
(i) Rs 50,000, (ii) Rs 30,000, and (iii) Rs 70,000, calculate the change in EPS
(base level of EBIT = Rs 50,000).
Solution
TABLE 5 EPS at Various EBIT Levels
Case 2 Base Case 1
–40% +40%
EBIT
Less: interest
Earnings before taxes
Less: Taxes
Earning after taxes
Earnings per share (EPS)
Rs 30,000
10,000
20,000
7,000
13,000
2.6
Rs 50,000
10,000
40,000
14,000
26,000
5.2
Rs 70,000
10,000
60,000
21,000
39,000
7.8
– 50%
+50%
Thus, a 40 per cent increase in EBIT in case 2 from the base level of EBIT has led to
50 per cent increase in EPS. And a decrease of 40 per cent in EBIT has decreased
the EPS by 50 per cent.
Alternative Definition of Financial Leverage
The procedure outlined above is merely indicative of the presence or
absence of financial leverage. Financial leverage can be more precisely
expressed in terms of the degree of financial leverage (DFL). The DFL can
be calculated by Eq. (3)
( )( ) | |
( ) | |( )
( ) | | ( )
( ) | | ( )
( ) | | ( )
( )
( ) | |
( ) | | ( )
( ) | |
( ) | | ( )
( )
( )
( )
( ) | | ( ) ( )
) 4 (
t 1 / D I EBIT
EBIT
t 1 / D I F V S Q
F V S Q
V S Q
F V S Q
t 1 / D I F V S Q
V S ?Q
DFL
t 1 / D I F V S Q
V S ?Q
t 1 by r denominato and numerator Dividing
D t 1 I F V S Q
t 1 V S ?Q
EPS
?EPS
/N t 1 V S ?Q ?EPS
ts, areconstan D and I F, Since,
N
D t 1 I F V S Q
N
D t 1 I EBIT
EPS
EBIT ?EBIT
EPS ?EPS
DFL ely, Alternativ
(3) 1
EBIT in change Percentage
EPS in change Percentage
DFL
p P
P
p
P
p
P
p
÷ ÷ ÷
=
÷ ÷ ÷ ÷ ÷
÷ ÷
=
÷
÷ ÷
×
÷ ÷ ÷ ÷ ÷
÷
=
÷ ÷ ÷ ÷ ÷
÷
=
÷
÷ ÷ ÷ ÷ ÷
÷ ÷
=
÷ ÷ =
÷ ÷ ÷ ÷ ÷
=
÷ ÷ ÷
=
÷
÷
=
> =
As a rule, when a percentage change in EPS resulting from a given percentage
change in EBIT is greater than the percentage change in EBIT, financial leverage
exists. In other words, financial leverage occurs when the quotient in Equation 3 is
more than one.
In both the examples, the relevant quotient is larger than one. Therefore, financial
leverage exists. But the degree of financial leverage is higher in Example 4 (2.03)
than in Example 5 (1.25). The higher the quotient of percentage change in EPS due
to percentage change in EBIT, the greater is the degree of financial leverage. The
quotient of 2.03 implies that 1 per cent change in EBIT will cause 2.03 per cent
change in EPS in the same direction (± increase/decrease) in which the EBIT
changes. With 1.25 quotient the proportionate change in EPS as a result of 1 per
cent change in EBIT will be comparatively less, that is, 1.25 per cent in either
direction.
( ) | |
1.25
10,000 Rs 50,000 Rs
50,000 Rs
1.25
40%
50%
2 Case 1.25,
40%
50%
1 Case : 5 e (ii)Exampl
2.03
0.35 1 2,000/ Rs Rs2,000 10,000 Rs
10,000 Rs
2.03
40% -
81.25
2 Case 2.03,
40%
81.25%
1 Case : 4 Example (i)For
5, and 4 Examples in 2 Case and 1 Case to 3 Equations Applying
=
÷
=
=
÷
÷
= =
+
+
=
=
÷ ÷ ÷
=
=
÷
= =
+
+
=
Degree of financial leverage (DFL): Applying Eq. (3)
(i) Case 1 = (+40% / + 40%) = 1
(ii) Case 2 = (-40% / -40%) = 1
Thus, the quotient is 1. Its implication is that 1 per cent change in EBIT will result in 1
per cent change in EPS, that is, proportionate. There is, therefore, no magnification in
the EPS.
There will be, however, no financial leverage, if there is no fixed-charged financing.
(Table 6).
TABLE 6 EPS at Various EBIT Levels
Case 2 Base Case 1
– 40% +40%
EBIT Rs 30,000 Rs 50,000 Rs 70,000
Less: Taxes (0.35) 10,500 17,500 24,500
Earnings available for equity-
holders
19,500 32,500 45,500
Number of shares 10,000 10,000 10,000
EPS 1.95 3.25 4.55
– 40%
+40%
Financial leverage involves the use of funds obtained at a fixed cost in
the hope of increasing the return to the equity-holders. When a firm earns
more on the assets purchased with the funds than the fixed cost of their
use, the financial leverage is favorable. Unfavorable leverage occurs
when the firm does not earn as much as the funds cost.
High fixed financial costs increase the financial leverage and, thus,
financial risk. The financial risk refers to the risk of the firm not being able
to cover its fixed financial costs. In case of default, the firm can be
technically forced into liquidation. The larger is the amount of fixed
financial costs, the larger is EBIT required to recover them. Thus, the DFL
depends on fixed financial costs.
EBIT-EPS Analysis
To devise an appropriate capital structure, the amount of EBIT under various
financing plans should be related to EPS. The EBIT-EPS analysis is a widely-used
method of examining the effect of financial leverage/use of debt. A financial
alternative that ensures the largest EPS is preferred, given the level of EBIT.
Example 6
Suppose a firm has a capital structure exclusively comprising of ordinary shares
amounting to Rs 10,00,000. The firm now wishes to raise additional Rs 10,00,000 for
expansion. The firm has four alternative financial plans:
(A) It can raise the entire amount in the form of equity capital.
(B) It can raise 50 per cent as equity capital and 50 per cent as 5% debentures.
(C) It can raise the entire amount as 6% debentures.
(D) 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 1,20,000, the tax rate is 35 per cent,
outstanding ordinary shares 10,000 and the market price per share is Rs 100 under
all the four alternatives.
Which financing plan should the firm select?
Solution
TABLE 7 EPS Under Various Financial Plans
Particulars Financing plans
A B C D
EBIT
Less: Interest
Earnings before taxes
Taxes
Earnings after taxes
Less: Preference dividend
Earnings available to
ordinary shareholders
Number of shares
Earnings per share (EPS)
Rs 1,20,000
—
1,20,000
42,000
78,000
—
78,000
20,000
3.9
Rs 1,20,000
25,000
95,000
33,250
61,750
—
61,750
15,000
4.1
Rs 1,20,000
60,000
60,000
21,000
39,000
—
39,000
10,000
3.9
Rs 1,20,000
—
1,20,000
42,000
78,000
25,000
53,000
15,000
3.5
The calculations in Table 7 reveal that given a level of EBIT of Rs 1,20,000, the financing
alternative B, which involves 50 per cent ordinary shares and 50 per cent debt, is the
most favorable with respect to EPS. Another disclosure of the table is that although the
proportion of ordinary shares in the total capitalization under the financing plan D is also
50 per cent, that is, equal to plan B, EPS is considerably different (lowest). The difference
in the plans B and D is due to the fact that interest on debt is tax-deductible while the
dividend on preference shares is not. With 35 per cent income tax, the explicit cost of
preference shares would be higher than the cost of debt.
Financial Break-even Point (BEP)
Financial break-even point (BEP) represents a point at which before-tax
earnings are equal to the firm’s fixed financial obligations. Symbolically, it is
computed as follows:
[I + D
p
+ D
t
)/(1 – t)] (5)
In other words, at financial BEP, EPS is zero.
Equation 5 gives before-tax earnings necessary to cover the firm’s fixed
financial obligations.
As fixed financial charges are added, the break-even point for zero EPS is
increased by the amount of the additional fixed cost. Beyond the financial
break-even point, increase in EPS is more than the proportionate increase in
EBIT. This is illustrated in Table 8, which presents the EBIT-EPS relationship
for the data in Example 6 under the various EBIT assumptions given in the
box:
1) Rs 80,000 (4 per cent return on total assets)
2) 1,00,000 (5 per cent return on total assets)
3) 1,30,000 (6.5 per cent return on total assets)
4) 1,60,000 (8 per cent return on total assets)
5) 2,00,000 (10 per cent return on total assets)
TABLE 8 EBIT-EPS Analysis under Various EBIT Assumptions for the Four Financing Plans of Example
6
(i) EBIT = Rs 80,000 (4 per cent return on investments)
Particulars Financing Plans
A B C D
EBIT
Less: Interest
EBT
Less: Taxes
EAT
Less: Preference dividend
EAT for equity-holders
EPS
80,000 80,000 80,000 80,000
— 25,000 60,000 —
80,000 55,000 20,000 80,000
28,000 19,250 7,000 28,000
52,000 35,750 13,000 52,000
— — — 25,000
52,000 35,750 13,000 27,000
2.6 2.38 1.3 1.8
(ii) EBIT = Rs 1,00,000 (5 per cent return)
EBIT 1,00,000 1,00,000 1,00,000 1,00,000
Less: Interest — 25,000 60,000 —
EBT 1,00,000 75,000 40,000 1,00,000
Less: Taxes 35,000 26,250 14,000 35,000
EAT 65,000 48,750 26,000 65,000
Less: Preference dividend — — — 25,000
EAT for equity-holders 65,000 48,750 26,000 40,000
EPS 3.25 3.25 2.6 2.67
(iii) EBIT = Rs 1,30,000 (6.5 per cent return)
EBIT 1,30,000 1,30,000 1,30,000 1,30,000
Less: Interest — 25,000 60,000 —
EBT 1,30,000 1,05,000 70,000 1,30,000
Less: Taxes 45,500 36,750 24,500 45,500
EAT 84,500 68,250 45,500 84,500
Less: Preference dividend — — — 25,000
EAT for equity-holders 84,500 68,250 45,500 59,500
EPS 4.22 4.55 4.55 3.97
(iv) EBIT = Rs 1,60,000 (8 per cent return)
EBIT 1,60,000 1,60,000 1,60,000 1,60,000
Less: Interest — 25,000 60,000 —
EBT 1,60,000 1,35,000 1,00,000 1,60,000
Less: Taxes 56,000 47,250 35,000 56,000
EAT 1,04,000 87,750 65,000 1,04,000
Less: Preference dividend — — — 25,000
EAT for equity-holders 1,04,000 87,750 65,000 79,000
EPS 5.2 5.8 6.5 5.3
Contd.
(v) EBIT = Rs 2,00,000 (10 per cent return)
EBIT 2,00,000 2,00,000 2,00,000 2,00,000
Less: Interest — 25,000 60,000 —
EBT 2,00,000 1,75,000 1,40,000 2,00,000
Less: Taxes 70,000 61,250 49,000 70,000
EAT 1,30,000 1,13,750 91,000 1,30,000
Less: Preference dividend — — — 25,000
EAT for equity-holders 1,30,000 1,13,750 91,000 1,05,000
EPS 6.5 7.6 9.1 7
It can be seen from Table 8 that when the EBIT level exceeds the financial break-even
level (Rs 25,000, Rs 60,000 and Rs 38,462 for financing alternatives, B, C and D
respectively) EPS increases. The percentage increase in EPS is the greatest when EBIT is
nearest the break-even point. Thus, in Plan C, an increase of 25 per cent in EBIT (from Rs
80,000 to Rs 1,00,000) results in a 100 per cent increase in EPS (from Re 1.3 to Rs 2.6),
whereas the percentage increase in EPS is only 40 per cent (from Rs 6.5 to Rs 9.1) as a
result of the change in EBIT at higher levels from Rs 1,60,000 to Rs 2,00,000 (i.e. 25 per
cent increase).
Contd.
Indifference point EBIT level beyond which benefits of financial leverage
accrue with respect to EPS.
The indifference point between two methods of financing can be obtained
mathematically (algebraic approach) as well as graphically.
Algebraic Approach
Mathematically, the indifference point can be obtained by using the following
symbols:
X = earnings before interest and taxes (EBIT) at the indifference point
N
1
= number of equity shares outstanding if only equity shares are issued
N
2
= number of equity shares outstanding if both debentures and equity
shares are issued
N
3
= number of equity shares outstanding if both preference and equity
shares are issued
N
4
= number of equity shares outstanding if both preference shares and
debentures are issued
I = the amount of interest on debentures
D
P
= the amount of dividend on preference shares
t = corporate income tax rate
D
t
= tax on preference dividend
For a New Company
The indifference point can be determined by using the following equations:
( ) ( ) ( )
( )
( )
( )
( ) ( )
( )
( ) ( )
(8)
N
D t 1 I X
N
t 1 X
: Debentures and shares Preference versus shares y (iii)Equit
(7A)
N
Dt 1 D t 1 X
N
t 1 X
: dividend Preference on tax with shares Preference versus shares Equity (ii)(b)
(7)
N
D t 1 X
N
t 1 X
: shares Preference versus shares Equity (ii)(a)
(6)
N
t 1 I X
N
t 1 X
: Debentures versus shares (i)Equity
4
p
1
3
p
1
3
p
1
2 1
÷ ÷ ÷
=
÷
+ ÷ ÷
=
÷
÷ ÷
=
÷
÷ ÷
=
÷
For an Existing Company
If the debentures are already outstanding, let us assume I
1
= interest paid on
existing debt, and I
2
= interest payable on additional debt, then the
indifference point would be determined by Equation 9.
( ) ( ) ( ) ( )
) 9 (
N
t 1 I I X
N
t 1 I X
2
2 1
1
1
÷ ÷ ÷
=
÷ ÷
Example 7
The financial manager of a company has formulated various financial plans
to finance Rs 30,00,000 required to implement various capital budgeting
projects:
1) Either equity capital of Rs 30,00,000 or Rs 15,00,000 10% debentures
and Rs 15,00,000 equity;
2) Either equity capital of Rs 30,00,000 or 13% preference shares of Rs
10,00,000 and Rs 20,00,000 equity;
3) Either equity capital of Rs 30,00,000 or 13% preference capital of Rs
10,00,000, (subject to dividend tax of 10 per cent), Rs 10,00,000 10%
debentures and Rs 10,00,000 equity; and
4) Either equity share capital of Rs 20,00,000 and 10% debentures of Rs
10,00,000 or 13% preference capital of Rs 10,00,000, 10% debentures of
Rs 8,00,000 and Rs 12,00,000 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.
Solution
Confirmation Table
Particulars Equity financing Equity + debt financing
EBIT Rs 3,00,000 Rs 3,00,000
Less: Interest — 1,50,000
Earning before taxes 3,00,000 1,50,000
Less: Taxes 1,05,000 52,500
Earnings for equity-holders 1,95,000 97,500
Number of equity shares 30,000 15,000
EPS 6.5 6.5
( ) ( ) ( )
( ) ( ) ( )
3,00,000 Rs /0.65 1,95,000 Rs X
1,95,000 Rs - 0.65X - Or
1,95,000 Rs - 1.3X 0.65X Or
15,000
97,500 Rs 0.65X
30,000
0.65X
Or
15,000
0.35 1 1,50,000 Rs X
30,000
0.35 1 X
Or
N
t 1 I X
N
t 1 X
(i)
2 1
= =
=
=
÷
=
÷ ÷
=
÷
÷ ÷
=
÷
Confirmation Table
Particulars Equity financing Equity + Preference financing
EBIT Rs 6,00,000 Rs 6,00,000
Less: Taxes 2,10,000 2,10,000
Earning after taxes 3,90,000 3,90,000
Less: Dividends on
preference shares
— 1,30,000
Earnings for equity-holders 3,90,000 2,60,000
Number of equity shares 30,000 20,000
EPS 13 13
( )
( )
( ) ( )
6,00,000 Rs X
20,000
1,30,000 Rs 0.65X
30,000
0.65X
Or
20,000
1,30,000 Rs 0.35 1
30,000
0.35 1 X
Or
3
N
p
D I X
1
N
t 1 X
(ii)
=
÷
=
÷ ÷
=
÷
÷ ÷
=
÷
Confirmation Table
Particulars Equity
financing
Equity + Preference +
Debentures financing
EBIT Rs 4,80,000 Rs 4,80,000
Less: Interest — 1,00,000
Earnings after interest 4,80,000 3,80,000
Less: Taxes 1,68,000 1,33,000
Earning after taxes 3,12,000 2,47,000
Less: Dividends including dividend tax
on preference shares — 1,43,000
Earnings available for equity holders 3,12,000 1,04,000
Number of equity shares 30,000 10,000
EPS 18.4 18.4
( )
( ) ( )
( ) ( )( ) ( )
000 , 80 , 4 Rs X
000 , 10
000 , 43 , 1 Rs 000 , 65 Rs X 65 . 0
000 , 30
X 65 . 0
Or
000 , 10
1 . 0 1 1,30,000 Rs 35 . 0 1 000 , 00 , 1 Rs X
000 , 30
35 . 0 1 X
Or
N
Dt 1 D I X
N
t 1 X
) iii (
4
p
1
=
÷ ÷
=
+ ÷ ÷ ÷
=
÷
+ ÷ ÷
=
÷
Confirmation Table
Particulars Equity
financing
Equity + Debt +
Preference financing
EBIT Rs 5,50,000 Rs 5,50,000
Less: Interest 1,00,000 80,000
Earnings before taxes 4,50,000 4,70,000
Less: Taxes 1,57,500 1,64,500
Earning after taxes 2,92,500 3,05,500
Less: Dividends on preference
shares
— 1,30,000
Earnings for equity-holders 2,92,500 1,75,500
Number of equity shares 20,000 12,000
EPS 14.625 14.625
( )( )
( ) ( )
( )( ) ( ) ( )
000 , 50 , 5 Rs X
000 , 12
000 , 30 , 1 35 . 0 1 000 , 80 X
000 , 20
35 . 0 1 000 , 00 , 1 Rs X
Or
N
D t 1 I X
N
t 1 1 X
) iv (
4
p
2
=
÷ ÷ ÷
=
÷ ÷
÷ ÷ ÷
=
÷ ÷
Graphic Approach
The indifference point can also be determined
graphically. In order to graph the financial plan, two
sets of EBIT-EPS coordinates are required for each
financial plan. The point at which the two lines
intersect is the IP.
In order to graph the financial plan, two sets of EBIT-EPS coordinates are
required. The EPS values associated with EBIT values of Rs 2,00,000 and Rs
6,00,000 are calculated and plotted on the graph paper under each financial
plan in case of Figure 1. It may noted that 100 per cent equity financing plan
starts from origin (O) because EPS would be zero if EBIT is zero.
However, EBIT required to have the value of the EPS as zero is Rs 1,50,000,
that is, the interest charges payable on 10% debentures of Rs 15,00,000.
Therefore, the starting point of 50 per cent equity financing plan is away from
the point of the origin (i.e. it starts from Rs 1.5 lakh). The point at which the
two lines intersect is the indifference point (IP). When we draw a
perpendicular to the X-axis from the point of intersection, we have EBIT
required for the IP. A line drawn from the point of intersection and joined with
the Y-axis determines the EPS at the indifference point of EBIT.
An important point to be remembered in relation to the drawing of 33 per cent
preference share financial plan (Fig. 2), is that EPS would not be zero if the
firm’s EBIT is Rs 1,30,000, because dividend payable on preference share is
not tax-deductible. The firm must earn so much more than Rs 1,30,000 that it
is left with Rs 1,30,000 after paying taxes. This amount can be calculated
dividing Rs 1,30,000 by (1 – t). The required amount is Rs 2,00,000 [Rs
1,30,000) ÷ (1 – 0.35)]. Thus, the starting point of preference share financial
plan would be Rs 2 lakh.
0 1 2 3 4 5 6 7
6.5
13
19.5
EBIT (Rs in lakhs)
Figure 1: EBIT-EPS Analysis
Debt Advantage
Debt + Equity
Alternative
Equity Alternative
Indifference Point
Equity
Advantage
E
P
S
(
R
s
)
The indifference points of Figs. 1 and 2 correspond to what we have determined
through the algebraic approach. But the utility of the EBIT-EPS chart lies in its
being more informative regarding the EBIT-EPS relationship. It gives a bird’s eye
view of EPS at various levels of EBIT. The EPS value at the estimated level of
EBIT can be promptly ascertained. Moreover, it more easily explains why an
equity financing plan is better than other plans requiring debenture and/or
preference shares for the EBIT level below the IP.
For instance, Fig. 2 indicates that for all EBIT levels below Rs 6 lakh, the EPS
under equity alternative is greater than 33 per cent preference share financing
plan and for all EBIT levels above Rs 6 lakh, the EPS is greater under 33 per cent
financing plan than 100 per cent equity financing. The IP can be compared with
the most likely level of EBIT. If the likely level of EBIT is more than the IP, the use
of fixed cost financing plan may be recommended, otherwise equity plan would
be more suitable.
To sum up, the greater the likely level of EBIT than the indifference point, the
stronger is the case for using levered financial plans to maximise the EPS.
Conversely, the lower the likely level of EBIT in relation to the indifference point,
the more useful the unlevered financial plan would be from the view point of EPS.
In other words, financial leverage will be favourable and shareholders will get
higher EPS if the return on total investment is more than the fixed cost (interest
and preference dividend). If the return is less than the fixed financial charge, the
EPS will decline with the use of debt and the leverage will be unfavourable. The
financial leverage will have no effect on EPS in case the return on investment is
exactly equal to the fixed financial costs.
0 1
6.5
13
19.5
EBIT (Rs in lakhs)
Figure 2: EBIT-EPS Analysis
Equity + Preference
Advantage
Equity + Preference
Alternative
Equity Alternative
Indifference Point
Equity
Advantage
E
P
S
(
R
s
)
2 3 4 5 6 7 8 9 10 11 12 13
26
32.5
The indifference point may be computed in another way using market value as
the basis. Since the operational objective of financial management is the
maximisation of share prices, the market price of shares of a firm with two
different financial plans should be identical. Thus, on the basis of level of EBIT
which ensures identical market price for alternative financial plans, the
indifference point can be symbolically computed by Equation 10.
where PE
1
= P/E ratio of unlevered plan and P/E
2
= P/E ratio of levered plan.
( )
( ) ( )
) 10 (
N
D t 1 I X
E / P
N
t 1 X
E / P
2
p
2
1
1 (
¸
(
¸
÷ ÷ ÷
=
(
¸
(
¸
÷
Example 8
Determine the indifference point at which market price of equity shares of a
corporate firm will be the same from the following data:
1. Funds required, Rs 50,000.
2. Existing number of equity shares outstanding, 5,000 @ Rs 10 per share.
3. Existing 10% debt, Rs 20,000
4. Funds required can be raised either by (a) issue of 2,000 equity shares,
netting Rs 25 per share or (b) new 15 per cent debt.
5. The P/E ratio will be 7 times in equity alternative and 6 times in debt
alternative.
6. Corporate tax rate, 35 per cent.
Confirmation Table
Particulars 15% Debt issue Equity issue
EBIT Rs 47,000 Rs 47,000
Less: Interest 9,500 2,000
Earning before taxes 37,500 45,000
Less: Taxes 13,125 15,750
Earning after taxes 24,375 29,250
Number of equity shares 5,000 7,000
Earnings per share 4.875 4.18
P/E ratio (times) 6 7
Market price of the share 29.25 29.25
( ) ( ) ( ) ( )
( ) ( )
47,000 Rs x i.e. 2,13,850, Rs or4.55x
37,050) Rs 7(3.9x 9,100) Rs or5(4.55x
5,000
6,175 Rs 0.65x
7,000
1,300 Rs 0.65x
5,000
0.65 9,500 Rs x
6
7,000
0.65 2,000 Rs x
7 Or
N
t 1 I I x
P/E
N
t 1 I x
P/E
2
2 1
2
1
1
1
= =
× =
÷
=
÷
(
¸
(
¸
÷
=
(
¸
(
¸
÷
(
¸
(
¸
÷ ÷ ÷
=
(
¸
(
¸
÷ ÷
Measures of Financial Leverages
Financial leverage measures the degree of the use of debt and other fixed-cost
sources of fund to finance the assets the firm has acquired. As shown above, the
use of debt has a magnifying effect on the earnings per share. It can be said that
the higher the proportion of debt in the capital structure, the higher is the financial
leverage and vice-versa. Broadly speaking, financial leverage can be measured in
two ways: (i) stock terms, and (ii) flow terms.
1) Stock Terms
It can be measured either by (a) a simple ratio of debt to equity, or (b) by the ratio
of long-term debt plus preference share to total capitalisation. Each of these
measures indicates the relative proportion of the funds to the total funds of the
firm on which it is to pay fixed financial charges.
2) Flow Terms
The financial leverage can be measured either by (a) the ratio of EBIT to interest
payments or (b) the ratio of cash flows to interest payment, popularly called the
debt service capacity/coverage. These coverage ratios are useful to the suppliers
of the funds as they assess the degree of risk associated with lending to the firm.
In general, the higher the ‘stock’ ratios and the lower the ‘flow’ ratios, the greater is
the risk and vice-versa.
COMBINED LEVERAGE: TOTAL RISK
Combined leverage is the product of operating leverage and financial leverage.
Total risk is the risk associated with combined leverage.
DCL = DOL X DFL (11)
Thus, the DCL measures the percentage change in EPS due to percentage
change in sales. If the degree of operating leverage of a firm is 6 and its
financial leverage is 2.5, the combined leverage of this firm would be 15(6 x
2.5). That is, 1 per cent change in sales would bring about 15 per cent change
in EPS in the direction of the change in sales. The combined leverage can
work in either direction. It will be favorable if sales increase and unfavorable
when sales decrease because changes in sales will result in more than
proportionate returns in the form of EPS.
) 13 (
I EBIT
on Contributi
I EBIT
EBIT
EIBT
on Contributi
DCL
) 12 (
sales in change %
EPS in change %
EBIT in change %
EPS in change %
sales in change %
EBIT in change %
DCL
÷
=
÷
× =
= × =
SOLVED PROBLEM
A plastic manufacturing company is planning to expand its assets by 50 per
cent. All financing for this expansion will come from external sources. The
expansion will generate additional sales of Rs 3 lakh with a return of 25 per
cent on sales before interest and taxes. The finance department of the
company has submitted the following plans for the consideration of the Board.
Plan 1: Issue of 10% debentures.
Plan 2: Issue of 10% debentures for half the required amount and balance in
equity shares to be issued at 25 per cent premium.
Plan 3: Issue equity shares at 25 per cent premium.
Balance sheet of the company as on March 31
Liabilities Amount Assets Amount
Equity capital (Rs 10 per share) Rs 4,00,000 Total assets Rs 12,00,000
8% Debentures 3,00,000
Retained earnings 2,00,000
Current liabilities 3,00,000 ________
12,00,000 12,00,000
Income statement for the year ending March 31
Sales Rs 19,00,000
Operating costs 16,00,000
EBIT 3,00,000
Interest 24,000
Earning after interests 2,76,000
Taxes 96,600
EAT 1,79,400
EPS 4.48
(a) Determine the number of equity shares that will be issued if financial plan 3
is adopted.
(b) Determine indifference point between (i) plans 1 and 2, (ii) plans 1 and 3,
and (iii) plans 2 and 3.
(c) Assume that the price earnings ratio is expected to remain unchanged at 8 if
plan 3 is adopted, but is likely to drop to 6 if either plan 1 or 2 is used to
finance the expansion. Determine the expected market price of the shares in
each of the situations.
1,34,000 Rs X
88,000
0.65 24,000 Rs X
40,000
0.65 54,000 Rs - X
2
N
t 1
2
I - X
1
N
2
I
1
I - X
(iii)
1,34,000 Rs X
88,000
0.65 24,000 Rs X
40,000
0.65 84,000 Rs - X
2
N
t 1
1
I - X
1
N
t 1
2
I
1
I - X
(ii)
1,34,000 Rs X
64,000
0.65 0,000 3 Rs - 24,000 Rs - X
40,000
0.65 60,000 Rs - 24,000 Rs - X
or
2
N
t 1
2
I
1
I - X
1
N
t 1
2
I
1
I - X
(i) (b)
12.5 Rs
6,00,000 Rs
48,000 issued shares of Number (a)
Solution
=
÷
=
×
÷
=
÷
=
× ÷
=
×
÷
=
÷ ÷
=
×
=
×
÷ ÷
=
÷ ÷
= =
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Verification table
Particulars Plans
1 2 3
EBS Rs 1,34,000 Rs 1,34,000 Rs 1,34,000
Less: Interest 84,000 54,000 24,000
Earnings before taxes 50,000 80,000 1,10,000
Less: Taxes 17,500 28,000 38,500
EAT 32,500 52,000 71,500
Number of equity shares (N) 40,000 64,000 88,000
EPS 0.812 0.812 0.812
(c) Determination of market price per share under various alternative financial
plans:
Particulars Plans
1 2 3
EBIT Rs 3,75,000 Rs 3,75,000 Rs 3,75,00
0
Less: Interest 84,000 54,000 24,000
Earnings before taxes 2,91,000 3,21,000 3,51,000
Less: Taxes 1,01,850 1,12,350 1,22,850
EAT 1,89,150 2,08,650 2,28,150
N 40,000 64,000 88,000
EPS 4.73 3.26 2.59
P/E ratio 6 6 8
Market price 28.38 19.56 20.72
MINI CASE
G Manufacturing company is an important producer of lawn furniture and
decorative objectives for the patio and garden. The last year’s income
statement and balance sheet are as follows:
Income statement
Sales
Variable costs
Contribution
Fixed costs
Earnings before interest and tax (EBIT)
Interest
Earnings before tax (EBT)
Taxation
Net Income after tax
Rs 75,00,000
46,90,000
28,10,000
14,00,000
14,10,000
2,00,000
12,10,000
6,05,000
6,05,000
Balance sheet
Liabilities Amount Assets Amount
Equity capital
Reserves and surplus
Long-term debt (10%)
Current liabilities
Rs 10,00,000
42,00,000
20,00,000
5,00,000
77,00,000
Fixed assets
Inventory
Receivables
Cash
Rs 60,00,000
6,00,000
7,00,000
4,00,000
77,00,000
Figures for industry comparison:
Normal asset turnover 1.2 : 1. Normal profit margin 20 per cent
For the current year, the forecasted sales are Rs 80,00,000 and it is likely that
variable costs will remain at approximately the same percentage of sales as
was in the last year. (Figures could be rounded off). Fixed costs will rise by 10
per cent.
G has short-listed the following two product lines to be sold through its
existing distribution channels:
(1) Production and sale of metal table and chair unit that will be sold for issue
around swimming pools. This will require an investment of Rs 20,00,000,
which would involve installation of manufacturing and packaging
machinery. Sales forecast are Rs 15,00,000 per annum, variable costs
account for 2/3rd of sales value, fixed costs are Rs 2,00,000 and no
additional working capital is needed.
(2) Hardwood planter with three separate components, will be appropriate for
medium sized shrubs. This will require an investment of Rs 30,00,000 with
forecasted sales per annum of Rs 25,00,000, variable costs 64 per cent of
sales value and fixed costs of Rs 5,00,000.
Two financial plans are available:
a) It could borrow on a 10 years note at 9 per cent for either or both of the
projects of an amount not to exceed Rs 60,00,000.
b) Cumulative preference shares with a 10 per cent dividend upto an amount
of Rs 30,00,000.
Financing through the issue of equity shares would not be possible at the
present time.
Required
1) Without the new proposals, what would be the company’s operating, fixed
charges and combined leverages next year? Would the company have
favorable financial leverage?
2) How does the acceptance of each project affect the differing leverages
including asset leverages?
3) With each financing alternatives, do the company’s future earnings per
share increase or decrease, why?
Solution
(1) Income statement at projected sales of Rs 80 lakh in current year
Sales revenue Rs 80,00,000
Less: Variable costs (Rs 80 lakh × 62.5% V/V ratio) 50,00,000
Contribution 30,00,000
Less: Fixed costs (Rs 14 lakh + 10%) 15,40,000
EBIT 14,60,000
Less: Interest 2,00,000
Earnings before taxes (EBT) 12,60,000
Less: Taxes (0.50) 6,30,000
Earnings after taxes 6,30,000
Determination of leverages (without the new proposals)
DOL = Contribution/EBIT (Rs 30,00,000/Rs 14,60,000) 2.0548
DFL = EBIT/EBT (Rs 14,60,000/Rs 12,60,000) 1.1587
DCL = Contribution/EBT (Rs 30,00,000/Rs 12,60,000) Or 2.0548 ×
1.1587
2.3809
The company is said to have favourable financial leverage if it earns more on the
assets purchased (with debt funds) than the interest it pays on debt. For the
purpose, ROR on capital employed is computed. It is (Rs 14,60,000/Rs 72,00,000) =
20.28 per cent. This return is higher than 10 per cent interest payable on long-term
debt. Evidently, the firm is having positive financial leverage.
(2) Income statement showing earnings of two projects, DOL and assets leverage
Particulars Projects
Metal table and
chair unit
Hardwood planter
Sales revenue Rs 15,00,000 Rs 25,00,000
Less: Variable costs 10,00,000 16,00,000
Contribution 5,00,000 9,00,000
Less: Fixed costs 2,00,000 5,00,000
EBIT 3,00,000 4,00,000
DOL (Contribution/EBIT) 1.667 2.25
Assets leverage (Sales/Total assets) 0.75 0.83
To determine other leverages, it will be useful to extend income statement to
include the impact of financing costs.
Income statement showing other leverages (DFL and DCL) and other ratios
Particulars Projects
Metal table and chair unit
(Investments Rs 20 lakh)
Hardwood planter
(Investments Rs 30
lakh)
(i) Financed through debt plan:
EBIT Rs 3,00,000 Rs 4,00,000
Less: Interest 1,80,000 2,70,000
Earnings before taxes (EBT) 1,20,000 1,30,000
Less: Taxes (0.50) 60,000 65,000
Earnings after taxes 60,000 65,000
DFL (EBIT/EBT) 2.5 2.0
DCL (DOL × DFL) 4.1675 4.5
Rate of return on capital employed (%) 15 13.33
(ii) Financed through cumulative preference share (Rs 30 lakh) +
Rs 20 lakh debt for two combined projects EBIT
7,00,000
Less: Interest (Rs 20 lakh × 9%) 1,80,000
Earnings before taxes 5,20,000
Less: Taxes (0.50) 2,60,000
Earnings after taxes 2,60,000
Less: Dividends to preference share holders (Rs 30 lakh × 10%) 3,00,000
EAT (40,000)*
*Since EAT is negative, this financial plan is worth rejecting and hence warrants no more
calculations for other leverages.
It is apparent that acceptance of the Hardwood Planter project will adversely
affect risk level (reflected in higher DOL, DFL and DCL). While the acceptance
of Metal Table project decreases operating risk (lower DOL), it increases total
risk (as DCL is 4.15). The asset leverages are also very low.
Though the ROR on capital employed is higher for both the projects than the
interest rate paid, the acceptance of these projects will decrease the firm’s
overall rate of return on capital employed (the existing ROR on capital
employed is 20, 28 per cent).
(3) The impact of financing alternatives on company’s future EPS:
Financial plan (a): Since the rate of return on capital employed is higher (for
both the projects) than the rate of interest (9 per cent) payable on funds
borrowed, the projects will increase EPS.
Financing plan (b): Under this plan, funds are to be raised by the issue of Rs
30 lakh cumulative 10 per cent Preference shares, the EPS will decrease as
payment of 10 per cent preference dividend requires 20 per cent pre-tax return
on Rs 30 lakh; the projected pre-tax return is 17.33 per cent (Rs 5,20,000/Rs
30,00,000). In fact, taking two projects in a combined manner, the firm has
negative returns for equity-holders. As a result, this financial plan will have
depressing effect on the EPS and is not desirable.
In sum, the firm should go for both projects only when debt financing is
possible for both such projects.
doc_590728780.pptx
This is a presentation explaining what is operating leverage, financial leverage and combined leverage with the help of detailed examples.
Chapter 3
Operating, Financial And
Combined Leverage
OPERATING, FINANCIAL AND
COMBINED LEVERAGE
Operating Leverage
Financial Leverage
Combined Leverage : Total Risk
Solved Problem
Mini Case
Leverage refers to the use of an asset or source
of funds which involves fixed costs or fixed
returns. As a result, the earnings available to
the shareholders/owners are affected as also
their risk. There are three types of leverage,
namely,
1) Operating
2) Financial
3) Combined
Operating Leverage
Leverage associated with asset acquisition or investment
activities is referred to as the operating leverage. It refers to
the firm’s ability to use fixed operating costs to magnify the
effect of changes in sales on its operating profits (EBIT) and
results in more than a proportionate change (±) in EBIT with
change in the sales revenue.
Degree of operating leverage (DOL) is computed in two
ways:
1) Percentage change in EBIT/Percentage change in sales
and
2) (Sales – Variable costs)/EBIT.
The operating leverage is favourable when increase in sales
volume has a positive magnifying effect on EBIT. It is
unfavourable when a decrease in sales volume has a negative
magnifying effect on EBIT. Therefore, high DOL is good when
sales revenues are rising and bad when they are falling.
The DOL is a measure of the business/operating risk of the firm.
Operating risk is the risk of the firm not being able to cover its
fixed operating costs. The larger is the magnitude of such costs,
the larger is the volume of sales required to recover them. Thus,
the DOL depends on fixed operating costs.
Example 1
A firm sells products for Rs 100 per unit, has variable operating costs of Rs 50 per unit and fixed
operating costs of Rs 50,000 per year. Show the various levels of EBIT that would result from sale
of (i) 1,000 units (ii) 2,000 units and (iii) 3,000 units.
Solution
If sales level of 2,000 units are used as a base for comparison, the operating leverage is illustrated
in Table 1
Table 1 EBIT for Various Sales Levels
Case 2
– 50%
Base Case 1
+ 50%
1. Sales in units 1,000 2,000 3,000
2. Sales revenue Rs 1,00,000 Rs 2,00,000 Rs 3,00,000
3. Less: Variable operating cost 50,000 1,00,000 1,50,000
4. Contribution 50,000 1,00,000 1,50,000
5. Less: Fixed operating cost 50,000 50,000 50,000
6. EBIT Zero 50,000 1,00,000
–100% +100%
From the results contained in Table 1, certain generalizations follow:
1) Case 1: A 50 per cent increase in sales (from 2,000 to 3,000
units) results in a 100 per cent increase in EBIT (from Rs 50,000
to Rs 1,00,000).
2) Case 2: A 50 per cent decrease in sales (from 2,000 to 1,000
units) results in a 100 per cent decrease in EBIT (from Rs 50,000
to zero).
Example 2
A firm sells its products for Rs 50 per unit, has variable operating costs of
Rs 30 per unit and fixed operating costs of Rs 5,000 per year. Its current
level of sales is 300 units. Determine the degree of operating leverage. What
will happen to EBIT if sales change: (a) rise to 350 units, and (b) decrease to
250 units?
Solution: The EBIT for various sales levels is computed in Table 2.
Table 2: EBIT at Various Sales Levels
Case 2
–16.7%
Base Case 1
+16.7%
1. Sales in units 250 300 350
2. Sales revenue Rs 12,500 Rs 15,000 Rs 17,500
3. Less: Variable cost 7,500 9,000 10,500
4. Contribution 5,000 6,000 7,000
5. Less: Fixed operating
cost
5,000 5,000 5,000
6. EBIT Zero 1,000 2,000
– 100% + 100%
Interpretation
In case 2, 16.7 per cent decrease in sales volume (from 300 units to 250 units)
leads to 100 per cent decline in the EBIT (from Rs 1,000 to zero). On the other
hand, a 16.7 per cent increase in the sales level in case 1 (from 300 units to
350 units) results in 100 per cent increase in EBIT (from Rs 1,000 to Rs 2,000).
The two illustrations (Tables 1 and 2) clearly show 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
favorable leverage, while the latter is unfavorable. Leverage, thus, works in
both directions.
Alternative definition of Operating Leverage
When proportionate change in EBIT as a result of a given change in sales is
more than the proportionate change in sales, operating leverage exists. The
greater the DOL, the higher is the operating leverage. Symbolically,
2)
level) base (at EBIT
level) base (at on Contributi Total
F V) Q(S
V) Q(S
?Q
Q
F - V) - Q(S
V) - Q(S ?
DOL
costs. fixed Total F
unit per cost Variable V
unit per price Selling S
units in quantity Sales Q
Where
V) - Q(S ? EBIT ? F, V) Q(S EBIT
Q ?Q
EBIT ?EBIT
DOL ely, Alternativ
1) 1
sales in change Percentage
EBIT in change Percentage
DOL
(
(
=
÷ ÷
÷
= × =
=
=
=
=
= ÷ ÷ =
÷
÷
=
> =
Since the DOL exceeds 1 in both the illustrations, operating leverage exists. However, the degree of
operating leverage is higher (3 times) in the case of the firm in Example 2 as compared to the firm in
Example 1, the respective quotients being 6 and 2. The quotients mean that for every 1 per cent
change in sales, there will be 6 per cent (Examples 2) and 2 per cent (Example 1) change in EBIT in
the direction the sales change.
2
50,000 Rs
1,00,000 Rs
2) (Case 2
50%
100%
1), (Case 2
50%
100%
DOL
get, we 1 Example to 2 and 1 Equations Applying
= =
=
÷
÷
=
+
+
=
6
1,000 Rs
6,000 Rs
2) (Case 6
16.7% -
100% -
1), (Case 6
16.7%
100%
DOL
2, Example in Similarly,
= =
= =
+
+
=
Operating leverage exists only when there are fixed operating costs. If there are no
fixed operating costs, there will be no operating leverage. Consider Example 3.
Example 3
Particulars Base Level New Level
1. Units sold 1,000 1,100
2. Sales price per unit Rs 10 Rs 10
3. Variable cost per unit 6 6
4. Fixed operating cost Nil Nil
Solution The relevant computations are given in Table 3.
TABLE 3 EBIT for Various Sales Volume
Particulars Base Level New Level
1. Sales revenues Rs 10,000 Rs 11,000
2. Less: Variable costs 6,000 6,600
3. Less: Fixed costs — —
4. EBIT 4,000 4,400
Applying Equation 1, DOL = 1. Since the quotient is 1, there is no operating
leverage.
Financial Leverage
Financial leverage is related to the financing
activities of a firm. It results from the presence of
fixed financial charges (such as interest on debt and
dividend on preference shares). Since such financial
expenses do not vary with the operating profits,
financial leverage is concerned with the effect of
changes in EBIT on the earnings available to equity-
holders. It is defined as the ability of a firm to use
fixed financial charges to magnify the effect of
changes in EBIT on the earnings per share (EPS).
Example 4
The financial manager of the Hypothetical Ltd expects that its earnings before
interest and taxes (EBIT) in the current year would amount to Rs 10,000. The firm
has 5 per cent bonds aggregating Rs 40,000, while the 10 per cent preference
shares amount to Rs 20,000. What would be the earnings per share (EPS)?
Assuming the EBIT being (i) Rs 6,000, and (ii) Rs 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
TABLE 4 EPS for Various EBIT Levels
Case 2 Base Case 1
–40% +40%
EBIT
Less: Interest on bonds
Earnings before taxes (EBT)
Less: Taxes (35%)
Earning after taxes (EAT)
Less: Preference dividend
Earnings available for ordinary
shareholders
Earnings per share (EPS)
Rs 6,000
2,000
4,000
1,400
2,600
2,000
600
0.6
Rs 10,000
2,000
8,000
2,800
5,200
2,000
3,200
3.2
Rs 14,000
2,000
12,000
4,200
7,800
2,000
5,800
5.8
– 81.25%
+81.25%
The interpretation of Table 4 is as follows:
Case 1:
A 40 per cent increase in EBIT (from Rs 10,000 to Rs 14,000)
results in 81.25 per cent increase in EPS (from Rs 3.2 to Rs
5.8).
Case 2:
A 40 per cent decrease in EBIT (from Rs 10,000 to Rs 6,000)
leads to 81.25 per cent decrease in EPS (from Rs 3.2 to Re
0.6).
Example 5
A company has Rs 1,00,000, 10% debentures and 5,000 equity shares
outstanding. It is in the 35 per cent tax-bracket. Assuming three levels of EBIT
(i) Rs 50,000, (ii) Rs 30,000, and (iii) Rs 70,000, calculate the change in EPS
(base level of EBIT = Rs 50,000).
Solution
TABLE 5 EPS at Various EBIT Levels
Case 2 Base Case 1
–40% +40%
EBIT
Less: interest
Earnings before taxes
Less: Taxes
Earning after taxes
Earnings per share (EPS)
Rs 30,000
10,000
20,000
7,000
13,000
2.6
Rs 50,000
10,000
40,000
14,000
26,000
5.2
Rs 70,000
10,000
60,000
21,000
39,000
7.8
– 50%
+50%
Thus, a 40 per cent increase in EBIT in case 2 from the base level of EBIT has led to
50 per cent increase in EPS. And a decrease of 40 per cent in EBIT has decreased
the EPS by 50 per cent.
Alternative Definition of Financial Leverage
The procedure outlined above is merely indicative of the presence or
absence of financial leverage. Financial leverage can be more precisely
expressed in terms of the degree of financial leverage (DFL). The DFL can
be calculated by Eq. (3)
( )( ) | |
( ) | |( )
( ) | | ( )
( ) | | ( )
( ) | | ( )
( )
( ) | |
( ) | | ( )
( ) | |
( ) | | ( )
( )
( )
( )
( ) | | ( ) ( )
) 4 (
t 1 / D I EBIT
EBIT
t 1 / D I F V S Q
F V S Q
V S Q
F V S Q
t 1 / D I F V S Q
V S ?Q
DFL
t 1 / D I F V S Q
V S ?Q
t 1 by r denominato and numerator Dividing
D t 1 I F V S Q
t 1 V S ?Q
EPS
?EPS
/N t 1 V S ?Q ?EPS
ts, areconstan D and I F, Since,
N
D t 1 I F V S Q
N
D t 1 I EBIT
EPS
EBIT ?EBIT
EPS ?EPS
DFL ely, Alternativ
(3) 1
EBIT in change Percentage
EPS in change Percentage
DFL
p P
P
p
P
p
P
p
÷ ÷ ÷
=
÷ ÷ ÷ ÷ ÷
÷ ÷
=
÷
÷ ÷
×
÷ ÷ ÷ ÷ ÷
÷
=
÷ ÷ ÷ ÷ ÷
÷
=
÷
÷ ÷ ÷ ÷ ÷
÷ ÷
=
÷ ÷ =
÷ ÷ ÷ ÷ ÷
=
÷ ÷ ÷
=
÷
÷
=
> =
As a rule, when a percentage change in EPS resulting from a given percentage
change in EBIT is greater than the percentage change in EBIT, financial leverage
exists. In other words, financial leverage occurs when the quotient in Equation 3 is
more than one.
In both the examples, the relevant quotient is larger than one. Therefore, financial
leverage exists. But the degree of financial leverage is higher in Example 4 (2.03)
than in Example 5 (1.25). The higher the quotient of percentage change in EPS due
to percentage change in EBIT, the greater is the degree of financial leverage. The
quotient of 2.03 implies that 1 per cent change in EBIT will cause 2.03 per cent
change in EPS in the same direction (± increase/decrease) in which the EBIT
changes. With 1.25 quotient the proportionate change in EPS as a result of 1 per
cent change in EBIT will be comparatively less, that is, 1.25 per cent in either
direction.
( ) | |
1.25
10,000 Rs 50,000 Rs
50,000 Rs
1.25
40%
50%
2 Case 1.25,
40%
50%
1 Case : 5 e (ii)Exampl
2.03
0.35 1 2,000/ Rs Rs2,000 10,000 Rs
10,000 Rs
2.03
40% -
81.25
2 Case 2.03,
40%
81.25%
1 Case : 4 Example (i)For
5, and 4 Examples in 2 Case and 1 Case to 3 Equations Applying
=
÷
=
=
÷
÷
= =
+
+
=
=
÷ ÷ ÷
=
=
÷
= =
+
+
=
Degree of financial leverage (DFL): Applying Eq. (3)
(i) Case 1 = (+40% / + 40%) = 1
(ii) Case 2 = (-40% / -40%) = 1
Thus, the quotient is 1. Its implication is that 1 per cent change in EBIT will result in 1
per cent change in EPS, that is, proportionate. There is, therefore, no magnification in
the EPS.
There will be, however, no financial leverage, if there is no fixed-charged financing.
(Table 6).
TABLE 6 EPS at Various EBIT Levels
Case 2 Base Case 1
– 40% +40%
EBIT Rs 30,000 Rs 50,000 Rs 70,000
Less: Taxes (0.35) 10,500 17,500 24,500
Earnings available for equity-
holders
19,500 32,500 45,500
Number of shares 10,000 10,000 10,000
EPS 1.95 3.25 4.55
– 40%
+40%
Financial leverage involves the use of funds obtained at a fixed cost in
the hope of increasing the return to the equity-holders. When a firm earns
more on the assets purchased with the funds than the fixed cost of their
use, the financial leverage is favorable. Unfavorable leverage occurs
when the firm does not earn as much as the funds cost.
High fixed financial costs increase the financial leverage and, thus,
financial risk. The financial risk refers to the risk of the firm not being able
to cover its fixed financial costs. In case of default, the firm can be
technically forced into liquidation. The larger is the amount of fixed
financial costs, the larger is EBIT required to recover them. Thus, the DFL
depends on fixed financial costs.
EBIT-EPS Analysis
To devise an appropriate capital structure, the amount of EBIT under various
financing plans should be related to EPS. The EBIT-EPS analysis is a widely-used
method of examining the effect of financial leverage/use of debt. A financial
alternative that ensures the largest EPS is preferred, given the level of EBIT.
Example 6
Suppose a firm has a capital structure exclusively comprising of ordinary shares
amounting to Rs 10,00,000. The firm now wishes to raise additional Rs 10,00,000 for
expansion. The firm has four alternative financial plans:
(A) It can raise the entire amount in the form of equity capital.
(B) It can raise 50 per cent as equity capital and 50 per cent as 5% debentures.
(C) It can raise the entire amount as 6% debentures.
(D) 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 1,20,000, the tax rate is 35 per cent,
outstanding ordinary shares 10,000 and the market price per share is Rs 100 under
all the four alternatives.
Which financing plan should the firm select?
Solution
TABLE 7 EPS Under Various Financial Plans
Particulars Financing plans
A B C D
EBIT
Less: Interest
Earnings before taxes
Taxes
Earnings after taxes
Less: Preference dividend
Earnings available to
ordinary shareholders
Number of shares
Earnings per share (EPS)
Rs 1,20,000
—
1,20,000
42,000
78,000
—
78,000
20,000
3.9
Rs 1,20,000
25,000
95,000
33,250
61,750
—
61,750
15,000
4.1
Rs 1,20,000
60,000
60,000
21,000
39,000
—
39,000
10,000
3.9
Rs 1,20,000
—
1,20,000
42,000
78,000
25,000
53,000
15,000
3.5
The calculations in Table 7 reveal that given a level of EBIT of Rs 1,20,000, the financing
alternative B, which involves 50 per cent ordinary shares and 50 per cent debt, is the
most favorable with respect to EPS. Another disclosure of the table is that although the
proportion of ordinary shares in the total capitalization under the financing plan D is also
50 per cent, that is, equal to plan B, EPS is considerably different (lowest). The difference
in the plans B and D is due to the fact that interest on debt is tax-deductible while the
dividend on preference shares is not. With 35 per cent income tax, the explicit cost of
preference shares would be higher than the cost of debt.
Financial Break-even Point (BEP)
Financial break-even point (BEP) represents a point at which before-tax
earnings are equal to the firm’s fixed financial obligations. Symbolically, it is
computed as follows:
[I + D
p
+ D
t
)/(1 – t)] (5)
In other words, at financial BEP, EPS is zero.
Equation 5 gives before-tax earnings necessary to cover the firm’s fixed
financial obligations.
As fixed financial charges are added, the break-even point for zero EPS is
increased by the amount of the additional fixed cost. Beyond the financial
break-even point, increase in EPS is more than the proportionate increase in
EBIT. This is illustrated in Table 8, which presents the EBIT-EPS relationship
for the data in Example 6 under the various EBIT assumptions given in the
box:
1) Rs 80,000 (4 per cent return on total assets)
2) 1,00,000 (5 per cent return on total assets)
3) 1,30,000 (6.5 per cent return on total assets)
4) 1,60,000 (8 per cent return on total assets)
5) 2,00,000 (10 per cent return on total assets)
TABLE 8 EBIT-EPS Analysis under Various EBIT Assumptions for the Four Financing Plans of Example
6
(i) EBIT = Rs 80,000 (4 per cent return on investments)
Particulars Financing Plans
A B C D
EBIT
Less: Interest
EBT
Less: Taxes
EAT
Less: Preference dividend
EAT for equity-holders
EPS
80,000 80,000 80,000 80,000
— 25,000 60,000 —
80,000 55,000 20,000 80,000
28,000 19,250 7,000 28,000
52,000 35,750 13,000 52,000
— — — 25,000
52,000 35,750 13,000 27,000
2.6 2.38 1.3 1.8
(ii) EBIT = Rs 1,00,000 (5 per cent return)
EBIT 1,00,000 1,00,000 1,00,000 1,00,000
Less: Interest — 25,000 60,000 —
EBT 1,00,000 75,000 40,000 1,00,000
Less: Taxes 35,000 26,250 14,000 35,000
EAT 65,000 48,750 26,000 65,000
Less: Preference dividend — — — 25,000
EAT for equity-holders 65,000 48,750 26,000 40,000
EPS 3.25 3.25 2.6 2.67
(iii) EBIT = Rs 1,30,000 (6.5 per cent return)
EBIT 1,30,000 1,30,000 1,30,000 1,30,000
Less: Interest — 25,000 60,000 —
EBT 1,30,000 1,05,000 70,000 1,30,000
Less: Taxes 45,500 36,750 24,500 45,500
EAT 84,500 68,250 45,500 84,500
Less: Preference dividend — — — 25,000
EAT for equity-holders 84,500 68,250 45,500 59,500
EPS 4.22 4.55 4.55 3.97
(iv) EBIT = Rs 1,60,000 (8 per cent return)
EBIT 1,60,000 1,60,000 1,60,000 1,60,000
Less: Interest — 25,000 60,000 —
EBT 1,60,000 1,35,000 1,00,000 1,60,000
Less: Taxes 56,000 47,250 35,000 56,000
EAT 1,04,000 87,750 65,000 1,04,000
Less: Preference dividend — — — 25,000
EAT for equity-holders 1,04,000 87,750 65,000 79,000
EPS 5.2 5.8 6.5 5.3
Contd.
(v) EBIT = Rs 2,00,000 (10 per cent return)
EBIT 2,00,000 2,00,000 2,00,000 2,00,000
Less: Interest — 25,000 60,000 —
EBT 2,00,000 1,75,000 1,40,000 2,00,000
Less: Taxes 70,000 61,250 49,000 70,000
EAT 1,30,000 1,13,750 91,000 1,30,000
Less: Preference dividend — — — 25,000
EAT for equity-holders 1,30,000 1,13,750 91,000 1,05,000
EPS 6.5 7.6 9.1 7
It can be seen from Table 8 that when the EBIT level exceeds the financial break-even
level (Rs 25,000, Rs 60,000 and Rs 38,462 for financing alternatives, B, C and D
respectively) EPS increases. The percentage increase in EPS is the greatest when EBIT is
nearest the break-even point. Thus, in Plan C, an increase of 25 per cent in EBIT (from Rs
80,000 to Rs 1,00,000) results in a 100 per cent increase in EPS (from Re 1.3 to Rs 2.6),
whereas the percentage increase in EPS is only 40 per cent (from Rs 6.5 to Rs 9.1) as a
result of the change in EBIT at higher levels from Rs 1,60,000 to Rs 2,00,000 (i.e. 25 per
cent increase).
Contd.
Indifference point EBIT level beyond which benefits of financial leverage
accrue with respect to EPS.
The indifference point between two methods of financing can be obtained
mathematically (algebraic approach) as well as graphically.
Algebraic Approach
Mathematically, the indifference point can be obtained by using the following
symbols:
X = earnings before interest and taxes (EBIT) at the indifference point
N
1
= number of equity shares outstanding if only equity shares are issued
N
2
= number of equity shares outstanding if both debentures and equity
shares are issued
N
3
= number of equity shares outstanding if both preference and equity
shares are issued
N
4
= number of equity shares outstanding if both preference shares and
debentures are issued
I = the amount of interest on debentures
D
P
= the amount of dividend on preference shares
t = corporate income tax rate
D
t
= tax on preference dividend
For a New Company
The indifference point can be determined by using the following equations:
( ) ( ) ( )
( )
( )
( )
( ) ( )
( )
( ) ( )
(8)
N
D t 1 I X
N
t 1 X
: Debentures and shares Preference versus shares y (iii)Equit
(7A)
N
Dt 1 D t 1 X
N
t 1 X
: dividend Preference on tax with shares Preference versus shares Equity (ii)(b)
(7)
N
D t 1 X
N
t 1 X
: shares Preference versus shares Equity (ii)(a)
(6)
N
t 1 I X
N
t 1 X
: Debentures versus shares (i)Equity
4
p
1
3
p
1
3
p
1
2 1
÷ ÷ ÷
=
÷
+ ÷ ÷
=
÷
÷ ÷
=
÷
÷ ÷
=
÷
For an Existing Company
If the debentures are already outstanding, let us assume I
1
= interest paid on
existing debt, and I
2
= interest payable on additional debt, then the
indifference point would be determined by Equation 9.
( ) ( ) ( ) ( )
) 9 (
N
t 1 I I X
N
t 1 I X
2
2 1
1
1
÷ ÷ ÷
=
÷ ÷
Example 7
The financial manager of a company has formulated various financial plans
to finance Rs 30,00,000 required to implement various capital budgeting
projects:
1) Either equity capital of Rs 30,00,000 or Rs 15,00,000 10% debentures
and Rs 15,00,000 equity;
2) Either equity capital of Rs 30,00,000 or 13% preference shares of Rs
10,00,000 and Rs 20,00,000 equity;
3) Either equity capital of Rs 30,00,000 or 13% preference capital of Rs
10,00,000, (subject to dividend tax of 10 per cent), Rs 10,00,000 10%
debentures and Rs 10,00,000 equity; and
4) Either equity share capital of Rs 20,00,000 and 10% debentures of Rs
10,00,000 or 13% preference capital of Rs 10,00,000, 10% debentures of
Rs 8,00,000 and Rs 12,00,000 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.
Solution
Confirmation Table
Particulars Equity financing Equity + debt financing
EBIT Rs 3,00,000 Rs 3,00,000
Less: Interest — 1,50,000
Earning before taxes 3,00,000 1,50,000
Less: Taxes 1,05,000 52,500
Earnings for equity-holders 1,95,000 97,500
Number of equity shares 30,000 15,000
EPS 6.5 6.5
( ) ( ) ( )
( ) ( ) ( )
3,00,000 Rs /0.65 1,95,000 Rs X
1,95,000 Rs - 0.65X - Or
1,95,000 Rs - 1.3X 0.65X Or
15,000
97,500 Rs 0.65X
30,000
0.65X
Or
15,000
0.35 1 1,50,000 Rs X
30,000
0.35 1 X
Or
N
t 1 I X
N
t 1 X
(i)
2 1
= =
=
=
÷
=
÷ ÷
=
÷
÷ ÷
=
÷
Confirmation Table
Particulars Equity financing Equity + Preference financing
EBIT Rs 6,00,000 Rs 6,00,000
Less: Taxes 2,10,000 2,10,000
Earning after taxes 3,90,000 3,90,000
Less: Dividends on
preference shares
— 1,30,000
Earnings for equity-holders 3,90,000 2,60,000
Number of equity shares 30,000 20,000
EPS 13 13
( )
( )
( ) ( )
6,00,000 Rs X
20,000
1,30,000 Rs 0.65X
30,000
0.65X
Or
20,000
1,30,000 Rs 0.35 1
30,000
0.35 1 X
Or
3
N
p
D I X
1
N
t 1 X
(ii)
=
÷
=
÷ ÷
=
÷
÷ ÷
=
÷
Confirmation Table
Particulars Equity
financing
Equity + Preference +
Debentures financing
EBIT Rs 4,80,000 Rs 4,80,000
Less: Interest — 1,00,000
Earnings after interest 4,80,000 3,80,000
Less: Taxes 1,68,000 1,33,000
Earning after taxes 3,12,000 2,47,000
Less: Dividends including dividend tax
on preference shares — 1,43,000
Earnings available for equity holders 3,12,000 1,04,000
Number of equity shares 30,000 10,000
EPS 18.4 18.4
( )
( ) ( )
( ) ( )( ) ( )
000 , 80 , 4 Rs X
000 , 10
000 , 43 , 1 Rs 000 , 65 Rs X 65 . 0
000 , 30
X 65 . 0
Or
000 , 10
1 . 0 1 1,30,000 Rs 35 . 0 1 000 , 00 , 1 Rs X
000 , 30
35 . 0 1 X
Or
N
Dt 1 D I X
N
t 1 X
) iii (
4
p
1
=
÷ ÷
=
+ ÷ ÷ ÷
=
÷
+ ÷ ÷
=
÷
Confirmation Table
Particulars Equity
financing
Equity + Debt +
Preference financing
EBIT Rs 5,50,000 Rs 5,50,000
Less: Interest 1,00,000 80,000
Earnings before taxes 4,50,000 4,70,000
Less: Taxes 1,57,500 1,64,500
Earning after taxes 2,92,500 3,05,500
Less: Dividends on preference
shares
— 1,30,000
Earnings for equity-holders 2,92,500 1,75,500
Number of equity shares 20,000 12,000
EPS 14.625 14.625
( )( )
( ) ( )
( )( ) ( ) ( )
000 , 50 , 5 Rs X
000 , 12
000 , 30 , 1 35 . 0 1 000 , 80 X
000 , 20
35 . 0 1 000 , 00 , 1 Rs X
Or
N
D t 1 I X
N
t 1 1 X
) iv (
4
p
2
=
÷ ÷ ÷
=
÷ ÷
÷ ÷ ÷
=
÷ ÷
Graphic Approach
The indifference point can also be determined
graphically. In order to graph the financial plan, two
sets of EBIT-EPS coordinates are required for each
financial plan. The point at which the two lines
intersect is the IP.
In order to graph the financial plan, two sets of EBIT-EPS coordinates are
required. The EPS values associated with EBIT values of Rs 2,00,000 and Rs
6,00,000 are calculated and plotted on the graph paper under each financial
plan in case of Figure 1. It may noted that 100 per cent equity financing plan
starts from origin (O) because EPS would be zero if EBIT is zero.
However, EBIT required to have the value of the EPS as zero is Rs 1,50,000,
that is, the interest charges payable on 10% debentures of Rs 15,00,000.
Therefore, the starting point of 50 per cent equity financing plan is away from
the point of the origin (i.e. it starts from Rs 1.5 lakh). The point at which the
two lines intersect is the indifference point (IP). When we draw a
perpendicular to the X-axis from the point of intersection, we have EBIT
required for the IP. A line drawn from the point of intersection and joined with
the Y-axis determines the EPS at the indifference point of EBIT.
An important point to be remembered in relation to the drawing of 33 per cent
preference share financial plan (Fig. 2), is that EPS would not be zero if the
firm’s EBIT is Rs 1,30,000, because dividend payable on preference share is
not tax-deductible. The firm must earn so much more than Rs 1,30,000 that it
is left with Rs 1,30,000 after paying taxes. This amount can be calculated
dividing Rs 1,30,000 by (1 – t). The required amount is Rs 2,00,000 [Rs
1,30,000) ÷ (1 – 0.35)]. Thus, the starting point of preference share financial
plan would be Rs 2 lakh.
0 1 2 3 4 5 6 7
6.5
13
19.5
EBIT (Rs in lakhs)
Figure 1: EBIT-EPS Analysis
Debt Advantage
Debt + Equity
Alternative
Equity Alternative
Indifference Point
Equity
Advantage
E
P
S
(
R
s
)
The indifference points of Figs. 1 and 2 correspond to what we have determined
through the algebraic approach. But the utility of the EBIT-EPS chart lies in its
being more informative regarding the EBIT-EPS relationship. It gives a bird’s eye
view of EPS at various levels of EBIT. The EPS value at the estimated level of
EBIT can be promptly ascertained. Moreover, it more easily explains why an
equity financing plan is better than other plans requiring debenture and/or
preference shares for the EBIT level below the IP.
For instance, Fig. 2 indicates that for all EBIT levels below Rs 6 lakh, the EPS
under equity alternative is greater than 33 per cent preference share financing
plan and for all EBIT levels above Rs 6 lakh, the EPS is greater under 33 per cent
financing plan than 100 per cent equity financing. The IP can be compared with
the most likely level of EBIT. If the likely level of EBIT is more than the IP, the use
of fixed cost financing plan may be recommended, otherwise equity plan would
be more suitable.
To sum up, the greater the likely level of EBIT than the indifference point, the
stronger is the case for using levered financial plans to maximise the EPS.
Conversely, the lower the likely level of EBIT in relation to the indifference point,
the more useful the unlevered financial plan would be from the view point of EPS.
In other words, financial leverage will be favourable and shareholders will get
higher EPS if the return on total investment is more than the fixed cost (interest
and preference dividend). If the return is less than the fixed financial charge, the
EPS will decline with the use of debt and the leverage will be unfavourable. The
financial leverage will have no effect on EPS in case the return on investment is
exactly equal to the fixed financial costs.
0 1
6.5
13
19.5
EBIT (Rs in lakhs)
Figure 2: EBIT-EPS Analysis
Equity + Preference
Advantage
Equity + Preference
Alternative
Equity Alternative
Indifference Point
Equity
Advantage
E
P
S
(
R
s
)
2 3 4 5 6 7 8 9 10 11 12 13
26
32.5
The indifference point may be computed in another way using market value as
the basis. Since the operational objective of financial management is the
maximisation of share prices, the market price of shares of a firm with two
different financial plans should be identical. Thus, on the basis of level of EBIT
which ensures identical market price for alternative financial plans, the
indifference point can be symbolically computed by Equation 10.
where PE
1
= P/E ratio of unlevered plan and P/E
2
= P/E ratio of levered plan.
( )
( ) ( )
) 10 (
N
D t 1 I X
E / P
N
t 1 X
E / P
2
p
2
1
1 (
¸
(
¸
÷ ÷ ÷
=
(
¸
(
¸
÷
Example 8
Determine the indifference point at which market price of equity shares of a
corporate firm will be the same from the following data:
1. Funds required, Rs 50,000.
2. Existing number of equity shares outstanding, 5,000 @ Rs 10 per share.
3. Existing 10% debt, Rs 20,000
4. Funds required can be raised either by (a) issue of 2,000 equity shares,
netting Rs 25 per share or (b) new 15 per cent debt.
5. The P/E ratio will be 7 times in equity alternative and 6 times in debt
alternative.
6. Corporate tax rate, 35 per cent.
Confirmation Table
Particulars 15% Debt issue Equity issue
EBIT Rs 47,000 Rs 47,000
Less: Interest 9,500 2,000
Earning before taxes 37,500 45,000
Less: Taxes 13,125 15,750
Earning after taxes 24,375 29,250
Number of equity shares 5,000 7,000
Earnings per share 4.875 4.18
P/E ratio (times) 6 7
Market price of the share 29.25 29.25
( ) ( ) ( ) ( )
( ) ( )
47,000 Rs x i.e. 2,13,850, Rs or4.55x
37,050) Rs 7(3.9x 9,100) Rs or5(4.55x
5,000
6,175 Rs 0.65x
7,000
1,300 Rs 0.65x
5,000
0.65 9,500 Rs x
6
7,000
0.65 2,000 Rs x
7 Or
N
t 1 I I x
P/E
N
t 1 I x
P/E
2
2 1
2
1
1
1
= =
× =
÷
=
÷
(
¸
(
¸
÷
=
(
¸
(
¸
÷
(
¸
(
¸
÷ ÷ ÷
=
(
¸
(
¸
÷ ÷
Measures of Financial Leverages
Financial leverage measures the degree of the use of debt and other fixed-cost
sources of fund to finance the assets the firm has acquired. As shown above, the
use of debt has a magnifying effect on the earnings per share. It can be said that
the higher the proportion of debt in the capital structure, the higher is the financial
leverage and vice-versa. Broadly speaking, financial leverage can be measured in
two ways: (i) stock terms, and (ii) flow terms.
1) Stock Terms
It can be measured either by (a) a simple ratio of debt to equity, or (b) by the ratio
of long-term debt plus preference share to total capitalisation. Each of these
measures indicates the relative proportion of the funds to the total funds of the
firm on which it is to pay fixed financial charges.
2) Flow Terms
The financial leverage can be measured either by (a) the ratio of EBIT to interest
payments or (b) the ratio of cash flows to interest payment, popularly called the
debt service capacity/coverage. These coverage ratios are useful to the suppliers
of the funds as they assess the degree of risk associated with lending to the firm.
In general, the higher the ‘stock’ ratios and the lower the ‘flow’ ratios, the greater is
the risk and vice-versa.
COMBINED LEVERAGE: TOTAL RISK
Combined leverage is the product of operating leverage and financial leverage.
Total risk is the risk associated with combined leverage.
DCL = DOL X DFL (11)
Thus, the DCL measures the percentage change in EPS due to percentage
change in sales. If the degree of operating leverage of a firm is 6 and its
financial leverage is 2.5, the combined leverage of this firm would be 15(6 x
2.5). That is, 1 per cent change in sales would bring about 15 per cent change
in EPS in the direction of the change in sales. The combined leverage can
work in either direction. It will be favorable if sales increase and unfavorable
when sales decrease because changes in sales will result in more than
proportionate returns in the form of EPS.
) 13 (
I EBIT
on Contributi
I EBIT
EBIT
EIBT
on Contributi
DCL
) 12 (
sales in change %
EPS in change %
EBIT in change %
EPS in change %
sales in change %
EBIT in change %
DCL
÷
=
÷
× =
= × =
SOLVED PROBLEM
A plastic manufacturing company is planning to expand its assets by 50 per
cent. All financing for this expansion will come from external sources. The
expansion will generate additional sales of Rs 3 lakh with a return of 25 per
cent on sales before interest and taxes. The finance department of the
company has submitted the following plans for the consideration of the Board.
Plan 1: Issue of 10% debentures.
Plan 2: Issue of 10% debentures for half the required amount and balance in
equity shares to be issued at 25 per cent premium.
Plan 3: Issue equity shares at 25 per cent premium.
Balance sheet of the company as on March 31
Liabilities Amount Assets Amount
Equity capital (Rs 10 per share) Rs 4,00,000 Total assets Rs 12,00,000
8% Debentures 3,00,000
Retained earnings 2,00,000
Current liabilities 3,00,000 ________
12,00,000 12,00,000
Income statement for the year ending March 31
Sales Rs 19,00,000
Operating costs 16,00,000
EBIT 3,00,000
Interest 24,000
Earning after interests 2,76,000
Taxes 96,600
EAT 1,79,400
EPS 4.48
(a) Determine the number of equity shares that will be issued if financial plan 3
is adopted.
(b) Determine indifference point between (i) plans 1 and 2, (ii) plans 1 and 3,
and (iii) plans 2 and 3.
(c) Assume that the price earnings ratio is expected to remain unchanged at 8 if
plan 3 is adopted, but is likely to drop to 6 if either plan 1 or 2 is used to
finance the expansion. Determine the expected market price of the shares in
each of the situations.
1,34,000 Rs X
88,000
0.65 24,000 Rs X
40,000
0.65 54,000 Rs - X
2
N
t 1
2
I - X
1
N
2
I
1
I - X
(iii)
1,34,000 Rs X
88,000
0.65 24,000 Rs X
40,000
0.65 84,000 Rs - X
2
N
t 1
1
I - X
1
N
t 1
2
I
1
I - X
(ii)
1,34,000 Rs X
64,000
0.65 0,000 3 Rs - 24,000 Rs - X
40,000
0.65 60,000 Rs - 24,000 Rs - X
or
2
N
t 1
2
I
1
I - X
1
N
t 1
2
I
1
I - X
(i) (b)
12.5 Rs
6,00,000 Rs
48,000 issued shares of Number (a)
Solution
=
÷
=
×
÷
=
÷
=
× ÷
=
×
÷
=
÷ ÷
=
×
=
×
÷ ÷
=
÷ ÷
= =
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Verification table
Particulars Plans
1 2 3
EBS Rs 1,34,000 Rs 1,34,000 Rs 1,34,000
Less: Interest 84,000 54,000 24,000
Earnings before taxes 50,000 80,000 1,10,000
Less: Taxes 17,500 28,000 38,500
EAT 32,500 52,000 71,500
Number of equity shares (N) 40,000 64,000 88,000
EPS 0.812 0.812 0.812
(c) Determination of market price per share under various alternative financial
plans:
Particulars Plans
1 2 3
EBIT Rs 3,75,000 Rs 3,75,000 Rs 3,75,00
0
Less: Interest 84,000 54,000 24,000
Earnings before taxes 2,91,000 3,21,000 3,51,000
Less: Taxes 1,01,850 1,12,350 1,22,850
EAT 1,89,150 2,08,650 2,28,150
N 40,000 64,000 88,000
EPS 4.73 3.26 2.59
P/E ratio 6 6 8
Market price 28.38 19.56 20.72
MINI CASE
G Manufacturing company is an important producer of lawn furniture and
decorative objectives for the patio and garden. The last year’s income
statement and balance sheet are as follows:
Income statement
Sales
Variable costs
Contribution
Fixed costs
Earnings before interest and tax (EBIT)
Interest
Earnings before tax (EBT)
Taxation
Net Income after tax
Rs 75,00,000
46,90,000
28,10,000
14,00,000
14,10,000
2,00,000
12,10,000
6,05,000
6,05,000
Balance sheet
Liabilities Amount Assets Amount
Equity capital
Reserves and surplus
Long-term debt (10%)
Current liabilities
Rs 10,00,000
42,00,000
20,00,000
5,00,000
77,00,000
Fixed assets
Inventory
Receivables
Cash
Rs 60,00,000
6,00,000
7,00,000
4,00,000
77,00,000
Figures for industry comparison:
Normal asset turnover 1.2 : 1. Normal profit margin 20 per cent
For the current year, the forecasted sales are Rs 80,00,000 and it is likely that
variable costs will remain at approximately the same percentage of sales as
was in the last year. (Figures could be rounded off). Fixed costs will rise by 10
per cent.
G has short-listed the following two product lines to be sold through its
existing distribution channels:
(1) Production and sale of metal table and chair unit that will be sold for issue
around swimming pools. This will require an investment of Rs 20,00,000,
which would involve installation of manufacturing and packaging
machinery. Sales forecast are Rs 15,00,000 per annum, variable costs
account for 2/3rd of sales value, fixed costs are Rs 2,00,000 and no
additional working capital is needed.
(2) Hardwood planter with three separate components, will be appropriate for
medium sized shrubs. This will require an investment of Rs 30,00,000 with
forecasted sales per annum of Rs 25,00,000, variable costs 64 per cent of
sales value and fixed costs of Rs 5,00,000.
Two financial plans are available:
a) It could borrow on a 10 years note at 9 per cent for either or both of the
projects of an amount not to exceed Rs 60,00,000.
b) Cumulative preference shares with a 10 per cent dividend upto an amount
of Rs 30,00,000.
Financing through the issue of equity shares would not be possible at the
present time.
Required
1) Without the new proposals, what would be the company’s operating, fixed
charges and combined leverages next year? Would the company have
favorable financial leverage?
2) How does the acceptance of each project affect the differing leverages
including asset leverages?
3) With each financing alternatives, do the company’s future earnings per
share increase or decrease, why?
Solution
(1) Income statement at projected sales of Rs 80 lakh in current year
Sales revenue Rs 80,00,000
Less: Variable costs (Rs 80 lakh × 62.5% V/V ratio) 50,00,000
Contribution 30,00,000
Less: Fixed costs (Rs 14 lakh + 10%) 15,40,000
EBIT 14,60,000
Less: Interest 2,00,000
Earnings before taxes (EBT) 12,60,000
Less: Taxes (0.50) 6,30,000
Earnings after taxes 6,30,000
Determination of leverages (without the new proposals)
DOL = Contribution/EBIT (Rs 30,00,000/Rs 14,60,000) 2.0548
DFL = EBIT/EBT (Rs 14,60,000/Rs 12,60,000) 1.1587
DCL = Contribution/EBT (Rs 30,00,000/Rs 12,60,000) Or 2.0548 ×
1.1587
2.3809
The company is said to have favourable financial leverage if it earns more on the
assets purchased (with debt funds) than the interest it pays on debt. For the
purpose, ROR on capital employed is computed. It is (Rs 14,60,000/Rs 72,00,000) =
20.28 per cent. This return is higher than 10 per cent interest payable on long-term
debt. Evidently, the firm is having positive financial leverage.
(2) Income statement showing earnings of two projects, DOL and assets leverage
Particulars Projects
Metal table and
chair unit
Hardwood planter
Sales revenue Rs 15,00,000 Rs 25,00,000
Less: Variable costs 10,00,000 16,00,000
Contribution 5,00,000 9,00,000
Less: Fixed costs 2,00,000 5,00,000
EBIT 3,00,000 4,00,000
DOL (Contribution/EBIT) 1.667 2.25
Assets leverage (Sales/Total assets) 0.75 0.83
To determine other leverages, it will be useful to extend income statement to
include the impact of financing costs.
Income statement showing other leverages (DFL and DCL) and other ratios
Particulars Projects
Metal table and chair unit
(Investments Rs 20 lakh)
Hardwood planter
(Investments Rs 30
lakh)
(i) Financed through debt plan:
EBIT Rs 3,00,000 Rs 4,00,000
Less: Interest 1,80,000 2,70,000
Earnings before taxes (EBT) 1,20,000 1,30,000
Less: Taxes (0.50) 60,000 65,000
Earnings after taxes 60,000 65,000
DFL (EBIT/EBT) 2.5 2.0
DCL (DOL × DFL) 4.1675 4.5
Rate of return on capital employed (%) 15 13.33
(ii) Financed through cumulative preference share (Rs 30 lakh) +
Rs 20 lakh debt for two combined projects EBIT
7,00,000
Less: Interest (Rs 20 lakh × 9%) 1,80,000
Earnings before taxes 5,20,000
Less: Taxes (0.50) 2,60,000
Earnings after taxes 2,60,000
Less: Dividends to preference share holders (Rs 30 lakh × 10%) 3,00,000
EAT (40,000)*
*Since EAT is negative, this financial plan is worth rejecting and hence warrants no more
calculations for other leverages.
It is apparent that acceptance of the Hardwood Planter project will adversely
affect risk level (reflected in higher DOL, DFL and DCL). While the acceptance
of Metal Table project decreases operating risk (lower DOL), it increases total
risk (as DCL is 4.15). The asset leverages are also very low.
Though the ROR on capital employed is higher for both the projects than the
interest rate paid, the acceptance of these projects will decrease the firm’s
overall rate of return on capital employed (the existing ROR on capital
employed is 20, 28 per cent).
(3) The impact of financing alternatives on company’s future EPS:
Financial plan (a): Since the rate of return on capital employed is higher (for
both the projects) than the rate of interest (9 per cent) payable on funds
borrowed, the projects will increase EPS.
Financing plan (b): Under this plan, funds are to be raised by the issue of Rs
30 lakh cumulative 10 per cent Preference shares, the EPS will decrease as
payment of 10 per cent preference dividend requires 20 per cent pre-tax return
on Rs 30 lakh; the projected pre-tax return is 17.33 per cent (Rs 5,20,000/Rs
30,00,000). In fact, taking two projects in a combined manner, the firm has
negative returns for equity-holders. As a result, this financial plan will have
depressing effect on the EPS and is not desirable.
In sum, the firm should go for both projects only when debt financing is
possible for both such projects.
doc_590728780.pptx