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Financial Management Unit 6
Sikkim Manipal University Page No. 106
Unit 6 Leverage
Structure:
6.1 Introduction
Learning objectives
6.2 Operating Leverage
Application of operating leverage
6.3 Financial Leverage
Uses of financial leverage
6.4 Combined Leverage
Uses of DTL
6.5 Summary
6.6 Solved Problems
6.7 Terminal Questions
6.8 Answers to SAQs and TQs
6.1 Introduction
A company uses different sources of financing to fund its activities. These
sources can be classified as those which carry a fixed rate of return and
those whose returns vary. The fixed sources of finance have a bearing on
the return on shareholders. Borrowing funds as loans have an impact on the
return on shareholders and this is greatly affected by the magnitude of
borrowing in the capital structure of a firm.
Leverage is the influence of power to achieve something. The use of an
asset or source of funds for which the company has to pay a fixed cost or
fixed return is termed as leverage. Leverage is the influence of an
independent financial variable on a dependent variable. It studies how the
dependent variable responds to a particular change in independent variable.
There are three types of leverage as shown in the following diagram 6.1 –
operating, financial and combined.
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Figure 6.1: Types of leverage
Operating leverage is associated with the asset purchase activities, while
financial leverage is associated with the financial activities. However,
combined leverage is the combination of operating leverage and the
financial leverage.
6.1.1 Learning objectives
After studying this unit, you should be able to:
Explain the meaning of leverage
Mention the different types of leverage
Discuss the advantages of leverage
6.2 Operating Leverage
Operating leverage arises due to the presence of fixed operating expenses
in the firm’s income flows. A company’s operating costs can be categorised
into three main sections as shown in figure 6.2 – fixed costs, variable costs
and semi-variable costs.
Figure 6.2: Classification of operating costs
Fixed costs
Fixed costs are those which do not vary with an increase in production or
sales activities for a particular period of time. These are incurred
irrespective of the income and value of sales and generally cannot be
reduced.
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For example, consider that a firm named XYZ enterprises is planning to
start a new business. The main aspects that the firm should concentrate
at are salaries to the employees, rents, insurance of the firm and the
accountancy costs. All these aspects relate to or are referred to as ―fixed
costs‖.
Variable costs
Variable costs are those which vary in direct proportion to output and
sales. An increase or decrease in production or sales activities will have
a direct effect on such types of costs incurred.
For example, we have discussed about fixed costs in the above context.
Now, the firm has to concentrate on some other features like cost of
labour, amount of raw material and the administrative expenses. All
these features relate to or are referred to as ―Variable costs‖, as these
costs are not fixed and keep changing depending upon the conditions.
Semi-variable costs
Semi-variable costs are those which are partly fixed and partly variable
in nature. These costs are typically of fixed nature up to a certain level
beyond which they vary with the firm’s activities.
For example, after considering both the fixed costs and the variable
costs, the firm should concentrate on some-other features like production
cost and the wages paid to the workers which act at some point of time
as fixed costs and can also shift to variable costs. These features relate
to or are referred to as ―Semi-variable costs‖.
The operating leverage is the firm’s ability to use fixed operating costs to increase
the effects of changes in sales on its earnings before interest and taxes (EBIT).
Operating leverage occurs any time a firm has fixed costs. The percentage change
in profits with a change in volume of sales is more than the percentage change in
volume.
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The illustration clearly tells us that when a firm has fixed operating expenses, an
increase in sales results in a more proportionate increase in earnings before interest
and taxes (EBIT) and vice versa. The former is a favourable operating leverage and
the latter is unfavourable.
Another way of explaining this phenomenon is examining the effect of the degree of
operating leverage (DOL). The DOL is a more precise measurement. It examines
the effect of the change in the quantity produced on earnings before interest and
taxes (EBIT).
DOL = % change in EBIT / % change in output
Solved Problem -1
A firm sells a product for Rs. 10 per unit, its variable costs are Rs. 5 per
unit and fixed expenses amount to Rs. 5000 p.a. Show the various
levels of EBIT that result from sale of 1000 units, 2000 units and 3000
units.
Solution
The various levels of EBIT that result from sale of 1000 units, 2000 units
and 3000 units is as shown under in table 6.1
Table 6.1: Various levels of EBIT
Sales in units 1000 2000 3000
Sales revenue Rs. 10000 20000 30000
Variable cost 5000 10000 15000
Contribution 5000 10000 15000
Fixed cost 5000 5000 5000
EBIT 000 5000 10000
If we take 2000 units as the normal course of sales, the results can be summed
as :
A 50% increase in sales from 2000 units to 3000 units results in a
100% increase in EBIT.
A 50% decrease in sales from 2000 units to 1000 units results in a
100% decrease in EBIT.
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To put in a different way,
(ΔEBIT/EBIT) / (ΔQ/Q)
EBIT is Q(S—V)—F
Where Q is quantity
S is sales
V is variable cost
F is fixed cost
Substituting this we get,
{Q(S—V)} / {Q(S—V)—F}
Solved Problem -2
Calculate the degree of leverage (DOL) of Guptha Enterprises based
on the information provided in the table 6.2
Table 6.2: Information of Guptha enterprises
Quality produced and sold 1000 units
Variable cost Rs.200 per unit
Selling price per unit Rs. 300 per unit
Fixed expenses Rs.20, 000
Solution
DOL = {Q(S–V)} / {Q(S–V)–F}
= {1000(300–200)}/{1000(300–200)–20000}
= 100000/80000
DOL = 1.25
The degree of operating leverage of Guptha enterprises is 1.25.
If the company does not incur any fixed operating costs, there is no operating
leverage.
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Solved Problem -4
The table 6.4 shows the statistics of a firm and its sales requirements.
Compute the degree of operating leverage (DOL) according to the values
given in the table.
Table 6.4: Statistics of a firm
Sales in units 1000
Sales revenue Rs. 10000
Variable cost 5000
Contribution 5000
Fixed cost 0
EBIT 5000
Solution
DOL= {Q(S—V)} / {Q(S—V)—F}
{1000(5000)} / {1000(5000) – 0}
= 5000000/5000000
= DOL=1
The degree of operating leverage according to the values given in the
table is 1.
Solved Problem - 3
Calculate the degree of leverage (DOL) of Utopia Enterprises based on
the information provided in the table 6.3
Table 6.3: Information of Utopia Enterprises
Quality produced and sold 2000 units
Variable cost Rs.300 per unit
Selling price per unit Rs. 400 per unit
Fixed expenses Rs.25, 000
Solution
DOL = {Q(S–V)} / {Q(S–V)–F}
= {2000(400–300)}/{2000(400–300)–25000}
= 200000/175000
DOL = 1.14
The degree of operating leverage of Utopia Enterprises is 1.14.
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As operating leverage can be favourable or unfavourable, high risks are attached to
higher degrees of leverage. As DOL considers fixed expenses, a larger amount of
these expenses increases the operating risks of the company and hence a higher
degree of operating leverage. Higher operating risks can be taken when income
levels of companies are rising and should not be ventured into when revenues
move southwards.
6.2.1 Application of Operating Leverage
The applications of operating leverage are as follows:
Business risk measurement
Production planning
Measurement of business risk
Solved Problem - 5
The table 6.5 given below shows the statistics of a firm and its sales
requirements. Compute the degree of operating leverage (DOL)
according to the values given in the table.
Table 6.5: Statistics of a firm
Sales in units 2000
Sales revenue Rs. 20000
Variable cost 10000
Contribution 6000
Fixed cost 0
EBIT 6000
Solution
DOL= {Q(S—V)} / {Q(S—V)—F}
{2000(10000)} / {2000(10000) – 0}
= 2000000/2000000
= DOL=1
The degree of operating leverage according to the values given in the
table is 1.
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Risk refers to the uncertain conditions in which a company performs. A
business risk is measured using the degree of operating leverage (DOL)
and the formula of DOL is:
DOL = {Q(S–V)} / {Q(S–V)–F}
Greater the DOL, more sensitive is the earnings before interest and tax
(EBIT) to a given change in unit sales. A high DOL is a measure of high
business risk and vice versa.
Production planning
A change in production method increases or decreases DOL. A firm can
change its cost structure by mechanising its operations, thereby reducing its
variable costs and increasing its fixed costs. This will have a positive impact
on DOL. This situation can be justified only if the company is confident of
achieving a higher amount of sales thereby increasing its earnings.
6.3 Financial Leverage
Financial leverage as opposed to operating leverage relates to the financing
activities of a firm and measures the effect of earnings before interest and
tax (EBIT) on earnings per share (EPS) of the company.
A company’s sources of funds fall under two categories –
Those which carry a fixed financial charges like debentures, bonds and
preference shares and
Those which do not carry any fixed charges like equity shares
Debentures and bonds carry a fixed rate of interest and have to be paid off
irrespective of the firm’s revenues. Though dividends are not contractual
obligations, dividend on preference shares is a fixed charge and should be paid off
before equity shareholders are paid any. The equity holders are entitled to only the
residual income of the firm after all prior obligations are met.
Financial leverage refers to the mix of debt and equity in the capital
structure of the firm. This results from the presence of fixed financial
charges in the company’s income stream. Such expenses have nothing to
do with the firm’s performance and earnings and should be paid off
regardless of the amount of earnings before income and tax (EBIT).
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It is the firm’s ability to use fixed financial charges to increase the effects of
changes in EBIT on the EPS. It is the use of funds obtained at fixed costs
which increase the returns on shareholders.
A company earning more by the use of assets funded by fixed sources is
said to be having a favourable or positive leverage. Unfavourable leverage
occurs when the firm is not earning sufficiently to cover the cost of funds.
Financial leverage is also referred to as “Trading on Equity”.
Solved Problem -6
The EBIT of a firm is expected to be Rs. 10000. The firm has to pay
interest at a rate of 5% on debentures of worth Rs. 25000. It also has
preference shares worth Rs. 15000 carrying a dividend of 8%. How
does EPS change if EBIT is Rs. 5000 and Rs. 15000? Tax rate may
be taken as 40% and number of outstanding shares as 1000.
Solution
The various changes of EPS if EBIT is Rs. 15,000, Rs. 10,000 and
Rs. 5,000 is shown under in table 6.6
Table 6.6: Various changes of EPS
EBIT 5000 10000 15000
Interest on debt 1250 1250 1250
EBT 3750 8750 13750
Tax 40% 1500 3500 5500
EAT 2250 5250 8250
Preference div. 1200 1200 1200
Earnings available to equity holders
1050 4050 7050
EPS 1.05 4.05 7.05
Interpretation
A 50 % increase in EBIT from Rs.10,000 to Rs.15,000 results in
74% increase in EPS
A 50 % decrease in EBIT from Rs.10,000 to Rs.5,000 results in
74% decrease in EPS
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This example shows that the presence of fixed interest source funds leads to a
value more than that occurs due to proportional change in EPS. The presence of
such fixed sources implies the presence of financial leverage. This can be
expressed in a different way. The degree of financial leverage (DFL) is a more
precise measurement. It examines the effect of the fixed sources of funds on EPS.
DFL = %change in EPS
%change in EBIT
DFL={ΔEPS/EPS} ÷ {ΔEBIT/EBIT}
Or DFL = EBIT ÷ {EBIT—I—{Dp/(1-T)}}
I is Interest, Dp is dividend on preference shares, T is tax rate.
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Solved Problem -7
Kusuma Cements Ltd. has an EBIT of Rs. 5,00,000 at 5000 units of
production and sales. The capital structure of the company is briefly
described in table 6.7
Table 6.7: Capital structure of the company
Capital structure Amount Rs.
Paid up capital 500000 equity shares of Rs. 10 each
5000000
12% Debentures 400000
10% Preference shares of Rs. 100 each 400000
Total 5800000
Corporate tax rate may be taken at 40%
Solution
EBIT 500000
Less Interest on debentures 48000
EBT 452000
DFL= EBIT ÷ {EBIT—I—{Dp/(1-T)}}
500000/(500000—48000—{40000/(1—0.40)}
DFL=1.30
The degree of financial leverage of Kusuma Cements Ltd. is found to
be 1.30.
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6.3.1 Use of Financial Leverage
Studying the degree of financial leverage (DFL) at various levels makes
financial decision-making, on the use of fixed sources of funds, for funding
activities easy. One can assess the impact of change in earnings before
interest and tax (EBIT) on earnings per share (EPS).
Like operating leverage, the risks are high at high degrees of financial leverage
(DFL). High financial costs are associated with high DFL. An increase in financial
costs implies higher level of EBIT to meet the necessary financial commitments.
Solved Problem - 8
XYZ Enterprises Ltd. has an EBIT of Rs. 2,00,000 at 4000 units of production
and sales. The capital structure of the company is briefly described in table 6.8
Table 6.8: Capital structure
Capital structure Amount Rs.
Paid up capital 200000 equity shares of Rs. 10 each
2000000
10% Debentures 500000
5% Preference shares of Rs. 100 each 500000
Total 3000000
Corporate tax rate may be taken at 50%
Solution
EBIT 200000
Less Interest on debentures 50000
EBT 150000
DFL= EBIT ÷ {EBIT—I—{Dp/(1-T)}}
200000/(200000—50000—{25000/(1—0.50)}
DFL=2.0
The degree of financial leverage of XYZ Enterprises is found to be 2.0.
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A firm which is not capable of honouring its financial commitments may be forced to
go into liquidation by the lenders of funds. The existence of the firm is shaky under
these circumstances.
On one side the trading on equity improves considerably by the use of borrowed
funds and on the other hand, the firm has to constantly work towards higher EBIT to
stay alive in the business. All these factors should be considered while formulating
the firm’s mix of sources of funds.
One main goal of financial planning is to devise a capital structure in order to
provide a high return to equity holders. But at the same time, this should not be
done with heavy debt financing which drives the company on to the brink of winding
up.
Impact of financial leverage
Highly leveraged firms are considered very risky and lenders and creditors
may refuse to lend them further to fuel their expansion activities. On being
forced to continue lending, they may do so with their own conditions like
earning a minimum of X% EBIT or stipulating higher interest rates than the
market rates or no further mortgage of securities.
Financial leverage is considered to be favourable till such time that the rate
of return exceeds the rate of return obtained when no debt is used.
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The company not using debt to finance its assets has a higher DFL compared to
that of a company using it. Financial leverage does not exist when there is no fixed
charge financing.
6.4 Total or combined leverage
The combination of operating and financial leverage is called combined
leverage. Operating leverage affects the firm’s operating profit EBIT and
financial leverage affects PAT or the EPS. These cause wide fluctuations in
EPS. A company having a high level of operating or financial leverage will
find a drastic change in its EPS even for a small change in sales volume.
Companies whose products are seasonal in nature have fluctuating EPS,
but the amount of changes in EPS due to leverages is more pronounced.
Solved Problem - 9
The following table 6.9 displays the balance sheets of two firms – firm A
and firm B.
Table 6.9: Balance sheets of firms A and B
Balance sheet of A Balance sheet of B
Equity capital
100000 Assets 100000 Equity capital
40000 Assets 100000
Debt @ 15%
60000
Total 100000 Total 100000 Total 100000 Total 100000
Both the companies earn an income before interest and tax of
Rs. 40000. Calculate the DFL and interpret the results thereof.
Solution
DFL= )}}T1/(Dp{IEBIT{
EBIT
Company A = 10040000
40000
Company B = 29.10900040000
40000
The degree of financial leverage of the companies A and B are 1 and
1.29.
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The combined effect is quite significant for the earnings available to ordinary
shareholders. Combined leverage is the product of degree of operating
leverage (DOL) and degree of financial leverage (DFL).
DTL = )}T1/(Dp{IF)VS(Q
)VS(Q
Solved Problem -10
Calculate the DTL of Pooja Enterprises Ltd., given the information
regarding the expenses, shares and sales of the company in table 6.10
Table 6.10: Details of Pooja Enterprises Ltd.
Quantity sold 10,000 units
Variable cost per unit Rs.100 per unit
Selling price per unit Rs.500 per unit
Fixed expenses Rs.10,00,000
Number of equity shares 1,00,000
Debt Rs.10,00,000 @ 20% interest
Preference shares dividend 10,000 shares of Rs.100 each @ 10%
Tax rate 50%
Solution
DTL = )}T1/(Dp{IF)VS(Q
)VS(Q
}5.0/100000{2000001000000)100500(10000
)100500(10000
DTL=1.53
Cross verification:
DOL = }F)VS(Q{
)}VS(Q{
1000000)100500(10000
)100500(10000
DOL=1.33
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EBIT = [Q(S-V)-F}
DFL= )}}T1/(Dp{IEBIT
EBIT
}5.0/100000{2000003000000
3000000
DFL=1.15
DTL=DOL*DFL
1.53 =1.33*1.15
Hence the degree of total leverage of Pooja Enterprises Ltd. is 1.54.
Solved Problem -11
Calculate the degree of total leverage of Utopia Enterprises Ltd., given
the following information regarding the expenses, shares and sales of the
company in table 6.11.
Table 6.11: Details of Utopia Enterprises Ltd.
Quantity sold 20,000 units
Variable cost per unit Rs.200 per unit
Selling price per unit Rs.600 per unit
Fixed expenses Rs.20,00,000
Number of equity shares 1,50,000
Debt Rs.20,00,000 @ 20% interest
Preference shares dividend 20,000 shares of Rs.200 each @ 10%
Tax rate 40%
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Solution
DTL = )}T1/(Dp{IF)VS(Q
)VS(Q
}6.0/400000{4000002000000)200600(20000
)200600(20000
DTL=1.62
Cross verification:
DOL= }F)VS(Q{
)}VS(Q{
2000000)200600(20000
)200600(20000
DOL=1.33
DFL= )}}T1/(Dp{IEBIT
EBIT
}6.0/400000{4000006000000
6000000
DFL=1.22
DTL=DOL*DFL
1.62 = 1.33*1.22
Hence the degree of total leverage of Utopia enterprises Ltd. is 1.60
Financial Management Unit 6
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Solved Problem -12
Calculate the degree of total leverage of CMA Enterprises Ltd., given the
following information regarding the expenses, shares and sales of the
company in table 6.12
Table 6.12: Details of CMA Enterprises Ltd.
Quantity sold 30,000 units
Variable cost per unit Rs.300 per unit
Selling price per unit Rs.700 per unit
Fixed expenses Rs.30,00,000
Number of equity shares 2,00,000
Debt Rs.30,00,000 @ 30% interest
Preference shares dividend 30,000 shares of Rs.200 each @ 20%
Tax rate 30%
Solution
DTL = )}T1/(Dp{IF)VS(Q
)VS(Q
}7.0/1200000{9000003000000)300700(30000
)300700(30000
DTL=1.88
Cross verification:
DOL= }F)VS(Q{
)}VS(Q{
3000000)300700(30000
)300700(30000
DOL=1.33
DFL= )}}T1/(Dp{IEBIT
EBIT
}7.0/1200000{9000006000000
6000000
DFL=1.77
DTL=DOL*DFL
1.33*1.77=2.35
Hence the degree of total leverage of CMA enterprises Ltd. is 2.35
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6.4.1 Uses of degree of total leverage (DTL)
Degree of total leverage (DTL) measures the total risk of the company as
DTL is a combined measure of both operating and financial risk
Degree of total leverage (DTL) measures the variability of EPS
6.5 Summary
Leverage is the use of influence to attain something else. The advantage a
company has, with the current status of the leverage can be used to gain
other benefits. There are three measures of leverage – operating leverage,
financial leverage and total or combined leverage. Operating leverage
examines the effect of change in quantity produced upon EBIT and is useful
to measure business risk and production planning. Financial leverage
measures the effect of change in EBIT on the EPS of the company. It also
refers to the debt-equity mix of a firm. Total leverage is the combination of
operating and financial leverages.
Self Assessment Questions
Fill in the blanks:
1. __________ arises due to the presence of fixed operating expenses in
the firms income flows
2. EBIT is calculated as _______.
3. Higher operating risks can be taken when ______ of companies are
rising.
4. Dividend on _________ is a fixed charge.
5. Financial leverage is also referred to as ___________.
6. Operating leverage is categorised into _____, ____ and _______.
7. The three types of leverage a company faces are ______, ________
and __________.
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6.6 Solved Problems
13. The information, shown in table 6.13, has been collected from
the annual report of Garden Silks. What is the degree of financial
leverage?
Table 6.13: Annual report of Garden silks
Total sales Rs.14,00,000
Contribution ratio 25%
Fixed expenses Rs.1,50,000
Outstanding bank loan Rs.4,00,000 @ 12.5%
Applicable tax rate 40%
Solution
DFL = EBIT / (EBIT-I) = 200000/200000-50000 = 1.33
EBIT = Sales*25% less fixed expenses
1400000*25% = 350000-150000 = 200000
14. Suppose X and Y have provided the information regarding the
sales and the cost of their expense in table 6.14. Which firm do you
consider to be risky?
Table 6.14: Information of X and Y
X Ltd. Y Ltd.
Sales in units 40000 40000
Price per unit 60 60
Variable cost p.a. 20 25
Fixed financing cost Rs. 100000 Rs. 50000
Fixed financing cost Rs. 300000 Rs. 200000
Solution:
DOL = Q(S-V) / Q(S-V)-F
Company X: 40000(60-20) / 40000(60-20)-400000
1600000/1200000 = 1.33
Company Y: 40000(60-25) / 40000(60-25)-250000
1400000/1150000= 1.22
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15. Calculate EPS with the following information shown in table 6.15.
Table 6.15: Information of a firm
EBIT Rs.11,80,000
Interest Rs.2,20,000
No. of outstanding shares 40,000
Tax rate applicable 40%
Solution:
Earnings per share is calculated using the table 6.16
Table 6.16 Earnings per share
EBIT Rs.11,80,000
Less interest Rs.2,20,000
EBT 9.60,000
Tax @ 40% Rs.3,84,000
EAT Rs.5,76,000
EPS = EAT/no of shares outstanding
576000/40000 = Rs. 14.4
16. The leverages of three firms is as shown in table 6.17 given
below. Which one of the combinations should be chosen for the
combined leverage to be maximum and what are the inferences?
Table 6.17: Leverages of three firms
A B C
Operating leverage 1.14 1.23 1.33
Financial leverage 1.27 1.3 1.33
Solution:
We should calculate the combined leverage to draw inferences.
Combined leverage of A is 1.14*1.27 = 1.45,
Combined leverage of B is 1.23*1.3 = 1.60,
Combined leverage of C is 1.33*1.33 = 1.77
We find that the combined leverage is highest for firm C and this
suggests that this firm is working under very high risky situation.
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6.7 Terminal Questions
1. Mishra Ltd. provides the information as shown in the table 6.11. What is
the degree of operating leverage?
Table 6.18: Details of Mishra Ltd.
Output 25,000 units
Fixed costs Rs.15,000
Variable cost per unit Rs. 0.50
Interests on borrowed funds Rs.15,000
Selling price per unit Rs. 1.50
2. X Ltd. provides the following information as shown in table 6.19. What is
the degree of financial leverage?
Table 6.19: Details of X Ltd.
Output 25,000 units
Fixed costs Rs. 25,000
Variable cost Rs. 2.50 per unit
Interest on borrowed funds Rs.15,000
Selling price Rs. 8 per unit
3. The information available in table 6.20 describes the sales, costs and
interests of two firms. Comment on their relative performance through
leverage?
Table 6.20: Sales and costs of two firms A and B
A Ltd. (Rs. In lakhs) B Ltd. (Rs. In lakhs)
Sales 1000 1500
Variable cost 300 600
Fixed cost 250 400
EBIT 450 500
Interest 50 100
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4. ABC Ltd. provides the information as shown in table 6.21 regarding the
cost, sales, interests and selling prices. Calculate the DFL.
Table 6.21: Details of ABC Ltd.
Output 20,000 units
Fixed costs Rs.3,500
Variable cost Rs.0.05 per unit
Interest on borrowed funds Nil
Selling price per unit 0.20
6.8 Answers to SAQs and TQs
Answers to Self Assessment Questions
1. Operating leverage
2. Q(S—V)—F
3. Income levels
4. Preference shares
5. Trading on Equity
6. Fixed costs, variable costs and semi-variable costs.
7. Operating leverage, financial leverage and combined leverage.
Answers to Terminal Questions
1. Hint DOL = }F)VS(Q{
)}VS(Q{
2. Hint DFL = )}}T1/(Dp{IEBIT{
EBIT
3. Hint calculate DFL
4. Hint calculate DFL = )}}T1/(Dp{IEBIT
EBIT