Leverage

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Chapter VIII

Leverage

Leverage: Financial ContextLeverage in the general sense means influence of poweri.e. utilizing the existing resources to attain somethingelse. To define leverage in terms of financial analysis-Leverage is the influence which an independentfinancial variable has over a dependent! related financialvariable. When leverage is measured between twofinancial variables it explains how the dependentvariable responds to a particular change in theindependent variable. To explain further, let X be anindependent financial variable and Y its dependentvariable, then the leverage which Y has with X can beassessed by the percentage change in Y to a percentagechange in X.

LY/LX = ~ Y/y

~XIx

where

LY/LX measure of the leverage whichdependent Y has with independent X

change in X

change in Y

percentage change in X

percentage change in Y

AX

I:1Y

A X.-x

A Y/y

Measures of Leverage

To better understand the importance of leverage infinancial analysis, it is imperative to understand thethree measures of leverage.. Operating Leverage

. Financial Leverage

.. CoinbinedJ Total Leverage

These three measures of leverage depend to a largeextent on the various income statement items and the

relationship that exists between them. Given below isthe Income Statement of XYZ Company Ltd. and therelatiqnship that exits between the various items of thestatement:

Income Statement of XYZCompany Ltd.

Hence,

EBIT = Q x S - Q x V - F = Q(S-V}--F

EPS = [(EBIT - I)(I-T)-Dp]/N

- [Q(S-V)-F-I] (I-T)-Dp- N

(i)

(ii)

. (iii)

where N =No. of, Equity Shareholders

The above three equations (i),(ii) and (iii)] whichestablish the relationship between the various items ofthe Income Statement form the base for themeasurement of the different leverages.

OPERATING LEVERAGE

Operating leverage examines the effect of the changein the quantity produced on the EBIT of the companyand is measured by calculating the Degree of OperatingLeverage (DO~).

DOL =Percentage change in EBIT/ Percentage changein Output

t. EBITJEBIT

t. QlQFrom Eq(i) EBIT =Q(S - V) - F

Substituting for EBIT, we getDOL = [Q(S - V)] / [Q(S - V) - F]Illustration 1

Calculate the DOL for XYZ Company Ltd. given ti;,;following additional information:

Quantity produced =Variable cost per unit =Selling price per unit =Fixed Asset =

=

( i\')

5,000Rs.200

Rs.500

Rs.90,OOO

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DOL of XYZ Company LId.. = [5.00)(500 - 200)]/[5CXX)(500- 2(x) - 9OO,OOOJ

= 2.50

Application and Utility of the Operating Leverage

It is important to know how the operating leverage ismeasured, but equally essential is to understand itsapplication and utility in financial analysis. Tounderstand the application of DOL one has tounderstand the behavior of DOL vis-a-vis the changesin the output by calculating the DOL at the variouslevels of Q.

Q = F/(S - V)

For XYZ Company LId.:

Q = 9,00,000/(500 - 200) = 3,000

After measuring the DOL for a particular company atvarying levels of output the following observations canbe made:. Each level of output has a distinct DOL.

DOL is undefined at the operating break-even point.

If Q is less than the operating break-even point,then DOL will be negative (which does not implythat an increase in Q leads to a decrease in EBIT).

If Q is greater than the operating break-even point.then the DOL will be positive. However, the DOLwill start to decline as the level of output increasesand will reach a limit of I.

..

.

IMPLICATIONS

Determining behavior of EstT

DOL answers the following type of question: Ifoutput (quantity produced and sold) is increased by10 percent by what percentage will the operatingincome increase? If the DOL of a firm is say. 2, thena 10% increase in the level of output will increaseoperating income by 25%. A large DOL indicatesthat small fluctuations in the levcl of output willproduce large fluctuations in the Icvel of operatingIncome.

In Table-8.1. two firms with different cost structuresare compared.

Financial Management

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Cost and Profit Schedules for

Bell Metal Works nnd Fibre Glass Ltd.

,.BeUMelalWorks'.,.,.,;.. ,..f'. ,Rm! Glass LknIted. .

~;.:SaIes TotaJ,<',!:m..Ti.:..UjIISt~j.,SaI!IS A;';ToIal:. EBJ;1:(Prod.ii:OOl. Ope ti1g'.' .1"".1~ piOOi~(I;}""'Y');:"~'i8tiOg. ..," >;;~

~;~~~PQ ..f~4...).!~~~~l*~1~';~.";C~'~,~

}~};,..00G1.J'~ ;;,~~~{~lIi~~~20.000. 2.00,000 .2.30.000 ~'(30,ooo) /'20.000; 2.00'00()~'OOO :'(90.000),

3O.ooo~.00.OOO '~oo,ocx)::'i~){o ""~"'3.oo:000~:40;OOb~(~ooi;

40.000 . 4,00.000 3.70,000, :3),000.,1: -40;000';4.00.000 :;,~:oo,ooo '.~';1'0.000

50;000,:5.00.000 4.40.000})~.E01m p'r,qMo~'~:oOO~'4.~»JOWi:W~

6O.000:'.6.00.0005.10,OOOl:.;i,~:~. ~ioPoJ;6,OO;ooO~1,9O.000".j.10,OOO

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~::i7,Oo.oood5,80..000:~~I::?o.oQQ.~i70r~ ': " ", ~'~~,~,.4P.QOO.,;1:60.":~909

-80:OOO~8,00.000 ,'i;;So;oo6'$i;Sb';ooo .~ '{S';90',oOO;;:60.000

ifs~:iiitl~~iFrom the table, we can see [hat Bell Metal Works haslower fixed costs and higher variable cost per unit when.compared to Fibre Glass Limited. The selling price perunit (P) of both firms is the same, viz., Rs.lO. Aninteresting point we notice that at an output of 50,000units both firms have the same profit i.e. Rs.60,000.However, as sales fluctuate. the EBIT of Bell MetalWorks fluctuates for less than the EBIT of FibreGlass Limited. This brings us to the conclusion thatthe DOL of Fibre Glass Limited is greater than theDOL of Bell Metal Works. Let us compute the DOLof these two firms at an output of 50,000 units.

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For Bell Metal \-Vorks:

DOL = [50.CXX>(10 - 7)] 1 [50,CXX>]0 - 7) - 90.000]= 2.5

For Fibre Glass Limited:

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DOL = [50.000 (10 - 5)J 1 [50.CXXXJO- 5) - 190,000]= 4.17

.11

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The figures prove our conclusion to be right.. Measurement of Business Risk

We know that the greater the DOL. the more sensitive

is EBIT to a given change in unit sales. i.e. the greateris the risk of exceptional losses if sales becomedepressed. DOL is therefore a measure of the firm's

business risk. Business risk refers to the uncertainty orvariability of the firm' s EB IT. So, every thing elsebeing equal, a higher DOL means higher business riskand vice-versa.

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". Production Planning

DOL is also important in production planning. Forinstance. thc finn may have the opportunity to changeits cost structure by introducing labor - saving

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machIi, 'y, thereby reducing variable labor overheadwhile liI'reasing the fixed costs. Such a situation willincrease DOL. Any method of production whichincrease s DOL is justified only if there is a very great

probahillty that sales will be high so that the firm canenjoy :he increased earnings of increased DOL.

FINANCIAL LEVERAGE

While operating leverage measures the change in theEBlT of a company to a particular change in theoutpU( i,he financial leverage measures the effect ofthe change in EBIT on the EPS of the company.Financial leverage also refers to the mix of debt and

equity in the capital structure of the company. Themeasure of financial leverage is the Degree ofFinancia! Leverage (DFL) and it can be calculatedas follows:

DFL = (percentage change in EPS)/ (percentagechange in EBIT)

DFL =(L\ EPSIEPS)/(6 EBITIEBIT)

Substituting Eq(ii) for EPS we get,

DFL = EBIT Eq(v)

EBIT - I - ~(i-T)

Taking the example of XYZ Company Ltd., which hasan EB IT of Rs.6,00,OOOat 5,000 level of production.

The capital structure of the company is as follows:

Capital. SIr.JCtJre, .' ,;'n i/', ,( ~ , "~'0:fr;;.j ,/:i;;ds\AmOOnt.(Rs.)

~d;:=.~~~~!,~:j~J!!!i~!1O'Y.Preferaoce.Sharns ':.,'.i;~.' ': ".,,,,-i".:p:,:i',:.:,.5000 PI8I~,ceShares CIRs.100'h/~~:'. ,;"':"':i~':j'Z"}/,.:..5,oo,OOOTotal ,;6,00,0000 .

Let us now calculate the DFL of XYZ Company Ltd.

Earnings Before Interest and Tax (EBIT) =Rs.6,00,000

Interest on Long-term Debt (I) = Rs.75.oo0Preference Dividend (Dp) = Rs.50,OOO

Corporate Tax (T) = 50%

DFL = 600,000

6,00.000 - 75,000 - 50,0001-0.5

= 1.41

Application and Utility of the Financial

leverage

Financial leverage when measured for various levelsof EBIT will aid in understanding the behavior of DFL

and also ex(>lain its utility in financial decision making.Consider the case of XYZ Company Ltd. to measureDFL for varying levels of EBIT.

Leverage

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The DFL at EBIT levci of 175000 is undefined and

this point is the Financial Break-even Point. It can beJefined as follows:

EBIT = I + Dp/(l - T)

The following observations can also be made fromstudying the behavior of DFL.. Each level of EBIT has a distinct DFL.. DFL is undefined at the financial Break-even Point.

. DFL will be negative when the EBIT level goes.below the Financial Break-even Point.

DFL will be positive fof .all values of EBIT thatare above the Financial Break-even Point. This willhowever start to decline as EBIT increases and willreach a limit of I.

By assessing the DFL one can understand the impactof a change in EBIT on the EPS of the company. Inaddition to this it also helps in assessing the financialrisk of the firm.

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IIImpact of Financial leverage on Investor'sRate of Return

Let us see with th~ help of a very simple example, howfinancial leverage affects return on equity. A companyneeds a capital of Rs.IO,OOO to operate. This moneymay be brought in by the shareholders of the company.Alternatively, a part of this money may also be broughtin through debt financing. If the management raisesRs.lO,Ooo from shareholders, the company is notfinancially leveraged and would have the foHowingbalancesheet.

LiabiUtles

EquitYCapita!

till

~~ 'j .', Rs."1. Cash . ' .".: -10,000 ,--

The company commences operations which leads tothe preparation of the following simplified version ofits income statement.

I

As.

10,000

Salesi Expoo*

EBIT :"Tax 0 50%

Net Profrt

Rs.'10.000-',7.000

- . 3.ooQ~1.500'

; ,

What is the return the company has earned on theowner's investment? We see that the return on equityis 15%. The net profit of Rs.1.500 may be paid fullyor partly to the shareholders as dividends or may beretained to finance future activities of the company.Either way the Return on Equity is 15%.

147

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What happens to the owner's rate of the return if themanagc'TIent decides to finance a part of thi totalinvestment required of Rs.IO,OOO through debtfinancing? The answer to this question depends on

. the proportion of total investment which themanagement decides to finance through debt (DebtEquity Ratio the finn aspires to), and. the interest rate on borrowed funds.

If the management has decided on a Debt Equity Ratio

of 2:1, total borrowings will amount to I0.000 x j =Rs.6,667. Assuming that the company is able to raisethis amount at an interest rate of say, 15%, thecompany's balance sheet will appear as follows:

::C:~tAI ,',",:}~;J~, ,3.~i~~';"""A~i~L,;}~.~Debt Capital: '- ',;~i: !<I..ti@~'1~i!.' "6,667r\"'\1:!o.>I~l, >'<;\j~"':>-~?"f' ;" ''..\

, ' , ,,~>. " 10:000 ~" '~";'To:ooo

The company now has an added financial burden ofpayment of interest on the amount it has borrowed. Theincome statement wil! now show as follows:

Rs,

1- . "pro I

~nses " ;'" .,', '7.000

£BIT, ",' , , -'t-..,'-;:':, ' . ,. ", ." '

,,

~'OOO

Interest Charges ',~'-- ", "1;000Profit before Tax (PaT),\;::" :, .;', , ,>', ',' ,:; ;'2,000

Tax Q 50% ,,:;1,~,f:,';'.' ,'::', 1,POO,Net Profrt . ' 1:000 '

Th~ use of debt in the company's capita! structure hascaused. the net profit to decline from Rs.I,500 toRs.I,OOO. But has the return on owner's capitaldeclined? Return on Equity now works out to 30%, asthe owner's have invested only Rs.3,333 now whichearned them Rs.I,OOO. What were the factors whichcontributed to this additional return? We can trace outtwo sources of this additional return:. though the company has to pay interest at 15% on

borrowed capital, the company's operations havebeen able to generate more than 15% which is beingtransferred on to the owners.

. the reduction in PBT has brought about a reductionin the amount of tax paid, as interest is a tax deductibleexpense, to the extent of Interest (I - tax rate) i.e.,

Rs.500. The greater the tax rate, the more is the taxshield available to a company which is financiallyleveraged.

As was seen in the above example, a company mayincrease the return on equity by the use of debt i.e.,the use of financial leverage. By increasing theproportion of debt in the pattern of financing i.e.. byincreasing the debt equity ratio, the company should beable to increase the return on equity.

Financial leverage and Risk

If increased financial leverage leads to increased returnon equity, why do companies not resort to everincreasing amounts of debt financing'! Why do financialand othCf tCfin lending ::1st:t!.!!i0!1~!!1~islon norms Jor

110 ,

Debt Equity Ratio? The answer is that as the companybecomes more financially leveragcJ, it becomes riskier,i.e., increased use of debt financing will lead toincreased financial risk which leads to:

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. Increased fluctuations in Ihe return on equity,

Increase in the interest rate on debts..Increased fluctuations in returns

In the previous example, let us assume that sales declineby 10% (from Rs.IO,OOO to Rs.9.000), expensesremaining the same. What happens to return on equity?The income statements for the financially unleveraged,and leveraged firms will appear as follows:

'Uole'ieraood .'.\leveraged R.m

~';;;1; ..~L;,."'t~~~~EBIT)~,?,'>,.I,t('r.",A:~.,,;",' . .2000,:.; , ,,' 2.000

I

lrite~,'q;~s"'~:~Y ':",' ",,::t':"~:;~'I! '..~'I.ooo""hf.<""~\""'" "",,', ' . . '" ... (6667 015)~~~¥;~(:;;:sL:"V';~;i,i';t'~~~S~' ,'. :.:' .."..~,:,:,l~:~;L:.,!;i;; ", ~-I.ooo

;i~~/, ,'~~ ,:ROE-:iit~oIRs.10,OOO' ,; .15%iROEat Sales01RS.9,OOO 1()%

We seethat a 10%decline in sales produces substantialdeclines in earnings and the rates of return on owner'sequity in both cases. But the decline is greater for thefinancially leveraged firm than for the financiaIlyun leveraged firm. Why is this so? The reason can betraced to .the fact that once a firm borrows capital,interest payments become obligatory and hence fixedin nature. The same interest payment which was thecause for increase in owner's equity when sales wasRs.'IO,OOO is now the cause for its more thanproportional decline when sales declines. Helice, thegreater the use of financial leverage. the greater thepotential fluctuation in return on equity.

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Increase in interest rates

Firms' that are highly financially leveraged areperceived by lenders of debt as risky. Creditors mayrefuse to lend to a highly leveraged firm or may do so

only at higher rates of interest or more stringent loanconditions. As the interest rate increases. the return on

equity decreases. However, even though the rate ofreturn diminishes, it might still exceed the rate of returnobtained when no debt was used. in which case financial

leverage would still be favorable.

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Implications

Let us again refer to our earlier example. In the firslsituation, the company was unleveraged, in thesecond situation the debt-equity ratio was 2: I. Thebalance sheet and income statements are reproducedhelow:

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Income Statements

DFL = EBITDEBIT-I-~

I-T

30003000 = 1

30003000 - 1000

1.5

Unleveraged =

Leveraged = =

What do these figures imply? This implies that if

EBIT is changed by 1%, EPS will also change byI %, the company uses no debt and by 1.5% when ituses debt in the ratio of2:1 (66.67% o£total capital).

This is proof of what we have stated earlier: Thegreater the leverage, the wider are fluctuations in thereturn on equity and the greater is the financial risk thecompany is exposed to. Through an EBIT-EPS analysis,we can evaluate various financing plans or degrees offinancial leverage with respect to their effect on EPS.

TOTAL LEVERAGE

A combination of the operating and financialleverages is the total or combined leverage. Thus,the degree of total leverage (DTL) is the measure ofthe output and EPS of the company. DTL is theproduct of DOL and DFL and can be calculated as

. follows:

DTL= % change in EPS / % change in output

: (bEPSIEPS)/(i\Q/Q)

DTL: DOL x DFL

= ([Q(S - V)]I[Q(S- V) - F]} X([Q(S- V) - FVQ(S- V) - F - I - [Dp'1- 1)))

- Q (S- V)- D

Q(S- V)-F-I-~. (I - T)

".----II.

IILev'Jrage

CaIoJtaIing !he OTllor XYZCo. lid. given !he IoIowing inlOl11\llioo:

EquityEamings = Rs.I,62.500

QuantityProduced(a) = 5000 1.Ir1i1s

VariableCostper unitM = Rs.200

SellIngPriceperIII~(S) = Rs.500Number01equityShareholders(N) = 5,00,000FixedExpenses(F) = Rs.9,OO,O'X>Inleresl(I) = Rs.75.000PrelerenceDividend(Op) = Rs.50,000

CoqxualeTax(T) = 50%

t!

5,000 (5,000- 2(0)DTL .

5 000 (500 - 200) - 9 000-75 000- 50,000, "(I - 0.5)

= 3.53DTL= DOL x DFL

= 2.5 X 1.41 = 3.53

Thus, when the oUtput is 5,000 units, a one percentchange in Q will result in 3.5% change in EPS.

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Appli.cations and Utility of Total Leverage

Before understanding what application the totalleverage has in the financial analysis of a company, letus make a few more observations by studying itsbehavior. Let us calculate the overall break-even pointand the DTL for the various levels of Q, given thefollowing information:

"'I

The overall break-even point is that level of output atwhich the DTL will be undefined and EPS is equal tozero.This level of output can be calculated as follows:

DF+I+~

(I - T)

(8 - V)

= [8.00,(0) + 80,(0) + ro,OOY(I- 05)Y(I,OXJ- (ill)

= 2,500.

Thus, the overall break-even point is at 2500 units.

Calculating DTL for various levels of output with thegiven information:

Q =

a".' ,1000

'2000. 2500

.~ 6.00,-'.5000 2.00,.:;

The following observations can be made from the abovecalculations:

. There is a unique DTL for every level of output.. At the overall break-even point of output the DTLis undefined.

DTl".(J!J7...4.00

149

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F = RS.8,OO,oooI = Rs.80,ooo

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Dp = Rs.60,OOOS = Rs.I,OOOV = Rs.600

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. If the level of '.Jutput is less than the overallbreak-even point. then the DTL will be negative.. If the level of output is greater than the overallbreak-even point. then the DTL will be positive.DTL decreases as Q increases and r~aches a limitof I. :

Further. the, DTL' .has the follow)ng applications in '

analyzing the financial performance o(a company:

1. Measures changes in EPS: DTL measures thechanges in EPS to a percentage change in Q. Thus,the percentage change in EPS can be easilyassessed as the product of DTL and the percentage

150

L.

2.

change in Q. For example, if DTL for Q of 3000units is 6 and there is a 10% increase in Q. theaffect on EPS is 60%.

Percentage change in EPS =DTL (Q = 3000) xPercent change in Q

",,6 x 10%

= 60%

Measures Total Risk: DTL measures the totalrisk of the company since it is a measure of bo.thoperating risk and total risk. Thus. by measuringtotal risk, it measures the variability of EPS fora given error in forecasting Q.

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Section I

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Self-Evaluation Exercises

Choose fthe. right answer from the alternatives given.The 1Ota1revenue of Saturn Ltd. for the year 1995-96 was Rs.12.5 lakhs. This was obtained on the sale of500 units al a price of Rs.2,5oo each. The variable and the fixed expense:; were Rs.I,500 per unit and

~RS.2,OO,OOOrespectively. The company has leveraged its capital structure to the extent of Rs.3,OO,OOO@1:5%1'.11.Sa~urn Ltd. has 50000 equity shareholders holding th~ shares at par. In addition to this the firmalso has issued 12% preference shares @ Rs.IOO each amounting to Rs.2 lakhs. The corporate tax rate isgiven as 40%.

Arnt')w(!J.rquestions from 8.1-8.6 on the basis of the information provided:

1, SaltEl} Ltd. has an EBIT of - and thus its EPS has been calculated to be -'

a. Rs.I0.5 lakhs and Rs.l1.58

Rs. J0.5 lakhs and Rs.7.56

Rs.3 iakhs and Rs.2.58

Rs.3 lakhs and Rs.J.56

Insufficient data.

b.

c.

d

e.

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4. The degree of total leverage of Saturn Ltd. is

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'I[I.5. The levels of output at which DOL and D11.. are undefined

151

2. The degree of operating leverage of the company is

a. 4.17

b. 1.67

c. -1.67

d. -4.67

e. Undefined.

3. The degree of financial leverage of the firm is

a. 4.41

b. 1.39

c. 1.09

d. -1.09

e. -1.39.

a. 6.13

b. 2.32

c. 1.82

d. -1.82

e. -2.32.

a. 215 and 115

b. 200 and 285

c. 200 and 215...

d. 200 and 95

c. 115 and 200.

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(:Financial Management

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6. The financial break-even point for the finn is ,(

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7. to changes in qu!ntity.cc~

Operating leverage measures the sensitivity of th~

a. Earnings per share

b. Profit after tax

c. Earnings before interest and tax

d. Earnings before tax but after interest

e. Expenditure. .

Degree of financial leverage can be given by which of the following fonnula takingEBIT = Earnings before interes~ and tax; Dp = Dividend on preference shares; T = Tax rate;I = Interest

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EBIT- Dp

EBIT - I - l=-TEBIT

DpEBIT + I + ! - T

Dp~

EBIT + I

EBIT

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c.

d.

9.

EBIT + I - 1 ~p T

e. None of the above.

Degree of financial leverage is

a. Undefined

below the financial break-even point.

b. Positive

NegativeZero

c.

d.

10.e. Has no relationship.

Degree of total leverage (DTL) can be calculated by which of the following formula given Degreeof operating leverage (DOL) and Degree of tinancialleverage (DFL).

a. DOL + DFL

b. DOL + DFLc. DFL - DOL

d. DOL x DFL

11.e. None of the above.

The following data are available for age group electronics.

Unit ~elling Price (P) = Rs.150

Unit Variable Price (Y) = Rs.80

Total Fixed Cost (F) = Rs.3.00.000.

152

a. Rs.3.00.000

b. Rs.2.85.000

c. Rs.l.15.000

d. Rs.l.05.000

e. Rs. 85.000

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of operating leverage for age groups when the output (Q) is 5000 units is

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12. Consider the following data for Symphony Enterprises.

Interest burden (1) = Rs.150,ooo

Tax rate (T) = 50 percent

. Preference dividend (Dp) = Rs.75,oooWhen the earnings before interest and taxes are Rs.5,OO,OOO,the degree of financial leverage is ii,

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Section II

1. Calc.1Iate th~ EBIT for the following:

a. P =Rs.20

P = Rs.70

Q = 25,000

Q =40,000

F = Rs.60,ooo

F = RS.3,oo,OOOI'!III

II

V:;: Rs.12

V = Rs.40b.

3.

Sac manufacturing sells 100 units, contribution per unit being 400 and fixed cost Rs.80,ooo, what is theDOL of Sac manufacturing? What will be the DOL if quantity sold rises to 300 unit:>?

Global computers sells 10000 units of wiper-it's flagship brand. The contribution per unit is Rs.lO &EBIT is Rs.60,ooo, what are the fixed costs?

12 company decides to sell 20,000 units of Alpha, generating EBIT of Rs.3,50,ooo. The DOL for thislevel is 3.5. Find out the range of variance in EBIT if the actual sales varies between +20% and - 10%.If P = 400; V =240; F = 80,000; 1= 30,000; T = 60% and Pref. Dividend =15,000

What is degree of financial leverage when sales is 40,000.

The following data are available for two firms X and Y.

@4.

5.

6.

(in Rs.)

153

The degree

a. 7

b. 6

c. 5

d. 4

e. 3

a. 5.5

b. 4.5

c. 3.5

d. 2.5

e. 1.5

Finn X:0'

FinnY"" ,"

Quantity 80,000"', " -c

-;:', 50,000,

Selling Price 20 <c 30

Variable Cost (per unit) 10 10,

Fixed Costs 60,000 . 30,000:' --:- ,:

Interest 20.000,,'" ' 15.000, :,'

Preferred Dividend 10.000 . '. ,",",'-',':

Nutnber of Equity Shares 15,000 Ju 10,000<' .Tax Rate 50% 50%

r :I '-

II

"

@8.

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h. Degree of tolal leverage

The following data is given for Plaza Limited: P =Rs.50, V =Rs.30, F = Rs.l ,00,000, I = Rs.50,OOO,T = 50 percent, and D =Rs.20,OOO. What is the DFL for Plaza Limited when the !evel of output is10,000?

The following data are available for the Broadway and Midway Companies:

Midway Co.

10,000 units

Rs.200

RS.150

Rs.30

Rs.6;00,000

("

P'

;S.4,OO,OOO.

15% ",,;

Required:

i. Calculate the ROE, DOL, DFL, DTL, operating break-even point, financial break-even point andoverall break-even point for each company.

ii. As a financial analyst which of the two companies would you describe as more risky? Give reasons.

The sales revenue of Leveret Company @ Rs.20 per unit of output is RS.20 lakhs and contribution isRs.1O lakhs. At the present level of operations, the DOL of the company is 2.5. The company does nothave any preference shares. The number of ordinary shares is I lakh. Applicable corporate income taxrate is 50% and the rate of interest on debt capital is 16% p.a. What are the EPS (at sales revenue ofRs.20 lakhs) and amount of debt capital of the company if a 25% decline in sales will wipe out EPS?

(Note: DOL - Degree of Operating Leverage; EPS - Earnings Per Share)

The following data pertain to Exotica Limited.

, Selling price per unit

Variable cost per unit

Fixed operatiJigcostsSales volume


For hoth Ihe firms calculz:.: the following

a. Earnings before interest and tax

Earnings per share

Operating break-even point

Finar.cial break-even point

h.

e.

d.

e. Over-all break-even poinl

Degree of operating leverage

Degree of financial leverage

r.

g.

7.

,'BfQadwa~,Co.

, ' " , , ,',,"'>",' "",J,,,,,, ,

~;:!:f~~i~:!'~~!;:r1!::I;u,":r~'... .Fixed operating cost p~r1~riitofoutput .Rs.6Q

Equity R'S.3,oo,OOO

JPreferen~:~?at~s<'" . Rs.l,oo,ooo j'

Debt, ' .':' Rs.6,OO,OOOInteresrrate~br{'debt, 16.25%

Di viden~:fate'~n; prefer~nce share";,,. :13%Tax rate"'"';''' ,.:'- ,60% 'd' ,,','

60%'':;

9.

10.

I~

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,...\-

(:r....

r....

r....

,.....

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p....

'.. 'p.....

#'...

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f'....

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r...

r...

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/'...

/"'",..,,.....

,."Rs.looRs.60

RsAO,OOO

1,200 units

,.'""'"'"

What is the financial leverage of the company if 10% change in sales will bring about 90% change in EPS?

What percentage increase in variable cost will result in a 750% increase in the existing operating leverage?

The operating and total leverages of Enigma Company are 2 and 5 respectively. Total variable costs at theexisting level of operations amount to Rs.6,50,OOO.Interest expense and dividend on preference shares areRs.75,OOOand Rs.36,OOOrespectively. Corporate income lax rale is 60%. Whal is the sales revenue of Ihecompany?

11.

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leverage

12. Selected financial data for Alacrity Limited are given below:

Variable e,!,pensesas;percentof sales';'.."~r~F ,;' 661%:~,' .. "", ',.., 3

, ,

"".,

Interest expenses

Degree of operating-leverage

Rs.20 lakhs

5

Degree offinancialleverage

Income tax rate

3~. 50%

, I--J

14.

The company has not raised funds through issue of preference capital.

What are the fixed expenses and profit after tax of the company?

1l1e DFL of Ajay Castings is 2. The company pays an annual interest of RS.I ,00,000 and a preferencedividend of Rs. !5,000. The tax rate for the company is 50%. By what percentage will there be a fal: inthe EPS if EBIT drops to Rs.1 ,30,OOQ? ,r

The DTL and DFL of a company are 3 aJ;\d 2 respectively. The company pays an annual interest ofRs.60,000 and preference share dividend of Rs.16,OOO. The total variable costs of the company areRs.2,OO,000 and the applicable income tax rate is 60%. What are the amounts of sales revenue and fixedoperating costs?

The Gudia Enterprises manufactures and sells a typical electronic toy. The selling price and variable costper lOy are Rs.20 and Rs.IO respectively. Operating fixed costs amount to Rs.5 !akhs. The interest expenseis Rs.2.5 lakhs and DFL is 2. What are its DOL and Sales Volume respectively?

The Sigma Company's operating and total leverage are 2 and 3 respectively at the present sales level of10,000 units. The selling price per unit of output is Rs.12 while its variable cost is Rs.6. The companyhas no preference share capital. Applicable corporate income tax rate is 50%. The rate of interest on thecompany's debt is 16% p.a. What is the amount of debt in the capital structure of the company?

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Solutions

Section I

\. c 2. b 3. b 6. e 7. c4. b 5. b

Section II

1. EBIT = Q(P - V) - F

= 25,000 (20 - 12) - 60,000

= 25,000 x 8 - 60,000

= Rs.1,40,000

EB IT = Q(P - V) - F

=40,000 (70 - 40) - 3,00,000

= Rs.900,000

DOL = Q(P- V)Q(P -V) - F

Q = 100, '(P - V) = 400 F = 80,000

100x 400DOL = =-1

100 x 400 - 80,000

a.

b.

2. . a.

b. if Q = 300 then

DOL = 300 (400) = 1,20,000300 x 400 - 80,000 1,20,000 - 80,000

= 1,20,000 = 340,000

3. (P - V)

EBIT

60,000

F

= Rs.1O

= Q(P - V) - F

= 10.000 (10) - F

= Rs.JOO.OOO- 60.000 = Rs.40,000

4. As the variation is from 10% below and 20% above

:. if Q is more than forecast by 20% then

L1EBIT = 3.5 x 0.2 = 0.7 = 70%

and if Q is less Ihan forecast by 10% then

~BIT = 3.5 (0.10) = -0.35== -35%

5. DFL = EBIT

EBIT - I - t,pI-t

- Q (P - V) - F

lQ(P-V)-F)J-I- t,p.' I-t

Q = 40,000; P = Rs.400; V = 240; F = !!O,OOO

J = 30,000; T = 0.6; t,p = ! 5,000

156

8. a 9. c 10. d I \. .1

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DFL ..:

=

DFL =

40.(X)O (400 - 240) - XO,OOOI ') O()()

~(),O()() (400 - 24()) - XO,(X)()- 10,000 -~-. . 1-0,6

40,000 ( 160) - XO,(X)O

~O,O(X) ( 160) - I 1O,(X)O - 37,500

M,OO,OOO - XO,OOO

M,O(),<X)O - 1,47.500

63,20,!X)O62,52,500

l,t1l0.

Leverago 'I!

it

II

h:

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EBIT = Q(P - V) - F

E.P.S = (EBIT - I) ~ - 1) - Dp

Operating BE.P (Units)Q = F/(P - V)

I.

2.

3.

Financial B.E.P (Rs.)Dp

EBIT = I + -]-T

Overall B.E.P (Units)

4.

5.

6.

7. DFL =

8.

X

80,000

, 20'

10

60,000

20,000

10,000

15,000

.50%

7,40,000

,9.33

6,000

40,000

10,000

1.081

1.057

1.142

. '- 10,000

,"""'.' ',50% '~

1\ III,

-9;10,000

2.73

I

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[

F+I+~

]I-T

P-V

DOL = Q (P- V)Q(P- V)-F

Q(P- V) - F

Q(P-V)-F-I- ~I-T

DTL = Q(P - V)

Q(P- V) - F - I - ~I-T

15,000

15,000 \\

111

2,250

1.309

1.015

1.047

/57

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-*

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6.

Given

I. Q

2. S.P.lUnit

3. Variable CostlUnit

4. Fixed Cost

5. Interest

6. Dp

7. No. of shares

8. Tax Rate

Required

28;000

28,000: ,

3,00,000 x 100

=9.33%

4

2,00,000(1,02,500 - 32,500)

2.86

=4 x 2.86

11.44

"

Financial Managemont

E[3(TD

EBIT- I-~I-T

Q(P, V)- F

10,000 (50 - 30) - 1,00,000Rs. I ,00,000

Substituting the value of EBIT and values of I, T, and Dp in (I)we gel

7. DFL

Ell IT ==

DFL = 1,00,000

1,00,000 - 50,000- 20,000

1,00,000 0.510,000

10

==

8. i.

".,

, ," ' "

:\'~S'y;~rs~:. Pref~rencedividendi~.':hf:;~~fit to equity shareholderS:

, " ", " " " " ' ,", '

Ifk.~::'.?ROE :',frofit avaHable,'toequity

,\'/shareholdets/equity 'xl 00

" 13,

(1,00,000 x 100).. "

',--" .~.

II

'15. ' , DOL = [Q(S -V)] ,

'. ,'" 'EBIT

l~;:.~.

':~,riFr. =PBtr.

,

[PBT - Preference dividend

],',' -; I-T

"

17. DTL ::;; DOL x DFL

158

2,ool#?'"'c97~5{)(f

:1,02;500

61,500

41,000

13,000

=

=

, (1)

,,'}'~~iP~;~:::d1~9*~~;~g~~!

60,000

1,40,000

84,000

56,000-

" 56,00056,000' .

6,00,000 x 100=9.33%

2.5

2,00,0001.40,000

1.43

= 2.5 x 1.43

3.575

=

=


EI3IT

E13IT- 1- J2L1-1'

Q(p. V)'- F

10,000 (50 - 30) - 1,00,000RS.I,OO,OOO

Substituting the value of EBIT and values of I, 1', and 01' in (I)we get

OFL7. . ,"'" (1)

EBiT =

OFL = 1,00,000

1,00,000 - 50.000 - 20,000

1,00,000 0.510,000

10=

8. i,

.,)~f;iK;;i,?!:M~9*~~~S§;

~,~,~it7rf~~(,<t~~'j'l='25,

2'00'000' '" ',',

, , "

,60,000

1,40,000

84,000

56,000

13,(I,OQ,OOOx 100)

, ,'='~~}.1 O() OOO' "',' ,

, ~'. "cq"97;500.'

. 1,02;500

61:500

41,000

13,000

I,IiIi

,liji;,;:'gF;fitt~equity shareholders., "',' ,', ',,", '

14j,~::<:iROE=.P['ofit availabk{'toequity;','/shareholders/equityxl00" '

.' 56,00056,000' ,

6.00,000 x 100

=9.33%

2.5

28,000

28.600' ,3,00,000 x 100

= 9.33%

4II..

15. . ' DOL =,[Q(S - V)], " EBIT

~~; :.§<~riFr.= ~BIT,

' ,"

[PBT - Preference dividend

]

'

,:.'; I-T

2,00,0001.40,000

1.43

=2.5 x 1.43

3.575

2,00,000(1,02,500 - 32,5(0)

2.86

=4 x 2.86

11.44

"Ii

= =17, DTI. ==DOL x DFL

= =

158

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::'Rs.

18.

19.Operating Break Even Point QF/(P-V)

-;<

Financial Break-even point =Level of PBrf at whichROE is equal to zero

. '~f;:>l Je:~\~,

'

,

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" .t...\" ..~ .'C'",.'~,'~1,'"75,000

,0 :=-CO.6){(X'--~97,50(}).- 13,000 ,;,,::,. 300 000'''. . "

20. Overall Break-even point =Operating Fixed Cost +

Interest + ~ / Contribution per unit1 - t

='0

= Rs.I,30,OOO

7;30:ooo~:c'Rs;8C'

9,125'units.,: :

Working Notes:

1.

Levorage

.': '.i:~~1\-¥i~~~y..Co.;

:';,:~{~~~~:(I ~:O:6)'XX ...r-60;OOO).

6,OO,O()O'.,.'.

=0

~'Rs.60,OOO

"";:,~~B!60,OOO. .' 'HRs.50

'~~,:,

'''''''' '

=7i200:'units I

4,.:l';',:..\..:.,::,::J{Broadwa y' Co '.-'f',", < . '. \c; Midwa y Co '. ,,',:;;,:",::.::.;)~~~,. : " c.'" " .' "'-, ' , ",' .

,/,,,~Rs.

Profit before interestTotal contribution

Less: Fixed operating 'cost" '

2. Interes t

1625. " "

Broadway Company - 6,00,000 x 100 ,= Rs.9?500 '"

,.

5;00,000

. 3,90.000

i2;00,000

. .

" "

Midway Company' -4;00;000 x'~1t~[]{s:~~~~<;.,Though ROE is the same for both the companies, Broadway Company is exposed to greater riskthan Midway Company. The DOL, DFL and DTL are much higher for Broadway Company thanMidway Cornpany. This is also reflected in the Break-even points calculated. Midway Companyis therefore better managed.

11.

9. Degree of Operating LeverageQ (P - V)

Q (P - V) - F

10lO-F

10

l1.=62.5

~.6.00,OOO10~--q5 =7.5

=

2.5 =

25 - 2.5 FF =

:. Fixed Cost

Contribution when sales decline by 25%:. EBIT =7.5 - 6 = 1.5 lakhs

==

Let the debt capital be 'x' lakhs

Interest on deht capital =O.16x

If EPS will he wiped out at a decline of 25% in sales revenue, PAT =0

PAT = (1.5 -0.16x)0.5 = 0

159

,

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~

"

Rnanclal Management

0.750.75 - 0.08x = 0; x = 0.08

'!I'-

~'-I

= 9.375

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Rs.9,37,500At sales revenue of Rs.20 lakhs,

EPS = [10 - 6 - 0.16 (9.375)] 0.5 = Rs.1.25

. Q (SP- VC)Degree of operating leverage =

VC)Q (SP - - FC

Where Q is the sales volume

SP = Selling price per unit

VC = Variable cost per unil

FC = Fixed cost1200 (100 - 60)

1200 ( 100 - 60) - 40,000

6

10.

DOL =

=

Degree of lOlal leverage

DTL = DFLx DOL9 = DFL x 6DFL = 1.5DOL = 6750% increase in DOL

:. DOL

51

51

51 (80,000 - 1200x)

40,80,000 - 61200x

60,OOOxx

Variable cost per unit

Less: previous variable costper unit

Increase

% increase

= % change in EPS% change in sales90109

==

(1 )

= 6 + 750% of651=

= Q (S - VC)

Q (S - VC) - FC

1200(100 - x)1200(100 - x)-40000

120000- 1200x8()(){}J- 1200x

~I.....

~

= 11"\

'-1.....

=

'"'-1

....

'I

(2)

.....

J

J

J

j

~

~

~

~

~

160

= 1,20,000 - 1200x

= 1,20,000 - 1200x

= 39.60,000= 66

= Rs.66

= Rs.60-= Rs.06-

6=60 x 100

= 10%

~

:),

~~

~

11. DOL = Q (P - V). or Sales- VariableCosts.Q (P - V) - F Sales- Vari;]blcCosts - Fixed Cost

We know that DOL = 2 and V = Rs.6,50.000

2 = S - 6,50,000S - 6,50,000- F

s-vD1'L=-II

S-V-F-l- ::l.1-1' .

We know thai D1'L =5, V = 6,50,000, I =75,000, Dr =36,00<'S - 6150,000

S - 6.50,000 - F- 75000- 36,000, 1-0.6

From (1) 2S - 13,00,000 - 2F =S - 6.50,000or 5 - 2F =6,50,000

S - 6,50.000

5 - F - 8,15,000or 55 - SF- 40,75.000 = S - 6,50,000or 4S - SF = 34,25,000

Multiplying (3) by 4 and subtracting it from (4) we get4S - SF = 34,25,000

- 4S -I-8F = (-) 26,00,000

3F = 8,25,000

~

III

~5 =

-!I

..

..From (2) 5 =

~

..

II!I

~,,.

f

f

,

Q (P - V)

Q (P - V) - F

Since Q (P - V) - F =EBIT =Rs.30 lakhs

DOL =

5 Q (P - V)30

Q(P - V) = ISO

EBIT =30

=5 x 30 =Q( P - V) - F =Subtracting (2) from (I) we get

Fixed Expenses = Rs. 120 lakhs..

161

Ulld T = 60%

Leverage

""'''' (I)

(2)

(3)

""'''''' (4)

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F 8,25,000RS.2,75,OOO= =

3S - 2 (2,75,000) = 6,50,000or 5 = 12,00,000.

12. DFL EBIT=EBIT - Interest

3 EBIT=EBI1'- 20

:. EBIT = Rs.30 lakhs

- Interest 20PBT 10Tax @ 50% 5PAT = Rs.5 lakhs

:,-

~-14.

....

Financial Managoment

13.EI3I1'

EI3IT - I - ~1-1'

[131'1'

'1

i1~

DFL =

2EI3IT - I 00000- 15,000

,. (I -0.5)

EI3IT = (EI3IT - 1.30.(00)2 EBIT :::

If E13IT drops to 1.30,000 i.e. a fall of 50%,EPS will fall hy 2 x 50% = 100%

...

2,60,000

,.-.-

DTL

DFLTherefore, DOLGiven DFL

EBIT

EBIT - I - J2.L1-1'

EBIT

EBIT - 60 000 - 16,000, 0.4

EBIT

EBIT - 1,00.000EBiTEBITGiven DOL

=

3

23/2 = 1.52

2 .,.

A

..

= ~.=

= 2

:::

2

2EBIT - 2,00,0002.00,0001.5

ContributionEBIT

::: 1.5

Contribution

Q (P - V)QP - QV

QP - 2,00,000QP

::: 1.5 EBIT3,00.0003,00.0003.00,0005.00,0005.00,000Contribution - EBIT

:::

:::

:::

:::

or sales revenue

Fixed Operating Costs

:::

:::

::: Q(P - V) - {Q(P - V) - F}3.00,000 - 2,00,000RS.I,OO,ooo

:::

15.EBIT

EBIT - I

Let the sales volume of the toys be x.x (20-10)-5

[x (20 - 10) - 5)1- 2.5

DFL :::

2 :::

::: 10,00.000::: 2.5,00,000

162

2IOx-5

:::lOx - 7.5

20x - 15 ::: lOx - 5lOx ::: 10x ::: I lakh units

DOC Q (P - V):::

Q (P - V) - F

1,00,000 x 10:::

(1,00,000 x 10) - 5.nO,OOo

,.=--

16. Q (P - V)Degree of operating leverage =

FQ (P - V) - 4

Where Q is the quantity sold.

P is the selling price

V is the variable cost

F is the fixed cost.

Substituting the data, we get

10,000(12 - 6)10,000 (12 - 6) - F

Degree of total leverage = Q (P - V)Q (P - V) - F - I - ~

I-T

2 =:. F = 30,000

'\ 10,000 (12 - 6)

10,000 (12 - 6) - 30,000 - I

The interest on debt is 16%. The debt component == 1~:~ =Rs.62,500

3 =:. Interest = 10,000

163

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Leverage

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Documents

Leverage