study: LEVERAGE

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Principles of Finance: LEVERAGE

No 1 The information of Horikuchi company Ltd. Are as follows.

Sales 10,000 units

Selling price per unit tk.20

Variable cost per unit tk.12

Fixed cost per unit tk.40,000

You are required to calculate DOL.

No 2 The operational data of Microsoft Ltd. Are as follows .

Sales 40,000 units @ tk.15 per unit . variable cost tk.8 per unit fixed cost tk.80,000 . what is DOL?

No 3 Calculate DOL following information .

Selling price per unit tk.45, Material cost per unit tk.10, Labour cost per unit tk.10 , Factory over head per unit tk.8 , Fixed cost tk.2,40,000 , Sales 20,000 units.

No 4 Z company manufacture and sells a single product . The company sales and expenses for June as follows :

Total(Tk.) Per unit (tk.)

Sales 4,50,000 30.00

Less : Variable expenses 1,80,000 12.00

Contribution Margin 2,70,000

Less :Fixed cost 2,16,000

Net income 54,000

Required :

ⅰ) What is the monthly break even point .

No 5 From the following particulars determine financial and operating leverage of Alaf –Beta Limited .

Production in unit 3,00,000

Fixed cost in tk. 3,50,000

Variable cost in tk. per unit 1.00

Interest expenses 25,000

Per unit selling price tk. 3.00

No 6 Following information are available of Akib Ltd.

Year EBIT EPS

2007 2,00,000 TK.20

2008 5,00,000 TK.60

Calculate DFL?

No 7 Asif ltd. Has the following information :

Sales 5000 units @ tk.20 per unit . Variable cost per unit tk.12, Fixed cost tk.20,000; Interest as debt tk.5,000 Calculate DTL.

No 8 The operating and cost data of Bithi ltd.

Sales tk.50,00,000

Variable cost tk.35,00,000

Fixed cost 10,00,000 ,15% interest on tk.25,00,000

Calculate the DTL?

No 9 A company has a capital of tk.8,00,000 of which 40% has been financed by equity capital (each share of tk.100 ) and 60% debenture . This company annual sales is 60,000 units the selling price of which tk.15 per unit and variable cost is tk.8 per unit . The company`s annual fixed cost is tk.2,00,000 corporate tax rate is 25% you are required to calculate the DOL,DFL,&DTL. If the company wants to increase sales in the next year by 25%&40%.

ANS : 1.909,1.354,2.586. %change of EBIT 47.72%,76.36% ,%change of EPS 64.66%, 103.44%.

No 10 Hasan company capital structure is composed of common stock capital of tk.1,00,000 (1,000 shares @tk.100 each) and of 15% debenture of tk.2,00,000.

Corporate tax rate of the company is 25% the company last year data are as follows : sales 20,000 units @tk.10 each .Variable cost @tk.4 per units .Fixed cost tk.70,000 .

A) What are the degree of operating leverage, financial leverage, and total leverage

B) What will be the impact of increasing sales by 40% and 60% ?

No 11 The selected financial data for A B C companies for the current year and 31^st December are as follows :

Company	A	B	C
Variable expenses as @ % of sales Interest expenses tk. Degree of operating leverage DOL Degree of financial leverage DFL Income tax rate	66⅔ 200 5 3 0.50	75 300 6 4 0.50	50 1,000 2 2 0.50

Prepare income statement for A,B,C companies .

ANS : EAT 50, 50, 500

No 12 from the following information relating to Banik Fertilizer Ltd. Compute the degree of operating leverage , degree of financial leverage, and degree of total leverage .

Year	EBIT	Sales in units	EPS (tk.)
2003	40,000	16,00,000	20
2004	45,000	19,00,000	25

No 13 Carolina Faster Inc. Makes a patented marine bulkhead latch that wholesales for $6.00 .Each latch has variable operating cost of $3.50 .Fixed cost are $50,000 per year. The firm pays $ 13,000 interest and preferred dividends of $7,000 per year .At this point the firm is selling 30,000 latches a year and is taxed at 40%.

a) Calculate the firm`s EBIT and net profits.

b) Calculate the firms degree of operating leverage .

c) Calculate its degree of total leverage.

d) Calculate the firms degree of total leverage.

No 14 The information of A and B company is given below .You are required to calculate the financial statement of the company :

Particulars	A Company	B Company
Variable cost % of sales	70%	40%
DOL	3 times	4 times
DFL	1.50 times	1.75 times
Number of share	1,000	1,500
Corporate tax rate	40%	40%
Interest expenses	Tk.10,000	Tk.15,000

No 15 1) Find the operating leverage from the following data :

Sales tk.50,000

Variable cost 60%

Fixed cost tk.12,000

2) Find the financial leverage from the following data :

Net Worth tk.25,00,000

Debt t Equity 3 t 1

Interest rate 12%

Operating profit tk.20,00,000

ANS : 2.5 times 1.818 times

No 16 A company recently sold 10,000 units at tk.7.50 per unit . Annual fixed cost is tk,22,500 and variable cost per unit is tk.3.00 Annual interest charge on debt capital of tk.80,000 at 10% and firm has 12% preferred stock of tk.40,000. The company is in 40% tax bracket you are required to :

a) Calculate the degree of operating, financial , and total leverage;

b) Calculate the earning per share (EPS) at

x) Current level of sales ;

xi) 12,000 units ;

xii) 15,000 units;

ANS : 2 times, 3.4615 times, 6.923 times. EPS TK.1.95, TK,4.65, TK.8.70.

NO 17 The balance Sheet of well Established company is as follows :

Liabilities	Tk.	Assets	Tk.
Equity capital(tk.10 per share) 10% Long term debt Retained earnings Current liabilities	60,000 80,000 20,000 40,000	Net Fixed assets Current assets	1,50,000 50,000
Total	2,00,000	Total	2,00,000

The company`s total assets turnover ratio is 3 times its fixed operating cost are tk.1,00,000 and its variable cost ratio is 40% .The income tax is 50% .

a) Calculate for the company different types of leverage.

b) Determine the likely level of EBIT if EPS is

1) tk.1 2) tk.3 3) tk.0

Help: Assets turnover ratio =

EPS =

ANS: 1.385 times, 1.032 times, 1.429 times. EBIT: 20,000.44,000.8,000

NO 18 Calculate the degree of operating , financial , and combined leverage under plan 1 & 2 respectively from the following information pertaining to the capital structure of a textile company:

Total sales tk.60,000

Variable cost as % of sales 60%

Fixed cost tk.10,000

Financial plan 1 Financial plan 2

Equity tk.30,000 tk.10,000

10% Debenture tk.10,000 tk.30,000

ANS : DCL 2.18 times

No 19 At present a company has 50,000 ordinary shares of tk.100 each . The company requires an additional capital of tk.12,50,000. In order to acquire the additional capital the company has been considering the following three alternatives :

1) Issue 12,500 ordinary shares , 2) Borrow tk.12,50,000 at 10% interest , 3) Issue 10% preference shares of tk.100 each.

If the Earning Before interest and tax (EBIT) of the company is tk.7,50,000 show the effect of these three alternatives on earning per shares . Assume tax rate is 40% .Which method of financing the company should select ?

ANS: tk.7.20,tk.7.5 tk.6.50

No 20 Tagar ltd. Provides the following data from its books of account ended on 31^st December .2011.

Sales 60,000 units

Selling price @ tk.15 per unit .

Variable cost @ tk.8 per unit.

Fixed operating cost (annually) tk.2,00,000 .

You are required to calculate the degree of operating leverage and the effect of leverage if the company plans to increase sale in next year by 25%.

ANS : 1.909 times

No 21 Find out Degree of total leverage from the following information:

Out put (in units ) 75,000 units

Fixed cost tk.7,00,000

Variable cost per units tk.7.50

Interest expenses tk.40,000

Unit selling price tk.25

ANS: DTL 2.29 times

No 22 Following information are available from the books of accounts of three companies:

Company	A	B	C
Sales in units Selling price per unit tk. Variable cost per unit Fixed cost tk. Interest charges tk. Proposed sales in units	40,000 20 10 3,00,000 25,000 50,000	15,000 40 25 1,25,000 30,000 20,000	30,000 25 12 2,40,000 50,000 45,000

You are required to calculate the degree of operating ,financial, and combined leverage. You are also required to show and explain the effect of all three leverages . Assume 25% corporate tax rate.

ANS: DOL: 4 times. 2.3 times . 2.6 times.

DFL: 1.33 times . 1.42 times . 1.50 times

DTL: 5.33 times. 3.195 times. 3.9 times

Prepared by,

Mursalin Sardar ; Cell -01925-425876

No 23 From the following information of a company calculate;

1) Degree of operating leverage and its effect on EBIT.

2) Degree of financial leverage and its effect of earning per share EPS

3) Degree of total leverage and its effect of EPS.

Income Statement

Sales	At present	25% increase	50% increase
Sales	80,000 Units	10,000 Units	12,000 Units
Selling price @ tk.20 each Variable cost @ tk.12 each	Tk.1,60,000 96,000	Tk.2,00,000 1,20,000	Tk.2,40,000 1,44,000
Contribution Fixed cost	64,000 32,000	80,000 32,000	96,000 32,000
Earning before interest and tax (EBIT)	32,000	48,000	64,000

Balance Sheet

Current Assets Net fixed assets Total assets	Tk,75,000 1,25,000	Debt capital (10% interest) Common Stock capital (1,500 shares @tk.100 each) Total capital & liabilities	tk.50,000 1,50,000
	2,00,000

			2,00,000

Assume that the corporate tax rate is 40%.

ANS ; 2times, 1.19 times , 2.38 times.

No 24 The capital structure of Y ltd. Is composed of ordinary share capital of tk.1,00,000 (tk.10 per share) and 10% debenture of tk.1,00,000.The sales of the company increased by 20% and thereby the volume of sales increased from 10,000 units to 12,000 units . Its selling price per unit is tk.12, variable cost per unit is tk.8 and fixed cost is tk.20,000 income tax rate of the company is 50%.

On the basis of the above data you are required to calculate ;

1) Percentage increase in earning per share (EPS)

2) Financial and operating leverage at sales level of 10,000 units.

ANS : % increase in EBIT 40%, % increase in EPS 80% ,

No 25 From the following data of two companies you are required to calculate and show the effect of :

a) Degree of operating leverage

b) Degree of financial leverage

c) Degree of combined leverage

d) Earning per share .

e) Rate of return on investment (ROI)

Help : ROI =

X 100

Company	A	B
Present sales in units Selling price per unit(tk.) Variable cost per unit (tk.) Fixed operating cost (tk.) Total Assets (tk.) Common Stock capital of tk.100 per share 10% Debenture Corporate tax rate Proposed increase in sale by 25% units	60,000 50 25 6,00,000 20,00,000 10,00,000 10,00,000 25% 75,000	80,000 40 18 8,60,000 20,00,000 8,00,000 12,00,000 25% 1,00,000

No 26 The operating and cost data of Commerce Publication are 31^st December 2003 as bellow.

Sales unit 50,000

Sales tk.25,00,000

Variable cost tk.15,00,000

Fixed cost tk.5,00,000

6% Debt tk.5,00,000

10% Preferred stock tk.5,00,000

common stock (per share 200 ) tk.10,00,000

Tax bracket of the company 50%

You are required to calculate ;

1) Degree of operating leverage. 2 times

2) Degree of financial leverage. 1.35 times

3) Degree of combined leverage . 2.70 times .

4) C/M ratio or P/V ratio . PV ratio =

x 100. 40%.

5) Operating break even point (in taka). 12,50,000

6) Operating break even point (in unit). 25,000

7) Financial break even point .1,30,000

8) If EBIT will be double answer the following questions.

a) How much % change in sales ? 50%

b) How much % change in EBIT ? 100%

c) How much % change in EPS ? 135.14%

No 27 Shipu and son Ltd.

December 31,2009

Total assets tk.5,00,000

ROI (assets) 30%

VC ratio 60%

DOL 5 times

Find out :a) Sales .18,75,000

c) Fixed cost . 6,00,000

d) PV ratio . 40%

e) BEP (tk.) .15,00,000

f) Assets turnover . 3.75

No 28 the financial information for the year 2003 for Sundur ltd. Is given:

Details	Amount
Sales (10000 units @ tk.50 each) Less: Variable cost (tk.20 per unit )	5,00,000 2,00,000
Contribution Less: Fixed cost	3,00,000 1,50,000
EBIT Less: Interest expenses	1,50,000 50,000
EBIT Less: Tax 40%	100,000 40,000
EAT	60,000

You have to calculate ;

DOL, DFL, DTL. BEP (TK.) & BEP (UNIT). Financial BEP , M/S ratio & tk. , PV ratio .

ANS ; 2 times, 1.5 times , 3 times , 2,50,000 .50,000 . 2,50,000 . 50%

Financial BEP = I+

M/S ratio =

X 100

M/S TK.= Total sales – BEP (tk.)

No 29 From the following information relating to Nayme & co. compute DOL, DFL, DTL.

Sales 20,000 units

Sales price tk.10 per unit

Variable cost tk.5 per unit

Fixed cost tk.5,00,000

Interest amount tk.3,00,000

ANS : 2 times . 2.5 times . 5 times.

No 30 Calculate the DOL, DFL, DTL. From the following information ;

Selling price per unit tk.45

Material cost per unit tk.10

Labour cost per unit tk.10

Factory over head per unit tk.8

Fixed cost tk.2,40,000

Interest amount tk.50,000

Sales 20,000 units

ANS: 3.4times , 2 times, 6.8 times.

NO 31 A company's capital structure is composed of common stock capital of tk.1,00,000 (1000 shares @ tk.100 each) and of 15% debenture of tk.2,00,000 corporate tax rate of the company is 25%. The company's last year data are as follows :

Sakes 20,000 units @ tk.10 each

Variable cost @ tk.4 per unit

Fixed cost tk.70,000

A) What are the degree of operating , financial , and total leverage.

B) What are the degree of operating leverage , financial, and total leverage if the sales increase by 40% ?

C) What will be the impact of increasing sale by 40% and 60% ?

ANS: 2.4,2.5,6/1.71,1.44,2.46 times.

No 32 Madhobi company's capital structure is composed by common stock capital of tk.1,00,000 ( 1000 shares @ tk.100 each) and of 15% debenture of tk.2,00,000. 10% preffered stock of tk.1,00,000 corporate tax rate of the company is 25 percent . The company's last year data is follows .

Sales 20,000 units @ tk.10 each

Variable cost @ tk.4 per unit

Fixed cost tk.70,000

Required :

A) What are degree of DOL, DFL, & DTL

B) What are the of DOL, DFL, & DTL if sales increase by 50%

C) What will be the impact on operating , financial, & total leverage if the sales increased by 50% .ANS : 2.4,7.5,18/1.64,1.65,2.74 times.

No 33 From the following information of Biswajit company ltd. Calculate DOL, DFL, & DTL/DML/DCL.

Production and sales 35,000 units

Variable cost :

Material tk.12 per unit

Labour tk.10 per unit

Overhade tk.15 per unit

Fixed cost annual tk.3,25,000

Interest cost annual tk.1,25,000

Selling price per unit tk.50

ANS : DOL.3.50 times . DFL .26 times. DTL. 91 times

No 34 A company recently sold 10,000 units at tk.75 per unit . Variable cost per unit is tk.30 and annual fixed cost is tk.2,25,000 .Annual interest charges on debt capital of tk.8,00,000 at 10% and the firm has 12% preferred stock of tk.4,00,000 . The company currently has 2,000 common stock . Assume that the company is in 40% tax bracket. You are required to

a) Calculate the degree of operating , financial, & total leverage .

b) Calculate the effect of degree of operating, financial, & total leverage if sales increase by 50% & 100%.

ANS: 2,3.46,6.92 times.

No 35 The following information are available from the books of accounts of China & Asma company.

Company	China	Asma
Sales in units Selling price per unit (tk.) Variable cost per unit (tk.) Annual fixed operating cost (tk.) 15%debt. Capital (tk,) Shares capital(tk.100 per unit) Proposed increase sale	40,000 30 11 1,28,000 3,00,000 1,50,000 50%	60,000 25 9 1,50,000 2,50,000 2,00,000 25%

Calculate :

1) Degree of operating leverage. 1.20/1.12/1.19/1.14.

2) Degree of financial leverage . 1.08/1.05/1.05/1.04.

3) Degree of total leverage . 1.30/1.18/1.25/1.19.

4) Break even point (BEP) . 6337 units.tk.202110

Assume a tax rate of 30%.

No 36 From the following data of two companies you are required to calculate and show the effect of increase in sales by 25%.

A) Degree of operating leverage,

B) Degree of financial leverage,

C) Degree of total leverage.

D) Break even point (BEP) ,

E) Financial BEP, Financial BEP = I+

Company	Shoel	Afzal
Present sales in unit Selling price per unit (tk.) Variable cost (tk.) Fixed cost (tk.) Total Assets(tk.) Common stock capital of tk.100 per share 10% debenture Corporate tax rate Proposed increase in sale by 25% units	60,000 50 25 6,00,000 20,00,000 10,00,000 10,00,000 25% 75,000	80,000 40 18 8,60,000 20,00,000 8,00,000 12,00,000 25% 1,00,000

Note: Sale Gi wewfbœ increase level _vK‡j DOL, DFL, DTL. kaygvÎ Present level G Ki‡Z nq Ges ewa©Z level G Impact/ Effect A_v©r cÖfve †`Lv‡Z nq|

No 37 From the following information you are required to calculate the degree of operating leverage , Degree of financial leverage , & Degree of total leverage. You are also required to show the effect if sales increase by 50%.

Income statement

Sales 20,000 units @ tk.20 per unit Less Variable cost @ tk.10 per unit	4,00,000 2,00,000
Contribution Less Fixed cost	2,00,000 80,000
EBIT Less Interest on debt capital @ 10%	1,20,000 20,000
Earnings before tax (EBT) Less Tax 40%	1,00,000 40,000
Net profit after tax ( EAT)	60,000

· Number of shares outstanding 6,000 shares and earning per share

=tk.10

Balance sheet

Current asset Net fixed assets	Tk.3,00,000 5,00,000	Debt capital Common stock capital	2,00,000 6,00,000
Total assets	8,00,000	Total capital	8,00,000

No 38 The well established company's most recent balance sheet is as follows :

Liabilities + owners equity	Taka	Assets	Taka
Equity capital ( tk.100 per shares) 10% Debt Retained earnings Current liabilities	1,00,000 2,00,000 40,000 60,000	Net fixed assets Current assets	3,00,000 1,00,000
Total	4,00,000	Total	4,00,000

Others information :

Assets turnover ratio = 3 times

Fixed operating cost = tk.2,20,000

Variable cost = 40%

Income tax rate =40%

Required :

1) Degree of operating leverage . 1.44 times

2) Degree of financial leverage .1.04 times

3) Degree of total leverage . 1.49 times

4) Determine the level of EBIT is EPS is tk.30 and confirm it .EBIT= 70,000

5) At what level will the EBIT of the firm equal to zero?

6) What is VC ratio ?

Help: EPS=

VC ratio =

X100

ZERO EBIT : Here Zero EBIT means break even sales (BES)=

CM ratio=

X 100

No 39 The financial data of Aphu ltd. And Dola ltd. For the year 2010 are given bellow :

Details Aphu ltd. Dola ltd.

VC ratio 60% 70%

Long term debt @ 12% 5,00,000 6,00,000

DOL 5:1 3:1

DFL 2:1 3:1

Tax rate 45% 45%

No of equity share 1,500 1,000

Required :

a) Prepare income statement both company.

b) Comments on financial status of the company.

No 39 Agora most recently sold 1,00,000 units at tk.7.50 each ; its variable operating cost are tk.3.00 per unit . and its fixed cost are tk.2,50,000 .Annual interest charges total tk.80,000 and the firm has 8,000 shares of tk.5 (annual dividend) preferred stock outstanding . It currently has 20,000 shares of common stock outstanding . Assume that the firm has 40% tax rate .

a) At what level of sales (in units ) would the firm break even on operating (that is EBIT tk.0)

b) Calculate the firm's earning per shares (EPS) in tabular from at (1) the current level of sales and (2) a 1,20,000 units sales level .

c) Using the current tk.7,50,000 level of sales as a base , calculate the firm's DOL.

d) 50% increase what is effect on this firm.

No 40 The capital structure of the Kohinur company consists of an ordinary share capital of tk.20,00,000 (tk.100 per share ) and tk.20,00,000 of 10% Debenture , sales increased by 50%from 1,00,000 units to 1,50,000 units , the selling price is tk.20 per unit ; variable costs amount to tk.12 per unit and fixed cost amount tk.4,00,000 .The income tax rate is assumed to be 50% .

You are required to calculate the following :

a) Earning per shares.

b) The degree of operating leverage at 1,00,000 and 1,50,000 units.

c) The degree of financial leverage at 1,00,000 and 1,50,000 units .

d) The percentage of increase in earning per shares

No 41 Tendulkar Toys produces beach balls selling 4,00,000 balls a year . Each ball produced has a variable operating cost of tk.0.84 and sells for tk.1.00 .Fixed cost are tk.28,000 . The firm has annual interest charges of tk.6,000. Preferred dividends of tk.2,000 and a 40% tax rate.

a) Calculate the operating BEP in units.

b) Calculate DOL

c) Calculate DFL

d) Calculate DTL

No 42

	2006	2007
Sales TC	Tk.10,00,000 Tk.20,000	Tk.15,00,000 Tk.40,0000

Find the DOL

If SPPU is tk.50 VCPU is tk.30 Fixed cost tk.50,000 .Find BEP (unit) and BEP (tk.)

No 43 A company currently selling 10,000 units @ tk.10 per unit .Variable cost tk.2 per unit .Fixed cost tk.20,000 .The company has to pay tk.as interest on loan and tk.6,000 as dividend to the preference shareholders. The company has 5,000 shares of common stock and in 40% tax rate.

Calculate :

a) DOL, DFL,& DTL.

b) Financial BEP in units and taka .

c) Operating BEP in units and taka.

d) Target sales units to earn profit of tk.1,60,000

No 44 Carolina Fastener Inc. makes a patented marine bulkhead latch that wholesale for tk.6.00 each latch has variable operating cost of tk.3.50 .Fixed operating cost are tk.50,000 per year .The firm pays tk.13,000 interest and preferred dividends of tk.7,000 per year . At this point the firm is selling 30,000 latches a year and is taxed at 40%

a) On the basis of the firm's current sales of 30,000 units per year and its interest and preferred cost , calculate its EBIT and net profit .

b) Calculate the firm's DOL, DFL, and DTL.

c) Calculate Carolina Faster's operating breakeven point.

No 45 Molly Jasper and her sister , Caitlin peters , got into the novelties business almost by accident, Molly a talented sculptor often made little figurines as gifts for friend s .Occasionally she and Caitlin would set up a booth at a crafts fair and sell a few of the figurines along with Jewlery that Caitlin made .little by little demand for the figurines now called Mollycaits grew and the sister s began to reproduce some some of the favorites in resin using molds of the originals . The day came when a buyer for a major department store offered then a contract to produce 1,500 figurines of various designs for tk.10,000. Molly and Caitlin realized that it was time to get down to business . To make book keeping simpler , Molly had priced all of figurines at tk.8.00 . Variable operating costs amounted to an average of tk.6.00 per unit . In order to produce the order , Molly and Caitlin would have to rent industrial facilities for a month , Which would cost them tk.4,000.

a) Calculate Molltcait's operating break even point.

b) Calculate Mollycait's EBIT on the department store order.

c) If Molly renegotiates the contract at a price of tk.10.00 What will the EBIT be?

No 46 The following information are available from the books of accounts of company A

Sales in units 40,000

Selling price per unit tk.20

Variable com per unit tk.12

Annual Fixed cost tk.1,28,000

15% Debenture capital tk.3,00,000

Shares capital (tk.100 per share) tk.1,50,000

Proposed increase sale 50%

Calculate and show the effect of