CHAPTER LEVERAGES - webmitr.com · 5 = EBIT EBIT – `12,000 5 (EBIT – `12,000) = EBIT 4 EBIT =...

Question 9: XYZ Ltd. has an average selling price of `10 per unit. Its variable unit costs are `7, and fixed costs amount

to `1,70,000. It finances all its assets by equity funds. It pays 35% tax on its income.

ABC Ltd. is identical of XYZ Ltd. except in the pattern of financing. The latter finances its assets 50% by debt, the

interest on which amounts to `20,000. Determine the degree of operating, financial and combined leverage at `7,00,000

sales for both the firms, and interpret the results.

Solution: Statement showing Computation of Leverages

Particulars XYZ Ltd. (`) ABC Ltd. (`)

Sales Revenue 7,00,000 7,00,000

Less: Variable Cost (70%s) (4,90,000) (4,90,000)

Contribution 2,10,000 2,10,000

Less: Fixed Costs (1,70,000) (1,70,000)

EBIT (Operating Profits) 40,000 40,000

Less : Interest NIL (20,000)

EBT 40,000 20,000

Less: Taxes (35%) (14,000) (7,000)

EAT 26,000 13,000

DOL = (Contribution/EBIT 5.25 5.25

DFL = (EBIT/EBT) 1 2

DCL = Contribution/EBT Or (DOL x DFL) 5.25 10.5

The DCL of the ABC Ltd. is higher due to higher financial leverage. Its total risk is, therefore higher although its DOL

(operating risk) is equal to that of the XYZ Ltd.

Question 10: The data relating to two Companies are as given below:

Particulars Company A Company B

Equity Capital `6,00,000 `3,50,000

12% Debentures `4,00,000 `6,50,000

Output (units) per annum 60,000 15,000

Selling Price/ unit `30 `250

Fixed Costs per annum `7,00,000 `14,00,000

Variable Cost per unit `10 `75

You are required to calculate the Operating leverage, Financial leverage and Combined leverage of two Companies.

(CA PE II Nov 2002)

Solution: Computation of Degree of Operating Leverage, Financial Leverage & Combined Leverage:

Particulars Company A (`) Company B (`) Sales Revenue (60,000 units x `30) (15,000 units x `250) 18,00,000 37,50,000

Less: Variable Costs (60,000 units x `10) (15,000 units x `75) (6,00,000) (11,25,000)

Contribution 12,00,000 26,25,000

Less: Fixed Costs (7,00,000) (14,00,000)

EBIT 5,00,000 12,25,000

Less: Interest @ 12% on Debentures (48,000) (78,000)

EBT 4,52,000 11,47,000

DOL= Contribution EBIT

`12,00,000 = 2.4

`5,00,000

`26,25,000 = 2.14

`12,25,000 DFL = EBIT EBT

`5,00,000 = 1.11 `4,52,000

`12,25,000 = 1.07

`11,47,000

DCL = DOL x DFL (2.4 x 1.11) = 2.66 (2.14 x 1.07) = 2.29

CHAPTER3 LEVERAGES

LEVERAGES By: CA Ashish Kalra

For Classes & Information: Visit www.igpinstitute.org & download IGP Mobile App

Question 11: You are given two financial plans of a company which has two financial situations. The detailed information

are as under:

Fixed Cost: Situation ‘A’ = `20,000

Situation ‘B’ = `25,000

Capital Structure of the company is as follows: (Amount in `)

Particulars Financial Plans

XY XM

Equity 12,000 35,000

Debt (Cost of Debt 12%) 40,000 10,000

52,000 45,000

You are required to calculate Operating Leverage and Financial Leverage of both the plans. (CA IPCC May 2011)

Solution: Statement Showing Computation of Operating Leverage (Amount in `)

Particulars Situation A Situation B

Sales (6,000 units @ `30 per unit) 1,80,000 1,80,000

Less: Variable Cost (6,000 units @ `20 per unit) (1,20,000) (1,20,000)

Contribution 60,000 60,000

Less: Fixed Costs (20,000) (25,000)

Operating Profit (EBIT) 40,000 35,000

Operating Leverage = Contribution

EBIT

`60,000 = 1.5

`40,000

`60,000 = 1.7143

`35,000

Statement showing Computation of Financial Leverage

Financial Plan Situation A Situation B

Plan XY Plan XM Plan XY Plan XM

Operating Profit (EBIT) 40,000 40,000 35,000 35,000

Less: Interest on Debt (4,800) (1,200) (4,800) (1,200)

Profit Before Tax (PBT) 35,200 38,800 30,200 33,800

Financial Leverage = EBIT

PBT

= `40,000

`35,200

= 1.136

= `40,000

`38,800

=1.031

= `35,000

`30,200

= 1.159

= `35,000

`33,800

= 1.036

Question 12: (i) You are required to calculate the Operating Leverage from the following data:

Sales `50,000

Variable Costs 60%

Fixed Costs `12,000

(ii) You are required to calculate the Financial Leverage from the following data:

Net Worth `25,00,000

Debt/Equity 3:1

Interest Rate 12%

Operating Profit `20,00,000

Solution: (i) Calculation of Operating Leverage: (Amount in `)

Sales 50,000

Less: Variable Cost (60% of Sales) (30,000)

Contribution 20,000

Less: Fixed Costs (12,000)

Operating Profit (EBIT) 8,000

Operating Leverage = Contribution = `20,000 = 2.5

Operating Profit `8,000

Installed Capacity 10,000 units

Actual Production and Sales 60% of installed capacity

Selling Price per unit `30

Variable Cost per unit `20

ADVANCED PROBLEMS: DOL & DFL


3


(ii) Calculation of Financial Leverage:

Calculation of Debt and Interest thereon:

(a) Debt = `25,00,000 x 3 = `75,00,000

(b) Interest on Debt = `75,00,000 x 12/100 = `9,00,000

Particulars Amount in ` Operating Profit 20,00,000

Less Interest on Debt (9,00,000)

Profit Before Tax 11,00,000

Financial Leverage = Operating Profit/Profit Before Tax = 20,00,000/11,00,000 = 1.82

Question 13: From the following details of X Ltd., prepare the Income Statement for the year ended 31st December 2014:

Financial Leverage 2

Interest `2,000

Operating Leverages 3

Variable cost as a percentage of sales 75%

Income tax rate 30%

(CA IPCE Nov 2015)

Solution: Income Statement (Amount in `)

Working Notes:

DFL = EBIT = EBIT .

EBT EBIT – Interest

2 = EBIT .

EBIT – `2,000

2 EBIT – `4,000 = EBIT

EBIT = `4,000

EBT = `4,000 – `2,000 = `2,000

DOL = Contribution

EBIT

3 = Contribution

`4,000

Contribution = `12,000

P/V ratio = 100% – Variable Cost ratio

= 100% – 75% = 25%

Sales = Contribution = `12,000 = `48,000

P/V ratio 25%

Question 14: Calculate the Operating Leverage for each of the four firms A, B, C and D from the following price and

cost data.

Particulars Firms

A (`) B (`) C (`) D (`)

Sale Price per unit 20 32 50 70

Variable Cost per unit 6 16 20 50

Fixed Operating Cost 80,000 40,000 2,00,000 Nil

Sales 48,000

Less: Variable Costs (75% x `48,000) (36,000)

Contribution 12,000

Less: Fixed Costs (Bal. fig.) (8,000)

EBIT 4,000

Less: Interest (2,000)

EBT 2,000

Less: Income Tax (30%) (600)

EAT 1,400

ADVANCED PROBLEM: DOL



What conclusions can you draw with respect to levels of fixed cost and the degree of operating leverage result?

Explain. Assume number of units sold is 5,000.

Solution: Computation of EBIT:

Particulars Firms

A (`) B (`) C (`) D (`)

Sales (units) 5,000 5,000 5,000 5,000

Sales Revenue (Units sold x Sale Price) 1,00,000 1,60,000 2,50,000 3,50,000

Less: Variable Cost (30,000) (80,000) (1,00,000) (2,50,000)

Contribution 70,000 80,000 1,50,000 1,00,000

Less: Fixed Operating Costs (80,000) (40,000) (2,00,000) Nil

EBIT (10,000) 40,000 (50,000) 1,00,000

DOL = Contribution

EBIT

`70,000

(`10,000)

= 7 times

`80,000

`40,000

= 2 times

`1,50,000

(`50,000)

= 3 times

`1,00,000

`1,00,000

= 1 time

The impact of Operating Leverage will exist only when there are fixed costs. In the case of Firm D, there is no

magnified effect on the EBIT due to change in sales. A 20% increase in sales will result in a 20% increase in EBIT.

Practically, it is very difficult to find a firm having DOL = 1, as all business organisations have an exposure of fixed

operating costs. In the case of all other firms, Operating Leverage exists. It is maximum in Firm A, followed by Firm

C & minimum in Firm B. The maximum DOL is 7 meaning that 1% change in sales will result in 7% change in EBIT level

in the direction of the change of sales level of Firm A.

Question 15: (a) Compute DFL from the following information:-

EBIT `50,000

8% Debentures `2,50,000

10% Preference Share Capital `1,00,000

Tax rate 35%.

(b) Compute DFL if EBIT becomes `1,50,000

Solution: (a) DFL = EBIT = `50,000 = `50,000 = `50,000 = 3.421

EBIT Int – Pref. div `50,000 – `20,000 – `10,000 `30,000 – `15,385 `14,615

(1 – t) 0.65

(b) DFL = EBIT = `1,50,000 = `1,50,000 = 1.309

EBIT Int – Pref. Div `1,50,000 – `20,000 – `15,385 `1,14,615

(1 – t)

Question 16: The following information is available for AMD Ltd.

PBDIT `830 Cr

Depreciation `6 Cr

Effective Tax Rate 30%

EPS `4

Book Value `30 per share

Number of Outstanding Shares 33 Cr

D/E ratio 1.5 : 1

Find: (a) Degree of Financial Leverage.

(b) Financial Break even point.

Solution: EBIT = PBDIT – Depreciation = `830 Cr - 6 Cr = `824 Cr

EPS = EAE .

No. of Equity Shares

EAE = EPS x No. of Equity Shares = `4 x 33 Cr. = 132 Cr

EBT = `132 Cr x 100

70

EBT = `188.57 Cr

(a) DFL = EBIT = `824 Cr = 4.37

DFL & FINANCIAL BREAK EVEN POINT

ADVANCED PROBLEM: DFL


5


EBT `188.57 Cr

(b) Financial Break Even Point = Interest on Debt = EBIT – EBT = `824 Cr – `188.57 Cr = `635.43 Cr

Question 17: From the following financial data of Company A and Company B: Prepare their Income Statements.

Particulars Company A (`) Company B (`)

Variable Cost 56,000 60% of sales

Fixed Cost 20,000 --

Interest Expenses 12,000 9,000

Financial Leverage 5 : 1 --

Operating Leverage -- 4 : 1

Income Tax Rate 30% 30%

Sales -- 1,05,000

(CA PCC Nov 2009)

Solution: Income Statements of Company A and Company B (Amount in `)

Particulars Company A Company B

Sales 91,000 1,05,000

Less: Variable cost (56,000) (63,000)

Contribution 35,000 42,000

Less: Fixed Cost (20,000) (31,500)

Earnings before Interest and Tax (EBIT) 15,000 10,500

Less: Interest (12,000) (9,000)

Earnings Before Tax (EBT) 3,000 1,500

Less: Tax @ 30% (900) (450)

Earnings After Tax (EAT) 2,100 1,050

Working Notes: Company A

(i) Financial Leverage = EBIT

EBIT - Interest

5 = EBIT

EBIT – `12,000

5 (EBIT – `12,000) = EBIT

4 EBIT = `60,000

EBIT = `15,000

(ii) Contribution = EBIT + Fixed Cost = `15,000 + `20,000 = `35,000

(iii) Sales = Contribution + Variable Cost = `35,000 + `56,000 = `91,000

Company B

(i) Contribution = 40% of Sales (as Variable Cost is 60% of Sales) = 40% of `1,05,000 = `42,000

(ii) Operating Leverage = Contribution

EBIT

4 = `42,000

EBIT

EBIT = `42,000 = `10,500

4

(iii) Fixed Cost = Contribution – EBIT = `42,000 – `10,500 = `31,500

Question 18: Alpha Ltd. has furnished the following Balance Sheet as on March 31, 2011:

Liabilities Amount in ` Assets Amount in `

Equity Share Capital (1,00,000) 10,00,000 Fixed Assets 30,00,000

(Equity share of `10 each) Current Assets 18,00,000

General Reserve 2,00,000

15% Debentures 28,00,000

Current Liabilities 8,00,000

48,00,000 48,00,000

PREPARATION OF INCOME STATEMENT FROM VARIOUS LEVERAGES

EPS & DCL



Additional Information:

(1) Annual Fixed Cost other than Interest `28,00,000 (2) Variable Cost Ratio 60% (3) Total Assets Turnover Ratio 2.5 (4) Tax Rate 30%

You are required to calculate:

(i) Earnings per share (EPS), and

(ii) Combined Leverage. (CA IPCC Nov 2011)

Solution: Total Assets = `48,00,000

Total Assets Turnover Ratio = 2.5

Total Sales = `48,00,000 x 2.5 = `1,20,00,000

Computation of Profit After Tax (PAT)

Particulars Amount in ` Sales 1,20,00,000 Less: Variable Cost (60% of Sales Contribution) (72,00,000) Contribution 48,00,000 Less: Fixed Cost (other than Interest) (28,00,000) EBIT 20,00,000

Less: Interest on Debentures (15% of 28,00,000) (4,20,000)

PBT 15,80,000 Less: Tax @30% (4,74,000) PAT 11,06,000

(i) EPS = PAT = `11,06,000 = `11.06

No. of Equity Shares 1,00,000

(ii) DCL = Contribution = `48,00,000 = 3.04

PBT `15,80,000

Question 19: The following information to XL Company Ltd. for the year ended 31st March, 2013 are available to you:

Equity Share Capital of `10 each `25 lakh

11% Bonds of `1,000 each `18.5 lakh

Sales `42 lakh

Fixed Cost (Excluding Interest) `3.48 lakh

Financial Leverage 1.39

Profit-Volume Ratio 25.55%

Income Tax Ratio Applicable 35%

You are required to calculate

(i) Operating Leverage

(ii) Combined Leverage and

(iii) Earning Per Share (CA IPCC May 2013)

Solution: P/V Ratio = Contribution

Sales

Contribution = 25.55%

`42 lakhs

Contribution = `10.731 lakhs

Income Statement

Particulars Amount in `

Sales 42,00,000

Less: Variable Cost (31,26,900)

Contribution 10,73,100

Less: Fixed Cost (3,48,000)

EBIT 7,25,100

Less: Interest (2,03,500)

DOL, DCL & EPS


7


EBT 5,21,600

Less: Tax @ 35% (1,82,560)

Earnings Available for Equity Shareholders (EAE) 3,39,040

(i) Operating Leverage = Contribution = `10,73,100 = 1.48

EBIT `7,25,100

(ii) Combined Leverage = Contribution = `10,73,100 = 2.06

EBT `5,21,600

(iii) Earnings per share (EPS) = EAE = `3,39,040 = `1.35616


Question 20: Z Limited is considering the installation of a new project costing `80,00,000. Expected annual sales

revenue from the project is `90,00,000 and its variable costs are 60% of sales. Expected annual fixed cost other than

interest is ̀ 10,00,000. Corporate tax rate is 30%. The company wants to arrange the funds through issuing 4,00,000 equity

shares of `10 each and 12% debentures of `40,00,000. You are required to:

(i) Calculate the Operating, Financial and Combined Leverages and Earnings per share (EPS).

(ii) Determine the likely level of EBIT, if EPS is (1) `4, (2) `2, (3) `0. (CA PE II Nov 2009)

Solution: (i) Calculation of Leverages and Earnings per Share (EPS)

Income Statement (Amount in `)

Sales Revenue 90,00,000

Less: Variable Cost @ 60% (54,00,000)


Less: Fixed Costs other than Interest (10,00,000)

Earnings before Interest and Tax (EBIT) 26,00,000

Less: Interest (12% on `40,00,000) (4,80,000)

Earnings Before Tax (EBT) 21,20,000

Less: Tax @ 30% (6,36,000)

Earnings After Tax (EAT) 14,84,000

1. DOL = Contribution = `36,00,000 = 1.3846

EBIT `26,00,000

2. DFL = EBIT = `26,00,000 = 1.2264

EBT `21,20,000

3. DCL = DOL x DFL = 1.38 x 1.23 = 1.6974

4. EPS = EAT = `14,84,000 = `3.71


(ii) Calculation of likely levels of EBIT at different EPS:

EPS = (EBIT – I) (1 – t)

Number of Equity Shares

(1) 4 = (EBIT – `4,80,000) (1 – 0.3)

4,00,000

EBIT – `4,80,000 = `16,00,000

0.70

EBIT – `4,80,000 = `22,85,714

EBIT = `27,65,714

(2) 2 = (EBIT – `4,80,000) ( 1 – 0.3)

4,00,000

EBIT – `4,80,000 = `8,00,000

0.70

EBIT = `4,80,000 + `11,42,857 = `16,22,857

(3) 0 = (EBIT – `4,80,000) (1 – 0.3)

4,00,000

EBIT = `4,80,000

Question 21: A company had the following Balance Sheet as on March 31, 2006:

Liabilities and Equity (` in Crores) Assets (` in Crores)

DOL, DFL, DCL & EPS



Equity Share Capital (1 crore shares of `10 each) 10 Fixed Assets (Net) 25

Reserves and Surplus 2 Current Assets 15

15% Debentures 20

Current Liabilities 8

40 40

The additional information given is as under:

Fixed Costs per Annum (Excluding Interest) `8 crores

Variable Operating Costs Ratio 65%

Total Assets Turnover Ratio 2.5

Income-Tax Rate 40%

Required: Calculate the following and comment:

(i) Earnings per share

(ii) Operating Leverage

(iii) Financial Leverage (iv) Combined Leverage (CA PE II Nov 2006, CA IPCC May 2014 Adapted)

Solution: Total Assets = `40 crores

Total Asset Turnover Ratio = 2.5

Hence, Total Sales = `40 crores x 2.5 = `100 crores

Computation of Profits after Tax (PAT) (` in Crores)

Sales 100

Less: Variable operation cost @ 65% (65)

Contribution 35

Less: Fixed cost (other than Interest) (8)

EBIT 27

Less: Interest on debentures (15% x 20) (3)

PBT 24

Less: Tax 40% (9.6)

PAT 14.4

(i) EPS = PAT = `14.4 crores = `14.40

No. of Equity Shares 1 crore equity shares

(ii) Operating Leverage = Contribution = `35 crores = 1.296

EBIT `27

It indicates the choice of technology and fixed cost in cost structure. It is level specific. When firm operates

beyond operating break-even level, then operating leverage is low. It indicates sensitivity of earnings before

interest and tax (EBIT) to change in sales at a particular level.

(iii) Financial Leverage = EBIT = `27 crores = 1.125

PBT `24 crores

The financial leverage is very comfortable since the debt service obligation is small vis-a-vis EBIT.

(iv) Combined Leverage = DOL x DFL = 1.296 x 1.125 = 1.458

The combined leverage studies the choice of fixed cost in cost structure and choice of debt in capital structure.

It studies how sensitive the change in EPS is vis-a-vis change in sales.

Question 22: P Ltd. has the following balance sheet and income statement information:

Balance Sheet as on March 31st

Liabilities Amount in ` Assets Amount in `

Equity Capital (`10 per share) 8,00,000 Net Fixed Assets 10,00,000

10% Debt 6,00,000 Current Asset 9,00,000

Retained Earnings 3,50,000

Current Liabilities 1,50,000

19,00,000 19,00,000

Income Statement for the year ending March 31st (Amount in `)

Sales 3,40,000

Less: Operating Expenses (including `60,000 depreciation) (1,20,000)

EBIT 2,20,000



9


Earnings Before Tax 1,60,000

Less: Taxes (56,000)

Net Earnings (EAT) 1,04,000

(a) Determine the degree of operating, financial and combined leverages at the current sales level, if all operating

expenses, other than depreciation, are variable costs.

(b) If total assets remain at the same level, but sales (i) increase by 20% and (ii) decrease by 20%, what will be the

earnings per share at the new sales level?

Solution: (a) Calculation of Degree of Operating (DOL), Financial (DFL) and Combined leverages (DCL).

DOL = Sales – Variable Costs = `3,40,000 – `60,000 = 1.273

EBIT `2,20,000

DFL = EBIT = `2,20,000 = 1.375

EBT `1,60,000

DCL = DOL x DFL = 1.273 x 1.375 = 1.75

(b) Earnings per share at the new sales level

Particulars Increase by 20% Decrease by 20%

(`) (`)

Sales Level 4,08,000 2,72,000

Less: Variable Expenses (72,000) (48,000)

Less: Fixed Cost (60,000) (60,000)

Earnings Before Interest and Taxes 2,76,000 1,64,000

Less: Interest (60,000) (60,000)

Earnings Before Taxes 2,16,000 1,04,000

Less: Taxes (75,600) (36,400)

Earnings After Taxes (EAT) 1,40,400 67,600

Number of Equity Shares 80,000 80,000

EPS 1.755 0.845

Question 23: The Share Capital of X Ltd. is ̀ 16,00,000 with shares of face value of ̀ 10. It has a Debt Capital of ̀ 5,00,000

at 12% interest rate. The sales of the firm are 2,50,000 units p.a. at a selling price of `6 p.u. and the variable cost p.u. is

`3. The fixed cost amount to `1,00,000 and the company pays tax @ 50%. If the sales increases by 20%, calculate: (a) Percentage increases in EPS.

(b) Degree of Operating Leverage at the two levels.

(c) Degree of Financial Leverage at the two levels.

Solution: (a) Income Statement (Amount in `)

Particulars 2,50,000 units 3,00,000 units

Sales

Less: Variable Cost

15,00,000

(7,50,000)

18,00,000

(9,00,000)

Contribution

Less: Fixed Cost

7,50,000

(1,00,000)

9,00,000

(1,00,000)

EBIT

Less: Interest

6,50,000

(60,000)

8,00,000

(60,000)

EBT

Less: Tax @ 50%

5,90,000

(2,95,000)

7,40,000

(3,70,000)

EAT 2,95,000 3,70,000

No. of Equity Shares 1,60,000 1,60,000

EPS 1.84375 2.3125

% change in EPS = `2.3125 – `1.84375 x 100 = 25.437%

`1.84375

(b) DOL = Contribution

EBIT

At Same Level At Incresed Level

= `7,50,000 = 1.1538 = `9,00,000 = 1.125

DOL, DFL & PERCENTAGE INCREASE IN EPS



`6,50,000 `8,00,000

(c) DFL = EBIT

EBT

At Same Level At Incresed Level

= `6,50,000 = 1.1016

`5,90,000

= `8,00,000 = 1.081

`7,40,000

Question 24: Coke (India), sells 5,00,000 bottles of soft drinks a year. Each bottle produced has a variable cost of `2.50

and sells for `4.50. Fixed operating costs are 5,00,000. The company has current interest charges of `60,000 and

preferred dividends of `24,000. The corporate tax rate is 40%.

(a) Calculate the degree of operating leverage, the degree of financial leverage, and the degree of total leverage. (b) Do

part (a) at the 750,000 bottle sales level. (c) What generalisation can you make comparing (a) to (b) after first finding the

Overall break–even point?

Solution: (a) Contribution = `2 x 5,00,000 bottles = `10,00,000

EBIT = `5,00,000

Interest = `60,000

Preference Dividend = `24,000

Tax rate = 40%

DOL = Contribution = `10,00,000 = 2 times

EBIT `5,00,000

DFL = EBIT = ` 5,00,000 = `5,00,000 = 1.25 times

EBT – PD `4,40,000 – `24,000 `4,00,000

(1 – t) 0.6

DTL = DOL x DFL = 2 x 1.25 = 2.5

(b) Contribution = Contribution per unit x Sales Volume = `2 x 7,50,000 bottles = `15,00,000

EBIT = `10,00,000

DOL = Contribution = `15,00,000 = 1.5

EBIT `10,00,000

DFL = EBIT = `10,00,000 = `10,00,000 = 1.11

EBT – PD `9,40,000 – `24,000 `9,00,000

(1 – t) 0.6

DTL = DOL x DFL = 1.5 x 1.11 = 1.66

Overall BEP = Operating FC + Interest + PD

(1 – t)

Contribution per unit

Case I Case II

`5,00,000 + `60,000 + `40,000

`2

`5,00,000 + `60,000 + `40,000

`2

= `6,00,000 = 3,00,000 units

`2

= `6,00,000 = 3 ,00,000 units

`2

As sales move away from overall BEP, riskiness both operational & financial reduces, thus situation II is better for firm.

Question 25: You are a Finance Manager in Big Pen Ltd. The degree of operating leverage of your company is 5.0. The

degree of financial leverage of your company is 3.0. Your Managing Director has found that the degree of operating

leverage and the degree of financial leverage of your competitor Small Pen Ltd. are 6.0 and 4.0 respectively. In his opinion,

the Small Pen Ltd. is better than that of Big Pen Ltd. because of higher value of degree of leverages. Do you agree with

the opinion of you Managing Director? Give Reasons.

Solution: Comparative statement of Leverages

Particulars Big Pen Ltd. Small Pen Ltd.

1. Operating Leverage = Contribution

EBIT

5

6

DOL, DFL, DTL & OVERALL BREAK EVEN POINT

TRADING ON EQUITY


11


2. Financial Leverage = EBIT

EBT

3. Combined Leverage = Contribution

EBT

3

15

4

24

The operating leverage of Big Pen Ltd. is 5 and of Small Pen Ltd. is 6. It means in the level of sales will have more

impact on EBIT of Small Pen Ltd. than that of Big Pen Ltd. The volume of fixed cost may be higher in case of Small

Pen Ltd. than that of Big Pen Ltd. The business risk of Small Pen Ltd. is also more as compared to Big Pen Ltd.

The Financial Leverage of Big Pen Ltd. is 3, and of Small Pen Ltd. is 4. It means the interest burden of Small Pen

Ltd. is higher than Big Pen Ltd. Financial Risk of Small Pen Ltd. is higher as compared to Big Pen Ltd.

The degree of combined leverage of Big Pen Ltd. is 15 and that of Small Pen Ltd. is 24. It means any change in sales

will show more impact on EPS in case of Small Pen Ltd.

In view of the above, the Managing Directors’ opinion about Small Pen Ltd. is wrong. Big Pen Ltd. carries less business

risk and financial risk as compared to Small Pen Ltd.

Question 26: Lovedove Ltd. and Lovelee Ltd. are both in the same business, having same Capital employed. Their capital

structure & extracts of Income Statement are as follows: (Amount in `)

Particulars Lovedove Ltd. Lovelee Ltd.

Equity share capital of `10 each 16,00,000 6,00,000

12% Debentures 1,00,000 11,00,000

Net Capital Employed 17,00,000 17,00,000

Earnings Before Interest and Taxes (EBIT) 5,10,000 5,10,000

Less: Debenture Interest (12,000) (1,32,000)

Profit Before Tax (PBT) 4,98,000 3,78,000

Less: Tax @ 35% (1,74,300) (1,32,300)

Profit After Tax (PAT) 3,23,700 2,45,000

Number of Shares 1,60,000 60,000

Show the impact of Trading on Equity by comparing EPS & DFL of the two companies.

Solution: Computation of ROI & Debt-Equity Ratio

Lovedove Ltd. Lovelee Ltd.

ROI = EBIT x 100

Capital Employed

`5,10,000 x 100 = 30%

`17,00,000

`5,10,000 x 100 = 30%

`17,00,000

Debt Equity Ratio = Debt .

Equity

`1,00,000 = 0.0625 : 1

`16,00,000

`11,00,000 = 1.8333 : 1

`6,00,000

Since ROI for both the companies is more than the rate of interest, therefore it can be concluded that both the companies

have a favourable financial leverage. Also, Debt/Equity ratio for Lovelee is more; this is will earn more earnings for its

shareholders.

DFL = EBIT

EBT

`5,10,000 = 1.024

`4,98,000

`5,10,000 = 1.349

`3,78,000

Lovelee Ltd. has a higher exposure of financial risk (as can be interpreted from DFL) and is using more debt in its capital

structure, this will help the company in magnifying the return for its equity shareholders.

EPS = EAT .

No. of equity shares

`3,23,700 = `2.02

1,60,000

`2,45,000 = `4.08

60,000

Question 27: ABC Limited has an average cost of debt at 10% and tax rate is 40%. The Financial leverage ratio

for the company is 0.60. Calculate Return on Equity (ROE) if its Return on Investment (ROI) is 20%.

(CA PCC May 2007)

Solution: ROE = [ROI + {(ROI – r) x D/E}] (1 – t)

= [20% + {(20% – 10%) x 0.60}] (1 – 0.40)

= [20% + 6%] x 0.60 = 15.60%

Question 28: Consider the following information for Omega Ltd.:

Particulars (` in Lakhs)

EBIT (Earnings before Interest and Tax) 15,750

Earnings before Tax (EBT) 7,000

IMPACT OF DCL ON EPS



Fixed Operating Costs 1,575

Required: Calculate percentage change in earnings per share, if sales increase by 5%. (CA PE II Nov 2007)

Solution: Contribution = EBIT + Fixed Operating Cost = `15,750 + `1,575 = `17,325

DCL = Contribution = `17,325 = 2.475

EBT `7,000

For every one percent change in sales, EPS will change by 2.475%. Hence, for 5% increase in sales, EPS will increase by

12.375%.

Question 29: The capital structure of the Progressive Corporation consists of an ordinary share capital of

`10,000,000 (shares of `100 par value) and `10,00,000 of 10% debentures. Sales increased by 20% from 1,00,000 units

to 1,20,000 units, the selling price is `10 per unit; variable cost amounts to `6 per unit and fixed expenses amount to

`2,00,000. The income tax rate is assumed to be 50%. You are required to calculate the following:

(i) The percentage increase in earnings per share;

(ii) The degree of financial leverage at 1,00,000 units and 1,20,000 units.

(iii) The degree of operating leverage at 1,00,000 units and 1,20,000 units.

Comment on the behaviour of operating and financial leverages in relation to increase in production from 1,00,000 units

to 1,20,000 units.


Particulars 1,00,000 units 1,20,000 units

Sales 10,00,000 12,00,000

Less: Variable Costs (6,00,000) (7,20,000

Contribution 4,00,000 4,80,000

Less: Fixed Costs (2,00,000) (2,00,000)

EBIT 2,00,000 2,80,000

Less: Interest (1,00,000) (1,00,000)

EBT 1,00,000 1,80,000

Less: Tax (50,000) (90,000)

EAT 50,000 90,000

Number of Equity Shares 1,00,000 1,00,000

EPS `0.5 `0.9

(i) Percentage increase in EPS = (0.9 – 0.5) x 100 = 80%

0.5

(ii) DFL = EBIT

EBT

At 1,00,000 units At 1,20,000 units

= `2,00,000 = 2 times

`1,00,000

= `2,80,000 = 1.555

`1,80,000

(iii) DOL = Contribution

EBIT

At 1,00,000 units At 1,20,000 units

= `4,00,000 = 2 times

`2,00,000

= `4,80,000 = 1.71 times

`2,80,000

As production increases from 1,00,000 units to 1,20,000 units, the DOL & DFL decreases implying risk decreases.

Question 30: Following information are related to four firms of the same industry:

Firm Change in Revenue Change in Operating Income Change in Earning per share

P 27% 25% 30%

Q 25% 32% 24%

R 23% 36% 21%

S 21% 40% 23%

Find out:

(i) Degree of Operating Leverage, and

PERCENTAGE INCREASE IN EPS, DOL AND DFL AT DIFFERENT SALES LEVEL

RELATIONSHIP BETWEEN DOL & DCL


13


(ii) Degree of Combined Leverage for all the firms. (CA IPCE May 2015)

Solution:

Question 31: The following summarizes the percentage changes in operating income, percentage changes in

revenues, and betas for four pharmaceutical firms.

Firm Change in Revenue Change in Operating Income Beta

PQR Ltd. 27% 25% 1.00

RST Ltd. 25% 32% 1.15

TUV Ltd. 23% 36% 1.30

WXY Ltd. 21% 40% 1.40

Required:

(i) Calculate the degree of operating leverage for each of these firms. Comment also. (ii) Use the operating leverage to explain why these firms have different beta. (CA PE II Nov 2004)

Solution: (i) Degree of operating leverage is computed as % Change in operating Income/ % Change in Revenue.

Firm Degree of Operating Leverage Beta

PQR Ltd.

RST Ltd.

TUV Ltd.

WXY Ltd.

25%/27% = 0.92

32%/25% = 1.28

36%/23% = 1.56

40%/21% = 1.90

1.00

1.15

1.30

1.40

(ii) There is a clear relationship between the degree of operating leverage and the beta. The greater the degree of

operating leverage, the more responsive income (and presumably stock returns) will be to changes in revenue which are

correlated with changes in market movements.

Question 32: The following details of RST Limited for the year ended 31st March, 2006 are given below:

Operating Leverage 1.4

Combined Leverage 2.8

Fixed Cost (Excluding interest) `2.04 lakhs

Sales `30.00 lakhs

12% Debentures of `100 each `21.25 lakhs

Equity Share Capital of `10 each `17.00 lakhs

Income Tax Rate 30%

Required:

(i) Calculate Financial leverage

(ii) Calculate P/V ratio and Earning per Share (EPS)

(iii) If the company belongs to an industry, whose assets turnover is 1.5, does it have a high or low assets leverage? (iv) At what level of sales the Earning before Tax (EBT) of the company will be equal to zero? (CA PCC May 2007)

Solution: (i) DCL = DOL x DFL

2.8 = 1.4 x DFL

DFL = 2

(ii) Operating Leverage = Contribution or C .

Contribution or C – Fixed Cost or F

1.4 = C .

C – `2,04,000

Firm

Degree of Operating Leverage (DOL)

= % Change in Operating Income

% Change in Revenue

Degree of Combined Leverage (DCL)

= % Change in EPS .

% Change in Revenue

P 25% = 0.926

27%

30% = 1.111

27%

Q 32% = 1.280

25%

24% = 0.960

25%

R 36% = 1.565

23%

21% = 0.913

23%

S 40% = 1.905

21%

23% = 1.095

21%

RELATIONSHIP BETWEEN DOL & BETA

MIXED CONCEPTS OF LEVERAGES & RATIOS



1.4 (C – `2,04,000) = C

1.4 C – `2,85,600 = C

C = `2,85,600 = `7,14,000

0.4

P/V Ratio = Contribution x 100 = `7,14,000 x 100 = 23.8%

Sales `30,00,000

EBT = Sales – VC – FC – Interest

= `30,00,000 – `22,86,000 – `2,04,000 – `2,55,000 = `2,55,000

PAT = EBT – Tax = `2,55,000 – `76,500 = `1,78,500

EPS = Profit After Tax = `1,78,500 = `1.05

No. of Equity Shares `1,70,000

(iii) Assets turnover = Sales = `30,00,000 = 0.784

Total Assets `38,25,000

0.784 < 1.5 means lower than industry turnover.

(iv) Overall BEP = Operating FC + Interest = `2,04,000 + `2,55,000 = `19,28,571

P/V Ratio 23.8%

Therefore, at 19,28,571 level of sales, the Earnings before Tax of the company will be equal to zero.

Question 33: X Ltd. details are as under:

Sales (@ 100 per unit) `24,00,000

Variable Cost 50%

Fixed Cost `10,00,000

It has borrowed `10,00,000 @ 10% p.a. and its equity share capital is `10,00,000 (`100 each). The company is in a tax

bracket of 50%. Calculate:

(a) Operating Leverage

(b) Financial Leverage

(c) Combined Leverage

(d) Return on Equity

(e) If the sales increases by `6,00,000; what will the new EBIT?


Sales 24,00,000

Less: Variable Cost (12,00,000)


Less: Fixed Cost (10,00,000)

EBIT 2,00,000

Less: Interest (1,00,000)

EBT 1,00,000

Less: Tax (50%) (50,000)

EAT 50,000

No. of equity shares 10,000

EPS 5

(a) Operating Leverage = Contribution = 12,00,000 = 6 times

EBIT 2,00,000

(b) Financial Leverage = EBIT = 2,00,000 = 2 times

EBT 1,00,000

(c) Combined Leverage = DOL x DFL = 6 x 2 = 12 times.

(d) ROE = EAT x 100 = `50,000 x 100 = 5%

Equity Funds `10,00,000

(e) Operating Leverage = % change in EBIT

% change in Sales

6 x 25% = % change in EBIT

% change in EBIT = 150%

Increase in EBIT = `2,00,000 x 150% = `3,00,000

New EBIT = `5,00,000

Question 34: The following data are available for the ABC Ltd. and XYZ Ltd.:-


15


Particulars ABC Ltd. XYZ Ltd.

Sales Volume 10,000 units 10,000 units

Selling Price per unit of output `200 `200

Variable Cost per unit of output `120 `150

Fixed Operating Cost per unit of output `60 `30

Equity `3,00,000 `6,00,000

Preference Shares `1,00,000 __

Debt `6,00,000 `4,00,000

Interest Rate on Debt 16.25% 15%

Dividend Rate on Preference Share 13% __

Tax Rate 60% 60%

(a) Calculate the ROE, DOL, DFL, DCL, Operating Break Even Point, Financial Break Even Point & Overall Break Even Point

for each company.

(b) As a financial analyst which of the two companies would you described as more risky? Give reasons.

Solution: (a) Income Statement (Amount in `)

Particulars ABC Ltd. XYZ Ltd.

Sales

Less: Variable Cost

20,00,000

(12,00,000)

20,00,000

(15,00,000)

Contribution

Less: Fixed Cost

8,00,000

(6,00,000)

5,00,000

(3,00,000)

EBIT

Les: Interest

2,00,000

(97,500)

2,00,000

(60,000)

EBT

Less: Tax

1,02,500

(61,500)

1,40,000

(84,000)

EAT

Less: Preference Dividend

41,000

(13,000)

56,000

-

EAT 28,000 56,000

(i) ROE = EAE x 100

Equity Share Holder’s Fund

ABC Ltd. XYZ Ltd.

`28,000 x 100 = 9.33%

`3,00,000

`56,000 x 100 = 9.33%

`6,00,000

(ii) DOL = Contribution

EBIT

ABC Ltd. XYZ Ltd.

`8,00,000 = 4 Times

`2,00,000

`5,00,000 = 2.5 Times

`2,00,000

(iii) DFL = EBIT

EBT - Preference Dividend

(1 - t)

ABC Ltd. XYZ Ltd.

= `2,00,000 = 2.857

`1,02,500 – `13,000

1 - 0.6

= `2,00,000 = 1,428

`1,40,000 – 0

(iv) DCL = DFL x DOL

ABC Ltd. XYZ Ltd.

= 4 x 2.857 = 11.428 = 2.5 x 1.428 = 3.573

(v) Operating BEP = Operating Fixed cost


ABC Ltd. XYZ Ltd.

= `6,00,000 = 7,500 units

80

`3,00,0000 = 6,000 units

50

(vi) Financial BEP = Interest + Preference Dividends



1 - t

ABC Ltd. XYZ Ltd.

= `97,500 + `13,000 = `1,30,000

(1 – 0.6)

= 60,000 + 0 = `60,000

(vii) Overall BEP = Operating F.C + Interest + Pre. Dividend

1 – t .


ABC Ltd. XYZ Ltd.

= 6,00,000 + 97,500 + 13,000

(1 – 0.6) = 9,125 Units

`80

= `3,00,000 + `60,000 + 0 = 7,200 Units

`50

(b) ABC Ltd. is more risky than XYZ Ltd. because its operating & financial leverage is higher than XYZ Ltd. and his combined

leverage is also higher.

Question 1: The following information is available in respect of two firms, P Ltd. and Q Ltd.: (` in Lakhs)

Particulars P Ltd. Q Ltd.

Sales 500 1000

Less: Variable Cost (200) (300)

Contribution 300 700

Less: Fixed Cost (150) (400)

EBIT 150 300

Less: Interest (50) (100)

Profit Before Tax 100 200

You are required to calculate different leverages for both the firms and also comment on their relative risk position.

[Ans: DOL: P Ltd = 2, Q Ltd = 2.33; DFL: P Ltd = 1.5, Q Ltd = 1.5; DCL: P Ltd = 3, Q Ltd = 3.5]

Question 2: Star Industries Ltd. a well established firm in plastics is considering the purchase of one of the two

manufacturing companies. The financial manager of the company has developed the following information about the two

companies. Both companies have total assets of `15,00,000. (Amount in `)

Particulars X Ltd. Y Ltd.

Sales Revenue

Less: Cost of Goods Sold

Selling Expenses

Administration Expenses

Depreciation

30,00,000

(22,50,000)

(2,40,000)

(90,000)

(1,20,000)

30,00,000

(22,50,000)

(2,40,000)

(1,50,000)

(90,000)

EBIT 3,00,000 2,70,000

Cost break-ups

Cost of Goods Sold : Variable Costs

Fixed Costs

9,00,000

13,50,000

18,00,000

4,50,000

Total 22,50,000 22,50,000

(i) Prepare operating statements for both the companies, assuming that sales increase by 20%. The total fixed costs

are likely to remain unchanged and the variable costs are a linear function of sales. Presume that 62.5% of selling

expenses of both companies varies with sales and the remaining remains fixed.

(ii) Calculate the degree of operating leverage at current level of sales.

(iii) If Star Industries Ltd. wishes to buy a company which has a lower degree of business risk, which company would

be purchased by it?

SELF ASSESSMENT PROBLEMS

BASIC PROBLEM: DOL, DFL & DCL

ADVANCED PROBLEM: DOL


17


[Ans: (i) EBIT : X Ltd = `6,90,000, Y Ltd : `4,80,000; (ii) DOL = X Ltd = 6.5, Y Ltd = 3.88; (iii) Y Ltd.]

Question 3: XYZ and Co. has three financial plans before it, Plan I, Plan II, Plan III. Calculate operating and

financial leverage for the firm on the basis of the following information and also find out the highest and lowest value of

combined leverage.

Production 800 units

Selling Price per unit `15

Variable Cost per unit `10

Fixed Cost: Situation A `1,000

Situation B `2,000

Situation C `3,000

Capital Structure Plan I Plan II Plan III

Equity Capital `5,000 `7,500 `2,500

12% Debt 5,000 2,500 7,500

[Ans: Situation A Situation B Situation C

DOL 1.33 2 4

Plan I Plan II Plan III Plan I Plan II Plan III Plan I Plan II Plan III

DFL 1.25 1.11 1.43 1.43 1.18 1.82 2.5 1.43 10

DCL 1.66 1.48 1.90 2.86 2.36 3.64 10 5.72 40 ]

Question 4: From the following, prepare Income Statements of Firms A, B and C.

Particulars Firm A Firm B Firm C

Financial Leverage 3:1 4:1 2:1

Interest `200 `300 `1,000

Operating Leverage 4:1 5:1 3:1

Variable cost as a % of sales 66.67% 75% 50%

Income tax rate 45% 45% 45%

[Ans: Sales - Firm A = `3,600, Firm B = `8,000, Firm C = `12,000]

Question 5: Majnu Ltd. sells its product @ `1,000 per unit. The variable cost of production is `600 per unit. The firm has

a fixed cost of `50,00,000.

(a) Compute the Operating BEP.

(b) Compute DOL, assuming that the sales of Majnu Ltd. is

(i) 12,500 units

(ii) 15,000 units

(iii) 20,000 units

(iv) 25,000 units

(v) 40,000 units [Ans: (a) Operating BEP = 12,500 units; (b) DOL = (i) ∞, (ii) 6, (iii) 2.67, (iv) 2, (v) 1 .45]

Question 6: X Corporation has estimated that for a new product, its operating break-even point is 2,000 units, if the

item is sold for ̀ 14 per unit. The cost accounting department has currently identified variable cost of `9 per unit. Calculate

the operating leverage for sales volume of `2,500 units and 3,000 units. What do you infer from the Operating Leverage of the sales volumes of 2,500 units and 3,000 units and their difference, if any? (CA IPCC Nov 2012 Adapted)

[Ans: DOL (2,500 units) = 5; DOL (3,000 units) = 3]

Question 7: Romeo Ltd. sells its product @ `10 per unit. The variable cost of production is `4 per unit. The firm has a

fixed cost of `4,00,000. The Company has 10% Bonds of `20,00,000.

(a) Compute the Financial BEP.

(b) Compute DFL, assuming that the sales of Romeo Ltd. is

(i) 1,00,000 units

DOL & OPERATING BREAK EVEN POINT

DFL & FINANCIAL BREAK EVEN POINT

ADVANCED PROBLEM: DOL, DFL, DCL

PREPARATION OF INCOME STATEMENT FROM VARIOUS LEVERAGES



(ii) 1,50,000 units

(iii) 2,00,000 units

(iv) 2,50,000 units

(v) 4,00,000 units [Ans: (a) Financial BEP = `2,00,000 (b) DFL = (i) ∞, (ii)1.67, (iii) 1.33, (iv) 1.22, (v) 1.11]

Question 8: Saraju Ltd. produces electronics components with a selling price per unit of `100. Fixed cost amount

to `2,00,000. 5,000 units are produced and sold each year. Annual profits amount to `50,000. The company’s all equity –

financed assets are `5,00,000.

The company proposes to change its production process, adding `4,00,000 to investment and `50,000 to fixed operational

costs. The consequences of such a proposal are:

(i) Reduction in variable cost per unit by `10

(ii) Increase in output by 2,000 units

(iii) Reduction in selling price per unit to `95

Assuming a rate of interest on debt is 10%, examine the above proposal and advice whether or not the company should

make the change. Ignore taxation. Also measure the degree of operating leverage and overall break- even- point.

[Ans: Increase in NP = `45,000; DOL (Present) = 5, (Proposed) = 2.85; BEP (Present) = 4000 units, (Proposed) = 5273 units]

Question 9: Compute Financial BEP, Overall BEP (in units), DFL, DCL & DOL from the following information:

Sales Quantity = 30,000 units

Selling Price p.u. = `150

Variable Cost p.u. = `100

Operating Fixed Cost = `5,00,000

Income Tax Rate = 40%

10% Debentures = `20,00,000

12% Preference Share Capital = `20,00,000

Retained Earnings = `20,00,000

Equity Share Capital (`10 shares) = `30,00,000

[Ans: Financial BEP = `6,00,000; Overall BEP = 22,000 units; DFL = 2.5; DCL = 3.75; DOL = 1.5]

Question 10: The balance sheet of Alpha Numeric Company is given below:

Liabilities (Amount in `) Assets (Amount in `)

Equity Capital (`10 per share) 90,000 Net Fixed Assets 2,25,000

10% Long Term Debt 1,20,000 Current Assets 75,000

Retained Earnings 30,000

Current Liabilities 60,000

3,00,000 3,00,000

The company’s total assets turnover ratio is 3, its fixed operating cost is `1, 50, 000 and its variable operating cost ratio

is 50%. The income – tax is 50%. You are required to:

(i) Calculate the different type of leverages for the company.

(ii) Determine the likely level of EBIT if EPS is: (a)`1, (b) `2 & (c) `0.

[Ans: (i) DOL = 1.5, DFL = 1.04, DCL = 1.56; (ii) EBIT = (a) `30,000, (b) `48,000, (c) `12,000]

Question 11: The following is the income statement of XYZ Ltd. for the year 1998:

(Amount in `)

Sales 50 lakh

Less: Variable Cost (10 lakh)

Less: Fixed Cost (20 lakh)

EBIT 20 lakh

Less: Interest (5 lakh)

Profit Before Tax 15 lakh

Less: Tax at 40% (6 lakh)

Profit After Tax 9 lakh

DOL & OVERALL BREAK EVEN POINT

DOL, DFL, DCL & EPS

LEVERAGES & BREAK EVEN POINTS


19


Less: Preference Dividend (1 lakh)

Profit for Equity Share Holders 8 lakh

The company has 4 lakh equity shares issued to the shareholder. Find out the degree of (i) Operating leverage, (ii) Financial

leverage, and (iii) Combined leverage. (iv) What would be the EPS if the sales level increases by 10% and the EPS if the

sales level decreases by 20%. [Ans: (i) DOL = 2, (ii) DFL = 1.5, (iii) DCL = 3, (iv) EPS = `2.6, `0.8]

Question 12: The following figures are available for success & Co:

Net sales `15 crores

EBIT as percentage of Net Sales 12%

Capital employed: (a) Equity `5 crores; (b) Preference Shares of `1 crore bearing 13% Rate of Dividend; (c) Debt @ 15%

`3 crores.

Given that its Combined Leverage = 3

The applicable Income Tax is to be taken as 40%.

You are required to calculate:

(i) The Return on Equity of the company; and

(ii) the Financial Leverage of the company

(iii) the Operating Leverage of the company. [Ans: ROE = 13.6%, DFL = 1.588, DOL = 1.889]

Question 13: If DOL is 2.5 and on 20% increase in sales from the present level, the EBIT changes to `30,00,000,

what is the present level of sales & fixed cost if variable cost ratio is 50%.

[Ans: Sales = `1,00,00,000; Fixed Cost = `30,00,000]

Question 14: Compute DFL from the following information:

EBIT = `20,00,000

10% Debentures = `50,00,000

Income Tax Rate = 40%

Equity Share Capital (`10 shares) = `45,00,000

(a) Using the concept of DFL, show the effect of DFL on EPS if EBIT is expected to increase by 30% from the present

level.

(b) If DFL is 2, determine the amount of 12% Preference Share Capital.

[Ans: (a) EPS will increase by 40%; (b) Amount of 12% Preference Share Capital = `25,00,000]

Question 15: The following information is available for ABC & Co.

EBIT `11,20,000

Profit before Tax `3,20,000

Fixed Costs `7,00,000

Calculate % change in EPS if the sales are expected to increase by 5%. [Ans: % Change in EPS = 28.4375%]

Question 16: The following data relate of Company XYZ Ltd.: (Amount in `)

Sales 2,00,000

Less: Variable Expenses (30%) (60,000)


Fixed Operating Expenses (1,00,000)

EBIT 40,000


Taxable Income 35,000

(1) Using the concept of combined leverage, by what percentage will taxable income & hence EPS increase if sales increase

by 6%?

(2) Using the concept of operating leverage, by what percentage will EBIT increase if there is a 10% increase in sale?

IMPACT OF DOL ON EBIT

IMPACT OF DFL ON EPS

IMPACT OF DCL ON EPS

IMPACT OF LEVERAGES ON EARNINGS

DOL, DFL & ROE



(3) Using the concept of financial leverage, by what percentage the taxable income and hence EPS will increase if EBIT is

increases by 7%? [Ans: (1) % Increase in EPS = 24%; (2) % Increase in EBIT = 35%; (3) % Increase in EPS = 8%]

Question 17: Jova Ltd., Kova Ltd. and Nova Ltd. give the following information relating to the accounting year

1.1.2000 to 31.12.2000. (` in Lakhs)

Particulars Jova Ltd. Kova Ltd. Nova Ltd. Net Assets 12 12 12

Less : Short Term Loan, Current Liabilities and Provisions (2) (2) (2)

10 10 10

Long Term Capital Employed Consisting of:

Equity Share Capital 4 5 7.5

10% Long Term Loan 6 5 2.5

Earnings Before Interest on Long Term Loan & Tax 1.5 1.5 l.5

Tax rate is 50%. Find out the effect of financial leverage.

[Ans: ROE : Jova Ltd. = 11.25%, Kova Ltd. = 10.00%, Nova Ltd. = 8.33%]

Question 18: A firm has sales of `75,00,000, variable cost of `42,00,000 and fixed cost of `6,00,000. It has a

debt of `45,00,000 at 9% and equity of `55,00,000.

(i) What is the firm’s R.O.I.?

(ii) Does it have favorable financial leverage?

(iii) What are the operating, financial, and combined leverage of the firm?

(iv) If the sales drop to `50,00,000, what will be the new E.B.I.T.?

(v) If the firm belongs to an industry whose capital turnover is 3, does it have a high or low capital turnover?

(vi) At what level of sales the EBT of the firm will be equal to zero?

(vii) If EBIT increases by 20%, by what percentage EBT will increase?

[Ans: (i) R.O.I. = 27%, (ii) Favorable (iii) DOL = 1.222, DFL = 1.176, DCL = 1.435, (iv) New E.B.I.T = 16,00,000, (v) Capital

Turnover = 0.75 times (low as compared to industry), (vi) `22,84,091, (vii) 23.52% ]

Question 19: The net sales of A Ltd. are `30 crores. Earnings before interest and tax of the company as a

percentage of net sales is 12%. The capital employed comprises `10 crores of equity, `2 crores of 13% Cumulative

Preference Share Capital and 15% Debentures of `6 crores. Income-tax rate is 40%.

(i) Calculate the Return-on-equity for the company and indicate its segments due to the presence of Preference Share

Capital and Borrowing (Debentures).

(ii) Calculate the Operating Leverage of the Company given that combined leverage is 3.

[Ans: (i) ROE = 13.6%, Segment due to Preference Shares = - 0.2%, Segment due to Borrowing = + 1.8%; DOL = 1.889]

Question 20: The following summarises the percentage change in E.P.S, percentage change in revenues, & betas for four

companies in automobile business.

Name of Companies Change in Revenues Change in EPS Beta

Tata Motors

Maruti Udyog

Ashok Leyland

General Motors

10%

20%

25%

30%

50%

80%

75%

75%

1.40

1.27

1.18

1.10

(a) Calculate the Degree of Combined Leverage for each of these companies.

(b) If the Degree of operating leverage of these four companies is 2.5, 2, 2.25 & 1.2 respectively for Tata Motors,

Maruti Udyog, Ashok Leyland and General Motors. Compute Degree of financial Leverage.

(c) Explain why these companies have different betas.

[Ans: (a) DCL = 5, 4, 3, 2.5; (b) DFL = 2, 2, 1.33, 2.083; (c) Higher the DCL, higher the Beta]

Question 21: Calculate the Degree of Operating Leverage, Degree of Financial Leverage and Degree of Combined

Leverage from the following data:

Sales `1,00,00,000

TRADING ON EQUITY

RELATIONSHIP BETWEEN DCL & BETA

MIXED CONCEPTS OF LEVERAGES & RATIOS


21


Debt/Equity 3/1

P/V Ratio 50%

Interest Rate 12%

Operating Profit `20,00,000

Capital Turnover Ratio 0.8 times

[Ans: DOL = 2.5, DFL = 2.28, DCL = 5.7]

Question 22: If the combined leverage and operating leverage figures of a company are 2.5 and 1.25 respectively, find the

financial leverage and P/V ratio, given that the equity dividend per share is `2, interest payable per year is `1 lakh, Total

Operating Fixed Cost `0.5 lakh and Sales `10 lakhs. [Ans: DFL = 2, P/V Ratio = 25%]

Question 23: Use the following data and solve the problem:

Total Sales 1,50,000 Units

Selling Price `25

Fixed Cost `2,80,000

Variable Cost `20

Debt `10,00,000 @ 11% interest rate

Equity `20,00,000

Face Value of Each Share `10

Tax Rate 45%

(a) How much the company’s sale have to come down so that the earnings before taxes is equal to zero?

(b) If EBIT doubles, what will be the new level of EBT?

(c) What are the operating and combined leverages?

(d) If the Assets turnover of the industry is 0.75, does the firm have a high or low degree of asset turnover?

[Ans: (a) Sales reduce by 72,000 units; (b) EBT = `8,30,000; (c) DOL = 1.596, DCL = 2.083; (d) High degree]

Question 24: Shamkeen Company is a closely held corporation with a capital structure composed entirely of common stock

and retained earnings. The stock-holders have an agreement with the company that states the company will purchase the

stock of a shareholder should a shareholder want to sell his or her holdings in the company. The agreement states that

the stock will be purchased at a price equal to the stock’s previous year-end book value per share.

Early in October 2004 Mrs. Jane Vadra, a widow of one of Shamkeen’s major stockholders, expressed an interest in selling

her stock in accordance with the buy – back pricing arrangement. Mrs. Jane Vadra owns 600,000 shares of the 3 million

shares of Shamkeen Company common stock.

The board of directors has concluded that the company must replace the capital used to repurchase the shares. The board

has assurance that it would be able to finance the acquisition of stock by borrowing the necessary funds through private

placement at an annual interest rate of 10%. Thus the company would have capital provided by debt and perhaps be able to

take advantage of financial leverage.

The Board and Mrs. Jane Vadra agreed that the exchange will take place on January 1, 2005. The book value per share of

common stock is projected to be `50 on December 31, 2004.

The controller of Shamkeen Company had prepared a forecast and Performa statements for the 2005 year.

An excerpt of the forecasted earnings statement for the year ended December 31, 2005 is presented below (in thousands

of `).

Shamkeen used a 40% income tax rate in forecasted statement. The Performa statements do not reflect the repurchase

of Mrs. Jane Vadra’s shares or the new issue of debt required to pay for the shares.

Particulars (` in ’000)

Income Before Interest & Taxes 50,000

Less: Income Taxes (40%) (20,000)

Net Income 30,000

(a) Revise the excerpt from Shamkeen Company’s forecasted earnings statement for the year ended December 31, 2005,

to reflect the long – term financing to be used to purchase Mrs. Jane Vadra’s common stock.

(b) Explain the impact the long-term debt financing would have on Shamkeen Company’s earnings per share and return on

stockholder’s equity using the forecasted data for 2005.

(c) Identify and discuss the advantages and disadvantages of financial leverage for a company that has a capital structure

similar to that of Shamkeen Company before and after this long – term debt has been added.

[Ans: (a) Net Profit (` in 000s) = 28,200; (b) EPS before Buyback = `10, EPS after Buyback = `11.75; ROE before

Buyback = 20%, ROE after Buyback = 23.5%; Advantage = Trading on Equity, Disadvantage = Increased financial risk & Ke]

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CHAPTER LEVERAGES - webmitr.com · 5 = EBIT EBIT – `12,000 5 (EBIT – `12,000) = EBIT 4 EBIT =...

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