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
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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
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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
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.
Solution: Income Statement (Amount in `)
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
LEVERAGES By: CA Ashish Kalra
13
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(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
LEVERAGES By: CA Ashish Kalra
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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%
(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
LEVERAGES By: CA Ashish Kalra
17
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[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)