Financial Management - Leverage Analysis

 

Financial Management

LEVERAGE ANALYSIS

 

Part A: Discussion of basic theories along with different relevant formulas

Part B: 13 Illustrations with solutions

Part A

Definition of Leverage

The term leverage may be defined as the risk-return implications associated with the employment of an asset or sources of funds for which the firm has to pay a fixed cost or fixed return. There are three types of leverage – operating leverage, financial leverage and combined leverage.

 

Operating leverage

The leverage associated with investment activities is referred to as operating leverage. It is determined by the relationship between the firm’s sales revenue and its earnings before interest and tax (EBIT). Operating leverage can be measured in terms of degree of operating leverage (DOL). The DOL measures in quantitative terms the extent or degree of operating risks.

 

1	DOL	= (%-age change in EBIT) ÷ (%-age change in sales revenue)
2	DOL	= Contribution ÷ ABS(EBIT) [Here, ABS(EBIT) means absolute value of EBIT ignoring whether the EBIT is positive or negative.]
3	DOL	= (EBIT + Fixed operating costs) ÷ ABS(EBIT)

 

DOL cannot be less than 1(one). DOL is equal to 1(one) when the amount of fixed operating cost incurred for operating activities is equal to ‘0’ (zero). Higher levels of risks are attached to higher degrees of operating leverage. The higher the fixed operating cost the higher is the firm’s operating leverage and its operating risk. Operating risk is the risk of the firm not being able to cover its fixed operating costs.

 

Financial leverage

The leverage associated with financing activities is called financial leverage. It represents the relationship between the firm’s earnings before interest and tax (EBIT) and the earnings per share (EPS). Financial leverage can be measured in terms of degree of financial leverage (DFL). The DFL measures in quantitative terms the extent or degree of financial risks.

 

4	DFL	= (%-age change in EPS) ÷ (%-age change in EBIT)
5	DFL	= EBIT ÷ [EBIT – I – {DP ÷ (1 – t)}]
6	DFL	= EBIT ÷ [EBT – {DP ÷ (1 – t)}]
7	DFL	= EBIT ÷ EBT [If DP = 0]
		I       = Interest
		DP     = Preference dividend
		t       = Rate of corporate tax

 

DFL cannot be less than 1(one). DFL is equal to 1(one) when the amount of interest and preference dividend (i.e., fixed financial charges) is equal to ‘0’ (zero). Higher levels of risks are attached to higher degrees of financial leverage. The higher the fixed financial charges the higher is the firm’s financial leverage and its financial risk. Financial risk is the risk of the firm not being able to cover its fixed financial costs.

 

Combined leverage

Operating leverage has its effects on operating risks and is measured by the percentage change in EBIT due to percentage change in sales revenue. Financial leverage has its effects on financial risks and is measured by the percentage change in EPS due to percentage change in EBIT. Since both these leverages are closely concerned with ascertaining the firm’s ability to cover fixed charges (fixed operating costs in case of operating leverage and fixed financial costs in case of financial leverage), if these two leverages are combined we will get combined leverage which can be measured in terms of degree of combined leverage (DCL). The DCL measures in quantitative terms the extent or degree of total risks.

 

8	DCL	= (%-age change in EPS) ÷ (%-age change in sales revenue)
9	DCL	= Contribution ÷ [EBIT – I – {DP ÷ (1 – t)}]
10	DCL	= Contribution ÷ [EBT – {DP ÷ (1 – t)}]
11	DCL	= Contribution ÷ EBT [If DP = 0]
12	DCL	= (EBIT + Fixed operating costs) ÷ [EBIT – I – {DP ÷ (1 – t)}]
13	DCL	= (EBIT + Fixed operating costs) ÷ [EBT – {DP ÷ (1 – t)}]
14	DCL	= (EBIT + Fixed operating costs) ÷ EBT [If DP = 0]
15	DCL	= DOL x DFL
		I       = Interest
		DP     = Preference dividend
		t       = Rate of corporate tax

 

Thus, the DCL measures the percentage change in EPS due to percentage change in sales revenue. Higher levels of total risks are attached to higher degrees of combined leverage.

 

Some more important and useful formulae:

16	%-age increase in EBIT	= DOL × %-age increase in Sales Revenue
17	%-age increase in EBT	= DFL × %-age increase in EBIT
18	%-age change in EPS	= DCL × %-age change in Sales Revenue
19	%-age increase in EBT	= DCL × %-age increase in Contribution
20	%-age increase in EBT	= DCL × %-age increase in Sales Revenue

 

Indifference point

When the alternative financing plans produce a same level of EBIT where EPS is also same irrespective of the debt-equity mix, the situation is referred to as ‘indifference point’ (also known as ‘indifference level’). In other words, it is the level of EBIT where the EPS will be equal under alternative financing plans.

Indifference point is also known as break-even point of EBIT for alternative financing plans. If EBIT exceeds the indifference point, the use of debt financing would be beneficial to maximise the EPS. On the other hand, if EBIT is less than the indifference point, the use of equity financing would be preferred for maximising the EPS.

The indifference point can be calculated by using the following equation:

[{(EBIT – I1) (1 – t)} – DP1] ÷ N1

= [{(EBIT – I2) (1 – t)} – DP2] ÷ N2

 

Where,     

I1	= Interest under first alternative plan
I2	= Interest under second alternative plan
t	= Rate of corporate tax
DP1	= Preference dividend under first alternative plan
DP2	= Preference dividend under second alternative plan
N1	= Number of equity shares under first alternative plan
N2	= Number of equity shares under second alternative plan

 

Financial break-even point

The amount of EBIT or the level of EBIT when the EPS will be ‘0’ (zero) under a particular financing plan is known as the “financial break-even point” of the financing plan. Financial break-even point is also known as “financial break-even level”. The financial break-even point can be calculated by using the following equation:

[{(EBIT – I) (1 – t)} – DP] ÷ N

= 0

 

Where,     

I	= Interest under a financial plan
t	= Rate of corporate tax
DP	= Preference dividend under a financial plan
N	= Number of equity shares under a financial plan

 

Income statement

	Particulars	Rs
	Sales	×××
Less	Variable cost	×××
	CONTRIBUTION	×××
Less	Fixed operating cost (e.g. depreciation, rent, ins. premiums, etc.)	×××
	EBIT	×××
Less	Fixed financial cost (e.g. interest on loan, debentures, etc.)	×××
	EBT	×××
Less	Income tax	×××
	EAT	×××
Less	Preference dividend	×××
	DIVISIBLE PROFIT [i.e. Profit Available For Equity Shareholders (PAFES)]	×××
	EPS (Earnings Per Share) [PAFES ÷ Number of equity shares outstanding]	×××
	MPS (Market Price per Share) [EPS × P/E Ratio]	×××

 

EBIT-EPS Analysis

EBIT-EPS analysis is one of the most widely used techniques employed in financial management to design an appropriate (i.e. optimum) capital structure of a company. Under two different situations the optimum capital structure of a company can be calculated in two different ways as follows:

1.    When P/E Ratio is not given in the problem

 The capital structure which generates the highest EPS (Earnings per share) is the  optimum capital structure.

2.    When P/E Ratio is given in the problem

 The capital structure which ensures the highest MPS (Market price per share) is   the optimum capital structure.

Part B

Illustration: 1

Crompton Ltd. a profit making company has a paid-up capital of Rs 100 lakhs consisting of 10 lakhs ordinary shares of Rs 10 each. Currently, it is earning an annual pre-tax profit of Rs 60 lakhs. The company’s shares are listed and are quoted in the range of Rs 50 to Rs 80. The management wants to diversify production and has approved a project which will cost Rs 50 lakhs and which is expected to yield a pre-tax income of Rs 40 lakhs per annum. To raise this additional capital, the following options are under consideration of the management:

(i)           To issue equity share capital for the entire additional amount. It is expected that the new shares      (face value of Rs 10) can be sold at a premium of Rs 15.

(ii)          To issue 16% non-convertible debentures of Rs 100 each for the entire amount.

(iii)    To issue equity capital for Rs 25 lakhs (face value of Rs 10) and 16% non-   convertible       debentures for the balance amount. In this case, the company   can issue shares at a premium of   Rs 40 each.

 

Advise the management as to how the additional capital can be raised, keeping in mind that the management wants to maximise the earnings per share to maintain its goodwill. The company pays income tax at 50%.

 

Solution: 1

Computation of EPS under three different options

Particulars	Option I	Option II	Option III
Capital structure of new issue	Only Equity	Only Debt	Equity + Debt
Total no. of equity shares after the new issue:
Existing	10,00,000	10,00,000	10,00,000
Add: New
Rs 50,00,000 ÷ 25	2,00,000
Rs 25,00,000 ÷ 50			50,000
Total no. of equity shares	12,00,000	10,00,000	10,50,000
	Rs	Rs	Rs
EBIT:
Existing	60,00,000	60,00,000	60,00,000
From the new project	40,00,000	40,00,000	40,00,000
Total EBIT	100,00,000	100,00,000	100,00,000
Less: Interest
For Project: II [Rs 50,00,000 × 16%]		8,00,000
For Project: III [Rs 25,00,000 × 16%]			4,00,000
EBT	100,00,000	92,00,000	96,00,000
Less: Income Tax @ 50%	50,00,000	46,00,000	48,00,000
EAT	50,00,000	46,00,000	48,00,000
EPS [EAT ÷ Number of Equity Shares]	4.17	4.60	4.57

 

Advice to the management:

Additional capital should be raised by adopting Option: II i.e. by issuing 16% NCD only, because Option: II has the highest EPS of Rs 4.60

 

Illustration: 2

Calculate the Degree of Operating Leverage (DOL), Degree of Financial Leverage (DFL) and the Degree of Combined Leverage (DCL) for the following firms and interpret the results.

Particulars	Firm K	Firm L	Firm M
1. Output (Units)	60,000	15,000	1,00,000
2. Fixed costs (Rs)	7,000	14,000	1,500
3. Variable cost per unit (Rs)	0.20	1.50	0.02
4. Interest on borrowed funds (Rs)	4,000	8,000	-
5. Selling price per unit (Rs)	0.60	5.00	0.10

 

Solution: 2

Computation of different leverages

	Particulars	Firm K	Firm L	Firm M
1	Output (units)	60,000	15,000	1,00,000
2	Selling price p.u. (Rs)	0.60	5.00	0.10
3	Variable cost p.u. (Rs)	0.20	1.50	0.02
4	Contribution p.u. (Rs)     [2 – 3]	0.40	3.50	0.08
5	Total contribution (Rs)    [1 × 4]	24,000	52,500	8,000
6	Fixed cost (Rs)	7,000	14,000	1,500
7	EBIT (Rs)                     [5 – 6]	17,000	38,500	6,500
8	Interest (Rs)	4,000	8,000	-
9	EBT (Rs)                      [7 – 8]	13,000	30,500	6,500
10	DOL                            [5 ÷ 7]	1.41	1.36	1.23
11	DFL                             [7 ÷ 9]	1.31	1.26	1.00
12	DCL                            [5 ÷ 9]	1.85	1.72	1.23

 

Interpretation:

Both DOL and DFL are highest in case of Firm K, whereas both DOL and DFL are lowest in case of Firm M. Therefore, Firm K is most risky and Firm M is least risky.

 

Illustration: 3

A firm has sales of Rs 10, 00,000, variable cost of Rs 7, 00,000 and fixed costs of Rs 2, 00,000 and debt of Rs 5, 00,000 at 10% rate of interest. What are the operating, financial and combined leverages? It the firm wants to double its Earnings before interest and tax (EBIT), how much of a rise in sales would be needed on a percentage basis?

 

Solution: 3

Computation of different leverages

	Particulars	Rs
1	Sales	10,00,000
2	Variable cost	7,00,000
3	Contribution                                       [1 – 2]	3,00,000
4	Fixed Operating Cost	2,00,000
5	EBIT                                                 [3 – 4]	1,00,000
6	Fixed Financial Cost (Interest)  [Rs 5,00,000 × 10%]	50,000
7	EBT                                                  [5 – 6]	50,000
8	DOL                                                 [3 ÷ 5]	3
9	DFL                                                 [5 ÷ 7]	2
10	DCL                                                 [3 ÷ 7]	6

 

We know, DOL = %-age change in EBIT ÷ %-age change in Sales

⇒ %-age increase in Sales = %-age increase in EBIT ÷ DOL

Let, EBIT can be doubled i.e. increased by 100%, if Sales are increased by x%.

∴ x = 100 ÷ DOL

⇒ x = 100 ÷ 3   [DOL is 3, as calculated above]

⇒ x = 33¹/₃

⇒ In order to double the EBIT (when DOL is 3), Sales would be needed to be increased by 33¹/₃%.

 

Verification:

	Particulars	Rs
1	Sales                              [Rs 10,00,000 × 1331/3%]	13,33,333
2	Variable cost                    [Rs 13,33,333 × 70%]	9,33,333
3	Contribution                                       [1 – 2]	4,00,000
4	Fixed Operating Cost	2,00,000
5	EBIT                                                 [3 – 4]	2,00,000

 

Illustration: 4

X Corporation has estimated that for a new product its break-even point is 2,000 units if the items are sold for Rs 14 per unit; the Cost Accounting department has currently identified variable cost of Rs 9 per unit. Calculate the degree of operating leverage for sales volume of 2,500 units and 3,000 units. What do you infer from the degree of operating leverage at the sales volumes of 2,500 units and 3,000 units and their difference if any?

 

Solution: 4

Computation of Operating Leverage

	Particulars	2,500 units	3,000 units
1	Sales @ Rs 14 p.u.	35,000	42,000
2	Variable cost @ Rs 9 p.u.	22,500	27,000
3	Contribution @ Rs 5 p.u.                [1 – 2]	12,500	15,000
4	Fixed cost           [W. N.]	10,000	10,000
5	EBIT                                           [3 – 4]	2,500	5,000
6	DOL                                           [3 ÷ 5]	5	3

 

Working note:

Break-Even Point is 2,000 units, i.e. at 2,000 units sales volume, Contribution = Fixed Cost. ∴ Fixed Cost = Contribution from 2,000 units ⇒ Rs 5 × 2,000 = Rs 10,000.

 

Assumption:

There is no interest cost. Entire fixed cost comprises fixed operating cost.

 

Inference:

When sales volume increased from 2,500 units to 3,000 units by 20%, operating income (EBIT) increased 100% from Rs 2,500 to Rs 5,000, i.e. 5 times of 20%, while Operating Leverage at sales level of 2,500 units is 5.

 

Therefore, it can be said that, with respect to a particular operating level,

%-age increase in Sales × DOL = %-age increase in EBIT

 

Illustration: 5

The following information is available for PKJ & Co.:-        

	Rs
EBIT	11,20,000
Profit before Tax	3,20,000
Fixed operating costs	7,00,000

 

Calculate % change in EPS if the sales are expected to increase by 5%.

 

Solution: 5

We know, %-age change in EPS = %-age change in Sales × DCL

Here, DCL  = Contribution ÷ EBT

                = (EBIT + Fixed operating costs) ÷ EBT

                = (11, 20,000 + 7, 00,000) ÷ 3, 20,000

                = 5.69

 

Therefore, if sales increase by 5%, EPS will increase by (5 × 5.69) % = 28.45%

 

Illustration: 6

XYZ and Co. has three financial plans before it, Plan I, Plan II and 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	Rs 15
Variable cost per unit	Rs 10
Fixed Cost:
Situation A	Rs 1,000
Situation B	Rs 2,000
Situation C	Rs 3,000

 

Capital Structure	Plan I	Plan II	Plan III
Equity Capital	Rs 5,000	Rs 7,500	Rs 2,500
12% Debt	Rs 5,000	Rs 2,500	Rs 7,500

 

Solution: 6

Computation of leverages for three different plans of capital structures

Situation A

	Particulars	Plan I	Plan II	Plan III
1	Sales (Rs 15 × 800)	12,000	12,000	12,000
2	Variable cost (Rs 10 × 800)	8,000	8,000	8,000
3	Contribution (1 – 2)	4,000	4,000	4,000
4	Fixed operating cost	1,000	1,000	1,000
5	EBIT (3 – 4)	3,000	3,000	3,000
6	Interest	600	300	900
7	EBT (5 – 6)	2,400	2,700	2,100
8	DOL (3 ÷ 5)	1.33	1.33	1.33
9	DFL (5 ÷ 7)	1.25	1.11	1.43
10	DCL (3 ÷ 7)	1.67	1.48	1.90

 

Situation B

	Particulars	Plan I	Plan II	Plan III
1	Sales (Rs 15 × 800)	12,000	12,000	12,000
2	Variable cost (Rs 10 × 800)	8,000	8,000	8,000
3	Contribution (1 – 2)	4,000	4,000	4,000
4	Fixed operating cost	2,000	2,000	2,000
5	EBIT (3 – 4)	2,000	2,000	2,000
6	Interest	600	300	900
7	EBT (5 – 6)	1,400	1,700	1,100
8	DOL (3 ÷ 5)	2	2	2
9	DFL (5 ÷ 7)	1.43	1.18	1.82
10	DCL (3 ÷ 7)	2.86	2.35	3.64

 

Situation C

	Particulars	Plan I	Plan II	Plan III
1	Sales (Rs 15 × 800)	12,000	12,000	12,000
2	Variable cost (Rs 10 × 800)	8,000	8,000	8,000
3	Contribution (1 – 2)	4,000	4,000	4,000
4	Fixed operating cost	3,000	3,000	3,000
5	EBIT (3 – 4)	1,000	1,000	1,000
6	Interest	600	300	900
7	EBT (5 – 6)	400	700	100
8	DOL (3 ÷ 5)	4	4	4
9	DFL (5 ÷ 7)	2.50	1.43	10
10	DCL (3 ÷ 7)	10	5.71	40

 

Highest Combined Leverage: Plan III / Situation C

Lowest Combined Leverage: Plan II / Situation A

 

Illustration: 7

The selected financial data for A, B and C companies for the year ended March, 2016 are as follows:

Particulars	A	B	C
Variable expenses as a %-age of Sales	66.67	75	50
Interest	Rs 200	Rs 300	Rs 1,000
Degree of Operating leverage	5: 1	6: 1	2: 1
Degree of Financial leverage	3: 1	4: 1	2: 1
Income tax rate	50%	50%	50%

 

Prepare Income Statements for A, B and C companies.

 

Solution: 7

Company A

1.   DFL = EBIT ÷ (EBIT – 200) = 3

    ⇒ 3EBIT – 600 = EBIT

    ⇒ 2EBIT = 600

    ⇒ EBIT = 300

 

2.   DOL = Contribution ÷ EBIT = 5

    ⇒ Contribution ÷ 300 = 5

    ⇒ Contribution = 1,500

 

3.   Variable expenses = 66²/₃% of sales

    ⇒ Contribution = 33¹/₃% i.e. 1/3^rd of sales

    ∴ Sales = 1,500 × 3 = 4,500, and

    ∴ Variable cost = 2/3^rd of sales = 2/3^rd of 4,500 = 3,000

 

4.   Fixed operating cost = Contribution – EBIT

    ⇒ Fixed operating cost = 1,500 – 300 = 1,200

 

Company B

1.   DFL = EBIT ÷ (EBIT – 300) = 4

    ⇒ 4EBIT – 1,200 = EBIT

    ⇒ 3EBIT = 1,200

    ⇒ EBIT = 400

 

2.   DOL = Contribution ÷ EBIT = 6

    ⇒ Contribution ÷ 400 = 6

    ⇒ Contribution = 2,400

 

3.   Variable expenses = 75% of sales

    ⇒ Contribution = 25% i.e. 1/4^th of sales

    ∴ Sales = 2,400 × 4 = 9,600, and

    ∴ Variable cost = 3/4^th of sales = 3/4^th of 9,600 = 7,200

 

4.   Fixed operating cost = Contribution – EBIT

    ⇒ Fixed operating cost = 2,400 – 400 = 2,000

Company C

1.   DFL = EBIT ÷ (EBIT – 1,000) = 2

    ⇒ 2EBIT – 2,000 = EBIT

    ⇒ EBIT = 2,000

 

2.   DOL = Contribution ÷ EBIT = 2

    ⇒ Contribution ÷ 2,000 = 2

    ⇒ Contribution = 4,000

 

3.   Variable expenses = 50% of sales

    ⇒ Contribution = 50% i.e. ½ of sales

    ∴ Sales = 4,000 × 2 = 8,000, and

    ∴ Variable cost = ½ of sales = ½ of 8,000 = 4,000

 

4.   Fixed operating cost = Contribution – EBIT

    ⇒ Fixed operating cost = 4,000 – 2,000 = 2,000

 

Income statements for companies ‘A’, ‘B’ and ‘C’

	Particulars	A	B	C
1	Sales	4,500	9,600	8,000
2	Variable cost	3,000	7,200	4,000
3	Contribution (1 – 2)	1,500	2,400	4,000
4	Fixed operating cost	1,200	2,000	2,000
5	EBIT (3 – 4)	300	400	2,000
6	Interest	200	300	1,000
7	EBT (5 – 6)	100	100	1,000
8	Income tax @ 50%	50	50	500
9	EAT (7 – 8)	50	50	500

 

Illustration: 8

The following data is available for XYZ Ltd.:

Particulars	Rs
Sales	2,00,000
Less : Variable cost @ 30%	60,000
Contribution	1,40,000
Less : Fixed Cost	1,00,000
EBIT	40,000
Less: Interest	5,000
Profit before tax	35,000

 

Find out:

(a)    Using the concept of financial leverage, by what percentage will the taxable income increase if EBIT increase by 6%?

(b)    Using the concept of operating leverage, by what percentage will EBIT increase if there is 10% increase in sales, and

(c)     Using the concept of leverage, by what percentage will the taxable income increase if the sales increase by 6%? Also verify results in view of the above figures.

 

Solution: 8

(a)    DFL = EBIT ÷ EBT = 40,000 ÷ 35,000 = 1.142857

%-age increase in EBT = DFL × %-age increase in EBIT

∴ %-age increase in EBT = (1.142857 × 6) % = 6.86%

 

(b)    DOL = Contribution ÷ EBIT = 1,40,000 ÷ 40,000 = 3.50

      %-age increase in EBIT = DOL × %-age increase in Sales

         ∴ %-age increase in EBIT = (3.50 × 10) % = 35%

 

(c)     DCL = Contribution ÷ EBT = 1,40,000 ÷ 35,000 = 4

      %-age increase in EBT = DCL × %-age increase in Sales

         ∴ %-age increase in EBT = (4 × 6) % = 24%

Illustration: 9

(i)      Find out operating leverage from the following data:

Sales	Rs 50,000
Variable Costs	60%
Fixed Costs	Rs 12,000

 

(ii)     Find out of financial leverage from the following data:

Net Worth	Rs 25,00,000
Debt/Equity	3: 1
Interest rate	12%
Operating Profit	Rs 20,00,000

Solution: 9

(I)

Particulars	Rs
Sales	50,000
Variable cost (60%)	30,000
Contribution	20,000
Fixed operating cost	12,000
EBIT	8,000
DOL (Contribution ÷ EBIT = 20,000 ÷ 8,000)	2.50

 

(II)

Particulars	Rs
Net Worth	25,00,000
Debt-Equity Ratio	3: 1
∴ Debt Capital (Rs 25,00,000 × 3)	75,00,000
Interest (Rs 75, 00,000 × 12%)	9,00,000
EBIT	20,00,000
∴ EBT (EBIT – Interest = 20,00,000 – 9,00,000)	11,00,000
DFL (EBIT ÷ EBT = 20,00,000 ÷ 11,00,000)	1.82

 

Illustration: 10

From the following, prepare Income Statements of A, B and C firms.

Particulars	A	B	C
Financial leverage	3: 1	4: 1	2: 1
Interest	Rs 200	Rs 300	Rs 1,000
Operating leverage	4: 1	5: 1	3: 1
Variable cost as a %-age of Sales	66.67	75	50
Income tax rate	45%	45%	45%

 

Solution: 10

Company A

1.   DFL = EBIT ÷ (EBIT – 200) = 3

    ⇒ 3EBIT – 600 = EBIT

    ⇒ 2EBIT = 600

    ⇒ EBIT = 300

 

            2.   DOL = Contribution ÷ EBIT = 4

    ⇒ Contribution ÷ 300 = 4

    ⇒ Contribution = 1,200

 

3.   Variable expenses = 66²/₃% of sales

    ⇒ Contribution = 33¹/₃% i.e. 1/3^rd of sales

    ∴ Sales = 1,200 × 3 = 3,600, and

    ∴ Variable cost = 2/3^rd of sales = 2/3^rd of 3,600 = 2,400

 

4.   Fixed operating cost = Contribution – EBIT

    ⇒ Fixed operating cost = 1,200 – 300 = 900

 

Company B

1.   DFL = EBIT ÷ (EBIT – 300) = 4

    ⇒ 4EBIT – 1,200 = EBIT

    ⇒ 3EBIT = 1,200

    ⇒ EBIT = 400

 

2.   DOL = Contribution ÷ EBIT = 5

    ⇒ Contribution ÷ 400 = 5

    ⇒ Contribution = 2,000

 

3.   Variable expenses = 75% of sales

    ⇒ Contribution = 25% i.e. 1/4^th of sales

    ∴ Sales = 2,000 × 4 = 8,000, and

    ∴ Variable cost = 3/4^th of sales = 3/4^th of 8,000 = 6,000

 

4.   Fixed operating cost = Contribution – EBIT

    ⇒ Fixed operating cost = 2,000 – 400 = 1,600

Company C

1.   DFL = EBIT ÷ (EBIT – 1,000) = 2

    ⇒ 2EBIT – 2,000 = EBIT

    ⇒ EBIT = 2,000

 

2.   DOL = Contribution ÷ EBIT = 3

    ⇒ Contribution ÷ 2,000 = 3

    ⇒ Contribution = 6,000

 

3.   Variable expenses = 50% of sales

    ⇒ Contribution = 50% i.e. ½ of sales

    ∴ Sales = 6,000 × 2 = 12,000, and

    ∴ Variable cost = ½ of sales = ½ of 12,000 = 6,000

 

4.   Fixed operating cost = Contribution – EBIT

    ⇒ Fixed operating cost = 6,000 – 2,000 = 4,000

Income statements for companies ‘A’, ‘B’ and ‘C’

	Particulars	A	B	C
1	Sales	3,600	8,000	12,000
2	Variable cost	2,400	6,000	6,000
3	Contribution (1 – 2)	1,200	2,000	6,000
4	Fixed operating cost	900	1,600	4,000
5	EBIT (3 – 4)	300	400	2,000
6	Interest	200	300	1,000
7	EBT (5 – 6)	100	100	1,000
8	Income tax @ 45%	45	45	450
9	EAT (7 – 8)	55	55	550

 

Illustration: 11

ABC Ltd. wants to raise Rs 5, 00,000 as additional capital. It has two mutually exclusive alternative financial plans. The current EBIT is Rs 17, 00,000 which is likely to remain unchanged. The relevant Information is:-

Present Capital Structure:

3,00,000 Equity shares of Rs 10 each and 10% Bonds of Rs 20,00,000.

Tax Rate:	50%
Current EBIT:	Rs 17,00,000
Current EPS:	Rs 2.50
Current Market Price:	Rs 25 per share
Financial Plan I:	20,000 Equity Shares at Rs 25 per share
Financial Plan II:	12% Debentures of Rs 5,00,000

 

What is the indifference level of EBIT? Identify the financial break-even levels.

 

Solution: 11

Formula for Indifference Level of EBIT:-

[{(EBIT – I₁) (1 – t)} – D_P1] ÷ N₁ = [{(EBIT – I₂) (1 – t)} – D_P2] ÷ N₂

 

Where,

I1	= Interest under first alternative plan
I2	= Interest under second alternative plan
t	= Rate of corporate tax
DP1	= Preference dividend under first alternative plan
DP2	= Preference dividend under second alternative plan
N1	= Number of equity shares under first alternative plan
N2	= Number of equity shares under second alternative plan

 

Here,

I1	20,00,000 × 10% = 2,00,000
I2	20,00,000 × 10% + 5,00,000 × 12% = 2,60,000
t	50% i.e. 0.50
DP1	Nil
DP2	Nil
N1	3,00,000 + 20,000 = 3,20,000
N2	3,00,000

 

Accordingly,

[(EBIT – 2, 00,000) × (1 – 0.50)] ÷ 3, 20,000

= [(EBIT – 2, 60,000) × (1 – 0.50)] ÷ 3, 00,000

⇒ (EBIT – 2, 00,000) ÷ 16 = (EBIT – 2, 60,000) ÷ 15

⇒ 16EBIT – 41, 60,000 = 15EBIT – 30, 00,000

⇒ EBIT = 11, 60,000

 

Therefore, the Indifference Level of EBIT is Rs 11, 60,000, and it implies that at this level of EBIT both the financial plans will generate same EPS.

 

Formula for financial break-even level of EBIT:-

[(EBIT – I) × (1 – t) – D_P] ÷ N = 0

 

Where,

I	= Interest under a financial plan
t	= Rate of corporate tax
DP	= Preference dividend under a financial plan
N	= Number of equity shares under a financial plan

 

Accordingly,

For Financial Plan I:-

[(EBIT – 2, 00,000) × (1 – 0.50)] ÷ 3, 20,000 = 0

⇒ EBIT = 2, 00,000

⇒ At EBIT of Rs 2, 00,000, EPS of Financial Plan I will be ‘0’.

 

For Financial Plan II:-

[(EBIT – 2, 60,000) × (1 – 0.50)] ÷ 3, 00,000 = 0

⇒ EBIT = 2, 60,000

⇒ At EBIT of Rs 2, 60,000, EPS of Financial Plan II will be ‘0’.

 

Illustration: 12

From the following financial data of Company A and Company B prepare their income Statements.

Particulars	Company A	Company B
Variable Cost (Rs)	56,000	60% of sales
Fixed Operating Cost (Rs)	20,000	-
Interest Expenses (Rs)	12,000	9,000
Financial Leverage	5:1	-
Operating Leverage	-	4:1
Income Tax Rate	30%	30%
Sales (Rs)	-	1,05,000

 

Solution: 12

Company A

1.   DFL = EBIT ÷ (EBIT – 12,000) = 5

    ⇒ 5EBIT – 60,000 = EBIT

    ⇒ 4EBIT = 60,000

    ⇒ EBIT = 15,000

 

2.   Contribution = EBIT + Fixed Operating Cost

⇒ Contribution = 15,000 + 20,000 = 35,000

 

3.   Sales – Variable Cost = Contribution

⇒ Sales = Variable Cost + Contribution

⇒ Sales = 56,000 + 35,000 = 91,000

 

Company B

1.   DOL = Contribution ÷ EBIT = 4

    ⇒ 40% of Sales ÷ EBIT = 4

    ⇒ 40% of 1, 05,000 ÷ EBIT = 4

    ⇒ 42,000 ÷ EBIT = 4

    ⇒ 4EBIT = 42,000

    ⇒ EBIT = 10,500

 

2.   Fixed Operating Cost = Contribution – EBIT

⇒ Fixed Operating Cost = 40% of Sales – EBIT

⇒ Fixed Operating Cost = 40% of 1, 05,000 – EBIT

⇒ Fixed Operating Cost = 42,000 – 10,500

⇒ Fixed Operating Cost = 31,500

 

3.   Variable Cost = 60% of sales

    ⇒ Variable Cost = 60% of 1, 05,000

    ⇒ Variable Cost = 63,000

Income statements for companies ‘A’, and ‘B’

	Particulars	Company A	Company B
1	Sales	91,000	1,05,000
2	Variable Cost	56,000	63,000
3	Contribution (1 – 2)	35,000	42,000
4	Fixed Operating Cost	20,000	31,500
5	EBIT (3 – 4)	15,000	10,500
6	Interest Expenses	12,000	9,000
7	EBT (5 – 6)	3,000	1,500
8	Income Tax (@ 30%)	900	450
9	EAT (7 – 8)	2,100	1,050

 

Illustration: 13

The XYZ Company plans to expand assets by 50%. To finance the expansion it is choosing between a straight 6% debt issue and equity issue. Its current balance sheet and income statement are shown below:

 

Balance Sheet of XYZ Company as at 31.03.2020

Liabilities	Rs	Assets	Rs
Equity share capital (@ Rs 10 per share)	10,00,000	Total assets	20,00,000
5% Debt	4,00,000
Current liabilities	6,00,000
	20,00,000		20,00,000

 

 

Income Statement of XYZ Company for the year ended 31.03.2020

Particulars	Rs
Sales	60,00,000
Less: Total cost (excluding interest)	53,80,000
EBIT	6,20,000
Less: Interest on debt (Rs 4, 00,000 × 5%)	20,000
EBT	6,00,000
Less: Taxes (@ 35%)	2,10,000
EAT (Net Income)	3,90,000

 

If the company finances the proposed expansion with debt, the rate of interest for the incremental debt will be 6% and the price/earnings ratio of the equity shares will be 10. On the other hand, if the expansion is financed by equity, the new shares can be sold at Rs 33.33 per share and the price/earnings ratio of the outstanding equity shares will be 12.

 

Required:

(a)    Assuming that net income before interest on debt and taxes (EBIT) is 10% on sales, calculate EPS at assumed sales of Rs 20 lakh, Rs 40 lakh, Rs 80 lakh and Rs 100 lakh under the alternative forms of financing the expansion programme (assume no fixed costs).

(b)    Using the price/earnings ratios indicated above, calculate the market price of equity shares at each sales level for both debt and equity methods of financing.

(c)     If the company follows the policy of seeking to maximize the market price of its equity shares, which form of financing should be employed?

Solution: 13