FINANCIAL LEVERAGE

FINANCIAL LEVERAGE.

The use of fixed charges sources of funds, such as debt and preference capital along with the owners’ equity in the capital structure is described as financial leverage or trading on equity.

Effect of Financial Leverage on the Shareholder’s earnings:

• Calculating EPS and Return on Equity.

The Earning per share can be calculated by dividing the earnings after interest and taxes, EAIT (i.e. net income, NI) by the number of outstanding common

shares.

• EBIT = X (Net operating Income, NOI)• Less: Interest = R • EAIBT = X – R• Tax = t (X – R) (t is the tax

rate)• EAIT (Net Income) = (X – R) – t (X – R)• NI = (X – R) (1 – t)• EPS = (X – R) (1 – t) / N -----(1)•

• If the earnings after interest and taxes, EAIT are divided by the shareholders’ funds (share capital plus reserves and surplus), we get return on equity in percentage. Thus,

• e = (X – R) (I – t) / E ----------(2) where e represents the common shareholders’ fund or net worth.

• Favorable and Unfavorable Financial Leverages

• The effect of the financial leverage may be favorable or unfavorable. Positive, or favorable, financial leverage occurs when the earnings per share increase due to the use of debt in the capital structure. This happens when the rate of return on the company’s assets is more than the cost of debt capital.

Favorable financial leverage is illustrated as follows:

• Example: 1.• Firms A and B are identical, except that Firm B is levered. The

following data relate to them:• A B• Assets. Rs. 5,00,000 Rs. 5,00,000• Debt 0 2,50,000(9%

Debenture)• Equity 5,00,000 2,50,000 • (50,000 Shares) (25,000 Shares)• Rate of return on Assets. 20% 20%• Calculate EPS for Firms A and B. Assume a 50% tax rate.

Table 1: Example of Favorable Financial leverage

• Firm A Firm B• EBIT Rs.1,00,000 Rs. 1,00,000• Less: Interest 0 22,500• • EAIBT 1,00,000 77,500• Less; Taxes @ 50% 50,000 38,750•

EAIT Rs. 50,000 Rs. 38,750•

No. of shares 50,000 25,000• EPS Rs.1.00 Rs.1.55

Unfavorable Financial Leverage• Negative, or unfavorable leverage occurs

when the earning per share decreases because of the use of debt in the capital structure. The following example explains the negative effect of financial leverage.

• Except the rate of return on assets, assume the same data for Firms A and B. If the rate of return is supposed to be 6 percent, the EPS will be as shown in the following table.

Table: 2 Example of Unfavorable Financial Leverage.

Firm A (Rs)

Firm B(Rs)

EBIT (6% of Rs. 5,00,000) Less: Interest EAIBTLess: taxes @ 50% EAIT No. of shares

EPS

30,000 030,00015,00015,00050,0000.30

30,00022,500 7,500 3,750 3,750 25,000 0.15

• If the rate of return on assets were just equal to the cost of debt i.e. 9% it can be seen that financial leverage will have no impact on the shareholders’ return. (Assume the same data for Firms A and B except the rate of return).

Table: 3: Example of neutral Financial leverage.

• Firm A Firm B• EBIT (9%of Rs. 5,00,000) Rs.45,000 Rs.45,000• Less: Interest 0 22,500• EAIBT 45,000 22,500• Less: Taxes @ 50% 22,500 11,250•

EAIT 22,500 11,250•

No. of shares. 50,000 25,000•

EPS Re. 0.45 Re.0.45

Conclusion:• We are thus led to an important conclusion:• (i) the financial leverage will have a favorable impact on EPS

only when the firm’s return on investment (r) exceeds the interest cost of debt (kd).

• (ii) the impact will be unfavorable if r < kd. • (iii) The financial leverage will have no impact on EPS, when r =

kd

• Effect of leverage• Favorable r > kd

• Unfavorable r < kd

• Neutral r = kd

EBIT–EPS ANALYSIS• One useful way of examining the effect of financial

leverage is to analyze the behavior of EPS with varying levels of EBIT under alternative financing plans. As noted earlier, the formula to calculate EPS is:

• EPS = (X –R) (1 – t) / N

• This equation can be rewritten as:• EPS = {(1-t)X – (1-t)R} / N • = (1-t)X /N - (1-t)R / N• Or EPS = - (1-t)R / N + (1-t)X /N -----------(3)

• If the level of leverage and tax rate are constant, the 1st part of Eq (3) is a constant. The constant part of the equation may be represented by a. EBIT is a changing variable and is represented by X. Thus,

• EPS = a + bx , • Where, a = - (1 – t) R/ N and b = (1-t) / N

• From the following data calculate EPS for the three alternative plans, if the levels of EBIT (X) are assumed to be Rs. 20 Rs. 40, Rs. 60, Rs. 80, Rs. 100, Rs. 120, Rs.140, Rs150.

F. Plan – I F. Plan – II F. Plan- III• (D = 0) (D = 50%) (D = 80%)• Assets Rs.1,000 Rs.1,000 Rs.1,000• Financed by• Debt at 6% 0 500 800 • Equity 1,000 500 200• (10 Shares) (5 shares) (2 shares) • Tax Rate 50% 50% 50%

• We know, EPS = a + bx• where a = - (1 – t) R/N• b = (1 – t) /N• F. Plan – I • a = - (1 - .5) 0 /10 = 0, • b = (1 – t)/ N = (1 – 0.5)/10 = 0.05• • F. Plan – II• a = - (1 - .5) 30/5 = - 0.5 x 6 = - 3• b = (1 – t) /N = (1 – 0.5) / 5 = 0.5/5 = 0.1

• F. Plan – III• a = - (1 - .5) x 48 / 2 = - 12• b = (1 - .5) /2 = .5 /2 = 0.25

Table – 4: EPS Calculation for Financial Plan - I

a bx EPS = a + bx

00000000

(0. 05) (Rs. 20) = Rs. 1 (0. 05) (Rs. 40) = Rs. 2 (0. 05) (Rs. 60) = Rs. 3 (0. 05) (Rs. 80) = Rs. 4 (0.05) (Rs. 100)= Rs. 5 (0.05) (Rs. 120)= Rs. 6(0.05) (Rs.140) = Rs. 7

(0.05) (Rs.150) = Rs. 7.5

Rs 1Rs 2Rs 3Rs 4Rs 5Rs 6Rs 7Rs 7.5

Table 5: EPS Calculation for Financial Plan - II

a bx EPS=a+bx-3-3-3-3-3-3-3-3

(0. 1) (Rs. 20) = Rs. 2 (0. 1) (Rs, 40) = Rs. 4 (0. 1) (Rs. 60) = Rs. 6 (0. 1) (Rs. 80) = Rs. 8 (0.1) (Rs.100) = Rs.10 (0.1) (Rs.120) = Rs.12 (0.1) (Rs.140) = Rs.14 (0.1) (Rs.150) = Rs.15

Rs(-)1Rs 1Rs 3Rs 5Rs 7Rs 9Rs 11Rs 12

Table 6: EPS Calculation for Financial Plan - III

a bx EPS=a+bx-12-12 -12 -12 -12 -12-12-12

(0. 25) (Rs. 20) = Rs. 5 (0. 25) (Rs, 40) = Rs. 10 (0. 25) (Rs. 60) = Rs. 15 (0. 25) (Rs. 80) = Rs. 20 (0. 25) (Rs.100) = Rs.25 (0. 25) (Rs.120) = Rs.30 (0. 25) (Rs.140) = Rs.35 (0. 25) (Rs.150) = Rs.37.5

Rs(-)7Rs (-)2Rs 3Rs 8Rs 13Rs 18Rs 23Rs 25.5

• A comparison of tables 4, 5 and 6 indicates that EPS of Financial Plan which employs more financial leverage, increases at a faster rate than that of financial plan which employs less financial leverage. But at low level of EBIT the danger of reduced EPS is more in case of financial plans employing more leverage.

GRAPHIC PRESENTATION OF EBIT – EPS ANALYSIS

• As noted earlier:• EPS = -(1 – t) R/N + (1 – t) X/N• = a + bx

• The EPS equations under three financial plans are as follow:• Financial Plan – I EPS = 0 + 0.05 x -------(4)• Financial Plan – II EPS = -3 + 0.1 x -------(5)• Financial Plan – III EPS = -12 + 0.25x -------(6)

• The EBIT – EPS analysis can be presented graphically. The effects of varying levels of EBIT on EPS under alternative financial plans are shown in Fig. 1. In the figure, the horizontal line is used to represent EBIT, while the vertical line represents EPS.

• Conclusion:1. Shareholders will benefit by the use of Financial leverage if r

> kd

2. Shareholders will reduce EPS if r < kd.3. Their earnings will not be affected by the level of leverage if

r = kd.

Figure 1

• EPS III (D=80%) • II (D=50%) • I (D=0)

• 30 48 60 80 100 X • 3% 4.8% 6% 8% 10%

• r < k r = k r > k

Degree of Financial leverage:• We have seen in the earlier example that financial leverage

affects the earning per share. When the firm’s EBIT is increasing, its EPS increases faster with more debt in the capital structure.

• The degree of financial leverage (DFL) is defined as the percentage change in EPS due to a given percentage change in EBIT:

• DFL = % Change in EPS / % Change in EBIT• Or DFL = (∆ EPS / EPS) / (∆ EBIT/ EBIT) -------- (1)

• The following formula can also be used to calculate Degree of Fin. Leverage

• DFL = EBIT / ( EBIT –R)

The above formula is derived as follows:

• DFL = (∆ EPS / EPS) / (∆ EBIT/ EBIT)• = (∆ EPS / ∆ EBIT) . (EBIT / EPS)• = {(1-t) / N}. (EBIT /EPS)• = EBIT / {N. EPS / (1-t)}• = EBIT / (EBIT –R)

• Since we know that EPS = - (1 – t) R/ N + {(1 – t) / N }EBIT• Or, d (EPS) / d (EBIT) = (1 – t) / N• Again EPS= (EBIT – R) (1 – t) / N• Or , N (EPS) / (1-t) = EBIT -R

In Tables 4, 5, and 6 we have calculated different EPSs for varying levels of EBIT under three alternative financial plans. These are summarized in Table 7.

Table: 7

r EBIT(Rs)

when D = 0, EPS(Rs)

D = 50%, EPS(Rs)

D = 80% , EPS(Rs)

2%4 %6 %8 %10 %12 %14 %15 %

20 4060 80100120140150

12345677.5

-1135791112

-7-23813182325.5

• When EBIT increase from 120 to 140• EPS increase from• Rs. 6 to 7 Financial Plan – I• Rs. 9 to 11 Financial Plan – II• Rs. 18 to 23 Financial Plan – III

• The DFL at EBIT = 120 is

• DFL (I) = {(7-6) / 6} / {(140 – 120) / 120} = 1 • Or, EBIT / (EBIT – R) = 120 / (120-0) = 1

• DFL (II) = {(11-9) / 9} / {(140-120) / 120} • = (2/9) (20/120) = 1.33• Or, EBIT / (EBIT – R) = 120 / (120 -30) • = 120 / 90 = 1.33

• DFL (III) = {(23-18)/18} / {(140-120)/120}• = (5/18) (120/20) = 1.67• Or, EBIT/(EBIT-R) = 120/(120-48)• =120/72=1.67

• This implies that for a given change in EBIT, EPS will change by 1 time, 1.33 times and 1.67 times for the three alternative financial plans respectively. That is the more the debt capital used in the capital structure, the more the EPS changes for a given change in EBIT. The change in EPS due to the use of debt capital is called the financial risk.

OPERATING LEVERAGE:• Operating leverage refers to the use of fixed

costs in the operation of a firm. • A firm will not have operating leverage if its ratio

of fixed costs to total costs is nil. For such a firm, a given change in sales would produce the same percentage change in the operating profit or EBIT.

• If the firm has fixed costs, it would have operating leverage and the percentage change in the operating profit would be more for a given change in sales.

• The Break – Even Analysis can help us to understand the impact of operating leverage on the operating profit.

• The Break – Even Analysis establishes a relationship between revenue and costs with respect to volume. The Break – Even point is that point of sales at which total revenue is equal to total costs.

Break–Even Analysis

• Assumption: • Total costs = Total Fixed cost + Total Variable cost.• When a cost changes in direct proportion to changes in volume, it is

called variable cost. Variable costs vary in a proportionate manner with volume. Mathematically, a liner relationship exists between a variable cost and volume.

• • cost• Total variable cost

• volume

• When a cost does not change with change in volume, it is called fixed cost. Fixed costs remain at the same level irrespective of the changes in volume. It is the total fixed cost which is constant.

• cost

• Fixed cost

• volume

• cost • &• revenue

How to calculate Break – Even Quantity (QBE)?• We know,• Total Cost = T. Variable Cost + T. Fixed Cost• Or T.C = T.VC + F = V.Q + F• where, V is variable cost per unit, Q is quantity, and F is total fixed

cost.

• Op. Profit (EBIT) =Total Revenue – Total Cost = P.Q – (V.Q + F) • { P= Price per quantity}• Or EBIT = P.Q – V.Q – F = Q (P – V) – F. • { (P- V) = contribution margin per unit}.

• At the break–even point (QBE), EBIT is zero•• 0 = QBE (P – V) – F

• or QBE (P – V) = F

• Or, QBE = F / (P-V) • = Total Fixed Cost / Contribution margin per unit

• Example:• The following illustration shows the impact of operating leverage on

the operating profit.• Consider the following information of the same firm under two

different situations:

Situation – I Low Automation

Situation – II High Automation

Price per product (Unit) P

V. Cost per Unit Fixed Cost (F)

Rs 8

Rs 4

Rs 280

Rs 8

Rs 2

Rs 480

• What are the B/E points for the firm under two situations? How much profits are earned by the firm if the sale ranges between Q = 70 units to 105 units.

• Situation I: QBE = F / (P-V) = 280 / (8-4) = 70 units

• Situation II: QBE = F / (P-V) = 480 / (8-2) = 80 units

Table 8a: Profit to be made by the firm at different sales volume under:

Situation – 1 (Low Automation)

Units Sales VC F TC EBIT r

707580859095100105

560600640680720760800840

280300320340360380400420

280280280280280280280280

560580600620640660680700

020406080100120140

0%2 % 4 %6 %8 %10 %12 %14 %

Table 8b: Profit to be made by the firm at different sales volume under:

Situation – II (High Automation)

Units Sales VC F TC EBIT r

707580859095100105

560600640680720760800840

140150160170180190200210

480480480480480480480480

620630640650660670680690

-60-300306090120150

-6%-3 % 0 %3 %6 %9 %12 %15 %

Degree of Operating Leverage

• The degree of operating leverage may be defined as the percentage change in operating profits resulting from a percentage changes in sales.

• Thus,

• DOL = % Change in Operating profit / % Change in Sales • = {∆EBIT / EBIT}/ {∆ Sales / Sales}• = {∆ EBIT / EBIT}/ {∆Q/Q}• = (P – V)Q /EBIT = (P – V)Q /{ Q(P-V) – F} • = contribution / (contribution – fixed cost)• = contribution / PBIT• [ since EBIT = Q(P-V) – F , or d(EBIT)/dQ = (P-V) ]

• In table 8, when Q changes from 100 units to 105 units• EBIT Changes from Rs. 120 to 140 (Low Automation Situation- I)• And, EBIT Changes from Rs. 120 to 150 (High Automation

Situation – II)• Thus, at Q = 100 Units• DOL (Low Automation) = {(140-120) / 120} / {(105-100)/100}• = (20/120) x (100/5) = 3.33

• Or, DOL= Q (P – V) / {Q (P – V) – F } = 100(8-4)/{100(8-4)-280}• = 400/120 = 10/3=3.33

• And DOL (High Automation)• = {(150-120) /120} / {(105-100)/100}• = (30/120) x (100/5) = 5.0

• Or, DOL = Q (P – V) / {Q (P – V)-F} = 100(8-2) / {100(8-2)-480 = 600/120 = 5.0

Combined Effect of operating and Financial leverage

• Degree of Financial Leverage• DFL = EBIT / (EBIT-R) = {Q (P – V) – F} / Q (P –V)- F – R

• Degree of operating Leverage• DOL = Q (P-V) / {Q (P-V) –F}

• The degree of operating and financial leverage can be combined to see the effect of total leverage on EPS associated with a given change in sales.

• The degree of combined leverage• = DFL x DOL= [{Q (P – V) – F} / Q (P –V)- F – R] x [Q (P-V) / {Q (P-V) –F}]• = Q (P – V) / {Q (P –V)- F – R}

• Under Situation – I, (low- automation), when Q changes from 100 unit to 105 unit EBIT change from Rs. 120 to Rs. 140. And at Q = 100, DOL = 3.33

• Again when Q changes from 100 unit to 105 units, EBIT changes from Rs. 120 to Rs. 140, and EPS changes from;

• Rs. 6 to Rs. 7 (Fin. Plan – I, when D = 0)• Rs. 9 to Rs. 11 (Fin. Plan – II, when D = 50%)• Rs. 18 to Rs. 23 (Fin. Plan – III, When D = 80%).

• And at that point• DFL = 1 (FP – I)• DFL = 1.33 (FP – II)• DFL = 1.67 (FP – III)

• Thus, when the firm uses low automation, the combined leverage at different financial plans are given below (when sales are Q = 100 Units).

• DCL = Q(P-V) / {Q(P-V)-F-R} = 100(8-4)/ {100(8-4)-280-0}=3.33 (FP – I)• DCL= Q(P-V) / {Q(P-V)-F-R} = 100(8-4)/ {100(8-4)-280-30}=4.44 (FP – II)• DCL= Q(P-V) / {Q(P-V)-F-R} = 100(8-4)/ {100(8-4)-280-48}=5.55 (FP – III)

• Alternatively we can calculate DCL = DFL x DOL• thus,• DCL = (10/3) x 1 = 3.33 (FP – I)• DCL = (10/3) x (4/3) = 4.44 (FP – II)• DCL = (10/3) x (5/3) = 5.55 (FP – III)

Combinations of operating and financial leverage.

Low AutomationDFLx DOL = DCL

High AutomationDFLx DOL = DCL

1 X (10/3) =3.33 (4/3) X(10/3) =4.44 (5/3) X (10/3)=5.55

1 X 5 =5(4/3) X5 = 6.67(5/3) X5 = 8.33

• Under High Automation.

• If Q change from 100 to 105 units (5%),•• EBIT change from Rs. 120 to 150.•• And table 6 shows that when EBIT changes from Rs. 120 to Rs.

150 , EPS changes from Rs. 18 to Rs. 25.5 i.e., a change of 41.67 % which is equal to [5 % x 8.33(DCL)].

Business Risk and Financial Risk

• Pepsi company, a soft drink manufacturer, is preparing to make a capital structure decision. It has obtained estimates of sales and the associated levels of EBIT from its forecasting group: There is a 25% chance that sales will total Rs400,000, a 50% chance that sales total Rs600,000, and a 25% chance that sales will total Rs800,000. Fixed operating cost total Rs200,000, and variable operating costs equal 50% of sales. These data are summarized, and the resulting EBIT calculated, in the following table.

Sales and Associated EBIT calculations

Probability of sales 0.25 0.50 0.25

Sales revenueLess: Fixed costLess: variable cost (50% of sales)EBIT

Rs400,000 200,000 200,000_______Rs0

Rs600,000 200,000 300,000_______Rs100,000

Rs800,000 200,000 400,000 _______Rs200000

The company’s current capital structure

Rs

Long-term debtEquity shares (25,000 shares at Rs20)

Total capital (assets)

0500,000________500,000

• Let us assume that the firm is considering seven alternative capital structures. If we measure these structures using the debt ratio, they are associated with ratios of 0, 10, 20, 30, 40, 50, and 60%.

• Assuming that (1) the firm has no current liabilities, (2) its capital structure currently contains all equity as shown, and (3) the total amount of capital remains constant at Rs500,000, the mix of debt and equity associated with the seven debt ratios would be as shown in the following table.

Capital Structures Associated with Alternative Debt Ratios

Debt ratio(1)

Total assets(2)

Debt(3)

Equity(4)

Number of equity share(5)

0%102030405060

Rs500,000500,000500,000500,000500,000500,000500,000

Rs050,000100,000150,000200,000250,000300,000

Rs500,000450,000400,000350,000300,000250,000200,000

25,00022,50020,00017,50015,00012,50010,000

Level of Debt, Interest Rate, and Rupee Amount of Annual Interest Associated with alternative capital structures.

Capital structure debt ratio

Debt Interest rate on all debt

Interest amount

0%102030405060

Rs050,000100,000150,000200,000250,000300,000

0.0%9.09.510.011.013.516.5

Rs0.004,5009,50015,00022,00033,75049,500

Calculation of EPS for debt ratio = 0%

Probability of EBIT .25 .50 .25

EBITLess: Interest

Net Profit before taxesLess: Taxes (T=0.40)

Net profits after taxesEPSExpected EPS = Rs2.40 Standard deviation of EPS = Rs1.70

Rs00.00_______0.000.00________0.00Rs0.00

Rs100,0000.00_________100,00040,000_________60,000Rs2.40

Rs200,0000.00_________200,00080,000________120,000Rs4.80



EBITLess: Interest



Rs04,500_______-4,5001,800________-2,700Rs(-)0.12

Rs100,0004,500_________95,50038,200_________57,300Rs2.55

Rs200,0004,500_________195,50078,200________117,300Rs5.21



EBITLess: Interest



Rs09,500_______-9,5003,800________-5,700Rs(-)0.28

Rs100,0009,500_________90,50036,200_________54,300Rs2.72

Rs200,0009,500_________190,50076,200________114,300Rs5.72



EBITLess: Interest



Rs015,000_______-15,0006,000________-9,000Rs(-)0.51

Rs100,00015,000_________85,00034,000_________51,000Rs2.91

Rs200,00015,000_________185,00074,000________111,000Rs6.34



EBITLess: Interest



Rs049,500_______-49,50019,800________-29,700Rs(-)2.97

Rs100,00049,500_________50,50020,200_________30,300Rs3.03

Rs200,00049,500_________150,50060,200________90,300Rs9.03

Expected EPS and Standard Deviation for Alternative capital Structures

Capital structure debt ratio Expected EPS SD of EPS

0%102030405060

Rs2.402.552.722.913.123.183.03

Rs1.701.882.132.422.833.394.24

Expected EPS for alternative capital structures

• 3.18

• 0 10 20 30 40 50 60 Debt ratio (%)

Ex

Exp

ecte

d E

PS

SD of EPS for alternative capital structures

• Financial Risk

• 1.70

• Business Risk

• 0 10 20 30 40 50 60 Debt Ratios (%)

SD

of E

PS

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FINANCIAL LEVERAGE