Financial Leverage 655p2o
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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 Rs.1,00,000 0
Firm B Rs. 1,00,000 22,500
EAIBT 1,00,000 Less; Taxes @ 50% 50,000
77,500 38,750
EBIT Less: Interest
EAIT No. of shares EPS
Rs. 50,000
Rs. 38,750
50,000 Rs.1.00
25,000 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. EBIT (6% of Rs. 5,00,000) Less: Interest EAIBT Less: taxes @ 50% EAIT No. of shares EPS
Firm A (Rs)
Firm B (Rs)
30,000 0 30,000 15,000 15,000 50,000 0.30
30,000 22,500 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. • • • • • •
EBIT (9%of Rs. 5,00,000) Less: Interest EAIBT Less: Taxes @ 50%
Firm A Rs.45,000 0 45,000 22,500
Firm B Rs.45,000 22,500 22,500 11,250
EAIT
22,500
11,250
No. of shares.
50,000
25,000
Re. 0.45
Re.0.45
• • EPS
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.
Assets Financed by Debt at 6% Equity Tax Rate
F. Plan – I (D = 0) Rs.1,000
F. Plan – II (D = 50%) Rs.1,000
F. Plan- III (D = 80%) Rs.1,000
0 1,000 (10 Shares) 50%
500 500 (5 shares) 50%
800 200 (2 shares) 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
0 0 0 0 0 0 0 0
(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
Rs 1 Rs 2 Rs 3 Rs 4 Rs 5 Rs 6 Rs 7 Rs 7.5
(0.05) (Rs.150) = Rs. 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(-)1 Rs 1 Rs 3 Rs 5 Rs 7 Rs 9 Rs 11 Rs 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(-)7 Rs (-)2 Rs 3 Rs 8 Rs 13 Rs 18 Rs 23 Rs 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 • Financial Plan – II • Financial Plan – III
EPS = 0 + 0.05 x EPS = -3 + 0.1 x EPS = -12 + 0.25x
-------(4) -------(5) -------(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.
• 1.
Conclusion: 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
3% 4.8% 6%
8%
10%
r
r=k
r>k
X
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 D = 50%, EPS D = 80% , EPS (Rs) (Rs) (Rs)
2% 4% 6% 8% 10 % 12 % 14 % 15 %
20 40 60 80 100 120 140 150
1 2 3 4 5 6 7 7.5
-1 1 3 5 7 9 11 12
-7 -2 3 8 13 18 23 25.5
• • • • •
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
•
or
•
Or,
•
=
QBE (P – V) – F QBE (P – V) = F
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
Rs 8
Rs 8
V. Cost per Unit
Rs 4
Rs 2
Fixed Cost (F)
Rs 280
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
70 75 80 85 90 95 100 105
560 600 640 680 720 760 800 840
280 300 320 340 360 380 400 420
280 280 280 280 280 280 280 280
560 580 600 620 640 660 680 700
0 20 40 60 80 100 120 140
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
70 75 80 85 90 95 100 105
560 600 640 680 720 760 800 840
140 150 160 170 180 190 200 210
480 480 480 480 480 480 480 480
620 630 640 650 660 670 680 690
-60 -30 0 30 60 90 120 150
-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(82)-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 DFL DFL
= = =
1 1.33 1.67
(FP – I) (FP – II) (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 DCL= Q(P-V) / {Q(P-V)-F-R} = 100(8-4)/ {100(8-4)-280-30}=4.44 DCL= Q(P-V) / {Q(P-V)-F-R} = 100(8-4)/ {100(8-4)-280-48}=5.55
• • • • •
Alternatively we can calculate thus, DCL = (10/3) x 1 = 3.33 DCL = (10/3) x (4/3) = 4.44 DCL = (10/3) x (5/3) = 5.55
DCL = DFL x DOL (FP – I) (FP – II) (FP – III)
(FP – I) (FP – II) (FP – III)
Combinations of operating and financial leverage. Low Automation DFLx DOL = DCL 1 X (10/3) =3.33 (4/3) X(10/3) =4.44 (5/3) X (10/3)=5.55
High Automation DFLx DOL = DCL 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 revenue Less: Fixed cost Less: 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 debt Equity shares (25,000 shares at Rs20) Total capital (assets)
0 500,000 ________ 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% 10 20 30 40 50 60
Rs500,000 500,000 500,000 500,000 500,000 500,000 500,000
Rs0 50,000 100,000 150,000 200,000 250,000 300,000
Rs500,000 450,000 400,000 350,000 300,000 250,000 200,000
25,000 22,500 20,000 17,500 15,000 12,500 10,000
Level of Debt, Interest Rate, and Rupee Amount of Annual Interest Associated with alternative capital structures. Capital structure Debt debt ratio
Interest rate on all Interest amount debt
0% 10 20 30 40 50 60
0.0% 9.0 9.5 10.0 11.0 13.5 16.5
Rs0 50,000 100,000 150,000 200,000 250,000 300,000
Rs0.00 4,500 9,500 15,000 22,000 33,750 49,500
Calculation of EPS for debt ratio = 0% Probability of EBIT
.25
.50
.25
EBIT Less: Interest
Rs0 0.00 _______ 0.00 0.00 ________ 0.00 Rs0.00
Rs100,000 0.00 _________ 100,000 40,000 _________ 60,000 Rs2.40
Rs200,000 0.00 _________ 200,000 80,000 ________ 120,000 Rs4.80
Net Profit before taxes Less: Taxes (T=0.40) Net profits after taxes EPS Expected EPS = Rs2.40 Standard deviation of EPS = Rs1.70
Calculation of EPS for debt ratio = 10% Probability of EBIT
.25
.50
.25
EBIT Less: Interest
Rs0 4,500 _______ -4,500 1,800 ________ -2,700 Rs(-)0.12
Rs100,000 4,500 _________ 95,500 38,200 _________ 57,300 Rs2.55
Rs200,000 4,500 _________ 195,500 78,200 ________ 117,300 Rs5.21
Net Profit before taxes Less: Taxes (T=0.40) Net profits after taxes EPS Expected EPS = Rs2.55 Standard deviation of EPS = Rs1.88
Calculation of EPS for debt ratio = 20% Probability of EBIT
.25
.50
.25
EBIT Less: Interest
Rs0 9,500 _______ -9,500 3,800 ________ -5,700 Rs(-)0.28
Rs100,000 9,500 _________ 90,500 36,200 _________ 54,300 Rs2.72
Rs200,000 9,500 _________ 190,500 76,200 ________ 114,300 Rs5.72
Net Profit before taxes Less: Taxes (T=0.40) Net profits after taxes EPS Expected EPS = Rs2.72 Standard deviation of EPS = Rs2.13
Calculation of EPS for debt ratio = 30% Probability of EBIT
.25
.50
.25
EBIT Less: Interest
Rs0 15,000 _______ -15,000 6,000 ________ -9,000 Rs(-)0.51
Rs100,000 15,000 _________ 85,000 34,000 _________ 51,000 Rs2.91
Rs200,000 15,000 _________ 185,000 74,000 ________ 111,000 Rs6.34
Net Profit before taxes Less: Taxes (T=0.40) Net profits after taxes EPS Expected EPS = Rs2.91 Standard deviation of EPS = Rs2.42
Calculation of EPS for debt ratio = 60% Probability of EBIT
.25
.50
.25
EBIT Less: Interest
Rs0 49,500 _______ -49,500 19,800 ________ -29,700 Rs(-)2.97
Rs100,000 49,500 _________ 50,500 20,200 _________ 30,300 Rs3.03
Rs200,000 49,500 _________ 150,500 60,200 ________ 90,300 Rs9.03
Net Profit before taxes Less: Taxes (T=0.40) Net profits after taxes EPS Expected EPS = Rs3.03 Standard deviation of EPS = Rs4.24
Expected EPS and Standard Deviation for Alternative capital Structures Capital structure debt ratio
Expected EPS
SD of EPS
0% 10 20 30 40 50 60
Rs2.40 2.55 2.72 2.91 3.12 3.18 3.03
Rs1.70 1.88 2.13 2.42 2.83 3.39 4.24
Expected EPS for alternative capital structures
•
3.18
•
SPE det c epx E
E x
0
10
20
30
40
50
60
Debt ratio (%)
SD of EPS for alternative capital structures
•
• •
1.70
SPEf o DS
•
Financial Risk
Business Risk 0
10
20
30
40
50
60
Debt Ratios (%)
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 Rs.1,00,000 0
Firm B Rs. 1,00,000 22,500
EAIBT 1,00,000 Less; Taxes @ 50% 50,000
77,500 38,750
EBIT Less: Interest
EAIT No. of shares EPS
Rs. 50,000
Rs. 38,750
50,000 Rs.1.00
25,000 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. EBIT (6% of Rs. 5,00,000) Less: Interest EAIBT Less: taxes @ 50% EAIT No. of shares EPS
Firm A (Rs)
Firm B (Rs)
30,000 0 30,000 15,000 15,000 50,000 0.30
30,000 22,500 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. • • • • • •
EBIT (9%of Rs. 5,00,000) Less: Interest EAIBT Less: Taxes @ 50%
Firm A Rs.45,000 0 45,000 22,500
Firm B Rs.45,000 22,500 22,500 11,250
EAIT
22,500
11,250
No. of shares.
50,000
25,000
Re. 0.45
Re.0.45
• • EPS
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.
Assets Financed by Debt at 6% Equity Tax Rate
F. Plan – I (D = 0) Rs.1,000
F. Plan – II (D = 50%) Rs.1,000
F. Plan- III (D = 80%) Rs.1,000
0 1,000 (10 Shares) 50%
500 500 (5 shares) 50%
800 200 (2 shares) 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
0 0 0 0 0 0 0 0
(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
Rs 1 Rs 2 Rs 3 Rs 4 Rs 5 Rs 6 Rs 7 Rs 7.5
(0.05) (Rs.150) = Rs. 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(-)1 Rs 1 Rs 3 Rs 5 Rs 7 Rs 9 Rs 11 Rs 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(-)7 Rs (-)2 Rs 3 Rs 8 Rs 13 Rs 18 Rs 23 Rs 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 • Financial Plan – II • Financial Plan – III
EPS = 0 + 0.05 x EPS = -3 + 0.1 x EPS = -12 + 0.25x
-------(4) -------(5) -------(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.
• 1.
Conclusion: 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
3% 4.8% 6%
8%
10%
r
r=k
r>k
X
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 D = 50%, EPS D = 80% , EPS (Rs) (Rs) (Rs)
2% 4% 6% 8% 10 % 12 % 14 % 15 %
20 40 60 80 100 120 140 150
1 2 3 4 5 6 7 7.5
-1 1 3 5 7 9 11 12
-7 -2 3 8 13 18 23 25.5
• • • • •
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
•
or
•
Or,
•
=
QBE (P – V) – F QBE (P – V) = F
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
Rs 8
Rs 8
V. Cost per Unit
Rs 4
Rs 2
Fixed Cost (F)
Rs 280
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
70 75 80 85 90 95 100 105
560 600 640 680 720 760 800 840
280 300 320 340 360 380 400 420
280 280 280 280 280 280 280 280
560 580 600 620 640 660 680 700
0 20 40 60 80 100 120 140
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
70 75 80 85 90 95 100 105
560 600 640 680 720 760 800 840
140 150 160 170 180 190 200 210
480 480 480 480 480 480 480 480
620 630 640 650 660 670 680 690
-60 -30 0 30 60 90 120 150
-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(82)-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 DFL DFL
= = =
1 1.33 1.67
(FP – I) (FP – II) (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 DCL= Q(P-V) / {Q(P-V)-F-R} = 100(8-4)/ {100(8-4)-280-30}=4.44 DCL= Q(P-V) / {Q(P-V)-F-R} = 100(8-4)/ {100(8-4)-280-48}=5.55
• • • • •
Alternatively we can calculate thus, DCL = (10/3) x 1 = 3.33 DCL = (10/3) x (4/3) = 4.44 DCL = (10/3) x (5/3) = 5.55
DCL = DFL x DOL (FP – I) (FP – II) (FP – III)
(FP – I) (FP – II) (FP – III)
Combinations of operating and financial leverage. Low Automation DFLx DOL = DCL 1 X (10/3) =3.33 (4/3) X(10/3) =4.44 (5/3) X (10/3)=5.55
High Automation DFLx DOL = DCL 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 revenue Less: Fixed cost Less: 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 debt Equity shares (25,000 shares at Rs20) Total capital (assets)
0 500,000 ________ 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% 10 20 30 40 50 60
Rs500,000 500,000 500,000 500,000 500,000 500,000 500,000
Rs0 50,000 100,000 150,000 200,000 250,000 300,000
Rs500,000 450,000 400,000 350,000 300,000 250,000 200,000
25,000 22,500 20,000 17,500 15,000 12,500 10,000
Level of Debt, Interest Rate, and Rupee Amount of Annual Interest Associated with alternative capital structures. Capital structure Debt debt ratio
Interest rate on all Interest amount debt
0% 10 20 30 40 50 60
0.0% 9.0 9.5 10.0 11.0 13.5 16.5
Rs0 50,000 100,000 150,000 200,000 250,000 300,000
Rs0.00 4,500 9,500 15,000 22,000 33,750 49,500
Calculation of EPS for debt ratio = 0% Probability of EBIT
.25
.50
.25
EBIT Less: Interest
Rs0 0.00 _______ 0.00 0.00 ________ 0.00 Rs0.00
Rs100,000 0.00 _________ 100,000 40,000 _________ 60,000 Rs2.40
Rs200,000 0.00 _________ 200,000 80,000 ________ 120,000 Rs4.80
Net Profit before taxes Less: Taxes (T=0.40) Net profits after taxes EPS Expected EPS = Rs2.40 Standard deviation of EPS = Rs1.70
Calculation of EPS for debt ratio = 10% Probability of EBIT
.25
.50
.25
EBIT Less: Interest
Rs0 4,500 _______ -4,500 1,800 ________ -2,700 Rs(-)0.12
Rs100,000 4,500 _________ 95,500 38,200 _________ 57,300 Rs2.55
Rs200,000 4,500 _________ 195,500 78,200 ________ 117,300 Rs5.21
Net Profit before taxes Less: Taxes (T=0.40) Net profits after taxes EPS Expected EPS = Rs2.55 Standard deviation of EPS = Rs1.88
Calculation of EPS for debt ratio = 20% Probability of EBIT
.25
.50
.25
EBIT Less: Interest
Rs0 9,500 _______ -9,500 3,800 ________ -5,700 Rs(-)0.28
Rs100,000 9,500 _________ 90,500 36,200 _________ 54,300 Rs2.72
Rs200,000 9,500 _________ 190,500 76,200 ________ 114,300 Rs5.72
Net Profit before taxes Less: Taxes (T=0.40) Net profits after taxes EPS Expected EPS = Rs2.72 Standard deviation of EPS = Rs2.13
Calculation of EPS for debt ratio = 30% Probability of EBIT
.25
.50
.25
EBIT Less: Interest
Rs0 15,000 _______ -15,000 6,000 ________ -9,000 Rs(-)0.51
Rs100,000 15,000 _________ 85,000 34,000 _________ 51,000 Rs2.91
Rs200,000 15,000 _________ 185,000 74,000 ________ 111,000 Rs6.34
Net Profit before taxes Less: Taxes (T=0.40) Net profits after taxes EPS Expected EPS = Rs2.91 Standard deviation of EPS = Rs2.42
Calculation of EPS for debt ratio = 60% Probability of EBIT
.25
.50
.25
EBIT Less: Interest
Rs0 49,500 _______ -49,500 19,800 ________ -29,700 Rs(-)2.97
Rs100,000 49,500 _________ 50,500 20,200 _________ 30,300 Rs3.03
Rs200,000 49,500 _________ 150,500 60,200 ________ 90,300 Rs9.03
Net Profit before taxes Less: Taxes (T=0.40) Net profits after taxes EPS Expected EPS = Rs3.03 Standard deviation of EPS = Rs4.24
Expected EPS and Standard Deviation for Alternative capital Structures Capital structure debt ratio
Expected EPS
SD of EPS
0% 10 20 30 40 50 60
Rs2.40 2.55 2.72 2.91 3.12 3.18 3.03
Rs1.70 1.88 2.13 2.42 2.83 3.39 4.24
Expected EPS for alternative capital structures
•
3.18
•
SPE det c epx E
E x
0
10
20
30
40
50
60
Debt ratio (%)
SD of EPS for alternative capital structures
•
• •
1.70
SPEf o DS
•
Financial Risk
Business Risk 0
10
20
30
40
50
60
Debt Ratios (%)
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