Lesson 23

Chapter-7

Leverages

Unit 3

Financing decisions

After studying this lesson, you should be able to:

Understand what financial leverage is.

Calculate the operating break-even point for quantity and for dollar revenues

Understand EBIT-EPS break-even, or indifference, analysis.

Describe the elements of total firm risk.

Understand what is involved in determining the appropriate amount of financial

leverage.

Now that you have understood operating leverage, we will be doing financial

leverage in today’s session.

Financial Leverage An Introduction

Financial leverage involves the use of fixed cost financing. Interestingly, financial leverage is

acquired by choice, but operating leverage sometimes is not. The amount of operating

leverage (the amount of fixed operating costs) employed by a firm is sometimes dictated by

the physical requirements of the firm's operations. For example, a steel mill by way of its

heavy investment in plant and equipment will have a large fixed operating cost component

consisting of depreciation. Financial leverage, on the other hand, is always a choice item. No

firm is required to have any long-term debt or preferred stock financing. Firms can, instead,

finance operations and capital expenditures from internal sources and the issuance of

common stock. Nevertheless, it is a rare firm that has no financial leverage. Why, then, do we

see such reliance on financial leverage?

Financial leverage is employed in the hope of increasing the return of common shareholders.

Favorable or positive leverage is said to occur when the firm uses funds obtained at a fixed

cost (funds obtained by issuing debt with a fixed interest rate or preferred stock with a

constant dividend rate) to earn more that the fixed financing costs paid. Any profits left after

meeting fixed financing costs then belong to common shareholders. Unfavorable or negative

leverage occurs when the firm does not earn as much as the fixed financing costs. The favor

ability of financial leverage, or "trading on the equity" as it is sometimes called, is judged in

terms of the effect that it has on earnings per share to the common shareholders. In effect,

financial leverage is the second step in a two-step profit-magnification process. In step one;

operating leverage magnifies the effect of changes in sales on changes in operating profit. In

step two, the financial manager has the option of using financial leverage to further magnify

the effect of any resulting changes in operating profit on changes in earnings per share. In the

next section we are interested in determining the relationship between earnings per share

(EPS) and operating profit (EBIT) under various financing alternatives and the indifference

points between these alternatives.

EBIT-EPS Break-Even or Indifference Analysis

Calculation of Earnings per Share:

To illustrate an EBIT-EPS break-even analysis of financial leverage, suppose that Cherokee

Tire Company with long-term financing of. $10 million, consisting entirely of common stock

equity, wishes to raise another $5 million for expansion through one of three possible

financing plans.

The company may gain additional financing with a new issue of

(1) All common stock,

(2) All debt at 12 percent interest, or

(3) All preferred stock with an 15 percent dividend. Present annual earnings before

interest and. taxes (EBIT) are $15 million but with expansion are expected to rise to

$2.7 million. The income tax rate is 40 percent, and 200,000 shares of common stock

are -now outstanding. -Common stock can be sold at $50 per share under the first

financing option, which translates into 100,000 additional shares of stock.

To determine the EBIT-EPS break-even, or indifference, points among the various financing

alternatives, we begin by calculating earnings per share, EPS, for some hypothetical level of

EBIT using the following formula:

EPS = (EBIT - /)(1 - t) – PD / NS

Where I = annual interest paid

PD = annual preferred dividend paid

t = corporate tax rate

NS = number of shares of common stock outstanding

Suppose we wish to know what earnings per share would be under the three alter-

native additional-financing plans if EBIT were $2.7 million. The calculations are shown

Table 16.3

COMMON

STOCK

DEBT PREFERRED

STOCK

Earning before interest and taxes (EBIT)

Interest (I)

Earnings before taxes (EBT)

Income taxes {(EBT) X (t)]

Earnings after taxes (EAT)

Preferred stock dividends (PD)

Earnings available to common shareholders

(EACS)

Number of shares of common stock

outstanding (NS)

Earnings per share (EPS)

$2700000

-----

$2700000

1080000

$1620000

--------

$1620000

30000

$5.40

2700000

600000

$2100000

840000

$1260000

----

$1260000

200000

$6.30

2700000

---

$2700000

1080000

$1620000

550000

$1070000

200000

$5.35

in Table 16-3. Note that interest on debt is deflected---before taxes, while preferred stock

dividends are deducted after taxes. As a result, earnings available to common shareholders

(EACS) are higher under the debt alternative than they are under the preferred stock

alternative, despite the fact that the interest rate on debt is higher than the preferred stock

dividend rate.

EBIT-EPS Chart:

Given the information in Table 16-3, we are able to construct an

EBIT-EPS break-even chart is similar to the one for operating leverage. On the horizontal

axis we plot earnings before interest and taxes, and on the vertical axis we plot earnings-per

share. For each financing alternative, we must draw a straight line to reflect EPS for all

possible levels of EBlT. Because two points determine a straight line, we need Two data

points for each financing alternative. The first is the EPS calculated for some hypothetical

level of EBlT. Fat the expected $2.7 million level of EBlT, we see in Table 16-3 that earnings

per share are $5.40, $6.30 and $5.35 for the common stock, debt, and preferred stock

financing .alternatives. We simply plot these earnings per –share levels to correspond with

the $2.7 million level of EBlT. Technically, it does not matter which hypothetical level of

EBlT we choose for calculating EPS. On good graph-paper one EBIT level is as good as the

next. However, it does seem to make common sense to choose the most likely, or expected,

EBlT level ,rather than some level not too likely to occur.

The second data point--chosen chiefly because of its ease of calculation-is where EPS is zero.

This is simply the EBlT necessary to cover all fixed financial costs for a particular financing

plan, and it is plotted on the horizontal axis. We can make use of Eq. (16-10) to determine the

horizontal axis intercept under each alternative. "We simply set the numerator in the equation

equal to zero and solve for EBIT. For the, common stock alternative we have

0 = (E BIT - 1)(1 - t) – PD

= (EBIT - 0)(1 - .40) - 0

= (EBIT)(.60)

EBIT = 0/(.60) = 0

Notice there are no fixed financing costs whatsoever (either on old or new financing).

Therefore, EPS equals zero at zero EBIT.3 For the debt alternative we have

0 = (EBIT- 1)(1 - t) – PD

= (EBIT - $600,000)(1 - .40) - 0

= (EBIT)(.60) - $360,000

=EBIT =$360,000/(.60) = $600,000

Thus, the after-tax interest charge divided by 1 minus the tax rate gives us the EBIT:-

necessary to cover these interest payments. In short, we must have $600,000 to Cover interest

charges, so $600,000 becomes the horizontal a)Jis intercept. Finally, for the preferred stock

alternative we have

0 = (EBIT - 1)(1 - t) – PD

= (EBIT - 0)(1 - .40) - $550,000

= (EBIT)(.60) - $550,000

EBIT = $560,000/(.60) = $916,667

We divide total annual preferred dividends by 1 minus the tax rate to obtain the EBIT

necessary to cover these dividends. Thus, we need $916,667 in EBIT to cover $550,OOO, in

preferred stock dividends, assuming a 40 percent tax rate. Again, preferred dividends are

deducted after taxes, so it takes more in before-tax earnings to cover them J than it does to

cover interest. Given the horizontal axis intercepts and earnings per share for some

hypothetical level of EBIT (like the "expected" EBIT), we draw a straight line through each

set of data points. The break-even or indifference, for Cherokee The Company is shown in

Figure 16-3

We see from Figure 16-3 that the earnings per share indifference point between the debt

and common stock additional-financing alternatives is $1.8 million in EBIT.4 If EBIT is

below that point, the common stock alternative will provide higher earnings per share.

Above that point the debt alternative produces higher earnings per share. The indifference

point between the preferred stock and\the common stock alternatives is $2.75 million in

EBIT. Above that point, the preferred stock alternative produces more favorable earnings

per share. Below that point, the common stock alternative leads to higher earnings per

share. Note that there is no indifference point between the debt and preferred stock

alternatives. The debt alternative dominates for all levels of EBIT and by a constant

amount of earnings per share, namely 95 cents.

Indifference Point Determined Mathematically:

The indifference point between two alternative financing methods can be determined

mathematically by first using

Eq. (16-10) to express EPS for each alternative and then setting these expressions equal

to each other as follows:

(EBIT1,2 - I1) (1 - t) – PD) /NS1 = (EBIT1,2 - I2)(1 - t) - PD2) / NS2

where EBITI,2 = EBIT indifference point between the two alternative financing methods

that we are concerned with-in this case, methods 1 and 2

I1,I2 = annual interest paid under financing methods 1 and 2

PD1, PD2 = annual preferred stock dividend paid under financing methods 1 and

2

t = corporate tax rate

NS1, NS2 = number of shares of common stock to be outstanding under financing

methods 1 and 2

Suppose that we wish to determine the indifference point between the common stock and

debt-financing alternatives in our example. We would have

Common Stock Debt

(EBIT1.2 - 0)(1 - .40) – 0) / 300,000 = (EBIT1,2 - $600,000)(1 - .40) – 0)/ 200,000

Cross-multiplying and rearranging, we obtain

(EBIT12)(.60)(200,000) = (EBIT1,2)(.60)(300,000) - (.60)($600,000)(300,000)

(EBIT12)(60,000) = $108,000,000,000

EBIT12 = $1,800,000

The EBIT-EPS indifference point, where earnings per share for the two methods

of financing are the same, is $1.8 million. This amount can be verified graphically in

Figure 16-3. Thus, indifference points can be determined both graphically and

mathematically.

Effect on risk

So far our concern with EBIT-EPS analysis has been only with what happens to the

return to common shareholders as measured by earnings per share.

We have seen in our example that if EBIT is above $1.8 million, debt financing is the

preferred alternative fro_ the standpoint of earnings per share. We know from our earlier

discussion, however, that the impact on expected return is only one side of the coin. The

other side is the effect that financial leverage has on risk. An EBIT-EPS chart does not

permit a precise analysis of risk. Nevertheless, certain generalizations are possible. For

one thing, the financial manager should compare the indifference point between two

alternatives, like debt financing versus common stock financing, with the most likely

level of EBIT. The higher the expected level of E13IT, assuming that it exceeds the

indifference point, the stronger the case that can be made for debt financing, all other"

things the same.

In addition, the financial manager should assess the likelihood of future EBITs I

actually falling below the indifference point. As before, Our estimate of expected! EBIT

is $2.7 million. Given the business risk of the company and the resulting possible

fluctuations in EBIT, the financial manager should assess the probability of EBITs falling

below $1.8 million. If the probability is negligible the use of the debt alternative will be

supported. On the other hand, if EBIT is presently only slightly above the indifference

In summary, the greater the level of expected EBIT above the indifference point and the

lower the probability of downside fluctuation, the stronger the case that can be made for

the use of debt financing. EBIT-EPS break-even analysis is but one of several methods

used for determining the appropriate amount of debt a firm might carry. No one method

of analysis is satisfactory by itself. When several methods of

analysis are undertaken simultaneously, however, generalizations are possible.

The indifference between the two alternatives methods:

(EBIT - I1) (1-T) (EBIT- I2) (1 – T)

E1 = E2

Where EBIT = Earning before interest and taxes

I1 = Interest charge in alternative 1.

I2 = interest charges in alternative 2.

T = rate of tax

E1 = Equity share in alternative 1.

E2 = Equity share in alternative 2.

Sanjay Manufacturing Ltd. wanted to finance a project, which has an outlay of Rs

60,00,000. It has the following two alternatives in financing the project cost.

Alternative1: 100% equity finance.

Alternative2: debt equity ratio 2:1.

The rate of interest payable on the debt is 18% p.a. The corporate orate of tax is 40%.

Calculate the indifference point between two alternative methods of financing.

Solution

Alternatives in financing and its financial charges:

(i) By issue of 6,00,000 equity shares of RS 10 each amounting Rs 60,00,000. No

financial charges involved.

(ii) By raising the funds in the following way:

Debt Rs. 40 lakhs.

Equity Rs. 20 lakhs (2,00,000 equity shares of Rs. 10 each)

Interest payable on debt = Rs. 40,00,000 X (18/100) = Rs. 7,20,000

We can calculated the break even or difference point as following ways:

(EBIT-0) (1-0.40) = (EBIT-7, 20,000) (1-0.40)

6,00,000 2,00,000

(EBIT-0) (0.60) = (EBIT-7,20,000) (0.60)

6,00,000 2,00,000

(in lakhs)

(EBIT-0) (0.60) = (EBIT-7.2) (0.60)

6 2

0.60 EBIT X 2 = (0.6EBIT X 6) – [(0.62 X 7.2) X 6]

0.60 X 7.2 X6 = (0.60 EBIT X 6) – (6.60 EBT X 2)

25.92 = 3.6 EBIT – 1.2 EBIT

2.4 EBIT = 25.92

Preference dividend (Dp) = Rs.50000

What is the degree of financial leverage when the earning before interest and tax EBIT

are Rs.400000? What percentage change would occur in the earning per share of Sylex if

EBIT increases by 10 percent?

Solution

EBIT

DFL = ------------------

EBIT – I – Dp/ 1-t

400000

DFL(EBIT = 400000) = --------------------------------------- = 2

400000 – 100000 –50000/ 1- .05

percentage change in EPS if EBIT increases by 5 percent = DFL* 5 percent = 10 %

Example to measure Impact of financial leverage on investor’s

Rate of return Let us see with the help of a very simple example, how financial leverage affects return

on equity. A company needs a capital of Rs.10000 to operate. This money may be

brought in by the share holders of the company. Alternatively, a part of this money may

also be brought in through debt financing. If the management raises Rs.10000 from

shareholders, the company is not financial leveraged and would have the following

balance sheet.

Liabilities Rs. Assets Rs.

Equity capital 10000 cash 10000

The company commences operations, which leads to the preparations of the following

simplified version of its income statement.

Rs.

Sales 10000

Expenses 7000

EBIT 3000

Tax @ 50% 1500

Net profit 1500

What is the return the company has earned on the owner investment? We see that the

return on equity is 15%. The net profit of Rs.1500 may be paid fully or partly to

shareholders as dividends or may be retained to finance future activities of the company.

Either way the return on equity is 15%.

What happens to the owner’s rate of the return if the management decides to finance a

part of the required total investment of Rs.10,000 through debt financing? The answer to

this question depends on,

• The proportion of total investment, which the management decides to finance

through debt and the interest rate on, borrowed funds.

• The interest rate on the borrowed funds.

If the management has decided on a Debt equity Ratio of 2:1, total borrowings will

amount to 10000*2/3 = Rs.6667. assuming that the company is able to raise this amount

at an interest of say , 15%, the company’s balance sheet will appear as follow;

liabilities Rs. Assets Rs.

Equity capital 3333 cash 10000

Debt capital 6667

Total 10000 10000

The company now has an added financial burden of payment of interest on the amount he

has borrowed. The income statement will now show as follows;

Rs.

Sales 10000

Expenses 7000

EBIT 3000

Interest charges 1000

Profit before tax(PBT) 2000

Tax @ 50% 1000

Net profit 1000

The use of debt in the company’s capital structure has caused the net profit to decline

from Rs.1500 to Rs.1000. But has the return on owner’s capital declined? Return on

equity now works out to 30%, as the owner have invested only Rs.3333 now which

earned them Rs.1000. what were the factors which contributed to this additional return.

• Though the company has to pay interest at 15% on borrowed capital, the

company’s operations have been able to generate more than 15%, which is being

transferred to the owners.

• The reduction in PBT has brought about a reduction in the amount of tax paid, as

interest is a tax deductible expenses, to the extent of interest (1-tax rate) i.e,

Rs500. the greater the tax rate, the more is the tax shield available to a company

which is financially leveraged.

As was seen in the above example, a company may increase the return on the equity by

use of the debt i.e., the use of financial leverage. by increasing the portion of debt in the

pattern of financing i.e., by increasing the debt equity ratio, the company should be able

to increase the return on equity.

Example of financial leverage and risk;

If Increased financial leverage leads to increased return on the equity, why do companies

not resort to even increasing amount of debt financing? Why do financial and other term

lending institution insist on norms for debt equity ratio? The answer is that as the

company come more financial leveraged, it become riskier, i.e., increased use of debt

financing will lead to increased financial risk which leads to;

• Increased fluctuations in the return on equity.

• Increase in the interest rate on debts.

Increased fluctuations in returns

In the previous example, let us assume that sales decline by 10%(fromRs.10000 to

Rs.9000), expenses remaining the same. What happens to return on equity? The income

statements for the financially unleveraged and leveraged firms will appear as follows.

Unleveraged firm

(0 Debt)

Leveraged firm

(Debt Equity ratio 2:1)

Sales 9000 9000

Expenses 7000 7000

EBIT 2000 2000

Interest charges - 1000

(6667*0.5)

PBT 2000 1000

Tax @ 50% 1000 500

Net profit 1000 500

Net profit @ sales of

Of Rs.10000

1500 1000

ROE @ sales of Rs.10000 15% 30%

ROE@ sales of Rs.9000 10% 15%

We see that a 10% decline in sales produces substantial declines in earnings and the rates

of return on owner’s equity in both cases. But the decline is greater for financially

leveraged firm than for the financially unleveraged firm. Why is this so? The reason can

be traced to the fact that once a firm borrows capital, interest payments become

obligatory and hence fixed in nature. The same interest payment, which was the cause for

increase in owner’s equity when sales decline. Hence, the greater the use of financial

leverages, the greater the potential fluctuation in return on equity.

Increase in interest rates

Firms that are highly financially leveraged are perceived by lenders of debt as risky.

Creditors may refuse to lend to a highly leveraged firm or may do so only at higher rates

of interest or more stringent loan conditions. As the interest rate increases, the return on

equity decrease. However, even though the rate of return diminishes, it might still exceed

the rate of return obtained when no debt was used, in which case financial leverage would

still be favorable.

Implications

Let us again refer to our earlier example. In the first situation, the company was

unleveraged, in the second situation the debt – equity ratio was 2:1. The balance sheet

and income statements are reproduced below.

Balance sheets -------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------- liabilities Assets Liabilities Assets Equity Equity Cash 10000 capital 10000 cash 10000 capital 3333 ------- -------- Debt 6667 10000 10000 ------- ------- -------- -------- 10000 10000 -----------------------------------------------------------------------------------------------

Income statements

unleveraged Leveraged

sales 10000 10000

Expenses 7000 7000

EBIT 3000 3000

Interest - 1000

PBT 3000 2000

tax@ 50% 1500 1000

Net profit 1500 1000

The degree of financial leverage(DFL) in each case is calculated as follows;

EBIT

DFL = -----------------------

EBIT – I – Dp/1-t

3000

Unleveraged = -------- = 1

3000

3000

leveraged = -------------------- = 1.5

3000 - 1000

What do these imply? This implies that if EBIT is changed by 1%, EPS will also change

by 1% when the company uses no debt and by 1.5% when it uses debt in the ratio of

2:1(66.67% of total capital). This proof of what we have stated earlier. The greater the

leverage, the wider are the fluctuations in the return on equity and the greater is the

financial risk the company is exposed to. Through an EBIT-EPS analysis, we can

evaluate various financing plans or degree of financing plans or financial leverage with

respect to their effect on EPS.

Combined or Total Leverage

Combined leverage is the measure of the total leverage due to both operating and fixed

financial cost. This is then equal to the product of the firm’s DOL and DFL and indicates

the responsiveness of EPS to Q.

Degree of total leverage( DTL) = DOL* DFL

= % change in EPS/ % change in Q

change in EPS/ EPS

= -------------------------

change in Q/ Q

Q(P-V)

= -------------------

Q(P-V) –F – I- Dp/1-t

Implications

A greater DOL or DFL will raise DTL. DTL is a measure of the overall risk ness or

uncertainty associated with shareholder’s earnings that arises because of operating and

financial leverage can be combined in a number of different ways(high business risk

being set off by a low financial risk and vice versa) to obtain a desirable degree of total

leverage and acceptable level of total risk.

Exercise.

The following data are available for the Broadway and Midway companies:

Broadway co. Midway co.

Sales volume 10000 units 10000 units

Selling price per unit of output Rs.200 Rs.200

Variable cost per unit of output Rs.120 Rs.150

Fixed operating cost per unit of output Rs.60 Rs.30

Equity Rs.300000 Rs.600000

Preference shares Rs.100000 --

Debt Rs.600000 Rs.400000

Interest rate on debt 16.25% 15%

Dividend rate on preference share 13% --

Tax rate 60% 60%

Required:

1. Calculate the ROE, DOL, DFL, DTL, operating break-even point ,financial break-

even point for each company.

2. As a financial analyst which of two companies would you describe as more risky?

Give reasons.

Solution:

Broadway co. Midway co.

Rs. Rs.

1. Selling price per unit 200 200

2. Less: variable cost per unit 120 150

3. Contribution 80 50

4. Operating fixed costs at 6,00,000 3,00,000

Sales volume of 10000 units

5.operating breakeven point = 6,00,000/80 3,00,000/50

Operating fixed cost/contribution per unit= 7500 units 6000 units

6. DOL=total contribution

------------------- 800000/200000 500000/200000

Total contribution- total operating

fixed cost = 4 2.5

7. Profit before interest& tax 200000 200000

8. Less; interest 97500 60000

9.profit before tax 102500 140000

10. Tax @ 60% 61500 84000

11. profit after tax 41000 56000

12. less: preference dividend 13000 --

(100000*13/100)

13.profit available to equity shareholders 28000 56000

14. ROE 28000*100 56000*100

-------------- =9.3% ------------- =9.3%

300000 600000

15. DFL 200000 200000

----------------=2.86 ----------- =1.43

102500-32500 140000

16. DTL=DOL*DFL = 4*2.86= 11.44 =2.5*1.43=3.575

17. Financial breakeven point = Rs.130000 =Rs. 60000

(Level of PBIT at which ROE is zero)

18. Overall breakeven point = 73000/80 = 360000/50

(Operating fixed cost+ interest+

Dp/1-t/contribution per unit) = 9125units = 7200 units

Working notes: Broadway co. Midway co.

1. Profit before interest and taxes;

Total contribution 800000 800000

Less; fixed operating cost 600000 300000

---------- -----------

200000 200000

2. Interest

Broadway company- 600000*16.25/100 = Rs. 97500

Midway company- 400000*15/100 = Rs.60000

Solution

Through ROE is the same for both the companies; Broadway Company is exposed to

greater risk than Midway company. This is also reflected in the breakeven points

calculated. Midway company is therefore better managed.

True/False Exercise

1. A DOL must be greater than or equal to zero.

2. The EBIT-EPS break-even analysis does not consider differences in risk.

3. The judgments of investment analysts are important for the firm to consider since

they understand and influence the financial markets.

4. The debt ratio is a perfect measure to examine financial risk.

5. A business that has some fixed operating costs but has no debt of any type and no

preferred stock can be considered risk-free.

1. FALSE

2. TRUE

3. TRUE

4. FALSE

5. FALSE

(Level of PBIT at which ROE is zero)

18. Overall breakeven point = 73000/80 = 360000/50

(Operating fixed cost+ interest+

Dp/1-t/contribution per unit) = 9125units = 7200 units

Working notes: Broadway co. Midway co.

1. Profit before interest and taxes;

Total contribution 800000 800000

Less; fixed operating cost 600000 300000

---------- -----------

200000 200000

2. Interest

Broadway company- 600000*16.25/100 = Rs. 97500

Midway company- 400000*15/100 = Rs.60000

Solution

Through ROE is the same for both the companies; Broadway Company is exposed to

greater risk than Midway company. This is also reflected in the breakeven points

calculated. Midway company is therefore better managed.

True/False Exercise

1. A DOL must be greater than or equal to zero.

2. The EBIT-EPS break-even analysis does not consider differences in risk.

3. The judgments of investment analysts are important for the firm to consider since

they understand and influence the financial markets.

4. The debt ratio is a perfect measure to examine financial risk.

5. A business that has some fixed operating costs but has no debt of any type and no

preferred stock can be considered risk-free.

1. FALSE

2. TRUE

3. TRUE

4. FALSE

5. FALSE