CHAPTER
Capital Structure, Leverage &
Firm’s Value




Business vs. financial risk
Optimal capital structure
Operating leverage
Capital structure theory
13-1
Capital Structure, Leverage &
Firm’s Value
Capital Structure and Leverage
13-2
What is Leverage
A firm can make use of different sources of
financing whose cost are different. These cost
may be classified into those which carry a fixed
rate of return and those on which the return
Vary.
The employment of an asset or source of funds
for which the firm has to pay a fixed cost or
fixed return may be termed as a Leverage.
13-3
Types of Leverage
There are two types of Leverage
 Operating Leverage: the leverage associated
with investment (asset acquisition) activities
is referred to as operating leverage.
 Financial Leverage: the leverage associated
with financing activities is referred to as
financial leverage.
13-4
What is operating leverage, and how
does it affect a firm’s business risk?


Operating leverage is the use of
fixed costs rather than variable
costs.
If most costs are fixed, hence do not
decline when demand falls, then the
firm has high operating leverage.
13-5
Effect of operating leverage

More operating leverage leads to more
business risk, for then a small sales decline
causes a big profit decline.
Rev.
Rev.
$
TC
$
} Profit
TC
FC
FC
QBE

Sales
QBE
Sales
What happens if variable costs change?
13-6
Using operating leverage
Low operating leverage
Probability
High operating leverage
EBITL

EBITH
Typical situation: Can use operating leverage
to get higher E(EBIT), but risk also increases.
13-7
What is financial leverage?
Financial risk?


Financial leverage is the use of debt
and preferred stock.
Financial risk is the additional risk
concentrated on common
stockholders as a result of financial
leverage.
13-8
Business risk vs. Financial risk


Business risk depends on business
factors such as competition, product
liability, and operating leverage.
Financial risk depends only on the
types of securities issued.


More debt, more financial risk.
Concentrates business risk on
stockholders.
13-9
An example:
Illustrating effects of financial leverage


Two firms with the same operating leverage,
business risk, and probability distribution of
EBIT.
Only differ with respect to their use of debt
(capital structure).
Firm U
No debt
$20,000 in assets
40% tax rate
Firm L
$10,000 of 12% debt
$20,000 in assets
40% tax rate
13-10
Firm U: Un-leveraged
Prob.
EBIT
Interest
EBT
Taxes (40%)
NI
Economy
Bad
Avg.
0.25
0.50
$2,000
$3,000
0
0
$2,000
$3,000
800
1,200
$1,200
$1,800
Good
0.25
$4,000
0
$4,000
1,600
$2,400
13-11
Firm L: Leveraged
Prob.*
EBIT*
Interest
EBT
Taxes (40%)
NI
Economy
Bad
Avg.
0.25
0.50
$2,000
$3,000
1,200
1,200
$ 800
$1,800
320
720
$ 480
$1,080
Good
0.25
$4,000
1,200
$2,800
1,120
$1,680
*Same as for Firm U.
13-12
Ratio comparison between
leveraged and un-leveraged firms
FIRM U
BEP
ROE
TIE
FIRM L
BEP
ROE
TIE
Bad
Avg
Good
10.0%
6.0%
∞
15.0%
9.0%
∞
20.0%
12.0%
∞
Bad
Avg
Good
10.0%
4.8%
1.67x
15.0%
10.8%
2.50x
20.0%
16.8%
3.30x
13-13
Risk and return for leveraged
and un-leveraged firms
Expected Values:
E(BEP)
E(ROE)
E(TIE)
Firm U
15.0%
9.0%
∞
Firm L
15.0%
10.8%
2.5x
Firm U
2.12%
0.24
Firm L
4.24%
0.39
Risk Measures:
σROE
CVROE
13-14
The effect of leverage on
profitability and debt coverage



For leverage to raise expected ROE, must
have BEP > kd.
Why? If kd > BEP, then the interest expense
will be higher than the operating income
produced by debt-financed assets, so
leverage will depress income.
As debt increases, TIE decreases because
EBIT is unaffected by debt, and interest
expense increases (Int Exp = kdD).
13-15
Conclusions



Basic earning power (BEP) is
unaffected by financial leverage.
L has higher expected ROE because
BEP > kd.
L has much wider ROE (and EPS)
swings because of fixed interest
charges. Its higher expected return
is accompanied by higher risk.
13-16
Capital Structure, Leverage & Firm’s
Value
Capital Structure & Firm’s Value
13-17
Relationship between capital structure & cost of capital
Assumptions




There is no income tax, corporate or
personal.
100% dividend payout ratio is assumed
The operating income is not expected to
grow or decline over time.
A firm can change its capital structure almost
instantaneously without incurring transaction
cost.
13-18
Net Income Approach
According to this approach, the cost of debt rD and the cost of equity rE remain
unchanged when D/E varies. The constancy of rD and rE with respect to D/E means
That ra the average cost of capital decline as D/E increases.
D
rA = rD [
D+E
E
]+ rE [
]
D+E
Where,
rD = Cost of Debt capital
D = Market value of debt
E = Market value of equity
13-19
Net Income Approach
Problem: there are 2 firms A & B similar in all aspects except in the capital
structure. Financial data for these firms are shown bellow,
Firm A
Firm B
O
Operating income
10,000
10,000
I
Interest on debts
0
3,000
rE
Cost of equity capital
10%
10%
rD
Cost of Debt capital
6%
6%
D
Market value of debt
0
50,000
E
Market value of equity
100,000
70,000
Required: Calculate the average cost of capital for firm A & B
(a) For Firm A
0
100,000
rA = 6%[
] + 10% [
100,000
100,000
(a) For Firm B
50,000
70000
rA = 6%[
] + 10% [
120,000
100,000
]
= 10%
]
= 8.5%
13-20
Net Operating Income Approach
According to this approach, the over all capitalization rate and the cost of debt
remain constant for all degree of leverage.
The cost of equity can be expressed as,
rE=rA + (rA – rD) (D/E)
Problem:
Firm A
Firm B
O
Net Operating income
10,000
10,000
rA
Overall Capitalization Rate
0.15
0.15
V
Total Market Value
66,667
66,667
I
Interest on debts
1000
3,000
rD
Debt capitalization rate
0.10
0.10
D
Market value of debt
10,000
30,000
E
Market value of equity
56,667
36,667
D/E
Financial Leverage
0.176
0.818
Ans: The Equity Capitalization rates of Firms A & B can be calculated as follows,
Firm A : rE= 15 + (15 – 10) 0.176 = 15.9%
Firm B : rE= 15 + (15 – 10) 0.818 = 19.1%
13-21
Traditional Approach
The main proposition of the traditional approach are,

The cost of debt capital, rD, remain more or less constant up to a
certain degree of leverage but rises thereafter at an increasing rate.

The cost of equity capital, rE, remain more or less constant or rises
only gradually up to a certain degree of leverage and rises sharply
thereafter.

The average cost of capital, rA, as a consequence of the above
behavior of rD & rE, (1) decreases up to a certain point (2) remain
more or less unchanged for moderate increase in leverage thereafter;
and (3) rises beyond a certain point.
13-22
Modigliani & Miller Position
So far, we have examined three conflicting views on capital structure. Which one is
correct? To answer this question we need a formal theory of capital structure.
Such a theory was first proposed by Franco Modigliani and Merton Miler in their
classic contribution on capital structure which is regarded by many as the most
important paper in modern Finance. Both of them subsequently became Nobel
Laureates in Economics.
Assumptions of Modigliani & Miller Position

Perfect capital Market: Information is freely available and there is no problem of
asymmetric information, transaction are costless, there are no bankruptcy costs,
securities are infinitely divisible.

Rational Investors & Managers: Investors rationally choose a combination of risk
and return that is most advantageous for them. Managers act in the interest of
shareholders.

Homogeneous Expectation: Investors hold identical expectations about future
operating earnings.

Equivalent Risk Classes: Firms can be grouped into “Equivalent Risk Classes” on
the basis of their business risk.

Absence of taxes: There is no Tax.
13-23
Modigliani & Miller Position
Proposition 1
MM’s First proposition is,
“The value of a firm is equal to its expected operating income divided by the
discount rate appropriate to its risk class. It is independent of its capital structure”.
In symbol:
V = D+E = O / r
Where,
V= Market Value of the Firm
D = Market Value of the Debt
E = Market Value of the Equity
O = Expected operating income
r = Discount rate applicable to the risk class to which the firm belongs.
Proposition 2
MM’s First proposition is,
“The expected return on equity is equal to the expected return on assets, plus a
Premium. The premium is equal to the debt-equity ratio times the differences
between the expected return on assets and the expected return on Debt.”
In symbol:
rE = rA +(rA – rD) (D/E)
Where,
Expected operating income
Expected return on assets = rA =
Market value of all securities
13-24
Problem
The following information is available for XYZ metals.
Net operating income
Tk. 40 Million
Interest on Debts
Tk. 10 Million
Cost of Equity
18%
Cost of Debts
12%
Required: use the NI Method & assume there are no tax
(a)
What is the average cost of capital of XYZ metals?
(b)
What happen to the average cost of capital of XYZ metals, if it employs Tk.
100 million of debt to finance a project which earns an operating income of
Tk. 20 Million?
Solution:
The market value of Debt = (Tk. 10 million / 0.12) = Tk. 83.33 million
The market value of Equity = (Tk. 30 million / 0.18) = Tk. 166.67 million
Hence, the average cost of capital for XYZ metals is:
83.33
166.67
12 x
+ 18 x
250.00
250.00
= 16%
13-25
Problem
If XYZ metals employs Tk. 100 million of debt to finance a project which earns an
Operating income of Tk. 20 million, the following financial picture emerge,
Net operating income
Interest on Debts
Equity earnings
Market value of equity
Market value of Debt
Market value of the Firm
Tk.
Tk.
Tk.
Tk.
Tk.
Tk.
60 Million
22 Million
38 million
211.11 million
183.33 million
394.44 million
183.33
12 x
394.44
= 15.21%
211.11
+ 18 x
394.44
13-26
Problem
The management of “P&G” subscribes to the NOI approach and believes that its
cost of debt and overall cost of capital will remain 9% and 12% respectively. If the
Debt/Equity ratio is 0.8, what is the cost of equity?
Solution:
As per the NOI approach, the cost of equity is,
rE = rA +(rA – rD) (D/E)
= 12+(12-9)0.8
= 14.4%.
13-27
Problem
Consider the following information for Optima Limited.
Net operating income
Tk. 210 Million
Corporate Tax rate
30%
Market(as well as book) value
Tk. 300 million
Capitalization rate applicable to
a debt free firm in the risk class to
Which Optima belongs
16%
Required:
What will be the value of Optima Limited according to Modigliani & Miller
Approach?
Solution:
According to Modigliani & Miller Approach,
(1-tc)
V=0
+ tcB
r
= 210 (1-0.3)/0.16+(0.3x300)
= 918.75+90 = 1008.75 million.
13-28
Capital Structure Decision
13-29
Capital Structure Decision
How can the optimal capital structure in practice?
There does not seem to be any single method or technique that enable a
firm to to ‘hit’ the optima capital structure. As you explore capital structure
Decision, you will realize that it is not amenable to a neat, structured
solution.
A variety of analysis are done in practice to get a handle over the capital
structure decision. One analysis looks at how alternative capital structure
influence the earnings per share. A second analysis assesses the impact of
alternative capital structure on return on equity. A third analysis relies on
certain leverage ratios. A fourth analysis determines the level of debt that
can be serviced by the expected cash flows of the firm. A fifth analysis
relies on what comparable firms are doing.
Admittedly, each of these analysis is incomplete and provides a partial
answer to the question” what capital structure maximize the value of the
firm?”
In practice, Firms commonly use one or more of these kinds of analysis along with
qualitative guidelines to address the capital structure issue.
13-30
EBIT-EPS Analysis
In our search for optimal capital structure, we need,inter alia, to
understand how sensitive is earning per share (EPS) to changes in earning
before interest & tax (EBIT) under different financing alternatives.
Basic Relationship
(EBIT – i) (1 – t)
EPS =
n
Where,
i = interest
t = tax rate
n = number of equity share
When Preference dividend (Dp) is payable, the relationship becomes,
(EBIT – i) (1 – t) - Dp
EPS =
n
13-31
EBIT-EPS Analysis
Problem:
Existing Capital Structure
: 1 million equity shares of Tk. 10 each.
Tax rate
: 50%.
Falcon Limited plans to raise additional capital of Tk. 10 million for
financing an expansion projects. In this context,it is evaluating two
alternatives two alternative financial plans: (1) issue of Equity shares ( 1
million Equity shares @ Tk. 10 each.) and (2) issue of debentures carrying
14% interest.
Required: What will be the EPS under the two alternative financial plans for
two levels of EBIT, say Tk. 4 million & 2 million?
13-32
EBIT-EPS Analysis
Equity Financing
EBIT 2000000
EBIT 4000000
Interest
Debt Financing
EBIT 2000000
EBIT 4000000
1,400,000
1,400,000
Profit Before
Taxes
2,000,000
4000000
6000000
2600000
Taxes
1000000
2000000
300000
1300000
Profit after
Taxes
1000000
2000000
300000
1300000
No. of Equity
Shares
2000000
2000000
1000000
1000000
EPS
0.50
1.00
0.30
1.30
13-33
ROI-ROE Analysis
We may look at the relationship between the Return on Investment (ROI)
& Return on Equity (ROE) for different level of financial leverage.
The influence of ROI & Financial Leverage on ROE is mathematically as
follows,
ROI = (EBIT/Total Assets)
ROE = [ROI+(ROI-r)D/E](1-t)
Where,
r = Cost of Debt
D/E = Debt-Equity Ratio
t = Tax rate
13-34
ROI-ROE Analysis
Problem
Korex Limited, requires an investment outlay of Tk. 100 million, is
Considering two capital structures:
Capital Structure “A”
Capital Structure “B”
Equity
100 Million
50 Million
Debt
0 Million
50 Million
Average cost of capital is fixed at 12%, the ROI(EBIT/Total Assets) may
vary widely. The Tax rate is 50%.
13-35
ROI-ROE Analysis
Capital Structure “A”
Capital Structure “B”
5% 10% 15% 20% 25%
5% 10% 15% 20% 25%
5
10
15
20
25
5
10
15
20
25
Interest
0
0
0
0
0
5
5
5
5
5
Profit before
Tax
5
10
15
20
25
0
5
10
15
20
Tax
2.5 5
Profit after Tax
7.5
10
12.5
0 2.5
5
7.5
10
2.5 5
7.5
10
12.5
0 2.5
5
7.5
10
RIO
EBIT
Return on
Equity
2.5% 5% 7.5% 10% 12.5%
13-36
0% 5% 10% 15% 20%
ROI-ROE Analysis
ROE
B
A
20
15
10
5
5
10
15
20
25
30
ROI
13-37
ROI-ROE Analysis
Looking at the relationship between ROI & ROE we find that,

The ROE under capital structure A is higher than the ROE under capital
structure B, when ROI is less than the cost of Debt.
 The ROE under two capital structures is the same when ROI is equal to
the cost of Debt. Hence the indifference/breakeven value of ROI is equal
to the cost of debt.

The ROE under capital structure B is higher than the ROE under Capital
structure A, when ROI is more than the cost of Debt.
Mathematical Relationship
The influence of ROI and Financial Leverage on ROE is mathematically as
follows,
ROI = (EBIT/Total Assets)
ROE = [ROI+(ROI-r)D/E](1-t)
Applying the above equation to Korex Limited, when its D/E ration is 1, we
may calculate the value of ROE for two values of ROI, 15% & 20%.
13-38
ROI-ROE Analysis
ROI = 15%
ROE = [15+(15- 10)1](0.5)
= 10.0%
ROI = 20%
ROE = [20 +(20 - 10)1](0.5)
= 15.0%
13-39
Ratio Analysis
Traditionally firms have looked at certain ratio to assess whether they have
a satisfactory capital structure. The commonly used ratios are:

Interest coverage ratio
 Cash flow coverage ratio

Debt service coverage ratio

Fixed asset coverage ratio
Interest coverage ratio
EBIT
Interest coverage ratio =
interest on debt
Suppose EBIT for Vitrex company were Tk. 120 million and the interest
burden on all debts were Tk. 20 million.
The interest coverage ratio = 120/20 = 6.
It means that even if EBIT drops by 83.5%, the earnings of Vitrex cover
its interest payment.
13-40
Ratio Analysis
Cash flow coverage ratio
EBIT+Depreciation+other non-cash charge
Cash flow coverage ratio =
Loan repayment installment
interest on Debt +
(1-Tax rate)
Consider the following data for Vitrx Limited
Depreciation
Tk. 20 million
EBIT
Tk. 120 million
Interest on Debt
Tk. 20 million
Tax rate
50%
Loan repayment installment
Tk. 20 million
13-41
Ratio Analysis
120 + 20
Cash flow coverage ratio =
20
20 +
(1-0.5)
= 3.5
Cash flow coverage ratio measure the debt capacity, covers the debt
service burden fully and focuses on cash flows.
13-42
Ratio Analysis
Debt service coverage ratio
Financial Institutions which provide the bulk of loan-term debt finance
judge the debt capacity of firm in terms of its debt service coverage ratio.
This is defined as,
 PATi +DEPi +INTi +Li
Debt service coverage ratio =
 INTi +LRIi +Li
Where,
PAT = Profit after tax for year i
DEP = Depreciation for year i
INT = Interest on long term loan for year i
LRI = Loan repayment installment for year i
L = Lease rental for year i
N = period of the loan
13-43
Ratio Analysis
Year
1
2
3
4
5
6
7
8
9
10
PAT
-2.0
10
20
25
30
40
40
50
55
55
DEP
12
10.8
9.72
8.75
7.87
7.09
6.38
5.74
5.17
4.65
INT
17.6
17.6
17.05
14.85
12.65
10.45
8.25
6.05
3.85
1.65
LRI
-
-
20
20
20
20
20
20
20
20
13-44
Ratio Analysis
 PATi +DEPi +INTi +Li
Debt service coverage ratio =
 INTi +LRIi +Li
DSCR = 521.17/270.00
= 1.93
Normally, financial institutions regard a dent service coverage ratio of 1.50
to 1.75 as satisfactory.
If the ratio is significantly less than 1.50 and the project is otherwise
Desirable, a term loan of a longer maturity may be provided.
If the ratio is significantly more than 1.75, the maturity may be shortened.
13-45
Ratio Analysis
Fixed Asset Coverage Ratio
Fixed Asset
Fixed Asset Coverage Ratio =
Term Loan
Financial institutions feel comfortable if the fixed asset coverage ratio is at
least 1.25
13-46
13-47
13-48
13-49