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CHAPTER Capital Structure, Leverage & Firm’s Value

Business vs. financial risk Optimal capital structure Operating leverage Capital structure theory

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Capital Structure, Leverage & Firm’s Value

Capital Structure and Leverage

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What is LeverageA 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.

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Types of LeverageThere 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.

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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.

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Effect of operating leverage

More operating leverage leads to more business risk, for then a small sales decline causes a big profit decline.

What happens if variable costs change?

Sales

$ Rev.TC

FC

QBE Sales

$ Rev.

TCFC

QBE

} Profit

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Using operating leverage

Typical situation: Can use operating leverage to get higher E(EBIT), but risk also increases.

Probability

EBITL

Low operating leverage

High operating leverage

EBITH

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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.

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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.

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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 Firm LNo debt $10,000 of 12% debt$20,000 in assets $20,000 in

assets40% tax rate 40% tax rate

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Firm U: Un-leveraged Economy Bad Avg. GoodProb. 0.25 0.50 0.25EBIT $2,000 $3,000 $4,000Interest 0 0 0EBT $2,000 $3,000 $4,000Taxes (40%) 800 1,200 1,600NI $1,200 $1,800 $2,400

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Firm L: Leveraged Economy Bad Avg. GoodProb.* 0.25 0.50 0.25EBIT* $2,000 $3,000 $4,000Interest 1,200 1,200 1,200EBT $ 800 $1,800 $2,800Taxes (40%) 320 720 1,120NI $ 480 $1,080 $1,680

*Same as for Firm U.

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Ratio comparison between leveraged and un-leveraged firms

FIRM U Bad Avg GoodBEP 10.0% 15.0% 20.0%ROE 6.0% 9.0% 12.0%TIE ∞ ∞ ∞

FIRM L Bad Avg GoodBEP 10.0% 15.0% 20.0%ROE 4.8% 10.8% 16.8%TIE 1.67x 2.50x

3.30x

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Risk and return for leveraged and un-leveraged firms

Expected Values:Firm U Firm L

E(BEP) 15.0% 15.0%E(ROE) 9.0% 10.8%E(TIE) ∞ 2.5x

Risk Measures:Firm U Firm L

σROE 2.12% 4.24%

CVROE 0.24 0.39

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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).

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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.

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Capital Structure, Leverage & Firm’s Value

Capital Structure & Firm’s Value

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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.

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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 ErA = rD [ ]+ rE [ ]

D + E D + E

Where, rD = Cost of Debt capitalD = Market value of debtE = Market value of equity

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Net Income ApproachProblem: 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 10,000I Interest on debts 0 3,000rE Cost of equity capital 10% 10%

rD Cost of Debt capital 6% 6%D Market value of debt 0 50,000E Market value of equity 100,000 70,000

Required: Calculate the average cost of capital for firm A & B(a) For Firm A

0 100,000rA = 6%[ ] + 10% [ ] = 10%

100,000 100,000(a) For Firm B

50,000 70000rA = 6%[ ] + 10% [ ] = 8.5%

120,000 100,000

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Net Operating Income ApproachAccording 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 10,000rA Overall Capitalization Rate 0.15 0.15V Total Market Value 66,667 66,667I Interest on debts 1000 3,000rD Debt capitalization rate 0.10 0.10D Market value of debt 10,000 30,000E Market value of equity 56,667 36,667D/E Financial Leverage 0.176

0.818Ans: 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%

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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.

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Modigliani & Miller PositionSo 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.

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Modigliani & Miller PositionProposition 1MM’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 / rWhere, V= Market Value of the FirmD = Market Value of the DebtE = Market Value of the EquityO = Expected operating incomer = Discount rate applicable to the risk class to which the firm belongs.Proposition 2MM’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 incomeExpected return on assets = rA =

Market value of all securities

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ProblemThe following information is available for XYZ metals.Net operating income Tk. 40 MillionInterest on Debts Tk. 10 MillionCost 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 millionThe market value of Equity = (Tk. 30 million / 0.18) = Tk. 166.67 millionHence, the average cost of capital for XYZ metals is:

83.33 166.6712 x + 18 x

250.00 250.00 = 16%

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ProblemIf 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 Tk. 60 Million

Interest on Debts Tk. 22 MillionEquity earnings Tk. 38 millionMarket value of equity Tk. 211.11 millionMarket value of Debt Tk. 183.33 millionMarket value of the Firm Tk. 394.44 million

183.33 211.1112 x + 18 x

394.44 394.44 = 15.21%

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ProblemThe 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%.

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ProblemConsider the following information for Optima Limited.Net operating income Tk. 210 MillionCorporate Tax rate 30%Market(as well as book) value Tk. 300 millionCapitalization 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.

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Capital Structure Decision

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Capital Structure DecisionHow 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.

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EBIT-EPS AnalysisIn 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 = nWhere,i = interest t = tax raten = number of equity share When Preference dividend (Dp) is payable, the relationship becomes,

(EBIT – i) (1 – t) - DpEPS = n

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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?

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EBIT-EPS Analysis

Equity FinancingEBIT 2000000 EBIT 4000000

Debt FinancingEBIT 2000000 EBIT 4000000

Interest 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

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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 DebtD/E = Debt-Equity Ratiot = Tax rate

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ROI-ROE Analysis

ProblemKorex Limited, requires an investment outlay of Tk. 100 million, is Considering two capital structures:

Capital Structure “A” Capital Structure “B”

Equity 100 Million 50 MillionDebt 0 Million 50 MillionAverage cost of capital is fixed at 12%, the ROI(EBIT/Total Assets)

may vary widely. The Tax rate is 50%.

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ROI-ROE Analysis

Capital Structure “A” Capital Structure “B”

RIO5% 10% 15% 20% 25%

5 10 15 20 25

0 0 0 0 0

5 10 15 20 25

2.5 5 7.5 10 12.5

2.5 5 7.5 10 12.5

2.5% 5% 7.5% 10% 12.5%

5% 10% 15% 20% 25%

5 10 15 20 25

5 5 5 5 5

0 5 10 15 20

0 2.5 5 7.5 10

0 2.5 5 7.5 10

0% 5% 10% 15% 20%

EBIT

Interest

Profit before Tax

TaxProfit after Tax

Return on Equity

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ROI-ROE Analysis

ROI

ROE

5

20

15

10

5 3025201510

A

B

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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 RelationshipThe 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%.

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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%

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Ratio AnalysisTraditionally 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 ratioEBIT

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.

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Ratio Analysis

Cash flow coverage ratioEBIT+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 millionEBIT Tk. 120 millionInterest on Debt Tk. 20 millionTax rate 50%Loan repayment installment Tk. 20 million

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Ratio Analysis

120 + 20 Cash flow coverage ratio =

2020 +

(1-0.5)

= 3.5Cash flow coverage ratio measure the debt capacity, covers the

debt service burden fully and focuses on cash flows.

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Ratio Analysis

Debt service coverage ratioFinancial 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

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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

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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.

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Ratio Analysis

Fixed Asset Coverage Ratio

Fixed AssetFixed Asset Coverage Ratio =

Term Loan

Financial institutions feel comfortable if the fixed asset coverage ratio is at

least 1.25

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