Capital Structure[1]

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Theory

of CapitalStructure


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INTRODUCTION TO

THE THEORY


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Assumptions

1.There are no corporate or personalincome taxes and no bankruptcy costs

2. The ratio of debt to equity for a firm ischanged.

3. The firm has a policy of paying 100% of

its earnings in dividends


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4. The expected value of the subjectiveprobability distributions of expected

future operating earnings for eachcompany are the same for all investorsin the market

5. The operating earnings of the firm arenot expected to grow


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The three rates

(1)ki= F/BF-annual interest charge

B- market value of debt

outstanding* ki - yield on the companys debt


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(2) ke= E/S

E- earnings available to commonstakeholders

S- Market value of stock outstanding

* ke - required return on equity


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(3)ko =O/V

O- Net operating earnings

V- Total Market value of the firm

* ko overallcapitalizationrate


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NET OPERATING

INCOME

APPROACH


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Net Operating Income

ApproachTo illustrate assume that a firm has $1,

000 in debt @10% interest, that the

expected value of annual operatingearnings is $1, 000 , and that the overallcapitalization rate is 15%. Given this

information we may calculate the valueof the firm as follows:


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Net Operating Income $ 1,000

Overall Capitalization Rate .15Total Value of the Firm $ 6, 667

Market Value of Debt

1,000Market Value of Stock $

5,667


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The earnings available to commonshareholders, is simply NET

OPERATING INCOME MINUSINTEREST PAYMENTS, or $ 1,000 - $100= $900. the implied required return

on equity is:

ke = $900$5,667 = 15.88%


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Net Operating Income $1,000

Overall Capitalization Rate .15Total Value of the Firm $6, 667

Market Value of Debt

3,000Market Value of Stock $3,667


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The implied required return on equity is:

ke= $700$3,667= 19.09%

thetotalvaluationofthefirmisunaffectedbyits

capitalstructure


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TRADITIONALAPPROACH


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The traditional approach to valuationand leverage assumes that there is an

optimal capital structure. The firm can increase the total value of

the firm through the judicious use of

leverage.


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The approach suggests that the firmcan initially lower its cost of capital and

raise its total value through leverage. Although investors raise the required

rate of return on equity, this does not

offset entirely the benefit of usingcheaper debt funds.


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As more leverage occurs, investorsincreasingly penalize the firms required

equity return until eventually this effectmore than offsets the use of cheaperdebt funds.


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The traditional position also impliesthat the cost of capital is notindependent of the capital structureof the firm and that there is anoptimal capital structure.


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MERTON MILLERSARGUMENT


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AssumptionsofMM

Approach Capital markets are perfect

The average expected future operating

earnings of a firm are represented bysubjective random variables

Firms can be categorized intoequivalent return classes.

The absence of corporate income taxesis assumed.


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Homemade Leverage &

Arbitrage Process Homemade leverage

The support idea that investors(arbitragers) are able to substitutepersonal or homemade leverage forcorporate leverage, thereby

replicating any capital structure mightundertake


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Arbitrage Process

Is the operational justification forthe MM approach and isessentially a balancing operation


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Arbitrage Process

Consider two firms identical in everyrespect except that company A is not

levered, while company B has $30,000of 12% bonds outstanding. According tothe traditional position, company B mayhave a higher total value and lower

average cost of capital than company A.the valuation of the two firms isassumed to be the following:


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Company A Company B

O Net operating income $10,000 $10,000

F Interest on Debt 3600

E Earnings available to

common stockholders $10,000 $6,400

Ke Required equity return 0.15 0.16S Market value of debt $66,667 $40,000

B Market value of stock $30,000

V Total value of firm $66,667 $70,000

Ko Implied overall capitalization rate 15% 14%

B/S Debt-to-equity ratio 0 75.00%


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Arbitrage steps

If you are a rational investors who owns 1percent of the stock of company b, the

levered firm, worth $400 (marketvalue) you should:

1. Sell the stock in company B for $400.


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1. Borrow $300 at 12% interest. Thispersonal debt is equal to 1% of the

debt of company B, your previousproportional ownership of thecompany.

2. Buy 1% of the shares of company A,the unlevered firm, for $666.67.


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Irrelevance in a CAPM

framework


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Both corporate and personal taxes,capital structure decisions by the firm

were irrelevant. Changes in capital structure have no

effect on the firms total valuation.

MILLER..


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MILLER..

Millers model suggest that in market

equilibrium personal and corporate taxeffects cancel out. His model impliesthat at the margin, personal tax rate

debt income, tpd, must equal thecorporate tax rate, te.


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INVESTOR CLIENTELES

ANDMARKETEQUILIBRIUM..

Different investorsdifferent personaltax rate.

Pension fundstax exempt;

High income individualshigh taxbrackets


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=))Millers position is based on the ideathat when the market is in

disequilibrium, corporations alter theircapital structures to take advantage ofclienteles of investors in different tax

brackets.


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COMPLETING THE MARKET

In the case of capital structure, the product isa financial instrument and the niche is an

unsatisfied investor clientele.

Clientele is unsatisfied simply because thereare not enough securities available at the

type necessary to satisfy its tax motivatedinvestment desires.


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Market equilibrium occurs when thetotal debt issued causes the two

marginal tax rates to be the same For all companies there is the total

optimal capital structure that depends

on the tax brackets of differentclienteles of investors and the amountof the funds that this clienteles need toinvest.


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Implication: if the corporate tax ratewere to increase relative to the personal

tax rate, the equilibrium would call forhigher total debt-to-equity ratios forcompanies overall.


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COUNTERARGUMENTS

If the tax rate on the stock income iszero , we would expect that there to be

an equilibration of returns betweencommon stocks and tax-exempt bonds,because the tax rate on municipal debtincome is zero.


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On the supply side of the equation,different corporations have diff. effective

tax rates at the margin. This makes themarket equilibrium process two-sidedand more likely that there will be a net

tax effect associated with corporateleverage.


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Corporate taxes

The advantage of debt in a world ofcorporate taxes is that interest

payments are deductible as anexpense.

They elude taxation at the corporatelevel, whereas dividends or retained

earnings associated with stock are notdeductible by the corporation for taxpurposes


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Example

Suppose the earnings before interesand taxes are $2000 for companies X

and Y., they are alike in every rwspectexcept in leverage. Company Y has$5000 in debt at 12% interest, whereas

company X has no debt. If the tax rateis 40% for each company we have


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Company X YEBIT $2,000 $2,000

Interest, income to debt holders 0 0

Profit before taxes $2,000 $2,000

Taxes 800 560

Income Available to stockholders $1,200 $ 840

Income to debt holders plus income

to stockholders $1, 200 $1,440


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Corporate taxes

Present value of tax shield =

tcrB = t

cB

r

tc

is the corporate tax rate

rthe interest rate on the debt

B the market value of the debt


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Tax shield is a thing of value and thatthe overall value of the company will

increase debt is employed than if thecompany has no debt

This is increased valuation occurs

because the stream of income to allinvestors is greater.


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Value of firm =

Value if unlevered + Value of tax

shield

The greater the amount of debt, thegreater the tax shield and the greater

the value of the firm, all other things arethe same.


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The original MM proposition assubsequently adjusted for corporate

taxes suggest that an optimal is to takeon a maximum amount of leverage.


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Uncertaintyoftax

Shield

Tax savings associated with the use ofdebt are not certain.

If reported income is consistently low ornegative, the tax shield on debt isreduced or even eliminated


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If the firm should go bankrupt andliquidate, the potential future tax savings

associated with debt would stopaltogether.

The greater the responsibility of going

out of business, the greater theprobability the tax shield will not beeffectively utilized.


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If earnings in a given year aresufficiently low, these other tax shields

may entirely use up the earnings athand.

As a result, the tax liability would be

zero, and the company would be unableto utilize interest payments as a taxdeduction.


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As a company takes on more debt, itincreases the probability that earnings

in some years will not be sufficient tooffset all the tax deductions.


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The uncertain nature of the interest taxshield, together with the possibility of at

least some tax shelter, redundancy,may cause firm value to rise less withleverage than the corporate taxadvantage alone would suggest.


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Leverage increases, the uncertaintyassociated with the interest tax shields

come into play. More leverage occurs, tax shield

uncertainty causes value to increase at

an ever decreasing rate and mayeventually to turn down.


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Value of firm = Value if unlevered + Purevalue of corporate tax shield Value lost

through tax shield uncertainty

> The last 2 factors combined give the presentvalue of the corporate tax shield. The greater

the uncertainty associated with the tax shield,the less important it becomes


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Corporate Plus Personal

Taxes

The presence of taxes on personalincome may reduce or possiblyeliminate the corporate tax advantageassociated with debt


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Corporate Plus

Personal Taxes

Present value of tax shield =

(1 tc)(1-tps)1 - 1 tpd B

tcandB as before are the corporate taxand market value of the firms debt


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Taxes

(1 tc)(1-tps)

1 - 1 tpdB

tps is the personal income tax applicable tocommon stock income

tpd is the personal tax rate applicable todebt income


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Taxes

Present value of tax shield = tc B

After tax income for debt holders =$1(1 tpd )

After tax income for stockholders =

$1(1 tc )


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Stock income is composed of:

- dividends

- capital gains

Dividend income large tax at the samepersonal tax rate as interest income

Capital Gains often are taxed at a lowerrate.


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A company will need to decide whetherto finance with debt or with stock.

If a dollar of operating earnings is paidout as interest to debt holders, thecompany pays no corporate tax on it

because interest is deductible as anexpense.


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If the dollar of operating earnings isdirected instead to stockholders, the

company pays a tax on those earningsat the corporate tax rate.

If the company is concerned with only

after tax income to the investor, it wouldfinance either with debt or stock


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If the personal tax rate on debt income> the corporate tax rate, the company

would finance stock If tpd < tc, it would finance debt

If tpd = tc, it would be a matter ofindifference whether debt orstock


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EFFECT OF

BANKRUPTCYCOSTS


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BANKRUPTCY

the reorganization or liquidation of afirm that cannot pay its debts.

Bankruptcy costs are more legal and

administrative expenses of bankruptcy They involves inefficiencies in operating

a company when it is about to gobankrupt as well as liquidation of assetsat distress prices below their economicvalues


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The levered firm may be less attractiveto investors that the unlevered one

If the firm goes bankrupt, assets can besold at their economic values with noliquidating or legal costs involved


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RELATIONSHIP TO

LEVERA

GE

The possibility of bankruptcy usually is not thelinear function of the debt-to-equity ratio, butit increases at an increasing rate beyondsome threshold.

The expected cost of bankruptcy increases inthis manner and would be expected to have a

corresponding negative effect on the value ofthe firm and on its cost of capital.


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TAXES AND BANKRUPTCY

COSTS

Both taxes and bankruptcy costs, therewill be an optimal capital structure.

The net tax effect will have a positiveinfluence on value, at least for moderateamounts of leverage; bankruptcy costsand tax shield uncertainty exert a

negative influence.


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Value of the firm =

Value as unlevered firm

+Present value of net tax shield on debt

Present value of bankruptcy costs


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OTHER

IMPERFECTIONS


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Other capital market imperfection impede theequilibration of security prices according totheir expected return and risks.

-it may result in leverage having an effect onthe value of the firm apart from taxes andbankruptcy costs.

-it must not be only material but also one-directional.


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CORPORATE AND

HOMEMADE

LEVERAGE NOT BEING

PERFECT SUBSTITUTE


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The perceived risks of personalleverage and corporate leverage may

differ. Despite the implication in the MManalysis that personal and corporateleverage are perfect substitutes, thereare various reasons for suspecting thatthis may not be the case.


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Personal

L

everage involves a certainamount of inconvenience for investors,which they do not experience incorporate leverage.


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In addition, stockholders havelimited liability with a stock investment,

whereas their liability with personalloans is unlimited. Moreover, the costof borrowing may be higher for anindividual than for the corporation.

INSTITUTIONAL


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INSTITUTIONAL

RESTRICTIONS

Restriction on investmentbehavior may retard the arbitrage

process. Many institutional investors,such as pension funds and lifeinsurance companies, are not allowedto engage in the homemade leverage.


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Regulatory bodies, often restrictstock and bond investments to a list of

companies meeting certain qualitystandards, such as only a safe amountof leverage.


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INCENTIVE ISSUES

ANDAGENCY COSTS

D bt h ld


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Debt holders vs.

EquityHolders

The equity of a firm can be viewed as acall option on the firms total value, the

value being associated or an asset ofthe option.

The writers of the option are the debt

holders.


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Assume that debt is represented bydiscount bonds paid at maturity.

The stockholders as having sold thefirm with the option to but it back at aspecified price.

The option has an exercise price equal

to the face value of the debt, and itsexpiration date is the maturity date.

V l f h i h i i


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Valueoftheoptionattheexpiration

date:Vo= max (Vf D,0)

Where:

Vf= the value of the firm at theexpiration date

D = the face value of the debt

max = the maximum value ofVf- D, or zero whichever is greater

V l f th d bt t th i ti


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Valueofthedebtattheexpiration

date:

Vf= min (Vf,D)

Where: min = Vfor D, whichever isless.


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EffectsofVarianceandthe Riskinessof

Assets


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The greater the variance or volatility in

value of the underlying assets, the greaterthe value of the option, all other things the

same.

It is in the interest of the option holders toincrease the variance of the firm.

An increase in the dispersion of the

probability distribution of possible firmvalues increases the value of their option.


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Black-ScholesOptionPricingModel

Suppose the total value of BelgraziaTube Company is $4 million, and it has justissued debt with a face value of$3 millionpayable entirely at the end of5 yrs. At thepresent the standard deviation of thecontinuously compounded rate of return on

the overall value of the company is .12.Also, the short-term, risk-free rate is 6%.


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Solve for d1 and d2

d1 = ln($4/$3) + [.06+1/2(.12)2]5

.125

= .623682

.268328

= 2.32

*ln refers to the natural log


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Solve for d1 and d2

d2= ln($4/$3) + [.06-1/2(.12)2]5

.125

= .551682

.268328

= 2.06


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Vo is the value of the stock

$4mil(.9898) - $3mil (.9803)

2.71828(.06x5)

= $1, 780,526

Value of debt = $4,000,000 - $1,780,526

= $2,219,474

Changing the


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Changingthe

ProportionofDebt

Option Pricing Formula - determine the

value of the common stock and that by

deducting this value from the value of the

total firm we can determine the value of

the debt.

By comparing values for different

proportions of debt, we are able todetermine the relationship between the

proportion of debt and valuation.


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Face Value of Debt = $1million

Value ofStock = $3,266,681

Value of the Debt =

$4,000,000-$3,266,681 = $733,319

Previous Example:

with $3million in debt, these values

were $2,084,431 and $1,915,569


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The Percentage Increase for Debt are:

Percentage

Change

Face Value ofDebt

$1,000,000 $3,000,000 200%

Value of Debt 733,319 1,915,569 161


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The increase in the face value of debt isaccompanied by a smaller percentageincrease in the value of debt, holdingconstant the total value of the firm.

Issuing debt and retiring stock andthereby increasing the proportion of debt

in the capital structure will result in adecline in the price of the existing debt andan increase in share price.


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Protective Covenants

Debt holders can protect themselvesagainst expropriation by imposingconstraint on the company.

These may be used to restrict thestockholders ability to increase the assetriskiness of the company.

Reputation of borrower may affect theterms of the loan.

The underinvestmentThe underinvestment


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The underinvestmentThe underinvestment

ProblemProblem

A positive NPV project should beaccepted but this may not always

happenThe underinvestment proposition can be

put in an option pricing modelframework

Agency Cost More


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Agency CostMore

BroadlyDefined

Monitoring requires the expenditure ofresources, and the costs involved are

one form of agency cost. Agency costs are ultimately borne by

the stockholders.

Every decision of the firm would need tobe monitored.


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It is not that monitoring costs per se arebad for the owners of the company: it isthat monitoring needs to be efficient.

Dividend and financing decisions can bemonitored with only moderate cost.

Production and investment decisions of

the firm are much more costly tomonitor.


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When there is little or no debt, lendersmay engage in only limited monitoring,

whereas with a great deal of debtoutstanding they may insist onextensive monitoring.

Monitoring costs would act as a furtherfactor decreasing firm value for extremeleverage.


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Organizational

IncentivestoManageEfficiency


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Jensens free cash flow theoryalleges that if managements are left

to their own devices they will invest incapital projects and acquisitions thatdo not provide sufficient expectedreturns.


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There is a need to incentmanagement to disgorge free cash

flow to stockholders, the rightfulowners of excess liquidity. This waycan the agency problem beresolved.


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FINANCIAL

SIGNALING


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It occurs when a capital structure

changes convey information to securityholders

It assumes an asymmetry in information

between the management andstockholders.

A t i I f ti


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Asymmetric Information

An information wherein one party in a

transaction has more or superiorinformation compared to another.

Often happens in transactions where

the seller knows more than the buyer,although the reverse can happen aswell.


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The greater the asymmetry in

information between the insider(management) and the outsiders(security holders), the greater the likelystock price reaction to a financingannouncement.


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SUMMARY

C it l St t


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Capital Structure

There is a great deal of controversy

whether capital structure as determinedby its financing decision affects itsoverall value.

T dition l App o ch


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TraditionalApproach

Argue that the firm can lower its cost of

capital and increase market value pershare by the judicious use of leverage.

Modigliani and Miller


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Modigliani andMiller

Approach

Argue that in the absence of taxes and

other market imperfections, the totalvalue of the firm and its cost of capitalare independent of capital structure.

Based on the notion that there is aconservation of investment value.

Taxes and Capital


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p

Structure

There is a substantial advantage to theuse of debt which is lessened with taxshield uncertainty particularly if leverageis high.


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Tax advantage was reduced ifpersonal income taxes was allowed

and higher personal tax rate ondebt income than on stock income

Bankruptcy Cost


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Bankruptcy Cost

It work to the disadvantage of leverage,particularly high leverage.

A combination of net tax affect withbankruptcy cost will result in an optimal

capital structure.


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Other market imperfections impede the

equilibration of security prices accordingto the expected return and risk. As aresult, leverage affect the value of thefirm.

Incentive Issues and


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Agency Cost

An option pricing model frameworkgives stockholders an option to buy

back the firm at the maturity of the debt.

An increase in the variance of the

associated asset (value of the firm) willincrease the value of the option.


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It is the stockholders advantage toincrease variance by increasing the

riskiness of the assets of the firm or byincreasing the proportion of debt.


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Debt holders can protect themselvesagainst this occurrence by imposing

protective covenants which involvesmonitoring costs, which is a form ofagency cost


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Stockholders, who ultimately bear thecost of monitoring, have an incentive tosee that it is efficient.

Monitoring cost likely to increase at anincreasing rate with leverage. It may

limit the amount of debt in an optimalcapital structure.


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In the context of agency costs,other incentive issues affecting

capital structure decisions wereanalyzed.

Financial Signaling


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Financial Signaling

It occurs when a capital structurechanges convey information to securityholders.

It assumes an asymmetry in information

between the management andstockholders.


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Capital Structure[1]