7-theory of capital structure - a review

8/13/2019 7-Theory of Capital Structure - A Review

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Theory of Capital Structure - A Review

Stein Frydenberg

April 29, 2004

ABSTRACT

This paper is a review of the central theoretical literature. The most important argu-

ments for what could determine capital structure is the pecking order theory and the static

trade off theory. These two theories are reviewed, but neither of them provides a complete

description of the situation and why some rms prefer equity and others debt under dif-

ferent circumstances. The paper is ended by a summary where the option price paradigm

is proposed as a comprehensible model that can augment most partial arguments. The

capital structure and corporate nance literature is lled with different models, but few, if

any give a complete picture.

JEL classication: G32

Sr-Trndelag University College, Department of business administration, Jonsvannsvn. 82, 7004 Trond-heim, Norway. E-mail: [email protected].

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2/41Electronic copy available at: http://ssrn.com/abstract=556631Electronic copy available at: http://ssrn.com/abstract=556631

The view that capital structure is literally irrelevant or that nothing matters in corporate

nance, though still sometimes attributed to us,...is far from what we ever actually said about

the real-world applications of our theoretical propositions. Miller (1988)

I. Introduction

The paper introduces the reader to two main theories of capital structure, which is the static

trade-off theory, and the pecking-order theory. Underlying these theories are the assumptions

of the irrelevance theorem of Miller and Modigliani. Since the irrelevance theorem is indeed

a theorem, the assumptions of the theorem, has to be broken before capital structure can have

any bearing on the value of the rm. If the assumptions of the irrelevance theorem are justied,

the theorem follows as a necessary consequence.

II. The Irrelevance Proposition

In complete and perfect capital markets, research has shown that total rm value is indepen-

dent of its capital structure. An optimal capital structure does not exist when capital markets

are perfect. Taxes and other market imperfections are essential to building or proving a posi-

tive theory of capital structure. Changes in capital structure benet only stockholders and then

if and only if the value of the rm increases. An expropriation of wealth from the bondholders

would in a rational expectations equilibrium be expected by the bondholders, and the stock-

holders would ultimately carry the costs of the expropriation. Miller and Modigliani (1958b)

wrote the seminal article in this eld of research, using an arbitrage argument. If a rm can

change its market value by a pure nancial operation, the investors in the rm can take actions

that replicate the resulting debt position of the rm. These transactions would merely change

the weights of a portfolio and should, in a perfect capital market, give zero prot. If the market

were efcient enough to eliminate the prots for the investors, any prot for the rm would be

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eliminated too. Modigliani and Miller in their original articles Miller and Modigliani (1958b)

and Miller and Modigliani (1958a) assume several strict constraints.

First, capital markets are assumed to be without transaction costs and there are no

bankruptcy costs.

All rms are in the same risk class.

Corporate taxes are the only government burden.

No growth is allowed since all cash ows are perpetuities.

Firms issue only two types of claims, risk free debt and risky equity. All bonds (includ-

ing any debts issued by households for the purpose of carrying stocks) are assumed to

yield a constant income per unit of time, and the income is regarded as certain by all

traders regardless of the issuer Miller and Modigliani (1958b)

Information is symmetric across insider and outsider investors.

Managers are loyal stewards of owners and always maximize stockholders wealth.

Copeland and Weston (1988)

Later, others such as Stiglitz (1974) and Merton (1990) have removed the assumption of

risk class. Myers (1984) said that lifting these restrictions, one at a time, start possible causes

for the capital structure puzzle. The theoretical models of capital structure in a world in

which capital markets are not perfect relates capital structure to several measurable and non-

measurable attributes of a rm. The irrelevance proposition provides conditions under which

the capital structure of a rm is irrelevant to total rm value. Turning the irrelevance propo-

sition around, the proposition also tells us which factors that may be the causes of corporatecapital structure. The assumptions giving irrelevance as a result may cause relevance if they

are broken. The question is, do they, and if so to what extent? And what if several imperfec-

tions exist simultaneously? Besides the irrelevance hypothesis of Modigliani and Miller there

are several other theories relevant to capital structure. These are the asset substitution hypoth-

esis, under-investment hypothesis, the free-cash ow hypothesis, the signaling hypothesis and

product markets arguments.

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.1. Value Additive Model of Capital Structure

State preference models have been used extensively in the nance literature as a general frame-work for explanation of the irrelevance hypothesis. Both Lewellen and Mauer (1988), Kraus

and Litzenberger (1973), Stiglitz (1969) and Hirshleifer (1966) have used this approach.

The MM Proposition 1

Assume perfect capital markets and no taxes on corporate

income. An equilibrium in the capital market requires thatthe value of the rm, V t , should be independent of the

proportions of debt and equity in the rms capital structure.

V t V B t V E t (1)

Let V be the total market value of the rm debt and equity.

V B = market value debtV E = market value equity

Dene a set of possible future states of nature, assumed to be nite and exhaustive. Given that

a state of nature occurs, all relevant future events are known with certainty. I do not, however,

know which state that will occur. The return to an investor depends on which state of nature

actually occurs. An investor thus has a bundle of state contingent returns. A security that

returns one dollar, if a certain state occurs and zero otherwise is called a primitive security.The price of this primitive security is called a state-price and is the price today for one dollar

tomorrow given that a particular state occurs. A complex security i.e. a stock or bond will

thus be composed of several primitive securities, one or more for each state in which the stock

gives dividend. In states where the stock pays more than one dollar, say ten dollars, the stock

must contain ten primitive securities. In the states where the stock does not give dividend,

for instance if bankruptcy occurs, the primitive security for this state is not included in the

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stocks bundle of primitive securities. The value to the investor of any particular bundle is

derived from the value to him of a marginal increase in his wealth in a given state. The value

now of any future contingent claim is dependent on the probability that the state will occur,

the investors preferences for a wealth increase in this state based on a representative agents

utility and the time preferences represented by the risk free rate of return.

Three assumptionsare made before I proceed with the multi-period state preference model.

These assumptions are: Assumption 1: The rms investment strategies are given - in partic-

ular, although specic investment decisions are not known, the rules governing those deci-

sions are known. These rules are consistent with maximization of the wealth of the securityholder. In other words, I am assuming that nancing and investment decisions are not con-

nected. Assumption 2: Perfect capital markets without transaction cost, informational asym-

metry or bankruptcy costs. Assumption 3: No taxes at either corporate or personal level. An

un-leveraged rms time t market value V t is expressed as eq. 2. According to Lewellen

and Mauer (1988), the levered and un-levered rm total values coincide and the irrelevance

proposition can be justied by the following statements:

V t

V t 1dP t 1 (2)

where

V t 1 is total rm value in state at time t 1,

= All the possible states of nature.

= State i of nature that the economy may have in time t , i = 1..n

B t 1 = Market value of debt in state at time t 1,

E t 1 = Market value of stocks in state at time t 1.

P t 1 = The distribution of corresponding state prices .

Rt 1 = Interest payment promised to bondholders at time t 1, which is state-independent.

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A leveraged rms time t market value is expressed as the sum of debt and equity value.

V t E t B t (3)

How the total rm value will be divided between stockholders and bondholders depend upon

when there is a default on debt obligations. There will be a default and consequently bankruptcy

when

Rt 1 E t 1 (4)

or when

Rt 1 B t V t 1 (5)

At the point of maturity, the bondholders claim will be worth:

V B t 1 min Rt 1 B t 1 V t 1 (6)

At the point of maturity, the equity holders claim will be worth:

V E t 1 max V t 1 Rt 1 B t 1 0 (7)

V E t 1 max E t 1 Rt 1 0 (8)

The value of the equity holders claim is equivalent to a call option on either E t 1 with

exercise price Rt 1, or on V t 1 with exercise price Rt 1 B t 1. In a risk neutral

evaluation, all cash ows are certain, given that a specic state occurs. The time t values of

equity and debt in the levered rm can then be written as:Equity :

E t

V E t 1dP t 1 (9)

Debt:

B t

V B t 1dP t 1 (10)

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Given the linearity of the operator, I can add together equity and bond values. Due to the

nature of the pay off of debt and equity investment, the total rm value can be written as

max V t 1 Rt 1 B t 1 0 min Rt 1 B t 1 V t 1 (11)

CASE 1

V E t 1 Rt 1 B t 1 (12)

eq 11 V t 1 (13)

CASE 2V E t 1 Rt 1 B t 1 (14)

eq 11 V t 1 (15)

The value of the leveraged rm is

E t B t

V E t 1 V B t 1dP t 1 V t 1 (16)

With the assumptions above, I have showed that the values of the unleveraged and leveraged

rm are equal. The original irrelevance proposition of Miller and Modigliani were based on

the notion of risk -classes, but

these risk - classes are not necessary. As Stiglitz (1969) and Kraus and Litzenberger (1973)

have shown, the irrelevance proposition hold in a more general time-state framework.

III. The Trade-off Theory

In this section I will review literature that suggest that debt has a central role in rm nancing.

Jensen (1986) argues that debt is an efcient means by which to reduce the agency costs asso-

ciated with equity. Klaus and Litzenberger show that with the tax advantages of debt, optimal

capital structure includes debt nancing. Ross (1977) and Leland and Pyle (1977) argue that

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debt can be valuable as a device for signaling rm value. The three main hypotheses that are

used to explain differences in capital structure between companies are the transaction-cost hy-

pothesis, the asymmetric information hypothesis and the tax hypothesis. According to Harris

and Raviv (1991), leverage increases with xed assets, non-debt tax shields, investment op-

portunities, and rm size and decreases with volatility, advertising expenditure, the probability

of bankruptcy, protability and uniqueness of the product.

This theory claims that a rms optimal debt ratio is determined by a trade-off between the

losses and gains of borrowing, holding the rms assets and investment plans constant. The

rm substitutes debt for equity, or equity for debt until the value of the rm is maximized.The gain of debt is primarily the tax-shelter effect, which arises when paid interest on debt

is deductible on the prot and loss account. The costs of debt are mainly direct and indirect

bankruptcy costs. The original static trade-off theory is actually a sub theory of the general

theory of capital structure because there are only two assumptions that are broken here, the no

tax incentive assumption and the no bankruptcy cost assumption. In the more general trade-

off theory several other arguments are used for why rms might try to adjust their capital

structure to some target. Leverage also depends on restrictions in the debt-contracts, take-over possibilities and the reputation of management. A negative correlation between debt

and monitoring costs is proposed by Harris and Raviv (1990). Diamond (1989) suggest that

vintage rms with a long history of credits will have relatively low default probability and

lower agency costs using debt nancing than newly established rms. A common factor for

all these rm characteristics are that they are proxies meant to measure some form of costs

related to a principal-agent problem. There may simultaneously be several principal-agent

problems between the different classes of securities in the rm or between stockholders andmanagers in the rm. This multiplicity of problems can easily confuse the analyst and lend an

air of incomprehensibility to the eld of corporate nance. A construction of a positive theory

of debt nancing, builds on arguments on the advantages and disadvantages of debt. First,

debt is a factor of the ownership structure that disciplines managers. Limiting control to a few

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and for nancial accounting purposes. Unlike permanent differences, timing differences are

capable of being reversed in future periods. In the deferred tax model, deferred tax is a long-

term liability.

Depending on the direction of the difference, deferred taxes could be a liability as well as

an asset. Discounting the deferred taxes is not presently accepted in any accounting standards.

Deferred taxes are the tax rate (28%) multiplied with the difference in income between the

nancial prot and loss account and the reported prot or loss for taxation purposes. If the

deductions are higher in the tax report, deferred taxes are positive. 1 The expense for taxes is

shown in the prot and loss account/income statement. In the deferred tax model, the amountrepresents the total tax to be paid on the accounting prot for that year. In other models, just

the amount to be paid is shown.

The 1992 tax-reform The Norwegian Tax Codes was changed in the 1992 tax-reform.

Consequently, this has inspired us to test whether a tax incentive of debt nancing exist in

Norway. The yearly regressions in Frydenberg (2001), display that the tax variable nondebt

is signicant in 1991, 92 and 1999 and year 2000 for the interest carrying debt variable.

According to Bhren and Michalsen (2001) page 261, these are the years, except for 1999,

that the Norwegian tax system is not neutral! This is a new contribution, using the natural

experiment in Norway, to show that the tax system matters for the debt ratio.

Before the accounting reform in 1992, taxes presented in the accounts referred to taxes

payable for the current year. After 1992, taxes include both payable taxes and changes in

deferred taxes. Changes in deferred tax occur as a result of temporary differences between

book value and tax book value, and tax loss carried forward. Sjo (1996) claims that the

marginal tax rate could inuence the debt structure whenever the tax codes are not entirely

neutral. A lower marginal tax rate should decrease leverage. With the tax-reform, dividend1This is common for accelerated depreciation. The depreciation percentage is 30 % for ofce equipment,

which is considerable more than the 1/5 linear economic depreciation in the nancial statements. The 10%difference multiplied with the tax rate of 28% is considered a long-term liability. Sooner or later, here alreadyafter three years, the nancial linear depreciations are higher than the accelerated tax depreciations and thedeferred taxes will be reduced with 28% of the difference between tax and nancial depreciations.

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taxes were substantially reduced. Dividends are no longer double taxed. The investors taxes

on dividends are reduced by the amount that is paid in the companies. This change would

increase the attractiveness of being a stockholder in Norwegian rms.

A change in incentives towards equity is a consequence of the tax-reform. Some authors

have claimed that the rms serve as a nancial intermediary. Firms may not have a tax in-

centive to increase debt if both the investor and the rm are in a tax position. The rm pays

the taxes on the equity return, while the investor pays the tax on the debt return. If the debt

investor is not in a tax position, he may have other tax deductions and deferrals, which give

him, zero taxable income, then the debt capital return is not taxed and there is an incentive torely on debt nancing. The nancial intermediary argument also claims that rms may lend at

more favorable terms than investors. The idea is that rms can make better use of the benets

of debt nancing if they are in a tax position.

The rm benets from a reduction of the taxes paid to the government. Interest rates paid to

debt holders are deductible in the prot and loss account and hence reduces the tax burden. For

private debt, this is clearly an advantage. The marginal tax advantage of interest deductibility

is expected to sink as leverage increases when the marginal tax rate is progressive. The last

amount of debt that is incurred does not invoke a very large tax effect since the marginal

tax rate decreases as the income is reduced. For corporate debt, however, the marginal tax

rate in Norway is 28% and constant for all prot levels. The tax incentive for debt nancing

is therefore not marginally decreasing as the leverage increases when the corporate tax-rate is

constant. The rm tax is a pure net-prot tax and where there is no prot, even the government

tax collector has lost his claim.

In his article Debt and taxes , Miller (1977) argues that the debt level is not dependent on

tax rate when both personal and corporate taxes are considered. Thakor (1989) is also critical

to the tax advantage of debt since debt was used prior to 1913 when there were no corporate

taxes in the US. Preferred stock pays a xed dividend such as debt but the dividends are not

tax-deductible. The issuance of such preferred stock also shows that the tax advantage of debt

only partly can explain the usage of debt.

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B. Bankruptcy Incentive

A bankruptcy without costs would not change the value of the rm. Stiglitz (1969) have shownthat the value of a security is the same, regardless of whether a bankruptcy would occur or not

under some specic conditions. There are, however, costs of nancial distress. These costs

are divided into direct costs and indirect costs. Bankruptcy costs are expected to increase for

all levels of leverage. Bankruptcy costs are not only the direct costs of transferring the assets

to the new owners, lawyers fee and court fees, but there are also indirect costs of bankruptcy

arising from the bankruptcy process itself. The bankruptcy trustee, as an agent of the court, has

the authority to operate the rm. Warner (1977) said that it is not clear if this agency relation

give the trustee any incentive to run the rm efciently and take decisions which are in fact

value maximizing. The stockholders face the possibility that they may lose control of the rm

when a nancial distress situation occurs. The option to receive dividends if the rm operates

protably in the future is thereby lost for the current stockholders. Indirect costs arise when

qualied employees that can pursue alternative opportunities quit the rm when bankruptcy is

closing in. Unrest in the organization is often the result, and suppliers and customers that rely

on continuous business relations may lose condence in the rm.

Risk shifting Risk shifting is described in Section F but is worth mentioning here too be-

cause the gains and temptation to play this game is strongest when the odds of default are

high. If the rm probably will go under anyway, why not make a nal bet that might salvage

the rm. The stockholders and management is betting with the creditors money. The point in

risk shifting is how stockholders of levered rms gain when business risk increase. This point

can also be described with a Call option.

C. Dividends Payments and Claim Dilution Problem

Brealey and Myers (2000) describe this as the cash in and run problem; stockholders can take

out the valuable assets, while bondholders are kept in the dark. Bonds are priced under the

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assumption that dividend policy remains unchanged. Reducing the investments by increasing

the dividends will reduce rm value, increase the risk of outstanding debt and harm the bond-

holders. The stockholders can pay out all the assets and leave the bondholders with an empty

shell. As the rm approaches bankruptcy and nancial distress is more and more transparent

for the rms stakeholders, management may chose to play games with the creditors. These

games can be played all the time, but stakes are higher near bankruptcy.

C.1. Claim Dilution

The stockholders can use the value of the assets as bait, and then switch to another strategy.

Bonds are priced under the assumption that no new debt will be issued. When the rm issues

new debt with the same or higher priority than the old debt, the claim of the old bondholders

will be reduced. The reason is that the probability of default on the old debt increases. The

rm starts with a conservative policy, issuing a limited amount of relatively safe debt. Then

the rm suddenly switch and issue a lot more. That makes all the debt risky, imposing a capital

loss on the old bondholders. Their capital loss is the stockholders gain.

D. Product Market Competition and Capital Structure

In his model, Titman (1984) postulate that a seller of a product enters contracts of service

to a product. A seller who can credibly enter this kind of service contract can demand a

higher price for his output product. If this service becomes too costly, he will renegade on the

contract. Bankruptcy is a possible method to renegade a service contract. A higher debt-ratioincreases the possibility of bankruptcy and consequently the mark-up - price the seller can

demand, since the customers view the debt ratio as a signal of possible bankruptcy.

Williams (1988) have also studied the capital structure problem when there are more than

one rm in the model. An agency problem occurs where a rm has to choose between two

technologies. One labor intensive and one capital intensive are the two available technologies.

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If the entrepreneur invests in the labor-intensive technology, he may consume some of the

investment proceeds from external nancing. The capital-intensive technology is assumed

to give higher returns than the labor-intensive technology. Debt can then be used to control

management incentives by setting the debt level so high that an investment in labor-intensive

industry is not feasible. An important conclusion from the industrial equilibrium literature is

that several nancing arrangements may coexist at the same time. Large capital-intensiverms

with high debt levels may coexist with smaller and marginally protable rms that are having

lower levels of debt. Williams (1988) model could therefore explain the large heterogeneity

of debt ratios observed in the data.

E. Optimal Contract and Corporate Governance Theory

In this section I explore three subjects that are often mentioned as possible causes of capital

structure decisions. First, I consider the corporate governance problem. How should the rm

be controlled? A tightly held rm where a majority or large shares of the stocks are controlled

by an individual or a group is supposed to be a more efcient managed rm than the rmcontrolled by entrenched self-interested managers. Second, operating risk has to be shared by

the owners of the rm and the debt-equity paradigm have shown remarkable ability to allocate

risk to the people that has the residual control rights of the rm, the equity holders. Third,

does transaction cost theory have anything to do with capital structure?

The corporate governance problem Aghion and Bolton (1988) and also Zender (1991)

emphasize that contracts that grant control to one class of agents exclusively may not be ef-cient because they fail to give the controlling agent the incentives to make the rst best

decisions. The intuition behind the existing nancial instruments equity and debt are that they

are designed so that in each state the owner of the residual control rights own the residual cash

ow. If this is not the case, there is a potential conict because owners of one of the security-

classes could expropriate wealth from owners of the other security class. The standard debt

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contract (SDC) is an optimal contract and dominates all other types of contracts in the Costly

State Verication(CSV) literature. A SDC minimizes the expected transfer of wealth from the

entrepreneur to the outside investor. See Allen and Winton (1995) for a comprehensive review

of the literature. The dening character of the CSV literature is that that the true cash ows

of the rm are only observable to the manager or entrepreneur. The cash ows of the rm are

only veriable at a cost in a bankruptcy process. The outside investor receives only a xed

sum of money when the entrepreneur income is not veried and a strictly lower payment when

income is veried. Ownership structure could be an important factor explaining the leverage

structure. Firms that are tightly controlled by major stockholders will have less agency costs.

Fama and Jensen (1983) argue that it makes sense to separate the nancial claims into only two

types: a relatively low risk component, the debt capital, and a relatively high risk component,

the equity capital. This is an optimal form of contracting because it reduces contracting costs

and it lowers the cost of risk-bearing services. Stockholders and bondholders do not have to

monitor one another. Only the bondholders must monitor the stockholders and not vice-versa.

This one-way monitoring will help to reduce contracting costs.

Risk sharing Members of a syndicate are eager to regulate two main elements in the partner-

ship. First, the payoffs from positive NPV-projects must be divided, and second, risk has to be

shared. The risk stems from the time varying realization of payoffs and liability if bankruptcy

occurs. In an equity-debt model, equity-owners carry almost all the risk, and receive all the

pay-off if the rm reaches a certain prot-target. On the other hand, if prots are below tar-

get they get no pay off. The debt owners have practically no risk and xed pay-off structure

unless losses incurred wipe out the equity. Neither equity nor debt owners can lose more thanwhat they have invested, guarantees set aside. A rst best solution to this risk-sharing problem

would be to give the risk-neutral investor all the risk and divide the pay-off accordingly. No

risk results in a risk free return for the debt owners. A second best solution makes the risk

averse investor carrying more risk than the optimal solution. This induces an excessive risk

premium that can be attributed to the non-optimal risk sharing; the less risk averse investor

should accept a larger risk.

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Transaction cost theory Coase (1937) suggested that the neo-classical literature of the rm

is consistent with there being one huge rm in the world and also that every division of a

rm could be divested to single autonomous rm. Organizations emerged because of mar-

ket failure, because of asymmetric information between agents. This asymmetric information

between members give organizations their reasons for existence. Williamson (1981) claimed

that other reasons for existence are transaction costs and economies of scale and scope. A

general employment contract between the rm and the employee reduces the necessary details

in a contract compared to contracts that specify exactly the content of the services provided

by the employee. Instead the rm can order the employee to perform tasks within a broadly

dened area. The organizations are not markets and they are not individuals. The literature

of rm nancing, views rms as something between. Firm nancing can be seen as a set of

contracts between people that cooperate towards a common goal while they are pursuing their

self-interest. Financing the investments of these organizations requires a trade off between

costs and benets of security and loan contracts. The literature of corporate nance relies on

the early work of Coase (1937) and Williamson (1981) that explain the reasons for existence

of organizations. The corporation has served as a major form for organizing economic activity.

The ability of the corporation to survive through the last century must reect benets from the

organizational structure that protects the real and nancial resources. The value of the corpo-

ration must be derived from costs and imperfections inherent in markets: information asym-

metries, transaction costs, economies of scale and scope, and forms of taxation. Financing is

a mirror image of the real activities of an organization. Asymmetric information and trans-

action costs faced by agents in the organization create an opportunity to organize economic

activity differently from how a market or a contractor-based activity would be organized. In-

stead of project nancing the rm takes on corporate debt, thereby reducing transaction costs,

and construct budgets and incentive schemes for the sub-divisions of a rm. 2

2A project manager is allocatedcapital from the rms investment budget. Alternatively, she couldhave raisedcapital in a bank or in the capital market. That would be difcult if the asset base for the project is shared withmany other projects and possible collateral is already occupied. The corporate debt reduces transaction costscompared to many separate project debts to different lenders.

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F. Risk Shifting (Asset Substitution) Problem

The basic idea, that increases in leverage induce equity holders to pursue riskier strategies, wasintroduced by Jensen and Meckling (1976). Since decisions concerning dividend payments,

issuance of new debt, and investments are made by the owners, these decisions are a potential

source of conict between equity investors and debt investors. The nancial structure affects

the cash ow through investment decisions. Smith and Warner (1979) argues that there are

four major sources of conict. These are dividend payments, claim dilution, asset substitution,

and under-investment.

Briey, asset substitution is an incentive problem associated with debt. Stockholders are

the residual claimants to the rm cash ow. Their claim is analogous to a call option on the

rms asset, with a strike price equal to the face value of the debt. It is well known that

the value of a call option increases as the risk in the underlying asset increases. Bonds are,

however, sold with the prospect of a certain level of risk. If stockholders increase risk beyond

this initial level, they can expropriate wealth from bond-investors. Bondholders will, under

rational expectations, recognize this incentive, and require a discount when they invest in debt-

securities in a rm. This discount is a cost that reduces the total value of a rm and as such

is eventually born in total by the stockholders. This risk shifting incentive can be mitigated

by covenants in the debt contract, legislation and by using convertible debt or straight debt

with warrants. The asset substitution problem can be described using a model that integrates

models used by Green (1984) and Green and Talmor (1986).

When the investment decision of the bondholders precede that of the stockholders, it is

to the stockholders advantage to choose a distribution of returns with relatively more weight

in the upper tail. Rothscild and Stiglitz (1970) have shown that increasing the investment in

the risky project is equivalent to increasing the mass in the tails of the distribution of total

return. How likely is this theory to have any effect in practice? Does lenders care about the

possible asset substitution when contemplating a loan to a rm? In the loan application pro-

cess the investment objects and future strategy is certainly a talking point. The problem is

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that it is almost impossible to construct a contract where the borrower cannot renegade and

invest in something more risky. That might not even be in the best interest of the lender ei-

ther. If rm management sees a better investment project than the one they originally lent

money for, should they not invest because the loan contract has restrictions on the possible

investments? It is likely that it is better to control management incentives through stock op-

tions and stock market monitoring than through costly restrictions in the loan contracts. The

risk-shifting incentive problem can be controlled through restrictions in the loan contract and

through management incentives. But such monitoring is costly and with uncertain effects. It

is therefore likely that lenders seek to insure themselves to an increase in business risk. The

simplest method is to demand collateral for the loan and to demand an equity of some size in

the rm before lenders grant a loan. This incentive is even addressed by legislature in Norway

that demands an equity of minimum 100.000 NOK. Even for a small rm, the amount is very

low and the demand for public disclosure of nancial report is therefore more important. In

the US, quarterly disclosures of nancial reports are the standard among listed rms, the ac-

tivities of management is therefore more transparent than in Norway. The conclusion must be

that the risk-shifting problem is hypothesized to be severe, but it is empirically very difcult

to measure, if not impossible.

G. Under-Investment Problem

The problem is that stockholders will have to share the extra value created by their additional

investments with creditors. Myers (1993)

Under-investment is dened as forgoing a project with a positive net present value. The

argument in this section was introduced by Myers (1977) and is called the under-investment

hypothesis. Highly levered companies are more likely to pass up protable investment oppor-

tunities. Firms expecting high future growth should therefore use a greater amount of equity

nancing.

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I 0 is the investment in product development made at time t = 0.

Due to the investment in product development, the rm holds a growth opportunity.

At t =1, the rm must invest an additional I 1, to get the cash ow X I 0 r from the product

developed.

The investment I 1 could for instance be machinery needed to produce

the developed product.

The investment option is rm specic and cannot be sold. The rm that made the initial

investment has an exclusive right to exercise the option. If the rm chooses not to invest, the

option has zero value. This constitutes an imperfection in the market for real options of this

category. First I consider a rm that is entirely equity nanced and then a rm that issues debt

to nance the initial investment I 0. The intuition behind the model is not complicated. The

consequences and practical implications of the model, however, is a subject for discussion.

The intuition is that an investor possessing a growth option will not share the gains of the

option with nanciers if the growth option has prior debt nancing. After having paid off the

debt holders to the option, there will be too little left for the investor of the prot that comes

from implementing the growth option.

When B0 V is fullled, the incentive not to invest in certain states are present.

Whether the option has any value when it expires depends on the assets future value and

also on whether the rm chooses to exercise. The funds needed to make the investment I 0 in

this case are raised by selling bonds with face value F. To be able to invest at t = 1, the rm must

raise I 1, and does so by outlays from the current stockholders. We abstract from the signalling

considerations of a security issue. The timing of events at time t = 1 is important. First,

the return is revealed to the stockholders, the initial investment becomes certain at this point.

Second, investment I 1 is made, and then the debt matures. The rm will invest if the return

cash ow is large enough to cover both the rst investment which is debt nanced and the

second investment which is equity nanced. However, since the rst investment, made at time

zero, is in fact sunk cost at time t = 1, the rm should make the investment if the return cash

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you do not invest, you walk away from the debt on the growth option. If the growth option

could be sold to the lender, she could invest herself as long the second investment, I 1, is

positive NPV. But, that is not possible, the growth option is a real-option which cannot be

sold in the market as described in the paper by Myers (1977). A contracting possibility would

therefore be that the lender and the rm split the prot otherwise lost, in a Nash (50/50)

bargain solution, by letting the rm exercise the growth option and nance only a part of the

new investment while the lender nanced the rest. As long as V(s) is larger than I 1, both

parties could be made better off by sharing the investment and gains than letting the option

expire unexercised. Imagine that the debt F is just a tiny bit larger than V(s)- I 1. The creditor

could then recoup almost half the debt in a bargaining solution. This is also seen in real life, it

is not uncommon for banks to grant further loans to a rm to salvage some of their outstanding

debt.

H. Free Cash Flow Problem

Debt creation, without retention of the proceeds of the issue, enables managers to effectivelybond their promise to pay out future cash ows. Thus debt can be an effective substitute for div-

idends, something not generally recognized in the corporate nance literature. Jensen (1986)

The argument of the free cash ow and the role of debt to control opportunistic management

is due to Jensen (1986). Debt reduces management opportunity to spend excess cash ow

in non-protable investments. Management has less control over the rms cash ows since

these cash ows have to be used to repay creditors. Jensen and Meckling (1976) have argued

that managerial incentives to allocate the rms resources to their private benet are largerwhen the rm is mainly equity nanced. The free cash ow term is the amount by which

a rms operating cash ow exceeds what can be protably reinvested in its basic business

and the emphasis is here on the word protably. Conicts of interest between stockholders

and managers over payout policies are especially severe when the organization generates sub-

stantial free cash ow. So, there is a dark side to the nancial slack. Too much of it may

encourage managers to take it easy, expand their perks, or empire-build with cash that should

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be paid back to stockholders. The problem is to motivate managers to disgorge the cash rather

than investing it below the cost of capital or wasting it in organizational inefciencies.

Jensen (1986) validates his stories by referring to the empirical literature on debt for com-

mon stock exchanges that leads to stock price increases. This evidence is, however, also

credited for the potential signalling effect of debt. Debt as a signal of high-quality rms is

treated in Section IV. The evidence from the leveraged buy out and going private transactions

is that many of the benets in an LBO seem to be due to the control function of debt. The

conclusion of this theory is that Jensen claim that by strapping the management to the mast

i.e. make them pay out xed amounts of money to the investors each year, the agency cost of free-cash ow can be reduced.

H.1. Protability

Protability affects leverage in at least two directions. First, higher protability usually pro-

vides more internal nancing. More earnings can be kept in the rm and hence a lower level

of debt. Less debt is then needed to nance already planned investments. Secondly, debtintroduces an agency cost argument. Management will refrain from the building of empires

and excessive consumption of perquisites, when large sums of money must be paid to creditors

each year. Debt keeps the rm slim and cost efcient. Unnecessary non-protable investments

will be avoided because creditors demand annual payments and claim any free cash ow. High

protability should result in higher leverage according to the free cash ow hypothesis, but a

high leverage would result in high protability on the basis of the pecking order hypothesis.

The problem is that leverage and protability are linked both ways, and that the causal direc-tion is uncertain. This problem could be avoided empirically if I estimate a system of two

equations instead of one equation. This approach is used in Stein Frydenberg (2001). Since

causality here works both ways, it would be possible to control these two effects by a system

of equations.

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IV. The Pecking Order Theory

According to the pecking order theory, the rms will prefer internal nancing. The rms

prefers internal to external nancing, and debt to equity if the rm issues securities. In the pure

pecking order theory, the rms have no well-dened debt-to-value ratio. There is a distinction

between internal and external equity. Several authors have been given credit for introducing

signaling as an argument in the discussion of debts explanatory factors. Ross (1977), Leland

and Pyle (1977) and Myers and Majluf (1984) are often quoted as the seminal articles in this

branch of the literature.

Myers and Majluf (1984) describes the preference like this: The rms prefer internal -

nancing, they target dividends given investment opportunities, then chose debt and nally

raise external equity. The pecking order was traditionally explained by transaction and issuing

costs. Retained earnings involve few transaction costs and issuing debt incurs lower transac-

tion costs than equity issues. Debt nancing also involves a tax - reduction if the rm has a

taxable prot. Myers and Majluf (1984) invoked asymmetric information to give a theoretical

explanation for the pecking order phenomena. The signaling model described in Section Aleads to a pecking order concept of capital structure, where retained earnings are preferred to

debt and debt is preferred to new equity. The signaling model showed that only low prot

type rms would issue equity in a separating equilibrium. Rational investors foresee this and

demand a discount in Initial Public Offerings (IPO). This discount is a cost of raising equity

that will be borne by the internal stockholders. Debt signals to the capital market that the

issuing rm is a high performance rm.

A. Asymmetric Information (Signalling) Problem

Asymmetric information between old and new investors, and managers and investors incite to

signaling games where the amount of debt, and the timing of new issues is viewed as a signal

of the performance of the rm. Akerlof (1970) introduced an adverse selection argument

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that explains why prices of used cars drops signicantly compared to new cars. The seller

of a used car will usually have more information about the true performance of the car than

the prospective buyer. The buyers best guess would be the average performance of cars in

the market. The buyer, when offered a car, expects the performance of the car to be below

average, otherwise the car would not have been offered to the market. Consequently, the

price of used cars decline and the only cars offered for sale are the cars not well made and

maintained. The buyers require a discount to compensate for the possibility that they might

purchase an Akerlof lemon. Earlier there used to be a tendency that cars built on Mondays for

some obscure reason had more problems than other cars. The focus on quality control may

have put this problem to an end, but still some cars seem to endure longer than others. The

heart of the matter is that the seller is aware of the upcoming reparations and problems, but

the buyer is not. A recent trend in Norway to overcome this problem is to require a complete

check of the car by an authorized workshop before buying. The work - shop produces a status

report on the technical condition of the car, which serves as a signal of performance of the

car to prospecting buyers. This signal reduces the asymmetric information in this market.

Analogously, the only rms for sale, in the market for corporate control, are those with below

average excellence. The rms will, according to the adverse selection argument only issue new

equity when the stock is overpriced. Issuing debt can be a signal to the capital market that the

rm is in fact an excellent rm and that the management is not afraid to borrow money. The

bankruptcy possibility is supposedly not large enough to let extensive borrowing bring about

the current managements control of the rm. The idea underlying the signaling models, is

that stockholders or managers signal private information to the security market in order to

correct the markets perception of excellence.

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rms. The notion that every rm can be described within the same capital structure model is

a bit too much to hope for at the moment.

Value relevance of capital Structure What factors have to be present for leverage to mat-

ter? First, there has to be market imperfections present like tax consideration, asymmetric

information, transaction costs and bankruptcy costs. But second, there has to be an absence of

the possibility to make a trade of the rm with the sub-optimal capital structure for the rm

with the optimal capital structure.

For leverage to matter for the value of a corporation,

it has to be the case that no clever arbitrageurs can

make money from such a situation.

Stulz (1990)

In a small rm, the stocks are not traded, if there exist an arbitrage possibility, the stock-

holders cannot take advantage of the arbitrage possibility. Two rms with equal future cash

ow should be worth the same. The capital markets are probably not perfect because in real

business life, capital structure is a subject of great concern to many nancial managers. Many

investors have tried to earn a higher return than the market return, some have managed just

that, but most have not. This fact is often used as an argument for an information efcient cap-

ital market. The markets may be efcient, but still less than perfect. Asymmetric information

may be present between the rms managers and the capital market, and we may still have

efcient markets, although in a semi-strong form. The insiders information about the rms

business future will not be discounted in the market prices of the rms stocks in this situation.

A denition of a perfect market is that costless trade in other assets can copy any cash ow.

The markets are complete, for any future state there exist a primitive security that gives a unit

income and the price today for that primitive security reects the probability for that state to

happen and the investors inter-temporal marginal substitution rate of consumption. However,

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the markets may be correlated and if your rm runs into difculties so will probably most

other rms do and the price you get for your assets in a recession could be very low.

An old adage in business is that everything is for sale, if only the price is right, but the

price in a recession may be ridiculously low compared to replacement values. Today, some

of the rms in the technology sector are trading at market values under their cash position.

The nancial markets have been prune to manias or nancial excesses. The prices tend to

overshoot in either positive or negative direction. You do not want to liquidate your stocks

or real assets in a recession time period. Therefore, common sense is to keep enough equity

to survive the next recession and rather sell your assets when the markets are favorable oncemore.

Haugen and Senbet (1988) claim that in the case of bankruptcy costs, market impediments

are easily eliminated through the inclusion of simple provisions in corporate charters and bond

indentures. Liquidation costs cannot explain capital structure they say, because if the rm is

to be liquidated on the basis of a rule instead of what maximizes the total value of all the

claimants, arbitrage prots arise, and informal reorganization will discipline management to

follow the liquidation rule that is optimal for existing security holders. This result is not readily

extended to other classes of market failure and agency costs, especially the risk-incentive

problem. The risk-incentive problem can be overcome through complex contracting, such as

the inclusion of call or conversion provisions in debt. The reasons for why capital structure

should matter are all related to the assumptions of the Miller and Modigliani theorem. If a

reason for capital structure relevancy were not included in the assumption, the theorem would

not hold. That is perhaps the beauty of the theorem, the all-inclusiveness of the assumptions.

If you could think of a reason for capital structure relevancy, which is not included in the

general assumptions of MM, then that would be a good research idea. Taxes, transaction

costs, asymmetric information, real options, bankruptcy costs and entrenchment of managers

are imperfections of well functioning capital market.

In a world of perfect markets, neither the under investment problem nor the bondholder-

stockholder conict would exist because in a world without contracting costs, the capital

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structure of the rm can always costless be changed, to make sure that a rm take advan-

tage of all protable investment opportunities and does not invest inefciently as a result of

leverage. Stulz (1990)

A key result of Merton Millers research is that for leverage to matter no clever arbitrageurs

can take advantage of a situation where leverage matters. The perfect market assumptions are

sufcient (second-order) conditions for leverage to be irrelevant, but not necessary conditions

(rst-order. Although the assumptions may be broken, we may still have the irrelevance. Chi-

ang (1984) say that the rst order (tangency) of a maximizing function is necessary for a

maximum point, the second order (convexity) is sufcient. So, we could have all the condi-tions of perfect capital market broken but still leverage would not matter if clever arbitrageurs

could take advantage of the situation. Miller shows that in equilibrium the coupon on taxable

bonds must be the coupon on tax-exempt bonds grossed-up for taxes at the corporate rate.

Think of the value of the rm as a convex function of the debt ratio. If the function is convex,

but increasing in the entire domain from zero to all debt nanced rm, we have no internal

optimum. An arbitrage exists if an investor could costless trade in the securities of the rms

and make money. Assume that one or more of the perfect market assumptions are broken andthat we have two rms A and B that are equal in intrinsic value, i.e. the cash ow these two

rms generate are equally distributed in time and magnitude. But rm B has a sub-optimal

high debt capital structure which makes the value of B lower than A. Is this an equilibrium

situation? No, smart speculators would sell stocks in rm A and buy more of stocks in rm B,

since both rms would eventually earn the same cash ow. Even though expected bankruptcy

costs in rm B may be higher than in rm A, that does not matter because we have assumed

that the rms are equal. If the high debt in rm B creates costs because management does notdare to pursue the best projects, then that will change the cash ows of rm B. Then the cash

ows are not equal anymore. The message is that leverage cannot matter if rms are equal

and arbitrage trading is allowed. But leverage could matter if rm cash ows are not equal

because some market imperfection plays a part in the equation and if arbitrage trading is not

allowed.

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It is therefore likely that leverage only matters for rms that do not have access to the

less than perfect Norwegian capital market. Firms that are closely held by families and not

traded are especially susceptible to such a situation. A young entrepreneur in the construction

segment with many good business ideas could launch positive NPV projects if he had the

money to back them. Being a small enterprise he is shut out of the equity market and can only

get bank nancing. The debt-ratio in this rm is therefore much higher than the ideal, because

the interest payments on the debt reduce the entrepreneurs willingness to raise capital and the

courage to enter high-risk and high-return projects. Even though the entrepreneur has many

good business ideas, he cannot easily get more equity to his ideas. The second step is that the

rm uses the pecking order theory to arrive, that is, they very seldom arrive at this target debt

structure. However, they use the pecking order to adjust as far as they can, under the given

transaction costs toward their target dent structure. The target debt structure was determined

in the rst step of the process, trading off various costs of debt versus equity. Evidence for the

pecking order; rms having low protability generally borrow more. Not because they belong

to industries with a high target debt ratio, but because they are on the top of the pecking order

and can nance most of their capital expenditures by retained earnings.

Option theory as a summarizing concept I will in this section describe how theories re-

ferred to earlier in this paper can be built into a coherent model. Not necessarily rigorously,

but intuitively giving ideas for future research and giving the reader a comprehensible model

to refer to. This idea was presented by Miller (1988), but I have elaborated the idea to incor-

porate also the assumptions of the MM propositions. The model I have in mind is the put-call

parity model for European options stated in eq. (17). A much-invoked analogy is that thestock of a rm can be compared to a call option on the rms assets. This is not entirely true,

the stock is more like a

down-and-out call on the rms assets. This call is not a standard call, but related to the

barrier option class of the down-and-out call type. If the value of the rm breaks down through

the barrier created by par value of debt, the rm is bankrupt and the equity of the rm has no

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value if the creditors take over the rm. A down and out call barrier option, where the option is

worthless once the underlying asset touches a oor is in general worth less than a regular call.

It is in general worth less than the regular call because the regular call is a sum of the down-

and-out and the down-and-in call. The down and in has a value if there is a possibility that

the asset price will reach the barrier in the options lifetime. ..barrier options regularly trade

in over-the-counter market. They are attractive to some market participants because they are

less expensive than the corresponding regular options. Hull (2003) The barrier 3 In this case

would be the par value of the debt. Let us for the sake of the argument; however, describe

the situation in the rm by European call and puts in a well-known parity. The put-call parity

model is given by:

S C e rT X P (17)

where

S = Asset value,

C = Equity of rm, a call on the assets

of the rm with a strike price X

P = The put option of the creditors with a strike of X.

This model will not generally hold unless the options are European. The bonds market

value is thus X minus the put option, P, while equity is worth C. A dening concept of options

is that they cannot have negative values. If S is larger than X, then the equity of the rm has

some value at the expiring date of the option. Interestingly the options has a time value so out

of the money call options has a value even if c S . Assuming the usual technical conditions

for option valuation in a perfect capital market, the call option is a function underlying of asset

S, strike price X, volatility of S parameterized by , interest rate r and the time T to date of

expire.

C 0 f S X r T (18)3A barrier option has an important result, the barrier call should be sold cheaper when there is downside skew

than when there is a at skew. See Nassim Taleb (1997).

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P0 f S X r T (19)

The theories of corporate capital structure can be incorporated in this model. 4

Risk substitution First, there is the risk substitution hypothesis presented by Jensen and

Meckling (1976) that is said to increase volatility of the underlying asset S. Both the call

and the put option will increase when the volatility of the underlying is increasing. If the

volatility increases and the put increases more than the call, then the rm value is decreased.

So, when volatility increases the risk may not be justly distributed on bond and stockholders.

The stockholders may gain at the bondholders expense as described by Jensen and Meckling

(1976). The vegas of put and call options are equal in the theoretical Black and Scholes pricing

formula. An interesting venue for future research could be to investigate the vegas of formulas

like the barrier options that can model the option value where the underlying is the value of the

rm. Barrier options often have quite different properties from regular options. For example,

sometimes vega is negative. Consider an up-and-out call option when the asset price is close

to the barrier level. As volatility increases the probability that the barrier will be hit increases.

As a result, a volatility increase causes a price decrease. Hull (2003) page 441 Since the call

must be considered a down-and-out call, while the put must be considered an up-and-in put,

there may be different signs of the vegas for these two options when the barrier is close to the

rm value.

Under-investment Second, there is the under-investment problem described by Myers (1977)that reduces the rm values because a debt nanced growth opportunity or real option might

not be exercised because debt investors normally receives their interest and principal loan be-4The relation between the variables in the option functions and the option values. Call options increase with

the stock price and the exercise price X. Put options decreases with the stock price and the exercise price X. Bothput and call options increase with the time T to maturity because the owner of a long lived option always has allthe exercise opportunities open to the owner of the short life option. Increasing the time T transfers value fromdebt owners who has X- P0 to equity owners who have C 0 at their disposal. Choosing the debt ratio in this modelwould amount to choosing another strike price for the debt.

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fore the equity investors receive their dividend and residual capital left in the rm after having

paid off all the creditors. That should reduce C 0 and increase P0. Both debt owner and equity

owners lose. Remember that the value of the bonds in this model is not P0, but X-P0. The eq-

uity owners have a right to sell the assets to the bondholders for the face value of debt X. If the

assets could be worth less than X, this guaranty for sale has a value P0, which the bondholders

must cover.

Tax incentive Third, the tax theory by Myers (1984) predict that X- P0 is tax subsidized and

cheaper than C. By weighting the capital structure towards debt, the after tax value of the rm

can be increased. The after tax value of the rm S = C 0 + X - P0 can be increased by shifting

over to debt nancing. This corporate level one-sided effect of tax-benets of debt nancing is

in many countries offset by the personal investor taxes on interest income. Depending on the

relative size of the corporate and personal tax-rates, a tax-incentive for debt might be present

for rms with taxable prots.

Bankruptcy costs Fourth, bankruptcy Warner (1977) theory predicts that an increase in Xbeyond sustainable levels of debt would incur expected direct and indirect bankruptcy costs

that would reduce the value of S, thus decreasing C 0, increasing P0. The market value of both

equity and debt would fall when the debt and equity investors start to believe that the rm

might run into serious nancial distress soon. This effect of expected bankruptcy costs are

predicted to off-set any incentive from taxes. One feature of the down-and-out call is that the

delta (1st. derivative of option with respect to underlying asset) is considerably higher near

the barrier than the regular option delta. When the asset price hit the barrier, the barrier deltagoes to zero. This phenomenon illustrate the agency cost problem of stockholders. A lower

delta means that stockholders do not get hit by the decline in asset price until the bankruptcy

barrier is reached. Then they lose all their claims. This atter delta function near bankruptcy

compared to a regular call option illustrate the tendency of stockholders to make desperate

actions near bankruptcy. With limited downside risk, they are inclined to bet with creditors

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money on high risk projects. Nassim Taleb (1997) page 315 describe this discontinuity at the

barrier.

Asymmetric information Fifth, the pecking order theory predicts that increases in internal

cash ow, discounted to market value of cash ows S, is cheaper than obtaining external equity

by increasing X. Increasing X is on the other hand cheaper than increasing C. The exercise

price X denes the level of debt, while C 0 and X-P0 denes the market value of respectively

equity and debt.

S C X P (20)

The un-leveraged rm is represented by S 0 initially, if the costs of changing the capital

structure is larger than the benets, then C 1 + X - P1 should be less than S 0. The new value of

the rm S 1 would be equal to the market value of equity, C 0, plus the market value of debt, X 1

-P1 ex post change of capital structure.

Finally, we have the interesting aspect of the feedback effect. Both C and P in eq. (17) are

endogenous functions of the underlying S that are part of the eq. (17). There is a feedback effect, a change of the equity value, C, would by eq. (17) lead to change in S and then next a

second change in the equity value, C. What is the mechanism that gives a change in S because

C changed in the rst place. Well, one could argue that a loss of equity would restrict the

investment possibilities of the rm, leading to a lower S. The value of the rm, S, is the sum

of two components, rst the equity value, C, and the debt value, X-P. If an exogenous change

of X, increasing the debt ratio, decreases the value of equity, C, more than the increase of the

market value of debt, X-P, then there is a net decrease of the value of the rm S.

If both P and C has the same sensitivity to changes in the underlying asset S, then the

change stops. This is probably not the case and this will therefore give a feedback loop towards

S once more. The case is that for a change in the debt ratio, X, to have any effect on the value

of the rm, the market value of equity and debt has to react differently to this change. If the

size of the debt was irrelevant; an increase of X of 2 units would result in a decrease of C

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equity C and a part of the debt X-P. If this is not possible, then maybe debt can be relevant. An

example is Myers (1977) real options, the rm in question is the only rm that can exercise

the growth option. It is therefore not possible to sell the growth option to another rm. If the

growth option was marketable in bits and pieces, the rm could sell out a share of the option

corresponding with the value of the debt on the option and be left with a pure-equity growth

option. This residual option would have to be exercised by the rm since it is a positive NPV

project. So, the stockholders in reality own a call option on the rms assets. The position of

the bondholders are that of someone having sold a put option to stockholders, giving them the

right to sell the rm to the bondholders for the face value.

The stockholders can either choose to buy the rms assets for the face value of debt or

choose to sell the rms assets to the bondholders for the face value of debt. The stockholders

can chose to walk away from the corporate debt and leave the bondholders with the assets. The

stockholders are then immune to future claims against them unless they have done something

unlawful as a member of the board in the bankruptcy process. The stockholders have the

option to bankrupt the rm which is a put option and the option to buy the assets for the

exercise price the face value of debt. The bondholders main upside is the option fee which isinterest they can receive for the loans they make to the rm.

The world of exotic options may help explain the phenomenon known as gamblers ruin.

The problem of not being able to take part in the next gamble, because you do not have the

necessary stakes for the next dealing of cards. A down-and-out also called a knock-out (KO)

option is an option that has a barrier. The value of the option turn zero once the underlying

assets fall below a barrier. There are thus several non-linear effects in the Greeks 5

5The Greeks are the rst derivatives of the option price with respect to stock price, time, interest rate,volatility and contract price.

Delta is rate of change of option price with respect to the underlying asset, C S . Theta is rate of change of option price with respect to the time to maturity, C T . Vega, is rate of change of option price with respect tovolatility C s . Rho is rate of change of option price with respect to interest rate

C r . Finally, the second

derivate of the option price with respect to the stock price is Gamma, 2C

2S .

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Owning levered equity in a rm can be considered like owning a knock-out call. If the

assets value sink below par value of debt, creditors might step on the collateral and claim the

assets. The equity owner then receives nothing. In the real world several complications as

bankruptcy proceedings and friendly bankers exist, but the main mechanism is that creditors

can claim the assets when the equity option is out-of-the-money or below the exercise value.

The difference between a vanilla call and a KO call is that the KO call expires abruptly at

the lower barrier while an out-of-the-money vanilla call still is worth something although the

intrinsic value is zero. The vanilla option owner has discretion to wait and see. A knock-in

call is the opposite to a knock-out call. The knock-in is worth nothing until the value of the

underlying increase above a barrier. It is shown in Nassim Taleb (1997) how to value these

calls and under which assumptions the parity Knock-out call + Knock-in call = Vanilla call

holds.

The conclusion of this discussion is that an exogenous change in one of the factors deter-

mining the option values might give a change in the value of the rm if either the put and call

options react differently or if they together does not neutralize the change in the debt ratio.

Why should an increase of the debt have any effect on the value of the rm? The free cashows generated from the operations of the rm is still the same. The point is that increas-

ing the debt is likely to change the investments the rm make. With a lot of debt on board,

the responsible manager might chose safer projects while the gambling manager might chose

riskier projects. Expecting these unpredictable effects, the stockholders change their beliefs

about value of the free cash ow of the rm. A change of beliefs often leads to a change of the

market value of debt and equity. It is often said that deviation from the normal is not good if

you want to succeed in business life. Good looking people with normal habits and behaviourare successful. Persons with an peculiar lifestyle and common looks are more often ousted

from business life. As Keynes famous beauty contest analogy depicts, in the stock market

you have to choose not the best looking stock available but the stock that a maximum number

of investors fancy. You could be right in your choice of the best future performing rm, but if

few investors agree with you, it is unlikely that the stock will appreciate in the near future.

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The stock markets perception of what constitutes a normal capital structure may punish

those rms that have a capital structure that deviates from the norm. Even though your rm

would have beneted from a higher debt ratio, bankers and investors perception of a normal

capital structure could force the debt ratio down. But why should the bankers perception of

a normal capital structure be any different from the cash ow maximizing capital structure.

Well, there could be asymmetric information about risk and return, that the banker seeks to

control by operating within certain limits. Bankers, being bureaucrats, survive by sticking to

the principle that it is better, do never anything really foolish than sometimes doing something

smart. Investing is after all a game of survival, not a game of being best in the class, because

unlike Survivor, the winner does not take it all.

References

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