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 arguments 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 firms prefer equity and others debt under different 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 finance literature is filled with different models, but few, if
any give a complete picture.
JEL classification: G32
Sør-Trøndelag
University College, Department of business administration, Jonsvannsvn. 82, 7004 Trondheim, Norway. E-mail: [email protected].
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The view that capital structure is literally irrelevant or that ”nothing matters” in corporate
finance, 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 firm. If the assumptions of the irrelevance theorem are justified,
the theorem follows as a necessary consequence.
II. The Irrelevance Proposition
In complete and perfect capital markets, research has shown that total firm value is independent 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 positive theory of capital structure. Changes in capital structure benefit only stockholders and then
if and only if the value of the firm increases. An expropriation of wealth from the bondholders
would in a rational expectations equilibrium be expected by the bondholders, and the stockholders would ultimately carry the costs of the expropriation. Miller and Modigliani (1958b)
wrote the seminal article in this field of research, using an arbitrage argument. If a firm can
change its market value by a pure financial operation, the investors in the firm can take actions
that replicate the resulting debt position of the firm. These transactions would merely change
the weights of a portfolio and should, in a perfect capital market, give zero profit. If the market
were efficient enough to eliminate the profits for the investors, any profit for the firm 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 firms are in the same risk class.
Corporate taxes are the only government burden.
No growth is allowed since all cash flows are perpetuities.
Firms issue only two types of claims, risk free debt and risky equity. All bonds (including 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 nonmeasurable attributes of a firm. The irrelevance proposition provides conditions under which
the capital structure of a firm is irrelevant to total firm value. Turning the irrelevance proposition around, the proposition also tells us which factors that may be the causes of corporate
capital 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 imperfections exist simultaneously? Besides the irrelevance hypothesis of Modigliani and Miller there
are several other theories relevant to capital structure. These are the asset substitution hypothesis, under-investment hypothesis, the free-cash flow 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 finance literature as a general framework 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 that
the value of the firm, Vt , should be independent of the
proportions of debt and equity in the firms capital structure.
Vt
= VB;t + VE ;t
(1)
Let V be the total market value of the firm debt and equity.
VB = market value debt
VE = market value equity
Define a set of possible future states of nature, assumed to be finite 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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stock’s 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 investor’s preferences for a wealth increase in this state based on a representative agent’s
utility and the time preferences represented by the risk free rate of return.
Three assumptions are made before I proceed with the multi-period state preference model.
These assumptions are: Assumption 1: The firm’s investment strategies are given - in particular, although specific investment decisions are not known, the rules governing those decisions are known. These rules are consistent with maximization of the wealth of the security
holder. In other words, I am assuming that financing and investment decisions are not connected. Assumption 2: Perfect capital markets without transaction cost, informational asymmetry or bankruptcy costs. Assumption 3: No taxes at either corporate or personal level. An
un-leveraged firm’s time t market value Vt is expressed as eq. 2. According to Lewellen
and Mauer (1988), the levered and un-levered firm total values coincide and the irrelevance
proposition can be justified by the following statements:
Z
Vt
=
Ω
V (Θ)t +1 dP(Θ)t +1
(2)
where
V (Θ)t +1 is total firm value in state Θ at time t + 1,
Ω = All the possible states of nature.
Θ = State i of nature that the economy may have in time t, i = 1..n
B(Θ)t +1 = Market value of debt in state at time t + 1,
E (Θ)t +1 = Market value of stocks in state at time t + 1.
P(Θ)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 firms time t market value is expressed as the sum of debt and equity value.
V (Θ)t
= E (Θ)t + B(Θ)t
(3)
How the total firm 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 (Θ)t +1
(4)
or when
Rt +1 + B(Θ)t
V (Θ)t +1
(5)
At the point of maturity, the bondholders’ claim will be worth:
V (Θ)B;t +1 = min[Rt +1 + B(Θ)t +1 ; V (Θ)t +1 ]
(6)
At the point of maturity, the equity holders’ claim will be worth:
V (Θ)E ;t +1 = max[V (Θ)t +1
(Rt +1 + B(Θ)t +1 ); 0]
V (Θ)E ;t +1 = max[E (Θ)t +1
Rt +1 ; 0]
(7)
(8)
The value of the equity holders’ claim is equivalent to a call option on either E (Θ) t +1 with
exercise price Rt +1 , or on V (Θ)t +1 with exercise price Rt +1 + B(Θ)t +1 . In a risk neutral
evaluation, all cash flows are certain, given that a specific state occurs. The time t values of
equity and debt in the levered firm can then be written as:
Equity :
E (Θ)t
Z
=
Debt:
B(Θ)t
Ω
Z
=
Ω
VE (Θ)t +1 dP(Θ)t +1
(9)
VB (Θ)t +1dP(Θ)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 firm value can be written as
max[V (Θ)t +1
(Rt +1 + B(Θ)t +1 ); 0] + min[Rt +1 + B(Θ)t +1 ; V (Θ)t +1 ]
(11)
CASE 1
VE (Θ)t +1 > (Rt +1 + B(Θ)t +1 )
(12)
eq:(11) ) V (Θ)t +1
(13)
VE (Θ)t +1 (Rt +1 + B(Θ)t +1 )
(14)
eq:(11) ) V (Θ)t +1
(15)
CASE 2
The value of the leveraged firm is
E (Θ)t + B(Θ)t
Z
=
Ω
VE (Θ)t +1 + VB (Θ)t +1 dP(Θ)t +1 = V (Θ)t +1
(16)
With the assumptions above, I have showed that the values of the unleveraged and leveraged
firm 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 firm financing.
Jensen (1986) argues that debt is an efficient means by which to reduce the agency costs associated with equity. Klaus and Litzenberger show that with the tax advantages of debt, optimal
capital structure includes debt financing. Ross (1977) and Leland and Pyle (1977) argue that
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debt can be valuable as a device for signaling firm value. The three main hypotheses that are
used to explain differences in capital structure between companies are the transaction-cost hypothesis, the asymmetric information hypothesis and the tax hypothesis. According to Harris
and Raviv (1991), leverage increases with fixed assets, non-debt tax shields, investment opportunities, and firm size and decreases with volatility, advertising expenditure, the probability
of bankruptcy, profitability and uniqueness of the product.
This theory claims that a firm’s optimal debt ratio is determined by a trade-off between the
losses and gains of borrowing, holding the firm’s assets and investment plans constant. The
firm substitutes debt for equity, or equity for debt until the value of the firm is maximized.
The gain of debt is primarily the tax-shelter effect, which arises when paid interest on debt
is deductible on the profit 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 tradeoff theory several other arguments are used for why firms might try to adjust their capital
structure to some target. Leverage also depends on restrictions in the debt-contracts, takeover 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 firms with a long history of credits will have relatively low default probability and
lower agency costs using debt financing than newly established firms. A common factor for
all these firm 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 firm or between stockholders and
managers in the firm. This multiplicity of problems can easily confuse the analyst and lend an
air of incomprehensibility to the field of corporate finance. A construction of a positive theory
of debt financing, 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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agents that control the common stock, while the rest of the capital is raised through bond sale,
can reduce agency cost of management.
Second, debt is a useful signaling device, used to inform investors a message of the firm’s
degree of excellence. Third, debt can also reduce excessive consumption of perquisites because creditors demand annual payments on the outstanding loans. Debt also has its disadvantages. First, there is the problem of agency cost of debt that includes risk substitution
and under investment. Second, debt also increases bankruptcy possibility by increasing the
financial risk of the firm. I will discuss this reasoning in the following sections.
A. The Theoretical Tax Incentive
Taxes
The hypothesis is that an increase in tax rate will increase value of firm tax-shield.
The firm reduces income by deducting paid interest on debt and thereby reducing their tax
liabilities. An increase in tax rates should hence increase leverage. Tax systems currently
adopted by most industrial countries can be classified into classical systems and imputation
systems. In the classical systems, interest payments are deductible at the corporate level, but
dividends are not. At the personal level dividends and interest are deductibles. Imputation
systems reduce or eliminate taxation of dividends by granting a tax credit to recipients of
dividends, equal to some fraction of the corporate tax paid on earnings used for dividends.
The tax incentive is a part of the static trade off theory that contends that a manager balance
increased financial risk and tax deductions. In Norway this is not necessarily true since the
tax system is and has been neutral towards debt and equity. After the tax reform in 1992,
dividends are not taxed as income for the investor, while interest income is. The firm pays the
dividends out of taxed earnings while interests on debts are tax deductible in the firm’s income
statement. So, in Norway, dividend and interest rate taxation should be neutral regarding
which financial instrument, debt or equity, firms have an incentive to issue. Norway have
had deferred taxation after the tax reform of 1992. Taxation, which, owing to tax legislation
results in timing differences, i.e., differences between incomes computed for taxation purposes
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and for financial accounting purposes. Unlike permanent differences, timing differences are
capable of being reversed in future periods. In the deferred tax model, deferred tax is a longterm 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
financial profit and loss account and the reported profit 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 profit and loss account/income statement. In the deferred tax model, the amount
represents the total tax to be paid on the accounting profit 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 financing exist in
Norway. The yearly regressions in Frydenberg (2001), display that the tax variable ’nondebt’
is significant in 1991, 92 and 1999 and year 2000 for the interest carrying debt variable.
According to Bøhren 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 influence the debt structure whenever the tax codes are not entirely
neutral. A lower marginal tax rate should decrease leverage. With the tax-reform, dividend
1
This is common for accelerated depreciation. The depreciation percentage is 30 % for office equipment,
which is considerable more than the 1/5 linear economic depreciation in the financial statements. The 10%
difference multiplied with the tax rate of 28% is considered a long-term liability. Sooner or later, here already
after three years, the financial linear depreciations are higher than the accelerated tax depreciations and the
deferred taxes will be reduced with 28% of the difference between tax and financial depreciations.
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taxes were substantially reduced. Dividends are no longer double taxed. The investor’s 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 firms.
A change in incentives towards equity is a consequence of the tax-reform. Some authors
have claimed that the firms serve as a financial intermediary. Firms may not have a tax incentive to increase debt if both the investor and the firm are in a tax position. The firm 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 to
rely on debt financing. The financial intermediary argument also claims that firms may lend at
more favorable terms than investors. The idea is that firms can make better use of the benefits
of debt financing if they are in a tax position.
The firm benefits from a reduction of the taxes paid to the government. Interest rates paid to
debt holders are deductible in the profit 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 profit levels. The tax incentive for debt financing
is therefore not marginally decreasing as the leverage increases when the corporate tax-rate is
constant. The firm tax is a pure net-profit tax and where there is no profit, 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 fixed 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 firm. Stiglitz (1969) have shown
that the value of a security is the same, regardless of whether a bankruptcy would occur or not
under some specific conditions. There are, however, costs of financial 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, lawyer’s 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 firm. Warner (1977) said that it is not clear if this agency relation
give the trustee any incentive to run the firm efficiently and take decisions which are in fact
value maximizing. The stockholders face the possibility that they may lose control of the firm
when a financial distress situation occurs. The option to receive dividends if the firm operates
profitably in the future is thereby lost for the current stockholders. Indirect costs arise when
qualified employees that can pursue alternative opportunities quit the firm 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 confidence in the firm.
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 firm probably will go under anyway, why not make a final bet that might salvage
the firm. The stockholders and management is betting with the creditors money. The point in
risk shifting is how stockholders of levered firms 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 firm value, increase the risk of outstanding debt and harm the bondholders. The stockholders can pay out all the assets and leave the bondholders with an empty
shell. As the firm approaches bankruptcy and financial distress is more and more transparent
for the firm’s 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 firm 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
firm starts with a conservative policy, issuing a limited amount of relatively safe debt. Then
the firm 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-ratio
increases 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 firm in the model. An agency problem occurs where a firm 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 financing. 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 financing arrangements may coexist at the same time. Large capital-intensive firms
with high debt levels may coexist with smaller and marginally profitable firms 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 firm
be controlled? A tightly held firm where a majority or large shares of the stocks are controlled
by an individual or a group is supposed to be a more efficient managed firm than the firm
controlled by entrenched self-interested managers. Second, operating risk has to be shared by
the owners of the firm and the debt-equity paradigm have shown remarkable ability to allocate
risk to the people that has the residual control rights of the firm, 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 efficient because they fail to give the controlling agent the incentives to make the first best
decisions. The intuition behind the existing financial 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
flow. If this is not the case, there is a potential conflict because owners of one of the securityclasses 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 Verification(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 defining character of the CSV literature is that that the true cash flows
of the firm are only observable to the manager or entrepreneur. The cash flows of the firm are
only verifiable at a cost in a bankruptcy process. The outside investor receives only a fixed
sum of money when the entrepreneur income is not verified and a strictly lower payment when
income is verified. 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 financial 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 partnership. 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 firm reaches a certain profit-target. On the other hand, if profits are below target they get no pay off. The debt owners have practically no risk and fixed pay-off structure
unless losses incurred wipe out the equity. Neither equity nor debt owners can lose more than
what they have invested, guarantees set aside. A first 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 firm
is consistent with there being one huge firm in the world and also that every division of a
firm could be divested to single autonomous firm. Organizations emerged because of market 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 firm 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 firm can order the employee to perform tasks within a broadly
defined area. The organizations are not markets and they are not individuals. The literature
of firm financing, views firms as something between. Firm financing 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 benefits of security and loan contracts. The literature of corporate finance 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 reflect benefits from the
organizational structure that protects the real and financial resources. The value of the corporation must be derived from costs and imperfections inherent in markets: information asymmetries, 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 transaction 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. Instead of project financing the firm takes on corporate debt, thereby reducing transaction costs,
and construct budgets and incentive schemes for the sub-divisions of a firm. 2
2 A project manager is allocated capital from the firm’s investment budget. Alternatively, she could have raised
capital in a bank or in the capital market. That would be difficult if the asset base for the project is shared with
many other projects and possible collateral is already occupied. The corporate debt reduces transaction costs
compared 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, was
introduced 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 conflict between equity investors and debt investors. The financial structure affects
the cash flow through investment decisions. Smith and Warner (1979) argues that there are
four major sources of conflict. These are dividend payments, claim dilution, asset substitution,
and under-investment.
Briefly, asset substitution is an incentive problem associated with debt. Stockholders are
the residual claimants to the firm cash flow. Their claim is analogous to a call option on the
firm’s 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 debtsecurities in a firm. This discount is a cost that reduces the total value of a firm 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 firm? In the loan application process the investment objects and future strategy is certainly a talking point. The problem is
17
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 either. If firm 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 options 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 firm 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 firm, the amount is very
low and the demand for public disclosure of financial report is therefore more important. In
the US, quarterly disclosures of financial reports are the standard among listed firms, the activities 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 difficult
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 defined 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 profitable investment opportunities. Firms expecting high future growth should therefore use a greater amount of equity
financing.
18
I0 is the investment in product development made at time t = 0.
Due to the investment in product development, the firm holds a growth opportunity.
At t =1, the firm must invest an additional I1 , to get the cash flow X (I0; α; r̃) from the product
developed.
The investment I1 could for instance be machinery needed to produce
the developed product.
The investment option is firm specific and cannot be sold. The firm that made the initial
investment has an exclusive right to exercise the option. If the firm 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 firm that is entirely equity financed and then a firm that issues debt
to finance the initial investment I0 . 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 financiers if the growth option has prior debt financing. After having paid off the
debt holders to the option, there will be too little left for the investor of the profit that comes
from implementing the growth option.
When B0 < V is fulfilled, the incentive not to invest in certain states are present.
Whether the option has any value when it expires depends on the asset’s future value and
also on whether the firm 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 firm must
raise I1 , 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 I1 is made, and then the debt matures. The firm will invest if the return
cash flow is large enough to cover both the first investment which is debt financed and the
second investment which is equity financed. However, since the first investment, made at time
zero, is in fact sunk cost at time t = 1, the firm should make the investment if the return cash
19
Figure 1.
The Firm’s Investment Decision with Prior Debt Financing
Return X in state s
6
d(s)=0
d(s)=1
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
I1 + F
p
I
-
s, State of the world
sb
sa
flow is larger than the equity investment at time t = 1. In some unfavourable states of nature
the firm will forgo a positive NPV investment, because of the seniority of the debt. From the
stockholders perspective, they would be throwing good money after bad money. This is a cost
that in a rational expectations equilibrium in the capital market will be borne entirely by the
stockholders. The bond holders will require a premium to finance a product development that
may not result in production in anticipation of the shareholders not being willing to supply the
firm with additional funds to buy the necessary machinery for the production if the return does
not cover the cost of the machinery. This premium reduces the value of the firm and is a cost
of debt financing compared to equity financing. Firms with growth options would hence be
reluctant to finance themselves with debt. I can illustrate this incentive not to invest in certain
unfavorable states of nature in a figure. Shaded area in Figure (G) is loss of value in some
states. A high F implies a larger loss of value.
Myers (1977) is often cited in the literature. This is partly due to the seminal real option
aspect, but also to the fact that he describes a unique incentive problem. Myers’ argument
hinges on the fact that that the lender has no additional collateral except the growth option. If
20
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 firm split the profit otherwise lost, in a Nash (50/50)
bargain solution, by letting the firm exercise the growth option and finance only a part of the
new investment while the lender financed the rest. As long as V(s) is larger than I1 , 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)- I1 . 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 firm 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 effectively
bond their promise to pay out future cash flows. Thus debt can be an effective substitute for dividends, something not generally recognized in the corporate finance literature. Jensen (1986)
The argument of the free cash flow and the role of debt to control opportunistic management
is due to Jensen (1986). Debt reduces management opportunity to spend excess cash flow
in non-profitable investments. Management has less control over the firm’s cash flows since
these cash flows have to be used to repay creditors. Jensen and Meckling (1976) have argued
that managerial incentives to allocate the firm’s resources to their private benefit are larger
when the firm is mainly equity financed. The ”free cash flow” term is the amount by which
a firm’s operating cash flow exceeds what can be profitably reinvested in its basic business
and the emphasis is here on the word profitably. Conflicts of interest between stockholders
and managers over payout policies are especially severe when the organization generates substantial free cash flow. So, there is a dark side to the financial slack. Too much of it may
encourage managers to take it easy, expand their perks, or empire-build with cash that should
21
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 inefficiencies.
Jensen (1986) validates his stories by referring to the empirical literature on debt for common 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 firms is
treated in Section IV. The evidence from the leveraged buy out and going private transactions
is that many of the benefits 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 fixed amounts of money to the investors each year, the agency cost of
free-cash flow can be reduced.
H.1. Profitability
Profitability affects leverage in at least two directions. First, higher profitability usually provides more internal financing. More earnings can be kept in the firm and hence a lower level
of debt. Less debt is then needed to finance already planned investments. Secondly, debt
introduces 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 firm slim and cost efficient. Unnecessary non-profitable investments
will be avoided because creditors demand annual payments and claim any free cash flow. High
profitability should result in higher leverage according to the free cash flow hypothesis, but a
high leverage would result in high profitability on the basis of the pecking order hypothesis.
The problem is that leverage and profitability are linked both ways, and that the causal direction 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.
22
IV. The Pecking Order Theory
According to the pecking order theory, the firms will prefer internal financing. The firms
prefers internal to external financing, and debt to equity if the firm issues securities. In the pure
pecking order theory, the firms have no well-defined 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 debt’s 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 firms prefer internal financing, they target dividends given investment opportunities, then chose debt and finally
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 transaction costs than equity issues. Debt financing also involves a tax - reduction if the firm has a
taxable profit. Myers and Majluf (1984) invoked asymmetric information to give a theoretical
explanation for the pecking order phenomena. The signaling model described in Section A
leads 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 profit
type firms 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 firm is a high performance firm.
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 firm. Akerlof (1970) introduced an adverse selection argument
23
that explains why prices of used cars drops significantly 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 buyer’s 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 firms for sale, in the market for corporate control, are those with below
average excellence. The firms 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
firm is in fact an excellent firm 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 management’s control of the firm. The idea underlying the signaling models, is
that stockholders or managers signal private information to the security market in order to
correct the market’s perception of excellence.
24
V. Summary of the Theoretical Literature
Capital structure remains enigmatic
Chirinko and Anuja R. Singha (2000).
Although we have come along way towards a better understanding of why and how firms
choose their capital structure, there are still unresolved issues. First, there is no current model
that put all the pieces of theory together in a model that might be suitable for textbook presentation and, hence, presentable to the general public. Thus, students when they enter the
job market have no comprehensive model to relate their capital structure decisions to. Second,
the empirical evidence is mixed and does not point out a single empirical model as a good
explainer of corporate practice. At the same time, everybody understands that borrowing too
much is not good for your firm’s health and not borrowing at all is a waste of precious equity. The academic community’s 40 year struggle with the issue since Miller and Modigliani
(1958b) have in essence found that your capital structure is a trade off between many interests
and that some times you would prefer to issue debt and sometimes equity. I think the root to
the problem here is exactly ”many interest”. The capital structure being a mirror image of the
real side of the balance sheet is a too complex fabric to fit into a single model. Academics
have not tried to make a single model for how firms should invest or operate; realizing that the
environments and circumstances a firm could be operating under is endless. Instead we have
several partial models for how firms should operate and invest contingent on the environment
and circumstances surrounding the firms. It is time to realize that this goes for the financing
aspect as well. I can only hope to make models that suit one type of firm well; other types of
companies need other approaches.
One of my contributions is to show that the theoretical models developed seem to explain
differently if I divide the data into several generic groups of firms. This idea is explored in
Frydenberg (2001). Models invented for homogenous firms should be tested on homogenous
25
firms. The notion that every firm 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 firm with the sub-optimal capital structure for the firm
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 firm, the stocks are not traded, if there exist an arbitrage possibility, the stockholders cannot take advantage of the arbitrage possibility. Two firms with equal future cash
flow 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 financial 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 efficient capital market. The markets may be efficient, but still less than perfect. Asymmetric information
may be present between the firm’s managers and the capital market, and we may still have
efficient markets, although in a semi-strong form. The insider’s information about the firm’s
business future will not be discounted in the market prices of the firm’s stocks in this situation.
A definition of a perfect market is that costless trade in other assets can copy any cash flow.
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 reflects the probability for that state to
happen and the investors inter-temporal marginal substitution rate of consumption. However,
26
the markets may be correlated and if your firm runs into difficulties so will probably most
other firms 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 firms in the technology sector are trading at market values under their cash position.
The financial markets have been prune to manias or financial 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 once
more.
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 firm is
to be liquidated on the basis of a rule instead of what maximizes the total value of all the
claimants, arbitrage profits 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 bondholderstockholder conflict would exist because in a world without contracting costs, the capital
27
structure of the firm can always costless be changed, to make sure that a firm take advantage of all profitable investment opportunities and does not invest inefficiently as a result of
leverage.Stulz (1990)
A key result of Merton Miller’s research is that for leverage to matter no clever arbitrageurs
can take advantage of a situation where leverage matters. The perfect market assumptions are
sufficient (second-order) conditions for leverage to be irrelevant, but not necessary conditions
(first-order. Although the assumptions may be broken, we may still have the irrelevance. Chiang (1984) say that the first order (tangency) of a maximizing function is necessary for a
maximum point, the second order (convexity) is sufficient. So, we could have all the conditions 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 firm as a convex function of the debt ratio. If the function is convex,
but increasing in the entire domain from zero to all debt financed firm, we have no internal
optimum. An arbitrage exists if an investor could costless trade in the securities of the firms
and make money. Assume that one or more of the perfect market assumptions are broken and
that we have two firms A and B that are equal in intrinsic value, i.e. the cash flow these two
firms generate are equally distributed in time and magnitude. But firm 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 firm A and buy more of stocks in firm B,
since both firms would eventually earn the same cash flow. Even though expected bankruptcy
costs in firm B may be higher than in firm A, that does not matter because we have assumed
that the firms are equal. If the high debt in firm B creates costs because management does not
dare to pursue the best projects, then that will change the cash flows of firm B. Then the cash
flows are not equal anymore. The message is that leverage cannot matter if firms are equal
and arbitrage trading is allowed. But leverage could matter if firm cash flows are not equal
because some market imperfection plays a part in the equation and if arbitrage trading is not
allowed.
28
It is therefore likely that leverage only matters for firms 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 financing. The debt-ratio in this firm is therefore much higher than the ideal, because
the interest payments on the debt reduce the entrepreneur’s 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
firm 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 first step of the process, trading off various costs of debt versus equity. Evidence for the
pecking order; firms having low profitability 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 finance 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 incorporate 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 the
stock of a firm can be compared to a call option on the firm’s assets. This is not entirely true,
the stock is more like a
down-and-out call on the firms 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 firm breaks down through
the barrier created by par value of debt, the firm is bankrupt and the equity of the firm has no
29
value if the creditors take over the firm. A down and out call barrier option, where the option is
worthless once the underlying asset touches a floor 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 downand-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 firm 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 firm, a call on the assets
of the firm 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 bond’s market
value is thus X minus the put option, P, while equity is worth C. A defining concept of options
is that they cannot have negative values. If S is larger than X, then the equity of the firm 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 σ, interest rate r and the time T to date of
expire.
C0 = f (S; X ; σ; r; T )
3A
(18)
barrier option has an important result, the barrier call should be sold cheaper when there is downside skew
than when there is a flat skew. See Nassim Taleb (1997).
30
P0 = f (S; X ; σ; 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 firm 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
firm. 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
firm value.
Under-investment
Second, there is the under-investment problem described by Myers (1977)
that reduces the firm values because a debt financed growth opportunity or real option might
not be exercised because debt investors normally receives their interest and principal loan be4 The
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. Both
put and call options increase with the time T to maturity because the owner of a long lived option always has all
the exercise opportunities open to the owner of the short life option. Increasing the time T transfers value from
debt owners who has X-P0 to equity owners who have C 0 at their disposal. Choosing the debt ratio in this model
would amount to choosing another strike price for the debt.
31
fore the equity investors receive their dividend and residual capital left in the firm after having
paid off all the creditors. That should reduce C0 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 equity 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 firm
can be increased. The after tax value of the firm S = C0 + X - P0 can be increased by shifting
over to debt financing. This corporate level one-sided effect of tax-benefits of debt financing 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 firms with taxable profits.
Bankruptcy costs Fourth, bankruptcy Warner (1977) theory predicts that an increase in X
beyond sustainable levels of debt would incur expected direct and indirect bankruptcy costs
that would reduce the value of S, thus decreasing C0 , increasing P0 . The market value of both
equity and debt would fall when the debt and equity investors start to believe that the firm
might run into serious financial 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 delta
goes 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 flatter 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
32
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 flow, discounted to market value of cash flows 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 defines the level of debt, while C0 and X-P0 defines the market value of respectively
equity and debt.
S C+X
P
(20)
The un-leveraged firm is represented by S0 initially, if the costs of changing the capital
structure is larger than the benefits, then C1 + X - P1 should be less than S0 . The new value of
the firm S1 would be equal to the market value of equity, C0 , plus the market value of debt, X1
-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 first place. Well, one could argue that a loss of equity would restrict the
investment possibilities of the firm, leading to a lower S. The value of the firm, S, is the sum
of two components, first 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 firm 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 firm, 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
33
with 1 units and increase of P with 1 units. In the put call parity they would neutralize the
change in X so that S would be left unchanged. It is likely that a firm close to bankruptcy,
will see that the market value of equity drops more than the market value of debt. The put-call
parity is based on no-arbitrage, if the equality of eq. (21) where replaced with a larger than
sign, then arbitrageurs could short-sell the assets, and buy stocks and bonds. That sounds like
the recipe of a leveraged buy-out. To get control over an undervalued firm where the market
value of stocks and bonds does not match the market value of assets, investors buy the stocks
with borrowed money, gets control in the board of directors and then sell out valuable assets
and daughter-companies. Finally they use the proceeds to reduce the debt to a comfortable
level. Buy-candidates that are cash-rich and debt-free are therefore especially vulnerable to
leveraged buy-outs. Management in these companies thus often entrench themselves in a
fortress of debt, effectively deterring any attempt of leveraged buy-out because the firm has
a high debt-ratio to begin with. Debt have been used as a defence mechanism by entrenched
managers often as reported by Garvey and Gordon Hanka (1997).
A highly levered firm is not so easy to acquire because the assets cannot be used as collateral for further debt.
∆S = ∆C + ∆X
∆P
(21)
The first theory I described was the risk shifting hypothesis. By increasing the volatility of
the option, the call option value increases and so does the put option value. The rate of change
of the option with respect to the volatility of the underlying asset is always positive. This is
true for both the call and the put option.
Since both the call and the put option increases monotonic with the volatility of the assets,
the debt market value decreases by the increase of p, the put option. The under-investment
hypothesis results in an increase (or decrease) in the asset value. The free cash flow hypothesis
result in an increase(or decrease) in the asset value S. The put-call parity is based on a nonarbitrage situation. We should be able to exchange a part of the underlying S for a part of the
34
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 firm in question is the only firm that can exercise
the growth option. It is therefore not possible to sell the growth option to another firm. If the
growth option was marketable in bits and pieces, the firm 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 firm since it is a positive NPV
project. So, the stockholders in reality own a call option on the firm’s assets. The position of
the bondholders are that of someone having sold a put option to stockholders, giving them the
right to sell the firm to the bondholders for the face value.
The stockholders can either choose to buy the firm’s assets for the face value of debt or
choose to sell the firm’s 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 firm 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 is
interest they can receive for the loans they make to the firm.
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 Greeks5
5 The
’Greeks’ are the first 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, ∆ = δC
δS . Theta is rate of change of
δC
option price with respect to the time to maturity,Θ = δT
. Vega, is rate of change of option price with respect to
δC
volatility ν = δC
δs . Rho is rate of change of option price with respect to interest rate ρ = δr . Finally, the second
derivate of the option price with respect to the stock price is Gamma, Γ =
35
δ2 C
.
δ2 S
Owning levered equity in a firm 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 determining the option values might give a change in the value of the firm 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 firm? The free cash
flows generated from the operations of the firm is still the same. The point is that increasing the debt is likely to change the investments the firm 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 flow of the firm. 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 behaviour
are 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 firm, but if
few investors agree with you, it is unlikely that the stock will appreciate in the near future.
36
The stock markets perception of what constitutes a normal capital structure may punish
those firms that have a capital structure that deviates from the norm. Even though your firm
would have benefited 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 flow 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.
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