The Microeconomic Firm under Uncertainty:
Theoretical Development and Empirical Test
Ren Raw Chen
Michael S. Long
Xiaoli Wang*
Initial Draft December 1, 2005
Current Draft April 20, 2006
Abstract
Our paper models and empirically tests the production behavior of firms operating under
uncertainty. The study compares firms operating in perfect competition with those
producing with product market power. Our model predicts that both types of companies
produce less under uncertainty from the cost of risk. In addition, our model predicts that
companies with market power have a greater market value, face more product market
uncertainty, use less leverage but have a similar default risk to firms in perfect
competition risk. We then empirically test our model using manufacturing firms that
operate in close to perfect market competition having little product differentiation and
operating in low concentrated industries versus those that have product market power
using advertising and/or R&D and operating in highly concentrated industries. The
empirical evidence supports our hypotheses.
We also investigate the “option against value” that occurs to companies when the real
product market changes greatly reduce or even eliminates firms’ product markets. Long,
Wang and Zhang (2006) originally presented this idea and tested it with just the machine
tool industry to describe dynamic downward changes in real product markets and the
resulting affect on individual firms’ values. We use actual default occurring over the next
ten years. We find smaller companies, less capital intensive firms and those in perfect
competition are more likely to have gone out of business. The default probability
estimates based on Merton’s Equity Option Pricing are than added as the probability of
an “option against value” occurring. We find while it predicts default, smaller companies
and companies in perfect competition are still more likely to experience product market
shift and default.
* Professors Chen and Long are at Rutgers Business School - Newark and New
Brunswick, Rutgers University. Dr. Wang is at Bears Stearns. Professor Long is contact
author at Mikessam@aol.com. We would like to thank the Whitcomb Center for
Research in Financial Services at Rutgers University for providing data support and Ileen
Malitz for her comments.
1
The Microeconomic Firm under Uncertainty:
Theoretical Development and Empirical Test
Financial markets value claims based upon what they expect to happen. One
needs only examine swings in major indices to see that beliefs are continually changing.
However, in the long run, the demand and uncertainty that firms face in their real product
markets must reconcile with their values in the financial markets. In this paper, we
connect these two related markets and investigate the effects of firm’s product demand
changes on their value, leverage decision and survival result. While many choose to
study such an issue under a straight option framework, we feel that an analysis based
upon a traditional micro economic model can better explain the relationships.
We model and then empirically test several factors that influence firm value by
comparing firms with market power in their product markets with those operating in
close to perfect competition. We first consider the importance of product market power
on firm value. Our model and supporting empirical evidence, not surprisingly, shows
that firms with product market power have a greater value as measured by their Tobin’s
Q ratio. This conclusion holds even though our second test indicates that firms with
product market power face greater uncertainty from product price fluctuations. While
this considers product market risk, we also show that firms operating with product market
power have a larger market risk as indicated by the larger equivalent unlevered beta
values. As a result of their greater risk, firms with market power use less leverage on
average then firms operating in closer to perfect product market competition.
We also investigate the probability of the “option against value” and its relation to
firm characteristics. While all firms are aware of the normal uncertainties in demand and
2
costs, we argue that most are less prepared for major structural changes in their industry.
This option against value occurs when a downward shift or shock in the product’s
demand function happens from changes in the real product market. As an example of this
counter action or value decrease consider when another firm exercises its growth option
on its competition. Specifically, Home Depot opens down the road exercising its growth
option on the local lumberyard that now suffers a large call against its value. We posit
that, even after adjusting for the probability of default using the Merton model, the
negative options are greater with smaller firms and those operating in perfect
competition. Our empirical evidence is consistent with these hypotheses also.
Our study is organized as follows. We first review the motivating literature
behind our basic premise. We then model the firm under uncertainty in a traditional two
period CAPM and discuss the “option against value.” From this, we present our
hypotheses. We then discuss our samples and the specific variables before presenting our
empirical results. Conclusions follow.
I. Background – Motivation and Literature Review
Our approach to valuation is motivated by two classic papers. The first is Merton
(1974). He first showed that capital structure, when returns are allocated between debts
and equity, could be expressed in terms of options. His idea motivated others to view a
myriad of economic activities in terms of contingent claims. It also popularized the
concept of splitting returns into varying risk tranches, such as with mortgage and asset
backed securities. In our paper, we implement and expand Merton’s view about equity as
an option, which will be exercised when a firm value is greater than its debt and expires
when firm value is less than debts outstanding or the firm goes into bankruptcy.
3
In the same year, Long and Racette (1974) demonstrated that systematic risk in
holding securities was a cost of doing business in a micro economic framework to the
firm. In perfect competition quantity is set where the expected product market price
equals the firm’s traditional variable operating costs plus the cost of risk. In equilibrium
this also equals the average cost that include the risk costs. Since the firm operates in
perfectly competitive product markets, it will have a zero net present value or earn zero
excess returns. However, this approach does not incorporate the effect of financial
leverage on the firm value. The all equity financing approach implicitly assumed that the
demand is always sufficient to cover cash fixed costs. Thus, there is never an option
against value.
In this paper, we now integrate the above two ideas. We first argue that firms
both in “perfect competition” and those with “market power” operate according to
traditional microeconomic framework with risk first without leverage and then expanded
to consider leverage and taxes. We then show that the real option against value is
exercised when the firm’s product demand drops sufficiently to eliminate its value. We
argue that the effect of the “option against value” is more pronounced for smaller firms
and we attribute this to their limited access to capital markets for information.
Why has it taken over thirty years to develop what will appear such an obvious
idea? It is two related empirical facts that motivate our study. The first is we learn from
brokers of businesses that small, closely held firms sell at very small multiples of
earnings. Also we observe, as have others that small public firms appear to earn greater
rates of return on average. To explain this situation, Long, Wang and Zhang (2006)
intuitively developed what they referred to as the “unwritten call option against value” or
4
just the “option against value” that comes from firms facing real product market risks.
The company’s unwritten call option against value results from competitors’ innovation
or growth changing its product demand function and thus reducing its value. While
normally it is the systematic risk that causes values to change, the potential for a jump, or
more specifically a dive, in the product demand creates an option from the firm’s
competition and destroys the firm’s value when it occurs. This second point is that we
now have the data to study in our micro-economic setting with risks that could not be
previously estimated.
What we do now is model these ideas as a real option against value. We must
remember that financial markets can either lead or lag the actual product markets where
value is created. We usually emphasize the leads where a firm develops a new product
and its equity market value increases well prior to the product actually being sold. With
the “.com” craze (or crazies as it turns out), the late 1990’s saw a whole industry develop
with businesses selling at large multiples of sales, not earnings. While the economy does
grow over time, one must remember that a new product such as automobiles 80 years ago
meant the demise of other industries such as buggy whips. In these situations the
financial markets react or follow the product markets. It is this competitive process in the
real product market that creates the “unwritten option against value.”
Obviously, many additional articles have been published over the last thirty years
that are related to and help motivate our study. Long and Racette (1977) extended their
earlier development of the firm under uncertainty to imperfect markets from just perfect
competition. Hite (1979) extended the theory of the firm under uncertainty to include
debt from the earlier all equity model.
5
Banz (1981) gets credit for first observing that smaller firms earn greater rates of
returns. However, it is Fama and French (1992) with their three-factor model that really
popularized the idea. They empirically documented that high book to market portfolios
and small over large firms portfolios along with traditional beta values explained the
observed market returns better than beta alone.
Berk (1995) shows why these results should be expected. His intuitive argument
is rather simple. The one period economy has two firms with the same expected end of
period cash flows. The riskier of the two firms will have its expected cash flow
discounted back at a higher rate giving it a smaller value. Thus the “smaller” firm will
have a greater expected rate of return. He then develops the idea formally. While a neat
idea, he never considers why or how risk varies between the two firms. There is never
any mention of the factors influencing risk or the underlying product markets.
The only paper that really considers product markets and financing is Alberts and
Hite (1983). They present an argument that shows why highly levered firms do not have
a greater value than firms in industries with low leverage. Using an M&M framework
with taxes, they explain that competition in the product markets eliminates the tax
savings from debt through lower product prices. It also explains why most firms within
an industry have similar leverage. However, it never considers firm size and valuation.
In related work there are many recent papers trying to predict bond defaults and
hence firm bankruptcy. The most widely sited is from the KMV consulting firm.1 It
applies Merton’s (1974) option pricing model to compute default measures for individual
firms for the next year. We use a similar default estimate. It is important to note that
1
This idea has not been published but appears in many working papers that KMV publishes. For a recent
version see, Crosbie and Bohn, 2003.
6
they take more of a financial engineering approach to bankruptcy and never really model
what causes it to occur. Even after considering the Merton default option, the size
relationship to bankruptcy is still significant as in Long, Wang and Zhang (2006). The
Merton model is based upon a drift approach of value in traditional option pricing versus
Long et al where value changes result from jumps or rather dives in the underlying
product demand for products.
II. Model of Firm Value
Our initial firm model follows Long and Racette (1974). The firm operates for a
single period with risk priced in a CAPM framework. The firm operates in perfect
competition and we, as they did, start with the basic supply and demand framework. We
then modify the model to allow for debt and then the option against value.
A. Basic model of firm
The implicit form of the industry demand curve under certainty, where p and q
denote price and quantity respectively, may be expressed as
(1)
f (q, p) = 0
following Leland [1972], we define the stochastic demand relation to be
(2)
g( p, q, m) = 0
where  is a stochastic component with some density dH (m) . If (2) has continuous partial
derivatives, it can be expressed alternatively as either p = p(q, m) or q = q( p, m) . However,
the only meaningful formulation of the demand curve confronting the perfectly
competitive firm is p = p(m) as the firm is a price-taker. The firm is expected to face an
expected price that is equal to its expected marginal revenue. The probability density
function of price, dH (m) , is assumed to be identical for all quantities which the firm
7
produces for a given expected price. This is a very reasonable assumption as in perfect
competition no one firm’s output decision will affect the product price.
Continuing with only firms operating in perfect competition, we make the
following assumptions for our initial analysis:
(1) The firm exists only for a single period and assets have zero salvage value at
the end of that period. Further, the firm holds no inventories.
(2) The firm has already made investments at the beginning of the period and
capital is fixed.
(3) Any debt repayments are treated as fixed costs and are due at time 1.
(4) Financial markets are perfect.
(5) Demand curves are stochastic and expected price is known. Marginal costs
are known with certainty.
(6) All investors are single period, expected-utility-of-terminal-wealth
maximizers with homogeneous expectations.
(7) The risk and return of a portfolio may be described completely by its standard
deviation and expected return.
Assumptions (1) through (3) are made primarily for convenience. The others are
essential to the format of our investigation.
In our single-period context, the present value of a firm’s shares is
(3)
V0 =
E [V 1 ]
1+ r
where E [V 1 ] is the expected end-of-period value of the flows accruing to those who hold
shares at the beginning of the period and r is the single-period, equilibrium rate of return
required by investors in the firm.
8
Following Sharpe (1964), we can rewrite the firm’s value to be
(4)
V0 =
1
[E [V 1 ] - g cov[R M ,V 1 ]]
1+ i
where i is the risk free rate of interest,  is the market price of bearing risk, and cov[R M ,V 1 ]
is the covariance between the market return and the firm’s value at time 1.2
Now from assumption (1), we may state that
(5)
V 1 = Revenue - Cost s
= pq - C (q) - F
Remember that the only uncertainty is in the actual product price. Therefore when we
substitute (5) into (4), we get
(6)
V0 =
1
[E [p ]q - C (q) - F - l q cov[R M , p ]]
1+ i
We will take the derivative of (6) with respect to q giving the value maximizing
position.
¶V0
¶ E [p ]
¶ cov[R M , p ]ù
1 é
êE [p ] + q
ú
=
- C ¢(q) - l cov[R M , p ] - l q
ê
ú
¶q
1+ i ë
¶q
¶q
û
1
=
[E [p ](1 + eD ) - C ¢(q) - l cov[R M , p ](1 + eR )]
1+ i
0=
(7)
where D and R represent the elasticity of demand and risk respectively from changes in
the quantity produced. However, in a perfectly competitive world where the firm is a
price taker both partial derivatives are 0 and equation (7) reduces to Long and Racette
(1974):
(8)
0=
¶V0
1
=
[E [p ] - C ¢(q) - l cov[R M , p ]]
¶q
1+ i
or {E [p ]- l cov[RM , p ]}= C ¢(q)
2
While we use the traditional single period CAPM, the same conceptual results can be obtained in the
continuous ICAPM of Merton (1973). However since little economic insight is gained here at a much
greater complexity, we develop our analysis with the traditional CAPM.
9
What we are doing is comparing the firm operating in a perfectly competitive
product market as given in equation (8) with the firm having market power shown in
equation (7) where elasticity is not equal to zero. When the price setting firm increases
its price, its expected demand decreases by the absolute value of its elasticity. Similarly,
its risk as measured by the covariance of its price and the market returns also increases
with a price increase, but decreases by the absolute value of its risk elasticity. If a
constant correlation of product price and market returns exists, the systematic risk varies
directly with the expected price. This in turn gives an equal elasticity of demand and
elasticity of risk (  D   R ) that we feel is a reasonable assumption. Equation (7) can
now be rewritten as
(9)
{[E [p ]- l cov[RM , p ]}(1 + e) = C ¢(q)
Our model has firms facing only demand uncertainty. We assume both the
market power and perfect competition firms operate with identical cost functions and at
the same marginal costs. Obviously, in this situation both would require the same initial
investment and produce the same Q.
The market power firm will always operate in the elastic portion of its demand
function where lowering price will increase its total revenue. Its elasticity will be less
than zero as it has market power and greater than –1 as it will always price and produce
where its total expected revenue is less than its maximum. Only with zero variable costs
would price be set to maximize total expected revenue.
In comparing equation (8) for perfect competition with equation (9) for the market
power firm, it is obvious that the market power firm will command a higher product price
10
and it will have a greater value for the same initial investment and output. Thus its
Tobin’s Q ratio should be greater.
We next consider the systematic risk that the two face. With the same quantity
being produced, it is obvious that the market power firm will have a higher price and
corresponding greater cov[p, R M ] . Thus market power firms will have greater systematic
risk. 3
With our assumption of equal elasticity for both the product demand and its risk,
we are assuming that the correlation of product price and market returns is a constant of
1.0. It remains an empirical question whether that relationship holds. Again as long as
the elasticity of demand and risk are close in magnitude, the overall relationships should
hold.
B. Value maximizing with leverage and taxes
Merton (1974) noted that the equity resembles a call option against the value of
the firm where the bondholders hold the underlying assets. This new approach to capital
structure now is used widely in the corporate finance literature. When debts are issued,
equity holders are effectively selling the assets of the firm to the debt holders in return for
cash and a call option. When the debts are due (so is the call option), the equity holders
will face the choice whether to buy the assets back from the debt holders (whether to
exercise the call option) and will do so only if the value of the assets exceed the
redemption value of the debts. Under the situation where the equity holders are unwilling
or unable to redeem the assets of the firm, the debt holders must takeover the firm. In our
3
A more recent paper [Ait-Sahalia, Parker, and Yoga, 20004] finds that the consumption of luxury goods
covaries significantly more with stock returns than does aggregate consumption. As firms with market
power produce these unique, their results are consistent with our model. However, we do not limit our
study to only luxury goods. Further, we consider market returns in measuring risk instead of aggregate
consumption.
11
two period model, we use Merton’s argument as our decision criteria for default. While
continuing with our two period model, we drop the assumption of no leverage and also
add profit taxes.
Hite (1977) is the first to model the idea of considering the firm’s output decision
as to effects on cost of capital. However, his model requires some strong assumptions
about the tax structure and he explicitly assumes away default. Dotan and Ravid (1985)
show that an interaction between the optimal level of investment and level of debt
financing exists. They find that the investment level and debt level must be determined
simultaneously and that a negative relationship exists between operating and financial
leverage. Their paper is more general than De Angelo and Masulis (1980) in that they
endogenize the nondebt tax shields.
In their model, the investment level is chosen along with the debt level based
upon the expected demand function. The output decision occurs after the price is
revealed. In comparing firms operating in perfect competition with those with market
power, our model is somewhat simpler as the firms in our model have identival cost
functions and a fixed investment level thus eliminating De Angelo and Masulis
arguments on debt levels.
However unlike Dotan and Ravid’s model, the firms in our model must make their
output decision prior to the actual price being known, but after the capital decision has
been made. This eliminates the interaction between the quantity selected and probability
of bankruptcy allowing us to solve the value maximizing quantity and resulting leverage
decisions independently. Obviously, this assumes away any agency problems between
debt and equity holders.
12
We model a tax shield savings from debt versus an increased chance of incurring
bankruptcy costs with increasing leverage. As we have a one period model, we will
follow earlier work (see, Rubenstein, 1973) and consider the entire debt payment tax
deductible. The value of the firm can now be expressed as
(10) V  qE ( P)   cov( RM , P   C (q)1  (1   )t c   (1   )t c D   K  B  D (1  i)
In equation (10), tc is the tax rate, D is the debt amount owed at time 1, and K = constant
cost of going bankrupt and B is constant increase in costs for debt level D.  is the
probability of default that is an increasing function with D and the variance of P. It
occurs when the actual product price P is low enough so that qP  C (q)  D  0 .
The firm now selects its debt level to maximize value. Taking the derivative of
equation (10) with respect to D gives
V
0
D




K  B  D   B  (1  i)  0
 qE ( P)   cov( RM , P   C (q) 
t c  (1   )t c 
tc D 
D
D
D






K  B  D   B  (1   )t c
 qE ( P)   cov( RM , P   C (q) 
tc 
tc D 
D
D
D


qE ( P)   cov( RM , P   C (q)  t c  t c D  K  B  D  D


B  (1   )t c

This gives the traditional tax shield, bankruptcy cost trade-off. When the tax rate is zero,
the firm would use no debt. Conversely, when bankruptcy is costless, the firm would be
totally debt financed.
13
C. The “call against value” from potential competition
Up to this point we have considered a traditional micro economic view of the firm
under risk. We find the cost of systematic risk decreases output, and that firms with
product market power tend to have greater values than firms operating in perfect
competition. Our addition of leverage and bankruptcy costs shows the traditional capital
structure trade off between increasing tax deductions and increasing expected bankruptcy
costs. We now expand the analysis to consider another downside situation where the
firm is unable to cover all expenses including both debt and fixed cash expenses. We
refer to these “bad” outcomes as the “call against value” as new competitors enter the
product market place taking away the firm’s existing customers.
One might consider that this would only affect the firms operating with some
product market power. After all the firms in perfect competition are price takers already.
However, these firms as a group face potential competition from totally new ways to
provide the good or service. Consider what happened to glassblowers when machines
were invented to produce glasses or mechanical desk calculators when electronic hand
held calculators became available. These sudden changes in product demand can cause
many firms to cease to exist.
In a one period world with limited liability, we saw that firms would produce less
because of the systematic cost of risk. But, that was without considering the “option
against value.” Now, still considering a one period world, the firm has an incentive to
increase the quantity produced as the default costs are shifted onto the providers of the
inputs. Thus in a one period world, the option value might increase the firm’s equity
value. However, an increase in value from considering a potential “bad” shift in demand
14
does not make economic sense. Thus to fully consider the “option against value,” we
must consider the model in a multi period framework.
Merton’s (1974) model of capital structure lays the foundation of the structural
credit risk models, but it has a major weakness in being only a one period model. When
debt comes due the equity holders must exercise the call option or default. Merton’s
model must be expanded to a multiperiod approach that is more consistent with real
world firms. What happens now when a downward shift causes the present value of
future cash flows to be too small to cover debt payments? The result from a downward
shift in demand this period is most likely going to give lower expected demands in future
periods.
Geske (1977) developed the solution for this situation that we will base our model
on. While solving the multi debt issue problem, Geske did not consider the situation of
the firm facing adverse incentives when doing poorly and shifting risk. This deals with
the agency theory literature that was being developed parallel over basically the same
time period. He considered the firm to default when its value dropped below the present
value of promised debt payments. Still Geske’s model considered the movement in
demands to be primarily a drift as in traditional option pricing models. While he handled
to multiperiod problem, he did not consider the downward fall in demand.
To see how Geske varies from traditional multi period models, consider Merton’s
intertemporal CAPM (Merton, 1973) as shown in equation (11) using product demand.
(11)
V0 =
1
[E [p ]q - C (q) - F - l q cov[R M , p ]]
i
Merton assumes that value is always great enough to cover the fixed costs and hence the
firm continues indefinitely.
15
With the “option against value,” the demand function shifts downward enough
that the firm ceases to exist. We posit this as a greater problem with smaller firms since
they cannot see the changes coming nor react to the market changes as quick as larger
firms; the smaller firm benefits less from capital market feedback about future prospects.
Further, unless totally perfect capital markets exist with temporary shifts, the smaller
firms have less access to them and thus incur a higher cost of capital. Thus the large
downward product demand shift is more likely to be fatal for smaller firms.
One would also expect less capital intense firms to have a higher call against
value. Instead of having a reserve of capital, these firms use immediate cash
expenditures in rents and other variable costs that make them more susceptible to bad
economic downturns.
Finally, the option value should be greater for firms operating in perfect
competition. They are earning no excess returns so a downturn in their demand will
affect their viability quicker than a firm currently earning access returns.
The idea of the “option against value” is relatively straight forward and we feel
that it actually exists for all firms.4 When this negative option is been called, its affect on
value is obvious. We posited size and its corresponding capital market feedback as
affecting the “option against value” along with product market power and capital
intensity.
4
As this is being written in early 2006, one only must consider the current financial position of General
Motors. It is still the largest producer of automobiles, is capital intensive, and operates in imperfect
markets with over a quarter of the total demand.
16
III.
Hypotheses
A. Comparing value maximizing firms
We can now consider the specific value related hypotheses to be empirically
tested. We compare firms operating in close to perfect competition with those having
product market power operating in imperfect competition. First, we note that firms
operating in imperfect competition will earn excess returns since where their price is
greater than their marginal revenue. As a result, they should be valued higher compared
to firms in competitive markets that earn only their required returns. We proxy this by
Tobin’s Q, the ratio of market value to replacement value of assets. Thus our first
hypothesis is
Hypothesis 1: H0 : The Q ratio is not significantly different between a firm in
a competitive and non-competitive industry. H1: A firm operating in imperfect
competition has a significantly higher Q.
As shown earlier, greater value also comes at a greater uncertainty of demand.
The price setting firm sets its quantity where the E(MR) = MC. Thus revenues will vary
more for companies with market power than those of price taking firms, whose expected
product price is equal to its marginal revenue for our second hypothesis.
Hypothesis 2: H0 : Sales uncertainty is not significantly different between a firm
with market power and a firm operating in perfect competition. H1: A firm operating
in imperfect competition has a greater uncertainty in sales.
Because of the greater risk, a price setting firm will use less leverage than price
taking firms, leading to Hypothesis 3.
Hypothesis 3: H0 : The leverage ratio is not significantly different between a firm
with market power and one operating in perfect competition. H1: A price taking
firm uses greater leverage.
17
As we posited earlier, systematic risk is created from the uncertainty of the
product demand. If it is the primary factor creating systematic risk, then the firm’s beta
values should have a linear relationship with the firm’s total risk having a slope of 1.0.
As we are looking at the beta of the firm and not just equity and leverage varies between
firms, we must calculate the beta of the equivalent unlevered firm. We use Hamada’s
approach (Hamada, 1969) to eliminate the leverage effect by assuming no systematic risk
with debt and an proportional tax savings from debt that equals the effective tax rate (t).
This gives BU = BL (1- L)/(1 – Lt) where L is the market leverage ratio.
Corollary: H0: A firm’s beta values has a linear relationship with the product
demand uncertainty. H1: A firm’s beta value and its demand uncertainty are
not linearly related.
This creates the sufficient condition for our fourth hypotheses. However, even if
the relationship is not linear we should still expect to find the firms operating in imperfect
competition to face greater systematic risk from their greater demand uncertainty.
Hypothesis 4: H0 : Firm beta values are not significantly different between firms in
perfect competition and firms in imperfect competition. H1: Firms operating in
imperfect competitive have higher firm beta values.
Our fifth hypothesis tests whether firms choose their leverage according to the
traditional tax savings versus increased expected bankruptcy cost trade-off theory. Our
model predicts that firms in imperfect competition face a greater product demand
uncertainty than those operating as price takers. Consistent with the tax benefits and
bankruptcy trade-off theory, the price-taking firms should use greater leverage. If these
two factors cancel out each other, we should expect to see no significant difference in
terms of the default probability between firms with market power and firms operating in
perfect competition. This gives us our fifth hypothesis.
18
Hypothesis 5: H0 : The probability of default is not significantly different
between a firm with market power and a firm operating in perfect competition.
H1: A firm with market power has a significantly greater default probability than
a firm operating in perfect competition.
B. Testing for option against value
Our final hypotheses consider the “call option against value.” We will empirically
test whether smaller firms, firms with less capital intensity and firms in perfect
competition show a greater likelihood of defaulting even after controlling for their a
priori chance of bankruptcy. Does the “call against value” idea of Long et al exist when
comparing firms in different industries and competitive situations? They argue that the
option against value should be greater for firms with less capital intensity, as fixed capital
creates a buffer to carry them over bad years. Further, they argue that the “call against
value” should be greater with small firms, since smaller companies usually have fewer
resources to react to these changes. Finally, firms with product market power are earning
excess returns. This also gives them a greater buffer from a downward demand shift also
meaning that the perfectly competitive firms should have a larger “call against value.”
We will consider these directly and then also consider the default probability estimate
that is based upon the Merton model of bankruptcy.
Hypothesis 6a: H0 : The firm’s capital intensity does not affect the probability of
default. H1: A firm having lower capital intensity has a significantly greater
probability of default.
Hypothesis 6b: H0: The firm’s size does not affect the probability of default.
H1: A smaller firm has a significantly greater probability of default.
Hypothesis 6c: H0: The firm’s product market position does not affect the probability
of default. H1: A firms operating in perfect competition has a significantly greater
probability of default.
19
IV. Empirical Tests
Our model compares firms operating in a classical economics framework under
perfect competition with a price for systematic risk versus similarly priced firms with
product market power. In this section, we perform the tests of our models’ predictions.
We first identify the sample selection. We then discuss the specific variables used to test
our hypothesis. Particular attention is paid to the estimation of the probability of default
or the KMV values. Finally, we present the results of our tests.
A. Sample Selection
In a modern economy, it is difficult to identify industries operating in perfect
competition as price takers. Only the production of basic commodities such as
agricultural products (corn, wheat, etc.), minerals (gold, silver, etc.) and energy products
(oil, coal, electricity, etc.) fall into pricing taking positions. As we do not feel that this
will give us an ample sample of publicly traded firms, we expand our data selection.
Other firms, such as machine tool producers, operating in industries with little or no
product differentiation are also included in our sample of firms operating in perfect
competition. Specifically, we screen our sample selecting firms in industries with low
concentration as measured by the HHI and also do not undertake enough R&D or
advertising to be reported on COMPUSTAT. The first criterion assures that they have no
market power to influence prices and the second criterion makes sure that they have not
created unique, difficult to copy products.
Herfindahl-Hirschman Index (HHI) measures market concentration.
Unfortunately, the data are only collected every five years. Since we require future data
to see which firms failed to survive, we base our sample on 1992 data as HHI are
20
calculated that year. We use COMPUSTAT SIC (data item 184) to match with the HHI.
For firms operating in multiple industries (for example, whose with reported SIC codes in
multiples of 10 or 100), we use the HHI for the sub-industry with the largest sales. For
example if a firm has a SIC with a three-digit, we assume that it operates in the
corresponding four digit industry with the largest sales. It is then assigned that
corresponding HHI value. Further, we consider only manufacturing firms that have SIC
from 2000 through 3999. ADR’s are excluded.
For the “perfect competition firms,” we select firms operating in low HHI
industries having HHI of less than or equal to 500. Further, we restrict our sample by
excluding companies that give positive advertising expenses or R&D expenditures as
reported on COMPUSTAT. The gives us 411 firms.
For the firms with “market power,” we select firms operating in high HHI
industries having HHI of greater than or equal to 970. The individual firms must also
report advertising to sales of greater than 1% or report positive R&D expenditures again
as reported on COMPUSTAT. The final sample here is 470 firms.
B.
Parameter Estimation
In this section, we present the definitions for our variables used in testing the
hypotheses. (For specific calculations of the variables, see Appendix 1.) Tobin’s Q
measures how the market estimates the firm’s current and future earning potential versus
what was initially invested and retained in the firm. We calculate Q as total assets minus
book value of equity plus the market value of equity over total assets. To minimize the
risk of skewed distribution as affected by a few outliers, we cap the measure Q at 7.5.
21
For the uncertainty of demand, we compute the size relative standard deviation of
sales from its growth trend. We use as our first estimate of sales uncertainty six years of
prior sales through our event year of 1992 requiring the firm to have at least four years of
data. We also use 11 years of data centered around the event year requiring at least five
observations of the firm. We calculate sales uncertainty as follows: (1) regress sales on a
time trend and then calculate the standard error from the estimate for each year. (2)
square the residuals, sum them, and divide by n – 1. (3) take the square root of (2) and
then divided by the firm’s average sales to get our uncertainty estimate.
Next, we consider leverage where debt level is calculated in two different ways:
just long-term debt and then total debt as the sum of long-term debt and short-term debt.
Leverage is then determined as the debt level over the corresponding firm value (value of
debt plus the market value of equity). Debt values are reported or book values from
COMPUSTAT for long-term debt and adding the short-term debt for total debt. The
market value of equity is the fiscal year end price times number of outstanding shares.
Where closing fiscal price is not reported, the year end calendar year price is substituted.
If the item is still missing, market equity is calculated as price times shares outstanding
from CRSP data.
We estimate the firms’ beta using the following procedure. We first estimate the
firm’s equity beta using 60 monthly returns ending with the firm’s fiscal year in 1992.5
We also use the market model with daily returns for 1992 as a robust check. For both
daily and monthly returns, both equal and value weighted market returns are used to
5
When less than 60 months of data are available, we use a shorter period with a minimum of 18
observations.
22
measure market risk. Finally, we truncate the equity beta estimates at 4.0 for upside
estimates and –2.0 on low estimates to minimize the influence of extreme values.
We need the firms’ beta values and not merely equity beta values to make our
comparison. Therefore, we determine the firm’s equivalent unlevered beta value using
Hamada’s method. For the leverage value, we use total leverage as interest expenses are
tax deductible on both long and short-term debts. For the tax rate we use both the
statutory tax rate in 1992 (34%) and a 10% rate that Graham (2000) feels more closely
reflects the effective tax advantage of debt.
The last variable that we estimate is the probability of default on equity. We use
a similar approach to KMV Consulting that is based upon Merton’s equity option work to
estimate the companies’ default probability using the Black-Scholes option pricing
model. For the specific procedure used to estimate the default probability, please refer to
Appendix 2.
-Insert Tables 1 & 2 hereTables 1 and 2 present the descriptive statistics of our samples where Table 1 is
for firms in perfect competition and Table 2 is for firms operating with product market
power. Several things deserve noting from these tables. The firms with market power
are over twice as large on average as those operating in perfect competition both in value
and sales.6
6
We lose a significant number of firms for not having specific data. For example we lose about a quarter
of our samples for not having market values and another quarter for not matching with CRSP to get beta
values. As our samples are still quite large, we do not feel that this will affect our final results.
23
C.
Empirical Results
Table 3 presents the results of the two sample t-tests for the variables. We
calculate them using both pooled variances and the Satterwhite method which should be
used when the sample variances of the two groups are not equal. We feel that the
Satterwhite is probably the better statistic as the variance of the two groups are most
likely not equal. However the results are almost identical for both methods.
- Insert Table 3 here The average values (median) for the Tobins Q ratio are 1.59 (1.18) for the
competitive firms and 2.53 (1.66) for the firms with product market power. The firms
with product market power have a significantly greater Tobin’s Q, rejecting hypothesis 1
as our model predicts. This shows that firms operating with product market power earn
greater returns on their investments or have greater chances of reinvesting in projects that
earn excess returns. While our value maximizing model is under uncertainty, these
results are consistent with traditional economics theory of firms with product market
power earning excess profits.
Hypothesis 2 investigates the sales uncertainty that firms in the different
competitive situations face. Our initial model under uncertainty shows firms with market
power should face greater product demand uncertainty and thus experience larger sales
uncertainties. The mean level of the sales uncertainty of the whole period is 0.28 (0.20)
for the product market power firms but only 0.21 (0.16) for those in perfect competition.
Their differences give a t-statistics of 4.11 that allow us to reject the null hypothesis of
equality. When we estimate the standard deviation using only data prior our event year,
the sales uncertainty drops to 0.19 (0.14) and 0.17 (0.13) for firms with market power and
24
firms operating in perfect competition respectively, but the difference is still significant at
the 10% level.
Comparison of the leverage levels between the two groups also supports our
model’s prediction. As indicated in Table 3, firms operating in perfect competition
having less product market risk, use substantially more leverage than firms with market
power. The mean of the total leverage is 0.33 (0.30) for firms operating in perfect
competition versus the mean of 0.18 (0.08) for those with market power. We also
estimate leverage using only long-term debt and obtain similar results. The t-statistics are
all significant at the 1% rejecting the null hypothesis of equal leverage.
As the competitive firms use greater leverage but face a lower product market
risk, we need to compare their systematic risks. For this, we follow Hamada’s approach
to calculate the equivalent unlevered beta values. We use both the statutory tax rate of
34% and a lower rate of 10% which Graham (2000) claims to represent the effective
advantage of debt. As the results are almost identical we report only the statutory rate
values. We also calculate beta using daily data over the event year with both an equal
weighted and value weighted index as robust tests. Regardless of how we view it, we
find that the sample with market power has a significantly greater mean level of
unlevered beta than firms operating in perfect competition. This allows us again to reject
the null of hypothesis 3 in favor of the alternative.
Our next hypothesis compares the probability of default between the higher risk
product market power firms and the higher levered competitive firms. The market power
firms have an average default probability value of 0.048 (0.000225) versus the perfect
competition firms with a slightly lower average but higher median of 0.038 (0.000355).
25
These give insignificant t-statistics of less than 1.0. Thus the null hypothesis 5 cannot be
rejected supporting the trade-off theory of capital structure.
It is important to note the large differences between the mean and median values
for both groups. Obviously a few firms have a significant chance to default while most
firms have a near zero chance of default. To correct for this, we transpose the default
probability to the log of
dp
1- dp
where dp represents the original default probability measure.
This variable now spans from a negative infinity to a positive infinity. We then rerun the
two-sample t test between the two groups. We obtain a similar result as indicated in
Panel E of Table 3.
- Insert Table 4 here We also investigate the cross-section relationship between sales uncertainty with
leverage and unlevered systematic risk. The results are reported in Table 4. Panel A
indicates a strong negative relationship between leverage and sales uncertainty; the
coefficients of sales uncertainty are significantly negative no matter whether we
investigate the two samples together or separately. In the combined runs of the two
groups, we include a market power dummy of 1 if a firm has market power and zero
otherwise. This coefficient is also negative and statistically significant suggesting that
firms operating with market power tend to use less leverage even when we control for the
sale uncertainty.
Panel B shows the tests of whether the risk in product market returns is perfectly
correlated with unlevered systematic risk (unlevered beta). We use a cross sectional
regression of unlevered beta on sales uncertainty. Again we include a dummy for the
product market power group. If the regression coefficient of sales uncertainty is not
26
significantly different from 1.0, then estimates of the standard deviation of sales can be
used to approximate unlevered beta values for closely held firms and different divisions
within a multi industry firm. As we expected, our empirical results give a significant
positive coefficient, but the magnitude is just over 0.70 using betas from an equally
weighted index. The high-dummy variable is also always significantly positive with a
magnitude of just under 0.30. Thus these two factors explain a very large proportion of
variation with a firm’s systematic operating risk. However, we must reject our corollary
of a linear relationship between unlvered beta and the relative standard deviation of sales.
D. Evidence on the “call options against value”
We posit three hypotheses that certain attributes of a company lead to a higher
“option against value.” Since there is no direct way to measure our dependent variable,
the “option against value,” we look at firm survival over the next ten years (post 1992) as
a measure they did not suffer from a severe option against value. We base our analysis
on the delist code of CRSP database. All our sample firms are classified into one of
three broad groups based on their data in 2002 (10 years after 1992): still trading (336),
merged or bought out (211) and delisted (228). Firms that are merged or bought out
could have resulted from a serve drop in value as a shift in their product demand occurs,
or someone else just thought they could operate the business better. The former shows an
option against value occurring while the later would be more consistent with the
continuing firms. Therefore, we omit these firms from our analysis.
Following Shumway and Warther (1999), we recognize that CRSP data cannot be
used directly in classifying small, delisted firms. We therefore manually verify the status
of the 228 delisted firms. We find that 194 companies have sufficient data to determine
27
their status directly. A substantial number of these 194 firms showed a tremendous drop
in value over 90%, were delisted, but still operate. Firms whose market value falls by
90% or more, are classified as having an option against their value exercised and they are
put into the bankruptcy group.
Among the remaining 34 firms where 12 firms are in the high HHI group and the 22
firms in the low HHI group. Ten firms are classified as continuing operation as their
delisting code suggests an insufficient number of market makers, insufficient number of
shareholders, price is too low, or delisted at the firm’s request. The remaining 24 firms
are classified as defaulting with 14 showing a code for insufficient capital and assets.
We now investigate the relationship between the “option against value” which is
approximated by the default or continuous occurrence and the firm characteristics. We
create a dummy variable which equals 0 if the firms is still alive and 1 otherwise. We
call this dummy variable “default dummy” and use it as our independent variable. Since
the default dummy is dichotomous with 0 or 1, we use logit regression. The independent
variables include the log of sales which is used to represent firm size,7 capital intensity
which is measured as truncated gross plant and equipment over total sales8, and a high
HHI firms’ dummy, which equals 1 for product market power firms and equals 0 for
perfect competition.
We are sure whether our results are from our “option against value” idea or merely a
verification of the Merton model for bankruptcy. To test between these two alternative
explanations, we now use the estimate of the bankruptcy probability using the Merton
7
We get similar results using the log of total assets and the log of market value of equity plus bookvalue of
debt. However since our model viewed sales uncertainty, we chose sales as the magnitude for size and for
capital intensity
8
We truncate the ratio at 5% and 100% to minimize the effect of outliers. The results are similar without
truncation. We also ran with net P&E and again received similar results.
28
equity option model. The specifics of our measurement are in Appendix 2. These
estimates are quite skewed with a vast majority of firms having values near zero. To
correct for the skewness of the default probability (dp) estimate, we transpose it to a new
variable that equals the log of
dp
1- dp
. We also run a probit analysis as a robust check and
the results are consistent. Therefore, we only report the logit values in Table 5.
-Insert Table 5 HerePanel A shows the results of the logit regression without including a default
probability measure. As seen in Panel A, all the independent variables are significant
with the expected signs. The coefficient of sales is negative suggesting that smaller
companies have larger odds to go bankrupt. The coefficient of the proportion of plant
and equipment in total assets is also negative again suggesting that firms with more
capital intensity tend to have a lower “default” likelihood. The dummy for firms in the
high HHI group is also negative suggesting firms that firms operating in perfect
competition are more likely to default than firms with product market power.
However, these results in Panel A could have two different explanations. It could
result from what we refer to as the “option against value” or it could be just a verification
of Merton’s model for bankruptcy. To differentiate these two alternative explanations,
we re-run the logit regression including the bankruptcy probability measure which we
estimate from the Merton equity option model. Panel B reports the results with the
original probability measure, and Panel C demonstrates the results of the transformed
default probability estimates.
The results are consistent with Panel A. The default probability measures are
significant and positive indicating a strong positive relationship between the default
29
likelihood and the estimated default probability measures. Even though when we control
the default probability measures in Panels B and C, we still find that the size variable and
product market control dummy variables are significantly related with the default
likelihood having the correct signs. While the capital intensity variable is no longer
significant, it does still have the correct sign. These suggest again that smaller firms and
those operating in perfect competition are more likely to go bankrupt. They also suggest
that something beyond Merton’s bankruptcy model influences the likelihood of
bankruptcy that is consistent with our explanation of the “call against value.”9
V. Concluding Comments
Our paper modeled the firm under uncertainty in a two period CAPM framework.
We then empirically tested our model using manufacturing firms that operate in close to
perfect product market competition and those that have product market power.
Our work reaffirms the importance of micro economics in finance. In recent
years, the area of financial engineering has gained considerable stature in pricing
complex contingent claims. Unlike the initial Black Scholes option pricing model,
financial engineering uses little economic insight such as no arbitrage conditions in its
goal to price claims. Over the same time period, finance has expended to consider most
of the interesting topics in management with its growth into corporate governance and
managerial motivation. Other than the belief that individuals operate to maximize their
own wealth, this is only loosely connected to economic theory.
9
We also run a two stage regression with the 0 or 1 dummy for default as our dependent variablel. The
purpose of these two stage regression runs is to separate out the default effect of the Merton model. The
first run considers the default probability measure. Using the residuals are the dependent variable, we
undertake the second stage using our other variables. The results are similar and thus are not reported here.
30
We have empirically confirmed the micro economic model of the firm under
uncertainty. Our paper has stepped back to consider basic financial economics using
current data that were not available thirty years ago and at the same time making use of
the modern financial engineering approaches to estimate default probability.
Our model predicts that companies with market power tend to have a greater
market value, face more sales uncertainty, use less leverage, but have a similar default
risk to firms operating in perfectly competitive product markets. Our empirical findings
confirm our models predictions.
We also investigate the “option against value” resulting from potential real market
changes that reduce the firms’ profits and even eliminate the firms at the extreme. Using
survivorship as a proxy for the probability of an “option against value” occurring, we find
that smaller firms, and firms operating in perfect competition are more likely to
experience this product market shift and thus have a larger “option against value.” These
variables are significant even after considering their probability of default from the
Merton bankruptcy model.
The final point is that basic modeling of the firm under uncertainty is correct and
verified by the data. To make a completely accurate valuation, one must also include the
“option against value” that results from competition in the firms real product markets.
An a priori estimate of this option value must wait for another study.
31
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33
Table 1
Descriptive statistics of firms operating in perfect competition
This table presents the descriptive statistics for 1992 for firms operating in perfect competition as
represented by firms in industries with low HHI (<500) and having no reported R&D or advertising
expenditures. These values are also before any truncation or Windorizing of variables except for beta
values. There are two estimates of the normalized standard deviation of sales, one is based on the whole
sample period (1987-1997), requiring at least 5 observations, the other is based on the sub sample period
(1987-1992) requiring at least 4 observations. Unlevered betas shown in the table are calculated using a tax
rate of 34% and total leverage. The sample for the monthly beta calculation requires the company to have at
least 18 months of observations in the period of (1987-1992). The sample for the daily beta calculation
requires the company to have at least 250 observations for the year 1992. The leveraged beta was
winsorized between (-2, 4) before calculating the equivalent unlevered betas. The default probability is
calculated using Merton Equity Option model as described in Appendix 2.
Characteristic
Obs
Mean
S.D.
Median
Min
Max
Market Value (MM$)
300
375.138
1587.45
40.9895
0.0797
24202.33
Annual Sales (MM$)
411
479.640
1602.32
75.4840
0.0130
22728.00
Tobin’s Q
296
1.5945
2.0190607
1.1787
0.5413
32.2776
Normalized Standard Deviation of Sales Based on:
whole period (1987-1997)
391
0.2133
0.1868
0.1569
0.0182
1.4282
Sub-period from 1987-1992
323
0.1669
0.14960
0.1258
0.0105
1.1116
Leverage based on
Long-term debt
All debt
300
300
0.2349
0.3304
0.2196
0.2576
0.1948
0.2986
0
0
0.9082
0.9947
Unlevered Beta
Monthly, Equal weighted index
Monthly, Value weighted index
Daily, Equal weighted index
Daily, Value weighted index
201
201
206
206
0.6854
0.8336
0.6118
0.3885
0.5229
0.7153
0.5600
0.5419
0.6272
0.7728
0.5615
0.3634
-0.6478
-1.9947
-0.7097
-0.9936
3.9821
3.9821
3.9821
3.9821
220
0.03832
0.0950
0.0004
0
0.7357
Default Probability
34
Table 2
Descriptive statistics of firms operating in with market power
This table presents the descriptive statistics for 1992 of the firms operating with market power or in
imperfect competition as represented by firms in industries with high HHI (>970) and having reported
R&D and/or advertising expenditures greater than 1% of sales. These values are also before any
truncation or Windorizing of variables except for beta values. There are two estimates of the normalized
standard deviation of sales, one is based on the whole sample period (1987-1997), requiring at least 5
observations, the other is based on the sub sample period (1987-1992) requiring at least 4 observations.
Unlevered betas shown in the table are calculated using a tax rate of 34% and total leverage. The sample
for the monthly beta calculation requires the company to have at least 18 months of observations in the
period of (1987-1992). The sample for the daily beta calculation requires the company to have at least 250
observations for the year 1992. The leveraged beta was winsorized between (-2, 4) before calculating the
equivalent unlevered betas. The default probability is calculated using Merton Equity Option model as
described in Appendix 2.
Characteristic
Obs
Mean
S.D.
Median
Min
Max
Market Value (MM$)
392
999.71
2919.07
82.34
0.48
22795.33
Annual Sales (MM$)
470
1743.97
8929.07
35.97
0.01
130590.00
Tobin’s Q
393
2.5374
2.7974
1.6644
0.2684
39.0307
Normalized Standard Deviation of Sales Based on:
whole period (1987-1997)
455
0.2807
0.28594
0.1977
0.0107
1.9611
Sub-period from 1987-1992)
344
0.1921
0.19491
0.13565
0.0086
1.4119
Leverage Based on:
Long-term debt
Total debt
392
392
0.1238
0.1821
0.1788
0.2312
0.0414
0.0763
0
0
0.8907
0.9571
Unlevered Beta
Monthly, Equal weighted index
Monthly, Value weighted index
Daily, Equal weighted index
Daily, Value weighted index
249
249
275
275
1.0061
1.2503
1.3198
0.9298
0.6455
0.8405
0.9356
0.8301
0.8612
1.1336
1.1221
0.7848
-0.0274
-0.5326
-0.5043
-1.8406
3.7718
4.0000
3.9512
3.7420
300
0.0482
0.1452
0.0002
0
0.9778
Default Probability
35
Table 3
Two sample t tests
Table 3 presents the results of two sample t tests about the mean of two different HHI groups. Two ways of
estimates normalized standard deviation of sales, one is based on the whole sample period (1987-1997),
requires at least 5 observations, the other is bases on the sub sample period (1987-1992) requiring at least 4
observations. Unlevered betas shown in the table are calculated based on the tax rate of 34% and adjusted
with total leverage. The sample for the monthly beta calculation requires the company to have at least 18
months of data in the period of (1987-1992). The sample for the daily beta calculation requires the
company to have at least 250 observations for the year 1992. The leveraged beta was winsorized between
(-2, 4) before calculating the equivalent unlevered betas. The default probability is based on Merton equity
option method as described in Appendix 2. The default probability index is the transformed variable which
equals logarithm of (default probability/(1-default probability)).
Panel A: Tobin's Q
Method
Variances
DF
t Value
Pr > |t|
Straight value
Pooled
Equal
687
-7.63
<.0001a
Satterthwaite
Unequal
642
-8.2
<.0001a
Capped value at 7.5
687
642
-7.629
-8.205
<.0001a
<.0001a
844
790
-3.99
-4.11
<.0001a
<.0001a
665
640
-1.87
-1.88
0.0622c
0.0601c
690
605
7.95
7.84
<.0001a
<.0001a
690
568
7.33
7.14
<.0001a
<.0001a
448
448
448
447
479
459
479
471
-5.69
-5.82
-5.58
-5.68
-9.64
-10.32
-8.15
-8.63
<.0001a
<.0001a
<.0001a
<.0001a
<.0001a
<.0001a
<.0001a
<.0001a
Pooled
Equal
518
Satterthwaite
Not Equal
512
Default probability index
Pooled
Equal
469
Satterthwaite
Unequal
429
Note: superscript a, b, c represents significance at 1%, 5% and 10% respectively
-0.881
-0.937
0.89
0.89
0.3786
0.349
0.374
0.3733
Pooled
Satterthwaite
Equal
Not Equal
Panel B: Sales Uncertainty
Based on whole period (1987-1997), requiring at least 5 observations
Pooled
Equal
Satterthwaite
Unequal
Based on data before 1992 (1987-1992), requiring at least 4 observations
Pooled
Equal
Satterthwaite
Unequal
Panel C: Leverage
Total Leverage
Pooled
Equal
Satterthwaite
Unequal
Long Term Debt Leverage
Pooled
Equal
Satterthwaite
Unequal
Panel D: Beta
Monthly, Equal weighted, total leverage
Monthly, Value weighted, total leverage
Daily, Equal weighted, total leverage
Daily, Value weighted, total leverage
Panel E: Default Probability (KMV)
Default probability
Pooled
Satterthwaite
Pooled
Satterthwaite
Pooled
Satterthwaite
Pooled
Satterthwaite
Equal
Unequal
Equal
Unequal
Equal
Unequal
Equal
Unequal
36
Table 4
Analysis of the relationship between leverage, beta and sales uncertainty
Unlevered betas shown in the table are calculated based on the tax rate of 34% and adjusted with total
leverage. The sample for the monthly beta calculation requires the company to have at least 18 months of
data in the period of (1987-1992). The sales uncertainty is deviation from the sales trend normalized by
average sales using the whole sample period (1987-1997) with requirement of at least 5 observations 10.
Panel A: Sales uncertainty and Leverage
Dependent
Independent Variables
Whole sample
Low HHI Firms High HHI Firms
High
Sales uncertainty HHI_dummy Sales uncertainty Sales uncertainty
-0.17391
-0.13369
-0.14564
-0.18305
(<.0001a)
(<.0001a)
(0.0916c )
(<.0001a)
Leverage: total
Leverage: long term debt
-0.13619
(<.0001a)
-0.10527
(<.0001a)
-0.12744
(0.086c)
-0.13902
(<.0001a)
Panel B: Beta and Sales uncertainty
Whole sample
High_HHI
Sales uncertainty
dummy
Monthly beta, equally weighted, total
leverage
Monthly beta, Value weighted, total
leverage
Monthly beta, equally
Long term debt leverage
Low HHI Firms High HHI Firms
Sales uncertainty Sales uncertainty
0.73895
(<.0001a)
0.27529
(<.0001a)
0.64181
(0.0012a)
0.79186
(<.0001a)
0.52779
(0.0029b)
0.37193
(<.0001a)
-0.03567
(0.897)
0.83465
(0.0003a)
0.70628
(<.0001a)
0.26685
(<.0001a)
0.59151
(0.0036a)
0.76879
(<.0001a)
weighted,
Monthly beta, Value weighted, Long
term debt leverage
0.46649
0.36272
-0.12179
0.78688
a
a
(0.0091 )
(<.0001 )
(0.6736)
(0.0006a)
Note: The number under the parenthesis is the P value of test that the coefficient equals 0. Superscript a, b,
c represents significance at 1%, 5% and 10% respectively
10
Robust tests using tax =10% for unlevered beta calculation, daily beta and using the sales uncertainty,
which is calculated based on the sub-sample (1987-1992) requiring at least 4 obs, show consistent results
for beta. However, for the leverage regression, the sales uncertainty over the entire period becomes
insignificant for the low hhi group and for the whole sample overall.
37
Table 5
Analysis of the relationship between default probability and firms characteristics
This table shows the results of regressing a binary logit regression of default dummy on firms’
characteristics measures. Default dummy=1 if firms cease to exist and 0 otherwise. Truncated Net P&E is
the measure of capital intensity. It is obtained as Property and Equity Net / Net Sales and then truncated
within 0 and 1. Log of sales is the measure of size. The default probability (dp) is based on Merton Equity
Option model as presented in Appendix 2. The default probability index is the transformed variable which
equal ln(dp/(1-dp)). High HHI Firms is a dummy =1 if a company belongs to the high HHI group and 0
otherwise.
Panel A: Binary Logit Regression (without Default Probability Variable)
Odds Ratio
Parameter
Parameter Estimate
S.D.
Estimate
Intercept
1.1355a
0.3166
Truncated Net P&E
-0.8572 a
0.3632
0.424
Size
-0.4047 a
0.0527
0.667
High HHI Firms
-0.812 a
0.2318
0.444
Log Likelihood
Ratio
86.6368
Panel B: Binary Logit Regression including Default Probability Variable DP
Odds Ratio
Log Likelihood
Parameter
Estimate
S.D.
Estimate
Ratio
Intercept
0.6544
0.4743
63.3053
Truncated Net P&E
-0.2408
0.513
0.786
Size
-0.4494 a
0.0806
0.638
Default probability
4.1782 a
1.2988
65.25
High HHI firm
-0.7521b
0.3149
0.471
Panel C: Binary Logit Regression including Default Probability index Variable
Odds Ratio
Log Likelihood
Parameter
Parameter Estimate
S.D.
Estimate
Ratio
Intercept
1.3205 a
0.4936
57.333
Truncated Net P&E
-0.0399
0.5296
0.961
Size
-0.4169 a
0.0820
0.659
Default prob._index
0.0702 a
0.0226
1.073
High HHI firm
-0.7239 b
0.3180
0.485
P value
<.0001
#Obs
522
P value
<.0001
#Obs
345
P value
<.0001
#Obs
319
Note: The number under the parenthesis is the P value of test that the coefficient equals 0. Superscript a, b,
c represents significance at 1%, 5% and 10% respectively.
38
Appendix 1: Data Definitions
The data item refers to COMPUSTAT unless otherwise indicated.
Variables name
Market Capitalization
Size
Measurements
Calculated as closing fiscal year price (data199)* shares outstanding (data25). If data199 is
missing, substitute with closing calendar year price (data 24). If still missing, use CRSP
database, CAPI =PRC*SHROUT
Ln(Sale_net (Data 12))
Tobin’s Q
(total asset(data6) – book value of equity(data60) + market value of equity (CAPI) )/total asset
Sales uncertainty,
whole
Sales uncertainty,
prior
Normalized deviation from sales trend based on whole sample period (1987-1997) with a
minimum of 5 observations
Normalized deviation from sales trend based on prior sample period (1987-1992) with a
minimum of 4 observations
Sales Uncertainty
Leverage
Leverage long term
Long-term debt (data item 9) / (Total liability (data181)+ CAPI)
Leverage total
Total liability(data181) / (data181 +CAPI)
EWRETRF
EWRETRF_trunc
VWRETRF_trunc
Levered beta, based on equally-weighted market, use past 60-month data ending at the fiscal
month of year 1992. The companies with observation smaller than 18 were excluded.
Levered beta, based on valueweighted market, use past 60-month data ending at the fiscal
month of year 1992. The companies with observation smaller than 18 were excluded.
Truncated equally weighted levered beta, by –2, and 4
Truncated value weighted levered beta, by –2, and 4
Equalbeta_long:
unlevered beta based on EWRETRF_trunc, adjusted by long term leverage
Equalbeta_total:
unlevered beta based on EWRETRF_trunc, adjusted by total leverage
valuebeta_long
unlevered beta based on VWRETRF_trunc, adjusted by long term leverage
valuebeta_total
unlevered beta based on VWRETRF_trunc, adjusted by total leverage
Betas
VWRETRF
“Option Against Value”
Default probability
Default probability based on Merton Equity Option, details will be provided in Appendix 2.
Default probability
index
Transformed variable of dp which equals ln(dp/(1-dp))
Gross P&E
Property & Equipment Gross (Data8)/Net Sales(Data12)
Net P&E
Property & Equipment Net (Data7)/Net Sales(Data12)
Truncated Gross
P&E
Truncated Net P&E
Truncated PE_Gross within 0 and 1
“Capital Intensive Measures”
Truncated PE_Net within 0 and 1
39
Appendix 2: Default Probability Estimates
The last variable that we estimate is the probability of default on equity. We use a similar
approach of KMV that is based upon Merton’s equity option model which uses the Black-Scholes option
pricing formula to estimate the companies’ default probability.
According to Merton (1974), the market value of a firm equity could be calculated according to
the following formula:
E = V N (d1 ) - e - rT FN (d2 )
Where F is the face value of the firm’s debt, r is the instantaneous risk-free rate. N () is the
cumulative standard normal distribution function.
d1 =
ln(V F ) + (r + 0.5s v2 )T
sv T
and d2 = d1 - s v T
N (d2 ) is the probability that the option will be the money, therefore 1 - N (d2 ) will be the default
probability.
For the parameter F, the value of debt, we use (short term debt + total debt)/2 to approximate the
value of debt coming due.
Since V and s v represent the value of the firm and volatility of the firm value respectively, which
are not directly observable, we use the following method to estimate:
(1)
We estimate the mean of the market capitalization M which equals price times
shares outstanding from CRSP from the past 12 months.
(2)
We estimate the volatility of company’s equity using past 24-month data with the
mean obtained in (1) and then standardized to an annual volatility s E .
(3)
Minimize the cost function as (V - M )2 + ( s V - s E )2 and estimate V and s V
simultaneously.
We then substitute V and s V into the Black-Scholes formula, and assume T = 1 to estimate the
default probability of the next year, which is 1 - N (d2 ) .
40