Some aspectsof the pure
theoryof corporatefinance:
bankruptcies
and take-overs:
reply
JosephE. Stiglitz
Professorof Economics
StanfordUniversity
This paper reaffirms
the earlier argumentthat ivhenindividuals
differin their expectations concerning the returnsto investments, there v'ill be an optimal debt-equity ratio, at a
sufficiently
high debt level. It assumes that in thejudgment of
lenidersthereis a finiteprobabilityof bankruptcy.The termsat
whichindividualsas well as firmscan borrowdepends on their
indebtedness and perceptions of potential lenders. Stapleton's
analysis rests on the unacceptable assumption that individuals
can-iborrow an arbitraryamount at the riskless rate, even
though the firm in which they have all their wealth invested
cannot. A newproofof thepotentialityofproductiveinefficiency
in the presence of bankruptcyis also presented.
* Stapleton has raised an interestingpoint in his commenton
my paper.' When there is an incomplete set of securities,demand curves for differentsecuritieswill be downward sloping.
The evaluation of the securityin the marketdepends on the
evaluation placed on the securityby the marginalpurchaser of
the marginalunit of the security.These demand curves will in
general depend on the distributionof wealth, attitudestowards
risk,and assessments of the returnsto various securities. In the
analysis of Section 3 of my paper I had assumed that the marginal purchaserof the firm'ssecuritieswas an individualof type
a, i.e., somebody who was optimisticabout the fortunesof the
firm,and the marginalpurchaser of the firm's bonds was an
individualof type b, somebody who was pessimisticabout the
fortunesof the firm.This would be the case so long as the total
value of the firmexceeded the net worth of the individualsof
typea. In thatcase, the calculations showingthe dependence of
thevaluationof the firmon the debt-equityratio of the firmwere
correct. The more subtle question was, how do I know who is
the marginalindividual purchasing each security,that in this
case the valuationof the firmexceeds the net worthof individuals-of type a?
This is a more complicated question to which Section 4 of
my paper was devoted. One approach is to make some
hypothesisconcerningmarketsegmentationor separability,i.e.,
the bondholdersand stockholdersare different
individuals. For
1 See [3].
THE BELL JOURNAL
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instance, that is the interpretationof my analysis provided by
Rubinsteinand by Scott.2 But both the assumption of market
segmentationand the assumptionson no borrowingand no short
sales can be dispensed with; they were introduced,with some
distaste, to simplifythe analysis. A more complete analysis
would have introducedthe possibilityof individual borrowing
and short sales, but with the terms of those contracts determined by the lender's subjective estimationof the individual's
capacity to carryout those contracts. Thus, if individualshave
no assets of their own (or wage income) other than that described in the model, then the terms at which equity owners
could borrow would essentiallybe the same as those at which
the firmcould borrow: firmbonds would defaultin exactly the
same states of naturethatthe correspondingindividualborrowings would default. Obviously, if the individual has other
sources of income and other liabilities,firmdebt and individual
debt are not perfectsubstitutes.The equilibriumwould then be
described by, say, a type individuals borrowingon personal
account fromb typeindividuals,and individualsof typeb would
sell shortsome securitiesto individualsof typea. If individuals
of type b were riskneutral,theywould like to sell an indefinite
amount of securities short. But individuals of type a do not
believe thatindividualsof type b can meet those commitments.
Thus, an unsecured shortsale would sell at a discount, and the
discountwould increase the more the shortsales, untilthe point
is reached where the individualof typeb no longerwishes to sell
any furthersecurities short. (Risk aversion obviously puts
anotherlimiton the amount of short sales.) These possibilities
forborrowingby the individualsof typea obviously affecttheir
demand for equities and affectthe demand for the firm'sbonds
as well. It is still the case, however, that there is an optimal
debt-equityratio for the firm.
Let me now relatethese remarksto Stapleton's comments.It
is trivialthatifall the shares and debt of a firmare owned by the
same kind of individual,the decompositioninto debt and equity
makes no difference.The case analyzed by Stapleton, where
individualscan borrow an arbitraryamount at the risklessrate,
even thoughthe firmin whichtheyhave all theirwealthinvested
cannot, is one such case. It requires, however, a peculiar kind
of misperceptionon the part of the lenders-one whichis inconsistentwith the intentof the analysis.
Anotherresultof the paper which may have been the subject
of some misunderstanding
is thatrelatingto the productiveefficiency of the economy withbankruptcy.Consider firstthe case
of whether there is multiplicativeuncertaintyin the returns
(gross of interestcosts, but net of all other costs), i.e., the
returnsto a one-periodinvestmentof I can be writtenas Oh(I),
where 0 is the stochastic variable. Let ^rbe the nominalrate of
interestand B the numberof bonds. The net returnis then
max {0h(I) - (1 + ?)B1,0}.
(1)
We let F(O) be the cumulative distributionof 0, so iT, the
probabilitythe firmwill not go bankrupt,is
712 / J. E. STIGLITZ
2
In [1] and [2], respectively.
ir
1 -F(t
h(I)
Note that the ratio of B to h(I) completely determinesthe
patternof returnsof the riskybonds:
1 + r = min{(1+ r),
Hj() }
(2)
Thus, 'r will simplybe a functionof h(I)/B. An individualwho
owns a firm,who is riskneutral,and can obtain a returnof + on
some other securitymaximizes3
h(I)fOdF(O)
-
+ O(B + WO- 1),
(1 + Ar)Bir
(3)
(1 + r)Blh(I)
where W1 is his initial wealth. Hence
hlfOdf- (1 +BP)BIT =
(4)
(1+f)Blh
and
r
+ (1 + r)h
-
.h/B.
(5)
Equation (5) can be solved for h/B. Since all firmswithinthe
risk class will then have the same patternof returnsfor their
riskybonds, theywill all have to pay the same nominalrate of
interest,and it is immediatethat the marketvalue will be proportionalto h(I). Hence h/B is proportionalto the debt-equity
ratio,so that(5) can be interpretedas sayingthatall firmswithin
the risk class will have the same debt equityratio.4But then (4)
impliesthath' will be the same forall firmswithinthe riskclass:
there is productiveefficiency.
On the other hand, if there is multiplicativeuncertaintyon
output,but not on returns,or if thereis marginalmultiplicative
uncertaintyon returnsbut not inframarginal
multiplicativeuncertainty,there will in general not be productive efficiency.
Assume, for instance, that we can write net returnsof thejth
firmin a given risk class as
Ohi(I) + ci.
Productiveefficiencyclearly requiresthatif thereare two firms
producing,which are identical except for theirvalues of c&and
the shape of the hi function,
hi' = hi'.
But now, the return on the risky bond is no longer just a
functionof B/h:
B+
(1+ P) =min( nki+ ~jr) ~O/ij(I)
cj}
When the implicationsof this are traced throughthe remaining
3
0 iS the maximumreturnhe can obtain on any other security;it is the
opportunitycost of capital. Again we restrictshortsales and individualborrowing.
4 This is not preciselycorrect; since r' is not necessarilyone-signed,there
may be more than one solution to the maximizationproblem.
THE BELL JOURNAL
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analysis, it is apparentthat there will not in general be productive efficiency.
References
1.
RUBINSTEIN,
M. "Corporate Financial Policy in Segmented Markets."
Journalof Financial and Qluantitative
Analysis, Vol. I (June 1966),pp. 1-35.
2. Scorr, J. H., JR. "A Theory of Optimal Capital Structure." Draft, December 1974.
3. STIGLITZ, J. E. "Some Aspects of the Pure Theory of Corporate Finance:
Bankruptciesand Take-overs." The Bell Journal of Economics and ManagementScience, Vol. 3, No. 2 (Autumn 1972),pp. 458-482.
714 / J. E. STIGLITZ