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An EBIT-Based Model of Dynamic Capital Structure
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Authors
Goldstein, Robert S
Ju, Nengjiu
Leland, Hayne E
Publication Date
2021-06-27
Peer reviewed
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An EBIT-Based Model of Dynamic Capital Structure
Author(s): Robert Goldstein, Nengjiu Ju, Hayne Leland
Source:
The Journal of Business,
Vol. 74, No. 4 (Oct., 2001), pp. 483-512
Published by: The University of Chicago Press
Stable URL: http://www.jstor.org/stable/3045394
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http://www.jstor.org
Robert
Goldstein
Washington
University
Nengjiu Ju
University of
Maryland
Hayne
Leland
University of
California, Berkeley
An
EBIT-Based Model of
Dynamic
Capital
Structure*
I.
Introduction
Most capital
structure models
assume that
the decision
of how much debt to issue is
a static choice.
In
prac-
tice, however,
firms
adjust
outstanding
debt
levels
in
response
to
changes
in firm
value.
In
this
article,
we
solve for the
optimal dynamic
capital
strategy
of a
firm
and
investigate the implications for
optimal lev-
erage
ratios
and the
magnitude
of
the tax benefits to
debt.
Below, we
consider. only the
option to
increase fu-
ture
debt levels. While
in
theory management
can both
increase and decrease future
debt
levels,
Gilson
(1997)
finds that
transactions costs
discourage
debt
reductions
outside of
Chapter
11. In
addition, equity's
ability
to
A
model of
dynamic
cap-
ital
structure
is
proposed.
Even
though
the optimal
strategy is
implemented
over an
arbitrarily
large
number of
restructuring-
periods, a
scaling
feature
inherent
in
the
framework
permits simple
closed-
form
expressions to be
obtained for
equity
and
debt
prices.
When
a firm
has
the option
to
increase
future debt
levels,
tax
ad-
vantages to debt
increase
significantly, and both the
optimal
leverage ratio
range
and
predicted
credit
spreads
are more in
line
with what is
observed
in
practice.
*
An earlier
version of this
article, entitled
"Endogenous Bank-
ruptcy,
Endogenous
Restructuring, and Dynamic
Capital Structure,"
was
presented
at
the 1998 Western Finance
Association. Most of
the work on
this article was
completed while the first author was
affiliated with
Ohio State
University.
We would like
to thank Pierre
Collin
Dufresne,
Domenico
Cuoco,
Jean
Helwege,
Rene Stulz,
Alex
Triantis, and
seminar participants
at Duke
University and Ohio
State
University
for their
insightful
comments. We
especially
thank
an
anonymous
referee for
many
insightful comments.
Any
remaining
errors are our
sole
responsibility.
(Journal of Business,
2001,
vol.
74, no. 4)
X
2001
by
The
University
of
Chicago.
All
rights
reserved.
0021-9398/2001/7404-0001$02.50
483
484 Journal
of
Business
force concessions when the
firm is in
distress (Anderson
and Sundaresan 1996;
Mella-Barral and Perraudin 1997) may further reduce
equity's incentive to
repurchase outstanding debt.'
Compared to
an otherwise
identical
firm
that is
constrained
to a static
capital
structure decision,
a firm's
option
to
increase future debt
levels has two im-
mediate consequences. First, management will choose
to issue a smaller
amount of debt initially. This might explain why most
static models predict
optimal leverage ratios that are well above what
is
observed
in
practice.
Second,
for
a given level
of initial
debt,
bonds issued from such a
firm
are
riskier, since the bankruptcy threshold rises with the level
of outstanding debt.
This might explain why most static models predict yield
spreads that are too
low.2 While covenants are often
in
place to protect debt
holders, in practice
firms typically have the option to issue additional debt
in the future without
recalling the outstanding debt issues. Furthermore,
in
the
event of bankruptcy,
it is typical that all unsecured debt receives
the
same
recovery rate, regardless
of the issuance
date.3
Clearly,
such debt is riskier than that modeled
in
both
the "traditional" static
capital
structure
models
(e.g.,
Brennan and
Schwartz
1978; Leland 1994;
Leland
and
Toft
1996),
and most corporate bond pricing
models (e.g., Longstaff and Schwartz 1995), where
it is assumed that the
bankruptcy threshold
remains constant over time.
Interestingly,
within
our
framework, when a
firm
has the right to issue additional
debt at a specified
upper boundary, Vu,
and
it is
assumed that
all
debt
will receive the same
recovery rate
in the
event
of
bankruptcy,
then the
present
value of the current
debt issue
is
the same as
if
it were callable at
par
when
firm
value
reaches
V,.
In
this sense,
it
is
clear that such debt
is
not
as
valuable
as
debt
issued
by a
firm constrained to never issue additional debt.
This lower
price
in
turn
implies
a
higher yield spread.
Models
of
dynamic capital
structure choice have
been
proposed by Kane,
Marcus, and
McDonald
(1984, 1985)
and
Fischer,
Heinkel, and
Zechner
(1989).
Concerned with the
possibility
of
arbitrage
inherent
in
the
"tradi-
tional
frameworks,"
Fischer
et
al.
base
their model on the
following
as-
sumptions:
1.
The
value
of an
optimally
levered
firm
can
only
exceed its unlevered
1. In addition, the fact
that equity prices tend to
trend upward and that a typical maturity
structure is a quickly decaying
function
of
time
(see
Barclay and Smith 1995) makes
the
option
to issue additional debt
a more important feature
to account for than the option to
repurchase
outstanding debt.
2. The strategic debt
service literature
of
Anderson
and Sundaresan (1996) and
Mella-Barral
and Perraudin (1997) also
help explain these puzzles.
However,
if
the maturity structure
of debt
were modeled as it is observed
in
practice, i.e., a quickly
decaying maturity structure
(Barclay
and
Smith 1995),
with an average maturity
of
about
7
years (Stohs
and Mauer 1996), rather
than as a
perpetuity,
as in
Mella-Barral
and Perraudin
(1997),
then
the
strategic
debt argument
by itself
is not sufficient
to
explain
the observed
yield
spreads.
3. Longstaff and Schwartz
(1995) report that
in December 1992, GMAC had 53
outstanding
long-term debt issues
listed in Moody's Bank and
Finance Manual and
that all would likely
receive
the
same recovery rate
in the
event
of
bankruptcy.
EBIT-Based
Model
485
value
by
the
amount
of transactions
costs
incurred
in
order
to
lever
it up.
2.
A
firm
that
follows
an
optimal
financing
policy
offers
a fair
risk-
adjusted
rate
of return. Therefore,
if
leverage
is
advantageous,
then
it
follows
that
unlevered
firms
offer
a
below-fair
expected
rate
of
return.
Their
first
assumption
is
intended
to
eliminate
the
following
arbitrage
strat-
egy:
purchase
the firm cheaply,
lever
it
up,
then
sell
for
a riskless
profit.
Their
second
assumption
implies
that
tax
benefits
to debt
are to
be
measured
as
a flow,
not as
an increase
in
value.
However,
we
argue
that
these
as-
sumptions
do
not
hold
in
practice.
First,
consider
a firm
whose
(well-en-
trenched)
management
refuses
to
take
on
debt
(e.g., Microsoft).
It
would
be irrational
for agents
to push
the
value
of
the
firm
up
to
its
optimally
levered
value,
since
shareholders
are currently
not
receiving
any
tax
benefits.
Furthermore,
the
above-mentioned
arbitrage
strategy
is not
operational:
usu-
ally,
a bidder
must
pay
a large
premium
in order
to
gain
control
of
man-
agement
to
force
an optimal
capital
structure
policy
to
be
followed.
This
premium
will
typically
eliminate
any
profit
from
such
a strategy.
Note
that
this
first assumption
predicts
that
no
portion
of the premium
paid during
a
managed
buyout
is due
to
increased
tax
benefits,
since
all benefits
are as-
sumed
to
be
embedded
into the
price
before
the
buyout.
This prediction
is
in conflict
with
the
findings
of
both
Kaplan
(1989)
and
Leland
(1989).
While
the second
assumption
might
be applicable
to
an all-equity
home
owner
who forgoes
tax
benefits
that are inherent
in a
mortgage
on
a
house,4
we
argue
that
it
is not
applicable
for
publicly
traded
assets. Rather,
rational
agents
in the economy
will
push
down current
prices
so that
fair
expected
return
is obtained
on
any
traded
asset
regardless
of the policies
followed
by
management.
Kane
et al.
(1984,
1985)
and
Fischer
et al.
(1989)
obtain relatively
simple
solutions
for the
optimal
dynamic
strategy
because
their
assumptions
effec-
tively
reduce
the
analysis
to
a
one-period
framework.5
Indeed,
the
boundary
conditions
satisfied
by
the levered
firm value
in Fischer
et
al.
(1989,
eqq.
[11]-[12])
are
exactly
the
boundary
conditions
satisfied
by
a
firm that wishes
to
be
leveraged
for
just
one
single
period.
As a
consequence
of
these as-
sumptions,
Fischer
et al.
(1989)
predict
that the
tax
benefits
to debt
are
mostly
negligible
and
that
tax benefits
to debt
are
an increasing
function
of
firm value
volatility.
Both
of
these
results
contradict
the
more
direct
tax-benefit
mea-
surements
of Graham (2000)
and the
results
obtained
below.
In
this
article,
we
determine
the
optimal
capital
structure
strategy
of a
firm
when
it
has the
option
to
increase
debt
levels
in the future.
In
particular,
we
investigate
the contingent
cash
flows
for
arbitrary
capital
structure
strategies
4.
This
example
was given
by
Kane
et
al.
(1985)
to
motivate
their
assumption.
5.
Kane
et
al.
(1985)
acknowledge
so much
themselves.