Executive
Summary
The economic fundament for valuation of interest tax
shields has been laid out
almost half a century ago. Modigliani-Miller (1963)
showed that a firm paying
taxes on income may lower the tax amount by resorting
to debt financing if in-
terest payments are tax deductible. These savings are
called tax shields because
debt financing shields income from taxes to some
extent. Modigliani-Miller’s
(1963) analysis influenced corporate finance theory in
various areas until present
time. Similar models which use alternative assumptions
make suggestions on how
to handle the tax shield valuation problem. Moreover,
the idea of the value con-
tribution of debt under corporate taxation is
integrated in almost every analysis
dealing with corporate financing today. Theory has
also provided several em-
pirical studies throughout the years which focus to
reveal market evidence on
interest rate tax shields. A recent study carried out
by Kemsley-Nissim (2002)
claims to find significant evidence for tax shield
values in the US market which
are even quantitatively consistent with the
implications by the basic Modigliani-
Miller (1963) analysis.
A critical investigation of tax shield valuation is
therefore justified as it is the
purpose of the paper at hand. The instructions for
what needs to be explored
are characterized by:
"Debt financing has an important advantage under the
corporate in-
come tax system in Switzerland. The interest that the
company pays
is a tax-deductible expense. In financial theory debt
is mostly treated
as constant, perpetual and particularly risk free.
Therefore the bene-
fits from future tax shields are considered to be risk
free as well. In a
real world setting tax shields are far away from being
risk free. There-
fore, traditional models with risk free interest rates
may give rise to a
significant bias in asset valuation".
How the issues raised in the instructions will be
addressed, what kind of findings
have been derived and how they need to be interpreted
will be summarized in
the following paragraphs.
The analysis starts by introducing a basic model for
interest tax shield valuation.
It is based on Modigliani-Miller’s (1963) analysis as
well as on its generalization
by Myers (1974) and will be used to demonstrate
notions of basic tax shield valu-
ation. The explicit and necessary assumptions
underlying this model will then be
subject to a critical analysis. This critical analysis
shall indicate which relevant
points regarding tax shield valuation have been
neglected and are likely to cause
bias in valuation.
A prominent point, that the basic analysis does not
integrate properly, is that
debt may by risky. Risky debt can lead to default
which causes subsequent tax
savings to be lost. Moreover, default may even be
costly which can offset a
considerable portion of the tax shield value at
present. A further simplification
with impact on tax shield values is that tax systems
are considered to be fully
symmetric. An immediate consequence of this
simplification is that the income
shielding effect of interest payments is considered to
always be fully effective even
if taxable income is negative. This is not entirely
correct in a real world setting.
Tax systems exhibit asymmetries which cause parts of
the tax benefits to be lost
if taxable income drops below zero.
An investigation of tax shield values regarding the
issues raised requires a more
comprehensive model than it is provided by the basic
setting. For this purpose,
a generic framework is proposed that puts tax shield
valuation in a dynamic en-
vironment and integrates default and asymmetric tax
systems. The framework is
comparable to several other models dealing with
related issues and it directly in-
corporates ideas from some of them. Mauer-Triantis’
(1994) work on interactions
between financing and operating decisions provides the
idea for the firm’s activity
model. The two authors consider a firm that produces
at fixed costs of production
a single commodity which it sells on the market. A
source of techniques to lever
a firm with debt was found in the capital structure
model by Brennan-Schwarz
(1978) as well as in the related but more general
analysis by Leland (1994).
We will incorporate Mauer-Triantis’ (1994) idea of a
firm operating in a single
commodity market into a binomial framework. The
commodity price is assumed
to follow a binomial process which determines the
firm’s net sales. Then, fixed
costs of production are imposed to get a process for
operational cash flows. In
pricing these cash flows the value of the unlevered
firm will be obtained. The
model then allows debt financing through defining a
firm’s debt policy as interest
expenses and debt repayment schedules. A consequence
of implementing debt in
such a dynamic framework is that default inevitably
comes into play. Default
will be accounted for by distinguishing scenarios of
unprotected and protected
debt with according rules defining when default
occurs.
An immediate advantage of the binomial model for the
system’s time-uncertainty
structure is that the interrelated cash flow streams
to the different value com-
ponents of the levered firm can be identified in
isolation. Thus, it is possible to
apply the usual binomial valuation procedure to value
debt, interest tax shields
and bankruptcy costs separately without loosing the
interdependencies among
them. In addition, it is possible to influence a
particular cash flow stream di-
rectly if necessary. This will be exploited by
influencing future tax shield amounts
according to exogenously given asymmetries in the tax
system. Equipped with
this generic framework it is possible to reconsider
tax shield valuation by more
realistic means.
The subsequent numerical analysis focuses on the
implementation of a long term
coupon bond in the framework in a similar way as it
has been considered by
Brennan-Schwartz (1978) and Leland (1994). The
valuation of the interest tax
shield is explored by assuming a reasonable base case
scenario characterizing
the firm’s operations and capital structure decision.
We will illustrate how the
present value of the interest rate tax shield behaves
under different calibrations
of the base case scenario regarding protected and
unprotected debt, symmetric
and asymmetric tax systems and the influence of
bankruptcy costs.
In addition to that the model will be used as a
rigorous benchmark for closed
form formulas calculating the tax shield value as they
are provided by the basic
valuation theory. A first object of comparison is the
tax shield value that is ob-
tained when debt is assumed to be risk free implying
that the risk free rate is the
discount rate for the stream of tax savings. Another
approach proposed by basic
theory considers default and therefore applies the
cost of risky debt as a discount
rate for tax shields. The results can again be
referred back to the framework in
order to validate their performance.
The results obtained by numerical analysis are widespread.
It is found that the
relative tax advantages of debt financing first
increase and then decrease in the
amount of debt employed. This behavior of leverage
premiums is entirely caused
by default when assuming there are no bankruptcy
costs. A raise in debt em-
ployed increases the possibility of default and more
tax shields are expected to
be lost. At a certain point of leverage the amounts of
tax shields lost exceeds
the amount that is additionally generated by debt and
value premiums cease.
The reduction of leverage premiums by default is
stronger for protected than for
unprotected debt because default is triggered earlier
due to debt protection. By
introducing asymmetries in the tax system, the
influence of default will be sus-
tained but tax shield values get additionally damped
by loss in tax savings when
taxable income becomes negative.
If bankruptcy starts to become costly, the value
effect of debt is not solely deter-
mined by the present value of the interest tax shield
but also by the present value
of bankruptcy costs. Tax shield values are offset by
the present value of the costs
that occur in the event of default. Leverage premiums
are still first increasing
in the amount of debt employed but the switch to
decreasing premiums occurs
already on smaller levels of leverage. If too much
debt is employed default will
be expected in near future which causes positive
premiums to turn into leverage
discounts.
In exploring different combinations of the forces
influencing tax shield values, a
wide range of leverage premiums can be detected. To
characterize the results, it
is convenient to use the maximal possible leverage
premiums as reference points.
If the model is calibrated in a for tax shields
favorable way fairly high maximal
leverage premiums are found. But more restrictive
scenarios can cut them down
substantially even in the absence of bankruptcy costs.
On a qualitative level, the results obtained by the
framework do clearly coincide
with the models provided by Brennan-Schwartz (1978)
and Leland (1994) when
similar scenarios are investigated. They are even
quantitatively comparable if
the differences in the model setups are taken into
account. Moreover, the par-
ticular implementation of the asymmetries in the tax
system as considered by
the proposed framework even allows investigating tax
shield valuation in more
restrictive scenarios than the two related models.
The framework is used as benchmark for the approaches
which either use the
risk free rate or the cost of risky debt as the
discount rate for the tax shields
and detects a poor performance in situations where
risks in tax shields come into
play. Results are only satisfying if leverage is low
and the influence of risks in
tax shields are negligible. As default and asymmetric
tax systems become rele-
vant the results of the basic approaches start to
deviate on a large scale from the
”true” tax shield values determined by the framework.
Even the use of the cost
of risky debt as the discount rate of tax shields
poorly captures the influence of
default on tax shield values.
A lot of space is left for further research. The
particular type of leverage scenario
were using a coupon bond requires an additional
investigation on the sensitivi-
ties of tax shield values with respect to the various
base case parameters. Fur-
thermore, the framework may provide a solid fundament
to explore other debt
instruments or policies. It is left open for
investigation if numerical analysis is
capable to overcome path dependencies that are
established in the framework
by modelling dynamics in future debt levels. Finally,
it is appropriate to check
the model implications against real world data. A
consequence of good model
performance would be to explore its implications on
other fields in finance such
as optimal capital structure considerations and the
pricing of risky debt.
