Executive Summary Modigliani-Miller

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.