Interest deductibility restrictions and organizational form
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Abstract
Using a theoretical model for risky investment decisions, we study the effect of interest deductibility restrictions on the choice of organizational form. We analyze the two most widely used approaches: first, rules that limit the interest deductibility if the firm’s leverage exceeds a specific level, and second, rules that restrict the interest deduction if the interest expenses exceed a specific percentage of the firm’s earnings. Although these restrictions apply uniformly for partnerships and corporations in many countries, we find that they usually distort the choice of organizational form. We demonstrate that only leveragebased interest deductibility restrictions can in theory be modified to achieve organizational form neutrality. However, this requires a legal form dependent application or absence of dividend taxation and in any case a full loss offset which is in contrast to current law in many countries. If one considers corporate loss offset limitations, both types of interest deductibility restrictions always distort the choice of organizational form. Thus, the introduction of interest deductibility restrictions is actually in conflict with the legislators’ often declared aim to design tax systems that are neutral with respect to the choice of organizational form.
Keywords
Thin capitalization Organizational form neutrality Choice of legal form Liability limitationJEL Classification
G3 H25 K34 M211 Introduction
In most countries, dividend payments are nondeductible for tax purposes whereas interest payments are. The different tax treatment of dividends and interest can create an incentive to use debt. To combat the excessive use of debt financing, many countries recently introduced new interest deductibility restrictions (see e.g., Webber 2010). Whereas prior rules only limit the deductibility for interest on relatedparty debt, there is a trend to extend the deductibility restriction to all interest payments including arm’slength payments (e.g., Australia, Belgium, Denmark, Germany, and Italy). Moreover, the new rules often apply not only to corporations but also to partnerships and sole proprietorships (e.g., Australia, France, and Germany). The approaches to determine excessive debt, however, differ from country to country. Mainly two approaches are used: most thin capitalization rules limit the deductibility of interest expense if the amount of debt exceeds a specific leverage ratio. Instead of the leverage ratio, earningsstripping rules specify an interest coverage ratio. In this case, interest expense is only deductible up to a certain percentage of the earnings before interest, taxes, depreciation, and amortization (EBITDA).
While there is a large body of research on the effect of taxes on capital structure decisions that has recently been reviewed by Feld et al. (2013), there are only a few studies investigating the economic effects of interest deductibility restrictions (IDR). Maßbaum and Sureth (2009) consider thin capitalization rules that are characterized by a given permitted debtequity ratio and investigate its impact on firms’ financing decisions using the capital structure model of Miller (1977). They show theoretically that thin capitalization rules may help explain why firms issue both debt and equity even if the former is generally privileged by the tax law. Empirical studies confirm the effectiveness of the leveragebased IDR to reduce firms’ debt ratios (e.g., Overesch and Wamser 2010; Buettner et al. 2012) and indicate a negative effect on firms’ real investments (Buettner et al. 2006). Moreover, also the effectiveness of the EBITDAbased IDR is studied. Maßbaum et al. (2012) use the German interest ceiling rule to theoretically study the impact on firms’ capital structure choices. They find that the deduction restrictions often, but not always reduce the benefit of debt financing. Empirical evidence indicates that the German rules indeed lead to lower debt ratios and interest payments (Buslei and Simmler 2012; Dreßler and Scheuering 2012) while there is yet no evidence on a negative shortterm effect on real investments (Buslei and Simmler 2012).
Although in many countries IDR are applied uniformly to partnerships and corporations, previous economic research has studied only the effect on corporations. One exception is the work of Schmidt (2010) who compares the effect of the German interest ceiling rule on the effective tax rate for partnerships and corporations using numerical examples. However, she neglects tax differences resulting from differences in liability restrictions between organizational forms and does not carry out any formal analysis. Also, the large international literature on how corporate taxes affect organizational form decisions (e.g., Edmark and Gordon 2013; Elschner 2013; Luna and Murray 2010) does not yet examine the impact of IDR.
The aim of the current paper is to fill this research gap by studying the effect of IDR on the choice of organizational form. Our contribution is to show that IDR not only distort capital structure and investment decisions, but, in general, also distort the choice of organizational form, even if the IDR are uniformly applied to corporations and partnerships. Only under very specific assumptions outlined in Sect. 3.1, IDR do not affect the choice of organizational form. Thus, IDR are typically in conflict with the legislators’ declared aim to design tax systems that are neutral with respect to the choice of organizational form. Note that in the following analysis we do not argue for or against organizational form neutrality, rather we simply assume that the legislator aims at achieving this kind of neutrality. This assumption is in line with several statements of legislators (Wagner 2006: 101). The claim for organizational form neutrality also finds support by economic researchers estimating the efficiency losses resulting from tax systems that are nonneutral with respect to the organizational form (e.g., Gravelle and Kotlikoff 1993; Goolsbee 1998). However, we acknowledge that there is an ongoing controversial discussion about the desirability of organizational form neutrality (e.g., Wagner 2006; Ewert and Niemann 2012).
For the purpose of our study we extend a model previously used by Blaufus and Hundsdoerfer (2008) and Blaufus and Mantei (2014) to incorporate leveragebased as well as EBITDAbased IDR. In a baseline model we will assume full loss offset, full deductibility of interest expenses as well as full taxability of default gains and show that this will lead to organizational form neutrality if tax rates for both forms are identical. Integrating IDR in the model, we find opposing effects: first, a dividend effect which privileges the corporation due to the fact that IDR increase only the corporate income tax burden but not shareholders’ taxes. Second, a default gain effect which arises if default gains and interest expenses are treated asymmetrically. If default gains (arising due to failure in debt redemption) are taxed to a higher extent than interest is deductible, this discriminates against the corporation. We demonstrate that organizational form neutrality can only be achieved in the case of leveragebased IDR and requires a full loss offset, a symmetric treatment of interest and default gains as well as either a legal form dependent IDR or absence of shareholder taxation which is in contrast to actual legal regulations. If we consider corporate loss offset restrictions, IDR always distort the choice of organizational form.
The remainder of this paper is organized as follows: in the next section we present the baseline model assuming full interest deductibility. Subsequently, we present the incorporation of leveragebased and EBITDAbased IDR and derive the effects on the choice of organizational form analytically. Section four extends the model with respect to corporate loss offset restrictions. In the fifth section, we provide numerical illustrations using a Monte Carlo simulation to examine the effects of changing leverage ratios, riskfree interest rates, and investment risk on tax differences between corporations and partnerships caused by IDR. The last section presents conclusions and discusses implications for tax policy and research.
2 Baseline model with full interest deductibility and full taxability of default gains
We consider a oneperiod model under uncertainty. Risk neutral investors found a company for a unique risky investment opportunity of size \(I_{0}\) at time \(t=0\) and decide about its legal form (\(lf\)). They can choose between a corporation (\(lf=c\)) with liability limited to the invested amount and a partnership (\(lf=p\)) with unlimited personal liability. We use the subscripts \(c\) and \(p\) to denote either legal form, and the subscript \(lf\) for the general case. The real investment is financed with debt amounting to \(\lambda I_{0}\) and equity amounting to \(\left( 1\lambda \right) I_{0}\), with exogenous \(0<\lambda \le 1\). Without loss of generality, we scale the initial investment expenditure to \(I_{0}=1\). Debt capital is offered by risk neutral creditors on a competitive capital market that is free of arbitrage. We assume that debt is offered by thirdparties and exclude internal debt from our analysis. Riskfree capital is available at the riskfree interest rate \(r_{f}\) and risky capital at an interest rate \(i>r_{f}\).
At time \(t=1\), the project results in a gross return of uncertain cash flows \(x\ge 0\), and debt service \(D_{lf}(x)\) (debt amortization plus interest) as well as a tax payment \(T_{lf}(x)\) are due. A corporate income tax \(T_{\rm cit}(x)\) and a shareholder level tax \(T_{s}(x)\) sum up to the total tax burden \(T_{c}(x):=T_{\rm cit}(x)+T_{s}(x)\) for corporations, while partnerships are treated as passthrough entities and taxed with personal income tax \(T_{p}(x)\). Once all payments are made, the firm is liquidated.
The cash flows’ probability distribution \(f(x)\) is independent of the legal form and \(x\) may or may not suffice to cover the firm’s liabilities. If the investors choose a partnership, we assume the potentially outstanding amount to be covered by sufficient collateral from private wealth. Liabilities are, therefore, always completely met and debt capital is available at the riskfree interest rate \(r_{f}\). The partnership’s payment to the creditors is independent of the project’s uncertain return, \(x\), and amounts to the constant \(D_{p}:=\lambda \left( 1+r_{f}\right) \).
Exogenous parameters are the investment amount \(I_{0},\) the leverage \(\lambda ,\) the riskfree interest rate \(r_{f}\) as well as the tax rates and the later introduced IDR parameters. Endogenous and certain are the riskfree debt service \(D_{p}\), the later introduced critical cash flows \(x_{\rm DG}\), \(x_{2p},\) \(x_{2l}\) and the dividend effect. All other variables including the risky interest rate are stochastic.
2.1 Assumptions on taxation

Full capitalization of the investment expenditure \(I_{0}\) in \(t=0\) and full depreciation in \(t=1\).

Proportional tax rates \(\tau _{lf}\).

Full and immediate loss offset. (This assumption is weakened in Sect. 4.)

Debt capital is redeemed before interest is paid.

Full deductibility of interest expenses.

Full taxability of default gains.
The taxation of the creditors’ interest income has no impact on the creditors’ calculus in (3) and is, therefore, neglected. To see this, assume that interest income is taxed at rate \(\tau _{i}\) and the creditors’ expected net payment is thus \(D_{p}^{\rm net}=\lambda (1+r_{f}(1\tau _{i}))\) in case of a partnership and \(E[D_{c}^{\rm net}]=\lambda +E[D_{c}\lambda ]\cdot (1\tau _{i})\) in case of a corporation. Now note that the term \((1\tau _{i})\) is cancelling out in \(E[D_{c}^{\rm net}]\mathop {=}\limits ^{!}D_{p}^{\rm net}\), resulting in condition (3) from above.
2.2 Expected tax payments
3 Interest deductibility restrictions (IDR)
To analyze an IDR, one has to specify the cases in which interest payments do and do not occur. While the partnership’s interest payment is certain and does not depend on the project’s return, the corporation’s interest payment or default gain do depend on the realization of \(x\). As long as \(x<\lambda +T_{\rm cit}(x)\), the corporation not only fails to pay any interest, but moreover realizes a default gain for paying back less than the nominal debt amount. For \(x>\lambda +T_{\rm cit}(x)\), debt capital is fully redeemed and interest paid at least partially. Full interest payment requires \(x\ge \lambda (1+i)+T_{\rm cit}(x)\). We define \(x_{\rm DG}\) and \(x_{0}\) as the critical gross returns that distinguish between the three cases, as is illustrated in Fig. 1.
3.1 IDR based on leverage ratio
3.1.1 General model
To simplify the comparison of \(E\left[ \Delta T_{p1}\right] \) and \(E\left[ \Delta T_{c1}\right] \) we solve \(E[{\rm IDR}_{1}(x)]\) in (11), rearrange the result, use that \((1\tau _{s})\tau _{\rm cit}=\tau \tau _{s}\) and obtain:
Lemma 1
All omitted proofs can be found in the "Appendix".
The first term, AT, represents the additional tax burden when a symmetric default gain exemption is assumed, i.e., \(\alpha '=\beta '\), and when dividend taxation is neglected. AT is constant and matches the partnership’s additional tax. For any positive shareholder tax rate \(\tau _{s}>0\), the second term is nonzero and countervails the additional tax burden with a negative ’tax factor’ \(\tau _{s}.\) We call this the dividend effect. For any \(\beta '\ne \alpha '\), i.e., asymmetric treatment of default gains, the third term becomes nonzero, which expresses the change in total tax burden caused by the asymmetric treatment. The effect’s sign depends on the relation of \(\alpha '\) and \(\beta '\).
3.1.2 Symmetric treatment of interest and default gains
We first consider symmetric treatment of interest and default gains (\(0<\alpha '=\beta '\le 1\)) in a tax system where dividends are taxexempt (\(\tau _{s}=0\)). Second, we consider a tax system where dividends are taxed at a rate \(\tau _{s}>0\).
Within our model framework, the following propositions hold:
Proposition 1
In a tax system with symmetric treatment of interest payments and default gains and without shareholder level taxation, investors are indifferent between a partnership and a corporation.
Proof
Note that the depicted equality holds for the expected values only. For any given \(x\), the actual tax payments do generally differ between the two forms.
The intuition for the organization form neutrality is as follows: The tax exemption of default gains works as a compensation for the interest deductibility restrictions. If interest and default gains are treated symmetrically for tax purposes, this ensures that the expected payments to the creditors are (partly) tax deductible. As the expected payments to the creditors do not depend on the legal form in our model, the effect of the IDR is the same for corporations and partnerships as long as no other tax difference (e.g., dividend tax) exists.
Proposition 2
In a tax system with symmetric treatment of interest and default gains and with shareholder level taxation, investors choose a corporation.
Proof
Integrating dividend taxation into a former neutral tax system with symmetric treatment of interest and default gains distorts the choice of organizational form. The allocation of the tax burden onto corporate level and shareholder level causes an advantage for the corporation that can, however, be compensated by adjusting the IDR’s parameters. To ensure neutrality of the tax system, the IDR’s design has to account for the organizational form. The partnership’s disadvantage due to the higher tax rate on firm level must be compensated by a lower restriction factor.
Within our model framework, the following proposition holds:
Proposition 3
In a tax system with symmetric treatment of interest and default gains and with shareholder level taxation, there exist specific \(\alpha _{p}'\ne \alpha _{c}'\) for partnerships and corporations such that investors are indifferent between a partnership and a corporation.
Proof
3.1.3 Asymmetric treatment of interest and default gains
We now consider asymmetric treatment of interest and default gains, \(\alpha '\ne \beta '\in [0,1]\), first in a tax system where dividends are taxexempt (\(\tau _{s}=0\)), and subsequently in a tax system where dividends are taxed at a rate \(\tau _{s}>0\).
Within our model framework, the following propositions hold:
Proposition 4
In a tax system with asymmetric treatment of interest and default gains and without shareholder taxation, investors choose a corporation if \(\alpha '<\beta '\) and a partnership if \(\alpha '>\beta '\).
Proof
The DG effect is a measure for discrimination. If it is positive (negative), corporations are ceteris paribus relatively discriminated against (privileged). Discrimination of an organizational form thus depends on the taxable treatment of default gains.
Proposition 5
In a tax system with asymmetric treatment of interest and default gains and with shareholder level taxation, investors choose a corporation if \(\alpha '<\beta '\) . For \(\alpha '>\beta '\) , the investors’ choice depends on the cash flows’ distribution assumption.
Proof
Proposition 6
For \(\alpha '\ne \beta '\), \(\tau _{s}\ge 0\) and \(0<\tau _{\rm cit}<1\) , there exist in general neither specific \(\alpha _{p}',\alpha _{c}'\) , nor other parameter modifications such that the investors are indifferent regarding the legal form.
Proof
A tax regime that is neutral to the choice of legal form for any possible distribution assumption requires that one form’s expected tax burden does not depend on the cash flow distribution if the other’s does not either. From (10) we know that the partnership’s expected tax burden is constant, i.e., does not depend on the distribution of \(x\). We have just seen that the dividend effect is constant, too, but the default gain effect in general is not. We now further analyze the default gain effect and show that no parameter tweaks can change this result. Given this, the tax system cannot be neutral.
Lemma 2
The default gain effect is the product of a tax factor, the expected shortfall in cash flows in case of \(x<x_{\rm DG}\) and the probability of \(x<x_{\text {DG}}\). The legislator can specify the tax factor, but obviously not the distribution dependent factors. The tax factor is zero if and only if \(\tau _{\text {cit}}=0\) (no corporate level taxation), \(\tau _{\text {cit}}=1\) (100 % taxation on corporate level), \(\tau _{s}=1\) (100 % taxation on shareholder level) or \(\alpha '=\beta '\) (symmetric treatment of interest payments and default gains). For any other parameters, the tax factor is nonzero and the DG effect is distribution dependent.\(\square \)
3.2 IDR based on EBITDA
Instead of defining a maximum admissible debt ratio, some tax jurisdictions limit the fraction of net earnings to be admissibly spent on interest. We consider an IDR that permits interest deduction up to the fraction \(\gamma >0\) of earnings before interest, taxes, depreciation and amortization (EBITDA). Exceeding interest payments are nondeductible. Typical values for \(\gamma \) are 30 % (Germany since 2008 and Italy) and 50 % (United States, applied as an additional condition after the debttoequity test). In line with our baseline model, we assume full depreciation of the investment expenditure at \(t=1\) with the result that the EBITDA equals the cash flows \(x\). The maximum amount of deductible interest expenses is thus \(\gamma x\) and the nondeductible interest amounts to \(\max \{D_{lf,2}(x)\lambda \gamma x;\,0\}\). Hence, the effectiveness of this IDR and, therefore, the additional tax burden, too, depend on the realization of \(x\): as \(x\) increases, the admissible amount of deductible interest increases. Note that in contrast to Sect. 3.1, the parameter \(\gamma \) denotes the deductible fraction of the EBITDA.
Within our model framework, the following proposition holds:
Proposition 7
In a tax system where interest deductibility is restricted to a fraction \(\gamma \) of EBITDA, the investors’ choice of organizational form depends on the cash flows’ distribution.
Proof
While the partnership’s interest payment \(\lambda r_{f}\) is certain, the deduction limit \(\gamma x\) is not. We define \(x_{2p}\) as the critical cash flow that just allows the partnership to deduct the whole interest, i.e., \(x_{2p}:=\frac{\lambda r_{f}}{\gamma }\). For \(x\ge x_{2p}\) (\(x<x_{2p}\)), interest expenses do not exceed (do exceed) the admissible amount \(\gamma x\). For \(x=0\), the admissible amount is zero and interest expenses are fully nondeductible.
If the IDR is instead effective for the corporation for some \(x\), one must determine the condition on \(x\) for the effectiveness. We define \(x_{2}\) as the minimum cash flow that allows full debt service, i.e., \(x_{2}:=\inf \{xD_{c2}(x)=\lambda (1+i)\}\). The excess interest, \(D_{c2}(x)\lambda \gamma x\), reaches its maximum at \(x_{2}\), because the actual interest remains constant from there on as the allowance limit further rises. It eventually becomes zero at \(x_{2u}:=\inf \{xD_{c2}(x)\lambda \gamma x=0,x>x_{2}\}\), which is an upper bound for the effectiveness of this IDR, similar to \(x_{2p}\) for the partnership. In case of default (\(x<x_{2}\)), there are three sub cases: no interest payment occurs if \(D_{c2}\left( x\right) \lambda \le 0\), thus, the restriction in interest deductibility cannot lead to an additional tax payment. For \(0<D_{c2}\left( x\right) \lambda <\lambda i\), interest liabilities are partly paid, but the IDR causes an increase in the tax base only if also \(D_{c2}\left( x\right) \lambda \gamma x>0\). We define \(x_{2l}:=\inf \{xD_{c2}(x)\lambda \gamma x\ge 0\}\), which is the lower bound for the IDR’s effectiveness.
Lemma 3
The impact on the advantageousness of a legal form is ambiguous. Without further knowledge on the cash flows’ probability distribution, it is undetermined if \(E[\Delta T_{c2}]>E[\Delta T_{p2}]\) or vice versa.\(\square \)
To further explain the occurring effects, we use \(x_{2p}\) from above and \(x_{2r}:=\inf \{xD_{c2}(x)\lambda \ge \lambda r_{f}\}\) that distinguishes between the cases where the corporation’s interest payment is greater or smaller than the partnership’s. If \(x_{2r}<x<x_{2u}\), the corporation’s additional tax payment exceeds the partnership’s due to the higher interest payment, as illustrated in Fig. 2. This risk premium effect discriminates against the corporation. If \(x<x_{2r}\), the corporation’s additional tax payment falls below the partnership’s, and it is even zero for \(x<x_{2l}\). This default effect, which privileges the corporation, is driven by the fact that the partnership is mostly hit by the IDR when cash flows are below the default threshold and the investors have to stand in for the interest payment. The magnitude of both effects and, therefore, the total impact of the IDR on the choice of organizational form depends on the distribution of the gross return \(x\).
4 IDR in the presence of a loss offset restriction (LOR)
The so far applied model assumes a full and immediate loss offset, resulting in a negative tax base when cash flows are small. While the actual due tax amount cannot be negative in most jurisdiction, taxable losses can usually be offset against income from other sources and future profits. Full loss offset may, therefore, be a realistic assumptions for sole proprietorships and partnerships. Opposed to that, a defaulting corporation can make use of its taxable losses usually only in instances where the sole corporate body is reused in another business, such as in shell company acquisitions. This is where loss offset restrictions (LOR) apply in many tax jurisdictions. This section assumes that shareholders and partnerships can, but corporations cannot offset taxable losses. This extends the presented model with a loss offset restriction rule that averts a negative assessment basis on corporate level such that \(T_{\text {cit*}}(x)\ge 0 \, \forall \, x\). Variables and functions in this section are marked with the subscript “\(*\)” to denote that a loss offset restriction applies.
4.1 Adjusted baseline model
Interaction between loss offset and interest deductibility restrictions is analyzed in the following.
4.2 Introduction of IDR
Lemma 4
As in the model with full loss offset in Sect. 3.1, AT is the additional tax caused by the leveragebased IDR when legal form specific effects are neglected, and the dividend effect reduces a corporation’s tax burden as compared to a partnership.
In combination of the LOR with the leveragebased IDR, an interaction effect results: in loss scenarios where the tax base is already negative, the IDR would only reduce tax refunds which are already excluded by the LOR. This effect is pro corporation because it renders the IDR partially ineffective for corporations. Thus, the disadvantage of the corporation compared to the partnership decreases. Furthermore, a symmetric treatment of interest and default gains that partially exempts default gains from taxation is no longer possible in the presence of an LOR (DG effect is always present). This is because an exemption would only add to an existing tax refund, which again is excluded by the LOR. This effect is contra corporation. Another contra corporation effect is that the excluded tax refunds in loss scenarios increase the expected default gain and thus the default gain effect. Creditors have to be compensated by paying a higher risk premium, to keep the expected creditors’ return constant.
Proposition 8
In a tax system with a loss offset restriction on corporate level, the introduction of a leveragebased IDR has an arbitrary effect on the investors’ choice of legal form depending on the cash flows’ distribution assumption.
Proof
It is analytically undetermined which of the counteracting and distribution dependent effects (dividend and interaction effects vs. default gain effect) stands out. The higher the probability that \(x\in [\lambda ,1+\lambda i]\), the more does the interaction effect reduce the LOR effect, pronouncing the corporation’s privilege from the dividend effect. Contrary to that, if \(P(x<\lambda )\) is sufficiently large, the default gain effect may overcompensate the dividend and interaction effects and turn the privileging into a discrimination of corporations. \(\square \)
Figure 4 illustrates the LOR tax as the area between the tariff function \(t_{1*}(x)\) and the abscissa.
The implication of Proposition 8 is that a leveragebased IDR cannot be neutral to the choice of legal form if an LOR on corporate level is present.
Next consider an EBITDAbased IDR:
Lemma 5
An EBITDAbased IDR is effective for a corporation with LOR if and only if \(\frac{\gamma }{1\gamma }<\lambda i\).
In a setting with an LOR, an EBITDAbased IDR is thus mostly ineffective, unless the \(\gamma \) parameter is utterly small or the firm is highly leveraged. Introducing the IDR in a tax system where only corporations are subject to an LOR, therefore, adds a stronger burden on partnerships than on corporations. The following analysis assumes \(\frac{\gamma }{1\gamma }<\lambda i\).
Lemma 6
If \(\gamma >i\) , an EBITDAbased IDR is ineffective in default scenarios, because \(x_{2t*}>x_{2*}.\)
Lemma 7
Proposition 9
In a tax system with a loss offset restriction on corporate level, the introduction of an IDR that limits deduction of interest to the fraction \(\gamma \) of EBITDA has an arbitrary effect on the investors’ choice of legal form depending on the cash flows’ distribution assumption, if the IDR is binding for a corporation and if the deduction parameter \(\gamma \) exceeds the risky interest rate \(i\).
5 Numerical illustrations
Sections 3 and 4 show that there are a number of cases where the outcomes depend on the assumed probability distribution of cash flows. The aim of this section is to illustrate the analytically found effects for reasonable parameter settings and distribution assumptions using German tax facts and gross return data from German firms as an example.
5.1 Setup
Tax parameters Following German tax law, we assume a corporate tax system with shareholder relief, where a corporate income tax rate of \(\tau _{\text {cit}}:=30\,\%\) is imposed on corporate level and a dividend tax of \(\tau _{s}:=25\,\%\) on shareholder level, which results in a total tax burden of \(\tau _{c}:=\tau _{\text {cit}}+\tau _{s}(1\tau _{\text {cit}})=47.5\,\%\). Partnerships are treated as passthrough entities and pay a personal income tax rate \(\tau _{p}\). We set \(\tau _{p}=\tau _{c}=:\tau \) so as to achieve neutrality in the baseline model.
Interest deductibility restrictions The IDR with a leveragebased restriction exhibits distribution dependent effects in the case of \(\tau _{s}>0\) (positive dividend taxation) and \(\alpha '>\beta '\) (asymmetric treatment of default gains). We now focus on this case and set \(\beta '=0\) (default gains are fully taxable) and \(\alpha =1.5\), which allows for a debttoequity ratio of 1.5 to 1, equivalent to a debttototal assets ratio of 60 %, and excludes interest expenses on exceeding debt from deduction. This is a typical allowance limit applied by a number of tax jurisdictions including France, the United States, and until 2008 also Germany. Other countries implemented the same rule with different debttoequity ratio limits, among them Canada (2 to 1), Japan and New Zealand (3 to 1), the Netherlands, Latvia and Lithuania (4 to 1) as well as Luxembourg (6 to 1). For a broader overview of allowance limits refer to Webber (2010).
The IDR’s impact on the choice of legal form splits up into two components, a dividend effect and a default gain effect. From the theoretical analysis we know that in the considered scenario (\(\tau _{s}>0\), \(\alpha '>\beta '\)), the default gain effect puts a higher burden on corporations, whereas the dividend effect always gives an advantage to corporations over partnerships. The choice of legal form depends on which effect stands out. The allowance parameter \(\alpha \) determines the total effect’s magnitude, but not the direction. If an IDR turns out to discriminate against one legal form, a higher \(\alpha \) results in a lower \(\alpha '\) and less discrimination, but cannot result in an advantage for the very legal form. We keep \(\alpha \) constant and vary \(\lambda \) between 0 and 1 to analyze which of the two effects usually stands out and which legal form is advantaged when realistic parameters are assumed.
The second common interest disallowance rule is one that limits the net interest expenses to a fraction \(\gamma \) of EBITDA. Typical values for \(\gamma \) are 30 % (Germany since 2008, Italy) and 50 % (United States, applied as an additional condition after the debttoequity test). In line with the current German law, we use a parameter value of \(\gamma =30\,\%\).
Interest rates Debt capital for a partnership with unlimited liability is available at the riskfree interest rate \(r_{f}\). Empirical rates are taken from defaultfree zero coupon bonds with term to maturity of ten years, as estimated by Deutsche Bundesbank for the debt securities market (Listed Federal securities, Svensson method). The ten year term is an estimate for an average loan period. We use 2012’s average daily value of 1.686 % for the riskfree interest rate \(r_{f}\). To test robustness, we present sensitivity analyses with varying \(r_{f}\).
The risk premium for a corporation with limited liability is endogenously determined by the condition \(E[D_{c}(x)]=\lambda (1+r_{f})\). This is one of the main contributions from the simulation: while there is no analytical solution to the endogenous interest rate, a numerical approximation is readily available at high precision. The lack of an analytical solution is caused by the fact that the relevant probability distributions, such as the normal distribution or Levy alphastable distributions have no closed form solutions for the cumulative distribution functions. Note that the probability of default is, too, endogenously determined by the interest rate, a connection that is often ignored.
Distribution assumption The firm’s project requires a onetime investment of \(I_{0}:=1\) at time \(t=0\) and results in an uncertain gross return of \(x\cdot I_{0}\) at time \(t=1\). Empirical data is needed to calibrate the probability distribution of \(x\). The challenge in adjusting the theoretical oneperiod model to a real world scenario is to fit empirical observations into the model’s distribution assumption of gross return earned by the modeled company. Real world data from going concern businesses can at most give an estimate. This restriction applies to empirical distribution data as much as to any theoretical distribution with empirically adjusted parameters. Note that we only use empirical data to obtain a reasonable distribution of cash flows.
Descriptives on the applied data set
Legal form  Obs.  Total assets in million Euro  

Mean  Median  SD  
GmbH (limited liability corporations)  40,574  94 %  36  2.7  410 
AG (stock corporations)  2,167  5 %  1,062  18.3  10,442 
Other  367  1 %  1,041  0.2  8,463 
Total  43,108  100 % 
We winsorize large values of \(x\) at the 1 % percentile and set negative values to zero. In our singleperiod modeling, a company cannot lose more than the initially invested amount, while in a multiperiod setting, each single period’s cash flow can well be negative. The resulting distribution has a mean value of \(\mu \approx 1.08\) and a standard deviation of \(\sigma \approx 17.41 \%\). Figure 5 shows the distribution’s density curve with data from 2012.
5.2 Leveragebased IDR
We perform the simulation with varying parameter combinations and measure the corporation’s tax advantage, cta, defined as the difference between the partnership’s and the corporation’s expected total tax burden, including shareholder level tax.
Consequently, we repeat each analysis with the alteration that the IDR is introduced in a model world with an existing loss offset restriction on corporate level. The reference point for legal form dependent effects is the adjusted baseline model where the LOR is already in effect: we consider only tax differences caused by the IDR on top of the LOR. The target function is thus the corporation’s net tax advantage, cnta, which is net of the LOR’s tax effect.
The picture remains essentially unchanged when different parameter values for the riskfree interest rate are applied or data samples with varying risk are used. Changing these parameters, \(\lambda _{\text {crit}}\) moves either left or right in the graph. The function \({\text {cta}}(\lambda )\) may become strictly positive or strictly negative for all \(\lambda >\lambda _{0}\), if the critical leverage moves right or left out of the domain of definition.
Influence from LOR. The graph of \({\text {cnta}}(\lambda )\) exhibits visually the same shape as \({\text {cta}}(\lambda )\), but the critical leverage is for most parameter combinations slightly larger when an LOR is effective, enlarging the range of possible \(\lambda \) where the corporation is privileged (Fig. 7). The main effect is that in events of loss, the IDR cannot affect the corporation, as the tax base is already negative and the due tax amount tight to zero by the LOR, but the IDR unchangedly affects the partnership, increasing the corporation’s net tax advantage \(cnta\) (interaction effect). In some cases (not illustrated in this figure), this effect can be compensated by an increase in the default gain effect, refer to Sect. 4.2. Figure 7 depicts the relative advantage for a corporation caused by the IDR (rather than the absolute advantage) taking the adjusted baseline model as the reference where the LOR is already effective.
If \(r_{f}=0\), the partnership pays no interest and is, therefore, not affected by the IDR. The corporation pays a risk premium and is negatively affected by the IDR if \(\lambda >\lambda _{0}\), which is why the corporation is discriminated against for small \(r_{f}\). As \(r_{f}\) increases, the dividend effect increases (pro corporation) and the default gain effect remains constant, depending only on \(\lambda \). If \(r_{f}\) is sufficiently large, \(\lambda \) looses its influence and the corporation is always privileged, because \(\lambda \) is restricted to the interval \([0,1]\), the default gain effect is, therefore, too, bounded above and is eventually dominated by the unrestricted dividend effect for large \(r_{f}\). For medium \(r_{f}\), the default gain effect can compensate the dividend effect if \(\lambda \) is sufficiently large. The critical leverage is thus increasing in \(r_{f}\) and enlarges the range of possible \(\lambda \) where the corporation is advantageous.
We find that risk seems to have a negative impact on the corporation’s tax advantage, reducing the critical leverage. This is because the dividend effect is independent from risk, whereas the default gain effect is a multiple of the expected default gain. That is why the distribution of cash flows below the critical cash flow \(x_{\text {DG}}\) does and that above \(x_{\text {DG}}\) does not affect \({\text {cta}}(\lambda )\) and \(\lambda _{\text {crit}}\). The greater the investment’s risk, the greater is in general the probability of a default gain, \(P(x < x_{\text {DG}})\), as well as the expected amount of default gain if one occurs. The default gain effect acts in the manner of a tax on default gains. If risk is low and \(P(x< x_{\text {DG}})=0\), the default gain effect vanishes and due to the dividend effect, the corporation is privileged for any \(\lambda \). Figure 9 shows the relation between the cash flow distribution’s standard deviation and \(\lambda _{\text {crit}}\).
5.3 EBITDAbased IDR
The EBITDAbased IDR is in a number of cases only binding for the partnership, but not for the corporation. As compared to the leveragebased IDR, the EBITDAbased IDR thus more often discriminates against the partnership. The reason is that the IDR can only bind when leverage is high and EBITDA is small, such that \(30\,\%\cdot {\text {EBITDA}}< \lambda \cdot i\). The greater the leverage and the smaller the EBITDA, however, the greater is the corporation’s probability of default, the smaller is the interest actually paid and the smaller is the chance that the IDR is at all binding for the corporation. Opposed to that, the partnership always pays full interest and is, therefore, mostly hit by the IDR in events of loss. When introduced on top of an existing loss offset restriction, this effect is a little less pronounced: the LOR increases the risky interest rate \(i\) demanded by creditors, thereby increasing the IDR’s upper binding bound \(x_{2u}=\frac{\lambda i}{30\,\%}\), moving it closer to the cash flow distribution’s peak value. This increases the chance that the IDR is binding for a corporation.
As with the leveragebased IDR, an increasing riskfree interest rate is usually pro corporation: A larger riskfree interest rate \(r_{f}\) increases both the due and the paid interest amount and increases the chance that the IDR binds for both legal forms. The effect is usually stronger for the partnership, thus increasing the corporation’s tax advantage, for relevant parameter combinations.
Contrary to the leveragebased IDR, a greater standard deviation in the distribution of cash flows increased the corporation’s advantage in the analyzed scenarios. This has no effect on the critical leverage, however, as corporations are privileged for any leverage in these cases.
6 Conclusion
Results for leveragebased interest deduction restrictions
Treatment of default gains and interest payments  Dividend taxation  Advantaged legal form 

Symmetric (\(\beta =\alpha \))  =0  Neutral 
Symmetric (\(\beta =\alpha \))  >0  Corporation 
Symmetric, legal form specific parameters  >0  Neutral 
\(\beta >\alpha \)  ≥0  Corporation 
\(\beta <\alpha \)  =0  Partnership 
\(\beta <\alpha \)  >0  Distribution dependent 
The effect of the EBITDAbased IDR on the organizational form depends on the cash flow distribution and is, therefore, theoretically undetermined. Moreover, if we assume corporate loss offset restrictions, both forms of IDR always distort the decision between limited and unlimited liability firms. The effect of corporate loss offset restrictions is threefold: first, due to the missing loss offset for corporations, IDR are ineffective in case of losses. This privileges the corporation. Second, a tax exemption of a default gain that could compensate for the restricted interest deductibility is not effective due to the missing loss offset. Third, due to the missing loss offset, creditors will receive lower payments in the case of insolvency. This increases the expected default gain and the risk premium. This in turn leads to a higher effect of the IDR. In contrast to the first effect, the other two effects discriminate against the corporation. Thus, the total effect is undetermined and depends on the distribution of the cash flows, the leverage ratio, and the riskfree interest rates as we additionally illustrate in Monte Carlo simulations.
The policy implications are obvious: if legislators aim to achieve organizational form neutrality, this aim is generally in conflict with the introduction of IDR even if a uniform treatment of organizational forms with respect to IDR (such as is implemented in many countries) is applied. Also note that although we restrict our analysis to only two forms of IDR, the leveragebased IDR is in fact comparable to a proportional limitation of interest deductibility such as is used, e.g., in Germany for trade tax purposes. For any given debt ratio one can show the identity of proportional restrictions and leveragebased IDR. Additionally, while our model covers only thirdparty debt it could easily be extended to internal debt. Many IDR treat payments on internal debt as constructive dividends. In these cases our results hold if (1) the tax rate on dividends equals the tax rate on interest revenues, (2) the interest rate equals the arm’s length interest rate, and (3) losses due to a debtor’s default are fully tax deductible at the same tax rate as interest payments. The last two conditions ensure the creditor’s calculus to remain unchanged and the first one implies that one can neglect tax effects on shareholder level caused by constructive dividends.
From a tax research perspective it is worth to mention that future studies investigating organizational from neutrality of tax systems should consider that different legal forms face different liability rules and a uniform application of tax rules may, thus, be inappropriate to achieve organizational form neutrality. Furthermore, our results are also relevant for the discussion of the tax effect on the amount of collateral a shareholder should offer to the creditors of his or her corporation. Often corporations are de facto not limited in their liability, but, on the contrary, their owners offer personal guarantees to receive a loan for the firm. Then, the assumptions on liability differences among the organizational forms in this paper do not hold. However, our findings then apply for the owners’ decision to offer a guarantee to the creditors or not—again a choice between limited and unlimited liability. The only difference is that in this case we would not have a dividend effect so that only the default gain effect remains. Therefore, one can conclude that IDR also distort the owners decision to offer collateral if default gains and interest payments are treated asymmetrically. Table 2 shows that legal rules that restrict the deductibility of interest expenses, but fully tax default gains (\(\alpha '>\beta '\)) such as, e.g., the current tax regime in Germany provides an incentive to secure a loan by offering collateral.
Of course the used model is subject to some limitations. Most important, we only used a singleperiod model with no information asymmetries between borrowers and lenders. In our opinion this is sufficient to show the main effects of IDR on the choice of organizational form. In addition, we assumed that earnings before interest, taxes, depreciation, and amortization do not depend on the legal form. This neglects the fact that the legal form decision may affect risk taking and, therefore, cash flows. However, since our focus is on tax nonneutrality to the legal form decision, we believe our point gets clearer when holding all other decisions constant, including the investment decision, switching only the legal form. Moreover, the choice of legal form affects the risk taking of managers only if creditors cannot perfectly monitor the corporate activities which is in contrast to our assumption of symmetric information. In sum, it seems useful to expand the model to a multiperiod setting in future research and maybe also to incorporate behavioral uncertainties resulting from information asymmetry.
Notes
Acknowledgments
The authors gratefully acknowledge the helpful comments of Rainer Niemann (editor) and two anonymous reviewers.
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