Skip to main content
SpringerLink
Log in

The effects on investment incentives of an allowance for corporate equity tax system: the Belgian case as an example

  • Original Research
  • Published:
Review of Quantitative Finance and Accounting Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

In the past years, allowance for corporate equity (ACE) tax systems have become more popular even though they are still quite rare. An ACE tends to make a tax system neutral in respect of whether a company is financed by debt or equity. Less attention is given to the effects on investment incentives by scientific literature. We construct a model based on the principle of a hurdle rate to show whether and how an ACE system could change a company’s decision between distribution and reinvestment. The analysis is extended by implementing the so called fairness tax. We find that the influence of the fairness tax on (re)investment incentives depends on the debt to total capital ratio and the return on equity. Hence, the introduction of an ACE does only in certain cases lead to a change from distribution to reinvestment. Interestingly, the fairness tax can increase the incentive to reinvest in few situations and can make the ACE system more attractive in respect of reinvestment.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Notes

  1. See also Wenger (1983) who proposed it regarding the equality of taxation of earned and capital income. See Bond and Devereux (1995) who extended the idea of Boadway and Bruce (1984) for uncertainty.

  2. For an analytical overview about ACE systems in practice see Klemm (2007) and for economic implications of ACE reforms De Mooij and Devereux (2011). Hebous and Ruf (2015) present a list of hard and soft ACE systems.

  3. For the impact of the Austrian tax reform on the capital structure see Frühwirth and Kobialka (2010).

  4. For an analysis of the former Italian tax reform see Staderini (2001) who found a decrease in leverage and an increase of retained earnings, both depending on the profitability and productivity of the firms.

  5. For a detailed discussion of the Croatian ACE system see Keen and King (2002).

  6. For details see Staubli and Küttel (2013). In February 2017 the proposal of a notional interest deduction was rejected in a national referendum as part of the corporate tax reform III.

  7. For details and alternative designs see Freebairn (2016).

  8. See Gordon (2011) who prefers an expenditure tax system with a business cash-flow tax instead of an ACE system for the UK.

  9. For an analysis of the ACE system as an alternative to thin capitalization rules see Rumpf (2009).

  10. To avoid this, Boadway and Bruce (1984) proposed an Allowance for Corporate Capital (ACC) system, in which the interest deduction is abolished and replaced by the deduction for the notional risk-free return on all capital. In the ACC system it is totally irrelevant whether the company is financed by equity or debt.

  11. The Belgian NID applies from tax year 2007 onwards. For details see art. 205 of the Belgian Income Tax Code and Peeters and Hermie (2011).

  12. Basis of calculation are the months July, August and September of the preceding tax year.

  13. Alternatively, if the participation amounts to at least 2.5 million EUR.

  14. See Aus dem Moore (2014), who refers to the explanatory memorandum no. 51-1778/001.

  15. For details see art. 219 and 233 of the Belgian Income Tax Code. According to the ECJ (2017), the fairness tax partly infringes the Parent-Subsidiary Directive.

  16. The hurdle rate represents an established approach to measure the implementation of new tax rules. For example, it was used to measure the effects of tax law changes in Germany (Schultze and Dinh Thi 2007) and the introduction of the dividend exemption system in Japan (Bachmann and Baumann 2016).

  17. For the value and the determinants of the debt tax shield see Menichini (2017) and for the valuation in different debt scenarios Couch et al. (2012).

  18. The basis for the calculation is the total amount of net equity. According to the Belgian NID system we do not cap the interest on equity on so called new equity.

  19. To abstract from the specific circumstances of the parent company, we assume the received dividend has no influence on the effective tax rate of the parent company. In practice, the dividend could increase the equity and therefore the ACE of the parent company if it is not resident abroad but the relevant equity would be reduced by the participation in the subsidiary.

  20. It is a simple multiplication of the three factors dividends \( Y_{t - 1}^{C} \), tax rate t p and the fraction of taxable dividends α. Obviously, the order of the factors is irrelevant.

  21. For a derivation of Eq. (11) see “Appendix 1”.

  22. For a detailed derivation of Eqs. (18) and (19) see “Appendix 2 and 3”.

  23. In the case of a negative r Equity , which we assume does not arise in our model, the lower hurdle rate has to be chosen.

  24. The range up to 5% for i E is realistic because the maximum NID rate in Belgium was 4.973% for SME in 2010 and has declined below 2% in 2016. A NID rate of 0% represents the case of no ACE system.

  25. In the parent-subsidiary case withholding taxes are irrelevant. Even though they could apply in cross-border situations, they are often limited up to zero within the EU or due to double tax agreements. Furthermore, companies can often get a tax credit for the withholding tax.

  26. This represents the maximum regular NID rate and is close to the average NID rate for the tax years 2011 to 2015.

  27. Within the European Union, the Belgian corporate tax rate of 33.99% is one of the highest (France: 38%). In contrast, Bulgaria for example has a corporate tax rate of 10% (Eurostat 2015).

  28. That outcome is similar to the effect of an increased debt tax shield due to higher corporate tax rates in a traditional tax system (e.g. Cheng and Tzeng 2014).

  29. For example see Bahng and Jeong (2012) who investigated the debt ratios of Australian firms in relation to the firm size, the profitability and the tangibility of assets.

  30. This holds for the case in which all other rates are constant in t − 1 and t.

  31. The average of the five-year average return on equity rates amounts to approximately 8.91%, 10.55% respectively (excluding the negative rates), which supports our assumption of the above used rate of return on equity.

  32. Notably, this does not illustrate the empirical comparison before and after introduction of the Belgian NID system because the used data are from periods where the NID system was in force.

  33. The D/C ratios in Table 4 which are closest to the real D/C ratios of the companies are in bold.

  34. As we assume a positive r Equity (Sect. 4), we can abstract from a common tax loss carryforward while a tax loss arising from the NID cannot be carried forward.

  35. For an example see Michel and Van den Berghe (2014).

  36. It becomes obvious, that in case of reinvestment a lower fairness tax could apply as in case of distribution.

  37. Whether an investor can really “save” taxes depends on the point of view (subsidiary or parent) and the basis of comparison.

References

Download references

Author information

Authors and Affiliations

  1. Chair of Business Taxation, Institute of Accounting, Finance and Taxation, Leipzig University, Grimmaische Strasse 12, 04109, Leipzig, Germany

    Carmen Bachmann, Martin Baumann & Konrad Richter

Authors
  1. Carmen Bachmann
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Martin Baumann
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Konrad Richter
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Carmen Bachmann.

Appendices

Appendix 1

The calculation of \( \Delta Debt \) is based on the following equations:

$$ \begin{aligned} & TC_{t - 1} = Debt_{t - 1} + Equity_{t - 1} \\ & TC_{t} = Debt_{t - 1} + \Delta Debt + Equity_{t - 1} + \Delta Equity \\ & \frac{{Debt_{t - 1} }}{{TC_{t - 1} }} = \frac{{Debt_{t} }}{{TC_{t} }} \\ \end{aligned} $$

This leads to:

$$ \Delta Debt = \left( {\Delta Equity + \Delta Debt} \right) \cdot \left( {\frac{{Debt_{t - 1} }}{{TC_{t - 1} }}} \right) $$

This can be reformulated as follows:

$$ \left( {1 - \frac{{Debt_{t - 1} }}{{TC_{t - 1} }}} \right) \cdot \Delta Debt = \left( {\frac{{Debt_{t - 1} }}{{TC_{t - 1} }}} \right) \cdot \Delta Equity $$

Which further leads to:

$$ \Delta Debt = \frac{{\frac{{Debt_{t - 1} }}{{TC_{t - 1} }} \cdot \Delta Equity}}{{\left( {1 - \frac{{Debt_{t - 1} }}{{TC_{t - 1} }}} \right)}} $$

Appendix 2

Calculation of \( hr_{1} \):

$$ \begin{aligned} & \Delta Debt + Y_{t}^{P,D} = \frac{{\Delta Debt + Y_{t}^{P, R} }}{{1 + r_{Equity} \left( {1 - t_{p} } \right)}} \\ & \quad \to \left( {1 + r_{Equity} \left( {1 - t_{p} } \right)} \right) \cdot \left( {\Delta Debt + Y_{t}^{P,D} } \right) - \Delta Debt = Y_{t}^{P, R} \\ \end{aligned} $$

Inserting Eq. (15) for \( Y_{t}^{P, R} \):

$$ \begin{aligned} & \to \left( {1 + r_{Equity} \left( {1 - t_{p} } \right)} \right) \cdot \left( {\Delta Debt + Y_{t}^{P,D} } \right) - \Delta Debt = \left( {Y_{t}^{C, R} \cdot \left( {1 - \alpha t_{p} } \right)} \right) + \left( {\left( {i_{D} \cdot Debt_{t} } \right) \cdot \left( {1 - t_{p} } \right)} \right) \\ & \to \left( {1 + r_{Equity} \left( {1 - t_{p} } \right)} \right) \cdot \left( {\Delta Debt + Y_{t}^{P,D} } \right) - \Delta Debt - \left( {\left( {i_{D} \cdot Debt_{t} } \right) \cdot \left( {1 - t_{p} } \right)} \right) = \left( {Y_{t}^{C, R} \cdot \left( {1 - \alpha t_{p} } \right)} \right) \\ & \to \frac{{\left( {1 + r_{Equity} \left( {1 - t_{p} } \right)} \right) \cdot \left( {\Delta Debt + Y_{t}^{P,D} } \right) - \Delta Debt - \left( {\left( {i_{D} \cdot Debt_{t} } \right) \cdot \left( {1 - t_{p} } \right)} \right)}}{{\left( {1 - \alpha t_{p} } \right)}} = Y_{t}^{C, R} \\ \end{aligned} $$

Inserting the upper term of Eq. (13) for \( Y_{t}^{C, R} \):

$$ \begin{aligned} & \frac{{\left( {1 + r_{Equity} \left( {1 - t_{p} } \right)} \right) \cdot \left( {\Delta Debt + Y_{t}^{P,D} } \right) - \Delta Debt - \left( {\left( {i_{D} \cdot Debt_{t} } \right) \cdot \left( {1 - t_{p} } \right)} \right)}}{{\left( {1 - \alpha t_{p} } \right)}} = Y_{t - 1}^{C} + EBIT_{t} \left( {1 - t_{c} } \right) + \left( {t_{c} \cdot \left( {\left( {i_{E} \cdot \Delta Equity} \right) + \left( {i_{D} \cdot \Delta Debt} \right)} \right)} \right) - \left( {i_{D} \cdot \Delta Debt} \right) \\ & \quad \to \frac{{\left( {1 + r_{Equity} \left( {1 - t_{p} } \right)} \right) \cdot \left( {\Delta Debt + Y_{t}^{P,D} } \right) - \Delta Debt - \left( {\left( {i_{D} \cdot Debt_{t} } \right) \cdot \left( {1 - t_{p} } \right)} \right)}}{{\left( {1 - \alpha t_{p} } \right)}} - Y_{t - 1}^{C} + \left( {i_{D} \cdot \Delta Debt} \right) - \left( {t_{c} \cdot \left( {\left( {i_{E} \cdot \Delta Equity} \right) + \left( {i_{D} \cdot \Delta Debt} \right)} \right)} \right) = EBIT_{t} \left( {1 - t_{c} } \right) \\ \end{aligned} $$

Inserting Eq. (12) for \( EBIT_{t} \):

$$ \begin{aligned} & \frac{{\left( {1 + r_{Equity} \left( {1 - t_{p} } \right)} \right) \cdot \left( {\Delta Debt + Y_{t}^{P,D} } \right) - \Delta Debt - \left( {\left( {i_{D} \cdot Debt_{t} } \right) \cdot \left( {1 - t_{p} } \right)} \right)}}{{\left( {1 - \alpha t_{p} } \right)}} - Y_{t - 1}^{C} + \left( {i_{D} \cdot \Delta Debt} \right) - \left( {t_{c} \cdot \left( {\left( {i_{E} \cdot \Delta Equity} \right) + \left( {i_{D} \cdot \Delta Debt} \right)} \right)} \right) = \left( {Y_{t - 1}^{C} + \Delta Debt} \right) \cdot \left( {1 - t_{c} } \right)\Delta hr_{1} \\ & \quad \to \frac{{\frac{{\left( {1 + r_{Equity} \left( {1 - t_{p} } \right)} \right) \cdot \left( {\Delta Debt + Y_{t}^{P,D} } \right) - \Delta Debt - \left( {\left( {i_{D} \cdot Debt_{t} } \right) \cdot \left( {1 - t_{p} } \right)} \right)}}{{\left( {1 - \alpha t_{p} } \right)}} - Y_{t - 1}^{C} + \left( {i_{D} \cdot \Delta Debt} \right) - \left( {t_{c} \cdot \left( {\left( {i_{E} \cdot \Delta Equity} \right) + \left( {i_{D} \cdot \Delta Debt} \right)} \right)} \right)}}{{\left( {Y_{t - 1}^{C} + \Delta Debt} \right) \cdot \left( {1 - t_{c} } \right)}} = hr_{1} \\ \end{aligned} $$

Further simplification:

$$ \begin{aligned} & hr_{1} = \frac{{\frac{{\left( {1 + r_{Equity} \left( {1 - t_{p} } \right)} \right) \cdot \left( {\Delta Debt + Y_{t}^{P,D} } \right) - \Delta Debt - \left( {\left( {i_{D} \cdot Debt_{t} } \right) \cdot \left( {1 - t_{p} } \right)} \right)}}{{\left( {1 - \alpha t_{p} } \right)}} - Y_{t - 1}^{C} + \left( {i_{D} \cdot \Delta Debt} \right) - \left( {t_{c} \cdot \left( {\left( {i_{E} \cdot \Delta Equity} \right) + \left( {i_{D} \cdot \Delta Debt} \right)} \right)} \right)}}{{\left( {Y_{t - 1}^{C} + \Delta Debt} \right) \cdot \left( {1 - t_{c} } \right)}} \\ & \quad \to hr_{1} = \frac{{\frac{{\Delta Debt + Y_{t}^{P,D} + r_{Equity} \left( {1 - t_{p} } \right)\Delta Debt + r_{Equity} \left( {1 - t_{p} } \right)Y_{t}^{P,D} - \Delta Debt - \left( {\left( {i_{D} \cdot \Delta Debt_{t} } \right) \cdot \left( {1 - t_{p} } \right)} \right)}}{{\left( {1 - \alpha t_{p} } \right)}} - Y_{t - 1}^{C} + \left( {i_{D} \cdot \Delta Debt} \right) - \left( {t_{c} \cdot \left( {\left( {i_{E} \cdot \Delta Equity} \right) + \left( {i_{D} \cdot \Delta Debt} \right)} \right)} \right)}}{{\left( {Y_{t - 1}^{C} + \Delta Debt} \right) \cdot \left( {1 - t_{c} } \right)}} \\ & \quad \to hr_{1} = \frac{{\frac{{Y_{t}^{P,D} + r_{Equity} \left( {1 - t_{p} } \right)\Delta Debt + r_{Equity} \left( {1 - t_{p} } \right)Y_{t}^{P,D} - \left( {\left( {i_{D} \cdot Debt_{t} } \right) \cdot \left( {1 - t_{p} } \right)} \right)}}{{\left( {1 - \alpha t_{p} } \right)}} - Y_{t - 1}^{C} + \left( {i_{D} \cdot \Delta Debt} \right) - \left( {t_{c} \cdot \left( {\left( {i_{E} \cdot \Delta Equity} \right) + \left( {i_{D} \cdot \Delta Debt} \right)} \right)} \right)}}{{\left( {Y_{t - 1}^{C} + \Delta Debt} \right) \cdot \left( {1 - t_{c} } \right)}} \\ \end{aligned} $$

Inserting Eq. (16) for \( Y_{t}^{P,D} \):

$$ \begin{aligned} & hr_{1} = \frac{{\frac{{\left( {Y_{t}^{C, D} \cdot \left( {1 - \alpha t_{p} } \right)} \right) + \left( {\left( {i_{D} \cdot Debt_{t - 1} } \right) \cdot \left( {1 - t_{p} } \right)} \right) + r_{Equity} \left( {1 - t_{p} } \right)\Delta Debt + r_{Equity} \left( {1 - t_{p} } \right)Y_{t}^{P,D} - \left( {\left( {i_{D} \cdot Debt_{t} } \right) \cdot \left( {1 - t_{p} } \right)} \right)}}{{\left( {1 - \alpha t_{p} } \right)}} - Y_{t - 1}^{C} + \left( {i_{D} \cdot \Delta Debt} \right) - \left( {t_{c} \cdot \left( {\left( {i_{E} \cdot \Delta Equity} \right) + \left( {i_{D} \cdot \Delta Debt} \right)} \right)} \right)}}{{\left( {Y_{t - 1}^{C} + \Delta Debt} \right) \cdot \left( {1 - t_{c} } \right)}} \\ & \quad \to hr_{1} = \frac{{\frac{{Y_{t}^{C, D} \cdot \left( {1 - \alpha t_{p} } \right)}}{{\left( {1 - \alpha t_{p} } \right)}} + \frac{{\left( {\left( {i_{D} \cdot Debt_{t - 1} } \right) \cdot \left( {1 - t_{p} } \right)} \right) + r_{Equity} \left( {1 - t_{p} } \right) \cdot Debt + r_{Equity} \left( {1 - t_{p} } \right)Y_{t}^{P,D} - \left( {\left( {i_{D} \cdot Debt_{t} } \right) \cdot \left( {1 - t_{p} } \right)} \right)}}{{\left( {1 - \alpha t_{p} } \right)}} - Y_{t - 1}^{C} + \left( {i_{D} \cdot \Delta Debt} \right) - \left( {t_{c} \cdot \left( {\left( {i_{E} \cdot \Delta Equity} \right) + \left( {i_{D} \cdot \Delta Debt} \right)} \right)} \right)}}{{\left( {Y_{t - 1}^{C} + \Delta Debt} \right) \cdot \left( {1 - t_{c} } \right)}} \\ \end{aligned} $$

Given Eq. (14) we can rearrange to:

$$ hr_{1} = \frac{{\frac{{r_{Equity} \left( {1 - t_{p} } \right)\left( {\Delta Debt + Y_{t}^{P,D} } \right) - \left( {i_{D} \cdot \Delta Debt} \right)\left( {1 - t_{p} } \right)}}{{\left( {1 - \alpha t_{p} } \right)}} + \left( {i_{D} \cdot \Delta Debt} \right) - \left( {t_{c} \cdot \left( {\left( {i_{E} \cdot \Delta Equity} \right) + \left( {i_{D} \cdot \Delta Debt} \right)} \right)} \right)}}{{\left( {Y_{t - 1}^{C} + \Delta Debt} \right) \cdot \left( {1 - t_{c} } \right)}} $$

Appendix 3

Calculation of \( hr_{2} \)

$$ \begin{aligned} & \Delta Debt + Y_{t}^{P,D} = \frac{{\Delta Debt + Y_{t}^{P, R} }}{{1 + r_{Equity} \left( {1 - t_{p} } \right)}} \\ & \quad \to \left( {1 + r_{Equity} \left( {1 - t_{p} } \right)} \right) \cdot \left( {\Delta Debt + Y_{t}^{P,D} } \right) - \Delta Debt = Y_{t}^{P, R} \\ \end{aligned} $$

Inserting Eq. (15) for \( Y_{t}^{P, R} \):

$$ \begin{aligned} & \left( {1 + r_{Equity} \left( {1 - t_{p} } \right)} \right) \cdot \left( {\Delta Debt + Y_{t}^{P,D} } \right) - \Delta Debt = \left( {Y_{t}^{C, R} \cdot \left( {1 - \alpha t_{p} } \right)} \right) + \left( {\left( {i_{D} \cdot Debt_{t} } \right) \cdot \left( {1 - t_{p} } \right)} \right) \\ & \quad \to \left( {1 + r_{Equity} \left( {1 - t_{p} } \right)} \right) \cdot \left( {\Delta Debt + Y_{t}^{P,D} } \right) - \Delta Debt - \left( {\left( {i_{D} \cdot Debt_{t} } \right) \cdot \left( {1 - t_{p} } \right)} \right) = \left( {Y_{t}^{C, R} \cdot \left( {1 - \alpha t_{p} } \right)} \right) \\ & \quad \to \frac{{\left( {1 + r_{Equity} \left( {1 - t_{p} } \right)} \right) \cdot \left( {\Delta Debt + Y_{t}^{P,D} } \right) - \Delta Debt - \left( {\left( {i_{D} \cdot Debt_{t} } \right) \cdot \left( {1 - t_{p} } \right)} \right)}}{{\left( {1 - \alpha t_{p} } \right)}} = Y_{t}^{C, R} \\ \end{aligned} $$

Inserting the lower term of Eq. (13) for \( Y_{t}^{C, R} \):

$$ \begin{aligned} & \frac{{\left( {1 + r_{Equity} \left( {1 - t_{p} } \right)} \right) \cdot \left( {\Delta Debt + Y_{t}^{P,D} } \right) - \Delta Debt - \left( {\left( {i_{D} \cdot Debt_{t} } \right) \cdot \left( {1 - t_{p} } \right)} \right)}}{{\left( {1 - \alpha t_{p} } \right)}} = Y_{t - 1}^{C} + EBIT_{t} - \left( {i_{D} \cdot \Delta Debt} \right) \\ & \quad \to \frac{{\left( {1 + r_{Equity} \left( {1 - t_{p} } \right)} \right) \cdot \left( {\Delta Debt + Y_{t}^{P,D} } \right) - \Delta Debt - \left( {\left( {i_{D} \cdot Debt_{t} } \right) \cdot \left( {1 - t_{p} } \right)} \right)}}{{\left( {1 - \alpha t_{p} } \right)}} - Y_{t - 1}^{C} + \left( {i_{D} \cdot \Delta Debt} \right) = EBIT_{t} \\ \end{aligned} $$

Inserting Eq. (12) for \( EBIT_{t} \):

$$ \begin{aligned} & \frac{{\left( {1 + r_{Equity} \left( {1 - t_{p} } \right)} \right) \cdot \left( {\Delta Debt + Y_{t}^{P,D} } \right) - \Delta Debt - \left( {\left( {i_{D} \cdot Debt_{t} } \right) \cdot \left( {1 - t_{p} } \right)} \right)}}{{\left( {1 - \alpha t_{p} } \right)}} - Y_{t - 1}^{C} + \left( {i_{D} \cdot \Delta Debt} \right) = \left( {Y_{t - 1}^{C} + \Delta Debt} \right) \cdot hr_{2} \\ & \quad \to \frac{{\frac{{\left( {1 + r_{Equity} \left( {1 - t_{p} } \right)} \right) \cdot \left( {\Delta Debt + Y_{t}^{P,D} } \right) - \Delta Debt - \left( {\left( {i_{D} \cdot Debt_{t} } \right) \cdot \left( {1 - t_{p} } \right)} \right)}}{{\left( {1 - \alpha t_{p} } \right)}} - Y_{t - 1}^{C} + \left( {i_{D} \cdot \Delta Debt} \right)}}{{\left( {Y_{t - 1}^{C} + \Delta Debt} \right)}} = hr_{2} \\ \end{aligned} $$

Further simplification:

$$ \begin{aligned} & hr_{2} = \frac{{\frac{{\left( {1 + r_{Equity} \left( {1 - t_{p} } \right)} \right) \cdot \left( {\Delta Debt + Y_{t}^{P,D} } \right) - \Delta Debt - \left( {\left( {i_{D} \cdot Debt_{t} } \right) \cdot \left( {1 - t_{p} } \right)} \right)}}{{\left( {1 - \alpha t_{p} } \right)}} - Y_{t - 1}^{C} + \left( {i_{D} \cdot \Delta Debt} \right)}}{{\left( {Y_{t - 1}^{C} + \Delta Debt} \right)}} \\ & \quad \to hr_{2} = \frac{{\frac{{\Delta Debt + Y_{t}^{P,D} + r_{Equity} \left( {1 - t_{p} } \right) \cdot Debt + r_{Equity} \left( {1 - t_{p} } \right)Y_{t}^{P,D} - \Delta Debt - \left( {\left( {i_{D} \cdot Debt_{t} } \right) \cdot \left( {1 - t_{p} } \right)} \right)}}{{\left( {1 - \alpha t_{p} } \right)}} - Y_{t - 1}^{C} + \left( {i_{D} \cdot \Delta Debt} \right)}}{{\left( {Y_{t - 1}^{C} + \Delta Debt} \right)}} \\ & \quad \to hr_{2} = \frac{{\frac{{Y_{t}^{P,D} + r_{Equity} \left( {1 - t_{p} } \right) \cdot Debt + r_{Equity} \left( {1 - t_{p} } \right)Y_{t}^{P,D} - \left( {\left( {i_{D} \cdot Debt_{t} } \right) \cdot \left( {1 - t_{p} } \right)} \right)}}{{\left( {1 - \alpha t_{p} } \right)}} - Y_{t - 1}^{C} + \left( {i_{D} \cdot \Delta Debt} \right)}}{{\left( {Y_{t - 1}^{C} + \Delta Debt} \right)}} \\ \end{aligned} $$

Inserting Eq. (16) for \( Y_{t}^{P,D} \):

$$ \begin{aligned} & hr_{2} = \frac{{\frac{{\left( {Y_{t}^{C, D} \cdot \left( {1 - \alpha t_{p} } \right)} \right) + \left( {\left( {i_{D} \cdot Debt_{t - 1} } \right) \cdot \left( {1 - t_{p} } \right)} \right) + r_{Equity} \left( {1 - t_{p} } \right) \cdot Debt + r_{Equity} \left( {1 - t_{p} } \right)Y_{t}^{P,D} - \left( {\left( {i_{D} \cdot Debt_{t} } \right) \cdot \left( {1 - t_{p} } \right)} \right)}}{{\left( {1 - \alpha t_{p} } \right)}} - Y_{t - 1}^{C} + \left( {i_{D} \cdot \Delta Debt} \right)}}{{\left( {Y_{t - 1}^{C} + \Delta Debt} \right)}} \\ & \quad \to hr_{2} = \frac{{\frac{{Y_{t}^{C, D} \cdot \left( {1 - \alpha t_{p} } \right)}}{{\left( {1 - \alpha t_{p} } \right)}} + \frac{{\left( {\left( {i_{D} \cdot Debt_{t - 1} } \right) \cdot \left( {1 - t_{p} } \right)} \right) + r_{Equity} \left( {1 - t_{p} } \right) \cdot Debt + r_{Equity} \left( {1 - t_{p} } \right)Y_{t}^{P,D} - \left( {\left( {i_{D} \cdot Debt_{t} } \right) \cdot \left( {1 - t_{p} } \right)} \right)}}{{\left( {1 - \alpha t_{p} } \right)}} - Y_{t - 1}^{C} + \left( {i_{D} \cdot \Delta Debt} \right)}}{{\left( {Y_{t - 1}^{C} + \Delta Debt} \right) \cdot \left( {1 - t_{c} } \right)}} \\ \end{aligned} $$

Given Eq. (14) we can rearrange to:

$$ hr_{2} = \frac{{\frac{{r_{Equity} \left( {1 - t_{p} } \right)\left( {\Delta Debt + Y_{t}^{P,D} } \right) - \left( {i_{D} \cdot \Delta Debt} \right)\left( {1 - t_{p} } \right)}}{{\left( {1 - \alpha t_{p} } \right)}} + \left( {i_{D} \cdot \Delta Debt} \right)}}{{\left( {Y_{t - 1}^{C} + \Delta Debt} \right)}} $$

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bachmann, C., Baumann, M. & Richter, K. The effects on investment incentives of an allowance for corporate equity tax system: the Belgian case as an example. Rev Quant Finan Acc 51, 943–965 (2018). https://doi.org/10.1007/s11156-017-0693-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11156-017-0693-2

Keywords

JEL Classification

Search

Navigation