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Review of Managerial Science

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23.04.2016 | Original Paper

Hold or sell? How capital gains taxation affects holding decisions

verfasst von: Annika Hegemann, Angela Kunoth, Kristina Rupp, Caren Sureth-Sloane

Erschienen in: Review of Managerial Science | Ausgabe 3/2017

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Abstract

Investments with exit flexibility require decisions regarding both the investment and holding period. Because selling an investment often leads to taxable capital gains, which crucially depend on the duration of an investment, we investigate the impact of capital gains taxation on exit timing under different tax systems. We observed that capital gains taxation delays exit decisions but loses its decision relevance for very long holdings. Often the optimal exit time, which indicates the maximal present value of future cashflows, cannot be determined analytically. However, we identify the breakeven exit time that guarantees present values exceeding those of an immediate sale. While, after-taxes, an immediate sale is often optimal, long holding periods might also be attractive for investors depending on the degree of income and corporate tax integration. A classic corporate tax system often indicates holdings over more than 100 periods. By contrast, a shareholder relief system indicates the earliest breakeven exit time and thus the highest level of exit timing flexibility. Surprisingly, high retention rates are likely to accelerate sales under a classic corporate system. Additionally, the worst exit time, which should be avoided by investors, differs tremendously across tax systems. For an integrated tax system with full imputation, the worst time is reached earlier than under partial or non-integrated systems. These results could help to predict investors’ behavior regarding changes in capital gains taxation and thus are of interest for both investors and tax policymakers. Furthermore, the results emphasize the need to control for the underlying tax system in cross-country empirical studies.

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See Carroll et al. (2012), pp. 7, 8.

See Edwards (2012), p. 1.

For an overview of the top marginal tax rates on capital gains of the OECD countries, see, e.g., Pomerleau (2014), p. 7.

See König and Wosnitza (2004), pp. 106–126.

See Gordon and Shapiro (1956), p. 104.

See Gordon and Shapiro (1956), p. 105. Note, that in the following, we consider γ to be exogenously given. Consistent with prior literature, we do not account for information asymmetry or other signaling causes. We further abstract from the retention rate being less sensitive to cash flows if dividend taxes are sufficiently high as suggested by empirical evidence. See e.g., Jacob and Jacob (2013).

See Eq. (5).

See König and Wosnitza (2000), p. 785; Sureth and Langeleh (2007), p. 315.

Determined by applying the geometric series.

See e.g., König and Wosnitza (2004), p. 139.

See König and Wosnitza (2000) for a model under an imputation system; for a more general approach, see Sureth and Langeleh (2007), pp. 315–317.

If we allowed for \(\gamma \ge \frac{i^{\tau }}{i^{\tau ^{c}}}\) we would model infinite growth. Infinite growth is unrealistic and excluded from our model for plausibility reasons. See Sureth (2006), pp. 58, 74; Sureth and Langeleh (2007), p. 317.

See Müller and Semmler (2003), who use a more complex approach and show theoretically that deferred capital gains taxes on hidden reserves reduce the price that arises from negotiations between seller and buyer.

See König and Wosnitza (2000), p. 786; Sureth and Langeleh (2007), p. 322.

Under a classic corporate tax system, income and corporate taxes are levied independently on shareholder and company levels. The withholding tax system, which was introduced in Germany in 2009, can be regarded as a classic corporate tax system.

E.g., the shareholder relief tax system was introduced in Germany in 2001 and later reformed and accompanied by a flat tax on most types of capital income. Today, the shareholder relief is only rarely applicable. If dividends and capital gains qualify for shareholder relief, then a fraction of 40 % is tax-exempted. The shareholder relief tax system actually still is in force in several countries, e.g., Luxembourg, Norway and France. See BMF (2013), pp. 12, 13.

In Germany, the full imputation tax system was implemented from 1977 to 2000. A full imputation tax system is actually present in Malta. See BMF (2013), p. 14.

See Eqs. (13) and (14), and Sureth and Langeleh (2007), p. 317.

See Halberstadt et al. (2009), p. 376.

For an overview of various tax rates in OECD countries, see OECD (2014) and, e.g., Schanz and Schanz (2011), pp. 146–154.

An interest rate of i = 0.1 is often used in analytical research. However, because currently interest rates are significantly lower, we conducted sensitivity analyses for lower rates, as well.

The opposing effects from these two growths processes can be clarified by taking a look at the underlying type of functions. This type of function has the form \((I_0 \, e^{wt}-I_0)\,e^{-i_\tau t}\) where w is the above-mentioned after-tax specific growth rate that may differ from \(i_\tau\). For illustrative purposes, we use the continuous-time form. For this kind of function, global extrema can be found.

See Sureth and Langeleh (2007), p. 320, for the full imputation tax system. Extending their study, we show the development for all three different tax systems over time.

The worst exit time \(z^{min}\) is increasing in i under all three tax systems. Additionally, we find the breakeven exit time \(z^{g}\) increasing in the interest rate in the numerical analysis of the interest sensitivity of \(V_{0}^{\tau }>1\). See Sects. 4.3 and 4.4 for further explanations about the worst exit time and breakeven exit time.

Investors will refrain from investment particularly in a setting with certainty concerning all future cash flows.

The investor would only carry out the investment if she or he is at least indifferent between the investment and the alternative financial investment.

See Rupp (2012), p. 37.

If the capital gains taxation is paid early, the influence on the present value after taxes \(V_{0}^{\tau }\) is strong. The discount effect is very weak for early exit times z.

For example the business tax reform 2008 in Germany and the tax reform 2000 in Germany.

See Sureth (2006), pp. 82–84, Sureth and Langeleh (2007), p. 320, and Rupp (2012), p. 36.

The curvature is driven by the growth and the discount effect.

Dividends are also fully subject to the income tax rate.

Note that he uses data from 2001 and 2004 where short-term capital gains were tax-exempted.

For empirical evidence on the impact of the corporate tax rate on investment, see e.g., Brandstetter and Jacob (2014) and Diller and Theelen (2014).

See Rupp (2012), pp. 29, 30.

We have defined \(\beta\) with \(\beta \in [0,1]\). For the underlying tax systems, \(\beta\) is set either equal to 0.5 or 1 and always greater than zero.

See Rupp (2012), pp. 31, 32.

See also Fig. 2.

\(\tau ^{c}=0.4; \tau =0.4\).

E.g., Becker et al. (2013) investigate the effect of payout taxes on the allocation of investment and report on the tax regimes across 25 countries between 1990 and 2008. Among these countries, 13 changed their tax system within the observed period. Spain and Mexico even have two variations of their tax systems. See Becker et al. (2013), p. 6.

See Ap Gwilym et al. (2006), p. 39, who provide a descriptive overview over the payout ratios between 1965/1973/1990–2004 of eleven countries that are considered representative for the industrialized world.

See Ap Gwilym et al. (2006), pp. 38, 39.

Fatemi and Bildik (2012), p. 677.

See Frère et al. (2012), p. 4.

See Frère et al. (2012), p. 14.

\(z^{min}\) denotes the exit time z where the global minimum is reached.

See Sureth and Langeleh (2007), pp. 320–321, and Rupp (2012), pp. 34–41.

See Fig. 6.

Because it is a matter of a limit value of \(V_{0}^{\tau }\), there is an error of \(1e-8\). See Eq. (33).

If \(\phi <1\), then the inequality \(0>\beta \tau ^{g}(1-\frac{1}{\phi })\) is satisfied. The capital loss tax refund for \(V_{0}^{\tau }[z=0]\) leads to the highest present value if the investor sells immediately at \(z=0\).

\(i \in (0,1)\), \(\tau \in [0,1)\), \(z\,\ge \,0\).

See Eq. (33).

See Kruschwitz and Löffler (2003) for similar problems with corporations that exist forever. Our results also indicate that there is no optimum holding period; thus, holding forever is an attractive option for the initial investor. This finding is in agreement with business valuation models that determine a minimum price for the seller such that she or he is at least indifferent between selling and holding. Only if the buyer bears the capital gains tax, i.e., pays the capital gains tax in addition to the discounted cash flow value, the vendor will be willing to sell the company.

Furthermore, this result enables us to draw conclusions on the impact of transaction costs that so far are disregarded in our setting. We could implement transaction costs in a plausible and simple case into our model as a function of the capital gains and thus a multiplier to the capital gain, similar to \(\tau ^{g}\) in Eq. (39). We will correspondingly find that \(z^{max}\) will remain unaffected.

See Fig. 1. The investor realizes a capital loss at \(z=0\) under the classic corporate tax system and shareholder relief tax system.

See Appendix.

This function f determines some \(x^{\ast}\) such that \(f[x^{\ast}]=0\) holds approximately in the following way. Assume that the first derivative \(f^{\prime}[x]\) of f is given, and let \(x_0\) be an initial guess in some neighborhood of the suspected zero \(x^{\ast}\). Then, compute for \(k=0,1,2, \ldots\) the next iterates \(x_{k+1}\) by \(x_{k+1} = x_k - \frac{f[x_k]}{f'[x_k]}\). This iteration is terminated when the absolute error satisfies \(|f[x_{k+1}]| < 10^{-8}\), which means that \(x_{k+1}\) is very close to the desired zero \(x^{\ast}\). Alternatively, for our numerical experiments, we performed at most 50 iterations, i.e., \(k=0,\ldots , 49\). Here, the function f is the right-hand side of the last identity in Eq. (41).

In the German full imputation tax system, the corporate tax rate from 1999 until 2000 was 40 %. Within the shareholder relief tax system, the corporate tax rate was 25 %. We choose the same tax rate for the classic corporate tax system.

The top marginal income tax rates in Germany were as follows: 1990–1999: 53 %, 2005: 42 % and 2012: 45 %. Considering the solidarity surcharge, it currently sums up to 0.475 %.

See also Protopapadakis (1983), who estimates average holdings periods of 21 to 34 years.

Under the classic corporate tax system for retention rates smaller than 0.4, a disadvantageous present value emerges, which we exclude. See Sect. 3.4.

The corporate taxation can be imputed only against the income tax on dividends.

Dividends are taxed without tax shield with a tax rate of 50 %, and capital gains are taxed at a rate of 25 %.

To highlight the relevance of the assumed range of retention rates, we give an example. If we look at the annual reports McDonald’s Corporation (2011, 2013), we find a retention ratio of, e.g., 24 % in 2007, 57 % in 2008 and 44 % in 2013. Relating to the example above, which is characterized by similar dividend rates, the holding period, which is necessary for a beneficial investment, varies between 17 (shareholder relief tax system, \(\gamma =0.2\)) and 113 (classic corporate tax system, \(\gamma =0.4\)) periods.

See Becker et al. (2013), p. 6.

By contrast, under a full imputation system, dividends are only subject to the income tax at 50 % and under shareholder relief to the corporate tax at a rate of 25 %, and only half of the dividends are subject to the income tax.

See Fig. 9.

Note that the corporate tax rate in the shareholder relief tax system is 25 %.

See Sureth (2006), pp. 75ff., and Rupp (2012), p. 46.

See Sureth (2006), pp. 97ff., and Rupp (2012), p. 48.

See Rupp (2012), p. 52.

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Titel: Hold or sell? How capital gains taxation affects holding decisions
verfasst von: Annika Hegemann
Angela Kunoth
Kristina Rupp
Caren Sureth-Sloane
Publikationsdatum: 23.04.2016
Verlag: Springer Berlin Heidelberg
Erschienen in: Review of Managerial Science / Ausgabe 3/2017
Print ISSN: 1863-6683
Elektronische ISSN: 1863-6691
DOI: https://doi.org/10.1007/s11846-016-0197-9

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