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Markus Diller

and Andreas Löffler

∗∗

Updated Version from 2011, January

Universität Passau, Wirtschaftswissenschaftliche Fakultät, Innstraße 27, 94032 Passau; E- Mail: markus.diller@uni-passau.de. Corresponding author.

∗∗ Universität Paderborn, Wirtschaftswissenschaftliche Fakultät, Warburger Str. 100, 33098 Paderborn; E-Mail: AL@wacc.de.

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A Note on Inheritance Tax and Valuation

Abstract

It has long been known in the literature how to include income taxes in the valuation of companies. In this paper, we clarify how to value a company when its owner becomes liable to inheritance tax.

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1 Introduction

The ultimate goal of any business valuation is to determine the price that a seller has to request for the surrender of his shares in order to attain the same consumption level as he would if he retained those shares. This is referred to as the marginal price of the shares. For some time it has been known that income taxes can have a large influence on these marginal prices. Therefore, more than a decade ago the association of CPAs in Germany decided to recommend the inclusion of income tax in any business valuation.1 Since then, both the theoretical and practical debate has gained in intensity.

Price determination from a financial theory perspective means that companies with identical cash flows also have identical prices. If both prices were different, there would be an arbitrage opportunity, which would violate one of the few undisputed paradigms of financial theory. Therefore, market participants are unable to increase their wealth by simply rearranging their portfolios. Because taxation affects cash flows, it is clear that taxes have to be included in any calculation of market values.

Regarding the impact of income tax on a company’s value, a few years ago a con- troversy broke out in the literature.2 The Anglo-Saxon literature largely ignored the income tax – for example, there is no reference in the very prestigious monograph Koller et al. (2005) on how to deal with income tax. Inheritance tax plays an important role in many jurisdictions,3 which will also exert influence on the market price of a company. To our knowledge, the question of how an inheritance tax would be taken into account in a company valuation, was not discussed in the literature. This is the goal of our paper.

In the next section we briefly present some national inheritance tax regimes before presenting our methodology. The main result is described in the third section. The paper concludes with a summary.

2 National Inheritance T ax Codes

The impact of taxes on company value results from an unequal taxation of the business to be valued and an alternative investment in the capital market. If financial assets and real investments are equally taxed, it is well known that this tax cannot influence the marginal price of the real investment. The situation is similar – as we will show – with inheritance tax. Here, too, the company’s value is affected by a different treatment of assets. The reason for this could be a different valuation of assets, a different tax rate or the explicit exemption of certain assets. In the following we wish to use selected

1 SeeSiepe (1997),Siepe (1998), (Institut der Wirtschaftsprüfer in Deutschland,2002, section A, Rn. 104 f.) andBallwieser et al. (2007).

2 See, for example, Ollmann and Richter (1999), Laitenberger (2000), Löffler (2001), Wilhelm (2005), Kruschwitz and Löffler (2005b) andRapp and Schwetzler (2008) to name a few.

3 In most countries taxes are levied both on inheritances and on (major) gifts.

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examples to show that the explicit exemption of companies from inheritance tax is in fact standard in international law.

Germany German inheritance tax law4 requires a valuation of the disputed assets at their fair market value. For financial assets, the determination of the market or nominal value is usually not a problem; also, no specific exemptions are allowed. For business assets (incl. shares in EU/EEA-based corporations, if the deceased directly held more than 25% in the nominal capital of that company), however, valuation rules and specifically the rules governing exemption and relief are extremely complex.

The law distinguishes between two types of relief. In the case of the so-called ”reg- ular relief” only 15% of the value is subject to inheritance tax. There is also the possi- bility of a full tax exemption. However, these reliefs are subject to certain conditions, most of which will not be discussed here and which are stricter in the case of full ex- emption.5 There is one necessary condition which has to be mentioned in the context of this paper. The transferee is not allowed to sell the business for a period of five years in the case of regular relief and for a period of seven years in the case of full exemption (”holding period”).

The tax rates depend on the relation between bequeather and beneficiary and can run up to 50%.

United Kingdom Under British inheritance tax law assets are generally valued at market value. The British regime also incorporates the idea of a relief of business assets.6 Financial assets, like in Germany, are not exempt from inheritance tax.

Business relief on transfers of certain types of businesses and of business assets can be claimed if they qualify as relevant business property and the transferor has owned them for a certain minimum period (two years).7 The relief rate is 100% for a business or shares in an unlisted company and 50% for a majority holding of shares in a listed company (more than 50% of voting rights).

The tax rate can reach as much as 40%.

France Under French inheritance tax, too, assets are valued at market value.8 Fi- nancial assets are not exempt from tax. French inheritance tax law also recognizes a substantial tax exemption for business assets. For shares in a qualifying business, the value is reduced by 75% in calculating the tax due. One necessary condition is that the assets must be held for more than six years.

The tax rate in France can reach 60%.

4 For an overview seeLüdicke and Fürwentsches (2009),Henselmann, Schrenker and Schneider (2010) or Langenmayr (2009).

5 For details seeScholten and Korezkij (2009).

6 For an overview seeRichter (2008).

7 However, if, in the case of a gift, the transferor dies within seven years, the property is taxed.

8 For details cf. Article 787 B Code Général des Impôt, CGI.

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3 Model

3.1 MarketValuation andInheritance Tax

Below we attempt to present the impact of inheritance tax on a company’s value in a formal model. For this purpose there should be a present (t = 0) and infinite future points of in time (t=1, . . . ,T, . . . ,∞). The present and future are certain. For simplic- ity, we disregard any additional tax burden and/or assume that these taxes are neutral in terms of financing decisions.

An investor can trade at any time and either invest in the riskless capital market (financial investment) or in a company (real investment). In the following, we assume that the nominal riskless interest rate isrf and constant over time.

The investor can buy or sell the company at any time. Shares are traded at market value (also referred to as fair price or company value), which we denote by Vt (t = 1, 2, . . .). The current market value of the company is denoted by V0. The company provides at timetthe certain cash flows of CFt.

The usual valuation equation (ignoring inheritance tax) reads

(1+rf)Vtno tax =CFt+1+Vt+1. (1) Now we introduce an inheritance tax into our model, so we want to describe the properties of this tax. We assume the following:

Taxpayer The investor is liable to tax.

Tax Object Both the company and a capital market investment are tax objects.

Tax Liability In case of a financial asset the tax base consists of interest and the invested amount; in the case of a real investment, the cash flow and a proportionate amountb∈[0, 1]of the enterprise value (“tax relief”) are taxed.

The tax base is taxed proportionally. The tax rate is independent of the tax base and isτ.

Time Next, we assume that in years T1,T2, . . . there are investors that are liable to taxation.

The assumption of one or more certain dates on which a legacy is payable limits our model. It would be realistic to suggest that the timing of the tax burden is uncertain.

We assume fixed points in time for an inheritance and we will abandon this restriction later on.

We need to stress that in our model, it is not only the time at which an inheritance of the real investment becomes effective that is important. Rather, it suffices for another investor (who at that moment does not yet own the real investment) to be present who will, at any of the mentioned points in time T1,T2, . . . receive an inheritance

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corresponding to the value of the enterprise. Assuming this investor acts rationally, he will liquidate his financial assets and – in order to avoid tax – invest in the enterprise.9 Consider the equation (1) at a point in time when no inheritance tax is due. It converts to

Vt(1+rf) =Vt+1+CFt+1. (2) To interpret this equation, we focus on an investor who at time t may have financial resources of Vt. There are two ways the investor can invest in a given period.

On the one hand, he can invest in the company att, realize the cash flow one period later and sell the company at a price of Vt+1. On the other, he can invest in the capital market using a portfolio with equivalent risk. Under the terms of an arbitrage-free market, both systems lead to identical results, reflected by the equation (2) from the perspective of timet+1. While the outcome of the capital market system is shown on the left side of the equation, on the right are the payment surplus and the proceeds on the sale.

After these preliminary considerations we now investigate how the equations change if investors are liable to inheritance tax and the markets are arbitrage-free. We concen- trate on the first point in time when an investor has to pay inheritance tax. This leads to

(1τ)1+rf

VT11=CFT1+VT1τ(CFT1 +bVT1)

or

1+rf

VT11=CFT1+ 1

1τ VT1. (3)

Equation (3) demonstrates in what direction the company’s value will move. If there is no exemption (b=1) the company value remains unchanged. If, however, the inheri- tance tax regime treats business assets preferentially, the picture changes dramatically.

Since the real investment is taxed less, any rational investor will value the company higher because of the tax relief. Equation (3) applies at all subsequent points in time at which an investor is liable to inheritance tax, and it is the starting point of our further considerations.

9 We point out that our model, where property is transferred through inheritance, is quite simple.

To understand this, assume that an inheritance will take place at timeT1. To determine its market value, we derive a relationship between the corporate values inT11 andT1by assuming that the company is acquired in T11 and sold inT1. In this situation, the price is paid by the deceased, but the heir inherits and realizes the value and the cash flow. A testator who follows the rules of the homo economicus and only maximizes his own utility has no interest in leaving an estate that does not increase its own utility. Apparently, then, there is a logical contradiction. But were we to accept this argument, then any determination of a company’s value even without inheritance tax but with a perpetual lifespan would be contradictory since no investor lives forever. Therefore, our model disregards this problem. In the economic literature so-called overlapping generations are used to circumvent that problem. In these models, the utility function of the deceased incorporates the consumption of his heirs.

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3.2 Valuation equation From (3) it immediately follows

V0 = CF1

1+rf +. . .+ CFT1 (1+rf)T1+ + 1

1τ

CFT1+1

(1+rf)T1+1)+. . .+ CFT2 (1+rf)T2+ +1

1τ

CFT2+1

(1+rf)T2+1 +. . .+ CFT3

(1+rf)T3 +1 1τ (· · ·)

��

(4) Equation (4) shows how the value of a company can be determined when an inheri- tance tax is present. If capital market and financial investments are taxed identically, no difference in value without taking inheritance tax into account can be ascertained.

However, when companies are given a tax advantage, there is a deviation to the value without tax.

In order to better understand this discrepancy, we modify the valuation equation (4). Usually, companies are valued by discounting cash flows CFt with the product of all riskless rates that have accrued until that time(1+rf)t. If an inheritance tax is due, any subsequent cash flow has to be multiplied by the expression 11τ. We now determine the value of a company using a modified equation where inheritance tax is not shown by a factor in front of the summand but instead shown in the riskless rate. This requires us to adjust the riskless rate rf for every point in time T when an inheritance can occur.

For these purposes, we assume that at timeTan investor will receive an inheritance.

How is the riskless interest rate to be modified so that after using rmf instead of rf in equation (2) the resulting value corresponds to (4)? The solution is simple, given that

1 1τ

1+rf = 1

1+rmf =⇒ rmf = (1+rf) 1τ

11, (5)

has to apply. If the riskless interest raterf for any point in timeTwhen an inheritance can occur were to be replaced by a modified riskless ratermf according to equation (5), the valuation formula that explicitly ignores the inheritance tax liability will produce an identical company value.

To understand the effect of equation (5), we have presented the functional depen- dence of the modified riskless ratermf on the actual riskless raterf for typical tax rates in figure1. It is evident that the modifications have, at times, a considerable impact.

This effect is even stronger if we assume that all costs of capital and all expected cash flows are constant over time and that a transfer is due every T years, i.e. T1 = T,T2 =2T, . . .. Equation (4) then simplifies to

V0= CF rf

(1+rf)T1 (1+rf)T11τ .

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riskless raterf

modified riskless ratermf

0% 5% 10% 15%

33.3%

23.3%

Figure 1: Modified riskless rate with an 50% inheritance tax and an allowance of b=50%

The effect of different ”holding periods” T on the value of the company is shown in figure2. Again, inheritance tax has an enormous impact on the value of the company.

holding period T company value

5 10 15 20

28.4

r1f =10

Figure 2: Company value with an 50% inheritance tax, an allowance of b=50%and riskless rate rf =10%.

3.3 Valuation equation under uncertainty concerning T1

In the last chapter we assumed that there is a certain point in time T1 at which the inheritance tax is due. In reality of course, the remaining lifetime of the testator is uncertain. Even if a transfer of ownership of the business to the next generation is planned at a fixed point in time, there is still the possibility of an earlier transfer in the case of death. The next chapter deals with this uncertainty. In contrast to equation (3) we concentrate on only one transition. As in the section above cashflows CF remain constant.

In the following we assume that a testator aged a dies at time TTmax with a particular probability pa+T at the end of the next year.10. Tmax denotes the point in

10 In the following death probabilities are used which are based on the life table (male) of the year 2007,

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time at which – if the transferor survives until then – the ownership of the company is transferred as a gift to the next generation in a planned way. So the transfer time (T) has a particular density function with:

f(T,a) =

pa+T T=1

pa+T·Tt=+aa+11(1pt) 1<T< Tmax

Tt=+aa+11(1pt) T= Tmax

0 Otherwise

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Of course, TTmax=1 f(T,a) =1 holds.11

First the value of the firm in the presence of an inheritance tax depending on the point of time of the transition has to be determined:

V0(T) =

T t=1

CF

1+rft + 1b·τ 1τ

t=T+1

CF

1+rft = CF rf

1+ (1b)τ (1τ)1+rfT

(7) Using the density function (6) we are able to determine the expected value of the enterprisedepending ona:

E[V0] =

Tmax

T

=1

f(T,aV0(T). (8)

Consider an investor who plans to transfer her firm to the next generation in 25 years. If there is no uncertainty regarding the point in time at which the transfer happens the firm value is given by 11.46 using formula (7). If this point in time is uncertain, the picture changes. Furthermore, the value will now depend on the age of the investor as the probabilities, which are used to determine the expected present value, change with a risinga: the older the transferor gets the less probable it is that he reaches the planned transition time. The firm value can now be calculated with formula (8) and is (as a function of his age) shown in figure 3.

4 Summary

For years CPAs have agreed that income tax has to be taken into consideration when valuating a company. In this study, we have investigated how valuation equations have to be adjusted when investors are liable to inheritance tax.

If business assets have an advantage over capital market investments as far as inher- itance tax is concerned, this will increase the company’s value. It is clear, by reference to an example based on simple figures, that a considerable increase can be observed within realistic parameters for European countries.

seeStatistisches Bundesamt (2010).

11 It would have been possible to use a geometric distribution as an approximation of the death and survival probabilities; but in order to get more realistic results we decided to apply real death proba- bilities.

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agea of investor company valueE[V0]

40 50 60 65 70

CFrf =10 10.56 11.63

Figure 3: Expected business value depending on the age of the transferor withτ=50%, b=50%, rf =10%and CF=1. The investor will transfer his company if he dies or, if he survives, in 25 years.

References

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Ollmann, Michael and Richter, Frank (1999) “Kapitalmarktorientierte Unternehmens- bewertung und Einkommensteuer: eine deutsche Perspektive im Kontext interna- tionaler Praxis”, in: Hans-Jochen Kleineidam (ed.), Unternehmenspolitik und Interna- tionale Besteuerung: Festschrift für Lutz Fischer, 159–178, Erich Schmidt, Berlin.

Rapp, Marc Steffen and Schwetzler, Bernhard (2008) “Equilibrium security prices with capital income taxes and an exogenous interest rate”,Public Finance Analysis (Finan- zarchiv), 64 (3), 334–351.

Richter, Andreas (2008) “Die Unternehmensnachfolge im britischen Erbschaftsteuer- recht”,Internationales Steuerrecht, 17, 59–62.

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Siepe, Günter (1997) “Die Berücksichtigung von Ertragsteuern bei der Unternehmens- bewertung”,Die Wirtschaftsprüfung, 50, 1–10 und 37–44.

— (1998) “Kapitalisierungszinssatz und Unternehmensbewertung”,Die Wirtschaftsprü- fung, 51, 325–338.

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