sooner or later? – paradoxical investment effects of capital gains taxation under simultaneous...

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Sooner or Later? – ParadoxicalInvestment Effects ofCapital Gains Taxation underSimultaneous Investment andAbandonment FlexibilityRainer Niemann a & Caren Sureth ba University of Graz, Institute of Accounting andTaxation , Universitaetsstr. 15, A-8010 , Graz , Austriab University of Paderborn, Department of Taxation,Accounting, and Finance , Warburger Str. 100,D-33098 , Paderborn , GermanyPublished online: 08 May 2012.

To cite this article: Rainer Niemann & Caren Sureth (2013) Sooner or Later? –Paradoxical Investment Effects of Capital Gains Taxation under Simultaneous Investmentand Abandonment Flexibility, European Accounting Review, 22:2, 367-390, DOI:10.1080/09638180.2012.682781

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Sooner or Later? – ParadoxicalInvestment Effects of Capital GainsTaxation under SimultaneousInvestment and AbandonmentFlexibility

RAINER NIEMANN∗ and CAREN SURETH∗∗

∗University of Graz, Institute of Accounting and Taxation, Universitaetsstr. 15, A-8010 Graz,

Austria; ∗ ∗University of Paderborn, Department of Taxation, Accounting, and Finance,

Warburger Str. 100, D-33098 Paderborn, Germany

(Received: August 2009; accepted February 2012)

ABSTRACT This paper analyzes the impact of capital gains taxation on investment timingdecisions for risky investment projects with entry and exit flexibility under differential taxrates for ordinary income and capital gains. We investigate whether capital gains taxationinfluences immediate and delayed investments asymmetrically, given the optimalabandonment decision. If capital gains taxation induces a lock-in effect, this effect isanticipated in the investment timing decision. In contrast to prior research, our numericalsimulations show that this lock-in effect of capital gains taxation can induce normal as wellas paradoxical effects on investment timing under simultaneous entry and exit flexibility. Aparadoxical timing effect, i.e., investment accelerated by capital gains taxation, especiallyemerges for high liquidation proceeds or, more conservative tax accounting, low interestrates, and low volatilities. In these cases, capital gains taxation reduces the value of theoption to invest and hereby increases the propensity to invest immediately. As a secondparadoxical tax effect, capital gains taxation may favor delayed real investment overfinancial investment. Facing these results, tax legislators should not use capital gainstaxation as a short-term tax policy instrument to influence investors’ timing decisions.

Correspondence Address: Rainer Niemann, University of Graz, Institute of Accounting and

Taxation, Universitaetsstr. 15, A-8010 Graz, Austria. Email: [email protected]

Paper accepted by Salvador Carmona.

European Accounting Review, 2013

Vol. 22, No. 2, 367–390, http://dx.doi.org/10.1080/09638180.2012.682781

# 2013 European Accounting Association

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1. Introduction

The taxation of capital gains is one of the key features of an income tax system. Many

jurisdictions, including the US, treat capital gains differently from ordinary income.

Other countries do not tax capital gains at all if some preconditions are met. For

example, Greece, Latvia, Poland, Romania, and Switzerland usually refrain from

taxing capital gains on selling non-business property. According to Austrian,

Danish, Dutch, Estonian, Bulgarian, Finnish, French, German, Hungarian,

Spanish, and Swedish tax law, gains and losses on the disposal of business property

are taxable as ordinary income, whereas gains on selling non-business securities are

subject to a flat capital gains tax rate. In the Czech Republic, Great Britain, Lithuania,

Luxembourg, Portugal, and Slovenia, private capital gains are tax-exempt if a certain

period of time is allowed to elapse between acquisition and disposal. Even countries

with tax systems close to theoretically ideal tax systems, such as the Nordic Dual

Income Tax, have developed a variety of capital gains tax regimes.

The influence of taxes on investment decisions has been a central issue of

accounting and public finance research for many years. Although real-world invest-

ment decisions are typically characterized by irreversibility, the implications of

capital gains taxes on investors’ general willingness to invest or divest under

timing flexibility have not been a focal issue until now. It is unknown whether

capital gains taxation accelerates or decelerates investment. Our paper closes

this research gap by simultaneously analyzing the influence of capital gains taxa-

tion on investment timing and abandonment decisions for risky investment

projects under differential tax rates for ordinary income and capital gains.

The impact of ordinary taxation on irreversible investments has been exten-

sively analyzed in accounting and public economics. Several studies focus on

the economic effects of individual and corporate income taxation, but neglect

real-world characteristics of tax systems like capital gains taxation.1 Conversely,

in their literature reviews Hanlon and Heitzman (2010), Shackelford and Shevlin

(2001), and Zodrow (1993) point out that analyzing the effects of capital gains

taxation is a focal issue in accounting research.

Capital gains taxation may lead to double taxation of corporate earnings, which

can be avoided by retaining profits at the corporate level and by deferred realization

of capital gains at the shareholder level. This so-called lock-in effect was derived

by Constantinides (1983) in an intertemporal capital market model. Numerous

empirical studies investigate whether capital gains taxation induces a supply-side

lock-in effect (present shareholders require higher prices to be compensated for

a capital gains tax liability) or a demand-side capitalization effect (potential share-

holders offer lower prices if they have to pay capital gains taxes in the future).

These papers indicate that capital gains taxes impact asset pricing and entrepre-

neurial decisions.2 See, for example, Akindayomi and Warsame (2007), Ayers

et al. (2002, 2003, 2007), Blouin et al. (2003), Cook and O’Hare (1992), Dai

et al. (2008), Landsman and Shackelford (1995), Lang and Shackelford (2000),

Liang et al. (2002), and Shackelford (2000) who empirically study the extent to

368 R. Niemann and C. Sureth

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which stock prices react to changes in the capital gains tax rate or how holding

periods or start-up investments are affected. Some of these studies provide

evidence for the capital gains tax lock-in effect, others find that, depending on

the parameter setting, either capitalization or lock-in prevails.

Recent analytical papers from the real option literature broaden the perspective

with respect to investment timing decisions. Schneider and Sureth (2010) inves-

tigate the impact of (ordinary) profit taxation under simultaneous entry and exit

flexibility. They neglect capital gains taxation and find a tax paradox caused by

the abandonment option. This means that investors tend to accelerate investment

after tax rate increases. Agliardi and Agliardi (2008, 2009) and Wong (2009) use

continuous-time real option models and analytically identify ambiguous effects

of indirectly progressive ordinary taxation on liquidation decisions. Agliardi

and Agliardi (2008, 2009) find that tax progressivity can either accelerate or

delay liquidation whereas they consider proportional tax rates to be neutral

with respect to liquidation policy. Using a similar model Wong (2009) confirms

that progressive tax rates distort the liquidation decision.

In recent years the accounting literature has started to pick up option pricing theory

as a framework to study investment decisions under timing flexibility. Hirth and

Uhrig-Homburg (2010) analyze investment timing under financial constraints, but

do not consider taxes. In an analytical model of call option exercise, Alpert (2010)

examines the impact of differential taxation on investment timing. Whereas

exercising a call option prematurely is known to be non-optimal in a world

without taxes, she proves that many early exercise events previously considered

irrational can be rationally explained by differential taxation of option and share

transactions. Consequently, differential taxation might exhibit an accelerating

impact on investment timing. However, Alpert (2010) analyzes only non-depreciable

financial assets and does not take liquidation decisions or put options into account.

In contrast to the empirical literature, we analyze the impact of capital gains taxes

on investment timing rather than lock-in or capitalization effects. Our model extends

prior real option literature by addressing two major issues arising in the context

of capital gains taxation. First, we analyze the effects of taxing capital gains on

investment timing by introducing an option to invest in the case of risky investment

opportunities. This means that the investor can choose between immediate and

delayed investment. We investigate whether capital gains taxes affect immediate

and delayed investment asymmetrically. Second, our model includes an option to

abandon a risky project realized in the past. Thus, the investor can choose

between liquidating and continuing a project. When deciding on investing immedi-

ately or later the investor anticipates the optimal liquidation decision. To our

knowledge, no existing real option model combines simultaneous entry and exit

flexibility with differential taxation of ordinary income and capital gains.

Applying numerical simulations we find that capital gains taxation is indeed

relevant for entrepreneurial investment timing decisions. We identify normal

as well as paradoxical effects caused by differential taxation. Investors are

defined to react normally if a rise in tax rates negatively affects their willingness

Paradoxical Investment Effects of Capital Gains Taxation 369

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to invest immediately. By contrast, a paradoxical effect occurs if an increase in

taxes increases the investor’s propensity to invest immediately.3 We find that

capital gains taxation may accelerate investment, especially for high liquidation

proceeds or more conservative tax accounting. We identify a second paradoxical

effect of capital gains taxation concerning the choice between risky real and

risk-free financial investment. Delayed real investment may be favored over

financial investment. In contrast to these two paradoxical reactions apparently

normal timing effects can be shown for particular settings. Whether a normal

or paradoxical tax effect occurs depends on project-specific data.

By integrating depreciable assets and differential taxation of ordinary income

and capital gains, our approach extends the model of Schneider and Sureth (2010)

who focus on current taxation and do not consider depreciable assets. Similar to

our results, they identify paradoxical timing effects only under simultaneous

entry and exit flexibility, but not in their benchmark case without abandonment

flexibility. Their model only includes ordinary taxation and zero liquidation

proceeds, so that their results are unaffected by capital gains taxation.

Similarly, Agliardi and Agliardi (2008, 2009) and Wong (2009) model an

option to abandon and abstract from capital gains taxation. By contrast, our

analysis integrates capital gains taxation into a model with simultaneous entry

and exit decisions. Whereas they investigate the impact of progressive income

taxation, our model relies on proportional taxation, but permits differential tax

rates for ordinary income and capital gains. They find proportional taxation to

be neutral with respect to liquidation decisions. However, we can identify

normal as well as paradoxical timing decisions under proportional and even

uniform tax rates. Consequently, a compound option setting tends to induce

ambiguous timing effects as already indicated by Schneider and Sureth (2010).

In line with the study by Alpert (2010) on financial call options, we apply numeri-

cal simulations to identify conditions for early and late entry decisions because

analytical solutions are unlikely. We extend Alpert’s approach not only with

respect to depreciable real investment objects but further integrate simultaneous

abandonment flexibility into our analysis. Whereas Alpert (2010) finds differential

taxation of option and share transactions being the cause for early exercise under

entry flexibility, we identify settings for normal and paradoxical timing due to differ-

ential taxation of ordinary income and capital gains in case of compound options.

The remainder of the article is organized as follows. We present the investment

model and the assumptions of our tax system, including a set of different tax

rates, in Section 2. Since the model leaves only limited room for analytical

solutions we investigate the economic effects of introducing capital gains taxes

numerically in Section 3. Section 4 concludes.

2. Model Setup

Our model is a discrete-time model with a discrete state space. We assume the

investor to have an exogenously given time horizon of T periods. At the end


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of the time horizon the investor has to terminate all economic activities. We

assume T = 3 periods as this time horizon is the shortest possible period that sim-

ultaneously permits us to analyze an option to invest and an option to abandon

and allows us to elaborate the effects of differential taxation. Allowing for

more periods would not provide further insights into the effects of taxes on

investment and abandonment strategies.

The model is based on a purely individual calculus and does not involve market

valuation. At the starting time t = 0, the investor owns initial equity capital I0,

which corresponds to the acquisition costs of a project with stochastic cash

flows. The project is defined as either an asset, a sole proprietorship, or a share

in a partnership. Hence, we look at asset deals rather than share deals. We

assume the investor to be risk-neutral. Therefore, we focus on expected future

values.

Cash flow uncertainty is modeled by a geometric binomial process. At any time

t the project’s cash flow denoted by pt moves either upward or downward

pt+1 = (1 + u)pt

with probability p

(1 + d)pt with probability 1−p

{(1)

with u . d, t = 0, . . . , T − 1

u the upward movement and d the downward movement. The publicly observable

initial value is given by p0. The upward probability p is the investor’s subjective

probability. The upward and downward movements u and d are also individual

estimates by the investor. The investment project is regarded as an innovative

combination of numerous single assets. The spanning property does not hold.4

As a result, the completed project yields cash flows that cannot be duplicated

by traded assets. The project’s resulting cash flows are not necessarily related

to the sum of the acquisition costs or liquidation proceeds of the single assets.

Therefore, the investor has to assess the entire project individually and cannot

refer to market values.

The investor has an option to delay, corresponding to a call option known from

financial option pricing theory. The option means that there is flexibility to invest

either in period t = 0 or in t = 1. The date of investment is denoted by tI [ 0; 1{ }.The earliest cash flows accrue one period after investment, i.e., p1 in t = 1 or p2

in t = 2. The initial outlay necessary to acquire the investment project is constant

and given by I0 = 1. In principle, the acquisition costs could be modeled as deter-

ministic or stochastic functions. For reasons of analytical simplicity, we focus on

a constant I0, which is normalized to unity.5 If the investor does not invest

immediately in t = 0 they do not receive the cash flow p1. In this case, the

equity capital yields the risk-free return r from financial investment. Then, at

time t = 1 the investor faces the decision to invest again. If they decide to

invest, they receive the remaining cash flows until the time horizon or the


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liquidation date is reached. Otherwise, their wealth is compounded at the exogen-

ously given interest rate r until t = 3. The interest rate r is the only parameter

determined by the market.

If the investor decides to carry out the project in t = 0 or t = 1 they also obtain

an option to abandon the project prematurely in t = 2. Without exercising that

option to abandon the investor would receive cash flows until the time horizon

t = 3. By contrast, if the option is exercised in t = 2, the investor abandons

the entire project and receives the liquidation proceeds L2, but no cash flows

p3. The liquidation or termination date is denoted by tL [ 2; 3{ }. The value of

the option to abandon (put option) can be easily computed as the difference

between the liquidation proceeds and the expected present value of remaining

cash flows.

In summary, the investor faces different decisions at three points in time:

. t = 0: decision to invest immediately or to postpone the decision until t = 1,

. t = 1: decision to invest or to refrain from real investment entirely,

. t = 2: decision to continue the business or to abandon the project (only if the

project was implemented in t = 0 or in t = 1).

The decision tree is displayed graphically in Figure 1. Here, decision nodes are

represented by numbered rectangles (11, 21, 22, 31,. . ., 38). Event nodes, i.e.,

the upward and downward movements of the cash flow process, are symbolized

by dots. The capital letter L indicates a liquidation decision by the investor.

Figure 1. Structure of decisions and events in the model.


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The investor’s objective variable is the future value after taxes at the time

horizon, denoted by FV. Although the investor can decide to abandon the

project at time t = 2, a uniform time horizon is needed to compare the optim-

ality of different decisions. We assume that the investor’s consumption is

financed by exogenous income from other sources. Hence, withdrawals are

not necessary.

The investment–liquidation problem can be solved by backward induction,

i.e., the decision to abandon (decision nodes 31–38 in Figure 1) has to be

solved first. Each decision node corresponds to a particular combination of

upward and downward movements. If the project is in place, the investor

observes the current cash flow p2. For each of the possible realizations as well

as for each initial timing decision the optimal abandonment decision has to be

reached. In other words, at each of the decision nodes 31–38 the investor

faces the decision of whether or not to continue the project.

Moving backwards, we arrive at time t = 1 (decision nodes 21 (u) and 22 (d),

respectively). Assuming that the investor has not invested in period t = 0, they

can choose between the deterministic future value from financial investment

and the uncertain future value of the project’s remaining cash flows. The investor

realizes the project at date t = 1 if its expected future value exceeds the future

value of financial investment. Moving backwards again, to the initial decision

node 11, the value of the project is defined as the future value of the remaining

cash flows, taking the option to abandon into account.6

Capital gains taxation affects the value of the options and in turn, the invest-

ment and divestment strategies. Due to the numerous non-linearities arising

from (nested) maximum operations, the optimal investment and liquidation

policy with and without capital gains taxation can be neither immediately

observed nor analytically determined. Thus, in the presence of capital gains taxa-

tion the following questions should be analyzed for an investor facing simul-

taneous investment and divestment flexibility numerically.

. What are the effects of varying the capital gains tax rate on investment timing

and liquidation policy?

. Does the level of liquidation proceeds affect investment timing?

. Does cash flow volatility affect investment and liquidation timing?

. To what extent does the interest rate affect investment and liquidation policy?

To isolate the impact of a capital gains tax, we assume that capital gains are

subject to the tax rate t g, which may differ from the tax rate t o on ordinary

(operating) income.7 The capital gains tax rate is defined as a multiple of the

ordinary income tax rate: t g = mt o with m ≥ 0. Moreover, interest income is

taxed at the rate t i. For simplicity, all tax rates are assumed proportional. We

neglect loss-offset limitations, which would further complicate the analysis. If

a tax base is negative, the taxpayer receives a tax reimbursement of

tax rate · tax base( ).


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If the project is in place, the tax base for ordinary income bot is defined as the

difference between cash flows pt and linear depreciation allowances8 dt:

bot = pt − dt = pt −

1

T= pt −

1

3(2)

The tax base from equation (2) results in the after-tax operating cash flow ptt :

ptt = pt − t obo

t = 1 − t o( )pt +t o

T= 1 − t o( )pt +

t o

3(3)

The project’s depreciation period for tax purposes is equal to its economic useful

life and is given by T = 3. Since the time horizon is also defined as T = 3, a

delayed project realized at time t = 1 still has a positive book value at time

t = 3. The same happens at t = 2 if a project acquired at t = 0 or t = 1 is aban-

doned in t = 2.

To determine the capital gains tax base, it is necessary to model the liquidation

proceeds endogeneously. We assume the liquidation proceeds Lt to be a multiple

of the project’s current book value BVt: Lt = l BVt with l ≥ 0 a coefficient indi-

cating whether the project is sold with a book profit (l . 1) or loss (l , 1). BVt

is the book value of the investment project at time t defined as the difference

between the initial investment (I0 = 1) and accumulated linear depreciation

allowances dt:

BVt = 1 −∑t

s=1

ds (4)

From an accounting perspective, the multiple l can also be interpreted as a con-

servatism parameter.9 If l . 1, the investor’s estimated liquidation proceeds

exceed the project’s book value. This means that the book value can be regarded

as a conservative estimate of the project’s current market value. For l , 1, the

investor expects a capital loss, which corresponds to less conservative or even

aggressive tax accounting rules.

We assume the factor l to be constant. In reality, however, changes in capital

gains taxation might affect this market-to-book ratio in either direction.10

Explaining the incidence of capital gains taxation would require a detailed set

of assumptions with regard to the supply and demand functions of all assets

under consideration. Therefore, we refrain from using a more sophisticated func-

tional form for l. Lt does not necessarily reflect the present value of remaining

cash flows. If Lt was identical to this state-dependent present value, an option

to abandon would have no separate positive economic value and hence would

be worthless.11 Furthermore, Lt does not depend on the realization of the cash

flow process but on the depreciation of the underlying asset and thus on


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investment timing. In this sense, Lt is endogenous. We can therefore study the

interdependencies of expected liquidation proceeds, i.e., tax accounting conser-

vatism, and capital gains taxation on investment and divestment timing.

If the option to abandon is not exercised in t = 2, the project is terminated at

the time horizon t = 3. If the project was implemented in tI = 0, its economic

useful life is fully exploited in t = 3 and the liquidation proceeds L3 as well as

the book value are equal to zero: L3|tI=0 = lBV3|tI=0 = 0. By contrast, if the

project was implemented in tI = 1, one period of economic life remains.

Hence, we assume that the project can be liquidated with positive liquidation pro-

ceeds at t = 3. Again, the liquidation proceeds are a multiple l of the project’s

book value at time t: L3|tI=1 = lBV3|tI=1 = l/3.

Using the above definition of the liquidation proceeds, the taxable capital gain

bgt is the difference of liquidation proceeds and the project’s book value:

bg2 = L2 − BV2 = l− 1( )BV2 (5)

bg3 = 0 if tI = 0

L3 − BV3 = l− 1( )BV3 if tI = 1

{(6)

This implies that the project’s book value, the depreciation deductions, and a poss-

ible capital gain are path-dependent and contingent on the time of investment.

Thus, the decision nodes 31 and 35 (uu) (and 32/36 (ud), 33/37 (du), 34/38

(dd), respectively) do not necessarily induce identical optimal liquidation

decisions.

Since the taxation of ordinary income and capital gains may differ, the investor

must distinguish between the different possible investment dates when deciding

to continue or abandon the project. If the project was realized in tI = 0, the book

value BV2 at time t = 2 is given by BV2|tI=0 = 13. In case of liquidation, the result-

ing capital gain or capital loss bg2

∣∣tI=0

= L2 − BV2|tI=0 = l− 1( )BV2|tI=0 =13l− 1( ) is taxed at the capital gains tax rate t g. The resulting net-of-tax liquida-

tion proceeds Lt2 are given by:

Lt2

∣∣tI=0

= L2 − t g bg2

∣∣tI=0

= 1 − t g( ) l3+ t g

3(7)

If the investor decides to continue the project, a capital gain or loss does not occur at

date t = T = 3, because the project’s remaining value and its book value are both

equal to zero. The investor abandons the project only if the after-tax liquidation pro-

ceeds, compounded at the after-tax interest rate rt = 1 − ti( )

r, exceed the expected

after-tax future value resulting from operating the project (see Appendix A).

1+rt( )Lt2

∣∣tI=0

=

1+ 1−t i( )

r[ ]

1−t g( )l3+t g

3

[ ]. E2 pt

3

[ ]= 1−t o( )p2q+t o

3

(8)

with q; p 1+u( )+ 1−p( )

1+d( ). This condition has to be checked separately for


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each of the possible realizations of the cash flow process in t=2 (decision nodes 31–

34). The optimal liquidation decision for delayed investment (decision nodes 35–

38) is very similar and is described in Appendix B. It should be noted that all

three (possibly different) tax rates ti, tg, and to as well as depreciation deductions

dt affect the decision to liquidate.

In Appendix C, we derive critical levels of the liquidation proceeds factor l

which induce an indifference between continuation and liquidation. It can be

shown12 that this indifference requires a lower critical liquidation proceeds

factor for delayed investment than for immediate investment.

l∣∣∣tI=1

− l∣∣∣tI=0

= − rt 3p2q 1 − t o( ) + t o[ ]1 − t g( ) 1 + 3rt + 2rt( )2

( ) , 0 (9)

As a consequence, abandonment is more likely under delayed investment than

under immediate investment effectively due to a higher strike price of the corre-

sponding put option in this setting. Whether capital gains taxation aggravates or

mitigates this effect depends on the ratio m of the capital gains tax rate and the

ordinary tax rate, as well as on the actual liquidation proceeds factor l.

The total value of flexibility F0 included in the investment opportunity at t = 0

can be computed by backward induction as the difference of the initial expected

objective value E∗0 FV[ ] = max E0 FV[ ]tI=0;E0 FV[ ]tI=1

{ }, i.e., the maximum of

the expected future values of immediate and delayed investment,13 and the

expected future value of after-tax cash flows from the real investment:

F0 = E∗0 FV[ ] −

∑3

t=1

1 − t o( )E0 pt[ ] + t o

3

[ ]1 + rt( )3−t (10)

3. Numerical Examples

Since the optimal investment timing and abandonment decisions are rather

complex and require many case differentiations, analytical solutions are unlikely.

Consequently, we focus on numerical simulations to elaborate the effects of

capital gains taxation. The following examples illustrate the impact of introdu-

cing and varying capital gains taxation. We identify parameter combinations

that affect investment timing decisions and try to assess the relevance of

capital gains taxation by varying the different determinants of investment

timing. Since the factor for the liquidation proceeds l is crucial for timing

decisions, we always modify the parameters m, r, p0, or u simultaneously with

l. By doing so, we try to derive as general results as possible, although the

reach of our model is necessarily limited due to its restrictive assumptions. For

ease of presentation, we focus on a symmetric distribution of upward and down-

ward movements of the cash flow process (p = 12, u = −d, q = 1).


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Obviously, the most prominent parameter regarding capital gains taxation is the

capital gains tax rate tg, represented by the multiple m. Varying m may induce

either normal or paradoxical effects with respect to optimal investment behavior,

depending on the factor for the liquidation proceeds l. These effects are shown

in Figure 2 based on the parameter setting r = 0.1, u = 0.2, p0 = 0.45,

t i = t o = 0.35. The black solid lines are different level curves of the difference

between immediate and delayed investment: E0 FV[ ]tI=0 −E0 FV[ ]tI=1 = const.

Whereas increasing the capital gains tax rate may reduce the advantage of

immediate investment if the liquidation proceeds are rather low, an apparently

paradoxical tax effect emerges for sufficiently high levels of the liquidation

proceeds: higher capital gains tax rates accelerate investment. This effect is

illustrated by the gray and white areas in Figure 2. The border between the

gray and white area displays all combinations of capital gains tax rates and

liquidation proceeds factors (m− l combinations) for which the investor is indif-

ferent to immediate or delayed investment (E0 FV[ ]tI=0 = E0 FV[ ]tI=1).

For combinations to the right of this indifference curve (white area), the inves-

tor prefers delayed investment, while for parameters on the left (gray area) they

prefer to invest immediately. Left-leaning level curves indicate the normal effect

of delayed investment for higher capital gains tax rates. By contrast, right-leaning

level curves illustrate the paradoxical effect of higher capital gains tax rates

accelerating investment. This result extends the current literature threefold:

first, capital gains taxation under entry and exit flexibility has not been analyzed

until now. Second, we cannot confirm the uniform effect of capital gains taxation

found in prior literature. Third, in contrast to most analyses we model a depreci-

able real investment rather than a financial asset which has further implications

Figure 2. Indifference curve and level curves of immediate and delayed investment forvarious m-l combinations.


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for accounting choices. For example, in some jurisdictions, taxpayers can choose

between linear and declining-balance depreciation allowances. Accelerated

depreciation allowances represent a higher degree of conservatism in tax

accounting. Against this background, higher (lower) liquidation proceeds can

be interpreted as more (less) conservative tax accounting in present value

terms. Figure 2 shows that investment timing and hereby the timing effects of

capital gains taxation depend on the degree of conservatism in tax accounting.

Consequently, the tax accountant’s decision on discretionary accruals determines

the taxable capital gain, the liquidation decision, and in turn the initial investment

timing decision. This result highlights that tax accountants may exert substantial

indirect influence on investment strategies.

The slope of the indifference curve reveals that the effects of capital gains tax

rate changes can be offset by variations of the liquidation proceeds. In order to

maintain the indifference to immediate and delayed investment after an

increase of the capital gains tax rate factor from m = 1.176 to m = 1.737, for

instance, the liquidation proceeds factor would have to rise from l = 1.2 to

l = 1.3.

According to traditional investment theory, real investment is most attractive

when interest rates are low. As delayed investment contains a substantial interest

income component, waiting becomes more attractive for higher interest rates.

For very high interest rates, financial investment is optimal. Each investment

alternative may be optimal for a particular interest rate interval. However,

there are combinations of parameters (not displayed in the following figure),

which imply that both immediate and delayed investment may be inferior for

all possible interest rates.

Figure 3 displays optimal investment timing decisions with and without

capital gains taxation for various combinations of the interest rate r and the

parameter for the liquidation proceeds l.14 As before, the parameter setting is

Figure 3. Immediate, delayed, and financial investment for different r-l combinations.


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given by u = 0.2, p0 = 0.45, ti = to = 0.35. If capital gains taxation applies,

the tax rate is tg = 0.35.

The total set of r-l combinations can be separated into three areas with

different optimal decisions:

. Immediate investment is optimal for low interest rates and rather low liquida-

tion proceeds. This area is bounded by the solid line (after capital gains taxa-

tion) and by the thick dashed line (after ordinary taxation without capital gains

taxation), respectively.

. Delayed investment is optimal for high liquidation proceeds. This area is

shown on the right-hand side of figure 3.

. For sufficiently high interest rates, financial investment is optimal, as shown by

the upper area bounded by the thin solid line.

The boundaries of the three areas are shifted by introducing capital gains taxa-

tion. These effects can be easily observed from the non-congruence of the areas

bounded by the solid and dashed line. However, capital gains taxation does not

have a uniform effect on investment timing. The four shaded areas indicate the

parameter combinations for which capital gains taxes alter the investment

decision (in descending order).

1. For the r-l combinations in the upper medium gray area delayed investment

is optimal without capital gains taxation, but financial investment is optimal

after the taxation of capital gains. This effect is straightforward because

financial investment (interest income) is unaffected by capital gains taxation.

2. The black area represents r-l combinations for which financial investment is

optimal without capital gains taxation and delayed investment is optimal with

capital gains taxation. This apparently paradoxical effect is due to the tax

reimbursement following a capital loss. In contrast to the paradoxical tax

effects described above, this effect does not refer to investment timing.

3. The parameter combinations in the light gray area favor delayed investment

under capital gains taxation.

4. A paradoxical timing effect emerges for the parameters in the lower medium

gray area. Here, immediate investment is favored by capital gains taxation.

In this example, for any given value of the interest rate r there exists an interval

of l-values (= 1) for which capital gains taxation alters the investment timing

decision.

Summarizing, capital gains taxation may accelerate as well as delay invest-

ment and might favor real as well as financial investment. This finding confirms

that, in contrast to prior literature, paradoxical effects of capital gains taxation

may emerge. Due to the various non-linearities in the model, the shaded areas

form non-convex parameter sets. These results highlight the distinctive parameter

sensitivity of the investment effects induced by capital gains taxation.


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Varying the volatility of cash flows, measured by the magnitude of upward and

downward movements u = −d, also reveals normal as well as paradoxical effects

of capital gains taxation, as shown in Figure 4 based on the parameter

setting r = 0.1, p0 = 0.45, t i = t o = t g = 0.35.

The numerical example in Figure 4 neglects financial investment and displays

only the decision between immediate and delayed investment. In accordance with

traditional option pricing theory, high volatility increases the option value and

favors delayed investment. Hence, for low values of u immediate investment is

optimal. This effect can be observed from the level curves of the difference of

immediate and delayed investment: E0 FV[ ]tI=0 −E0 FV[ ]tI=1 = const. as

defined by the thin solid lines. The higher the liquidation proceeds, the lower

the critical value of volatility for which investment should be delayed. Obviously,

there is a substitutional relation of volatility and liquidation proceeds.

The area bounded by the thick solid line represents the u-l combinations for

which immediate investment is optimal after capital gains taxation. The corre-

sponding combinations without capital gains taxation are bounded by the dashed

line. The two shaded areas display the parameter combinations for which capital

gains taxation alters the investment timing decision. For the u-l combinations in

the upper light gray area (l , 1) capital gains taxation delays investment. By con-

trast, for the u-l combinations in the lower medium gray area (l . 1) capital gains

taxation accelerates investment. These results confirm that capital gains taxation

may influence investment timing in either direction.

The effects of varying the initial cash flow p0 also confirm the results from our

previous numerical examples. The interval of liquidation proceeds for which

Figure 4. Immediate and delayed investment for different combinations of volatility u andliquidation proceeds l.


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immediate investment is favored by capital gains taxation is larger for higher

initial cash flows p0.

The impact of varying the capital gains tax rate on the total value of flexibility

– the combination of the option to wait and the option to abandon – also depends

on the liquidation proceeds. Figure 5 shows the value of flexibility F0 for the par-

ameter setting r = 0.1, u = 0.2, l [ 0.9, 1, 1.1{ }, p0 = 0.45, ti = to = 0.35 as a

function of the multiple m for different levels of the liquidation proceeds (upper

dashed line: l = 1.1, thick solid line: l = 1, thin solid line: l = 0.9). It can be

easily observed that the value of flexibility decreases for higher taxation of

capital gains and increases for higher tax reimbursements for capital losses.

Again, for positive capital gains, paradoxical tax effects are likely, because

lower option values accelerate investment.

4. Economic Implications

We analyze the impact of capital gains taxation on optimal investment timing and

abandonment policy under uncertain cash flows. As a main innovation we model sim-

ultaneous entry and exit flexibility for depreciable real investment projects. In con-

trast to the hitherto literature that focuses on financial assets, our analysis addresses

the relevance of accounting choices (e.g., depreciation patterns). Since the level of

taxable capital gains is affected by the degree of tax accounting conservatism it is

evident that decisions on discretionary accruals may indirectly affect investment

strategies. As a main result, we cannot confirm the uniform effect of capital gains

taxation found in prior research but identify normal and paradoxical effects.

Entrepreneurial flexibility and partial irreversibility of investment are modeled

simultaneously by means of an option to invest and an option to abandon. Thus, an

investor can choose to either invest immediately or postpone investment until the

next period. Once an investment project is in place, the investor is not bound to the

project for infinity. Rather, there exists an option to abandon the project prematurely.

Figure 5. Value of flexibility as a function of the capital gains tax rate.


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Due to the interdependencies of the investment and liquidation decision, even

this three-period model is rather complex.15 Nevertheless, it enables us to elab-

orate normal as well as paradoxical effects of differential taxation. First, in con-

trast to prior research we find that capital gains taxation may accelerate

investment, especially for high liquidation proceeds or more conservative tax

accounting, low interest rates, and low volatilities. In these cases, capital gains

taxation reduces the value of the option to invest and thereby increases the pro-

pensity to invest immediately. We identify a second paradoxical tax effect that

does not refer to timing. Rather, capital gains taxation may favor delayed real

investment over financial investment due to tax reimbursements resulting from

capital losses. Furthermore, the apparently normal timing effect emerges for

low liquidation proceeds, high interest rates, and high volatilities and means

that real investment is delayed due to the introduction of capital gains taxation.

Since integrating taxes substantially increases the complexity of the optimal

simultaneous investment and abandonment decisions, analytical solutions are

unlikely. To derive the model’s main economic implications, extensive numerical

simulations are necessary. We find that capital gains taxation is indeed relevant for

entrepreneurial investment timing decisions. As a consequence, neglecting the

implications of capital gains taxation may lead to wrong investment decisions.

The final effect depends on project-specific data, such as the initial cash flow, vola-

tility, or the interest rate. Against this background it seems unlikely that a more

sophisticated model, including a more complicated functional specification of

the liquidation proceeds, will be able to provide parameter-independent predic-

tions of the investment effects of capital gains taxation.

With this model there are some caveats that should be discussed. As a purely

individual approach the model does not consider market valuation of the invest-

ment project. If the project is a traded asset and the spanning property holds, the

liquidation proceeds follow a stochastic process equivalent to the cash flow

process. Then, traditional option pricing methods could be used to derive the

optimal decisions. However, we consider this situation to be more unlikely

than our assumption of liquidation proceeds proportional to the project’s book

value. Moreover, our model does not reveal parameter-independent general

effects of capital gains taxation. If such effects existed, we would expect them

in simple models like ours rather than in more complex models.

Although investment timing effects are notoriously hard to observe, especially

when it comes to real investment, it would be desirable to verify our numerical

results in an empirical study. Since some recent tax reforms in OECD countries

included higher capital gains taxation, it would be worthwhile examining their

impact empirically. Below, we describe two examples for which we can derive

testable hypotheses.

In Austria, private gains on the disposal of real estate until 2012 were taxable

only if the assets were held for less than ten years (‘speculation period’).

However, the tax base for these taxable capital gains was broadened in 2007.16

This tax reform element corresponds to a higher m in our model. According to


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our results, we would expect a paradoxical timing effect, i.e., a relative increase in

immediate compared with delayed real estate investment by individuals, assuming

that the expected liquidation proceeds exceed the asset’s book value (l . 1).

In Austria and in Germany, gains on the disposal of sole proprietorships or par-

ticipations in partnerships are subject to reduced capital gains tax rates if the tax-

payer meets certain conditions.17 In 2004, preferential taxation in Germany was

reduced, which also implied a higher m in our model. Hence, it should be verified

whether or not this increased capital gains taxation was accompanied by a relative

increase in immediate compared with delayed establishment of sole proprietor-

ships by individuals, as our results suggest.

Apart from the investment timing effects, a possible capitalization effect of

capital gains taxation could be empirically verified by checking whether these

two examples of increased capital gains taxation actually had a significant

impact on the realized liquidation proceeds factor l.

We illustrate the investment and liquidation effects of repealing the current

tax-exemption of capital gains in some countries and the effects of differential

taxation of different classes of income. Our results indicate that capital gains

taxation can induce normal as well as paradoxical effects. These findings

confirm the distinctive parameter sensitivity of the investment effects induced

by capital gains taxation and tax accounting conservatism. In any case, the pro-

nounced sensitivity of entrepreneurial investment timing decisions with respect

to changes in the parameters show that tax policy-makers should not use

capital gains taxation as a short-term tax policy variable in order to balance the

budget or as an instrument to influence investors’ timing decisions.

Acknowledgments

This paper has benefited from helpful comments by the editors Salvador Carmona and

Steven Young and two anonymous referees on earlier versions of this paper. The

authors also thank workshop participants at the European Accounting Association

Annual Meeting and the Annual Meeting of the German Academic Association for

Business Research. Rainer Niemann gratefully acknowledges support by the Austrian

Science Fund (FWF, P 22324-G11). Caren Sureth gratefully acknowledges support

by the German Research Foundation (DFG SU 501/1-2 and DFG SU 501/4-1).

Appendix A. Expected After-tax Future Value of Immediate Investment

The expected future value after taxes at date t = 2 can be computed assuming the

stochastic process as exogenous:

E2 FV[ ]tI=0 = p 1 + u( )p2 1 − t o( ) + t od3[ ]+ 1 − p

( )1 + d( )p2 1 − t o( ) + t od3[ ]

= 1 − t o( )p2q + t o

3

(11)


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with q ; p 1 + u( ) + 1 − p( )

1 + d( ) as an auxiliary variable. In the symmetric

scenario described by p = 12; u = −d, q simplifies to q = 1.

Appendix B. Optimal Liquidation Decision for Delayed Investment

If the project was acquired in period t = 1, it was depreciated for only one period

in t = 2. Thus, the book value still amounts to BV2|tI=1 = I0 − d2 = 23. The poss-

ible liquidation proceeds are given by 23l. The resulting capital gain b

g2

∣∣tI=1

=L2 − BV2|tI=1 = 2

3l− 1( ) is taxed at the rate tg, so that the after-tax liquidation

proceeds are given by:

Lt2

∣∣tI=1

= L2 − t g bg2

∣∣tI=1

= 2

31 − t g( )l+ 2

3t g (12)

If the investor decides to operate the project until the time horizon, it still has a

positive book value BV3|tI=1 = 13, because it was depreciated for only two periods.

Assuming that the liquidation proceeds in t = 3 equal L3 = lBV3|tI=1 = l3, the

investor realizes a capital gain or loss that is also subject to the capital gains

tax rate tg.18 The capital gains tax base and the associated after-tax liquidation

proceeds are given by:

bg3

∣∣tI=1

= l− 1( )BV3|tI=1 = l− 1

3

Lt3

∣∣tI=1

= L3 − t g bg3

∣∣tI=1

= 1 − t g( ) l3+ 1

3t g

(13)

The after-tax liquidation proceeds have to be added to the operating cash flows

in t = 3 if the optimal liquidation decision is considered. Liquidation in t = 2 is

optimal if the compounded after-tax liquidation proceeds exceed the

expected after-tax operating cash flows plus the after-tax liquidation proceeds

in t = 3:

1 + rt( ) Lt2

∣∣tI=1

= 1 + rt( ) 2

31 − t g( )l+ 2

3t g

[ ]

. E2 FV[ ]|tI=1 = 1 − t o( )p2q + t o

3+ 1 − t g( ) l

3+ t g

3

(14)

The optimal liquidation decision depends on all tax rates ti, tg, and to, the interest

rate r, as well as the date of investment tI .

Appendix C. Indifference between Continuation and Abandonment

We can derive values of a critical capital gains tax rate tg

or a critical level

of the liquidation proceeds given by a multiple l at which the investor is


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indifferent as to continuing or abandoning the project in the case of immediate

investment:

E2 pt3

[ ]∣∣tI=0

=! 1 + rt( ) Lt2

∣∣tI=0

tg∣∣tI=0

= 1

l− 1l− 3 1 − t o( )p2q + t o

1 + rt

( )

l∣∣∣tI=0

= 3 1 − t o( )p2q + t o

1 + rt( ) 1 − t g( ) − t g

1 − t g

(15)

and in case of delayed investment

E2 FV[ ]|tI=1 =!

1 + rt( ) Lt2

∣∣tI=1

tg∣∣tI=1

= 1

l− 1l− 3 1 − t o( )p2q + t o

1 + 2rt

( )

l∣∣∣tI=1

= 3 1 − t o( )p2q + t o

1 + 2rt( ) 1 − t g( ) − t g

1 − t g

(16)

Appendix D. Total Value of Flexibility

The investor’s remaining objective value at the decision nodes 31–34

(immediate investment) is defined as the maximum of the compounded after-

tax liquidation proceeds and the expected future value from continuing the

project:19

E∗2 FV[ ]tI=0 = max 1 + rt( ) 1 − t g( ) l

3+ t g

3

[ ]; 1 − t o( )p2q + t o

3

{ }(17)

For delayed investment (decision nodes 35–38), the remaining objective value is

given by:

E∗2 FV[ ]tI=1 = max 1 + rt( ) 2

31 − t g( )l+ 2

3t g

[ ];

1 − t o( )p2q + t o

3+ 1 − t g( ) l

3+ t g

3

⎧⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎩

⎫⎪⎪⎪⎪⎪⎬⎪⎪⎪⎪⎪⎭

(18)

The value of the option to abandon (put option) inherent in the investment project

can be computed as the difference between the remaining objective value and the


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compounded expected after-tax cash flow:

E∗2 FV[ ] − E2 FV[ ] ≥ 0 (19)

For positive tax rates and positive liquidation proceeds, comparing equations (17)

and (18) shows that E∗2 FV[ ]tI=1 . E∗

2 FV[ ]tI=0, which confirms our finding that

this tax system tends to delay investment.

Moving backwards to time t = 1, we arrive at decision nodes 21 (u) and 22 (d),

respectively. The future value from financial investment FVfin,t

T is simply the

initial wealth compounded at the after-tax interest rate rt:

FV fin = 1 + rt( )3 I0 = 1 + r 1 − t i( )[ ]3

(20)

This value is compared with the expected future value of investing in t = 1,

which consists of the compounded expected after-tax cash flow from period

t = 2, the operating cash flow from period t = 3, taking into account the

option to abandon, and the compounded interest income from period t = 1:

E1 FV[ ]tI=1 = 1 + rt( )E1 pt2

[ ]+ E1 E∗

2 FV[ ]tI=1

[ ]+ rt 1 + rt( )2 (21)

The investor acquires the project in period t = 1 if its expected future value

exceeds the future value of financial investment:

E1 FV[ ]tI=1 . FV fin (22)

In the upward state (p1 = 1 + u( )p0) and the downward state (p1 = 1 + d( )p0),

respectively, the investor can reach the following expected future values after

taxes from investing:

E1 FVx[ ]tI=1 = p 1+ rt( ) 1− t o( ) 1+ u( ) 1+ u Iu( ) 1+ d Id( )p0 +t o

3

[ ]

+ p max

1+ rt( ) 2

31− t g( )l+ 2

3t g

[ ];

1− t o( ) 1+ u( ) 1+ u Iu( ) 1+ d Id( )p0q+ t o

3+ 1− t g( )l

3+ t g

3

⎧⎪⎪⎨⎪⎪⎩

⎫⎪⎪⎬⎪⎪⎭

+ 1− p( )

1+ rt( ) 1− t o( ) 1+ u Iu( ) 1+ d Id( ) 1+ d( )p0 +t o

3

[ ]

+ 1− p( )

max

1+ rt( ) 2

31− tg( )l+ 2

3t g

[ ];

1− t o( ) 1+ u Iu( ) 1+ d Id( ) 1+ d( )p0q+ t o

3+ 1− t g( )l

3+ t g

3

⎧⎪⎪⎨⎪⎪⎩

⎫⎪⎪⎬⎪⎪⎭

+ rt 1+ rt( )2

(23)with the indicator variables Ix =

1 if p1 =p0 1+ x( )0 otherwise

{, x [ u,d{ }


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The remaining objective value is defined as the maximum of the future values of

real and financial investment:

E∗1 FVu[ ]tI=1 = max 1 + rt( )3;E1 FVu[ ]tI=1

{ }E∗

1 FVd[ ]

tI=1= max 1 + rt( )3;E1 FVd

[ ]tI=1

{ } (24)

The decision whether or not to delay investment is addressed in decision node 11

(t = 0). The expected value of delayed investment can be written as:

E0 FV[ ]tI=1 = p E∗1 FVu[ ]tI=1 + 1 − p

( )E∗

1 FVd[ ]

tI=1(25)

The expected future value of investing immediately is defined as the sum of the

compounded expected operating cash flows of periods t = 1, 2 and the remaining

objective value in the decision nodes 31–38:

E0 FV[ ]tI=0 = 1 + rt( )2 E0 pt1

[ ]+ 1 + rt( )E0 pt

2

[ ]+ E0 E∗

2 FV[ ]tI=0

[ ](26)

Immediate investment is optimal if E0 FV[ ]tI=0 . E0 FV[ ]tI=1. Again, the inves-

tor’s initial expected objective value is the maximum of both terms:

E∗0 FV[ ] = max E0 FV[ ]tI=0;E0 FV[ ]tI=1

{ }(27)

The total value of flexibility F0 included in the investment opportunity at t = 0

can be computed as the difference between the initial expected objective value

E∗0 FV[ ] and the expected future value of after-tax cash flows:

F0 = E∗0 FV[ ] −

∑3

t=1

1 − to( )E0 pt[ ] + to

3

[ ]1 + rt( )3−t (28)

Notes

1Neutral tax systems as a reference concept for analyzing tax effects have been proved under

certainty by Brown (1948), Johansson (1969) and Samuelson (1964). Under uncertainty,

enriching the real option literature by integrating taxation (e.g., Agliardi, 2001; Alvarez and

Koskela, 2008; Gries et al., 2012; Niemann, 1999; Niemann and Sureth, 2004, 2005; Pante-

ghini, 2001, 2004, 2005; Pennings, 2000; and Sureth, 2002) leads to investment rules that

consider managerial flexibility, irreversibility and tax effects.2For a recent detailed overview of the empirical literature on capital gains tax effects on asset

prices and investment decisions, see Niemann and Sureth (2009).3See Schneider and Sureth (2010); Gries et al. (2012).4See, for example, Dixit and Pindyck (1994, pp. 147 ff.); Trigeorgis (1996, pp. 72 ff.). A very

user-friendly guide to the critical determinants of successful application of this approach

with several examples is Amran and Kulatilaka (1999).


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5It can be easily shown that the decision rule for combined investment cost and cash flow uncer-

tainty is similar to the decision rule under cash flow uncertainty only. Combined uncertainty

simply requires the change of the numeraire from monetary to project units. See Dixit and

Pindyck (1994, pp. 207 ff.).6For a detailed numerical analysis comprising all technicalities in a stylized pre-tax case, see

Niemann and Sureth (2009).7We do not distinguish between depreciation recapture and increases in value when computing

the capital gains tax base.8For simplicity, we do not take other depreciation schedules such as declining balance

depreciation into account.9There is no perfect analogy of variations of the multiple l and the degree of accounting

conservatism. Different degrees of conservatism do not affect cash flows, whereas different

multiples l induce different cash flows.10See Dai et al. (2008) for lock-in versus capitalization effects of capital gains taxation. In our

model, the parameter l captures both the lock-in and the capitalization effect of capital gains

taxation. It is an empirical question which effect dominates. In our model, a capitalization

effect decreases l.11The same would be true for a put option on a stock with a variable strike price that is always

equal to the current stock price.12See equations (15) and (16) in Appendix C.13For a detailed description of the remaining objective values at the decision nodes at time t = 2

and t = 1, the value of the option to abandon (put option), and the derivation of the value of

flexibility by backward induction, see Appendix D.14For a related simulation on non-depreciable financial investments see Alpert (2010).15The effect of tax-induced complexity can be observed exemplarily in Hundsdoerfer et al.

(2008).16See Section 30 of the Austrian Income Tax Code in connection with No. 6654a Income Tax

Directives.17See Section 34 (3) German Income Tax Code.18Note that real-world tax systems may be characterized by different tax rates for sale and liqui-

dation proceeds. This implies that taxpayers minimize their tax burden by arranging the facts

that determine the tax base. These tax planning strategies are reflected by the optimization cal-

culus in our model. Although sale and liquidation are very much related, tax systems often apply

different tax rates for these different ways to quit an investment. Integrating different tax rates in

a decision model can complicate the calculus considerably. See, for example, Hundsdoerfer

et al. (2008) who show how investment and financing decisions can be optimized simul-

taneously. Based on simple premises they evaluate an indivisible investment project that is

carried out in a corporation and find that the decision problem turns out to be rather complex

if different tax rates have to be considered.19Superscripts ∗ indicate optimal decisions. Subscripts t in the expectations operator Et ·[ ] indicate

the time of taking the expectation.

References

Agliardi, E. (2001) Taxation and investment decisions: A real options approach, Australian Economic

Papers, 40, pp. 44–55.

Agliardi, E. and Agliardi, R. (2008) Progressive taxation and corporate liquidation policy, Economic

Modelling, 25, pp. 532–541.

Agliardi, E. and Agliardi, R. (2009) Progressive taxation and corporate liquidation: analysis and

policy implications, Journal of Policy Modeling, 31, pp. 144–154.

Akindayomi, A. and Warsame, H. A. (2007) Effects of capital gains taxation changes on stock prices:

evidence from the February 2000 Canadian budget, Accounting Perspectives, 6, pp. 369–387.


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10 0

8 O

ctob

er 2

013

Alpert, K. (2010) Taxation and the early exercise of call options, Journal of Business Finance &

Accounting, 37, pp. 715–736.

Alvarez, L. H. R. and Koskela, E. (2008) Progressive taxation, tax exemption, and irreversible

investment under uncertainty, Journal of Public Economic Theory, 10, pp. 149–169.

Amran, M. and Kulatilaka, N. (1999) Real Options: Managing Strategic Investment in an Uncertain

World (Boston: Harvard University Press).

Ayers, B. C., Cloyd, C. B. and Robinson, J. R. (2002) The effect of shareholder-level dividend taxes

on stock prices: evidence from the Revenue Reconciliation Act of 1993, The Accounting Review,

77, pp. 933–947.

Ayers, B. C., Lefanowicz, C. E. and Robinson, J. R. (2003) Shareholder taxes in acquisition

premiums: the effect of capital gains taxation, Journal of Finance, 58, pp. 2783–2801.

Ayers, B. C., Lefanowicz, C. E. and Robinson, J. R. (2007) Capital gains taxes and acquisition

activity: evidence of the lock-in effect, Contemporary Accounting Research, 24, pp. 315–344.

Blouin, J. L., Raedy, J. S. and Shackelford, D. A. (2003) Capital gains taxes and equity trading:

empirical evidence, Journal of Accounting Research, 41, pp. 611–651.

Brown, E. C. (1948) Business-income taxation and investment incentives, in: L. A. Metzler et al.

(Eds) Income, Employment and Public Policy, Essays in Honor of Alvin H. Hansen,

pp. 300–316 (New York: Norton).

Constantinides, G. M. (1983) Capital market equilibrium with personal tax, Econometrica, 51,

pp. 611–636.

Cook, E. W. and O’Hare, J. F. (1992) Capital gains redux: why holding periods matter, National Tax

Journal, 45, pp. 53–76.

Dai, Z., Maydew, E., Shackelford, D. A. and Zhang, H. H. (2008) Capital gains taxes and asset prices:

capitalization or lock-in? Journal of Finance, 63, pp. 709–742.

Dixit, A. K. and Pindyck, R. S. (1994) Investment under Uncertainty (Princeton: Princeton University

Press).

Gries, T., Prior, U. and Sureth, C. (2012) A tax paradox for investment decisions under uncertainty,

Journal of Public Economic Theory, 14, pp. 521–545.

Hanlon, M. and Heitzman, S. (2010) A review of tax research, Journal of Accounting and Economics,

50, pp. 127–178.

Hirth, S. and Uhrig-Homburg, M. (2010) Investment timing when external financing is costly, Journal

of Business Finance & Accounting, 37, pp. 929–949.

Hundsdoerfer, J., Kruschwitz, L. and Lorenz, D. (2008) Investment valuation with tax-optimized

financing decisions and a tax-optimized default alternative, Business Research, 1, pp. 9–24.

Johansson, S. E. (1969) Income taxes and investment decisions, Swedish Journal of Economics, 71,

pp. 104–110.

Landsman, W. R. and Shackelford, D. A. (1995) The lock-in effect of capital gains taxes: evidence

from the RJR Nabisco leveraged buyout, National Tax Journal, 48, pp. 245–259.

Lang, M. H. and Shackelford, D. A. (2000) Capitalization of capital gains taxes: evidence from stock

price reaction to the 1997 rate reduction, Journal of Public Economics, 76, pp. 69–85.

Liang, J.-W., Matsunaga, S. R. and Morse, D. C. (2002) The effect of the expected holding period on

the market reaction to a decline in the capital gains tax rate, Journal of the American Taxation

Association, 24, pp. 49–64.

Niemann, R. (1999) Neutral taxation under uncertainty, FinanzArchiv, 56, pp. 51–66.

Niemann, R. and Sureth, C. (2004) Tax neutrality under irreversibility and risk aversion, Economics

Letters, 84, pp. 43–47.

Niemann, R. and Sureth, C. (2005) Capital budgeting with taxes under uncertainty and irreversibility,

Journal of Economics and Statistics, 225, pp. 77–95.

Niemann, R. and Sureth, C. (2009) Investment effects of capital gains taxation under simultaneous

investment and abandonment flexibility, arqus Discussion Paper No. 77, www.arqus.info.

Panteghini, P. M. (2001) Dual income taxation: the choice of the imputed rate of return, Finnish

Economic Papers, 14, pp. 5–13.


Dow

nloa

ded

by [

UQ

Lib

rary

] at

01:

10 0

8 O

ctob

er 2

013

http://www.arqus.info

Panteghini, P. M. (2004) Wide versus narrow tax bases under optimal investment timing,

FinanzArchiv, 60, pp. 482–493.

Panteghini, P. M. (2005) Asymmetric taxation under incremental and sequential investment, Journal

of Public Economic Theory, 7, pp. 761–779.

Pennings, E. (2000) Taxes and stimuli of investment under uncertainty, European Economic Review,

44, pp. 383–391.

Samuelson, P. A. (1964) Tax deductibility of economic depreciation to insure invariant valuations,

Journal of Political Economy, 72, pp. 604–606.

Schneider, G. and Sureth, C. (2010) Capitalized investments with entry and exit options and

paradoxical tax effects, Review of Managerial Science, 4, pp. 149–169.

Shackelford, D. A. (2000) Stock market reaction to capital gains tax changes: empirical evidence from

the 1997 and 1998 tax acts, Tax Policy and the Economy, 14, pp. 67–92.

Shackelford, D. A. and Shevlin, T. (2001) Empirical tax research in accounting, Journal of Accounting

and Economics, 31, pp. 321–387.

Sureth, C. (2002) Partially irreversible investment decisions and taxation under uncertainty – a real

option approach, German Economic Review, 3, pp. 185–221.

Trigeorgis, L. (1996) Real Options – Managerial Flexibility and Strategy in Resource Allocation

(Cambridge, MA: MIT Press).

Wong, K. P. (2009) Progressive taxation, tax exemption, and corporate liquidation policy, Economic

Modelling, 26, pp. 295–299.

Zodrow, G. R. (1993) Economic analyses of capital gains taxation: realizations, revenues, efficiency

and equity, Tax Law Review, 48, pp. 419–527.


Dow

nloa

ded

by [

UQ

Lib

rary

] at

01:

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