We analyze the impact of differential capital income taxation on the value of risky investment under irreversibility. Under a uniform tax rate, raising the tax rate can either increase or reduce the value of a risky project. Many countries have introduced a separate flat tax on capital income. In contrast to uniform taxation, differential capital income taxation crowds out risky real investment. This dysfunctional effect can neither be corrected by generous depreciation schedules nor by increasing the flat tax rate. This tax discrimination of risky real investment might have contributed to the current crisis.Capital Income Taxation, Flat tax, Risk-taking, Investment decisions, Uncertainty

Caren Sureth

Rainer Niemann

English

Research Papers in Economics

     
 
 
  
  
Volume 31, Issue 2 
  
The Impact of Differential Capital Income Taxation on the Value of Risky 
Projects 
  
 
 
Rainer Niemann  
University of Graz 
Caren Sureth  
University of Paderborn
Abstract 
We analyze the impact of differential capital income taxation on the value of risky investment under irreversibility. 
Under a uniform tax rate, raising the tax rate can either increase or reduce the value of a risky project. Many countries 
have introduced a separate flat tax on capital income. In contrast to uniform taxation, differential capital income 
taxation crowds out risky real investment. This dysfunctional effect can neither be corrected by generous depreciation 
schedules nor by increasing the flat tax rate. This tax discrimination of risky real investment might have contributed to 
the current crisis.
 
Citation: Rainer Niemann and Caren Sureth, (2011) ''The Impact of Differential Capital Income Taxation on the Value of Risky Projects'', 
Economics Bulletin, Vol. 31 no.2 pp. 1047-1054. 
Submitted: Dec 10 2010.   Published: April 06, 2011. 
 
     1. Introduction
The impact of income taxes on the value of risky real investment has been analyzed
in valuation literature at least since Domar and Musgrave (1944). Utility function-based
approaches have been extended with respect to progressive income taxes and information
asymmetry by Fellingham and Wolfson (1985), for example. In recent years, the tax planning
and risk-taking literature has been enriched by real option theory (see Altug et al. 2001,
Niemann and Sureth 2004, Klassen and Sansing 2006, Alvarez and Koskela 2008, Agliardi
and Agliardi 2009). Accounting for conditions of uncertainty and ﬂexibility, real option
theory permits an analysis of the eﬀects of taxation on risk-taking for irreversible investment
decisions. Integrating option values into the decision calculus shows that even risk-neutral
investors tend to delay risky projects.
Since the 1990s, many countries have introduced separate ﬂat tax rates on capital income.
Tax systems like the Nordic dual income tax levy a low proportional tax rate on all kinds
of capital income (Nielsen and Sørensen, 1997). Moreover, abstracting from ﬂexibility dif-
ferential tax rates on diﬀerent assets depending on their risk exposure are examined (Bulow
and Summers 1984, Gordon 1985, Weisbach 2004, Niemann 2008). Weisbach (2004) ﬁnds
that investors may eliminate the tax on risk inherent in such tax systems by costly portfolio
adjustments.
Other schedular taxes with diﬀerential taxation of selected types of capital income (e.g.,
dividends and interest income) were subsequently implemented in Austria, Belgium, Italy,
Germany, Greece, and the Netherlands (Genser and Reutter, 2007). Although these schedu-
lar tax systems with diﬀerential taxation of diﬀerent kinds of capital income have gained
considerable importance throughout Europe, the degree to which they aﬀe c tt h ev a l u eo f
risky projects and hence encourage risk-taking has not yet been suﬃciently analyzed. In a
real options context diﬀerential taxation of diﬀerent kinds of capital income has not been
analyzed at all until now.
To close this research gap, we model a tax system that diﬀerentiates between capital
income from real investment and from ﬁnancial investment. We integrate this system into a
real option framework. Whereas we ﬁnd ambiguous eﬀects of a uniform capital income tax
on risk-taking, diﬀerential taxation substantially decreases the willingness to realize risky
projects.
2. Model setup
We use the Dixit-Pindyck (1994) paradigm and consider an option to invest in a project
with stochastic cash ﬂows. The risk-neutral individual investor faces the decision between
investing either immediately or at a later point of time. If the tax system favors earlier
investment, it implicitly encourages risk-taking.1
We assume a simple income tax system in continuous time with a proﬁt tax base equal to
cash ﬂow  less depreciation allowances .C a s hﬂows follow a geometric Brownian motion
1This eﬀect is important to be considered as Sgroi (2003) shows that the attempt to gather more infor-
mation to overcome uncertainty at least partially will generate additional delays.
1with d
 = d + d,w h e r e and  denote the drift and volatility parameters. The tax
rate  on proﬁts from real investment is assumed to be deterministic and constant. Under an
immediate loss-oﬀset,2 the after-tax cash ﬂow  is deﬁned as  =( 1− )  + .A sl o n g
as the option to invest is not exercised, available funds yield the risk-free constant capital
market rate , which is subject to the tax rate .  is a separate tax rate levied on income
from ﬁnancial investment, such as interest income or dividends, which might diﬀer from the
ordinary tax rate . Hence, the risk-free after-tax interest rate  is given by  =( 1− ) .
To exclude arbitrage opportunities, we assume   .
To derive a rule for optimal investment timing, ﬁrst we have to assess the value of the
underlying project. If the project is in place, its economic value consists solely of its expected
future cash ﬂows. Assuming risk neutrality, the after-tax project value  is determined by
its expected present value:
 = E
∙Z ∞

 
−(−)d
¸
=
(1 − )
 − 
+ 
Z ∞

E[] 
−(−)d
=
(1 − )
 − 
+  E[] (1)
with , the present value of depreciation deductions.
Given  , the value of the option to invest can be determined. As long as the option to
invest is not exercised, its only payoﬀ is the expected appreciation. Determining the post-
tax option value  requires an instantaneous return that in equilibrium equals the after-tax
risk-free rate:  
! = E[d] The application of Itô’s lemma to the stochastic diﬀerential
d yields the partial diﬀerential equation 
 + 1
22 2 2
2 + 
 −   =0  Assuming
a perpetual real option, the time derivative 
 vanishes, leading to the ordinary diﬀerential
equation 1
22 2 d2
d2 + d
d −   =0with the general solution
 ()=
  0 =
1
2
−

2 +
sµ
1
2
−

2
¶2
+
2
2  1 (2)
where  is a constant to be determined. The well-known boundary conditions are  (0) = 0,
 (∗)= (∗)−0,w i t h0 =1as the initial investment, and
d(∗)
d =
d (∗)
d .3 Finally, we
obtain the critical investment threshold ∗:

∗ =

 − 1
 − 
1 − 
(0 −  ) (3)
The critical value ∗ indicates whether investment should be delayed or not. If the currently
observed realization  is higher than the critical value ∗, the investment should be carried
out immediately, otherwise it must be postponed until ∗ is reached.
2By contrast, the eﬀects of asymmetric taxation in a real options setting are investigated by Panteghini
(2001) and Panteghini (2005).
3For an economic interpretation of the boundary conditions see Dixit and Pindyck (1994), p. 141.
23. Tax rate diﬀerentials and the value of risky projects
From ∗, it is not obvious how taxes aﬀect risk-taking — whether they delay or foster
risky projects.4 I nt h ec a s eo fac o m p r e h e n s i v ei n c o m et a x(  = ) the partial derivatives
with respect to the tax rate may take either algebraic sign. For given tax parameters , 
and  higher volatility  delays investment and lowers risk-taking. Typically, the functional
relation of risk and taxes, i.e., , ,a n d, cannot be derived analytically. Numerical
simulations are necessary to get an impression of the dominant forces.
It is well known that introducing uniform tax rates on the return of both real and ﬁnancial
investment can increase or decrease the investment threshold for low depreciation deductions.
By contrast, given suﬃciently high depreciation allowances, realistic uniform tax rates may
easily halve the critical threshold.5
To ﬁnd how diﬀerential capital income taxation aﬀects risk-taking we model two separate
tax rates. Further, we account for diﬀerent degrees of risk involved in the real investment.
We study various combinations of the tax rate  on proﬁts from real investment and volatility
, each inducing identical investment thresholds ∗.
Formally, this means that the critical threshold’s total diﬀerential d∗ taking into account
the variables  and  is set to zero, whereas the other determinants are kept constant.
d
∗ =
∗

d +
∗

d
! =0
d
d
= −
∗

∗

for d
∗ = d = d = d =0  (4)
With respect to  we analyze two diﬀerent alternatives: Under the ﬁrst assumption, both tax
rates always coincide ( = ), which means that potential variations of  are accompanied
by identical variations of the ﬁnancial tax rate: d =d. In the second alternative, we keep
 constant: d =0 .
As a result, d
d represents the slope of “investment threshold isoquants” and is deﬁned as
the negative ratio of two partial derivatives. This slope indicates whether higher tax rates 
on the return from the real investment encourage (increasing isoquants) or discourage risk-
taking (decreasing isoquants).6 We determine these isoquants for diﬀerent settings of , ,
and  while keeping the tax rate on income from ﬁnancial investment  constant. Hence, we
study a schedular tax system that has gained importance in many countries.7 The pre-tax
case can be observed for  =0and serves simultaneously as the reference case for neutral
taxation. Thus, neutral tax systems are characterized by horizontal isoquants.8
4This well-known result is also true for tax-free models and under certain assumption for irreversible
investment with ﬁnancial constraints. See, e.g., Caggese (2007) and Holt (2007).
5See Niemann and Sureth (2004).
6Alvarez and Koskela (2008) show that for suﬃciently high volatilities, the investment threshold decreases
with increasing tax rates under progressive taxation. Further, Altug et al. (2001) study the implications
of tax risk an irreversible investment decisions and provide suﬃcient conditions for increases in tax risk to
reduce investment.
7See OECD (2009) and the Excel ﬁles provided there for an overview of time series of ordinary tax rates
and special tax rates on capital income.
8Niemann and Sureth (2004) derive neutral tax systems under risk aversion and irreversibility.
30 0.2 0.4 0.6 0.8
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8
0
0.2
0.4
0.6
0.8
1
r = 0.1,  = 0.2,  = 0.02,  =  r = 0.1,  = 0.2,  = 0.02,  =  r = 0.1,  = 0.99,  = 0.02,  = 
 
 0 0.2 0.4 0.6 0.8
0
0.2
0.4
0.6
0.8
1

1.0
0.8
0.6
0.4
0.2
0.0
1.0
0.8
0.6
0.4
0.2
0.0
1.0
0.8
0.6
0.4
0.2
0.0   0.0          0.2             0.4            0.6          0.8 0.0          0.2           0.4            0.6          0.8 0.0           0.2           0.4           0.6          0.8
Figure 1: --isoquants of the critical investment threshold ∗
T h el e f tg r a p ho fﬁgure 1 displays the ambiguous eﬀect of a uniform tax rate for all
types of capital income.9 Increasing the tax rate may either encourage (for suﬃciently low
values of ) or discourage risk-taking (for high values of ). This eﬀect can be explained
analytically by the signs of the partial derivatives in eq. (4). Whereas ∗
 may take either
sign for  = , depending on the level of depreciation allowances, increasing the volatility
always increases this critical investment threshold: ∗
  0. Hence, d
d ∈ R.
By contrast, diﬀerential taxation of real and ﬁnancial investment delays real investment
and hence discourages risk-taking. This eﬀect can be alleviated by higher depreciation rates.
However, even an (almost) immediate write-oﬀ cannot overcompensate this disincentive, as
shown in the right graph. Holding the tax rate on capital income  constant, increasing
the tax rate  always reduces the project value10 and hence ∗
  0.S i n c e ∗
  0,t h e
slope of the isoquant must be negative. Further, risk-taking is penalized even if  .
Qualitatively, the “risk-taking penalty” emerges regardless of the level of capital income
taxation. Increasing  reduces the value of real investment projects, but does not aﬀect
alternative ﬁnancial investments. Consequently, the option to wait becomes relatively more
attractive and risky projects will be delayed.
The eﬀects of varying both tax rates  and  simultaneously can also be analyzed by
setting the total diﬀerential of the critical investment threshold with respect to the variables
 and  equal zero while keeping the other determinants constant:
d
∗ =
∗

d +
∗

d
! =0
d
d
= −
∗

∗

for d
∗ = d = d = d = d =0  (5)
9Using various models, Näslund (1968) also ﬁnds ambiguous eﬀects of taxes on risk-taking.
10For a given investment threshold ∗ the investment project always yields a positive net present value.
Even if losses may occur during some time intervals, the resulting tax reimbursement cannot be the dominant
value driver, so that increasing the tax rate  tends to postpone rather than accelerate the investment
decision.
4Again, d
d represents the slope of “investment threshold isoquants”, i.e., the slope of identical
investment thresholds for the plotted combiniations of the tax rates  and .A sa b o v e ,t h e
tax system would be neutral for horizontal isoquants. Examples are illustrated in ﬁgure 2
for diﬀerent levels of depreciation allowances:
 =0 1,  =0 01,  =0 02,  =0 2  =0 1,  =0 2,  =0 02,  =0 2
Figure 2: --isoquants of the critical investment threshold ∗
Obviously, the isoquants are always increasing. This means that an increase in the
investment tax rate  must be accompanied by a corresponding increase in the capital
income tax rate  in order to keep the investment threshold constant. If both tax rates
are independent, the partial derivatives have opposing algebraic signs. As mentioned above,
increasing the investment tax rate  increases the critical investment threshold: ∗
  0.B y
contrast, increasing the capital income tax rate  r e d u c e st h ed i s c o u n tr a t ea sw e l la st h e
option value and hence accelerates investment: ∗
  0. As can be observed by comparing
the left hand side and the right hand side of ﬁgure 2, the isoquants may be concave or convex,
and the slope may exceed or fall short of unity. The higher the depreciation allowances, the
smaller is the partial derivative ∗
 a n dw i t hi tt h es l o p eo ft h ei s o q u a n t s .
In other words, a reduction of the capital income tax rate  must come along with a
corresponding reduction in the investment tax rate . Otherwise, real investment will be
replaced by ﬁnancial investment. In recent tax policy developments in Europe only capital
income tax rates were reduced, increasing the likelihood to crowd out risky real investment
projects.
4. Conclusions
In recent years, schedular taxation with ﬂat tax rates on ﬁnancial capital income have
been introduced by many jurisdictions without considering the negative implications for
5risk-taking. While the tax legislators intended tax simpliﬁcation, our model indicates that a
ﬂat tax is likely to crowd out risky real investments. Even extremely generous depreciation
schedules or increasing the ﬂat tax rate on ﬁnancial income will be insuﬃcient to correct this
dysfunctional eﬀect. It remains an open question whether the recently introduced preferential
taxation of ﬁnancial capital income in many countries contributed to the current crisis. If tax
politicians want to foster risky real investment by adjusting tax rates, our results indicate
they have to abolish the diﬀerential taxation of diﬀerent types of capital income. The dual
income tax with its uniform tax rate on capital income could serve as a starting point for
such a reform.
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7

A Model of Dynamic Tax Planning with an Application to Estate Freezes”

Asymmetric Taxation under Incremental and Sequential Investment”

Corporate tax asymmetries under investment irreversibility”

Financing Constraints, Irreversibility and Investment Dynamics”

Investment under Uncertainty,

Investment, irreversibility and ﬁnancial imperfection: the rush to invest and the option to wait”

Irreversible investment and the value of information gathering”

Moving Towards Dual Income Taxation in

Progressive taxation and corporate liquidation: Analysis and policy implications”

Progressive Taxation, Tax Exemption and Irreversible Investment under Uncertainty”

Proportional Income Taxation and Risk-Taking”

Some Eﬀects of Taxes on

Taxation and Risk-Taking with Multiple Tax Rates”

Taxation of Corporate and Capital Income, http://www.oecd.org/ctp/tax database.

Taxation of Corporate Capital Income: Tax Revenues versus Tax Distortions”

Taxes and Risk Sharing” T h eA c c o u n t i n gR e -view 40,

The Impact of Diﬀerential Taxation

The Impact of Differential Capital Income Taxation on the Value of Risky Projects

http://www.accessecon.com/Pubs/EB/2011/Volume31/EB-11-V31-I2-P98.pdf

The Impact of Differential Capital Income Taxation on the Value of Risky Projects

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