Reprint of Cybergeo, European Journal of Geography, 50, 1-36, March 1998.
The multinational companies cost of capital and regional policy :
tax cut or capital grant ?
M. MIGNOLET1
F.U.N.D.P.,
8, Rempart de la Vierge, B-5000 NAMUR (BELGIUM)
e-mail : michel.mignolet@fundp.ac.be
Key-words
Effective tax rate, Income from capital, Cost of capital, Open economy, Regional policy
assessment, Multinational company.
INTRODUCTION
Regional economics is concerned with spatial distribution of economic activities between core
and peripheral regions.
This question found a renewed topicality when were discussed the completion of the Single
European Market and their implications for the disparities in the economic growth of regions.
Various studies2 stated that the progress of the European integration strengthened the natural
propensity for the firms, particularly the multinational companies, to concentrate higher value
added activities in core regions deserting the periphery.
Regional policy has long been implemented in most of the industrialised countries with the
purpose of achieving a better balance in the activities distribution in space. The underlying
reasons are generally that the governments want to reduce chronic unemployment and underinvestment in depressed areas and to alleviate congestion and overcrowding in core regions.
Of course a pro-active policy of reducing disparities in the European Union also exists. Its
resources have extensively grown since 1987 (implementation of the reform of structural
funds) in order to foster the convergence across regions3.
Much of regional policy relies on capital (and labour) subsidies and tax incentives in order to
stimulate investment in lagging regions. Through these advantages, the public sector intends
to encourage newly installed capital both by stimulating investment from indigenous
entrepreneurs and by attracting foreign direct investment from multinational companies4.
1
I wish to thank Jack Mintz and the other seminar participants at the University of Toronto (April 1995) and two
anonymous referees for their useful comments. Thierry Piraux and Alain Moussiaux are also acknoledged for
their precious help in calculating first derivatives of the function of capital cost.
2
See for instance OUGHTON (1993) and YOUNG and HOOD (1993) mentioned by YOUNG, HOOD and
PETERS (1994).
3
The process of convergence across regions in the European Community between 1975 and 1990 is evaluated
empirically by NEVEN and GOUYETTE (1994).
4
This distinction refers respectively to the investment creation effect and to the investment diversion (or
displacement) effect. See MIGNOLET (1992).
1
Whether regional policy is effective or not remains an much debated question. HEAD, RIES
and SWENSON (1994) show5 that tax breaks and investment subsidies significantly affect the
location decision. HARRIS (1983) and BEGG and Mc DOWELL (1987)6 are other previous
examples7 concluding to the effectiveness of the public intervention. Conversely FAINI,
GALLI and GIANNINI (1993) or BACHETTA (1994)8 have doubts as to the efficiency of
regional policy.
The papers mentioned above and others I have knowledge fail to pay attention to the tax
aspects affecting foreign direct investment income.
When the investment is cross-border, at least two tax systems claim jurisdiction over the same
income. Moreover one has not only to consider the rules of tax systems both in the country of
the parent9 and in the country of its affiliate10 but also to examine the interaction between
these systems.
This paper sets out to show that the international taxation rules strongly influences the cost of
capital values. Depending on the particular case, tax provisions may either reinforce or
mitigate the impact of regional policy on the rate of return of a marginal investment.
The purpose of the paper is therefore to show that one cannot really assess the efficiency of a
regional policy aimed at attracting foreign direct investment disregarding the matter of
international tax rules on income from capital.
In order to achieve this goal, I shall use a theoretical framework first constructed by KING and
FULLERTON (1984)11 and extended by ALWORTH (1988) to deal with international issues.
This powerful approach measures the marginal effective tax rate on capital income
quantifying the distorsive effects of tax systems on the investment return. It enables
complicated provisions of tax codes to be modelled in a rigorous manner. Nowadays it is the
most familiar model and is internationally used12.
For the needs of this paper, the only formula of capital cost extracted from ALWORTH
(1988) is sufficient. Its meaning and its foundations are explained in section 2. Our interest is
to deepen the analysis of regional and fiscal policy on the cost of capital. The first derivatives
5
In the same way as agglomeration economies.Their study relies on a sample of Japanese manufacturing
companies which have invested between 1980 and 1992 in 34 states of U.S.A.
6
HARRIS (1983) asserts that capital subsidies succeeded in stimulating investment of the less favoured regions
in the United Kingdom. A survey conducted by BEGG and Mc DOWELL (1987) displays that financial aids are
taken in account when computing the present value of new investment projects.
7
See also DEVEREUX (1992) in his survey on behalve of the Ruding Committee, who concluded that at least
for multinational corporations ‘ taxation does appear to have a significant impact on the location of real activities
‘ [ quoted by TANZI (1995) ].
8
Mentioned in NEVEN and GOUYETTE (1994).
9
Also called the home country or the residence country.
10
Also called abroad, the source country or the host country.
11
See also AUERBACH (1983) and BOADWAY (1987).
12
See O.E.C.D. (1991), C.E.E. (1992), JORGENSON and LANDAU (1993), E.B.R.D. (1993) and SHAH
(1995) respectively for developed (the first three references), in transition and developing countries. Some
applications integrating regional policy are given in GUIOT et MIGNOLET (1995) and in MIGNOLET,
PIRAUX et VEREECKE (1997).
2
of the function of capital cost with respect to the rate of capital grant and to the rate of
corporate tax are accordingly also calculated.
The implementation of this methodological approach gives results which are presented and
commented in section 3.
But before displaying the methodology and the implementation results, it is useful in a first
section to express the main assumptions which this approach is built on.
1. THE ASSUMPTIONS
In order to prevent the analysis from becoming too complex, I have to make some simplifying
assumptions.
First of all, one supposes that the location decision is elastic to the relative capital costs in the
different settlement regions. The cost of capital is in turn depending on regional policy and on
international tax environment.
The overriding tax-related determinants of investment and location decisions are likely the
height of tax schedule on corporate income, the definition of tax base, the financial and tax
incentives to invest in both the host and home countries.
For the sake of simplicity, I leave aside afterwards the question of possible cross-country
differences in the definition of the tax base13.
I also consider the simplest form14 of international company, composed by a parent (head
office) and a wholly dependent affiliate (a branch or a subsidiary) located abroad. The relevant
shareholder of the parent company is assumed to be an individual investor residing in the
home country (the same country as the parent company). Of course the ultimate shareholder is
subject to personal taxes on the received return.
Numerous financing arrangements are possible. In each case, they have particular tax
consequences. The parent company can provide funds to the subsidiary by purchasing new
shares issued by the affiliate or by lending to the subsidiary15.
In order to finance these outflows, the parent raises funds by issuing new equity domestically,
retaining earnings or borrowing on its own account in the home country. These arrangements
are « parent-dependent financial policies ». Others are autonomous on the part of the affiliate.
The subsidiary (or branch) can retain its profits rather than repatriate them to the parent or
borrow locally. Each of these eight financing possibilities are examined here. More complex
financial arrangements are ignored in this study16. So is also the issuing of new shares to nonmajority shareholders (i.e. not to parent).
13
I also assume that the affiliate is making no tax losses.
More complex group structures and possibilities for treaty shopping are beyond the scope of this study.
15
And, of course, charging interest on the funds. The multinational firms have of course many methods other
than dividends and interests for repatriating funds. These methods, including transfer pricing or fees and
royalties, are ignored here.
16
Some complex financing structures are examined by PIERRE (1996) and by HESPEL (1997).
14
3
The exchange rates between currencies in the home and the host countries are constant and
equal to unity. The inflation rates are common across countries and stable over time.
The expected tax parameters are assumed to be invariant in the future17.
2. THE THEORETICAL FRAMEWORK
Specific models of effective tax rates have been proposed in the economic literature for about
ten to fifteen years. They enable the impact of the tax system and other public policy to be
assessed.
ALWORTH (1988) extended the commonly used approach of KING and FULLERTON
(1984) in order to include the complex matter of the international taxation. It is his theoretical
framework which is at the root of this paper.
I set out first to describe in broad outline the main concepts and mathematical expressions of
Alworth’s model and then to derive some natural indicators for apprehending the sensibility of
capital cost to regional policy taking into account the international tax context.
2.1. The Alworth’s model
The user cost of capital is the concept which underpins this approach. It is the minimum rate
of return the investment project must yield before taxes in order to provide the saver with a
determined net of tax return. It captures into a summary statistic the financial cost (N), the
economic depreciation () of the asset and all provisions of the tax system which may affect
the investment return including amortisation allowances and a wide number of newly installed
capital incentives. « It is a forward-looking measure in the sense that it is derived from an
explicit optimising framework centred on the investment decision of the firm »18.
The general expression for the capital cost, denoted p, in the Alworth’s model19 is :
p


1
1  f 1 A  f 2 *  f 3 g N       
1  *
(1)
In (1), A and g are respectively the present discounted value of tax savings from standard
depreciation allowances and of capital grants after corporate tax on a unit of investment. f1 ,f2
and f3 express in turn the proportion of the investment expense which is qualifying for
17
That amounts to saying that there is no time-inconsistency.
ALWORTH (1988).
19
If one ignores any corporate wealth taxes (wc) and the tax treatment of inventories in periods of inflation. The
mathematical expression allowing for these two special tax issues is the following :
18
p


1
1  f 1 A  f 2 *  f 3 g  N       (1  d1 *) wc  d 2 *  
1  *
where d1 and d2 are dummy variables. The first, d1 , is equal to unity if corporate wealth taxes are deductible
against corporate tax base and is equal to zero if wealth taxes are not deductible. The second, d2, is equal to unity
for inventories and is equal to zero for other assets.
The proportion of inventories taxed on a historic cost basis is denoted by the symbol  so that the additional tax
incurred by the firm is equal to *.
4
standard depreciation allowance, which is entitled to immediate expensing (100 per cent
depreciation) and on which a capital subsidy can be granted.  is the rate of economic
depreciation, assumed to be exponential and , the inflation rate of installed capital goods. 
and  are supposed to be constant over time.
Let us define more extensively the corporate and personal taxes on retained and distributed
profits and N, the financial cost of capital.
a. The tax parameters on corporate profits
* is the effective corporate tax rate which would apply if no profit of the foreign affiliate
were distributed. It includes the host and home country taxes. Symmetrically the taxation of
remittances by affiliate is apprehended through the parameter * which expresses the
opportunity cost of retaining earnings in the affiliate in terms of gross dividends before
personal taxes in the hands of the final shareholder in the home country.
*and* are functions whose expression depends on the system of company taxation and
method of double tax relief20.
The cross-border investment, as already mentioned, gives rise to a potential double taxation
on the return to corporate capital. One distinguishes the international (juridical) double
taxation when a same income is taxed by two different national jurisdictions and the domestic
(economic) double taxation when in the same jurisdiction dividends are taxed twice, once by
the tax on corporation and one by the personal tax.
In order to reduce or to eliminate the international double taxation, residence countries can
apply three methods, respectively credit, exemption and deduction. The first and third
methods are divided into two according to whether taxes can be deferred or not.
The basic principle of the tax credit method is simple. The residence country allows taxes
paid in the host country as a credit against the tax liability in the home country. In practice, tax
credits are limited to the domestic tax bill on this income. Accordingly the taxpayer will pay
the higher of the domestic and the foreign tax on his foreign-source income21.
Two cases can be distinguished for the credit system, respectively when a deferral is applied
and when there is no deferral. In the former case, the home country defers taxation on the
income of foreign affiliate until earnings are repatriated to the parent. In the latter case, the tax
liability in the home country is immediate, whatever foreign profit is retained or distributed.
20
The total tax liability, including on distributions by the parent company, is therefore equal to
T   * Ya 
1 *
G
* h
where Ya is the foreign taxable profit and Gh, the gross dividend distributed by the parent company attributable
to foreign earnings.
21
The limitation on tax credits may apply to taxes paid in each individual foreign country (it is the so-called « per
country limitation ») or double taxation relief may be calculated by averaging the tax credits for high tax
countries with the tax credits from low tax countries (it is the so-called « overall limitation »). Sometimes there is
also a limitation by type of income.
5
Under the method of exemption, the income from foreign source is exempt from domestic
tax22.
The third method implements a deduction mechanism. The tax paid in the source country is
deductible from the tax base in the residence country. Just like the credit method one may
distinguish two cases respectively when a deferral is applied and when there is no deferral.
ALWORTH (1988) identified the mathematical expressions of * and * for each of these
methods of reducing or eliminating international double taxation23. They are presented in table
1. When there is « overspill »24 under the credit methods (with and without deferral), * and
* take the values of the exemption method case.
In table 1 subscripts h and a mean respectively the home country and abroad. So h and a
express the company tax rates on undistributed profits in home and host country.
Symmetrically a measures the additional income received by the parent company if the
affiliate distributes a unit of retained earnings.
TABLE 1 : Values of * and * under the different systems of double tax relief
General
parameters

Credit no
deferral

*
h
*


*
h
Credit with
deferral
1  h
h
1  a
Exemption Deduction no deferral

ha

a

a

 h  a   h (1   a )
 h (1   a )
a 
a   h (1  a )
Deduction
with deferral

 h a (1  h )

a
Source : ALWORTH (1988), p. 82.
The parameter h expresses on the other hand the opportunity cost of retaining profit in the
parent company in terms of dividends foregone for the ultimate shareholder. The value of this
last parameter is function of the treatment of economic double taxation in home country.
The main standard systems of integrating the company taxes with the personal tax on dividend
are the following.
Under the classical system, profits distributed to the final shareholder are fully liable to both
corporation tax and personal income tax. In the split-rate (also called « two-rate ») system,
distributed profits are taxed at a lower rate than retained earnings. The dividend deduction
system allows companies to deduct a percentage of gross dividends from the tax base. The
22
Exemption can also be provided in the source country. It is the case when a tax holiday is awarded for specific
periods of time.
23
See ALWORTH (1988), p 72-82.
24
This is the case when foreign taxes are higher than domestic taxes. This situation is also called the « excess
credit » case.
6
imputation system consists in considering a part of the corporate tax liability as a prepayment
of personal taxes due by the final shareholder.
Except for the classical system, where it is equal to unity, the value of h exceeds unity.
b. The financial capital cost, N
N denotes the financial capital cost. It is variable according to the source of finance. Function
of the real interest rate r, assumed internationally identical as well for borrowing as for
lending, it expresses the rate at which the firm has to discount after-tax cash flows.
There are no transaction costs and there is no uncertainty25.
ALWORTH (1988) identifies the mathematical expressions of N for the financial
arrangements mentioned above. Table 2 summaries these results.
2.2. The multinational companies cost of capital and regional policy
Is the multinational companies cost of capital affected by regional policy and to what extent ?
The tools naturally available for measuring the sensibility of a function-objective with respect
to control variables are well known. They are called first derivatives and elasticity.
Regional policy may take different forms26 : lowering of tax scales, granting of financial aids
(interest subsidies, capital grants,...) or decreasing of tax base (special depreciation
allowances, investment credits,...).Accordingly one can distinguish three channels used by the
country source in order to attract foreign direct investment : da, dg’27 and dA, so that the first
derivatives and elasticity expressions can be written as follows :
P P
P
,
and
 a g '
A
 p , a 
P  a
.
 a P
 p ,g 
P g '
.
g ' P
 p, A 
P A
.
A P
where P  p  
25
So that there is no risk premium to be added to any financial capital costs.
This listing is not of course exhaustive.
27
The symbol g’ is here different of this one, g, defined in (1). The first is a ‘ variable-instrument ‘ measuring the
height of the net subsidy granted in the source country. The second is a ‘ variable-result ‘ assessing the net
advantage received by the group, taking into account the double taxation system on the profits of the parent and
of its affiliate. The analytical expressions for g and g’ will be given in section 3.
26
7
TABLE 2 : Financial capital costs, N, on foreign investments
Method of financing
Mathematical expression for N
Autonomous financial policies of the affiliate
r.(1  * * )
1. Borrowing in the host country
2. Retention by the affiliate
r (1  mb )
1 z
Parent-dependent financial policies
Borrowing by the parent
rh (1   h )  r ' M
3. Lending to the affiliate
*
4. Purchase of new shares issued by the affiliate
r h (1  h )
*
New shares issues by the parent
r  r' M
5. Lending to the affiliate
*
r (1  mb )
(1  ms ) *
6. Purchase of new shares issued by the affiliate
Retentions by the parent
( r  r ' M )(1  mb )
( *   h )  (1  z)
7. Lending to the affiliate
8. Purchase of new shares issued by the affiliate
r (1  mb )
(   h )  (1  z)
*
Source : ALWORTH (1988), p. 142
 Where M is defined as follows :  * (1   * * )  h (1   h ) , for the credit system with or
 * (1   * * )  h (1  wb ) ,
without
deferral,
for
the
exemption
system,  * (1   * * )  h 1  wb  (1   a )h  ,for the deduction system without deferral and
 * (1   * * )  h (1  wb   h ) for the deduction system with deferral,
8
* and  are the proportions of interest payment which are deductible from the tax
base. * refers to a debt incurred by the affiliate and , by the parent,
mb,z and ms are the personal tax rates on interest income, on accrued capital gains28
and on dividend payments,
wb is the withholding tax rate on remittances by the affiliate to the parent,
r’ is the interest rate on intracompany borrowings which may not coincide with the
market interest rate, r.
The cost of capital is defined in gross terms. It corresponds in (1) to p + . This choice is
convenient because it permits to avoid generally in numerical examples, a value of capital cost
around zero and therefore a sensibility of the elasticity sign to the capital cost sign. The cost of
capital, P, just as parameters a , g’ and A are defined considering an investment project with
an initial cost of one monetary unit. Therefore, the first derivatives express the variation in the
after-tax rate of return, result of a unit change in corporate tax rate, in grant rate or in
depreciation allowance29.
The elasticity values provide on the other hand a pure measure by making the ratio of
variation percentages respectively of the investment project rate of return and of each control
variable.
The next section will expound some of the most interesting results obtained by this approach.
I shall disregard the public policies which operate a decrease of tax base in order to focus on
lowering of tax scales ( da ) and granting of financial subsidies ( dg’ ). In the remainder of the
paper, the former approach will be specified as a pure tax policy and the latter, as a pure
financial aid.
3. THE MAIN RESULTS
In order to display the major role of international tax rules on the capital cost of
multinationals, the best way is to point out how different are the analytical expressions of our
indicators ( first derivatives and elasticity values ) for the various combinations of financial
arrangements and systems of double tax relief. That is what is precisely done for the first
derivatives of pre-tax rate of return with respect to capital grant rate. The analytical
expressions become really more and more complex successively for the corresponding
elasticity, the derivative and the elasticity of capital cost with respect to the corporation tax
rate in the source country. Accordingly they are not reproduced here.
In all cases, numerical values will be given for illustrating the diversity of the effects of a
lowering of tax schedules or of an increasing of capital grant for the different considered
combinations of financial arrangements and systems of double tax relief.
The present section is divided into three subsections focusing respectively on financial grant,
on tax cut and on a comparison between these both public policies aimed at attracting foreign
direct investment. But before examining the results, the numerical values of tax and general
parameters are to be specified to make explicit the scenario illustrating the approach.
28
29
It is the effective tax rate measured on an accrual basis from capital gains. See KING (1977).
It is the present discounted value of depreciation allowances by investment unit.
9
One assumes that interest payments are fully deducted from the tax base, whether the debt is
incurred by the affiliate or by the parent. Accordingly * and are equal to unity. The
corporate tax rates in source and home countries, a and h , are respectively equal to 30 % and
40 %. a and h , the opportunity costs of retaining profits in source and home countries are
equal to unity. There is no withholding tax on remittances by the affiliate to the parent so that
wb is set to zero. The interest rates, r and r’, are assumed to be equal to 8 %. mb, ms and z , the
personal tax rates on interest income, dividend payments and accrued capital gains are equal
to 10 %, 10 % and 0 %, respectively30. A, the present value of tax savings from straight-line
depreciation allowances is defined by the following expression
*
L
0
1  Nu
 * (1  e  NL )
e du 
L
NL
where L, the asset life for tax purposes is assumed to be equal to 10 ( years ). Moreover the
capital stock depreciates at an exponential rate equal to 2/L, that is to say that  is worth 0.2. g
is the present value of capital grant after all corporate taxes on an unit of capital. Today policy
makers are used to define the capital grants in terms of net equivalent subsidies. This concept,
denoted by g’, refers to the present discounted value of cash payments net of corporate tax. It
is defined a priori in the country which grants the financial aid in function of the tax
parameters in use in the jurisdiction. Here one assumes that g’ is equal to (1  a ) G (i.e. g’ is
equal to 0.12) where G denotes the gross grant rate before all taxes31. Of course for a
multinational company, the ultimate advantage, g , will depend on the system of double tax
relief. Finally the net capital grant g will be equal to (1  * )G .
One also considers that the investment is entirely qualifying for straight-line depreciation
allowances and for granting a capital subsidy. Therefore, f1 and f3 are equal to unity and f2 ,to
zero. That is to say that no immediate expensing is admitted.
Last general assumption, the income of foreign affiliate, net of corporate tax in the source
country is assumed to be entirely paid as dividend to the parent company. Accordingly Ga is
equal to (1  a ) a Ya . This amount, once the personal and corporate taxes in the home country
have been deducted, is distributed to the ultimate shareholder who receives Gh, equal to
(1  * ) *Ya .
3.1. The financial grant and the capital cost of multinational companies
What is the effect of an increase of one cent in the capital subsidy granted to an investment of
one monetary unit on the capital cost of multinational companies ?
30
The tax parameters have been chosen to be appropriate for illustrating the approach without generating too
many non-neutralities among the methods of financing. Generally the tax systems are responsible for much more
distortions than those which are present here through the values given to the parameters h , g ,  ,  , wb ,,mb ,
ms and z.
31
Since a has been set to 0.3, G is worth roughly 17.14 %.
10
It strongly depends both on the financial arrangement and on the system of double tax relief,
as shown in table 3. Table 3 exhibits the analytical expressions of the first derivatives of gross
capital cost with respect to capital grant32.
Except the case of retention by the affiliate the first derivatives look very different for most
financial arrangements according to the tax relief systems. They also appear to be very
disparate for each mode of reducing or eliminating international double taxation when the
different methods of financing are compared the ones against the others.
In order to illustrate how different are the results of first derivatives, some numerical values
have been given to the parameters. Results of this approach are shown in table 4. As already
mentioned the scenario which is considered rather minimises tax distortions with respect to
what is usually recorded in the tax systems of most countries.
The cost of capital values and the corresponding elasticity values with respect to capital grant
are also shown in table 4. The first statistics appear in italics, the second in bold type.
What lessons can be drawn from the reading of table 4 ?
Let us first have a look at the derivatives results. A capital subsidy equivalent to one cent
granted to an investment project with an initial cost of one monetary unit yields a lowering of
the gross capital cost between 0.277 and 0.433 cent. The results dispersion looks important :
while the arithmetical average of the first derivatives is worth around -0.341, the standard
deviation amounts to 0.031.
The corresponding results expressed in terms of elasticity are the following. An increase of
one percent of capital grant (g’)33 involves a decrease of gross capital cost between 0.128 and
0.198 %. The arithmetical average of elasticity results is equal to 0.171 % and the standard
deviation, 0.015 %.
It seems therefore that the yield of a regional policy aimed at attracting foreign direct
investment is strongly affected by the international tax system.
Let us compare the results line by line in table 4.
The first derivatives look higher in absolute values and by decreasing order for the tax regimes
admitting deferral ( deduction, then credit ). Should one reason in terms of elasticity, the
sensibility appears to be upper for the exemption system34.
Whatever the indicator one chooses, regional policy has always an upper yield (in decreasing
the gross capital cost values) when deferral is applied rather than when tax liability on
foreign profits are immediate. Actually when the deferral is applied, the home country
Treasury is making a free-interest loan on the deferred taxes.
A particular result appears for the financing by retained profits of the affiliate. The sensibility
of capital cost to capital grant - if we consider the derivatives indicator - is strictly identical
whatever the double tax relief system.
32
Solving
P
g'
comes to solve
P g
.
g g '
where
g 1   *

g ' 1   a
33
That is to say a rise of 0.12 cent for an investment with an initial cost of one monetary unit.
This result is mainly explained by the weaker values of the gross capital cost recorded for the exemption
system.
34
11
Table 3 : Sensibility of gross capital cost with respect to capital grant
P
Analytical expressions of the first derivatives
g'
a. Autonomous financial policies of the affiliate
Credit with
deferral
Credit
deferral
no
Borrowing in the host country
Retention by the affiliate
 f 3 (1   * h )r     
 f 3 (1  mb )(1  z) 1 r     
1  a
1  a
 f 3(1   * a )r     
 f 3 (1  mb )(1  z) 1 r     
1 a
1  a
Credit with
deferral
 f 3(1   * a )r     
1 a
1  a
Exemption
 f 3(1   * a )r     
 f 3 (1  mb )(1  z) 1 r     
 f 3 (1  mb )(1  z) 1 r     
1 a
1  a
Deduction
no deferral
 f 3 (1   * $ )r     
1  a
 f 3 (1  mb )(1  z) 1 r     
Deduction
with deferral
 f 3(1   * a )r     
 f 3 (1  mb )(1  z) 1 r     
1 a
1  a
1  a
b. Parent-dependent policies : borrowing by the parent
Credit no
deferral
Lending to the affiliate
Purchase of new shares
issued by the affiliate
 f 3r (1   h )  r ' h (1   * )     
 f 3 r (1   h )     
1  a
Credit with
12
1  a
1  a
 f 3 r (1   h )      
1  a
 f 3 (r h  r '( '  1  wb ))h1a1     
 f 3 r (1   h )a1     
 f 3 r a   r ' h ( a*  a )     
deferral
Exemption
1  a
1  a

 f 3  h r  r '( h (1   * $ )   h1  1    
Deduction
no deferral

 f 3 r (1   h )  1     

 f 3 r (1   h )a1 (1   h ) 1     
1  a
1  a

 f 3  h r  r '( 'h  h (1  wb   h ))h1a    
Deduction
with
deferral
1  a
1  a
c. Parent-dependent policies : new shares issues by the parent
Credit
deferral
no
Lending to the affiliate
Purchase of new shares
issued by the affiliate
 f 3r h1  r ' h (1   * )     
 f 3 rh1     
1  a
1  a
Credit with
deferral
 f 3 rh1  r '  a (1   * )     
1  a
 f 3 rh1    
1  a
Exemption
 f 3 rh1a1  r ' a (1   * a  a1 (1  wb ))     
 f 3 rh1a1     
Deduction
no deferral
Deduction
with deferral


1  a
1  a
 f 3 (r  r '(h  (1   * $ )   ))h1 1     
 f 3 rh1 1     
1  a
1  a
 f 3 ra1h1  r ' (1   * a  a1 )     
 f 3 ra1h1     
1  a
1  a
13
d. Parent-dependent policies : retentions by the parent
Lending to the affiliate

Purchase of new shares
issued by the affiliate
Credit no
deferral
 f 3  (r  r ' h h (1   * ))(1  mb ) (1  z ) 1    
Credit with
deferral
 f 3 (r  r ' ( a*  1   h ))(1  mb )    
Exemption
 f 3  (r  r ' h ( '1  wb ))(1  mb )    
1  a


 f 3 rh1     
1  a

 f 3 r (1  mb )     
1  a

 f 3 r (1  mb )     
1  a
1  a

1  a



Deduction
no deferral
 f 3 (r  r ' (h  (1   * $ )   ))(1  mb )     
Deduction
with
deferral
 f 3  (r  r ' ( h  'h (1  wb   h )))(1  mb )( k  1  z ) 1    

 f 3 r (1  mb )    
1  a
1  a


(  f 3(r (1  mb )
( k  1  z) 1     ))
1  a
/ (1   a )
where   h (1   * h ) ,  h   h (1   h ) ,  a  h (1   a ) ,  *  a* (1   * h ) ,  '  a (1   * a ) ,
h  h (1   h ) ,  a*  h (1   * a ) , a  h (1   a ) ,   (1   h ) 1 (1   a ) ,    a   h (1   a )

and  $   a   h (1   a )  1 ,   (1  mb )(1  ms ) 1 ,   h (  1) 1  1  z

1
,
  (1  wb   h )(1   h ) 1 ,   h (   1)  1  z  ,   h (a  1)  1  z ,
1
k  h a (1   h )  1 ,    h (1  wb  (1   a ) h ) .
14
1

Table 4 : Sensibility of capital cost with respect to capital grant
A numerical example of values obtained by the first derivatives
a. Autonomous financial policies of the affiliate
Credit no deferral
Credit with deferral
Exemption
Deduction
no deferral
Deduction
with deferral
Borrowing in the host country
Retention by the affiliate
-0.311
21.05
-0.178
-0.323
21.00
-0.185
-0.323
21.00
-0.185
-0.291
21.11
-0.165
-0.323
21.00
-0.185
-0.346
24.68
-0.168
-0.346
23.03
-0.180
-0.346
23.03
-0.180
-0.346
29.65
-0.139
-0.346
23.03
-0.180
b. Parent-dependent policies : borrowing by the parent
Lending to the affiliate
Credit no deferral
Credit with deferral
Exemption
Deduction
no deferral
Deduction
with deferral
-0.311
21.05
-0.178
-0.323
21.00
-0.185
-0.277
17.00
-0.196
-0.277
19.05
-0.146
-0.323
21.00
-0.185
15
Purchase of new shares
issued by the affiliate
-0.311
21.05
-0.178
-0.323
21.00
-0.185
-0.311
19.99
-0.187
-0.311
24.26
-0.128
-0.357
24.05
-0.178
c. Parent-dependent policies : new shares issues by the parent
Lending to the affiliate
Credit no deferral
Credit with deferral
Exemption
Deduction
no deferral
Deduction
with deferral
-0.357
25.91
-0.165
-0.376
25.77
-0.175
-0.323
21.00
-0.185
-0.323
26.04
-0.149
-0.399
27.84
-0.172
Purchase o new shares issued
by the affiliate
-0.357
25.91
-0.165
-0.376
25.77
-0.175
-0.357
24.05
-0.178
-0.357
31.47
-0.136
-0.433
30.95
-0.168
d. Parent-dependent policies : retentions by the parent
Lending to the affiliate
Credit no deferral
Credit with deferral
Exemption
Deduction
no deferral
Deduction
with deferral
-0.346
24.68
-0.168
-0.363
24.57
-0.177
-0.315
20.29
-0.186
-0.315
24.79
-0.152
-0.383
26.42
-0.174
Purchase of new shares
issued by the affiliate
-0.346
24.68
-0.168
-0.363
24.57
-0.177
-0.346
23.03
-0.180
-0.346
29.65
-0.140
-0.414
29.22
-0.170
Using the elasticity statistic leads to different sensibility results according as a deferral is
applied or not. This comment is due to the cost of capital values which strongly rise when no
deferral is admitted. Without the tax deferral privilege the equity cost for retained earnings of
the affiliate is obviously increased by the value of the tax deferral.
Let us continue by the results comparison column by column.
16
Without surprise the borrowings by the affiliate either to the parent company or locally are the
cheapest methods of financing. These financial policies provide the lowest costs of capital35.
Once again, the result gives rise to opposite diagnoses of the sensibility of capital cost to
regional policies according as one reasons in terms of derivatives or in terms of elasticity. The
first derivatives are generally36 upper for financing by equity rather than by debt. The
situation is strictly contrasted for the elasticity results.
3.2. The lowering of tax scales and the capital cost of multinational companies
What is at present the impact of lowering tax scales on the capital cost of multinational
companies ? As mentioned earlier, the analytical expressions of the sensibility indicators are
really too complex to be reproduced here. The table 5 exhibits therefore only the numerical
values of the first derivatives and the elasticity values of the capital cost with respect to
corporate tax scale in the source country.
What lessons can be drawn from the reading of table 5 ?
Insofar as the lowering of tax rate is provided to multinational corporations, its effectiveness
will depend upon the methods used to relieve international double taxation in the residence
country. Hence there is a clear diversity among the results in table 5 when comparing lines the
ones against the others, except for the autonomous financial policies of the affiliate (table 5a).
For the exemption and the deduction (with and without deferral) systems, results also look
very different according to the method of financing. This comment is expressed from the
reading of table 5 column by column.
A priori a positive sign is expected for the derivatives and the elasticity values . A lowering
of tax scale on corporation should reduce the capital cost of multinational companies.
The table 5 shows that the results are matching with the expectations only for less than 40 %
of cases. The sensibility of capital cost with respect to the lowering of corporate tax rate a
from 30% to 29% is sometimes negative, sometimes positive and sometimes equal to zero.
A lowering of tax rate keeps the cost of capital unchanged when the credit method without
deferral is applied. In this case, the tax department of the residence country allows taxes paid
in the host country as a credit against its own tax liability.
If the source country lowers the corporate tax rate and if one assumes that there is no ‘excess
credit’37 it is the Treasury of the residence country rather than the parent company that
benefits from the incentive provision. The derivatives and elasticity results are positive in
accordance with the a priori expectations, when the investment is financed by retained
earnings of the affiliate and when the finance is provided by purchase of new shares from the
35
Except for the credit systems ( with or without deferral ) when the finance is provided by retentions of the
parent company which in turn lends to the affiliate or purchases new shares issued by the affiliate.
36
The restrictions expressed above in note (31) are also to be considered.
37
It is also the case when a full credit is applied against the domestic tax liability for taxes paid abroad. Under
this pure credit system, the refund of unused credits is even allowed.
17
Table 5 : Sensibility of gross capital cost with respect to corporate tax rate
A numerical example of values obtained by the first derivatives
a. Autonomous financial policies of the affiliate
Credit no deferral
Credit with deferral
Exemption
Deduction
no deferral
Deduction
with deferral
Borrowing in the host country
Retention by the affiliate
0
21.05
0
-0.05
21.00
-0.07
-0.05
21.00
-0.07
-0.05
21.11
-0.07
-0.05
21.00
-0.07
0
24.68
0
0.08
23.03
0.11
0.08
23.03
0.11
0.17
29.65
0.18
0.08
23.03
0.11
b. Parent-dependent policies : borrowing by the parent
Lending to the affiliate
Credit no deferral
Credit with deferral
Exemption
Deduction
no deferral
Deduction
with deferral
0
21.05
0
-0.05
21.00
-0.07
-0.10
17.00
-0.18
-0.24
19.05
-0.38
-0.05
21.00
-0.07
18
Purchase of new shares
issued by the affiliate
0
21.05
0
-0.05
21.00
-0.07
0.04
19.99
0.06
0.10
24.26
0.12
0.10
24.05
0.12
c. Parent-dependent policies : new shares issues by the parent
Lending to the affiliate
Credit no deferral
Credit with deferral
Exemption
Deduction
no deferral
Deduction
with deferral
0
25.91
0
-0.05
25.77
-0.06
-0.05
21.00
-0.07
-0.17
26.04
-0.20
0.05
27.84
0.05
Purchase of new shares issued
by the affiliate
0
25.91
0
-0.05
25.77
-0.06
0.10
24.05
0.12
0.20
31.47
0.19
0.20
30.95
0.19
d. Parent-dependent policies : retentions by the parent
Lending to the affiliate
Credit no deferral
Credit with deferral
Exemption
Deduction
no deferral
Deduction
with deferral
0
24.68
0
-0.05
24.57
-0.06
-0.05
20.29
-0.07
-0.00
24.79
-0.00
0.04
26.42
0.05
Purchase of new shares
issued by the affiliate
0
24.68
0
-0.05
24.57
-0.06
0.08
23.03
0.11
0.17
29.65
0.18
0.17
29.22
0.18
parent (under the exemption and deduction systems of double taxation relief38).
38
Positive values for the sensibility indicators are also observed when the finance is provided by a loan from the
parent to the affiliate, under the deduction system with deferral, and when the parent company raises funds either
by issuing new equity domestically or by retaining its own earnings.
19
In absolute terms, the values of the sensibility indicators appear to be weak. I shall come back
to this question in the next subsection when I shall compare both policies (lowering of tax rate
and capital grant).
More often, the derivatives and elasticity results are negative . This means that the cost of
capital is increasing when the corporate tax rate is lowering. This is particularly the case when
the affiliate finances the investment by borrowing, locally or to the parent company or when
the residence country applies the credit system with deferral. This last system is precisely
implemented by the tax department in the U.S.A., United Kingdom and Japan.
How to explain that the sensibility indicators are negative ?
A lowering in the corporate tax rate generates three effects : the first is direct, the second and
the third are induced:
- the direct effect implies a immediate reduction of the capital cost ;
- the second effect takes place through the intermediary of the financial cost, N, which may
increase. This is mainly the case when the investment is financed by a borrowing of the
affiliate, locally or to the parent company. The net financial cost is, in that way, equal to the
proportion of interest payments that are not deductible from the tax base39 ;
- the third effect occurs via tax savings due to depreciation allowances and via grant capital.
Depreciation allowances and capital grant values are often affected by the corporate tax rate
through a double mechanism. On the one hand, the tax savings and the net equivalent subsidy
(after corporate tax) are of course function of the tax rate height. On the other hand, if the
depreciation for tax purpose is not immediate40 and if the financial aid is distributed on
several stages, the cash flows have to be discounted. The discount rate is defined by the
financial cost.
In this exercise, I consider a pure tax advantage so that g is assumed to be invariant whatever
the value of a41. This amounts to saying that the capital grant is defined in terms of net
equivalent subsidy. As I assume for the sake of simplicity that the public aid is totally paid the
day where the investment expenditure takes place, no discounting is required. In these
conditions, the third effect mentioned above is only induced by a variation of the present value
of depreciation allowances.
The lowering of the corporate tax rate a may reduce the discounted value of tax savings due
to depreciation allowances through a double possible way. Because
A
 * (1  e  NL )
NL
A is decreasing twice with a respectively when * depends on a first and secondly via N
when N increases.
Whether the sign of sensibility indicator is positive or negative depends upon the relative
weight of three effects : the first operates positively, the two others, negatively. The reading of
39
The financial cost is obviously measured for an investment expenditure of one monetary unit.
This is the case for the immediate expensing.
41
Of course it may be different according to the considered system of relieving double taxation but inside a
particular system, g is constant.
40
20
table 5 reveals that the second and the third effects often dominate the first one so that the
sensibility indicator is often negative.
3.3. Comparing both public policies
What is the best policy to be implemented : a capital grant or a lowering42 of corporate tax
rate ? In order to compare both policies, it is necessary to consider an identical shock, i.e. a
same cost for the public sector.
By assumption, the cost associated to the capital grant Cg is equal to one cent for an
investment project of one monetary unit,
Cg = dg = 0.01
Table 5 examines the impact of a lowering in the tax rate from 30 to 29% on the capital cost
values. The total cost of this policy Ccorresponds to the tax revenue foregone on the income
from newly installed capital. Because economic depreciation has been assumed to be
exponential at rate , the present value of Cis :

C  d a  Pe  ( N   ) u du 
0
d a P
N  

where Pe-(N+) expresses nominal profits which increase at the rate of inflation, decrease in
value at the rate of depreciation and are discounted at the rate N.
Applied to our scenario, C varies between 0.917 and 1.259 cent according to the 23 relevant
cases44.
For an equal public cost, it appears that granting a capital subsidy has a better yield than
lowering the corporate tax rate.
Other scenarios are studied in BINON et MIGNOLET (1997), in particular when excess credit
is observed (this is the case when a > h). Those results do not modify my general
conclusion : a capital subsidy is almost always a better policy choice than a lowering of tax
scale.
Two last remarks before concluding... First, a tax cut benefits both to newly installed and to
existing capital. This aspect has been ignored here because I only focus on regional policy
aimed at fostering the formation of new capital. Including this feature implies that one reasons
42
I disregard the paradoxical cases where the first derivatives of the capital cost with respect to the corporate tax
rate in the source country a is negative. This situation is observed not less than 17 times out of 40 in table 5.In
these cases, an increasing of the corporate tax rate in the source country is lowering the cost of capital value.
43
One ignores in this measure the induced effects on the discounted value of depreciation for tax purposes and on
the financial cost.
44
See note 38. The only cases considered are those for which the first derivative of P with respect to a is positive
(15 cases out of 40) or equal to zero (8 cases out of 40).
21
in terms of average effective tax rate and not on marginal effective tax rate on income from
capital. IWAMOTO (1992)45 opens up some promising research prospects in this field.
Second, space is not neutral as the neo-classical theory expects. Marginal productivity of an
investment project is not the same wherever it is located. MIGNOLET (1998) extends the cost
of capital framework by accounting for space.
CONCLUSION
The present paper showed that the regional policy impact on capital cost of multinational
companies is extremely variable according to the international tax system in use and to the
way implemented to attract foreign investment.
First, the yield of a same policy depends on the method of alleviating the international double
taxation : credit with or without deferral, exemption, deduction with or without deferral.
Secondly, different policy tools generate differentiated effects. What is to be recommended : a
reducing of the corporate tax rate or and increasing of the capital subsidy46 ?
The former policy has been implemented in the free enterprise zones (in the United Kingdom)
or in similar policy approaches in Ireland or in the European Development Area, for example.
The latter is the commonly used tool in numerous countries and is moreover promoted by the
Structural Funds policy.
Whatever the system of relieving double taxation and the financial arrangement to finance the
investment, the present study reveals that a capital grant is a better policy than an equivalent
lowering of corporate tax rate. Would the location decision be elastic to the capital cost of a
marginal investment47 , one must accept the idea that a capital subsidy is a better incentive to
attract foreign investment. The result is explained by the fact that a lowering of tax rate is
reducing the present value of depreciation allowances and, in some financial arrangements, is
increasing the financial cost used for discounting cash flow.
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See also MIGNOLET (1994) for a first generalization integrating personal taxation and MIGNOLET et
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46
Both policies have been defined in such a way that they give rise to a same discounted cost for the public
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47
In this study, the fact that a lowering of corporate tax scales also benefits to the existing capital has been left
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24