INTERNATIONAL CAPITAL MARKET SEGMENTATION IN THE FACE OF JOINT
OPERATING AND CAPITAL BUDGETING DECISIONS OF MULTINATIONAL FIRMS

Veikko Jskelinen*, Timo Salmi**, Yrj Wasiljeff


Originally Working paper 76 - 23, May 1976
European Institute for Advanced Studies in Management

Rewritten as WWW publication http://uwasa.fi/~ts/icms/ May 1996
FTP version ftp://garbo.uwasa.fi/pc/research/tsicms10.zip
University of Vaasa, Finland

*Helsinki School of Economics, Finland
**University of Vaasa, Finland


                      ALL RIGHTS RESERVED



ABSTRACT


A recent (in 1976) development of international financial theory is
the application of mathematical programming models to the capital
budgeting decisions of the multinational firm. This application is
an extension of the capital budgeting theory developed by
Weingartner [26] for the uninational firm. The investment and
financing decision models for the multinational firm developed so
far treat, however, the on-going operations (production,
intersubsidiary trade, and sales to customers) as given. This
simplification ignores the fact that the on-going operations are
interrelated with the capital budgeting decisions of the
multinational firm. Suboptimal decisions may thus be indicated. This
paper presents a deterministic linear programming model for the
simultaneous investment, operating, and financial decisions in the
multinational firm, explicitly taking the interactions between the
decisions into account.

The model is then applied to hypothetical examples in order to
explore whether barriers to capital flows could effectually separate
the international capital market into distinct national segments for
the multinational firms as they evidently do for the uninational
firms. The results support the view that effective segmentation does
not result. This is because the multinational firm can bypass the
restrictions by utilizing intersubsidiary trade. Partial
segmentation occurs, however, when imperfections exist as barriers
to capital transfers between the subsidiaries in different
countries. This is reflected in the model as a decrease in the value
of the multinational firm's objective function as compared to the
case with no restrictions on the intersubsidiary capital transfers.


1 INTRODUCTION

1.1 THE PROBLEM OF INTERNATIONAL CAPITAL MARKET SEGMENTATION

A recent problem of financial theory is whether the results
established for the single country firm also apply to the
multinational firm without major modifications. As a review of the
research by Naumann-Etienne [14] points out, a central issue in
extending the one-country results to the multinational case is
whether restrictions to the international capital flows effectively
segregate the national capital markets.

The findings of Agmon [2] and Solnik [22] (concerning the equity
markets) indicate that one cannot reject the one market hypothesis
on the basis of the present empirical evidence. The findings of
Lessard [10] imply that the international capital market can be
considered only partially segmented. He presents empirical evidence
to show that "the international structure of equity returns can be
characterized by a world element and a set of country elements ...".

In support of this empirical evidence it can be argued that barriers
to capital flows do not effectively segment the international
capital market in the presence of multinational firms. Robbins and
Stobaugh [17, Ch. 5] propound that the physical and monetary flows
which necessarily occur between the subsidiaries of the
multinational firms provide an efficient means for circumventing the
restrictions on capital flows._1/

Our paper extends the linear programming approach to simultaneous
optimal investment, operating, and financial decisions in the
multinational firm. Furthermore, the model to be developed is
utilized in order to explore the relevance of capital market
segmentation in the presence of the multinational firm. This is done
by observing the behavior of a hypothetical multinational firm under
varying assumptions about the restrictions on physical and financial
flows between the firm's subsidiaries in two different countries.
Figure 1 delineates the essence of the four different situations to
be explored._2/


F i g u r e  1


                #                                   #
         $$$    #    LLL                     $$$    #    LLL
          :     #     :                       :     #     :
          :     #     :                       :     #     :
          v     #     v                       v     #     v
        +---+   #   +---+                   +---+   #   +---+
MM <... |   |   #   |   | ...> MM   MM <... |   |   #   |   | ...> MM
MM ---> |   |   #   |   | <--- MM   MM ---> |   | <---> |   | <--- MM
        +---+   #   +---+                   +---+   #   +---+
          :     #     :                       :     #     :
          v     #     v                       v     #     v
                #                                   #
         [_]    #    [_]                     [_]    #    [_]
                #                                   #

             Case 1                               Case 2
     complete segmentation                 intersubsidiary capital
                                           transfers allowed




                #                                   #
         $$$    #    LLL                     $$$    #    LLL
          :     #     :                       :     #     :
          :     #     :                       :     #     :
          v     #     v                       v     #     v
        +---+   #   +---+                   +---+   #   +---+
MM <... |   | <...> |   | ...> MM   MM <... |   | <...> |   | ...> MM
MM ---> |   | <---> |   | <--- MM   MM ---> |   |   #   |   | <--- MM
        +---+   #   +---+                   +---+   #   +---+
          :     #     :                       :     #     :
          v     #     v                       v     #     v
                #                                   #
         [_]    #    [_]                     [_]    #    [_]
                #                                   #

              Case 3                              Case 4
    intersubsidiary trade with         barriers to capital transfers
    capital transfers allowed


    --->   financial flow allowed      ...>   physical flow allowed

    +-+
    | |    affiliate                   [_]    investment
    +-+

    $$$    local loan market           MM
    LLL    local loan market           MM     local sales

    #      barrier



1.2 REVIEW OF RELEVANT RESEARCH ON CAPITAL BUDGETING MODELLING IN
    THE UNINATIONAL FIRM

The historical development of economic and financial theories of
capital budgeting can be classified into three stages:_3/
 (1) Traditional capital theory,
 (2) Conventional managerial approaches to capital budgeting,
 (3) Mathematical programming approaches to capital budgeting.

Lorie and Savage [11] pointed in 1955 to the inadequacy of the
conventional approaches to capital budgeting decisions by
demonstrating the failure of Dean's [5] internal rate of return
approach under the assumption of capital rationing._4/ Weingartner
[26] showed in 1963 how the problem of the simultaneous selection of
investment projects and the sources of financing (in the uninational
firm) can be uniquely solved in the case where the projects
considered are dependent, the total capital expenditures are limited
for more than one time period, and the net revenues of a project can
vary in sign. In 1959 Charnes, Cooper, and Miller [4] published the
pioneering application of linear programming to joint operating and
financial decisions of the firm._5/ Weingartner's work did not
account for the fact that the on-going operations of the firm are
interrelated with the capital budgeting decisions. Jskelinen [8]
established in 1966 how decisions on the on going operations
(production and sales), investments in additional production
capacity, and financing can be treated simultaneously in a linear
programming formulation. The further developments of the
mathematical programming approaches to the capital budgeting
decisions of the uninational firm, mainly in order to account for
uncertainty, are not pertinent to our present approach, but the
interested reader can trace the references back e.g. from [3] and
[6].


1.3 REVIEW OF RELEVANT DECISION MODELS FOR THE MULTI-
    NATIONAL FIRM

Constructing mathematical programming models for capital budgeting
decisions in the multinational firm is an emerging research trend of
international financial theory. Merville [13] presented in 1971 a
chance-constrained mixed integer linear programming model to solve
the problem of rationing capital in the multinational firm. His
model can be regarded as a reduced extension of Weingartner's well
known "basic horizon model". Arya [3] extended independently in 1972
the "basic horizon model" into the multinational setting in a more
comprehensive manner. The major decision variables of his
deterministic mixed binary linear programming model involve the
selection of the investment projects, both intersubsidiary and local
borrowing and lending, and dividends paid to the parent company. The
decisions on production, intersubsidiary trade, sales to customers,
and investments in capacity increase are not considered in his
model. Velasco [24] presented in 1973 a linear goal programming
approach to the investment and financing decision of the
multinational firm. The on-going operations are included in his
approach as constants of the model only. Hamilton and Moses [7]
applied in 1973 a multiperiod mixed integer model for the
go/no-go-type investment and operating strategy selection, and the
simultaneous financing decision in a multinational corporation.

Velasco's duality analysis reveals that each subsidiary has its own
unique cost of capital, although the costs are interdependent._6/
The same result is indicated by [21, pp. 288-289] and [20, pp.
85-88]. This result, together with the results referred to in
Section 1.1, implies that the effectively segregated international
capital market concept cannot be advocated. On the other hand, we
cannot apply a single pool of capital approach to the financing
decision of the multinational firm, either.

Joint operating and financial decisions of the multinational firm
were presented by Salmi [18] in 1972 in the framework of a
deterministic linear programming formulation, and independently by
Mehta and Inselbag [12] in 1973. Decisions on investments in
additional capacity and transfer pricing are included in the former
work, but not in the latter. On the other hand, the handling of
inventories is excluded from the former.

It is our purpose to present a deterministic one-period linear
programming model for the multinational firm for simultaneous
decisions on investments in increasing the existing capacity as well
as in new acquisitions. Production, sales to outside customers,
interaffiliate trade, and interaffiliate as well as outside
borrowing sources are simultaneously considered. This is achieved by
combining the relevant features of the models developed by Arya [3],
Jskelinen [8], and Mehta and Inselbag [12]. The extension of our
one-period model into a multiperiod case is technically
straightforward. However, in practice there is always the problem of
the dimensionality of the multiperiod models, which tends to make
them unwieldy.


2 EXPOSITION OF THE MODEL

2.1 GENERAL FEATURES

The aim of our model is the maximization of the after tax present
value of the global sum of the net income streams to the affiliates
of the multinational firm after translation_7/ into the parent
country currency. The usual assumption of centralized planning
coordinated by the headquarters is made. The decisions covered by
the model were given in the preceding section, and the decision
making situation is depicted by Case 3 of Figure 1. The
multinational firm has a total of K affiliates_8/ in different
countries, it produces a total of I different products, J(k)
investment options are open to the affiliate in country k, and
additional investments in the existing capacity are possible for
each affiliate. We assume that fractional investment projects are
acceptable,_9/ since it is to be feared that in actual practice the
mixed integer codes cannot handle problems large enough.
Deterministic currency exchange rates are assumed in the model._10/


2.2 DECISION VARIABLES

The decision variables of the model are listed below. The input data
constituting the constants of the model are listed in the appendix
at the end of the paper. All the decision variables are
non-negative.

x(ik)    = the number of units of product i to be sold to customers
           by affiliate k.

y(ik)    = the number of units of product i produced by affiliate k.

y(ikh)   = the number of units of product i exported from affiliate
           k to affiliate h (and thus imported by the latter from
           the former).

z(k)     = the accepted fraction of the investment in capacity
           increase in affiliate k.  z(k) E [0, 1].

w(jk)    = the accepted fraction of affiliate k's j:th investment
           option. w(jk) E [0, 1].

d(k)     = borrowing by affiliate k from the local money market in
           the local currency.

e(k)     = lending by affiliate k to the local money market in the
           local currency. (This decision variable also serves as
           the closing cash balance.)

m(kh)    = the interaffiliate loan granted by affiliate k to
           affiliate h. The loan is denominated in the currency of
           the host country of the granting affiliate k.

The model treats the interaffiliate transfer prices as
predetermined, although in actual practice they constitute an
additional set of decision variables for the multinational firm. It
would be easy to include this feature in the present model along the
lines developed by Salmi [18] and [20, Sec. 3.2.5, 3.3.2]._11/ The
choice between short-term and long-term borrowing as presented by
Arya [3] is omitted, too.


2.3 OBJECTIVE FUNCTION

The objective of the model is to maximize the translated global
after-tax sum of the net earnings from the on-going operations and
the proper annuities of the net earnings from the investment options
accepted in the different affiliates. For each affiliate the
objective function includes sales revenue less production cost plus
exports revenue less imports costs including the price,
transportation and an ad valorem import duty less interest on
borrowing from the local sources plus interest on the interaffiliate
loans granted less interest and stamp duty on interaffiliate
borrowing plus interest on local lending less one annuity of the
capacity increase investment cost plus the annuities of the net
earnings on the investment options less fixed and predetermined
costs. The objective function of the model is given on the next
page.

          translation
          coefficient          sales revenue
       K                     I
  max    tr(k)[1-t(k)]   {    p(ik)x(ik)
      k=1      after-tax    i=1
               coeffic.

       production cost            export revenue
     I                      I   K
  -    c(ik)y(ik)       +       p(ikh)y(ikh)
    i=1                    i=1 h=1
                               h!=k


            i m p o r t s   c o s t s   transfer
     I   K                              price
  -       [ut(ihk) + (1 + uc(ik))v(hk)p(ihk)] y(ihk)
    i=1 h=1  transpor-      duty   currency
        h!=k tation                conversion

    interest on               interest on inter-
    local borrowing           affiliate lending
                            K
  - rd(k)d(k)           +     rm(kh)m(kh)
                           h=1
                           h!=k

        costs on inter-                    interest on
        affiliate borrowing                local lending
     K
  -    v(hk) [rm(hk)  +  sm(hk)] m(hk)    + re(k)e(k)
    h=1       interest    stamp-duty
    h!=k


  annuity of capacity              net annuities from
  increase investment cost         investment options
                              J(k)
  - rg(k)g(k)z(k)           +    [s(jk)-rf(jk)f(jk)] w(jk)
                              j=1

  fixed and pre-
  determined costs

  - U(k) }


The detailed discussion of the model will be confined to selected
items, because of the limited space. A host of the assumptions made
have to be interpreted directly from the mathematical presentation
of the model with the help of the lists of the variables and the
constants.

The procedure for calculating the after-tax yields of the affiliates
by a multiplication with the coefficient (1-t(k)) is oversimplified.
A proper general procedure for handling the income taxes is
discussed in [20, Sec. 3.2.8 and 3.2.9]. Subtracting the production
cost instead of the cost of the items sold is also an
oversimplification. A better matching procedure can be found in
[12].

Technically our model includes only a single one-year fixed and
predetermined costs period. The actual planning horizon must,
however, cover a much longer time-period, because assuming one-year
investments only would be meaningless. Therefore the following
method is adopted. All the revenues and expenses of each option are
replaced by equivalent net annuities over the predicted economic
life-span of the investment option. The net annuities are then used
as figures of merit in the objective function.

To be more specific about this method, let the life span of the
investment w(jk) be n(jk) years. Assume that a relevant subjective
(absolute) rate of interest q(k) can be agreed on._12/ With some
trivial arithmetic it is easy to see that the coefficient needed in
order to get the annuity required is given by

                         n(jk)
             q(k)[1+q(k)]
   rf(jk) = ------------------
                     n(jk)
             [1+q(k)]     - 1

For the investments in capacity increase z(k) we need apply the
method for the initial cost only, because the other relevant factors
are reflected by other terms of the objective function. Thus the
pertinent cost for such an investment is rg(k)g(k)z(k), where rg(k)
is defined analogously to rf(jk), g(k) is the total expenditure for
the investment in the capacity increase, and z(k) represents the
fraction of the capacity increase. Had we omitted the coefficient
rg(k), the current period would have been excessively burdened with
the entire expenditure of acquiring the additional capacity, which
would lead to being overcautious about capacity increases. Thus, by
adopting the method discussed above, we have accounted for the fact
that the additional capacity usually is available for more than one
year. When the process described is followed, using a one-period
model is not as strong a simplification as it might seem at the
first sight.


2.4 OPERATING CONSTRAINTS

This section gives the constraints relating to the physical
activities of the multinational firm.

Sales Constraints
-----------------

  sales     sales potential
  x(ik)    X(ik)      i = 1,..., I
                       k = 1,..., K


Inventory Balance Equations
---------------------------

  production   imports    sales       exports
             K                      K
  y(ik)  +     y(ihk)  - x(ik) -     y(ikh)
            h=1                    h=1
            h!=k                   h!=k

  required                initial
  closing inventory       inventory

  = He(ik)            -   Hb(ik)         i = 1,...,I
                                         k = 1,...,K

Storage cost is excluded, because in our one-period approach it is
not essential.


Capacity Constraints
--------------------

     capacity      capacity      initial
     usage         increase      capacity
   I
     a(ik)y(ik) - b(k)z(k)     Y(k)      k = 1,...,K
  i=1

Only one dimension of capacity is assumed in the above. Extension
into a more general case is trivial: only an additional index is
needed.


Investment in Capacity Increase
-------------------------------

  z(k)   1      k = 1,...,K


z(k) means the accepted fraction of the additional capacity (b(k))
that can be acquired in affiliate k. The relevance of a fractional
solution depends, naturally, on the nature of the pertinent
production process. If, say, paper-making machines constituted the
relevant capacity, fractional solutions should be treated as
preliminary approximations only. Had we defined the z(k):s as binary
variables, a mixed binary linear programming model would have
resulted. Furthermore, integer values beyond one might also be
relevant for various cases.


Other Investment Options
------------------------

  w(jk)   1      j = 1,....,J(k)   k = 1,...,K


2.5 FINANCIAL CONSTRAINTS

This section gives the constraints relating to the financial flows
in the multinational firm.

Cash Balance Equations
----------------------

The cash balance equations see to it for each affiliate that cash
outflows cannot exceed the cash inflows. They are denominated in the
pertinent local currencies.

      sales revenue          exports revenue
   I                  I   K
     pp(ik)x(ik)  +       pp(ikh)y(ikh)
  i=1                i=1 h=1
                         h!=k

    local borrowing      interaffiliate borrowing
    less interest        less interest and stamp-duty
                      K
  + [1 -rd(k)]d(k) +    [1 - rm(hk) - s(hk)] m(hk)
                     h=1
                     h!=k

    interaffiliate lending       production
    less interest                expenditure
     K                         I
  -    [1 - rm(kh)] m(kh)  -    cp(ik)y(ik)
    h=1                       i=1
    h!=k

               i m p o r t s   e x p e n d i t u r e s
     I   K
  -        { ut(ihk) + [pp(ihk) + uc(ik)p(ihk)] v(hk) } y(ihk)
    i=1 h=1   transpor-   transfer   duty         currency
        h!=k  tation      price                   conversion


    capacity increase
    investment expenditure
                           J(k)
  - g(k)z(k)             -     [ f(jk)    -  s(jk) ] w(jk)
                           j=1  expenditure   annual
                                              earnings

    closing      fixed and predeter-       initial
    cash         mined expenditures        cash

  - e(k)    =   Up(k)                  -   Eb(k)      k = 1,...,K

In the cash flows we do not compute annuities for the investments,
as we did in the objective function.


Minimum Cash Balance Constraints
--------------------------------

  closing       required minimum
  cash          closing cash
  e(k)         Ee(k)


Local Borrowing Constraints
---------------------------

  local         maximum local
  borrowing     borrowing potential
  d(k)         D(k)


Interaffiliate Loan Granting Constraints
----------------------------------------

For management policy reasons a maximum acceptable level of
interaffiliate loans granted by an affiliate can be imposed by the
management. In our numerical examples these constraints are
redundant.


     interaffiliate     maximum level
     lending            acceptable
   K
     m(kh)            M(k)       k = 1,...,K
  h=1
  h!=k

This concludes the presentation of the model developed.


3 FOUR NUMERICAL EXAMPLES

This chapter discusses four fictitious numerical examples of the
model solved for the simultaneous assessment of operating,
investment and financing plans of the multinational firm. These
examples simulate different cases of capital market segmentation.
The major features of the four numerical examples are delineated by
Figure 1 of Section 1.2. The appendix at the end of the paper
listing the parameters of the model gives the input data for case 3,
which is the most extensive of the examples, and which is based on
the full-blown version of the model. As is easily seen, the other
cases are reduced versions of case 3. The numerical values of the
input data remain unaltered throughout the cases. The four examples
differ from each other with respect to the physical and financial
alternatives which are assumed to be available to the affiliates.
Exhibit 1 on the depicts the results of the four runs in a tabular
form. The starred items are on their upper bound. A detailed
presentation of the four numerical examples is documented in [25].


E x h i b i t  1        Solutions

               Case 1     Case 2     Case 3     Case 4
Objective
function $      1311       1338       1480       1430

Variable
x11             1578       1600*      1600*      1600*
x21                0          0          0          0
x12              867        867       1012        895
x22             1000*      1000*      1000*      1000*
--------------------------------------------------------
y11             1578       1600        545        428
y21                0          0       1000       1000
y12              867        867       2067       2067
y22             1000       1000          0          0
--------------------------------------------------------
y112                                     0          0
y212                                  1000       1000
y121                                  1055       1172
y221                                     0          0
--------------------------------------------------------
z1             0.675      0.743      1.000*     0.632
z2             1.000*     1.000*     1.000*     1.000*
w11                0      1.000*     0.955          0
w12            1.000*     1.000*         0      1.000*
w22            1.000*     1.000*     1.000*     1.000*
--------------------------------------------------------
d1  $           2300*      2300*      2300*      2300*
d2  L            590        792        800        563
--------------------------------------------------------
m12 $                         0          0
m21 L                       197        395
--------------------------------------------------------
e1  $            700        700        700        700
e2  L            350        350        350        350


First, we assume that the affiliates cannot interact at all: both
physical flows and capital transfers between the affiliates are
prohibited. This is case 1. Affiliate 1 (in the USA in our numerical
example) is short of funds in the example while affiliate 2 (in
England) has ample funds as is seen from the fully utilized
borrowing capability in the former and the unutilized borrowing
capability in the latter.

In case 2 we relax the barrier to capital transfers between the
affiliates. In the numerical example it is optimal for the
multinational firm to grant a loan of L197 from affiliate 2 to
affiliate 1. The value of the objective function of the
multinational firm is increased, because lifting the barrier on
capital transfers alleviates the shortage of funds in affiliate 1,
which borrows from affiliate 2.

Case 2 omits, however, the important fact that the affiliates of the
multinational business enterprises may trade their products with
each other. We include the possibility of interaffiliate trade in case
3. (The complete model presented in the previous chapter was
developed particularly for this general case. Suitably reduced
versions are applied in the other cases.) In the numerical example
the affiliates now trade in both directions in the different products.
The composition of the accepted investment options is altered with
the changing situation of capital rationing. A capital transfer of
L395 occurs in the form of an interaffiliate loan from affiliate 2 to
affiliate 1. This loan is not the only financial flow between the
affiliates in case 3. The interaffiliate payments for the
interaffiliate trade amount to $600 and L738.50 respectively. The
net flow from affiliate 2 to affiliate 1 is thus L833.50. The value
of the objective function in the numerical example is increased
again, since with the introduction of the interaffiliate trade the
multinational firm can better utilize its pattern of production costs
and sales potential.

Next, let us observe what happens in the numerical example if the
interaffiliate capital transfers were prohibited by the respective
governments, but the inter affiliate trade and the payments on this
trade could still be employed by the multinational firm. The flow of
funds from affiliate 2 to affiliate 1 would not cease! The
interaffiliate payments for the interaffiliate trade, which would be
optimal for this case 4, would amount to $600 and L820.40
respectively. This means a net flow of L520.40 towards affiliate 1.
Funds needed in affiliate 1 are thus acquired from affiliate 2 with
the help of interaffiliate trade. This is indicated by the fact that
in case 3 a net flow of L438.50 resulted from the inter affiliate
trade, while now in case 4 it is L520.40. If the transfer prices had
also been made decision variables the distinction would have been
more marked. The value of the objective function is decreased when
compared with case 3, where there are no barriers between the
interaffiliate capital transfers. When compared with the completely
segmented case 1, the value of the objective function is increased.

No general conclusions can be drawn from the four hypothetical
examples discussed. Nevertheless, they clearly indicate that
barriers to capital flows are in adequate in segregating the
national capital markets from each other in the presence of
multinational business enterprises. This arises from the proposition
that the multinational firm can circumvent the barriers by employing
interaffiliate trade as suggested by our simulated numerical
examples. This result is in agreement with the earlier results
referred to in Section 1.1.

In the presence of multinational firms a necessary condition for
segregating the markets would be barriers both to capital transfers
and trade between the affiliates, as in case 1 of the numerical
example. On the other hand, when barriers to capital flows exist,
but interaffiliate trade is allowed (case 4), the value of the
objective function for the multinational firm is decreased in our
numerical example when compared to the case of no barriers on
interaffiliate trade and capital transfers (case 3). One tentative
interpretation of this behavior would be to say that partial
segmentation is indicated in case 4. Thus, two different kinds of
segmentation occur in our numerical example: (l) The effective
segmentation of case 1, where neither capital transfers nor trade is
allowed between the relevant nations, and (2) the partial
segmentation of case 4, where the capital transfers, but not trade,
are prohibited by the respective governments.


4 CONCLUSION

The primary purpose of this paper was to develop a deterministic
one-period linear programming model for joint operating, investment,
and financial planning in the multinational firm. Sales to
customers, production, interaffiliate trade, investments both in
capacity increase and other options, and both local and
interaffiliate borrowing and lending are simultaneously treated in
our approach. A simple discounting procedure was adopted for the
investments in our one-period approach in order to keep the size of
the model within manageable bounds and yet cover a planning horizon
long enough to account for the future effects of the present
investments. It was noted that, if necessary, the model could also
be solved by mixed binary or integer linear programming computer
codes. Four numerical examples to demonstrate the model behavior
were discussed. The examples seem to support the view that barriers
to capital movements result only in partial segmentation of capital
markets if interaffiliate trade of the affiliates of multinational
firms is permitted.


APPENDIX: A LIST OF INDICES AND PARAMETERS OF THE MODEL

The numerical values shown in parentheses after each item give the
input data of our basic numerical example (case 3 of Figure 1).

Indices
-------

k,h = indices for affiliates. They are also used to indicate the
      relevant countries and currencies.
      k = 1,...,K   h = 1,...,K   (K = 2)
        (k = 1 => the headquarters in the USA)
        (k = 2 => the subsidiary in England)

i = index for product.   i = 1,...,I
      (I = 2)

j = index for investment option.   j = 1,...,J(k)
      (J(1) = 1, J(2) = 2)


Parameters
----------

tr(k)   = the translation coefficient applied on the after tax yield
          in affiliate k.
            (tr(1) = 1$/$   tr(2) = 2$/L)

t(k)    = the absolute income-tax rate in country k.
            (t(1) = 0.47   t(2) = 0.52)

p(ik)   = the sales price of product i in country k in the local
          currency.
            (p(11) = $5   p(12) = L 2.0)
            (p(21) = $3   p(22) = L 2.7)

c(ik)   = the unit variable cost of product i produced in affiliate
          k, stated in the local currency.
            (c(11) = $1.8   c(12) = L0.8)
            (c(21) = $1.0   c(22) = L1.0)

p(ikh)  = the unit transfer price of product i transferred from
          affiliate k to affiliate h, stated in the host country
          currency of the exporting affiliate k.
            (p(112) = $1.7   p(121) = L0.9)
            (p(212) = $0.9   p(221) = L0.7)

v(hk)   = the exchange rate of currency h in country k.
            (v(21) = 2$/L   v(12) = 0.5L/$)

uc(ik)  = the absolute rate of the ad valorem duty imposed on
          product i imported by affiliate k. The duty is paid by the
          importing affiliate k in the local currency.
            (uc(11) = 0.24   uc(12) = 0.22)
            (uc(21) = 0.24   uc(22) = 0.22)

ut(ihk) = the unit transportation cost of an item of product i
          transferred from affiliate h to affiliate k. It is paid by
          the importing affiliate k in the local currency.
            (ut(112) = L0.06   ut(121) = $0.12)
            (ut(212) = L0.12   ut(221) = $0.24)

rd(k)   = the absolute rate of interest on the borrowing by
          affiliate k from the local money market.
            (rd(1) = 0.08   rd(2) = 0.11)

rm(kh)  = the absolute rate of interest on the interaffiliate loan
          granted by affiliate k to affiliate h.
            (rm(12) = 0.09   rm(21) = 0.09)

sm(kh)  = the absolute stamp-duty rate on the interaffiliate loan
          granted by affiliate k to affiliate h. The stamp-duty is
          paid by affiliate h raising the loan.
            (sm(12) = 0.01   sm(21) = 0.005)

re(k)   = the absolute rate of interest on the closing cash of
          affiliate k deposited locally in bank.
            (re(1) = 0.08   re(2) = 0.08)

g(k)    = the total expenditure of investing in the capacity
          increase in affiliate k, stated in the local currency.
            (g(1) = $1200   g(2) = L700)

rg(k)   = the coefficient for calculating one annuity of the
          capacity increase investment cost in affiliate k. For
          details see the discussion in Section 2.3.
            (rg(1) = 0.4164   rg(2) = 0.3292)
            (E.g. the latter indicates a life-span of four years
            with a 12% interest rate.)

f(jk)   = the total expenditure of the j:th investment option for
          affiliate k, stated in the local currency.
            (f(11) = $500  f(12) = L110)
                          (f(22) = L 90)

rf(jk)  = the coefficient for calculating one annuity of the total
          expenditure of the j:th investment option for affiliate k.
          For details see the discussion in Section 2.3.
            (rf(11) = 0.2774   rf(12) = 0.4164)
                              (rf(22) = 0.3292)

s(jk)   = the annual earnings from the j:th investment option of
          affiliate k, stated in the local currency.
            (s(11) = $200   s(12) = L55)
                           (s(22) = L40)

U(k)    = the fixed and predetermined costs in affiliate k, stated
          in the local currency.
            (U(1) = $3000   U(2) = L2000)

X(ik)   = the sales potential of product i for affiliate k.
            (X(11) = 1600   X(12) = 1200)
            (X(21) = 1000   X(22) = 1000)

Hb(ik)  = the initial inventory of product i in affiliate k.
            (Hb(11) = 300   Hb(12) = 250)
            (Hb(21) = 200   Hb(22) = 200)

He(ik)  = the closing inventory required for product i in affiliate
          k.
            (He(11) = 300   He(12) = 250)
            (He(21) = 200   He(22) = 200)

a(ik)   = the capacity usage in affiliate k per an unit of product
          i.
            (a(11) = 2.2   a(12) = 1.5)
            (a(21) = 2.5   a(22) = 1.8)

Y(k)    = the initial capacity in affiliate k.
            (Y(1) = 3000   Y(2) = 2500)

b(k)    = the additional capacity that can be acquired in affiliate
          k.
            (b(1) = 700   b(2) = 600)

pp(ik)  = the cash portion of p(ik).
           (pp(11) = $3.0   pp(12) = L1.5)
           (pp(21) = $2.5   pp(22) = L2.0)

pp(ikh) = the cash portion of p(ikh).
            (pp(112) = $1.5   pp(121) = L0.7)
            (pp(212) = $0.6   pp(221) = L0.5 )

cp(ik)  = the cash portion of c(ik).
            (cp(11) = $1.8   cp(12) = L0.6)
            (cp(21) = $0.5   cp(22) = L0.4)

Up(k)   = the cash portion of U(k).
            (Up(1) = $3000   Up(2) = L2000)

Eb(k)   = the initial cash in affiliate k, stated in the local
          currency.
            (Eb(1) = $500   Eb(2) = L250)

Ee(k)   = the minimum closing cash in affiliate k, stated in the
          local currency.
            (Ee(1) = $700   Ee(2) = L350)

D(k)    = the maximum borrowing capability of affiliate k from the
          local money market, stated in the local currency.
             (D(1) = $2300   D(2) = L800)

M(k)    = the maximum acceptable level of interaffiliate lending by
          affiliate k, stated in the local currency.
             (M(1) = $2000   M(2) = L700)


REFERENCES


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[2] Agmon, Tamir. "The Relations among Equity Markets: A Study of
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[10] Lessard, Donald. "World, Country, and Industry Relationships in
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[11] Lorie, James H. & Savage, Leonard J. "Three Problems in
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[13] Merville, Larry Joe. An Investment Decision Model for the
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[14] Nauman-Etienne, Ruediger. "A Framework for Financial Decisions
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[15] Nieckels, Lars. Transfer Pricing in Multinational Firms: A
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[16] Petty, John William. An Optimal Transfer-Pricing System for the
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[19] Salmi, Timo. "Some Aspects of Production and Profit Adjustment
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[20] Salmi, Timo. Joint Determination of Trade, Production, and
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[21] Slavich, Denis Michael. The International Financing Decision: A
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[22] Solnik, Bruno H. "An Equilibrium Model of the International
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NOTES:

1) The same proposition is indicated in [19].

2) It is very difficult to obtain permission for the use of the
confidential internal data of multinational corporations. For this
reason we must use fictitious data to simulate real-life decision-
making situations.

3) Arya [3, pp. 9-67] provides a fairly comprehensive survey of the
development of capital budgeting decision theory.

4) Although advocated already earlier by scholars of economics the
managerial application of the internal rate of return and cut-off at
the marginal cost of capital can with good reason be attributed to
Dean in 1951. Dean's approach is widely applied by managers of
business enterprises as a sophisticated rule of thumb for the
capital budgeting decisions. However, Lorie and Savage [11] and
Weingartner [26] showed that Dean's approach is not consistent with
the maximization of the net worth of the firm.

5) They also demonstrated the fundamental fact that the cost of
capital to the firm need not be known in advance, because the linear
programming approach solves it simultaneously with the operating
and financing decisions of the firm.

6) This is consistent with the result in [4] demonstrating the
variability of the opportunity cost of capital along the time-
dimension.

7) Translation is needed, because the yields for the subsidiaries
located in different countries are denominated in foreign
currencies. For a discussion on translation problems see e.g. [23,
Ch. 3].

8) We use the word "affiliate" for both the headquarters and the
subsidiaries of the multinational firm. It is assumed for expository
convenience that no more than one affiliate of the firm is located
in any country.

9) For a relevant discussion see [26, Ch. 3 and Sec. 8.4].

10) The inclusion of stochastic currency exchange rates (i.e. the
inclusion of the so-called currency risk) in linear programming
models for joint operating and financial planning has been
demonstrated by Jskelinen and Salmi [9] in 1974, and Salmi [20].

11) Operations research models for optimal transfer pricing
decisions in the multinational firm have also been constructed by
Petty [16] and Nieckels [15]. These models treat, however, the other
decision variables as predetermined.

12) The generic method for obtaining this opportunity cost rate
would be the one advocated by Charnes, Cooper and Miller [4], but
their suggestion cannot be applied here, since it would require a
multiperiod model, which might be too large to be computationally
feasible for multinational business enterprises. Instead, an
iterative procedure for finding plausible q(k)-values might be
devised.
  We assume, however, that the decision maker is able to give
subjective estimates for these opportunity cost rates. Furthermore,
when compared with the other congenial operations research models
for the multinational firm, no actual simplification is involved.
