multinational corporate financing … corporate financing and foreign exchange parity relations...
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MULTINATIONAL CORPORATE FINANCING AND FOREIGN EXCHANGE PARITY RELATIONS
M. Shahid Ebrahim* Ike Mathur**
Date of current draft: February 4, 2002
*National University of Singapore, Singapore **Washington University, St. Louis, MO. Correspondence address: Ike Mathur Olin School of Business Washington University Campus Box 1133 One Brooking Drive St. Louis, MO 63130-4899 email: [email protected] Phone: 314-935-7257 Fax: 314-935-6359
MULTINATIONAL CORPORATE FINANCING AND FOREIGN EXCHANGE PARITY RELATIONS
Abstract
Given the increasing importance of financing in foreign currency denominated debt, researchers have shown the conditions under which raising capital denominated in a foreign currency becomes feasible. We extend this literature in the context of a multinational corporation (MNC) by modeling the rivalry between equity and debt under a modified general equilibrium framework. We derive (i) international exchange rate parity relations as extensions of the risk free debt finance models under risk aversion and market imperfections such as taxes, and (ii) optimal capital structure of an MNC using the principle of Pareto-optimality. JEL Classifications: G32; F23; F30 Keywords: Multinational financing; Pareto-optimal financial contracts
I. Introduction
Globalization of business has emerged as one of the dominant corporate trends in the
past three decades. For many multinational corporations (MNCs), growth from overseas
operations has outstripped the growth in their domestic markets. MNCs face major
considerations regarding their investment and financing decisions. They are exposed to
exchange rate risk, political instability, threats of expropriation and other types of risk that are
unique to their international scope of operations. MNCs have to deal in a number of
currencies, understand the intricacies of different money markets and cope with the laws of
various foreign governments. Yet, they are willing to undertake these risks due to the
potential for enhanced returns associated with expanding and operating in foreign markets.
An optimal financing mix for MNCs is a significant managerial consideration. In
general, compared to purely domestic firms, MNCs can access more alternatives to finance
themselves. They are also exposed to more risk, especially foreign exchange risk, than
domestic firms. MNCs seek to obtain the best possible financing mix to attain their corporate
objective.
Several papers have addressed the issue of financing and investment decisions of
MNCs, generally using either the capital asset pricing model or the market imperfections
approach. Early work incorporated the International Capital Asset Pricing Model (ICAPM).
For example, Mehra (1978) prices securities in the presence of exchange rate risk. He finds
that the ICAPM beta needs to take into account exchange risk in addition to the covariance of
the security with the world market portfolio. If not, there will exist a systematic bias in the
capital budgeting decision process. Senbet (1979) shows that in the absence of differential
taxes, the international financing mix is irrelevant. Presence of foreign exchange risk and
differential international interest rates, in the absence of differential taxes, still make
2
financing decisions irrelevant. Only in the presence of differential taxes does there seem to
exist a global hurdle rate that incorporates the exchange rate risk. He concludes that in the
presence of differential taxes the choice of the appropriate hurdle rate has to incorporate
exchange rate risk to obtain the appropriate discount rate to be used for multinational
projects.
Other authors have used the market imperfections approach. Shapiro (1984) discusses
MNC financing by considering the presence or absence of corporate income taxes and
flotation costs according to the following rule: Borrow in the weaker currency country in the
presence of corporate taxes, and borrow in the stronger currency country in the presence of
flotation costs. Rhee, Chang and Koveos (1985) extend Shapiro's (1984) work to the case
where both taxes and flotation costs are present in a country and conclude that if the tax effect
dominates, then the MNC should borrow in the country that has the weaker currency.1
Madura and Fosberg (1990) use a net present value (NPV) analysis under assumptions of
perfect competition and conclude that project selection should be based on high NPVs and
low risk.
More recently, there is an emerging focus on developing equilibrium models to
explain MNC financing. For example, Chowdhry and Coval (1998) develop an equilibrium
model that incorporates risk-free debt to derive rules for financing the subsidiary of an MNC.
In general, any analysis of optimal MNC financing should (i) separate the financing
and investment selection processes, (ii) address the project selection criterion when a project
has a high NPV but also has a high variance, and (iii) distinguish between risky and risk-free
debt financing sources and obtain a financial mix of risk-free or risky debt in conjunction
1 The adjectives 'weaker' and 'stronger' used for currency by Shapiro (1984) and Rhee, Chang and Koveos (1985)
imply currency anticipated to depreciate or appreciate, respectively.
3
with domestic or foreign financing.2 We present a modified general equilibrium model in this
paper in which the investment decisions are separated from financial decisions. We also
develop a methodology of MNC financing that is based on dominant models of financing
involving either risk-free, risky, domestic or foreign debt, or any combinations of these debts.
We present a general strategy for analyzing projects that range from high risk-high NPV to
low risk-low NPV profiles.3 We incorporate the conflict of interest between risk averse
equity owners of an MNC and that of its financiers while including the deadweight costs of
bankruptcy and taxes. In this regard we emulate Diamond (1989) and Hirshleifer and Thakor
(1992) who have discussed agency issues stemming from the conflict between equity and
debt.
Our contribution to the literature includes the following unique results. (i) A set of
equivalent conditions related to foreign exchange parity conditions. In contrast to the existing
theoretical literature, our endogenously determined real domestic and foreign interest rates are
not at par due to agent risk aversion, heterogeneity, and market imperfections such as taxes.
The same is the case for the endogenously determined futures contract with respect to the
expected exchange rate at the investment horizon. Given the substantial debate on deviations
of basic parity conditions from the actual observed conditions (see, e.g., Cheung and Lai
(1998, 2000), Grossman and Rogoff (1995), Hollifield and Uppal (1997), Lothian (1998),
Lothian and Taylor (1996), Mark (1995), Rogoff (1996), and Sercu et al (1995)), our study
provides the basis for future empirical research on these parity conditions. (ii) Optimal
capital structure of an MNC is uniquely determined under each financing scheme. Since 2 Risk-free debt denotes debt that is repaid fully at maturity and is independent of the state of the economy. In
contrast, risky debt entails default in some states of the economy and full payment in the remaining. Risky debt is, thus, state dependent.
3 In our modified general equilibrium analysis, taxes constitute leakages, as they are considered exogenous. The rationale behind this assumption stems from the study by Finnerty (1988) who states that, historically, securities are created in response to unexpected economic, tax and regulatory shocks.
4
leverage is feasible with a variety of securities, optimal capital structure involves searching
for financial packages that are Pareto-efficient.
This paper is organized as follows: Section II derives the equity holder's objective
function, while Section III considers lender constraints. The market clearing equilibrium
conditions and related results are discussed in Section IV, with the conclusions provided in
Section V.
II. The Equity Holder's Objective Function
In this section, we first present basic elements of the model followed by modeling the
objective function of the equity holder in the MNC.
II.a. Elements of the Model
Consider a two-period model, where an economic agent is the equity holder of the
MNC. This agent maximizes the expected utility of consumption at time t = 0. The MNC has
access to a foreign project with a net operating income (d1~ ) and a liquidating value (P1
~ ) in
period t = 1, where both d1~ and P1
~ are positive random first-order Markov processes. The
minimum value of the sum of net operating income plus liquidating value is positive.4 There
also exist other agents, both domestic and foreign, in this economy who perform the vital
function of lending. They make adequate funds available via a risk-free or a risky loan. The
MNC has the choice of borrowing from domestic or foreign sources of lending. The analysis
in the following sections demonstrates the optimal pricing of the project and that of loans.
4 This assumption is a necessary condition for risk-free debt.
5
II.b. Modeling the Equity Holder's Objective Function
The goal of the equity holder is to optimize the expected utility of consumption:5, 6 Max E0 {U(c0) + γU(c1
~ )}
(in Qd, Qf, c0, c1, s)
subject to the constraints
c0 = w0 - s e0 P0 + Qd + e0 Qf (1)
c1~ = w1
~+ s [(e1
~ ) (d1~ +P1
~ )]AT - Qd(1+rd~)AT - Qf [(e1
~ ) (1+rf~)]AT (2)
c1~ = w1
~+ {(e1
~ ) [s (d1~ +P1
~ )- Qf (1+rf~)] }AT - Qd(1+rd
~)AT (2')
c1~ = w1
~+{F[s(d1c+P1c)-Qf(1+rfc)]+(e1
~ )[s((d1~ -d1c)+(P1
~ -P1c))-Qf(rf~-rfc)]}AT
-Qd(1+rd~)AT (2a)
where
E0{ } is the expectation operator at time 0,
c0 is the consumption of equity-holder at t = 0,
c1~ is the stochastic consumption of equity-holder at t = 1,
w0 is the endowment at t = 0,
w1~ is the risky endowment at t = 1,7
γ is the discount factor,
s is the fractional investment in a foreign venture,
Qd is the amount of funds borrowed domestically,
Qf is the amount of funds borrowed from a foreign source,
5 The consumption levels of agents in our model at the two time periods are evaluated as the residual of
endowments/ payoffs after payments towards purchase/ debt obligations. We abstract away from the fact that the consumption baskets of domestic agents differ from that of foreign ones, as this is not the focus of this paper.
6 A domestic and/or foreign loan has been assumed in this model. We do not consider foreign currency debt swapped into domestic currency as it is equivalent to domestic debt. Finally, there is also the possibility of a cross-currency loan. This latter alternative is not evaluated in this paper. However, this alternative can be readily incorporated in the model.
7 A risky endowment enables us to incorporate systematic risk and reduce unsystematic risk.
6
e0 is the value of the exchange rate in dollars per foreign currency at t = 0,
e1~ is the value of the exchange rate in dollars per foreign currency at t = 1,
P0 is the price of the foreign venture at t = 0 in the foreign currency,
rd~ is the real domestic interest rate,
rf~ is the real foreign interest rate,
rfc is the optimal real foreign interest rate hedged,
d1~ is the net operation income (NOI) of the project received at t = 1 in the foreign
currency,8
d1c is the optimal NOI of the project hedged at t = 1,
P1~ is the liquidating value of the project at t = 1 in the foreign currency,
P1c is the optimal liquidating value of the project hedged at t = 1,
F is the price of the futures contract for hedging the optimal [s(d1c+P1c)-Qf(1+
rfc)] amount of foreign currency, 9
AT represents after-tax terms.
The Lagrangian L using Equations (1) and (2) can be written as follows:
L = E0{[U(c0)+γU(c1~ )]+ λ0[w0 - s e0 P0 + Qd + e0 Qf - c0]
+λ1γ[ w1
~+ s [(e1
~ ) (d1~ +P1
~ )]AT - Qd (1 + rd~)AT - Qf [(e1
~ ) (1+rf~)]AT - c1
~ ]},
where λ0 and λ1 are the Lagrange multipliers for the two constraints, respectively.
The first-order necessary conditions (FONCs) are given by:
8 The MNC faces transaction risk when the NOI and/or the liquidating value of the project is a function of
exchange rates. However, this issue can be resolved with a futures contract as demonstrated in Equation (10) in Section IV.
9 Both F and [s (d1c + P1c)-Qf (1 + rfc)] are evaluated endogenously in our model.
7
δLδc0
= 0 ⇒ λ0 = U'(c0) , (3)
δLδc1
= 0 ⇒ λ1 = E0(U'(c1~ )) , (4)
δLδs ≥ 0 ⇒ - λ0 e0 P0 + γE0{λ1 [e1
~ (d1~ +P1
~ )]AT } ≥ 0
⇒ γE0{λ1 [e1~ (d1
~ +P1~ )]AT } - λ0 e0 P0 ≥ 0
Using equations (3) and (4), we obtain the following results:
P0 ≤ γE0{[U'(c1
~ )U'(c0)] [(
e1~
e0) (d1
~ +P1~ )]AT} (5)
If the MNC has access to a futures market in the foreign currency, it can reduce
currency risk as follows:
P0 ≤ γE0{[U'(c1
~ )U'(c0) ] [(
Fe0
)(d1c+P1c) + (e1~
e0)((d1
~ - d1c) + (P1~ - P1c))]AT} (5a)
The left side of Equations (5) and (5a) are the initial costs of the project. The right
side represents the present value of the cash flows from the project at the end of the project.
Equations (5) and (5a) state that, at the margin, if the discounted benefit of the project is
greater than the cost of the project, then the MNC should accept the project. Equation (5a)
helps reduce currency risk. It can be separately derived using the same Lagrangian procedure
described above by using Equations (1) and (2a).
Equations (5) and (5a) are similar to the risk neutral NPV decision criterion used in
previous research. However, in the present analysis, the investment and the financing
decisions have been separated. Furthermore, the analysis also incorporates a risk-averse
version of the NPV rule. Thus, Equations (5) and (5a) can be viewed as two-period versions
of the Lucas (1978) model incorporating taxes and exchange rates.
8
Differentiating the Lagrangian with respect to the amount of funds borrowed
domestically, we obtain
δLδQd
≥ 0 ⇒ λ0 - γ E0{λ1(1+ rd~)AT} ≥ 0
Substituting equations (3) and (4), we obtain
⇒ 1 - γ E0{[U'(c1
~ )U'(c0)](1+ rd
~)AT} ≥ 0 (6)
Equation (6) states that financing with a domestic loan is feasible only if, at the margin, the
benefit of borrowing a single unit of domestic currency exceeds the cost of it. This result is
consistent with the NPV criterion.
Finally, differentiating the Lagrangian with respect to the amount of foreign funds
borrowed, we obtain δLδQf
≥ 0 ⇒ e0λ0 - γ E0{λ1[(e1~ )(1+ rf
~)]AT} ≥ 0
Substituting equations (3) and (4), we obtain
⇒ 1 - γ E0{[U'(c1
~ )U'(c0)][(
e1~
e0)(1+ rf
~)]AT} ≥ 0 (7)
Here again, currency risk can be reduced by the MNC if it hedges with a futures
contract, which implies that10
⇒ 1 - γ E0{[U'(c1
~ )U'(c0)][(
Fe0
) (1+rfc) + (e1~
e0)( rf
~ - rfc)]AT} ≥ 0 (7a)
The interpretation for Equations (7) and (7a) is similar to that for Equation (6). Namely,
Equations (7) and (7a) state that financing with a foreign loan is feasible only when, at the
margin, the benefit of borrowing foreign funds exceeds the cost of foreign debt financing.
10 If the MNC is fully diversified, then hedging currency risk partially reduces both systematic as well as project
specific (idiosyncratic) risk. However, if the MNC is not diversified then hedging partially reduces the unsystematic risk.
9
Since the loan is in the foreign currency, its desirability is influenced not only by the interest
rate but also by the exchange rate. The exchange rate is explicitly modeled in Equation (7).
The futures contract is explicitly modeled in Equation (7a).
III. Lender FONCs and Constraints
We assume that lenders are also risk averse and optimize the expected utility of
consumption. Given these assumptions, we can derive the following profitability conditions
(FONCs) for the domestic and foreign lender:
For the domestic lender:11
γ' E0{[U'(c'1
~ )U'(c'0)](1+ rd
~)AT'} - 1 ≥ 0 (6a)
For the foreign lender:
γ" E0{[U'(c"1
~ )U'(c"0)][(
e1~
e0)(1+ rf
~)AT"] } - 1 ≥ 0 (7b)
γ" E0{[U'(c"1
~ )U'(c"0)][(
Fe0
) (1+rfc)AT" + (e1~
e0)( rf
~ - rfc)AT"] } - 1 ≥ 0 (7c)
The first term on the right side in Equations (6a), (7b) and (7c) show the fractional
discounted proceeds of the cash flows when the debt matures. Equations (6a), (7b) and (7c)
have the same economic intuition as their counterpart Equations (6), (7) and (7a) but are
viewed from the perspective of the lenders. These results state that the intertemporal marginal
rate of substitution (MRS) times the grossed up factor consisting of after-tax payoffs
(adjusted for currency risk in the case of a foreign loan) exceeds a unit of currency loaned.
11 The terms γ', γ″, c1′, c1″, c0′ and c0″ have the same meaning as before. However, they represent the parameters
for domestic and foreign lenders in domestic and foreign currencies, respectively. To elaborate on this point, c0′
= w0′ - Qd, c0″ = w0″ - Qf, c'1~ = w'1
~+ Qd(1 + rd
~)AT
, and c"1~ = w"1
~+ Qf(1 + rf
~)AT
10
For the debt market to be in equilibrium, the MRS for both the borrower and the lender has to
adjust to a unique cost of funds.
III.a. Domestic Risk-Free Loan
We first consider the situation for risk-free domestic borrowing. In this scenario,
where there is no default risk and only corporate taxes, the maximum amount of domestic
loan plus interest would be constrained only by the asset returns in dollars in the worst
scenario:
(QdRF)Max(1+rd
RF)AT'
≤ Min {(e1~
e0)s (d1
~ + P1~ )
AT}
(QdRF)Max ≤
Min {[(e1~
e0)s(d1
~ +P1~ )]
AT}
(1+rdRF)
AT'
(8)
The left side of Equation (8) represents the maximum amount of the domestic loan, while the
numerator on the right side is equal to the minimum terminal cash flow from the foreign
project.
III.b. Foreign Currency Risk-Free Loan
In this alternative we extend the analysis to a default free foreign currency loan. In this
scenario, in the absence of default risk and only corporate taxes, the maximum amount of
foreign loan plus interest would be constrained by the asset returns in foreign funds in the
worst scenario:
(QfRF)Max(1+rf
RF)AT' ≤ Min {s (d1
~ + P1~ )
AT}
(QfRF)Max ≤
Min {s (d1~ +P1
~ )AT}
(1+rfRF)
AT'
(9)
11
As in Equation (8), the left side of Equation (9) is the maximum amount of the foreign
currency loan. This amount is equal to or less than the minimum terminal cash flow from the
project.
III.c. Domestic Risky Loan
With this third alternative, we remove the condition that the domestic loan has to be
risk free. For the domestic risky loan we extend the profitability condition given by
equation (6a) in the following manner:12
γ'⌡⌠
0
c
[U'(c'1
~ )U'(c'0)][
k[(d1j~ +P1j
~ )e1j~ ]
QdR ]δj+ γ'
⌡⌠
c
∞
[U'(c'1
~ )U'(c'0)][1+rd
R]AT'
δj ≥ 1. (6b)
The first integral involves the default alternative when the lender receives a fraction k of the
terminal cash flow (d1j~ +P1j
~ ) in the foreign currency. In this equation, k is the sum of direct
and indirect bankruptcy costs, and e1j~ is the stochastic exchange rate in period t = 1. The
second integral represents payment in full in the normal states of the economy.
III.d. Foreign Currency Risky Loan
The final alternative considers borrowing in the foreign currency. For this risky loan
alternative, we extend the profitability condition (Equation (7b)) to state the following:
γ"⌡⌠
0
c
[U'(c"1
~ )U'(c"0)][
k[(d1j~ +P1j
~ )]Qf
R ]δj+ γ"⌡⌠
c
∞
[U'(c"1
~ )U'(c"0)][(
e1j~
e0)(1+rf
R)]AT"δj ≥ 1. (7d)
12 δj = f(d1j+P1j)δ(d1j+P1j), where f(.) represents the probability density function.
12
Here also, the first integral involves default, while the second incorporates full payment in the
normal states of the economy. No exchange rate variable is incorporated in the first integral
since the default occurs in foreign funds.
IV. Market Clearing Equilibrium Conditions
The following conditions are necessary for equilibrium:
(i) For the project market to be in equilibrium, the fractional investment (s) by the
MNC must equal one, i.e., s = 1.
(ii) For the money market to be in equilibrium, funds borrowed must equal funds
lent, i.e., QBorrowed = QLent
(iiia) For the initial capital constraint to be met for the borrower, the initial
consumption level should be positive:13
c0 = w0 - s e0 P0 + Qd + e0 Qf > 0
⇒ (Qd + e0 Qf) > e0 P0 - w0 using Condition (i) above.
(iiib) For the initial capital constraint to be met for either the domestic or foreign
lender, the initial consumption levels should again be positive:
c'0 = w'0 - Qd > 0 ⇒ Qd < w'0 and
c"0 = w"0 - Qf > 0 ⇒ Qf < w"0
(iv) The optimal amount of foreign currency hedged by the MNC is equal to
[s(d1c+P1c)-Qf(1+ rfc)] = [(d1c+P1c)-Qf(1+ rfc)] using Condition (i) above. This
amount is also equal to the optimal amount of foreign currency hedged by the
foreign lender, i.e., Qf(1+ rfc). ⇒ [(d1c+P1c)-Qf(1+ rfc)] = Qf(1+ rfc). ⇒
(d1c+P1c) = 2 Qf(1+ rfc). 13 The strict inequalities in the equations apply for risk-averse borrowers and lenders, respectively. They can be
relaxed to equal zero for risk-neutral investors.
13
IV.a. Derived Results
Two theorems are derived from the model presented.
Theorem 1. In competitive markets, the FONCs yield the arbitrage-free foreign exchange
parity relationships given below as Equations (10)-(13) under the assumption of risk-free debt
financing. Further assumptions reconcile our results with the existing literature.
Proof. Foreign Exchange Expectations:
Solving Equations (7), (7a), (7b) and (7c) simultaneously results in the following
condition:
F = {E0[(
U'(c1~ )
U'(c0))e1~ ]
E0(U'(c1
~ )U'(c0))
}= {E0[(
U'(c"1~ )
U'(c0"))e1~ ]
E0(U'(c"1
~ )U'(c0"))
} (10)
Thus, Equation (10) provides a pricing mechanism for a futures contract to reduce
transaction risk. It should be noted that Equation (10) is a non-linear function of the future
exchange rate at t = 1. Further assumption of risk neutrality and the absence of taxes provides
the well-known condition that the futures (forward) exchange rate is equal to the expected
value of the exchange rate at t = 1:
F = E0[e1~ ] (10a)
International Fisher Relation:
Solving Equations (6) and (7) simultaneously provides the following relationship:
γE0{(U'(c1
~ )U'(c0))[ [(
e1~
e0)(1-τd)+τd] (1+rf
RF(1-τdf))-(1+rd
RF(1-τd))]} = 0, (11)
where τ is the effective tax rate imposed on the MNC by the foreign (f) and domestic (d)
governments, respectively.
14
Equation (11) provides a non-linear relationship between the exchange rate at t = 1
and real domestic and foreign interest rates. These rates are not necessarily equal, which is in
contrast to the existing theoretical literature that assumes equality of real interest rates across
the globe.
Assumption of risk neutrality leads to the solution given below, which is similar to
that of Shapiro (1984):
E0{[(e1~
e0)(1-τd)+τd] (1+rf
RF(1-τdf))} = (1+rd
RF(1-τd)) (11a)
Applying the stringent condition of no taxes produces a relation similar to the
International Fisher Effect as given below:
E0{(e1~
e0)(1+rf
RF)} =
Fe0
(1+rfRF
)= (1+rdRF
) (11b)
Interest Rate Parity (IRP):
Solving Equations (6a), (7b), and (7c) and substituting the futures price in place of the
risky currency rate at t = 1 provides the following relationship:
Fe0
= [(1+rd
RF(1-τ'd))
(1+rfRF
(1-τ"f))](
MRSdLMRSfL
) (12)
where the other symbols have the same meaning as before and MRS signifies the marginal
rate of substitution [=γE0(U'(c1
~ )U'(c0))] of the domestic lender (dL) and the foreign lender (fL),
respectively. Equation (12) indicates that futures pricing relative to the spot rate is a function
of real (after tax) interest rates and the MRS of domestic versus foreign investors. This result
is different from the traditional literature where the relative pricing of futures and spot rates is
a function of purely nominal interest rates. The difference between our result and the existing
literature is due to the fact that investors in our model optimize utility of consumption derived
15
from assets whose payoffs are evaluated in real terms (after tax) instead of nominal terms.
Furthermore, since tax policy, wealth (in the form of endowments), and the risk aversion of
agents varies across domestic and foreign economies, Equation (12) shows that the IRP in
terms of real interest rates does not hold, in general. The deviations from IRP (in terms of real
interest rates) are due to the impact of differential taxes and the MRS of the agents in the two
economies (which is further impacted by the wealth and risk aversion parameters across
economies). These theoretical results are supported by international evidence (in, for
example, International Financial Statistics), which indicates that real interest rates vary across
countries.
The results reported above are unique since our model takes the exchange rate as an
exogenous stochastic variable and evaluates the interest rates endogenously while previous
literature has assumed that interest rates are exogenous and evaluates their impact on
endogenous exchange rates.
Relative Purchasing Power Parity (RPPP):
Substituting the Fisher Relation (see Fisher, 1930) in Equation (12) generates the
following relationship:
Fe0
= (1+πf1+πd
)[1+id
RF-τ'd(id-πd)
1+ifRF
-τ"f(if-πf)](
MRSdLMRSfL
) (13)
where i and π are the nominal interest rates and expected inflation rates in domestic (d) and
foreign (f) countries, respectively. Here too our results are different from the traditional RPPP
literature as explained in the case of IRP due to the optimization of utility of consumption of
payoffs of assets in real terms. This result is obtained because when taxes are zero and the
two MRS are the same, then the pricing of futures relative to the spot rate is equal to the ratio
of real domestic and foreign interest rates.
16
Theorem 2. The investor will iteratively evaluate the net effects of the four types of loans,
i.e., domestic/risk-free, domestic/risky, foreign/risk-free, and foreign/risky, in such a manner
that maximizes the investor�s expected utility without reducing the same for that of the
lenders.
Proof. An optimal capital structure involves either risk-free or risky debt depending on the
Pareto-optimality of one form of debt contract over that of the other.14 To determine the
optimal capital structure, one needs to numerically evaluate the sum of the expected utilities
of each agent in the economy after solving for the various endogenous parameters Qd, Qf, rd,
rf, rfc, P0, P1c, d1c, c0, c'0, c"0, c1~
, c'1~
, and c"1~
given the (i) budget constraints, i.e., Equations
(1), (2), (2'), (2a) and footnote (11); (ii) market clearing conditions, i.e., the equations in
Section IV; (iii) the pricing function of the project in competitive markets, i.e., Equations (5),
(5a) with the equality sign; and (iv) the pricing function of the various financing packages
given below.
Risk-Free Loan
In general, for a risk-free loan, there exists a unique interior solution as long as the
following necessary conditions are satisfied:
(i) The minimum of the sum of NOI plus the liquidating value of project (after repayment
of loan) in the next period is positive. This condition implies that the payoff in the
worst state of the economy in the future should be at least sufficient to meet the
principal and interest payments. Equations (8) and (9) satisfy the requirements of this
condition for the domestic and foreign risk-free loans, respectively.
(ii) At the margin, the discounted value of the expected MRS of the entrepreneur times
the compound factor, consisting of one plus the after tax cost of borrowing, equals the
discounted value of the deterministic MRS of the financier times the compound
14 Our model has the capacity to incorporate market imperfections such as taxes and flotation costs. We derive a
wide array of optimal contracts for the MNC stakeholders emanating from the five different ways of leveraging based on the vital principal of Pareto-optimality.
17
factor, consisting of one plus the lending rate. All these terms again equal the unit
amount of funds loaned. Alternatively, the following three conditions should be met.
(a) For the domestic risk-free loan, Equations (6) and (6a) should be satisfied
simultaneously:
γ E0U'(c1
~)(1+rd
RF(1-τd))
U'(c0) = γ' U'(c'1)(1+rdRF
(1-τ'd))U'(c'0)
= 1 (14)
(b) For the unhedged foreign risk-free loan, Equations (7) and (7b) should be satisfied
simultaneously:
γ E0{[U'(c1
~)
U'(c0)][[(e1~
e0)(1-τd)+τd](1+rf
RF(1-τdf))]}
=γ" E0{[U'(c"1
~)
U'(c"0)][(e1~
e0)(1+rfRF(1-τ"
f))]} = 1 (14a)
(c) For the hedged foreign risk-free loan, Equations (7a) and (7c) should be satisfied
simultaneously:
γ E0{[U'(c1
~)
U'(c0)][[(Fe0)(1-τd)+τd] (1+rfc(1-τdf))+[(
e1~
e0)(1-τd)+τd] [(rf
RF-rfc)(1-τdf)+τdf]]}
= γ" E0{[U'(c"1
~)
U'(c"0)][(Fe0)(1+rfc(1-τ"
f))))+(e1~
e0)[(rf
RF-rfc)(1-τ"f)+τ"
f]]} = 1 (14b)
Risky Loan
In general, for a risky non-recourse loan, there exists a unique interior solution as long
as the following necessary conditions are satisfied:
(i) The loan is structured in such a way that it involves default in some state of the
economy in the next period.
(ii) The interest rate contracted for risky debt is greater than that for risk-free debt.
(iii) The debt ratio for risky debt is greater than that of risk-free debt.
(iv) At the margin, the discounted value of the expected MRS of the entrepreneur times the
compound factor, consisting of one plus the variable after-tax cost of borrowing, equals
the discounted value of the expected MRS of the financier times the compound factor,
18
consisting of one plus the payoffs from lending. All these terms again equal the unit
amount of funds loaned. That is, the following three conditions should be met. (a) For the domestic risky loan, Equations (6) and (6b) should be satisfied
simultaneously:
γ ⌡⌠
0
c
U'(c1~
)[d1j+P1j]U'(c0)Qd
R δj+ γ ⌡⌠
c
∞
U'(c1~
)(1+rdR(1-τd))
U'(c0) δj =
γ' k ⌡⌠
0
c
U'(c'1~
)[d1j+P1j]U'(c'0)Qd
R δj+ γ' ⌡⌠
c
∞
U'(c'1~
)(1+rdR(1-τ'd))
U'(c'0) δj = 1. (15)
(b) For the unhedged foreign risky loan, Equations (7) and (7b) should be satisfied
simultaneously:15
γ ⌡⌠
0
c
U'(c1~
)[d1j+P1j]U'(c0)Qf
R δj+ γ ⌡⌠
c
∞
U'(c1~
)[[(e1~
e0)(1-τd)+τd](1+rf
R(1-τdf))]U'(c0) δj =
γ" k ⌡⌠
0
c
U'(c"1~
)[d1j+P1j]U'(c"0)Qf
R δj+ γ" ⌡⌠
c
∞
U'(c"1~
)[(e1~
e0)(1+rf
R(1-τ"f))]U'(c"0) δj = 1. (15a)
It should be noted from the above risky loan pricing Equations (15) and (15a) that the
expectations for both agents are comprised of the sum of two integrals: one in the default
state of the economy and the other in the normal state. In the default state, the borrower ( the
MNC) loses tax credits and pays the lender the residual NOI and the liquidating value of the
project. But due to the direct and indirect costs of bankruptcy (see Kim, 1978), the lender
receives a fraction (k) of the proceeds. However, in the normal state of the economy, the
15 Incidentally, it is not feasible to hedge an MNC using risky foreign debt, as the minimum amount to be hedged in
the worst (bankrupt) state of the economy is zero.
19
borrower faces an after-tax cost less than the pre-tax cost due to interest expense write-off.
Thus, in equilibrium, the bankruptcy costs are incorporated in such a way that the lender does
not face them. It is the equity holder who bears these costs in the form of higher interest rates.
V. Conclusions
As Eiteman et al (2001) point out, foreign currency capital is becoming an
increasingly important source of financing for MNCs. Different authors, including Mehra
(1978), Senbet (1979), Shapiro (1984) and Chowdhry and Coval (1998) have shown or
derived the conditions under which it becomes feasible for an MNC to raise capital
denominated in a foreign currency. We extend the literature on this important topic of
multinational financing by deriving a modified general equilibrium model for an MNC in
which we (i) separate the investment decision from the financing decision, (ii) consider
financing by both risk-free and risky domestic and foreign debt, and (iii) propose a general
strategy for analyzing a variety of projects ranging from high risk-high NPV to low risk-low
NPV.
Our starting point is the consideration by the MNC of a project that is acceptable if the
project's net present value is positive. The MNC will borrow either domestically or in a
foreign currency provided the benefits of borrowing exceed the costs of borrowing. These
basic results are consistent with actual MNC investment and financing practices.
Next, we consider the conditions under which lenders would be willing to lend money
to the MNC. Five alternatives --risk-free and risky domestic and foreign debt-- are
considered, and conditions under which lending would occur are derived.
Next, we show that if capital markets are competitive, then opportunities for arbitrage
do not exist. That is, there is no advantage for the MNC in seeking foreign currency debt
20
financing. Finally, we reconsider the various parity relations under a stringent set of
conditions.
The model presented holds important implications for MNCs. The model
demonstrates the optimal domestic and foreign currency denominated financing mix for
MNCs by combining risk-free and risky loans from both domestic and foreign sources based
on the principle of Pareto-optimality, and provides a financing solution in the special case,
not addressed by Madura and Fosburg (1990), when both the project returns and risks are
high.
Although this paper discusses risky debt in the form of junk bonds, other forms of
debt such as income bonds, preferred stock and those involving esoteric features such as
options can be brought into the realm of the current analysis. Irrespective of the form of debt
specified in the model, the following statement holds true: Optimal capital structure of an
MNC entails the Pareto-efficient design of securities.
21
References Cheung, Y.-W., and K.S. Lai, 1998, Parity reversion in real exchange rates during the post-
Bretton Woods period, Journal of International Money and Finance 17(4), 597-614. Cheung, Y.-W., and K.S. Lai, 2000, On the purchasing power parity puzzle, Journal of International Economics 52, 321-330. Chowdhry, B., and J.D. Coval, 1998, Internal financing of multinational subsidiaries: Debt
vs. equity, Journal of Corporate Finance 4, 87-106. Diamond, D.W., 1989, Reputation acquisition in debt markets, Journal of Political Economy
97, 828-862. Eiteman, D.K., A.I. Stonehill, and M.H. Moffet, 2001, Multinational Business Finance, 9th
ed. (Addison-Wesley: Reading, MA). Finnerty, J.D., 1988, Financial engineering in corporate finance: An overview, Financial
Management (Winter), 14-33. Fisher, I., 1930, The Theory of Interest (Macmillan: New York). Grossman, G., and K. Rogoff, 1995, Handbook of International Economics 3 (North Holland:
Amsterdam). Hirshleifer, D., and A.V. Thakor, 1992, Managerial conservatism, project choice and debt,
Review of Financial Studies 5(3), 437-470. Hollifield, B., and R. Uppal, 1997, An examination of uncovered interest rate parity in
segmented international commodity markets, Journal of Finance 52(5), 2145-2170. Kim, E. H, 1978, A mean variance theory of optimal capital structure and corporate debt
capacity, Journal of Finance 33(1), 45-63. Lothian, J., 1998, Some new stylized facts of floating exchange rates, Journal of
International Money and Finance 17(1), 29-40. ______, and M. Taylor, 1996, Real exchange rate behavior: The recent float from the
perspective of the past two centuries, Journal of Political Economy, 488-509. Lucas, R.E., 1978, Asset prices in an exchange economy, Econometrica 46, 1426-1445. Madura, J., and R.H. Fosberg, 1990, The impact of financing sources on multinational
projects, Journal of Financial Research 13, 61-69. Mark, N., 1995, Exchange rates and fundamentals: Evidence and long-horizon predictability,
American Economic Review, 201-218.
22
Mehra, R., 1978, On the financing and investment decisions of multinational firms in the presence of exchange risk, Journal of Financial and Quantitative Analysis 13, 227-244.
Rhee, S.G., R.P. Chang, and P.E. Koveos, 1985, The currency-of-denomination decision of
debt financing, Journal of International Business Studies 16, 143-150. Rogoff, K., 1996, The purchasing power parity puzzle, Journal of Economic Literature 34,
647-668. Senbet, L., 1979, International capital market equilibrium and the multinational firm
financing and investment policies, Journal of Financial and Quantitative Analysis 14, 455-480.
Sercu, P., R. Uppal, and C. van Hulle, 1995, The exchange rate in the presence of transaction costs: Implications for tests of purchasing power parity, Journal of Finance 50(4), 1309-1319. Shapiro, A.C., 1984, The impact of taxation on the currency-of-denomination decision for
long-term foreign borrowing and lending, Journal of International Business Studies 15, 15-25.