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: mathur@olin.wustl.edu 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

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