optimal timing of foreign direct investment under uncertainty
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This article was downloaded by: [McGill University Library]On: 20 November 2014, At: 12:40Publisher: RoutledgeInforma Ltd Registered in England and Wales Registered Number: 1072954Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH,UK
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Optimal Timing of ForeignDirect Investment UnderUncertaintyKamal Saggi PhD (Economics) aa Department of Economics , Southern MethodistUniversity , Dallas, TX, 75275, USAPublished online: 20 Oct 2008.
To cite this article: Kamal Saggi PhD (Economics) (1998) Optimal Timing of ForeignDirect Investment Under Uncertainty, Journal of Transnational ManagementDevelopment, 3:2, 73-87, DOI: 10.1300/J130v03n02_04
To link to this article: http://dx.doi.org/10.1300/J130v03n02_04
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Optimal Timing of Foreign Direct Investment
Under Uncertainty Kamal Saggi
SUMMARY. This paper constructs a two period model to examine a firm's choice between exporting and foreign direct investment (FDI) in the face of demand uncertainty. FDI involves higher fixed costs, some of which are sunk, whereas exporting involves a higher mar- ginal cost. Initial exporting yields information about demand without incurring the fixed costs of FDI since export sales reveal the state of demand abroad. It follows then that exporting carries an option val- uo-if a significant portion of fixed costs of FDI are sunk, a firm may initially export to a market and directly invest if demand conditions abroad are favorable. [Arficle copies available for a fee front The Haworth Doc~cuenf Delivety Service: 1-800-342-9678. E-mail address: [email protected]]
KEYWORDS. Foreign Direct Investment, Uncertainty, Optimal Timing
INTRODUCTION
During the past decade, a wave of economic liberalization has swept across the world. Many hitherto closed economies now wel-
Kamal Sami. PhD (Economics). is Assistant Professor. Deoartment of Eco- nomics. ~ o u 6 & ~ethodist university, Dallas, TX 75275. ('E-mail: ksaggi@ mail.srnu.edu)
[Haworth co-indcxing entry note]: "Optimal Timing o f Foreign Direct lnvestmc~it Under Uncer- tainty." Saggi. Kamal. Co-published simultaneously in Journal o/'Tran.~nurio~~alMo~~ngenrenl Develop- 1ne1r1 (Internationnl Business Press, an imprint o f Thc Haworth Press. Inc.) Vol. 3, No. 2, 1998, pp. 73-87; and: Clohalizarior~ o ~ r d Regio~mlizo~io~r: Srraregies. Policies, and Ecoeonric E~~v i~onn~enrs fed: Jcnn-Louis Mucchielli. Peter J. Bucklcy, and Victor V. Cordell) lntcniatio~~nl Business Press, an imprint of The I4awonli Press. Inc.. 1998. pp. 73-87. Single or multiple copies ofthis articlc arc available fbr a fee from The Haworth Document Delivery Service [I-800-342-9678. 9:00 a.m. - S:00 p.m. (EST). E-moil address: [email protected].
O 1998 by The Haworth Press, Inc. All rights reserved. 73
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74 GLOBALIZATION AND REGIONALlZATlON
come investment from industrialized coun~ies. However, the relative newness of economic reforms in these economies implies that for- eign firms are not fully familiar with local consumer tastes and preferences. This lack of familiarity with potential consumers trans- lates into an environment of demand uncertainty for potential inves- tors in these new markets. How does the existence of such uncer- tainty affect a firm's choice between exporting and foreign direct investment (FDI)? How does it influence the dynamics of a finn's optimal entry strategy?
To highlight the dynamic issues facing a film choosing between exporting and FDI in an uncertain environment, I construct a two period model where a firm faces an uncertain demand curve abroad. The basic trade-off confronting the firm is best understood by first considering the case in which the uncertainty facing the firm persists in both periods if it does not do FDI immediately, i.e., first period export sales do not resolve uncertainty. While exporting economizes on fixed costs (some of which are irreversible) by avoiding the construction of a new plant, it also involves a higher marginal cost than FDI since shipping goods abroad incurs tariff and/or transporta- tion costs. Due to the above trade-off, a firm finds exporting relative- ly more profitable than FDI if the expected market for its product is small and the firm sticks with its initially adopted entry mode in both periods. But if export sales reveal the state of the demand abroad, i.e., if the second period demand is highly correlated with first period demand, the firm can first test the foreign market via its exports and directly invest only if the market is large enough. In such a situation, there arises the interesting possibility of a switch from exporting to FDI. Alternatively, of course, the firm could adopt FDI immediately and then switch back to exporting in case of low demand. Which of the preceding hvo strategies is inore profitable is determined by the degree to which the fixed costs of FDI are sunk. Assuming a linear demand function, this paper demonstrates that when a significant portion of the initial FDI investment is sunk, the option value of exporting in the case where export sales yield information about demandmakes it optimal to delay FDI relative to the case where exporting fails to provide such information.
The central lesson of the paper is that, when market demand is uncertain, the degree to which the fixed costs of FDI are sunk plays a
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crucial role in detennining when to export and when to do FDI. For example, in industries in which investments into production facilities are sunk only to a small degree, it is advantageous to undertake FDI sooner rather than later. The opposite implication obtains for indus- tries in which there is considerable inter-firm variation in technolo- gies of production so that one firm's production facility is of little use to another. In these industries, caution is advisable: a firm should explore the market via exports and switch to FDI only if demand conditions are favorable. While investing into developing countries, the latter scenario s e e m more appropriate since mul&ational firms often use technologies that cannot be easily absorbed by local firms. The limited absorptive capacity of local rivals makes it difficult to sell plants in case of an unfavorable outcome.
The argument of this paper is not specific to demand uncertainty. In fact, it would apply in any scenario where exporting helps re- solve uncertainty. In a fully dynamic context, uncertainty about foreign markets is usually resolved slowly via learning so that the optimal timing of FDI, among other things, will depend on the speed with which this learning occurs. In my model, for the sake of simplicity, learning is assumed to take place in one shot-the firm's first period sales reveal the state of the nature.
The assumption that FDI involves additional fixed costs, a signif- icant proportion of which may be sunk, with respect to exporting is central to the argument of the paper and a few words need to be said about how such costs may arise. First, it should be noted that this point is well accepted in the mainstream literature (Horstmann and Markusen 1991). Constructing new plants in foreign countries in- volves many irrecoverable investments. These could arise from the need for costly information acquisition regarding optimal location, possible local suppliers of inputs, local regulation, tax and environ- mental policies, labor laws and so on. Clearly, such information is useful only if production actually takes place in the foreign market. More concretely, a certain fraction of the actual plant and equip- ment investment that must be made before production can begin may also be sunk. Lastly, if it takes time for the firm to recover a portion of its fixed costs (in case of shut down), the opportunity cost of capital tied into a non-profitable activity also need to be part of the calculus of profit maximization.
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It is generally recognized that any theory of the multinational firm must confront at least two issues. First it must explain why a firm prefers to serve a foreign market via building a branch plant abroad. And second is the more subtle issue of internalization: what motivates a firm to internalize transactions as opposed to relying on arm's length market arrangements? The OLI paradigm, where 0 stands for ownership, L for locational and I for internalization, has evolved to provide convincing answers to the above questions and is a widely accepted framework for analyzing issues related to the emergence of multinational firms. However, even the OLI frame- work has little to say about the dynar~zic evolution of a firm's busi- ness strategies. Clearly, firms need to make many important deci- sions that have a dynamic aspect. A central dynamic issue is when, if ever, to switch from exporting to FDI? While the above question is clearly central, very little attention has been devoted to it. There- fore, the question addressed in this paper falls squarely out of the OLI paradigm and the paper suggests that the theory of the multina- tional firm, as developed in the OLI paradigm, suffers from the lack of a dynamic vision.
The theoretical economics literature on FDI too has paid little attention to the issues that arise in a dynamic and uncertain environ- ment. Several papers have examined the behavior of a multinational enterprise under cost and demand uncertainties but this line of re- search has generally taken the existence of a multinational firm as a given (Das 1983, Itagaki 1991). Strategic timing of FDI in order to preempt local entry has also been studied (Horstrnann and Markusen 1987) but the FDI decision involves dynamic choices that are inde- pendent of any strategic considerations and it is the latter that are the focus of this paper. While the dynamic decision process involved in the entry mode decision has been explored (Buckley and Casson 1981), the impact of uncertainty on this process has been ignored.
MODEL
Basic Set Up
There are two countries: H a n d F. A monopolist in H faces an uncertain demand curve in F and must choose between exporting
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and FDI. Under exporting, the finn supplies the F market from its H plant at a constant marginal cost of c + t, where t is the unit tariff and/or transportation cost. Under FDI, the firm sets up a plant in F incurring a fixed investment G and it supplies the F market at a constant marginal cost c. A proportion P of the fixed cost G is sunk; if the firm wants to sell its plant and shut down production abroad, it can recover only (1 - P)G of its original investment G. A com- . pletely equivalent interpretation of this idea is that P characterizes the time profile of the investments required to sustain a foreign plant: the firm must pay P G of its fixed cost in the first period and (1 - P)G of it in the second period. Of course, under the alternative formulation all fixed investments once undertaken would be sunk.
Let D(p; 8) denote the demand function facing the firm, where 8 is a random variable distributed as follows:
where OH > OL. Further suppose that
There are two periods and at the beginning of each period, the firm chooses between exporting and FDI. The firm's first period pricing decision is made under uncertainty since it sets its price before 8 is realized. Since there is a one-to-one mapping between the firm's first period sales and 0 the firm uncovers the realization of 0 from its first period sales. In the second period the firm chooses its price as well as its mode of operation knowing the realization of 0.
The basic decision problem of the firm is to choose between one of the following four strategies:
1. Export for both periods. Under continual exporting, the firm faces marginal cost c + s in both periods and incurs no sunk costs.
2. Export for the first period and build a plant in F a t beginning of the second period. Under this optimal switching strategy,
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the firm faces marginal cost c + z for the first period and fixed costs G and marginal cost c for the second period.
3. Build a plant in F at t = 0 incurring fixed costs G and supply the F market from that plant in both periods. Under continual FDI, the firm can supply the F market at marginal cost c in both periods if it decides to maintain its plant abroad.
4. Build a plant in F a t t = 0 incurring fixed costs G and supply the F market from that plant only in the first period. In the second period, the fm sells the plant abroad recovering (1 - P)G of its original investment G and supplies the foreign market from its home plant at marginal cost c + z.
Profits Under Different Eutry Strategies
The situation facing the firm in the second period depends upon its first period choice. Suppose that the firm exports in the first period and consider its situation in the second period.
Second Period Choice Given First Period Exporting
In the second period, the firm learns the value of 8 from its sales. Denote the realized value of 8 by OR. If it switches to FDI, it maximizes its profits by solving the following problem:
F II2(8,) z Max (p - c)(oR - p ) P
where the subscript on ll denotes the time period and the super- script the mode of supply. If we replace c by c + z in the above problem then we have the case where the firm continues to export in the second period so that
E n2(OR) = Max (p - c - r)(OR - p ) !J
Solving the above problems yields
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K u t ~ d Suggi
and
E Note that for any given OR, n$(oR) > n2(OR) since the firm in- curs lower marginal cost of selling in the F market under FDI than under exporting.
Since FDI involves fixed costs G while exporting involves a higher marginal cost (c + r as opposed to c), it immediately follows that the size of the market relative to the fixed cost determines whether or not FDI is more profitable than exporting. Note that if the firm does not construct a plant abroad in the first period, it does
F so in the second period if ll2(8,) - G > l l $ ( ~ ~ ) . Similarly, when market demand is low, the firm prefers export-
ing to FDI if ~ ( B J - G > Therefore, we can define two critical fixed cost levels GH and GL such that the firm is indifferent between exporting and FDI in the second period un-
der the two possible states. Clearly, GH = IlT(ElH) - nf(oH) F E
and GL = n2(oL) - n2(eL). For the problem to be interesting, its clear that we need GL < G < GH SO that, given that it ex- ported in the first period, the firm prefers to continue with exporting when demand is low whereas it prefers to switch to FDI if demand is high. In what follows, we assume GL < G < GH.
Second Period Probletn Given First Period FDI
If the firm undertakes FDI in the first period, it can either choose to continue with FDI or switch to exporting in the second period. Clearly, since GL < G < G,,, the firm switches to FDI if the market demand is high. When market demand is low, it scraps its foreign plant and switches back to exporting if
where the LHS of the above inequality gives its FDI profits under low demand and the RHS gives exporting profits plus the scrap
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value of the foreign plant. Clearly, the above equation is satisfied only when j3 is small enough. Now consider the firm's problem at the beginning of the first period.
Avo Period Problem
In the first period, when setting the price, the firm faces an uncertain demand curve does and its first period profits under FDI are given by
In other words, in the first period, everything is as if the firm faces the following demand curve:
Solving the above problem yields
Similarly, its first period exporting profits are given by E
H I = Ma& - c - T ) ( E , - p ) P
which implies
Therefore, at t = 0, the firm faces the following expected profit streams under its two choices:
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1 . Exporting at 1 = 0 yields the following expected payoff:
The above equation says that in the first period exporting yields E
expected profits Il l(0). Whether or not the firm persists with ex- porting in the second period depends upon the realization of 8. If 0, = eL (which happens with probability q) it continues with
E exporting in which case its profits are given by n2(OL). With proba- bility 1 - q, it turns out that 0, = O L and the film switches to FDI in the second period in which case its profits are given by
nC(e,) - G.
2. Foreign Direct Investment at t = 0 yields the following ex- pected payoff:
If the firm chooses FDI at 1 = 0, and market demand turns out to be high, it is pointless to switch back to exporting since FDI is more profitable under the high demand state. However, if market demand is low,'the firm may find it profitable to switch back to exporting. -
The term Max{rIf(elj + (1 - P)G, d ( 0 , ) j compares profits under exporting with those under FDI in the low demand state, where the term (1 - P)G equals the fraction of its initial investment that the firm is able to recover when it switches back from FDI to exporting.
The central point of this paper is that the degree to which costs of FDI are sunk (parametrized by P ) plays a crucial role in determining the f inds choice between FDI and exporting. To see this, suppose that p = 0, so that the firm could recover all of its fixed costs by scrapping its plant. In such a situation, the firm faces no incentive to delay FDI since if demand turns out to be low in the second period, it can easily recover its investment.
We are now in a position to describe the firm's optimal entry strategy. It is helpful to consider two different cases:
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Case 1: lI:(eL) + (1 - P)G, > d ( e L ) . In this case, the firm switches to exporting after undertaking FDI in the first period, if it turns out that market demand is low. It undertakes FDI in the first period if
Case 2: lI;(eL) + (1 - P)G, 5 nf(81). In case 2 , the firm con- tinues to produce via its plant abroad, if ii constructs one in the first period since the scrap value of the plant abroad is low and it under- takes FDI in the first period if
When P is close to 1, the scrap value of the foreign plant is low and it is clear that GJ < G. From above we have
and
In other words, as the probability of a bad state increases, the critical value of the fixed cost that deters first period FDI, under cases 1 and 2 both, shrinks. Under a pessimistic outlook on the foreign market, the firm delays FDI even if fixed costs of FDI are small. On the other hand, as tariffltransportation costs (t) increase, the threshold required to deter FDI increases since exporting be- comes relatively less profitable.
The firm's optimal strategy can also be seen in Figures 1 and 2. Figure 1 shows case 1.
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Kanral Saggi
Fixed Cost
FIGURE 1. Entry Strategy Under Case 1
Export in the first period and switch to FDI only if
exporting only if demand is low
Fixed Pnct
10 Beta
FIGURE 2. Entry Strategy Under Case 2
1 i
/Export in the first period and switch to FDI only it demand is
1- PUI In ootn perloas I
I
Beta
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84 GLOBALIZATION A N D REGIONALIZATION
The G curve is derived by plotting the relationship defined by the following equation:
Clearly, since in case 1, the firm finds it optimal to switch back to exporting if it chooses FDI in the first period and demand is low in the next period, only the area above the G curve is relevant. Along the curve G, the firm is indifferent between switching back to ex- porting or maintaining its first period plant in case of low. The G curve is upward sloping since the bigger the fixed investment of FDI, the bigger must be the proportion of that investment which is irrecoverable for the firm to stay indifferent between switching back to exporting or continuing with FDI in case of low demand. The F curve is derived from comparing two period profits under FDI with those under exporting, given that the firm opts for export- ing in the second period in case of low demand even if it undertakes FDI in the first period. Along the F curve, the firm is indifferent between FDI and exporting in the first period. This curve is down- ward sloping because the higher the degree of irreversibility of the initial FDI investment, the smaller that investment needs to be in order to deter first period FDI on the firm's part. Note that when P is very close to zero, the firm always prefers FDI in the first period (the F curve never touches they axis and blows up t op when p goes to zero). Above the F curve as well as the G curve is the region in which the firm adopts exporting in the first period and switches to FDI only if demand turns out to be high. Figure 2 can be similarly understood.
In case 2 only area below the G curve applies. The horizontal line just plots G. Above this line, the fm adopts exporting in the first period, whereas below it the firm chooses to do FDI. If case demand turns out to be low, the firm sticks with FDI. If instead it adopted exporting, it switches to FDI in case demand is high.
Comparison with a Benchmark Case
The incentive to delay FDI that is provided by the possibility of learning about the state of the demand via exporting and then switching to FDI in case of a good state is most clearly brought to
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light by considering the case where exporting does not yield such information. Consider then the alternative case where the nature of the uncertainty is such that exporting reveals no information about demand but FDI does. This scenario captures the idea that 'being' in the market is usefwl in terms of learning about consumer tastes. In such a scenario, if the firm exports in the first period, it faces exactly the same decision in the second period as it does in the first since nothing new is learnt from exporting. Therefore, if it exports
E for both periods, its total expected profits equal 2ll1 (E,). If, how- ever, it chooses FDI, its profits equal
Therefore, the firm chooses FDI if
We know that in the case in which exporting provides informa- tion about demand, the firm undertakes FDI if
Since q < 1, to show that FDI is more likely in the case exporting does not yield information about demand, it is sufficient to show
that ~T?(E@) < (1 - q) lTf (oH) + But since profits are convex in market size, the preceding condition follows immediately from Jensen's inequality. Therefore, a smaller fixed cost is suffi- cient to deter FDI in the case in which exporting yields information about demand.
CONCLUSION
The liberalization of many Asian and formerly communist econ- omies has created new opportunities for firms from the industrial- ized countries. However, it is quite likely that these firms do not have such a clear sense of consumer tastes and hence demand in
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these new foreign markets. In such scenarios, initial exporting to these markets may serve as a useful learning tool. Consumer tastes can first be gauged via exports. While many products may have to be modified to suit consumer tastes abroad, a firm can at least determine whether or not its existing products fulfill consumer tastes by first exporting to the foreign market. Such a strategy may have helped avoid losses for companies such as Pepsi that were quick to invest in such markets only to find later that these new markets (such as India) were not as receptive to its products as it may have believed.
By constructing a simple model, I show that in the face of de- mand uncertainty, exporting and FDI are not mere substitutes for each other but might as well be 'complements' in the sense that if first period exports are high, then a firm may proceed to directly invest in the foreign market. A testable implication of this paper is that lagged exports of an industry from country A to country B (in industries which sunk costs are large) should be positively corre- lated with current FDI of country A in country B.
The theoretical literature on international investment has paid little attention to the issues that arise due to the existence of demand uncertainty in foreign markets. Still less attention has been paid to the dynamics of business strategies that firms adopt when con- fronted with such difficulties. This paper has made a small attempt to analyze the implications of demand uncertainty for the dynamic choice between exporting and FDI. While the analysis provides some important insights, there is much that remains to be done. Extending the framework developed in this paper to the case of multiple firms is an obvious first step. In that scenario, strategic forces are likely to lead to more interesting results. However, the monopoly case studied in this paper proves useful in demonstrating the incentive for delaying FDI in order to learn about demand in foreign markets.
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Das, S. P. (1983). Multinational enterprise under uncertainty. Carladion Jourr~al of Eco~tontics, 420-428.
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hagaki, T. (1991). A two-step decision model of the multinational enterprise under foreign demand uncertainty. Jourr~al of Infert~a~iottal Ecot~otnics, 185-190,
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