Exploring modes of entry into international markets: direct investment or contractual relations.

Fernandes, Rui ; Gouveia, Borges ; Pinho, Carlos 等

Introduction

A fundamental problem in new markets approach is how the foreign markets (FMs) should be served, considering the inherent costs of doing business abroad. The traditional explanation to enlarge business into FMs relies on cost advantages, scale economies, product differentiation or brand reputation. Despite the possible advantages there is always a doubt regarding the entry mode (EM) and related amount that the multinational company (MNC) wish to afford.

In this paper, we provide an alternative approach to the traditional evaluation using discounted cash flows technique, to support the choice between EM using a subsidiary (own company (OC) or joint venture (JV)), direct exporting (DE) and a local distributor (LD). In this last choice, the MNC adopts a contractual arrangement with a local provider to maximize the information regarding local market.

The setting when a MNC seeks to sell its products in a new FM is that the revenues are uncertain. In entering the FM the MNC can exercise the option to invest immediately, in its own sales operation, or contract a local agent and eventually invest later using better market knowledge.

Within this setting, we derive two research questions: (1) the optimal mode of entry, also as the (2) moment for future changes. The model predicts that a contractual arrangement is more likely when markets are on average small, there is down-side risk in sales revenue and the change between LD and OC can be achieved in a short period of time.

The research challenge, using the existing background literature, is related with the high costs of switching between different EMs, forcing a period of inaction, during which the corporation continues to use its current mode, even if the immediate profits favored switching strategies. In sum, existing studies on dynamic EM choice emphasize the value of the option to defer; however, when facing high uncertainty and irreversibility of investment, MNCs tend to choose low-commitment EMs and hesitate to make switching decisions.

With this study we enrich the application of real options (RO) theory to the international business literature on choice of host markets EMs under demand uncertainty. Our model implies that the choice of EM depends mainly on the market uncertainty magnitude.

This paper is structured as follows. In the next two sections, the background theory is supported and the reasoning for the used techniques to solve the problem is presented. Section 3 illustrates the problem under study. Section 4 presents the formulation of the models, with generic sets. Section 5 describes the MNC case study, presents and discusses the results. The paper concludes with some final remarks, limitations and a discussion on future research.

1. Literature review

The process of globalization represents one of the most significant trends that accelerate rapid growth of global corporative strategies. Firms that want to internationalise must decide on a fitting EM in order to make the best use of their scarce resources. But it's important to analyse MNCs' motives for exploring a FM. Therefore, MNCs aim international markets for two main reasons: (1) FMs are growing faster than the domestic markets; and (2) searching greater sales volume in order to achieve higher competitiveness, through cost advantage or releasing resources for additional efforts in a product/ service push strategy.

According to Czinkota and Ronkainen (1995) and recently following Hollensen (2011), the motives for entering a FM can be split in proactive and reactive. Proactive motives are related with growth goals, economies of scale, tax or other legal benefits. On the other hand, reactive reasons are due to competition, limited domestic market or over-capacity. Despite the fact that the EM decision received considerable attention in the literature with numerous theoretical and empirical contributions (e.g. Brouthers, Hennart 2007; Morschett et al. 2010) its determinants remain inconclusive (B. B. Nielsen, S. Nielsen 2011).

When a firm is going to explore a FM, the choice of the best EM is decided by the firm's expansion strategy in which, most frequently, the EM has been examined in terms of selecting between OC and a JV (Morschett et al. 2010). The decision of how and the moment to enter a FM can be highly risky due to firms' industry competitive conditions, mainly in the critical start-up stage, confronting the speed to get accepted profitability levels versus the survival capacity (Mudambi, Zahra 2007). Information asymmetry and distinct differences in operational environments between countries have also been explored in the literature (Luo, Shenkar 2011).

Companies can expand into FMs using the following mechanisms (Root 1994):

--exporting: (1) direct exporting (DE) using a domestic-based export department, or (2) export sales representatives sent abroad to find business;

--overseas direct investment: (1) creating a new OC, or acquire a participation on an existing firm to handle sales, promotion and distribution activities, or (2) establishing a JV;

--foreign-based distributors or agents: LDs might be given exclusive rights to represent the company in the host country.

The EM that a MNC chooses has advantages and disadvantages that will determine the resources to commit, the risk level, the degree of control and potential return over the operations, (Erramilli, Rao 1993) and may affect the overall exporting performance (Brouthers 2002; Pineda, Hurtado 2011).

EM has been one of the most researched field in international management (Werner 2002) and is presented as the structured way organizations employ to gain, entry and operate in a new FM (e.g. Sharma, Erramilli 2004). Past studies have suggested that the choice of EMs is related to a firm's familiarity with the FM (e.g. Kim, Hwang 1992; Sarkar, Cavusgil 1996), which means that firms with prior host market experience are more likely to choose a direct investment mode. A number of FM characteristics can affect the choice of market servicing modes. The commonly examined characteristics are attractiveness and market size (Sarkar, Cavusgil 1996). Root (1994) suggests that small markets favour EMs which require a low break-even sales volume (e.g. DE), while markets with high sales potential justify the employment of high resource commitment (OC or JV). Recently, industry environment, the country risk, location and legal rules have also been considered in studies regarding EMs (Ghauri, Cateora 2010; Malhotra, Sivakumar 2011). For Mudambi and Zahra (2007), when industry conditions are highly uncertain, new international ventures exhibit advantages in terms of value-adding and disruption capabilities, which enable higher growth rates. According to Morschett et al. (2010), companies prefer cooperative EMs in situations with a higher country risk. Driffield et al. (2010) and Duanmu (2011) correlated, despite their opposite views, the country risk with the level of foreign ownership. Arslan and Larimo (2011) found that different legal systems results in preference of acquisitions.

The DE has advantages like low investment level and the possibility to postpone an investment decision (Johanson, Vahlne 1990); the common disadvantages are trade barriers (e.g. tariffs) and logistic factors (Hill 2007). DE allows a firm to internationalize without major investment effort and minimum risk; briefly, it can be the first step in the internalization process (Hollensen 2011). However, it is also associated with a low profit return (incorporates only part of the margin) and provides little control (Agarwal, Ramaswami 1992). In opposition to the gradual internationalization approach, some firms, according their strategic challenge (Kwon, Konopa 1993) and location related factors (Chung, Enderwick 2001), enter a FM through direct investment. In contrast to DE, direct investment offers the firm a higher degree of control over its international business and greater revenues. However, direct investment modes are also associated with greater risks, they imply higher management commitment and operations complexity. The most widely used direct modes include JVs, wholly OCs, and strategic alliances (Kwon, Konopa 1993). JVs represent an agreement between two parties to operate in a particular market, aiming performance incentives with knowledge share (Duarte, Suarez 2010), which may minimize entering costs for start-up the business (Fey, Shekshnia 2011). One of the disadvantages is the need of a win to win partnership. The firm will not have a tight control on the business and the shared ownership may cause conflicts. We found a category of studies based on a RO approach that consider whether JVs can be viewed as effective RO. These studies suggest that a JV provides a firm with the ability to exploit upside potential by acquiring the partner's equity (option to grow), or to avoid future downside losses by selling the equity to its partner (option to abandon) (Estrada et al. 2010; Fisch 2011). Foreign direct investment using OC involves capital, technology and personnel, and can be made through the acquisition of an existing entity or the establishment of a new subsidiary or extension (branch). Direct ownership provides a high degree of control and better knowledge about the market. However, it requires a high level of investment and a high degree of commitment. Acquisitions are often made as part of a company's rapid growth strategy, whereby it is more beneficial to take over an existing firm's operations when compared to expanding on its own (Lee, Lieberman 2010). Nevertheless there could be limited influence of local management and as a consequence, the participation relies on a special distribution agreement.

According to Hill (2007) the decisions about entering in a FM can be progressive and split in: market choice, time, scale of entry and strategic commitments. The chain of establishment, or "Uppsala model", is one of the earlier schools of thoughts and draws on the assumption that the entry option into new markets is the result of a series of staged and incremental decisions (Edwards 2002). Mudambi and Zahra (2007) compared the performance of MNCs by adopting direct investment with those that follow a sequential approach and found that a new venture strategy is no more likely to fail than a sequential approach to internationalisation. Later on, Kalinic and Forza (2012) found that a sequential approach targeting host market relationships and a flexible strategic focus will affect the speed of internationalization.

2. Reasoning to choose ro to solve the problem

Investment analysis is usually conducted using the Net Present Value (NPV) approach. Under NPV approach, the potential investor chooses the best combinations of alternative markets to explore, based on the projected values and its budgeting limitations. The NPV indicates the magnitude of potential investment, using implicit assumptions that reflect the basic inadequacy of this approach (Smit, Trigeorgis 2004; Dixit, Pindyck 1994). These limitations can be overcome by using a different perspective on investment under uncertainty, which is recognized as the RO approach.

The NPV assumes that the investor has to make the investment now or the investment will not be available in future. However, in the real world there's usually the possibility to delay the investment option until new information arrives and uncertainty about the future market is reduced. This possibility introduces the "value component" to the investment option that impacts the decision to invest and its timing.

The usage of the RO technique is deemed appropriate only if there is (Dixit, Pindyck 1994) uncertainty, managerial flexibility, and totally or partially irreversible investment. While RO valuation has been recognized by the scientific community, the approach yet lacks a practical breakthrough (Lander, Pinches 1998). The models presented in this paper aim at facilitating the understanding and practical application of the RO. The framework we propose is organized across organizational, strategic, valuation and controlling aspects of RO. The first layer focuses on organizational aspects of RO valuation--input parameters (Claeys, Walkup 1999). The second layer refers to the link of RO value to strategy frame. The third layer refers to valuation aspects for which we propose different techniques. The fourth and final layer is about the controlling aspects of RO. Options are only valuable if they are exercised accordingly, as so, monitoring the respective decision rules and properly execution will enhance the learning process (Copeland, Howe 2002). One of the most important questions in RO analysis is to determine the optimal timing in which the investor should exercise his opportunity. Time is critical since the value of the investment opportunity depends on the market potential that changes over time. An appropriate investment analysis approach must be able to address these challenges.

Recent studies have also used the benefits of RO methodology to support EMs choices under uncertainty (Brouthers, Dikova 2010; Cuypers, Martin 2010; J. Li, Y. Li 2010). In this article, we further extend this last stream of research by quantifying MNCs' choice of market EM under uncertainty as options, including the decision time frame.

3. Problem description

Research question (RQ) 1--choose location. We consider two factors: the market uncertainty level and the option entry costs. Our main question is in which location should the MNC establish its investment in moment zero--that is, which location provides the MNC with a higher option value? Demand uncertainty concerning potential upside benefits associated with international expansion will be measured as the demand uncertainty in the target market. Two practical questions must support the decision to define the market uncertainty: (a) what is the potential market size and (b) what is the growth potential for the product/service in that country?

RQ 2--choose FM entry mode (EM). We also consider two factors: the market uncertainty level and the option entry costs. Our main question is what EM should the MNC use when deciding in moment zero--that is, which EM provides the MNC with a higher option value? The options exist in the identified EMs: (a) DE and LD provide options to growth in the future or to give up by minimizing investment costs; (b) OC provides options realizing full capacity to explore market opportunities; (c) JV provides options as it can be possible to buy the partner position.

RQ 3--change FM sales existing mode. Our main question relates with the moment to change the actual EM to a new one--that is, what is the moment at which a new mode can provide the MNC with a higher option value?

Next section presents the model development to quantify decisions for research questions 2 and 3. Research question 1 is considered in the demand process representation.

4. Model formulation

In this section we present the mathematical formulation with generic sets. The parameters and the objective function will follow.

Demand uncertainty in the FM is the uncertainty concerning potential upside benefits associated with international expansion. McGrath (1997) suggests that two factors may influence demand uncertainty: potential FM size and potential growth rate. Folta and Miller (2002) make a similar argument suggesting that the level of market uncertainty and size of the market have a combined effect on the option value. Following (Brouthers et al. 2008) suggestion we included in the model factors like operating revenues and costs.

We consider a situation in which a producer (P) of established products [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], located in origin country (O), has decided to sell his products in a FM f [member of] F, a market in which P has no sales experience. Among the options available for selling in f we find four as potentially profitable: (a) DE, (b) contracting with a LD, (c) establishing OC sales operation (throw subsidiary or branch concept) and (d) participation in a JV.

The problem resolution will be split according each challenge for research questions (RQ) 2 and 3. The model for RQ 2 is a single period model, formulated as a profit maximization problem with a stochastic variable. The model for RQ 3 will be treated in continuous time, assuming that there is a deferring option without limit in time and that the investment, once implemented, will produce impacts in perpetuity (Dixit, Pindyck 1994). One important consequence of this assumption is that as time tends to infinite (T = [infinity]), the cash flows tend to zero. In this line, the investment can be seen as an optimal stopping problem, where "stopping" means that the investment decision is implemented.

We now list the sets and indexes to support a general application for different investment modes and business realities:

--F = {1, 2, .., p}: foreign countries (= FMs), each country is represented by f [member of] F, where p represents the total number of available locations: [absolute value of F] = p;

--[X.sub.f] [subset] F: [X.sub.f] is a subset of F that represents the direct tax rate (on profits) inside each FM f [member of] F and is represented by [[chi].sub.f] [member of] [X.sub.f];

--[PHI] [subset] I = {1, 2, ... g}: [??] is a sub set of I that represents all sku's inside product group I, each sku is represented by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], where g represents the total number of product groups to be traded in FM f [member of] F: [absolute value of I] = g;

--[??] = {-DE, LD, OC, JV}: alternative foreign EM, represented by [lambda], where [absolute value of [??]] = 4.

To facilitate the formulation of the model, we introduce the following notation:

--[[gamma].sub.f] ([lambda]) represents the present value of investment, for each EM [lambda] [member of] [??] and FM f [member of] F;

--[[phi].sub.f] ([lambda]) represents the operating costs to run the business after investment, for each EM [lambda] [member of] [??] and FM f [member of] F;

--[c.sub.v] represents the unit product variable cost;

--[p.sub.vf([lambda])] unit product selling price for each EM [lambda] [member of] [??] and FM f [member of] F;

--[c.sub.LD] represents the co-participation on sales value, applied to a local distributor;

--[p.sub.t] represents the unit transfer price;

--[[chi].sub.f] represents the tax rate applied in FM f [member of] F.

4.1. Modelling the demand process

The main source of uncertainty affecting the investment decision is the market demand. We assume that the demand is a stochastic variable, denoted by Q and follows a geometric Brownian motion (similar assumption in Bengtsson (2001)), subject to jumps modelled as a Poisson process, such that:

dQ = [[mu].sub.Q]Qdt + [[sigma].sub.Q]Qd[z.sub.Q] + Qdq, (1)

where: [[mu].sub.Q] = instantaneous demand drift, [[sigma].sub.Q] = market demand volatility, d[z.sub.Q] = [epsilon](t) [square root of dt]; [epsilon](t) [approximately equal to] N(0,1), d[z.sub.Q] = increment of a wiener process, where [epsilon](t) is a serially uncorrelated and normally distributed random variable; dq = (1 + u) with probability [[lambda].sub.u] and demand jumps intensity represented by u. The time required since the decision to the availability of the EM (mainly when a subsidiary or partnership is needed) will be denoted as "preparation stage" and is represented with n. This moment considers mainly the legal affairs and resources allocation to endow start-up operation.

It's expectable that in a certain moment t, including the preparation period, there will be a demand level that supports the decision to invest in a new FM, using one of the available EMs [??] or change the actual existing operating mode, considering the preparation period and the outcome results. To model our problem, we will assume a different profit function prior (no sales in FM or existing operating mode) and after the decision (entry in the foreign country using one of the available EMs or change the existing mode) that we will denote as [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], respectively.

We also assume that the decision to invest in a FM is affected only by profit advantages, and not by competitive advantages through proper market positioning, such as the degree of product differentiation (simplification also defended by Hamada (2010)).

4.2. Model I--choice of market EM model

At time zero, the MNC compares the RO value of investing in FMs and chooses the location, which provides a higher option value. Formally, the MNC's optimal profit function to enter in a single FM f [member of] F, in moment t + n, is represented as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (2)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (3)

where [rho] is the discounted rate.

4.3. Model II--choice the moment for changing the actual EM

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (4)

Now we denote by [t.sup.*] the timing of the decision to change the actual mode to support sales in FM, therefore we split to moments, before [t.sup.*] and after [t.sup.*], for which a different profit function will be applied: for simplification we will denote [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (5)

Considering only the members that depend on t (relevant moment impacting the decision process), the previous formula comes as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (6)

As stated before, we assume the existence of a preparation period n during which the change will occur. This is logic and is according the reality as firms cannot endow such decisions with instantaneous results.

5. Application of the framework to a case study

Model I

To support the application of the proposed models, we will use the case study of a MNC that wants to extend its operations to a new FM. The management team has decided to use DE but, considering the potential growth of the target market, the MNC wants to prepare conditions for an additional and fast extension of its operations. The values used in the case study are presented in Table 1--appendix B.

Figure 1 provides results comparing the entry options with the demand quantity evolution. It is assumed that DE is always an available entry option and the values reported consider the difference between DE and other possible alternatives like LD, OC and JV. Analysing the results we conclude that the demand quantity, for demand volatility level equal to 20%, influences the options regarding the EM in a new FM. LD option has the same value as DE despite the quantity level; as such the difference between these two EMs is close to zero. OC option value increases as the demand quantity increases, which reflect the scale effect (this has been one of the valid arguments used for long time in transaction cost theory (Anderson, Gatignon 1986)). JV is not a profitable option in the conditions presented and it seems to be worst as the quantities increase.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

On Figure 2 we study the effect of demand volatility on the available options value, for demand quantity equal to 100.000 sqm. The values report the difference between LD, OC and JV when compared with DE. The results show that in very high uncertain FM (more than 40% volatility levels) the option using OC compared with DE is negative, meaning that the company in such FM should opt for DE as the risk is high. In general, as the volatility levels increase, the alternative entry options, when compared with DE, become less attractive. At the end, Figure 2 supports that when uncertainty is high the firm opts to invest in low-commitment EMs such as DE or LD. Indeed, the learning process argument has been supported by the literature that suggests collaborative EMs like LDs and JVs to be especially suited for exploring FM and building capabilities (Ireland et al. 2002; Kogut, Kulatilaka 2001; Meyer et al. 2009). At the end, the model results support that entering a FM in the face of high uncertainty can be rational, even though traditional theories of market entry, using the NPV, advise not to invest (Fisch 2008).

Figure 3 considers the effect of tax regimes (direct taxes on profits) in FMs. The results show that the tax policies can influence the decision on the EM; more aggressive tax regimes are less attractive for direct investment to establish the local operation (OC or JV). According to Figure 3 the option for OC versus DE has no additional value for tax rates above 30%. The interpretation of these results must be complemented with previous studies, like the one from Davies et al. (2010) that explored the relation between taxation and foreign investment. We also show that even with harmonized taxes, the international firm may choose OC. As such, in non-cooperative tax regimes, the host country can use its profit tax strategically in order to enforce a more desirable EM.

[FIGURE 3 OMITTED]

Model II

The model II explores the moment for the change. In the case study we will consider the change from the actual mode DE to OC mode. The results can also be extended to other EMs.

In Figure 4 the analysis refers to the impact of demand behaviour (volatility level, jumps probability and intensity) on the trigger moment (optimal quantity level) in the option to change from the actual mode DE to a new one OC. The trigger moment is defined considering the demand quantity level and assumes that the investor can cover a bigger share of fixed costs at higher growth rates over time and, as such, he is willed to switch into OC earlier (Hiller, Yalcin 2009). In particular, the results show that the demand level required for the change in the EM increases as the volatility level increases, which means that, in high unpredictable markets, the time to decide investing in a subsidiary is much longer when compared with more stable markets. These results complement the work of Fisch (2008), by analysing the success of applying RO reasoning to the timing of entry.

An additional simulation in Figure 5 considers the impact of the preparation period in the moment for the change in the EM. Figure 5 describes the relation between the preparation periods--steps--to endow the initiative to invest in a subsidiary. As the steps to ramp-up the operation become longer and time consuming, the decision must be anticipated in time, even if the demand levels are still low. A possible interpretation of these results is that the early movers prefer a non-equity mode with lower preparation period; on the other hand, the late movers prefer the equity mode as their EM strategy (Isa et al. 2012). Complementary, these findings follow the study carried out by Schwens and Kabst (2009) where the early movers, as compared to late movers, preferred cooperative modes of market entry with less preparation period, such as DE or LDs.

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

Conclusions

We extend applications of RO theory to enrich the foreign investment literature on choice of EM under uncertainty. Our models provide an example to illustrate how to apply RO to topics in international business.

Specifically, by taking into consideration market volatility in FMs, we have examined the conditions under which each EM, such as DE, LD, OC or a JV, is optimal. Complementary, we introduce the relevant timing moment to endow a corporative decision on EM option.

Our results indicate that EM choice essentially depends on the magnitude of FM uncertainty. When uncertainty is high, firms are inclined to invest in low-commitment EMs, such as DE, as they valuable options to abandon. If FM uncertainty is low, MNCs may change their decisions by investing in high commitment market modems, such as OC or JV, as they are more likely to provide valuable growth options, such as first mover advantages. If a wholly owned EM is selected, firms need to choose between starting that venture from the beginning or acquiring an existing venture (acquisition) reducing the preparation period.

The results have important implications for theory development and future research. EM choice is one important international strategic decision that firms make; future research may wish to examine other critical international strategic decisions, such as international market selection. In addition, there may be future opportunities to further expand the decision criteria relevant to explaining market EM choices by taking a broader view of the factors contributing to value the new market entry.

At the end, the results provide partial support for internationalization theory, as well as justify the validity of using high-commitment EMs, even under high levels of uncertainty.

The results of this study are likely to be helpful in the formulation and support of market entry strategies. However, caution must be exercised while generalising the findings of the current study. This study is based on a single case and presents a number of limitations typical for this type of international research. In order to control the possible existence of country or industry key determinants, it is necessary to repeat the research in other industries with different attractiveness considering the number of players (Tran et al. 2012) and different demand behaviours. For future, carrying out the application of the model with additional case studies, would allow having a control group in order to understand whether the strategic focus differs between successful and unsuccessful internationalizations.

Caption: Fig. 1. Simulation of different options for entering in a FM, considering different demand quantity levels

Caption: Fig. 2. Simulation of different options for entering in a FM, considering different volatility levels

Caption: Fig. 3. Simulation of different options for entering in a FM, considering different tax rates

Caption: Fig. 4. Simulation of the trigger moment for the change of EM, considering different demand volatility levels, jumps probability and intensity levels

Caption: Fig. 5. Simulation of the trigger moment for the change of EM, considering different preparation periods to support the investment

APPENDIX A

Technique resolution for Model II: from DE to OC. In the actual situation investment has already been decided to change from DE to OC.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (A1)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (A2)

Because we assume that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] follows a geometric Brownian motion subject to a Poisson process (see extended equation (1)), the expected optimal value [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] at time [t.sup.*] comes as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (A3)

We are going to define a simple notation for each part of equation:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

We can obtain the profit value p, in actual moment, by maximizing equation (A2), satisfying the following differential equation:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (A4)

Initial condition: [pi](0) = 0; Value matching condition: [pi](Q) = A.Q + B.Q + C + E; Smooth condition: [partial derivative]v/[partial derivative]Q = A + B, with Q = [Q.sup.*]. If we consider (A4) a second order Cauchy-Euler function (Ross 1996), the solution can be written as: [pi](Q) = [a.sub.1][??]; where [r.sub.1] is the result of the following non-linear equation: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. For a given value of Q and for t = 0, the value [Q.sup.*] that maximizes [pi](Q) is given by the solution of the following equation:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (A5)

APPENDIX B

Table 1. Data to support the case study

notation             value      unit         notation       value

[MATHEMATICAL       100.000      sqm                          14
  EXPRESSION NOT
  REPRODUCIBLE
  IN ASCII]
[[mu].sub.Q]           5          %       [p.sub.vf(LD)]    26.25
[[sigma].sub.Q]       20          %         [c.sub.LD]     5%pv(LD)
r                      5          %       [p.sub.vf(OC)]      35
n                     1/4       years       [p.sub.t]         17
[p.sub.vf(DE)]        25      euros/sqm     [X.sub.f]         25
[.sub.pvf(JV)]        35      euros/sqm         h             50
[[lambda].sub.u]      10          %             u             3

notation              unit           notation

[MATHEMATICAL       euros/sqm    [[phi].sub.fDE)]
  EXPRESSION NOT
  REPRODUCIBLE
  IN ASCII]
[[mu].sub.Q]        euros/sqm    [[gamma].sub.DE)]
[[sigma].sub.Q]         %        [[phi].sub.fLD)]
r                   euros/sqm   [[gamma].sub.fLD)]
n                   euros/sqm    [[phi].sub.f(OC)]
[p.sub.vf(DE)]          %       [[gamma].sub.f(OC)]
[.sub.pvf(JV)]          %        [[phi].sub.f(JV)]
[[lambda].sub.u]        %       [[gamma].subf(JV)]

notation             value       unit

[MATHEMATICAL       55.000    euros/year
  EXPRESSION NOT
  REPRODUCIBLE
  IN ASCII]
[[mu].sub.Q]        45.000      euros
[[sigma].sub.Q]     80.000    euros/year
r                   45.000      euros
n                   250.000   euros/year
[p.sub.vf(DE)]      350.000     euros
[.sub.pvf(JV)]      100.000   euros/year
[[lambda].sub.u]    150.000     euros

doi: 10.3846/16111699.2013.809786

References

Agarwal, S.; Ramaswami, S. 1992. Choices of foreign entry mode: impact of ownership, location, and internationalisation factors, Journal of International Business Studies 23(1): 1-27. http://dx.doi.org/10.1057/palgrave.jibs.8490257

Anderson, E.; Gatignon, H. 1986. Modes of foreign entry: a transaction cost analysis and propositions, Journal of international Business Studies 17(3): 1-26. http://dx.doi.org/10.1057/palgrave.jibs.8490432

Arslan, A.; Larimo, J. 2011. Greenfield investments or acquisitions: impacts of institutional distance on establishment mode choice of multinational enterprises in emerging economies, Journal of Global Marketing 24(4): 345-356. http://dx.doi.org/10.1080/08911762.2011.602323

Bengtsson, J. 2001. Manufacturing flexibility and real options. Department of Production Economics, I IE, Linkoping Institute of Technology, S-581 83, Sweden.

Brouthers, K. 2002. Institutional, cultural and transaction cost influences on entry mode choice and performance, Journal of International Business Studies 33(2): 203-221. http://dx.doi.org/10.1057/palgrave.jibs.8491013

Brouthers, K.; Brouthers, L.; Werner, S. 2008. Real options, international entry mode choice and performance, Journal of Management Studies 45(5): 936-960. http://dx.doi.org/10.1111/j.1467-6486.2007.00753.x

Brouthers, K.; Dikova, D. 2010. Acquisitions and real options: the greenfield alternative, Journal of Management Studies 47: 1048-1071. http://dx.doi.org/10.1111/j.1467-6486.2009.00875.x

Brouthers, K.; Hennart, J. 2007. Boundaries of the firm: insights from international entry mode research, Journal of Management 33: 395-425. http://dx.doi.org/10.1177/0149206307300817

Chung, H.; Enderwick, P. 2001. An investigation of market entry strategy selection: exporting vs foreign direct investment modes--a home-host country scenario, Asia Pacific Journal of Management 18: 443-160. http://dx.doi.org/10.1023/A:1012871225166

Claeys, J.; Walkup, G. Jr. 1999. Discovering real options in oilfield exploration and development. Society of Petroleum Engineers, Richardson, TX.

Copeland, T.; Howe, K. 2002. Real options and strategic decisions, Strategic Finance 83(10): 8-11.

Cuypers, I.; Martin, X. 2010. What makes and what does not make a real option? A study of international joint ventures, Journal of International Business Studies 41: 47-69. http://dx.doi.org/10.1057/jibs.2009.17

Czinkota, M.; Ronkainen, I. 1995. International marketing. Sydney: The Dryden Press.

Davies, R.; Egger, H.; Egger, P. 2010. Profit taxation and the mode of foreign market entry, Canadian Journal of Economics/Revue canadienne d'economique 43: 704-727.

Dixit, A.; Pindyck, R. 1994. Investment under uncertainty. Princeton: Princeton University Press.

Driffield, N.; Mickiewicz, T.; Pal, S.; Temouri, Y. 2010. Bridging the gap? Corruption knowledge and foreign ownership, Economics and Finance Working Paper. Brunel University. 10-19.

Duanmu, J. 2011. The effect of corruption distance and market orientation on the ownership choice of MNEs: evidence from China, Journal of International Management 17(2): 162-174. http://dx.doi.org/10.1016/j.intman.2011.01.003

Duarte, C.; Suarez, M. 2010. External uncertainty and entry mode choice: cultural distance, political risk and language diversity, International Business Review 19(6): 575-588. http://dx.doi.org/10.1016/j.ibusrev.2010.03.007

Edwards, R. 2002. FDI--strategic issues, in B. Bora (Ed.). Foreign direct investment--research issues. London: Routledge. http://dx.doi.org/10.4324/9780203469699.ch3

Erramilli, M.; Rao, C. 1993. Service firms' international entry mode choice: a modified transaction-cost analysis approach, Journal of Marketing 57: 19-38. http://dx.doi.org/10.2307/1251852

Estrada, I.; Fuente, G.; Cruz, N. 2010. Technological joint venture formation under the real options approach, Research Policy 39: 1185-1197. http://dx.doi.org/10.1016/j.respol.2010.05.015

Fey, C.; Shekshnia, S. 2011. The key commandments for doing business in Russia, Organizational Dynamics 40(1): 57-66. http://dx.doi.org/10.1016/j.orgdyn.2010.10.003

Fisch, J. 2008. Internalization and internationalization under competing real options, Journal of International Management 14: 108-123. http://dx.doi.org/10.1016/j.intman.2007.05.012

Fisch, J. 2011. Real call options to enlarge foreign subsidiaries--the moderating effect of irreversibility on the influence of economic volatility and political instability on subsequent FDI, Journal of World Business 46(4): 517-526. http://dx.doi.org/10.1016/j.jwb.2010.10.012

Folta, T.; Miller, K. 2002. Real options in equity partnerships, Strategic Management Journal 23: 77-88. http://dx.doi.org/10.1002/smj.209

Ghauri, P.; Cateora, P. 2010. International marketing. 3rd ed. Edinburgh Business School, United Kingdom.

Hamada, K. 2010. Outsourcing versus in-house production: the case of product differentiation with cost uncertainty, Seoul Journal of Economics 23(4): 439-459.

Hill, C. 2007. Foreign market entry, international business--competing in the global market place. Boston: McGraw Hill.

Hiller, S.; Yalcin, E. 2009. Switching between domestic market activity, export and FDI, Working Paper. Department of Economics, Aarhus University, Denmark. 1-34.

Hollensen, S. 2011. Global marketing: a decision-oriented approach. 5th ed. Essex: Prentice Hall.

Ireland, R.; Hitt, M.; Vaidyanath, D. 2002. Alliance management as a source of competitive advantage, Journal of Management 28: 413-146. http://dx.doi.org/10.1177/014920630202800308

Isa, C.; Saman, H.; Nasir, S.; Rahman, N. 2012. Entry mode and entry timing decisions by Malaysian construction firms in international market, Proceeding for ASEAN Entrepreneurship Conference (AEC2012), 5 November, 2012, Selangor, Malaysia.

Johanson, J.; Vahlne, J. 1990. The mechanism of internationalization, International Marketing Review 7(4): 11-24. http://dx.doi.org/10.1108/02651339010137414

Kalinic, I.; Forza, C. 2012. Rapid internationalization of traditional SMEs: between gradualist models and born globals, International Business Review 21: 694-707. http://dx.doi.org/10.1016/j.ibusrev.2011.08.002

Kim, W.; Hwang, P. 1992. Global strategy and multinationals' entry mode choice, Journal of International Business Studies 23(1): 29-54. http://dx.doi.org/10.1057/palgrave.jibs.8490258

Kogut, B.; Kulatilaka, N. 2001. Capabilities as real options, Organizational Science 12: 744-758. http://dx.doi.org/10.1287/orsc.12.6.744.10082

Kwon, Y.; Konopa, L. 1993. Impact of host country market characteristics on the choice of foreign market entry mode, International Marketing Review 10(2): 60-76. http://dx.doi.org/10.1108/02651339310032552

Lander, D.; Pinches, G. 1998. Challenges to the practical implementation of modeling and valuing real options, The Quarterly Review of Economics and Finance 38(4): 537-567. http://dx.doi.org/10.1016/S1062-9769(99)80089-1

Lee, G.; Lieberman; M. 2010. Acquisition vs. internal development as modes of market entry, Strategic Management Journal 31:140-158.

Li, J.; Li, Y. 2010. Flexibility versus commitment: MNEs' ownership strategy in China, Journal of International Business Studies 41: 1550-1571. http://dx.doi.org/10.1057/jibs.2010.25

Luo, Y.; Shenkar, O. 2011. Toward a perspective of cultural friction in international business, Journal of International Management 17(1): 1-14.

Malhotra, S.; Sivakumar, K. 2011. Simultaneous determination of optimal cultural distance and market potential in international market entry, International Marketing Review 28(6): 601-626. http://dx.doi.org/10.1108/02651331111181439

McGrath, 1997. A real options logic for initiating technology positioning investments, Academy of Management Review 22(4): 974-96.

Meyer, K.; Wright, M.; Pruthi, S. 2009. Managing knowledge in foreign entry strategies: a resource-based analysis, Strategic Management Journal 30: 557-574. http://dx.doi.org/10.1002/smj.756

Morschett, D.; Schramm-Klein, H.; Swoboda, B. 2010. Decades of research on market entry modes: what do we really know about external antecedents of entry mode choice?, Journal of International Management 16: 60-77. http://dx.doi.org/10.1016/j.intman.2009.09.002

Mudambi, R.; Zahra, S. 2007. The survival of international new ventures, Journal of International Business Studies 38: 333-352. http://dx.doi.org/10.1057/palgrave.jibs.8400264

Nielsen, B. B.; Nielsen, S. 2011. The role of top management team international orientation in international strategic decision-making: the choice of foreign entry mode, Journal of World Business 46(2): 185-193. http://dx.doi.org/10.1016Zj.jwb.2010.05.003

Pineda, J.; Hurtado, J. 2011. Does the foreign market entry mode choice affect export performance? The case of the Spanish hotel industry, Journal of Business Economics and Management 12(2): 301-316. http://dx.doi.org/10.3846/16111699.2011.573270

Root, F. 1994. Entry Strategies for international markets. NY: Lexington Books.

Ross, S. 1996. Stochastic processes. 2nd ed. Wiley series in probability and mathematical statistics. New York: John Wiley & Sons, Inc.

Sarkar, M.; Cavusgil, S. 1996. Trends in international business thought and literature: a review of international market entry mode research: integration and synthesis, The International Executive 38(6): 825-847. http://dx.doi.org/10.1002/tie.5060380608

Schwens, C.; Kabst, R. 2009. How early opposed to lateinternationalizers learn: experience of others and paradigms of interpretation, International Business Review 18(5): 509-522. http://dx.doi.org/10.1016/j.ibusrev.2009.06.001

Sharma, V.; Erramilli, M. 2004. Resource-based explanation of entry mode choice, Journal of Marketing Theory and Practice 12: 1-18.

Smit, H.; Trigeorgis, L. 2004. Strategic investment: real options and games. New Jersey: Princeton University Press.

Tran, V.; Sibley, D.; Wilkie, S. 2012. Second mover advantage and entry timing, The Journal of Industrial Economics 60: 517-535. http://dx.doi.org/10.1111/j.1467-6451.2012.00490.x

Werner, S. 2002. Recent developments in international management research: a review of 20 top management journals, Journal of Management 28: 277-305. http://dx.doi.org/10.! 177/014920630202800303

Rui Fernandes (1), Borges Gouveia (2), Carlos Pinho (3)

(1) Superior School of Industrial Studies and Management, Polytechnic Institute of Porto, Rua D. Sancho I. 981, 4480-876 Vila do Conde, Portugal

(2,3) Department of Economics, Management and Industrial Engineering, Aveiro University, Campus Universitdrio de Santiago, 3810-193 Aveiro, Portugal

E-mails: (1) rfernandes.ar@amorim.com (corresponding author); (2) bgouveia@ua.pt; (3) cpinho@ua.pt

Received 14 March 2013; accepted 27 May 2013

Rui FERNANDES. PhD in Industrial Management and Graduated in Finance, he is Assistant Professor at the Superior School of Industrial Studies and Management, Polytechnic Institute of Porto, where he teaches in Master of Corporate Finance and collaborates in many international seminars. CFO at Amorim Revestimentos, SA and board member at its international companies in Europe, USA and Japan.

Borges GOUVEIA. PhD and Aggregate in Electrotechnical and Computer Engineering. He is Full Professor at University of Aveiro. Board member of Galp Energia, SGPS, S.A.

Carlos PINHO. PhD and Aggregate in Applied Economics and Master in Finance. He is associated Professor at University of Aveiro and Director of the Doctorate in Accounting.