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The paper incorporates cooperative game theory into a real option method in a foreign direct investment setting and examines the operational decisions of a multinational corporation in a cooperative framework, where the corporation is endowed with an abandonment option and shares its profit with the host country. In particular, we investigate how the abandonment options affect the optimal investment timing and the optimal profit share of a foreign direct investment using a real option game method. We show that the flexibility of the abandonment option induces the corporation to investment earlier, which indicates the negative effects on investment trigger. The result is consistent with intuition since the abandonment option provides insurance and thus reduces the overall risk of the project. We also find that the introduction of the abandonment option reduces the optimal profit share in a cooperative framework and in turn the lower profit share increases the investment trigger, thereby having a positive effect on the investment threshold to hinder the investment. By numerical analysis, we find that the overall effect of the abandonment options is inversely related to the investment trigger. These findings provide quantitative analysis about the decisions regarding cooperation in international investment extraction projects.

The globalization trend of foreign direct investment is increasingly strengthening and foreign direct investment has been experiencing rapid growth in recent years. According to the latest world investment report of the United Nations, the output value of multinational corporations and their parent companies accounts for nearly a quarter of global GDP [

Previous studies have extensively examined the investment timing decisions for foreign direct investment, thus providing decision-making information [

In early research about the abandonment option, after the seminal work by Robichek and Van Horne [

The purpose of the paper is to investigate the effects of abandonment options on investment timing and profit share in a cooperative game, combine real options with the bargaining game, and drive the investment timing of FDI and the optimal profit share between HC and MNC.

The most correlated literatures to our study are Brandão de Brito and de Mello Sampayo [

Our article incorporates cooperative game theory into the investment problem of foreign direct investment in a cooperative game using real options game model. In the model, MNC is endowed with the abandonment option after investment and cooperates with HC to extract natural resources and share the net project profit. During the investment process, MNC may be faced with the risk of asset expropriation by HC without any compensation and the loss of suck costs [

In particular, we explore the optimal investment timing of foreign direct investment with and without the abandonment option in real options game model, respectively, and investigate the effect of the abandonment options on investment trigger. We also examine the optimal profit share of HC and MNC by using Nash Bargaining Solutions in a cooperative framework in two cases and obtain main three interesting results.

The first one is that if the investment project is partially reversible, the optimal investment trigger of MNC with an abandonment option is smaller than that without. That is, the flexibility of the abandonment option induces the multinational corporation to investment earlier, which indicates the negative effects on investment trigger. So, MNC with an abandonment option has the incentive to invest in the project earlier than without. When MNC holds an option of abandonment and the project is completely irreversible, which indicates that the project has no salvage value, then two optimal investment thresholds in two cases are the same regardless of the abandonment option. The results show that the abandonment option pulls down the investment threshold.

The second is that the introduction of the abandonment option reduces the optimal profit share in a cooperative framework and in turn the lower profit share increases the investment trigger, thereby having a negative effect on the investment threshold if the multinational corporation is more risk averse. That is, the optimal profit share of MNC with the abandonment option is lower than that without, if the relative risk aversion is greater than some critical value. Moreover, the profit share is inversely related to the investment trigger. The results show that MNC with more risk aversion has considered the influences of the option to exit on the management flexibility, and HC gives up part of its profits from the project to induce MNC to invest in the absence of an abandonment option. Therefore, the optimal share is analytically determined in the bargaining process, depending on whether the project has an abandonment option or not.

Finally, we conclude that the two investment timing triggers decrease with the profit share and the abandonment option has two opposite effects on the investment in general, which is the positive effect, thereby pulling down the investment trigger and the other is the negative effect by increasing the critical investment value. By numerical analysis, we find that the overall effect of the abandonment options is inversely related to the investment trigger. The results indicate that the influences of the profit sharing ratio on the investment behavior dominate the influences of the abandonment options and MNC pays more attention to the profit sharing ratio.

The remainder of this paper is organized as follows. The model is presented in Section

In the model, we assume that MNC and HC sign an agreement on engaging in the extraction of natural resources in the model. HC is finance-constrained and cannot pay for the total extraction cost of the project, while MNC can undertake investment cost

When MNC decides to abandon the project, HC will pay the salvage value of the project

For the sake of simplicity, we assume that the operating cost, which is generally supposed to be constant in most models, is zero [

In order to investigate the effects of the abandonment option and profit share ratio on the investment timing of FDI, the model solves decision problems of MNC by using backward induction. First, as a bench mark, we derive the optimal exit and investment decisions of MNC without the option of abandonment. And, then, we compare the results to those in which MNC has the abandonment options. Finally, we determine the profit share ratio for both parties according to whether MNC possesses the option of abandonment or not.

In this section, we derive the postinvestment extractive project value before exercising the abandonment option and deduce the optimal exit decision by maximizing the profit of MNC.

After investment, MNC holds an option of abandonment. The abandonment option can be viewed as a perpetual American put option with an exercise price equal to the salvage value of project

Let

So, prior to abandonment, the expected net present value of MNC after investment is given by

Similarly, HC’s expected net present value is

Applying Ito’s lemma, the value of active MNC,

Under these conditions,

Substituting (

Similarly, the value of HC,

HC gets the ownership of the extraction project while MNC is sold the salvage value of project

Next, the optimal investment decision is endogenously determined by the model. When the profit flow is sufficiently high or above a certain trigger, MNC will invest in the project immediately by incurring the initial investment cost. Therefore, we know that the optimal rule to exercise the option to invest is equivalent to finding a sufficiently high threshold

As a benchmark, we first consider the investment decision in the absence of the abandonment option. When the abandonment option is prohibited, the profit distribution ratio of MNC is

If abandonment is prohibited, MNC will perpetually run the extractive project. Therefore, when the project is undertaken, the expected net profit value of MNC,

Note that the optimal investment trigger

To sum up, then, the value of MNC is expressed as

In this section, we assume that MNC holds an option of abandonment and possesses the profit share

When the investment threshold satisfies the inequality

The expression

We solve implicitly the investment trigger, which satisfies the following equation:

To sum up, we rewrite the value of MNC:

(a) When abandonment is prohibited, the investment trigger can be given by

Proposition

Irrespectively of whether MNC is endowed with the abandonment option or not, the optimal investment timing is negative with the profit share.

The intuition of Proposition

The determination of profit share can be solved by Nash bargaining game. The bargaining process is carried out between MNC and HC. We derive the solution about the optimal profit share by the Nash Bargaining Solution, which is created by Harsanyi [

Both players share the same information about future profit

As in Moretto and Rossini [

Both players play cooperative game at

When the abandonment option is absent, the optimal profit share,

The result is consistent with Di Corato [

For given

If the relative risk aversion ratio

Proposition

The abandonment option has two opposite effects on the optimal investment trigger.

Proposition

In this part, we first analyze some properties of profit shares

According to (

Dependence of

As seen in Figure

Dependence of

In this section, we discuss how the investment thresholds change with the profit share

Figure

(a) Effect of profit shares on investment triggers. (b) Effect of profit shares on the difference.

In addition, Figure

Figure

Investment triggers change with volatility.

Figure

Relationships between expected growth rate and investment thresholds.

In this paper, we examine the investment timing of foreign direct investment and the optimal profit share between HC and MNC with an option of abandonment in a cooperative framework. Combining the real options with bargaining game, the results show that when the project is partially reversible in the presence of abandonment option, the investment threshold of FDI is always less than that under no exit option and the abandonment option has a negative impact on the investment trigger. When the project is completely irreversible, the investment timing in both cases remains the same. In addition, we demonstrate the relationship between the profit shares without an exit option

Although this paper draws some practical conclusions, it did not consider the impacts of the political risk on the investment of MNC. If we incorporate the change of tax rate or nationalization into the model, the relationship of the investment timing and the profit sharing under political risk will be further studied. This is the future direction of study.

(1) According to (

(2) We rewrite (

Differentiating

Substituting (

Calculating the following expression:

Needless to say, the authors are responsible for any detected errors.

The authors declare that they have no conflicts of interest.

The authors thank seminar participants at Department of Finance, School of Management, Huazhong University of Science of Technology. Finally, the authors acknowledge the financial support from Natural Science Foundation of China (no. 70871046, no. 71171091, and no. 71471070).