Optimum structure of corporate groups

Artsidakis, Stylianos; Thalassinos, Yiannis; Petropoulos, Theofanis; Liapis, Konstantinos Article Optimum structure of corporate groups Journal of Risk and Financial Management Provided in Cooperation with: MDPI – Multidisciplinary Digital Publishing Institute, Basel Suggested Citation: Artsidakis, Stylianos; Thalassinos, Yiannis; Petropoulos, Theofanis; Liapis, Konstantinos (2022) : Optimum structure of corporate groups, Journal of Risk and Financial Management, ISSN 1911-8074, MDPI, Basel, Vol. 15, Iss. 2, pp. 1-16, https://doi.org/10.3390/jrfm15020088 This Version is available at: https://hdl.handle.net/10419/258811 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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Journal of Risk and Financial Management 15: 88. https://doi.org/10.3390/ jrfm15020088 Academic Editors: Theodoros Stamatopoulos, Eleftherios I. Thalassinos and John Malindretos Received: 18 January 2022 Accepted: 9 February 2022 Published: 18 February 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Journal of Risk and Financial Management Article Optimum Structure of Corporate Groups Stylianos Artsidakis 1,* , Yiannis Thalassinos 2, Theofanis Petropoulos 1and Konstantinos Liapis 1 1Department of Economic and Regional Development, Panteion University, Syngrou Av. 176-71, 17671 Athens, Greece; f.petr[email protected] (T.P.); [email protected] (K.L.) 2Department of Economics and Finance, Gulf University for Science and Technology, Hawally 32093, Kuwait; [email protected] *Correspondence: [email protected] Abstract: Corporate groups consist of a set of companies, often described as subsidiaries, which are usually controlled by one single entity, the parent or holding company. The term control means the parent company’s rights to direct the relevant activities of other companies. A parent company can control a subsidiary either directly or indirectly through its voting power. Groups’ structure can be very complex usually with multiple crossholding and loop participations driving to not observable sharing rights. The aim of this paper is to examine how the parent company of a group with given participation rates can increase its capital by changing the share structure of the group and maintain management control over the group while the least capital comes from the majority. Furthermore, using evolver software we derive to the new optimal structure of the group and the maximum parent’s cash inflow from shares exchange. The value of this research to show the possibility for a parent company to create additional capital, by maximizing the minority interest, and at the same time direct voting rights in its favor. Keywords: group of companies; direct and indirect control; voting rights; ownership structure; equity; majority; non-controlling interest; capital 1. Introduction Corporate structure under a group of companies has been an ever-increasing phenomenon for many decades. Corporate groups consist of a set of legally independent companies, often described as subsidiaries, which are usually controlled by one single entity, the parent company. The most simplified form of such an organization is known as the pyramid structure, beginning on the top with the parent company, followed by subsidiaries and sub-subsidiaries. The parent company has the power to direct all relevant decisions of its subsidiaries either with direct control, i.e., the parent company has the ownership or else holds the majority of the shares and is actual the ultimate beneficiary owner, or indirect, by having the power to control the voting rights in its favor, i.e., acting again as the UBO. Often, questions arising from the terms power of control and ownership of a company. In business corporation’s theory, owners of a company’s equity are its stakeholders. A company’s share capital is divided to shares and each shareholder owns a certain proportion of it. However, this ownership is not sufficient to determine who is controlling the company. As often imposed in the Articles of Association, critical decisions within the company need the approval from the majority of the shareholders. Assuming the simplest voting system of one-share-one-vote, depending on the holding shares we can determine each shareholder’s voting power. The one whose voting rights represent the majority of the votes, has the power to control the company and direct its strategy, while the others, represent (as addressed in bibliography and business practices) the non-controlling interest or minority. Group structure can be very complex and frustrating in terms of shareholders and voting rights. Direct management control is most of the time the most simple and straightforward. If a company has the majority of the voting rights over another company, it can J. Risk Financial Manag. 2022,15, 88. https://doi.org/10.3390/jrfm15020088 https://www.mdpi.com/journal/jrfm J. Risk Financial Manag. 2022,15, 88 2 of 16 exercise management control on that company. Indirect control on the other hand, can be very tricky and crucial on determining who has the control power. Situations where there are cross-shareholdings between the group’s companies, circular ownership or even an extended and complicated pyramid structure can drive to covert power control. This is the case, where a parent company withholds a small portion of the shares of a company, but through its subsidiaries can maintain the control over other shareholders. That is, starting with a low investment the parent can multiply the controlled capital. Taking into consideration the above, in a group of companies the parent company holds the majority of the voting rights over the other companies and has the power to decide and direct investment and management policies within the group. Our aim is to examine how parent companies can redirect the share capital of the group, in such a way that will permit them to maintain management control and at the same time to absorb capital gains from this redirection. Management control is determined as direct and indirect voting rights in any general assembly in any subsidiary company. Under this question a shadow dual problem arises: that the minimum of majority interest is equal to maximum minority interest without management control. For simplicity reasons we are not taking into consideration agency problems that can arise between the shareholders of a company, as such we strict our calculations in one-share-one-vote shares. In our research we conclude that under certain constraints there is always an optimum point at which the parent company manages to maintain control of the group by minimizing its direct and indirect rights in group’s companies. At this point the capital gain from the share redistribution is the maximum possible. The role of the constraints and the importance of each one in the process is being described with available cash for investment having the greatest weight. The paper is organized as follows: We start with previous research under the concept of control, ownership, and minority/majority interest. Then, we present our theoretical procedure and the structure of the model. Next, we test our model presenting our findings and finally, we conclude the main key points and quote further questions that arise. 2. Literature Review Group structure and determination of direct and indirect shareholdings within the group has been tested and examined in detail over the last years. Most research has been focused in how to evaluate the complexity of voting rights within the group and therefore to present the actual controlling rights and the wealth creation. Since, as stated above, ownership does not reflect the actual control of firm, a very common argument is the conflict between the shareholders, and more precisely those who have the control power of the group with those who are not part of it–the minority interest. Although all can agree that in terms of maximize potential earnings all shareholders share the same concerns, disagreements arise in managing aspects such as investment policies or corporate control. This often occurs due to private benefits from a certain production choice. In most of the literature, control, in terms of voting rights, is considered as holding the majority of voting thresholding. Demarzo (1993) in his study presented this scenario, arguing that in a corporation with voting rights, the choice of production will be made by the holders of the majority stake. This can be achieved by either one large shareholder holding at least half of the voting rights or with collisions between smaller shareholders in order to achieve it. Bennedsen and Wolfenzon (2000) shows that in case of equity dilution among shareholders, coalitions are formed to seize control in a company. Such control provides them with cash flow private benefits that are burned through the non-controlling shareholders. Of course, there are different views supporting that control can be succeeded with a holding percentage less than half. In a study of 27 wealth economies’ large corporations, La Porta et al. (1999) show that most of the companies are controlled through pyramids structures, multiple class of shares deriving different voting rights and participation of shareholders in the Board of Directors. Through these methods, a shareholder can leverage his voting rights and maintain control with less J. Risk Financial Manag. 2022,15, 88 3 of 16 cash flow rights than 50%. In accordance with La Porta, Claessens et al. (2000) examined the ownership structure in Asia corporations to find that control is achieved mostly through pyramids structures and crossholdings among firms. Determining who has control power within a group corporation can be a difficult task, especially when control is gained through shareholder coalitions. This issue arises frequently in complex structures where holdings through multiple control chains and loops are met. In such situations determining who is the key shareholder that holds the integrated control needs a thoroughly investigation. Gambarelli and Owen (1994) were the first trying to find out the winning coalitions in group structures by applying a gametheoretical approach, following this perspective by Prati and Denti (2001). More recent, Crama and Leruth (2007,2013) ,Karos and Peters (2015); Hu and Shapley (2003) have used power indexes to measure power of direct and indirect control. Bertini et al. (2016) made a deep analysis on the different methods that have been presented and pointed out that most of them used the Shapley–Shubic, the Banzhaf and the Johnston power indexes. Although they find some similarities among the methods, they concluded that each one takes into account different considerations, thus no common conclusions could be made. Measurement group structure and the power of control through direct and indirect voting rights has been studied extensively in the literature. Brioschi et al. (1989) presented a well-known model by which they calculated the integrated control and companies’ value within a pyramid group. Representing participation rates in the form of matrixes and using linear algebra they mathematically described the value of a firm, the majority and minority of the group and the ways a group can raise capital without losing management control. Their model was implemented in the Italian manufacturing for the period 1980–1986 and proved the distinction between ownership and control. In two different studies Ellerman (1991) and Flath (1992) used the same procedure to calculate the gross income and ultimate ownership in Yugoslavian and Japanese keiretsu system. They found that indirect gains are worthwhile, and their impact should not be overlooked. Baldone et al. (1997) used the matrix calculation but eliminated own share effects. Chapelle and Szafarz (2002) following voting share, integrated ownership and majority voting rules approach analyzed in deep the pyramid structure and used ratios to reveal the actual control pattern of the largest Belgian holding company. Chapelle (2005) following Brioschi et al. model and adding more control considerations in the input-output matrix created a separation ratio to distinguish ownership from control. Her results show common ground in Italy and Belgium but different situation in US and Netherlands. Almeida et al. (2008) combined pyramid structures with companies’ position in the group and the degree of financing. Their findings in Korean family business groups showed that pyramid investments are not positive for small shareholders. Finding who has the actual control in a group can drive us to a lot of conclusions. The most important is if and how the controller uses his power relevant to minority shareholders. Does controlling a company mean wealth maximization for all related parties or is there a portion which actually burns the cost of an investment decision? Brioschi et al. (1999) show that under certain circumstances control benefits can raise the minority’s wealth. On the other hand, Meoli et al. (2006) research two acquisitions in Italy from a pyramid group structure to find that in both cases the non-controlling interest burned over the 85% of the acquisition and the majority took advantage of large private benefits. 3. Theoretical Approach 3.1. Effective Participation, Direct Plus Indirect Participations Let ndenote the number of companies which belong to the group. We assume there is a company whose share capital is owned by no other firm, neither an outsider investor, and exercises control over those companies through either the parent or holding company. Additionally, within the group, part of the share capital of companies is owned by other companies of the group and vice versa. This creates intra-group equity linkages that drives complex indirect control from the parent company. J. Risk Financial Manag. 2022,15, 88 4 of 16 Let ϕij be the percentage Participation Between Subsidiaries (PBS), then, the n × n matrix Φn×n=ϕijrepresents the direct intra-group shares participations. Let ϕij be the percentage Participation Between Subsidiaries (PBS), then, the n × n matrix Φn×n=ϕijrepresents the direct intra-group shares participations. Let a i be the percentage of Direct Participation of Holding Company (DPHC) in any subsidiary company, then n × 1 matrix An×1=[ai] represent parent’s direct share participation on group’s companies. The Φn×n and An×1 are positive matrixes with 0 ≤ϕij ≤ 1 and 0 ≤ai≤ 1, ∈[0, 1] where 1 represents the 100% participation. Rows and columns represent the companies of the group and each of the intersection entries represents the intra-group participation rates. Obviously if no participation rate exists the entry number will be zero and same applies for the intersection of same companies i.e., the diagonal of the matrix. Each row shows the participation rate of a group’s company to others within the group and each column shows the participation rates of group’s companies within the company we observe. Parent company’s integrated management control on a company iresults from the shares that the parent holds as investment in its assets (direct participation) and from the percentage of company’s shares held by companies whose equity percentage is held by the parent company (indirect participation). In order to make it clearer let us assume three companies A, B and C, where A holds a percentage of B and C shares while B holds a percentage of C shares. If αb , αc and b c the participation percentages, company A’s integrated control over company C, let it be G, equals to: G = αc+αb* bc. In order to find the parent’s Effective Integrated Participation (EIP), we use the Leontief input-output matrix method and derive to: Gn×1=I−ΦT−1 n×n×An×1(1) where Gn×1=[gi]the column vector of EIP to subsidiary I, ∀j=1, 2 . . . n subsidiaries; In×nthe integrated matrix; Φn×n=ϕij the PBC and ΦTn×n=ϕji the transpose matrix PBC and generally T denotes transpose matrixes; An×1=[αi]the DPHC. Vector of Management Control The sum of company’ s shares held from the parent company and/or from other group’s companies results to the accumulated control from the group. In a Group, the holding has Effective Management Control (EMC) through the shares of PBC in any subsidiary. Thus: Ci=ai+∑n i=1ϕij (2) with Cithe EMC ∈[0, 1] where 1 represents the 100% participation. Minority Interest There are also several external shareholders from other group’s companies, withholding a portion of share capital on the subsidiaries. In order to distinguish these holdings from the group we will refer them from now on as minority or Non-Controlling Interest (NCI) shareholders. We need to mention that what applies for the parent company about control applies here as well. Integrated minority control of subsidiary i, is the sum of their direct holding shares plus any indirect effect from subsidiaries crossholdings. In order to calculate NCI we introduce the column vector U1xn =[ui] , where u i = 1 ∀i=1, 2 . . . n subsidiaries. J. Risk Financial Manag. 2022,15, 88 5 of 16 Using the Equation (1) we can write: Mn×1=Un×1−Gn×1⇔[mi]=[ui]−[gi](3) where miis the NCI and ∈[0, 1] and 1 represents the 100% participation. Vector of Net Assets In order to keep our approach simple, we assume that the companies’ property has been measured to its fair value, and thus, the value of each company is equal to their net assets. In other words: Book Value =Equity =Assets −Liabilities =Net Assets (4) We denote the net assets of the group as the vector: NA 1×n=naj∀j=0, . . . . . . , n(5) where nα0net assets of parent company. Vector of Participations’ Value Given the net assets (value) of the companies we can calculate the total Participation Value for both the parent company and the subsidiaries. Thus, we denote the below vector: PV 1×n=pvj= a.=[pn0]=∑n i,j=1(naj×αi), parent0s participation value (6) b.=pnj= n ∑ j=1 n ∑ i=1 (ϕij ×naj)!, subsidiaries0participation value (7) Available Cash and Cash Equivalents for Investment Available Cash and Cash Equivalents (CCE-CE) is a portion of net assets. This element is essential for every company that wants to invest, based on already available funds and without the need to raise more capital. Taking into consideration that net assets of company iis given by the above NA matrix, we can write cash and cash equivalents as portion of the given net assets matrix: Let vector P1×n=pj∀j=0, 1, 2 . . . ncompanies (8) denoting the scalar percentage portion of C&CE where p0 the scalar portion of parent company. Thus: CE1×n=cej=pj×naj∀j=0, 1, 2 . . . ncompanies (9) 3.2. Maximizing Minority Interest Without Losing Control In order to start we need to denote the object function. What we need is the parent company to maintain control of the group but at the minimum level. Minimum level is defined as the minimum integrated participation of holding company in its subsidiaries. In order to find this level, the following needs to be minimized: Holding’s direct participations, holdings indirect participations or both. Objective Function (OF) is Equation (1) which has to be minimized. Thus: OF minEIP or minGn×1or min [I−ΦT−1 n×n×An×1](10) J. Risk Financial Manag. 2022,15, 88 6 of 16 Multiple Variables affect our model in order to solve the above question and several restrictions should be taken under consideration: Restriction of Management Control: EMC or Ci=ai+∑n i=1ϕij ≥50% ∀i=1, 2 . . . n subsidiaries in order the parent company to achieve the control of the Group. (11) DPHC An×1=[ai]≥0∀i=1, 2 . . . n subsidiaries (12) PBS Φn×n=ϕij≥0∀i,j=1, 2 . . . n subsidiaries (13) PV PV1×n=dpj≤cej∀j=0, 1, 2 . . . ncompanies (14) If we would like a mandatory minimum DPMC to exist for management purposes, then the restriction 2 has no practical view as it is, because any participation has to be equal to a minimum percentage rate in order to belong in a direct participation’s portfolio of parent company and any acquired company a i has to be higher or equal to a minimum x% according to law, accounting, management, or organization requirements. The reason for the above is that is not easy for the group managing or controlling the group accounting and the multiple voting rights with low or zero direct participation. Thus 2 and 3 are reconsidered to: DPHC An×1=[ai]≥x% (15) PBS Φn×n=ϕij≥y% (16) where xand ydenote the minimum participation rates as per management’s requirements. Now let us denote Φνn×n and Aνn×1 the new matrixes representing the optimal direct intra-group share participations, and the optimal parent’s direct share participation on group’s companies. Following the same calculations, we derive to the new EIP from the parent company: Gνn×1=I−ΦνT−1 n×n×Aνn×1(17) What the new EIP represents is an allocation of companies’ assets between investments in other companies’ share capital and liquidity. In fact, there is no change in the share capital (value) of any of the companies. Company A trades company B’s shares resulting to a decrease on investments account and an increase in cash and cash equivalents. Given the above we can also calculate this allocation with the use of matrixes and find the final cash inflow in parent company’s cash account. Now given that ∆ Gis the difference between the formal and the latter EIP we denote: ∆Gn×1=[δgi]=[gi]−[gνi]∀i=1, 2 . . . n subsidiaries (18) where ∆ Grepresents the effective integrated control share rights (direct and indirect) that the holding company lost or acquired by trying to minimize integrated participation but at the same time maintain the control of the group. These share rights represent the difference resulting from the redistribution of the shares within the group. The new total cash inflow in the parent company is represented as: NCF1×1=[nc fι]=NA1×n×∆Gn×1=naj×[δgi]∀i=1, 2 . . . n subsidiaries (19) 3.3. The Model We assume a group of companies with given participation rates between the companies and given equity values (net assets). With the above data we can calculate the initial EIP, NCI, PV and CCE as per our theoretical approach. Our target is to show how the parent J. Risk Financial Manag. 2022,15, 88 7 of 16 company of the group can raise capital by minimizing the EIP, i.e., change both direct and indirect participation rates of the group, while holding the EMC to control levels. In mathematical programming problems and especially in this case where programming is quadratic as we have matrixes multiplication, if we minimize integrated control under some specific constraints, then, mathematically, and deterministically there is only one solution, the optimal one. In case the structure of the group is different or any of the constraints that we have defined have changed, using the same method the optimal solution of the problem will be different and unique. We start by minimizing the EIP and test three different constraint models. Each model tests different assumptions regarding the participation rates and the CCE available for investments. For every model, using the evolver software we end up with an optimal solution, that is, the optimal structure of the group. After applying the new structure, we can find the differences between the initial and the optimal EIP. The value of these differences represents the maximum consolidated cash increase of the parent company. Due to minimizing EIP, we can also calculate the new NCI, and at the end of this research we present some questions that arise. 4. Estimations 4.1. The Static Model Our group consists of 10 companies. Company M represents the holding or parent company, while the rest are its subsidiaries. Rows represent the participations of each company to others in the group and columns represents the participation analysis of each company’s equity. As we can see from the below table (Table 1), the parent company has a 50% direct participation to each of the subsidiaries and no crossholdings exist between the subsidiaries. Our group is simple, and the effective management control derives only from the direct participation of the parent (sum of each subsidiary column). Table 1. Original Group Structure. M A B C D E F G H I M 0.00 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 A 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 B 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 C 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 D 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 E 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 F 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 G 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 H 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 I 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 EMC 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 Source: Author’s Assumptions. Given the above we present matrix A n×1 and Φn×n as per out theoretical approach (Table 2): J. Risk Financial Manag. 2022,15, 88 8 of 16 Table 2. Matrix A and Matrix Φ. MATRIX A–DPHC MATRIX Φ’–PBS M A B C D E F G H I A 0.5 A 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 B 0.5 B 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 C 0.5 C 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 D 0.5 D 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 E 0.5 E 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 F 0.5 F 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 G 0.5 G 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 H 0.5 H 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 I 0.5 I 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Source: Author’s Calculations. The effective integrated participation is given by the equation: Gn×1=I−ΦT−1n×n∗ An×1which results to Table 3: Table 3. Effective Integrated Participation. M A 0.5 B 0.5 C 0.5 D 0.5 E 0.5 F 0.5 G 0.5 H 0.5 I 0.5 Source: Author’s Calculations. We also assume a given Vector of Net Assets representing the value of each company (Table 4): Table 4. Net Assets. M A B C D E F G H I NA EUR 60,000 EUR 30,000 EUR 25,000 EUR 20,000 EUR 15,000 EUR 10,000 EUR 5000 EUR 4000 EUR 2500 EUR 1000 Source: Author’s Assumptions. We then apply three models with different assumptions as per the structure of the group and the available cash for investments. Solving our model by minimizing the integrated management control under our assumptions we derive the optimal structure of the group and the maximum capital increase from the parent company for given values. 4.2. Model Applications 4.2.1. Inputs We start with the structure of our static model. Our model’s goal and assumptions are summarized as per below in Table 5: J. Risk Financial Manag. 2022,15, 88 15 of 16 Our primer model must be fulfilled with its own shares between the subsidiaries and from the subsidiaries to parent. Moreover, the initial purchase cost of any acquisition must be taken into account in order to examine the negative or positive goodwill that arise. Author Contributions: K.L. in collaboration with Y.T. conceived the idea and wrote the conclusions. S.A. wrote the introduction, the literature review and the empirical results. T.P. helped with the structure of the model. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Conflicts of Interest: The authors declare no conflict of interest. Notes 1 Although this constraint seems equal to Models 1 and 2, in fact ce 1j for j= 0, 1, 2, . . . ,nare different as the portion of availanble C&CE changes. 1 Although this constraint seems equal to Models 1 and 2, in fact ce 1j for j= 0, 1, 2, . . . ,nare different as the portion of availanble C&CE changes. 2Last Constraint in Table 5. References Almeida, Heitor, Sang Yong Park, Marti G. Subrahmanyam, and Daniel Wolfenzon. 2008. Beyond Cash Flow and Voting Rights: Valuation and Performance of Firms in Complex Ownership Structures. EFA Athens Meetings Paper. Available online: https: //ssrn.com/abstract=1101865 (accessed on 14 August 2021). Baldone, Salvatore, Francesco Brioschi, and Stefano Paleari. 1997. Ownership measures among firms connected by cross-shareholdings and a further analogy with input-output theory. Paper Presented at 4th JAFEE International Conference on Investment and Derivatives; pp. 258–80. Bennedsen, Morten, and Daniel Wolfenzon. 2000. 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