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A Development Bank’s Choice of Private Equity partner: A Behavioral Game-

theoretic Approach

Authors: R. Fairchild, Maria Musatova, Troy A. Weeks, Ian Crawford.

December 12th 2011

Word Count: 12342

Abstract

We consider a development bank’s investment choice (whether to invest through the private-equity sector or to invest directly) when financing an entrepreneur in an emerging economy. If the bank chooses to finance through the PE-sector, it then faces the choice of which PE-manager to select. We consider both economic (value-adding abilities) and behavioural factors (empathy, trust, relationship-souring) affecting this choice. When investing through the PE-sector, triple-sided moral hazard problems occur, as the bank, the PE-manager, and the entrepreneur all contribute to value-creation. When investing directly, the bank removes a layer of fees and profit share, and a double-sided moral hazard problem exists (as only the bank and the entrepreneur are now involved in value-creation). We demonstrate that the bank’s choice is affected by relative abilities and the potential level of empathy generated by a PE-manager.

1. Executive Summary

Global economic growth is being driven increasingly by entrepreneurial activity in emerging and developing economies. As in developed economies, entrepreneurs face difficulties in obtaining finance through traditional sources, such as banks and stock markets, due to the high degree of uncertainty and risk surrounding their ventures. Venture capitalists and private equity funds specialise in financing such enterprises. In recent years, development banks (DBs) have taken a major role in financing entrepreneurs in emerging economies, with an explicit mission of facilitating economic growth, and providing ‘transition impact’. Frequently, DBs have chosen to finance such entrepreneurs through local private equity (PE) funds. However, some DBs have also chosen to finance entrepreneurs directly, without involving the PE-sector. In this paper, we address the following important questions. What factors affect a) the DB’s choice of investing through the PE-sector, and b) the DB’s choice of manager within the sector? In order to consider these questions, we develop a theoretical analysis that examines both economic (value-creating ability) and behavioral factors (empathy, trust, relationship-souring) affecting the DB’s choice, and the performance of the entrepreneurial venture. Such performance may be subject to extreme incentive (moral hazard) problems. The intuition behind our analysis is that, in economic terms, local PEs may be better placed than the DB to assist their entrepreneur in creating value. Furthermore, in behavioural terms, local PEs may be able to develop

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empathetic relationships with their entrepreneurs, which may lead to trust, hence mitigating incentive problems. If the DB decides to invest into the entrepreneur’s venture through the PE-sector, then we consider PE-managers’ attributes along two dimensions: value-creating ability, and the potential to become empathetic and trusting/trustworthy in his relationship with the entrepreneur. The DB considers both dimensions in making its decision. We demonstrate that it is possible that the DB may choose a PE with lower technical value-creating ability, but higher potential for creating empathy and trust in his relationship with the entrepreneur. Furthermore, if the DB invests through the PE-sector, a form of triple-sided moral hazard problem exists, as three parties (the DB, the PE and the entrepreneur) are involved in value-creation, and in sharing the cashflows. Therefore, the DB may choose to invest directly into the entrepreneurial venture, as a) this eliminates a layer of fees and profit share that would otherwise be paid to the PE-fund, and b) only a double-sided moral hazard problem now exists. However, the DB trades this off against the potential value-creation that could result from the empathy and trust developed between a local PE-manager and its entrepreneur. Our analysis has positive (descriptive) and normative (prescriptive) implications. At the descriptive level, it helps to explain the observed patterns of investment by DBs (mainly investing through local PE-funds). Also, it suggests that, in practice, unobservable behavioural characteristics, in addition to economic characteristics, may drive a DB’s decision. At a prescriptive level, our analysis provides the following recommendations for DB investment managers. We suggest that such managers should consider both economic and behavioural factors when assessing PE-teams’ suitability for investing into entrepreneurs in emerging markets. The DB managers should ask two major questions: what are the economic value-adding capabilities of the PE-team? What personable (behavioral) qualities do they bring? That is, would these PE-managers be able to create empathetic and trusting/trustworthy relationships with their entrepreneurs, which may mitigate incentive problems, and enhance value-creation? A further interesting implication of our analysis is that, in assessing the personable characteristics of the PE-team, the DB should be careful not to become ‘too attached’ to the team, as this may lead to inefficient decision-making by the DB.

2. Introduction

Entrepreneurial activity is a major source of global innovation, employment creation and economic growth. However, since such activity may be inherently risky and uncertain, in particular for small and medium sized enterprises (SMEs), entrepreneurs often face difficulties obtaining finance through traditional channels, such as banks or the stock market. Venture capital (VCs) and private equity funds (PEs) often fill this ‘equity-gap’ by specialising in direct equity financing of innovative entrepreneurial activity. Furthermore, in contrast to traditional financiers, VCs and PE-managers tend to provide more than just finance. They also provide value-adding capabilities.

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A recent phenomenon is the increase in entrepreneurial activity in developing/emerging economies. As in developed economies, start-up activity is predominately financed by private equity and venture capital. Furthermore, as in the developed economies, the performance of private equity/venture capital financed early stage companies and SMEs may be seriously hindered by severe moral hazard and information-based problems. These problems are exacerbated for investors in private equity and venture capital funds in emerging markets by the relative absence of robust signals of quality such as a private equity investment track record and reputation due to the relatively young nature of the industry in these markets, and are further exacerbated by weak governance systems and institutions. In response to these impediments to growth, development banks1 (DBs) have emerged as major players in the financing of entrepreneurial activity in developing markets. However, rather than financing entrepreneurs in developing countries directly2, DBs often invest into entrepreneurial ventures through local or regional financial intermediaries, such as venture capital or private equity funds. To date, there has been little academic research (either theoretically or empirically) into the role of development banks, their involvement with private-equity partners, and the effects on entrepreneurial incentives through the PE sector and performance. Particularly, we lack an understanding of the tri-partite relationship that exists between DBs, PE-partners and entrepreneurs in developing economies. In order to address these issues, in this paper, we develop a rigorous, formal, game-theoretic analysis of the role of development banks in co-financing start-up entrepreneurs in developing economies. Our objective is to address the following key research questions: a) What is the role of the development bank in financing entrepreneurial activity in emerging economies? b) What economic and behavioural factors are important in affecting the bank’s choice of PE-financier? c) How does the tri-partite relationship that exists between bank, private equity firm and entrepreneur affect the players’ incentives and the venture’s performance? An analysis of these research questions is important. Indeed, As Settel et al (2009) note: “While a large number of articles review the growth, evolution, and performance of the private equity industry in emerging markets, we are unaware of any study that has systematically examined the important role of multilateral development finance institutions in the private equity industry.” In addressing these issues, we contribute to five strands of existing venture capital/private equity research. First, by considering a tri-partite relationship between banks, PE-firms, and entrepreneurs, we extend the research that analyses double-sided moral hazard in venture capital/entrepreneur relationships. That is, we consider triple-sided moral hazard. Second, we contribute to the growing research that considers an entrepreneur’s choice of financier (we take a different focus by considering the development bank’s choice of finance-partner). Third, existing research focuses on the economic factors affecting this choice. We consider both the economic and behavioural factors affecting the bank’s choice. Fourth, we contribute to the recently

1 In practice, we argue that there are three types of development bank: country specific, regional and multinational. In this paper, we focus on multinational development banks. 2 Some DBs finance entrepreneurs directly. We consider this later in the paper.

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emerging research that is beginning to analyse the role of venture capital/private equity in emerging economies. Finally, we contribute to the nascent research on the involvement of development banks in financing entrepreneurs in emerging economies. We now provide an overview of the literature in each of these areas in order to provide a context for our model. 2.1. Models of triple-sided moral hazard

There is now a large body of research that examines double-sided moral hazard problems that exist between venture capitalists and entrepreneurs. The idea is that both entrepreneurs and venture capitalists (VCs) contribute to wealth-creation in the venture. However, they may take individually rational self-interested actions that reduce or destroy total value3. Fairchild (2011) notes that scholars consider two types of moral hazard problem. First, as the E and the VC may both exert unobservable effort in attempting to create value for the venture, they may face the problem of double-sided effort-shirking4. Second, the players may face ex post conflict (after they have exerted effort, and the venture has achieved some success). This may take the form of various types of conflict (such as double-sided hold-up/renegotiation/expropriation problems), after value has been created5. Our model incorporates both problems (ex ante double-sided effort-shirking and ex post conflict). However, we extend the analysis in an interesting direction by considering the impact of triple-sided moral hazard among three players. Our model is closely related to those of Yousfi (2008) and Yang (2010). Yousfi considers a financing game involving three players (entrepreneur, LBO fund, and bank). In his model, an entrepreneur wishes to engage in a leveraged buyout of his company. He involves both an active LBO-fund, and a passive bank. The bank provides debt-finance, while the LBO-fund takes an equity-position in the company. Double-sided moral hazard problems exist (between the LBO-fund and the entrepreneur) in the form of effort-shirking. We develop Yousfi’s analysis as follows. First, by allowing the development bank to be an active player, with a complementary set of value-additive contributions, we consider triple-sided moral hazard. Second, as the PE financing model is an indirect (usually equity) financing model (see section 3.1), we consider that our bank has an equity stake in the venture (rather than debt). Finally, in contrast to Yousfi, we consider ex post, as well as ex ante moral hazard. Yang (2010) considers triple-sided moral hazard in a general business context, involving three players. In his model, one player is required to provide up-front start-up effort. After her efforts are completed, she is no longer required, and the other two players are required to exert ongoing efforts that contribute to the success of the project. Yang’s focus is on the optimal profit-sharing contract over time.6 In our

3 As noted by Cable and Shane (1997), this is the classic prisoner’s dilemma problem, where mutual cooperation between the E and the VC may maximise each player’s payoff, but they each have the incentive to ‘defect’, destroying value, and both end up worse off. 4 Double-sided effort shirking has been analysed by Houben (2003), Casamatta (2003), Schmidt (2003), Repullo and Suarez (2004), Fairchild (2004), (2011) and de Bettignies (2008), among others. 5 Double-sided ex post hold-up/expropriation problems have been analysed by Smith (1998), Landier (2001), Repullo and Suarez (2004), Chemla et al (2004), and Bigus (2002) among others. 6 Other papers exist, considering the co-existence of three players (two financiers and an entrepreneur): eg Casamattta 2003, Repullo and Suarez 2004, Elitzur and Gavious (2003). Casamatta (2003),

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model, we do not consider the optimal allocation of the cash-flows (the players in our model have equal equity-shares). Our focus is on the development bank’s choice of PE-fund (or investing directly), taking the equity-shares as given. 2.2. Choice of financier

In considering the development bank’s choice whether to involve PE-financing, and, if so, which one, we complement the existing research on entrepreneurial choice of financier7. For example, Landier (2001), Ueda (2004), and Winton and Yerramilli (2004) consider an E’s choice between traditional bank debt financing or venture capital finance. Chemmanur and Chen (2006), Leshchinskii (2002) and Fairchild (2011) analyse the E’s choice of VC or angel-financing. De Bettignies and Brander (2007) consider the E’s choice between traditional bank-finance and venture capital. In their analysis, the E considers the following trade-off when making his choice. When choosing the bank, the E holds all of the equity (as the bank provides debt), but the bank cannot help to create value. In contrast, the VC provides value-adding abilities, but takes some of the equity. Hence, we build on this work by allowing the development bank to take an equity-stake and add value. 2.3. Behavioural factors

Existing venture capital and private equity research focuses on the effect of economic incentives. A major contribution of our analysis is that we consider both the economic and behavioural factors affecting the performance of private equity-financed entrepreneurship. In particular, we develop the procedural justice literature8, by developing a formal analysis of the effects of social preferences (fairness, trust, empathy, reciprocity) on performance. In doing so, we build on Fairchild’s (2011) model9. According to Fairchild (2011), De Clerq and Sapienza (2001) introduce the term ‘relational rents’, which refers to the value-creating potential of fairness, trust and reciprocity. As they note, “no in-depth analysis has been made of how relational rents might be created for both parties in the dyad.” Fairchild (2011) takes the important

considers three players. However, in contrast to us, the form of problem is double-sided moral hazard in the form of effort-shirking, as only two players exert effort. In Repullo and Suarez (2004), and in Elitzur and Gavious (2003), there is a form of ‘staged’ triple-sided moral hazard, as follows… 7 For future research in our model, it would be interesting to consider choices at two stages of the relationship: the DB’s choice of PE firm, and the PE’s choice of E (ie by including two Es in our model, rather than one). Furthermore, we could also consider the E’s choice of PE. As we increase these permutations, the model could become very rich. 8 See Fairchild (2011) for a review of the procedural justice literature which provides a conceptual framework for analysing fairness, trust, empathy, and reciprocity in venture capital. 9 Fairchild (2011) considers the effect of value-creating ability and empathy on an entrepreneur’s

choice between venture capital or angel financing, and focuses on double-sided moral hazard. In contrast, we incorporate behavioural factors (specifically empathy) into a triple-sided framework, involving a development bank, a private equity manager, and an entrepreneur.

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first step in analysing this in a double-sided framework. We extend the behavioral analysis to a triple-sided framework. We base our model of reciprocity on Sally’s (2001) sympathy game. This involves players considering their partner’s payoffs, and this is modelled by a player placing an empathy weighting on a partner’s payoff. Following Fairchild (2011), the bank trades-off two factors when considering the choice of PE: the PE’s value-adding abilities, and the empathetic relationship that can be created between the PE and the E. Following Sally (2001), empathy can be considered in terms of psychological and geographical closeness. 10 2.4. PE in developing countries

The use of private equity finance during a firm’s development has become more common in developed economies. As Settel et al (2009) note11, in the United States alone, “the industry grew from modest origins in the 1970s and 1980s, to more than $20 billion raised in 1995, $80 billion raised in 2000, and more than $150 billion in 2006.” In emerging economies, private equity financing is a much younger form of financing and still represents a nascent industry. Whilst capital available for private equity and venture capital financing in global emerging markets still lags behind developed markets (measured as a percentage of GDP), it has nonetheless become an increasingly important destination for international investment capital for private equity and venture financing.12 Much of the existing research on private equity focuses on the developed economies. For example, Schmidt and Wahrenburg (2004) consider the relationship between investors and European VC-funds, considering the effects of reputation, bargaining power, and contractual design. However, recently, scholars are beginning to examine the impact of private equity on entrepreneurial activity in developing markets. Balboa and Marti (2007) examine the factors affecting investors’ choice of private equity firms in developing markets. The authors note that in developed markets, investors are likely to base their choices on managerial reputation, which is linked to track record. However, in emerging markets, such track record or reputation may not be available, due to the immaturity of the asset class in those markets. Investors then face extreme asymmetric information problems, and fund managers, in the absence of reputation and track record, need to find other means of signalling quality. Hazarika et al (2009) analyse the effect of institutional and cultural differences on global VC-investing, both in developed and developing economies.

10 Bengtsson and Abraham Ravid (2009) consider the effect of geographical location and culture on venture capital contracts and performance. 11 Settel et al obtain this information from Kaplan (2007). 12 For example the Emerging Markets Private Equity Association EM PE Annual Review, April 2011 and EMPEA Fundraising Review (2003-2005) show the dramatic increase in fundraising for PE funds in emerging markets with capital raised increasing from approximately USD$3,356 million in 2003 to fully US$ 66,517 millio in 2008.

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Meuleman and Wright (2011) analyse the process by which later-stage UK private equity firms invest across borders into continental Europe. They find that the presence of local private equity investors is very important in motivating cross-border investment. This has parallels with our model, in which the development bank typically prefers to invest into entrepreneurship in developing economies if it is able to involve a ‘local’ (including sub-regional) PE. 2.5. Development Banks

A major contribution of our analysis is that we develop a rigorous theoretical analysis of the involvement of development banks. Our model is close in spirit to Hainz and Kleimeier (2010), who consider optimal loan contracts (full recourse versus non-recourse/project finance loans) between development banks and entrepreneurs in developing markets characterised by high political risk. Hainz considers a double-sided moral hazard model in which the entrepreneur and the development bank both exert value-creating effort. The entrepreneur’s effort affects operational success, while the development bank acts to mitigate political risk. Thus, according to Hainz, development banks perform an important role as a political umbrella. In contrast to Hainz’ approach, we consider triple-sided moral hazard, as, in addition to the development bank and the entrepreneur, we consider a third player (the private equity manager) who also exerts value-creating effort. Furthermore, in our model, all three players take an effective equity-position in the venture (in contrast to the loan contract offered by the bank in Hainz’s model). Pissarides (1999) provides one of the first discussions of the challenges facing multilateral development banks (focussing on the European Bank for Reconstruction and Development13 (EBRD)) in financing entrepreneurial activity in emerging markets (Central and Eastern Europe). She argues that lack of finance provides the main obstacle to the growth of SMEs. She notes that the EBRD’s policy towards SME-financing focuses on institution-building, a commercial approach, and financial system orientation. Furthermore, according to the author, the EBRD recognises the importance of co-financing with local investment or commercial banks, equity participation in local (or regional) investment or commercial banks, and (most relevant to our model) equity participation in regional or country/sector specific investment and venture capital funds. Importantly, Pissarides (1999) notes the crucial importance of the experience of the venture capital fund managers. She argues that the main reason why some funds do not perform well is that the managers lack expertise. Furthermore, she notes that EBRD provides a certain political comfort with regard to the countries of operation14. A contribution of our analysis is that we compare triple-sided and double-sided moral hazard problems. In our analysis, the development bank chooses whether to involve

13 Pissarides (1999) notes the “The EBRD has a special mission. At the time of its creation, one of the features that distinguished the EBRD from the World Bank and the European Investment Bank was its mandate to support the private sector.” The bank in our model focuses on this role. 14 Indeed, Settel et al (2009) quote Teresa Barger of IFC: “Fund management is all about value-

addition. Only successful managers have a development impact by building great companies.”

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the private-equity sector (in which case, the bank then chooses which PE-manager to involve) in financing the entrepreneur, or to finance the entrepreneur directly without PE-involvement. In the first case, a triple-sided moral hazard problem exists, as three players (the bank, the chosen PE-manager, and the entrepreneur) all exert effort in creating value. In the second case, only a double-sided moral hazard problem exists, in that only two players (the bank and the entrepreneur) are involved in creating value. An interesting trade-off for the bank in making this choice of involving the PE-sector or investing directly, is that the bank may have lower value-creating ability than the PE sector. It would seem, therefore, that the bank would prefer to involve the private-equity sector as co-investors in the enterprise. However, by involving the PE-sector, the bank’s share in the venture is diluted (that is, in the triple-sided moral hazard case, the cashflows from the venture are shared between three players, while in the double-sided case, they are shared between two players). To make our analysis concrete, we consider two cases. In the first case, the bank is unable to help the venture create value without involving the PE. In this case, the value of the venture, and the players’ payoffs collapse to zero. As long as the bank gets a positive payoff from involving the PE sector, it will choose to do so. In our second case, the bank has some value-creating ability, but this is strictly less than the value-creating ability of the PE-sector. Now, the bank may choose to finance directly, or still involve the PE-sector, depending on the bank’s ability relative to the PE-sector’s ability. In our modelling approach, we have in mind the following simplified intuition. The development bank is located in a developed country (eg UK or US). Its policy is to finance entrepreneurial activities in foreign developing economies. However, due to the distance involved, the bank finds it difficult to seek out decent entrepreneurial opportunities, and finds it difficult to assist in adding operational value. In addition to these economic impediments, in terms of behavioural factors, the distance involved means that the bank and the E are unable to build up empathetic relationships. Therefore, the bank seeks private equity partners that specialise in financing entrepreneurs in developing economies, and in building relationships with them. In short, the PE partners have more time, resources and expertise to dedicate to this activity than the DB has. Indeed, according to Settel et al (2009),“multilateral development finance institutions often believe that providing support to small and medium enterprises can be crucial to a region’s development. However, overseeing many direct equity investments in SMEs would be tactically difficult for many of the MDFIs given the intense requirement for their operational and strategic involvement. For this reason, MDFIs often turn to funds to manage their SME investments.” The rest of the paper is organised as follows. In section 3, we consider the relevant features of MDB’s in more detail (particularly, we consider the rationale for existence, the banks’ objectives, and the financing arrangements). In section 4, we begin by presenting and describing the model. We then solve for the triple-sided moral hazard game, involving the bank, the private equity firm, and the entrepreneur. In section 5 we compare with the double-sided moral hazard case, where the bank can finance the E directly. Section 6 presents the policy implications of our analysis. Section 7 concludes.

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3. Features of Development Banks

In this section, we consider features of development banks that are relevant to our model. We focus on a) the rationale and objectives of DBs, b) the financing arrangements. Settel et al (2009) identify that the strategies of MDFIs vary as follows: a) African Development Bank (infrastructure development), b) European Bank for Reconstruction and Development (restructuring, transition and efficiency, c) European Investment Fund (support to SMEs, entrepreneurship), d) Inter-American Investment Corporation (support to SMEs, entrepreneurship), e) International Finance Corporation (financial market development), Islamic Development Bank (infrastructure development), Multilateral Investment Fund (support to SMEs, entrepreneurship). In this paper, we focus on the role of supporting SMEs and entrepreneurship (in addition to political risk mitigation). Whilst we focus on the DB’s role of supporting SMEs and entrepreneurship as engines of employment creation and economic in this paper, we identify three broad objectives for a DB, when electing to finance SMEs through a PE fund rather than investing directly: (a) Capital Multiplier – first, as has been noted above (see section 2.4), in emerging

economies there are frequently significant informational asymmetries as a result of the absence of many of the indicators of PE manager quality that are typically found in developed economies. DBs, through their experience and knowledge of the economies in which they operate, are able to effectively signal to the market its assessment of fund manager quality in the absence of more traditional quality signals, thereby catalysing capital into the PE/VC fund. Indeed some DBs, such as the EBRD, have for some time published aggregated PE/VC return data which has the effect of signalling to market the returns that can be achieved in the economies in which it invests. DBs thereby seek to achieve a multiplier effect with their capital by mobilising additional private and public sources of capital for financing of local enterprises.

(b) Institution Building – secondly, by investing in PE/VC funds, DBs seek to develop (applying the DBs own institutional know-how, experience and value-add to the formation and governance of the fund) institutional quality fund management teams and local specialised investment capacity, capable of continuing to assist and build value in local enterprises in the long-term. Objectively, in the longer term, DBs should seek to develop efficient and sustainable markets able to function on a standalone basis without the continuing support historically provided by the DBs themselves. Whilst many DBs have the capacity and do engage in a range of direct financing activities, by investing through PE/VC funds, DBs are able to effectively leverage their capital and resources and achieve a multiplier effect in developing additional skilled long term local and regional investment capacity in those markets. Implicit in this objective also is the recognition that specialised, adequately resourced, locally and

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regionally based PE firms may be in a position to better access, monitor and create value in the enterprises in which they invest.

(c) SME Expansion – finally, whilst Pissarides (2009) notes that lack of finance provides the main obstacle to the growth of SMEs, an important distinction can be made with respect to a DB’s choice of investment in a PE/VC fund. The provision of finance to SMEs can be provided via a variety of mechanisms including the provision of SME financing lines to local banks and by the DBs themselves providing direct debt and equity financing. The decision of a DB to invest through PE/VC funds, we argue, is additionally motivated by a desire to provide more than just capital alone, but rather to provide active long-term value additive support to enterprises in need of strategic, financial and operational value creation which is not available from passive (typically debt) financing or which may be beyond the resources and capabilities of the DB.

The strategy of DBs investing in private equity is in practical terms is therefore, at an instiutional level, frequently not a binary choice between investing directly or indirectly via PE partners. Rather it is more commonly one of complementarity, leveraging the DBs institutional attributes (including political risk mitigation) whilst recognising its institutional limitations to create deeper and more efficient financing markets through a combination of direct and indirect investment decisions. In this paper, we focus on the role of DBs in supporting SMEs and entrepreneurship (in addition to political risk mitigation). We assume a simple equity contract, where the three players share the equity equally. We note that this is a simplification. In section 3.1, we briefly outline the ‘real-world’ features of the “indirect financing model.” 3.1 The indirect financing model

Presented below in Diagram 1 is a simplified outline of the private equity indirect financing model. These structures, in their various forms, are one of the most significant sources of enterprise financing in developed economies, and increasingly in developing economies. Whilst the strategies and forms of PE funds vary, most fund structures are ultimately intended to provide an efficient mechanism to enable investors to pool financial resources in an actively managed collective investment vehicle without incurring an additional level of intermediate taxation simply by virtue of having pooled financial resources with other investors. That is, the burden of taxation is intended to fall on a fund investor based on its own tax residency and status as if the PE fund investor had invested directly in the underlying enterprise and there was no intermediate fund vehicle. These vehicles are typically, though not universally, structured as a limited partnerships, but the ultimate structure in each case is modified to reflect the tax and regulatory status of the fund’s investors, countries targeted for investment and the PE team itself. The structure in Diagram 1 therefore represents a highly stylised version of a PE fund structure.

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Diagram 1: Simplified indirect financing model

A PE firm may be formed of PE principals as owners or employees of an independent fund management company, or of a “sponsor” financial institution such as an investment bank or insurance company. The general partner of the fund is ultimately responsible for the operation of the fund and investment decision making and is typically owned by the PE fund’s principals or sponsor. Other investors, including the DB, are referred to as limited partners, reflecting their limited liability status in the fund. As can be seen from the financing model, the PE firm will receive a management fee to provide working capital for the operation of the fund. Additionally, the PE firm is incentivised to actively create value in the underlying enterprises by being entitled to receive a proportion of the profits generated for the investors in the fund, including the DB (often 20% of profits) in addition to that earned on the PE firm’s own investment in the fund. Usually this is only after investors have first received back their invested capital plus a minimum preferred return, or “hurdle rate” expressed as an annual rate or internal rate of return on the investor’s invested capital (often 8%). This is commonly referred to as the “carried interest”.

Private Equity Fund (Limited Partnership)

General

Partner

Investee Company

Investee Company

Investee Company

Investee Company

Investee Company

Development Bank

Other Investors

PE Financial Commitment

Limited Partners Investment

Advisor

PE Principals

Management

Fee

Profit Share (Carried Interest)

Paid on Capital Gain

Simplified Cash Flows

Return of Capital and

Capital Gain

Investment

Capital

Return of Capital

and Capital Gain

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A PE firm or sponsor is typically expected to invest capital in a fund in order to create alignment of interest, and thereby to also invest in the underlying entrepreneurial ventures invested in by the fund. In practice, whilst most independent PE firms are likely to only invest in the range of 1% - 5% of a PE fund’s capital, financial sponsors will frequently invest a significantly higher proportion of a fund’s capital. Although a simplifying assumption, we have taken it as given in our model that the DB and the PE each have equal equity stakes in the PE fund and thereby obtain an equal equity stake in the underlying venture together with the entrepreneur. For the purpose our model we can also disregard the existence of the PE fund itself and look through to the DB and PE as though they were direct investors in the venture. 3.2 Value-add of DBs

In developing our model, we follow the analysis of Hainz and Kleimeier (2010) that DBs add value through the provision of a political umbrella and political risk mitigation. We argue in addition here that, although the prevailing focus in existing literature has been on political risk mitigation as a DB’s principal value-creating attribute, in the context of a PE fund, DBs have, in addition, a wider set of direct and indirect contributions in the value creation chain. For example, as has been seen from the recent European emerging market fundraising figures,15 DBs continue to play a significant role in the establishment of new PE funds in emerging economies. The extensive breadth and depth of DBs participation in funds across differing geographies, markets and sectors thereby enables the DB to bring to a more narrowly focussed PE fund a perspective and network and industry know-how which we argue is frequently unrivalled amongst other investors in those markets. This frequently includes participation on the fund governance advisory committee through which the DB can in turn directly bring to bear its wider market and industry awareness to the benefit of the PE firm and underlying E. Moreover, by virtue of the experience and important financial role played by DBs in emerging economies, DBs are frequently able to have a material impact on the form, terms and governance of PE funds and on PE management team composition. This close engagement in formation and governance, which, perhaps appearing initially ephemeral, sets in place governance and structures which are expected to enhance the prospects of successful value creation in underlying Es. We can in that respect therefore express the value contribution of a DB as a continuing function of the DB’s participation throughout the life of the fund.16 Nonetheless, in this paper we have adopted the DB’s role in mitigating political risk as a proxy for a DB’s wider set of complementary value-creating attributes.

15 See for example EVCA Central and Eastern Europe Statistics 2010 July 2010, which indicates that during 2010 development banks and government sources comprised 58% of all capital raised by private equity funds in central and eastern Europe. Although a significant increase on previous years, it nonetheless illustrates the importance of development banks to the private equity asset class in those markets and their ability to act as a strong positive influence on the formation and governance principles of funds established in those markets. 16 See footnote 24.

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4. The Model

We consider a game consisting of 1 development bank (B), 2 private equity firms

( })2,1{: ∈iPEi , and an entrepreneur )(E . All players are risk-neutral and the

discount rate is zero.

The E is wealthless, and requires finance 0>I to develop her idea. The E passively accepts finance from whoever provides it17. The bank can choose to finance the E directly, or it can choose to invest in the E through one of the PE firms. Particularly,

the bank supplies finance ,II B ≤ and the chosen PE firm supplies ,PI with

.III PB =+ In this paper, our interest is not in modelling these capital contributions:

we simply take them as exogenously given. Each player possesses its own specific skills. For example, the PE firm has operational/technical and marketing expertise. The E has technical expertise18. The bank has finance expertise, and also expertise in understanding the environment of the country, mitigating political risk etc19. If the bank involves the PE-sector, then, in addition to providing finance, the PE-sector provides value-adding capabilities at the ‘operational’ stage. The bank provides political risk-mitigating efforts. If the bank does not involve the PE-sector, it is left to the bank (in addition to its political risk-mitigation efforts) to help the E create value at the operational stage. In the main part of the model, we assume that the bank cannot create value without involving a PE. Therefore, the bank will never choose to finance the E directly. It must involve a PE. The bank decides which PE-firm to partner and supply finance to. The bank works to mitigate political risk, and the PE works with the E to build the venture. This enables us to focus on the B’s choice of PE. It also enables us to consider triple-sided moral hazard (as three parties are involved in value-creation). In section 5, we allow the bank to create value at the operational stage without the involvement of the PE (although the bank’s ability to do so may be less than the PE-sector’s ability). Now the bank chooses between the two PEs or investing directly. This enables us to compare triple-sided and double-sided moral hazard. The timeline of the game is as follows. Date 1: (Financing Stage): The bank B decides whether to finance the E directly, or whether to involve the PE-sector. If the bank chooses the latter, then it chooses one of the PE firms to join the tryad. The bank and the chosen PE firm provide the required finance to the E. This enables the E to begin to expand his firm. We take as given that,

17 Hence, we do not consider the E’s choice of financier: see footnote 5 for a discussion of interesting future research. 18 See Houben (2002) who builds on this idea of complementary expertise in her double-sided moral hazard/adverse selection model. In her model, the E has technical expertise, while the VC has marketing/strategy expertise. 19 See Hainz and Kleimeier (2010) for a model in which development banks mitigate political risk. His model focuses on loan contracts.

14

if the bank chooses to finance directly, it shares the cashflows equally with the E: that

is, the equity-shares are .2/1== EB αα If the bank choose to involve the PE-sector,

then all three parties have equal equity-stakes in the venture20,

.3/1=== EPEB ααα

Date 2: (Value-creating Effort level stage I: PE and E create operational value): If the bank chooses one of the PEs to co-finance the E, then, in this first stage of value-creation, the chosen PE and the E work together to create venture value.

Specifically, the E and iPE exert respective efforts Ee and PEe . If the bank finances

the E directly, then the B and the E work together to create venture value.

Specifically, the E and B exert respective efforts Ee and Be . Effort is costly for any

of the players, with cost of effort21 ,2

EE ec β= .2

PEPE ec β= .2

BP ec β=

The operational stage succeeds with probability ,)( 2

1

PEEj eep γ= in which case the

venture provides cashflow ,0>R or fails with probability ,1 p− in which case it

provides zero income. The parameter jγ represents the synergistic, value-creating

abilities of the pair of players involved at this stage, where },,{ Bij∈ depending on

whether the PE or the bank are involved at the operational stage.

We assume that :21 γγ > the 1/ PEE dyad has higher synergistic abilities than the

2/ PEE dyad. In our main analysis, the bank has no operational synergistic ability

( ).0=Bγ In section 5, we consider a case where the bank has some synergistic

ability: .0>Bγ

Note that the partners’ efforts are complementary in affecting the success probability of the venture (particularly, if either of them exert zero effort, the project is doomed to fail, regardless of the other player’s efforts)22. If the project ultimately fails at this stage, the game ends, and all three players (the PE, the E and the bank) receive zero income. If the project succeeds, the game continues to date 3.

20 The assumption of equal equity-stakes is a simplifying assumption. In practice, the financing situation is complex, with the bank taking an indirect stake in the venture (the indirect financing model: see section 3.1). The analysis of the financing arrangement is not the focus of this paper: we leave this analysis for future research. 21 These are standard cost-of-effort functions in the VC and PE literature, and demonstrate increasing marginal cost of effort. 22 As noted by Elitzur and Gavious (2003), and Repullo and Suarez (2004), if efforts are complementary in this way, one Nash equilibrium of the game is that both players exert zero effort (that is, if a player is expecting his partner to exert zero effort, his own best-response is also to exert zero effort). As is standard, we ignore this dismal equilibrium in our analysis, and derive the equilibrium that involves positive effort.

15

Date 3: (Value-creating Effort Level Stage II: B mitigates political risk): If the venture has succeeded at date 2, then, at date 3, the bank decides whether to exert effort to mitigate political risk23. Note that our timeline is formulated such that the B can observe at this stage whether the venture has succeeded at the first, operational stage. The assumption here is that political risk mitigation is an ongoing factor that may affect the triad throughout its life24. Political risk is modelled as follows. If the bank is successful in mitigating this risk, then the triad keeps all of the income generated at the date 2 operational stage. If the bank is unsuccessful in mitigating this risk, then the tryad loses all of the income. The

probability of successful political risk-mitigation is ,Beq ψ= where Be represents the

bank’s political risk-mitigation efforts, and ψ represents the bank’s ability at

mitigating this risk. The bank faces a cost-of-effort of .2

Beβ

If the bank’s efforts are unsuccessful, the venture loses all of the income, and the game ends with all three players (the bank, the PE, and the E) getting zero income. If the bank’s efforts are successful, the venture keeps the income, and the game continues to date 4. Date 4: (Ex Post Conflict between E and PE): Given success at the date 2 operational stage, and success at the date 3 political risk mitigation stage (note that the

overall joint probability of this success is ),ipq such that the project achieves positive

income of ,R we enter the date 4 ex post conflict stage25,26. At the conflict stage, the

E and the PE either cooperate27, in which case, project income of R is retained, or they ‘defect’, in which case, empathy is destroyed, and the relationship is soured (a la Hart and Moore 2008, Hart 2009). This destroys some of the project income, such that

income becomes ,Rφ where 1<φ represents the ‘souring’ parameter. We analyse

this stage in more detail in section 4.1. Date 5: The players (B, PE and E) all receive their payoffs, and the game ends. In our analysis, we wish to consider both economic and behavioural factors affecting the bank’s selection of PE partner, and contracting and performance in the B/PE/E triad. In particular, we analyse positive (trust, empathy, fairness) and negative (relationship-souring) behavioral factors. We model this as follows. The players are

23 The development bank does not only exert effort in mitigating political risk, see section 3.2. In this paper, we focus on political risk mitigation. 24 In future extensions to the model, we could onsider simultaneous effort stages, so the bank cannot observe the

operational success or failure when making her own effort decision (and the PE and E cannot observe the political risk mitigation success), and a case where the bank moves first, so that the PE and E can observe the bank’s political risk-mitigation success. 25 For other models of expropriation in venture capital, see Ueda (2004), and Fairchild (2011). 26 Of course, if the venture fails, it provides zero income, and the stealing stage is irrelevant. 27 In section 5, we consider direct financing of the entrepreneur by the bank (without involving the PE-sector). In that case, this ex post conflict occurs between the entrepreneur and the bank.

16

not purely self-interested, but have some feelings/consideration for each others’ well-being/payoffs. We operationalise this in the model by attaching an empathy

parameter28 )1,0[∈θ to the other players’ payoffs. When ,0=θ we have the

standard, homo economicus model of pure self-interest. Increasing θ represents

increasing empathy. Note that θ is strictly less than unity. Players do not consider others’ payoffs as exactly equal to their own.

In our analysis, PE1 has higher ability than PE2, but PE2 has empathy )1,0(2 ∈θ for

E, while PE1 has zero empathy29, 01 =θ for E. In terms of developing countries, it

could be that PE1 is based in a different country/has a different cultural background compared to the E, while PE2 is in the same country/has the same cultural background/understanding of the E. This provides an interesting trade-off for the bank when selecting the PE, based on both economic and behavioral factors. Our model considers the following features of the triple-sided problem. First, involving the PE-sector is beneficial in creating value. Furthermore, it may create empathy between the PE and the E (as the PE may be culturally/geographically close to the E). On the down-side, it creates triple-sided moral hazard (in the form of triple-sided effort-shirking). Furthermore, effort incentives are further weakened, as the equity is now split between three players. We now proceed to analyse our first case, where the bank has zero value-creating

ability at the operation stage: .0=Bγ In this case, if the bank finances the E directly,

without involving the PE sector, the venture is doomed to failure, and, therefore, the venture value, and the player’s payoffs, collapse to zero. Therefore, as long as the bank is expecting positive payoff from involving the PE sector, it will choose to do

so. Therefore, in our first case, with ,0=Bγ we are considering triple-sided moral

hazard, where the bank must involve the PE-sector in financing the E. We solve the game by backward induction.

4.1: Ex post Conflict (Date 4)

We begin by solving the final stage of the game: the ex post conflict stage. We take as

given that the bank has chosen a particular iPE to provide finance to the E, and we

take as given that the project has succeeded, both at the operational and the political

risk mitigation-stage, providing income .0>R We base our analysis of the ex post conflict stage on Fairchild’s (2011) model30, as follows. The PE and the E decide simultaneously whether to cooperate or defect. If

28 Sally (2001) first developed the sympathy game. In his model, sympathy is derived endogenously as an equilibrium of the game. In our model , we simplify by taking empathy exogenously. 29 This approach to the problem (one player having higher ability: the other having higher empathy) is inspired by the approach of Fairchild (2011) who considers this in the context of VC versus angel-financing. 30 See section 3.1 of Fairchild (2011).

17

they cooperate, the project income of 0>R is retained, and the E and the PE obtain

their success cashflows of 3

R each. Furthermore, empathy is maintained, and

therefore, effectively, their payoffs become ).1(3

θ+R

If one player cooperates, but

the other defects, then empathy is destroyed. Furthermore, the player who choses to cooperate obtains a payoff of zero, while the player who defected obtains a payoff of

.Rµ If both players defect, then project income becomes ,RR <φ and they each

achieve a payoff of .3

Rφ

Since the players make their decision to cooperate or defect simultaneously, then (as in Fairchild 2011), this can be represented as the following normal form game (where the E chooses between strategy C or D down the side of the matrix, and the PE chooses between strategy C or D along the top of the matrix):

iPEE \ C D

C G1, G2 G3, G4

D G5, G6 G7, G8

We note that C represents ‘cooperation’, and D represents ‘defection’. (G1) – (G8) represent the ‘game payoffs’ from the four combinations of simultaneous strategies (the first payoff in each ‘cell’ belongs to the E, while the second payoff belongs to the PE). Hence, the payoffs are:

).1(3

iPEE

Ri

θ+=∏=∏ (G1, G2)

.,0 RiPEE µ=∏=∏ (G3, G4)

.0, =∏=∏iPEE Rµ (G5, G6)

.3

RiPEE

φ=∏=∏ (G7, G8)

Recall that PE2 has empathy )1,0(2 ∈θ for E, while PE1 has zero empathy, 01 =θ for

E. We assume the following:

.3

)1(3

2

RR

R>>+ µθ (A.1)

We solve for the Nash equilibrium of the conflict game by considering each player’s best responses to the other player’s strategy choices. Assumption A.1 ensures that, in

the 1\ PEE dyad (with zero empathy), (G4) > (G2), and (G5) > (G1): that is, if 1PE

18

is expecting the E to cooperate, 1PE ’s best response is to defect (and similarly, if E is

expecting 1PE to cooperate, E’s best response is to defect).

Furthermore, (G8) > (G6), and (G7) > (G3) for sure: if a player is expecting his partner to defect, his best response is also to defect.

Therefore, in the case of the 1\ PEE dyad, each player’s dominant strategy31 is to

defect. Therefore, in the 1\ PEE dyad, the equilibrium consists of both players

defecting, the relationship is soured, and they each achieve a payoff of .3

Rφ Since

,33

RR<

φ we note that this represents a prisoner’s dilemma, since they would have

both been better off cooperating.

In the case of the 2\ PEE dyad with empathy ,2θ assumption A.1 ensures that (G2) >

(G4), and (G1) > (G5): that is, if 1PE is expecting the E to cooperate, 2PE ’s best

response is also to cooperate (and similarly, if E is expecting 2PE to cooperate, E’s

best response is also to cooperate). However, it is still the case (as in the 1\ PEE

dyad) that (G8) > (G6), and (G7) > (G3) for sure: if a player is expecting his partner to defect, his best response is also to defect (since defection by at least one player destroys empathy, the payoffs, and the best responses, become the same as in the

1\ PEE dyad). Hence, in the case of the 2\ PEE dyad with empathy ,2θ we obtain

multiple equilibria (either both players cooperate, each achieving payoffs of

),1(3

2θ+R

or both players defect, each achieving payoffs of ).3

Rφ Following

Fairchild (2011), we assume that the players coordinate on the superior equilibrium (mutual cooperation). Hence, we are able to state the following: Proposition 1: Given assumption A:1, the equilibrium of the date 4 conflict game is

as follows:

a) In the 1\ PEE dyad, both players defect in equilibrium, due to low empathy

(low trust). The relationship is soured. Hence, they each achieve date 4

success payoffs of .3

Rφ

b) In the 2\ PEE dyad, both players coordinate on cooperation in

equilibrium, due to high empathy (high trust). Empathy is maintained. Hence,

they each achieve date 4 success payoffs of ).1(3

2θ+R

31 In game theory, a dominant strategy is such that it is a player’s best strategy, regardless of the strategy played by one’s opponent.

19

4.2: Bank’s effort stage (Date 3) We now move back to date 3 to consider the bank’s decision to exert effort to mitigate political risk. First, we take as given that the bank observes that the venture has succeeded at the operational stage. Furthermore, the bank correctly anticipates the E/PE behaviour at the forthcoming ex post conflict stage. The bank chooses its optimal effort level to maximize its expected payoff:

δβ +−=∏ 2

3BB e

rq (4)

Where },{ RRr φ∈ if the bank has chosen PE2 or PE1 respectively. Substituting for

,Beq ψ= into (4), and solving ,0/ =∂∏∂ BB e we obtain the bank’s optimal effort

level, and the success probability at the bank’s effort stage, in the cases of PE1 and

PE2. Furthermore, note that },0{ ∆∈δ from choosing PE1 or PE2 respectively. This

represents an emotional benefit (to be discussed further below). Proposition 2: The bank’s optimal political-risk mitigating effort level, and the success probability, is, respectively:

,6

*βψr

eB = ,6

*2

βψ r

q = (5)

Where },{ RRr φ∈ if the bank has chosen PE2 or PE1 respectively.

Therefore, the bank’s effort-level, and the success probability, is higher when the PE2

has been chosen than when PE1 has been chosen. This is because the bank correctly

anticipates that the PE2/E dyad is more trustworthy at the date 4 ex post conflict

stage.

4.3: E/PE effort stage.

Now we move back to solve for the date 2 E/PE effort stage, given that the bank has

chosen .iPE

If E has matched with 2PE , then they correctly anticipate a) no conflict at date 4, and

b) high political risk-mitigation by the bank at date 3, and therefore empathy is maintained throughout. Therefore, the E and PE2 choose date 2 effort levels to maximise the following payoffs:

22

1

2 )1()(3

EEPEE eeeR

q βθγ −+=∏ (6)

20

22

1

2 22)1()(

3PEEPEPE eee

Rq βθγ −+=∏ (7)

Where (from proposition 2), .6

*2

βψ R

q =

If E has matched with PE1, the players correctly anticipate a) ex post conflict at date 4, b) low political risk-mitigation by the bank, and therefore empathy is destroyed. Therefore, E and PE1 choose effort levels to maximise the following payoffs:

22

1

1 )(3

EEPEE eeeR

q βγφ

−=∏ (8)

22

1

1 22)(

3PEEPEPE eee

Rq βγφ

−=∏ (9)

Where (from proposition 2), .6

*2

βφψ R

q =

In both cases (E and PE1, or E and PE2) we derive the E’s and PE’s optimal effort

levels by solving ,0=∂

∏∂

E

E

e 0=∂

∏∂

i

i

PE

PE

e (using equations 6 – 9).

We then substitute into 2

1

)( PEEi eep γ= in order to obtain the operational success

probability at the first effort stage. Next, we substitute into pq (given equilibrium q

from proposition 2) to obtain the overall, joint probability of success from the two effort stages, viewed from the beginning of the game. We thus obtain the following: Proposition 3: The PE’s and the E’s optimal date 2 effort levels, and success

probabilities, are as follows:

a) If B has chosen 2PE to partner E, there is high date 3 political risk mitigation

by the bank, and there is no ex post (date 4) conflict between 2PE and E .

Hence, the optimal date 2 effort levels, date 2 success probability, and overall

(joint date 2 and date 3) success probabilities, are:

.72

)1(

12

)1(**

2

2

2

2

2

2 βθγψ

βθγ +

=+

==RRq

ee PEE

21

2

22

2

2

2

1

2272

)1(*)*(*

βθγψ

γ+

==R

eep PEE

.432

)1(**

3

32

2

4

βθγψ +

=R

pq

b) If B has chosen 1PE to partner E, there is low date 3 political risk mitigation

by the bank, and there is ex post (date 4) conflict between 2PE and E. Hence,

the optimal date 2 effort levels, date 2 success probability, and overall (joint

date 2 and date 3) success probabilities are:

2

22

1

2

11

7212**

βφγψ

βφγ RRq

ee PEE ===

2

222

1

2

2

1

1172

*)*(*βφγψ

γR

eep PEE ==

.432

**3

332

1

4

βφγψ R

pq =

We observe the following: The E and the PE’s optimal effort levels at the date 3 operational stage are a)

increasing in the PE/E synergy level ,iγ b) increasing in the empathy parameter (in

the case of PE2), and decreasing in the souring parameter (in the case of PE1): we term these the direct effects on the PE/E effort levels. When they have higher synergistic ability, they work harder. When they like each other (empathy), they work harder for each other. When they dislike each other (souring), they work less. Proposition 4 also demonstrates ‘indirect’ effects (as the PE and the E anticipate the bank’s future (date 3) political risk mitigation efforts, which, in turn, are affected by the bank’s anticipation of the date 4 ex post conflict between the PED and the E. Hence, the date 2 operational effort levels of the PE and the E are increasing in the

anticipated date 4 political risk-mitigation efforts of the bank )(q . Therefore, the

bank’s political risk-mitigation ability, and the souring parameter, are ‘magnified’ ie, they are squared. This reflects the triple-sided moral hazard problem, as actions at date 3 and 4 ‘come in twice’ at date 2.

4.4 Bank’s choice of PE firm.

Finally, we move back to solve for the banks’ choice of PE-firm, and we consider the effect on enterprise value. In order to analyse this, we substitute the optimal effort levels, and success probability, from proposition 3, into the expressions for venture value, and the bank’s payoff, to obtain the following:

22

Proposition 4: The effect of the bank’s choice of PE on expected venture value, and the bank’s expected payoff, is as follows:

a) If B has chosen 2PE to partner E, there is high date 3 political risk mitigation

by the bank, and there is no ex post (date 4) conflict. Hence, equilibrium

venture value, and equilibrium payoffs are:

.432

)1(3

42

2

4

βθγψ +

==R

qpRV

.2592

)1(

3*

3

42

2

42 ∆+

+=∆+−=∏

βθγψ

βR

epV

BB

b) If B has chosen 1PE to partner E, there is low date 3 political risk mitigation

by the bank, and there is ex post (date 4) conflict. Hence, equilibrium venture

value, and equilibrium payoffs are:

.432 3

442

1

4

βφγψ

φR

RqpV ==

.2592

*3

442

2

4

βφγψ R

B =∏

In making its choice, the bank simply compares its payoffs in propositions 4a) and 4b). Furthermore, we consider the effect on firm value by comparing firm values in

proposition 4a) and 4b). We define a critical level of empathy ,'θ such that firm

values )()( 21 PEVPEV = are equated. We also define a critical level of empathy ''θ

where the bank’s payoffs are equalised under the two PEs. We note the inclusion of the parameter ∆ in the bank’s payoff in 4a). The idea here is that, when considering the behavioural factors involved in choosing PE2 (empathy, trust), the bank may take a ‘detached’ view, considering the effect of the amenability of the PE-team on their relationships with the E, and how this may affect value creation between the E and the PE. However, when considering behavioural factors, the bank itself may become “attached” to the PE-team, which may cloud judgement.

It is interesting to note that (when ).0=∆

23

.1'''2

2

42

1 −==γ

φγθθ (10)

Therefore:

a) )()( 21 PEVPEV > and )()( 21 PEPE BB ∏>∏ when ).''',0[ θθθ =∈

b) )()( 12 PEVPEV > and )()( 12 PEPE BB ∏>∏ when '.'' θθθ =>

Therefore, we are able to state our first main result as follows:

Proposition 5: When the DB is emotionally-detached ),0( =∆ such that ,''' θθ = the

effect of PE/E empathy on the bank’s choice of PE firm, and the effect on venture-

value, is as follows :

a) If empathy between 2PE and E is low: ],''',0[ θθθ =∈ then the bank will

choose 1PE (due to economic factors/ability):

).,*(),*( 21 PEBPEB BB ∏≥∏ This is the value-maximising choice:

).,(*),(* 2010 PEBVPEBV ≥

b) If empathy between 2PE and E is high: ,''' θθθ => the bank switches to

2PE : ).,*(),*( 12 PEBPEB BB ∏≥∏ This is the value-maximising choice:

).,(*),(* 1020 PEBVPEBV ≥

Note that the effects of the choice of PE on venture value is affected by economic (PE ability) and behavioural factors (empathy/trustworthiness). In proposition 4a), empathy/trust is so low that the economic factor (PE ability) dominates. In 4b), empathy is sufficiently high that behavioural factors dominate, both by inducing the bank to choose the PE2, and in determining that PE2 provides higher value than PE1 (in this case, the higher empathy/trustworthiness more than compensates for the lower ability). Note that when the DB is detached, her decision-making is aligned with value-maximisation.

Next, consider the case where the bank becomes emotionally attached to PE2 ).0( >∆

This implies that '.'' θθ > Hence, we are able to state our second main result:

Proposition 6: When the DB is emotionally-attached to PE2 ),0( >∆ such that

,''' θθ > the effect of PE/E empathy on the bank’s choice of PE firm, and the effect on

venture-value, is as follows :

a) If empathy between 2PE and E is low: ],'',0[ θθ ∈ then the bank will choose

1PE (due to economic factors/ability): ).,*(),*( 21 PEBPEB BB ∏≥∏ This is

the value-maximising choice: ).,(*),(* 2010 PEBVPEBV ≥

24

b) If empathy between 2PE and E is medium: ],'','[ θθθ ∈ then the bank

switches to 2PE : ).,*(),*( 12 PEBPEB BB ∏≥∏ However, this is the value-

minimising choice: ).,(*),(* 1020 PEBVPEBV <

c) If empathy between 2PE and E is high: ,''' θθθ => the bank continues to

choose to 2PE : ).,*(),*( 12 PEBPEB BB ∏≥∏ This is the value-maximising

choice: ).,(*),(* 1020 PEBVPEBV ≥

Note the contrast between propositions 5 and 6. When the bank becomes

emotionally attached to PE2, we obtain an inefficient empathy-interval ],'','[ θθθ ∈

where the bank switches to PE2, but this does not maximise venture value. 4.5: Numerical Example

In order to analyse our results in propositions 5 and 6, we consider the following numerical example:

,300=R ,4=ψ ,5.0=φ ,1000=β ,101 =γ .22 =γ ,01 =θ ].1,0[2 ∈θ .0≥B

Solving (using excel)32, we obtain the following chart:

Bank's choice of PE and effect on venture value

0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

40.00

45.00

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Empathy

Bank's payoff/venture value

The diagram demonstrates the following (see proposition 5). The lower two lines are the bank’s expected payoffs under PE1 and PE2 (the horizontal line is the payoff under PE1: the upward sloping lie is the payoff under PE2: that is, the bank’s payoff under PE1 is unaffected by PE2’s empathy: in contrast, it is increasing in empathy under PE2).

32 The excel spreadsheet, showing these detailed calculations, is available on request form the authors.

25

The upper lines represent the expected venture value under PE1 and PE2 (again the horizontal line is venture value). As noted above, the bank’s decision-making is aligned with economic value-maximisation, when the bank considers both economic and behavioural factors in a detached way.

Next, we allow the bank to become ‘emotionally’ involved: .0>∆ (we focus on

).5.0=∆ Examining the payoffs in proposition 4a), this will shift the bank’s payoff

upwards, as follows:

Bank's choice of PE and effect on venture value

0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

40.00

45.00

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Empathy

Bank's payoff/venture value

As noted in proposition 6, when the bank becomes ‘emotionally’ involved, the payoff under PE2 shifts upwards, and the critical empathy level shifts to the left. Now, there is an inefficient interval, where the bank chooses PE2 but PE1 maximises value. This provides an insightful policy implication for DBs when assessing PE-teams: behavioural factors are important, but the bank needs to be careful not to ‘overplay’ them.

5. Bank can finance E directly.

Thus far, we have considered the case where :0=Bγ therefore, due to lack of

synergistic ability, the bank chose to involve the PE-sector in investing in an entrepreneur. However, according to Settel et al (2009), “Some MDFIs prefer to make direct equity investments rather than investments in private equity funds. This approach eliminates the layer of fees paid to external fund managers, but it requires

26

that the MDFI have a much larger and experienced investment staff as well as a higher risk appetite33.” We consider this in this section, by considering the case where the bank has some synergistic ability, which may, or may not be, greater than that of the PE-sector34. Now the bank chooses between financing the E directly (double-sided moral hazard) or involving the PE-sector (triple-sided moral hazard). In making its choice, we note the following interesting trade-offs for the bank (embodied in Settel’s quote above). First, by involving the PE-sector, the value-creating ability of the triad is high, but the B must share the cashflows between two other players (the PE and the E). Further, if the B has chosen PE2, empathy between the PE and the E mitigates moral hazard (that is, it enhances trust, eliminates the ex post conflict, and improves effort). If the B finances directly, the cashflows are shared between two players (rather than three) but the bank has lower value-creating ability.

Furthermore, there is no empathy between B and E: that is, .0=Bθ

As previously, we solve backwards. Firstly, we take as given that the bank has chosen to finance the entrepreneur directly at date 1, and we take as given that the date 2 operational and date 3 political risk-mitigation stages have occurred successfully, so

that the project provides income of .0>R First, we consider the ex post date 4 conflict stage. When the bank finances the E directly, we consider conflict between the bank and the E (in contrast to that between the E and the PE in the previous case). We now note two main differences compared to our previous analysis (when the bank financed the E through the PE-sector). Now, the success income is shared between two players (the bank and the E) rather then three. Furthermore, there is zero empathy between the bank and the E. We make the following assumption:

.2

RR >µ (A.2)

Given this assumption (and reproducing the analysis in section 4.1), it is easy to observe that each player’s (the E and the B’s) dominant strategy is defection. Hence, we are able to state the following result: Proposition 7: When the B finances E directly, then, due to lack of empathy/trust,

there is ex post conflict in the case of success. Therefore, the bank and the E each

obtain a payoff .2/Rφ

33 In addition to requiring higher ability when investing directly, Settel et al (2009) note that by investing directly, DBs may lose on the following; “relationships with fund managers can generate many co-investment opportunities that the MDFI may not otherwise have access to.” We do not model this here, but leave it for future research. However, intuitively, we note that, if we included this factor into our model, it would weaken the bank’s incentives to invest directly, thereby strengthening its incentives to involve the PE-sector. 34 In our numerical example, the bank has higher (lower) synergistic ability than PE2 (PE1).

27

Hence, we note the first ‘down-side’ for the bank choosing to finance E directly. There is a lack of empathy/trust35 between the B and the E, which results in ex post conflict. We now move back to date 3 to solve for the bank’s political risk-mitigation efforts. The bank correctly anticipates ex post conflict. Therefore, given the success payoff in proposition 7, it chooses its political-risk mitigating effort to maximise

2

2BB e

Rq βφ

−=∏ (12)

Solving ,0=∂

∏∂

B

B

e we obtain the following result:

Proposition 8: When the bank finances E directly, the bank’s optimal date 3 political-risk mitigating effort level, and the success probability, is, respectively:

βψφ4

*R

eB = , βφψ

4*

2 Rq = (13)

In section 5.1, we compare these results with those under TSMH. . Next, we move back to the date 2 operational stage to derive the B’s and the E’s optimal effort levels. When the bank finances the E directly, the players optimise

,)(2

22

1

EBEBE eeeR

q βγφ

−=∏ (14)

,)(2

222

1

BBBEBB peaeeR

q −−=∏ βγφ

(15)

Where Ba is the bank’s operational effort, and Be is, as already noted, the bank’s

subsequent political risk mitigation effort. Hence, the last term is the bank’s expected cost at the political risk mitigation stage, looking forward from the operational stage

(since there is a probability p that we will reach the political risk mitigation stage).

35 Intuitively, PE2 has an advantage over the bank, in that the PE2 is geographically and culturally close to the E, which creates empathy, while the DB is “far and distant.”

28

Solving ,0=∂

∏∂

E

E

e ,0=∂

∏∂

B

B

e, we obtain the following results:

Proposition 9: When the bank finances the E directly, the optimal date 3 effort levels,

success probabilities, and the expected value is as follows:

2

222

328**

βψφγ

βφγ RRq

ae BBBE === (16)

2

2222

32βψφγ R

p B= (17)

3

4332

128βψφγ R

pq B= (18)

3

4442

128βψφγ

φR

RpqV B== (19)

Therefore, payoffs are as follows:

.1024

33

4442

βψφγ RB

E =∏ (20)

.1024 3

4442

βψφγ RB

B =∏ (21)

In section 5.1, we compare these results with those under TSMH. 5.1: Triple-sided versus double-sided moral hazard

In this section, we compare the key results in our triple-sided (indirect financing) and double-sided (direct financing) moral hazard cases. The following table compares the players’ optimal effort levels, the venture values, and the players’ payoffs in the two cases (note that DF is an abbreviation for ‘direct-financing’).

29

Variable Ratio

DFPE1 Ratio

DFPE2

Bank’s political risk efforts TSMH/DSMH

3

2

)(*

)(* 1 =DFe

PEe

B

B φ32

)(*

)(* 2 =DFe

PEe

B

B

Bank’s operational effort/PE effort36

BB DFa

PEe

γγ 121 )

3

2(

)(*

)(*=

BB DFa

PEe

γγ

φ222 )

3

2(

)(*

)(*=

Ratio of venture values

BDFV

PEV

γγ 131 )

3

2(

)(*

)(*=

BDFV

PEV

γγ

φ232 )

3

2(

)(*

)(*=

Ratio of Payoffs

BB

B

DF

PE

γγ 141 )

3

2(

)(

)(=

∏

∏

BB

B

DF

PE

γγ

φ242 )

3

2(

)(

)(=

∏

∏

First, we note that the 2/3 ratio (raised to various powers) appears throughout the table. This reflects the effect of the equity-stakes in the triple-sided (the bank shares its equity three ways: with the E and the PE) compared with the double-sided moral hazard case (where the bank only shares the equity with one other party: the E). Hence, the bank exerts less effort when involving the PE-sector than when financing directly. That is, the bank’s effort incentives are weakened when it shares the equity with the PE-sector (as noted above, Settel argues that by financing directly, the bank avoids a layer of fees to the PE-sector). Reading down the table, we note that this equity-dilution-effect is amplified as we consider the bank’s optimal operational effort, the venture value, and the ratio of payoffs. We also note that the ratios are affected by the PE’s and B’s relative abilities. Reading across the table, we note that the souring parameter has an effect when

comparing financing through 2PE compared to direct financing (this reflects the

comparison between lack of trust/empathy in the direct financing case and

trust/empathy when involving 2PE ).

5.2 Bank’s date 1 decision

Finally, we move back to date 1 to consider the bank’s decision to finance the E directly or to finance through the PE-sector. In doing so, we make reference to

diagram 2, where we consider }.7.5,5{∈Bγ

Our focus is on the effect of the relative abilities of the bank and the PE-sector, and

the empathy level under 2PE , on a) the bank’s decision (to finance through the PE-

sector or to finance directly), and b) venture value.

36 Note that, in our previous TSMH case, the bank had no synergistic ability at the operational stage, and so did not exert effort at that stage. Instead, the effort was exerted by the PE (and, of course, the E). In our DSMH case, where the bank finances the E directly, the bank exerts effort at the operational stage. Hence, here we compare the banks’ operational effort in the DSMH case with the PE’s operational effort in the TSMH case.

30

In order to consider the effect of relative abilities, we define four critical values for

relative ability. The first critical value ,'2

1

2

γ

γ B is such that ).,(),( 1PEBEB BB ∏=∏

Therefore,

4

2

1

2

)3

2('=

γ

γ B (22)

The second critical value, ''2

2

2

γ

γ B , is such that ).,(),( 2PEBEB BB ∏=∏ Therefore,

4

4

2

2

2)1(

)3

2(''

φθ

γ

γ +=

B . (23)

The third critical value, ,'''2

1

2

γ

γ B is such that ).,(),( 1PEBVEBV = Therefore,

.)3

2(''' 3

2

1

2

=

γ

γ B (24)

Finally, the fourth critical value, ,2

2

2IV

B

γ

γ is such that ).,(),( 2PEBVEBV =

Therefore,

4

3

2

2

2)1(

)3

2(

φθ

γ

γ +=

IV

B . (25)

Comparing (22) – (25), we note two possible cases:

a) .''''''2

1

2

2

1

2

2

1

2

2

1

2IV

BBBB

<

<

<

γ

γ

γ

γ

γ

γ

γ

γ

b) .''''''2

1

2

2

1

2

2

1

2

2

1

2IV

BBBB

<

<

<

γ

γ

γ

γ

γ

γ

γ

γ We consider both cases.

Hence, we are able to state the following:

31

Proposition 10: The effect of the bank’s/PE-sector’s relative operational ability, and

PE2/E empathy, on the bank’s financing choice and venture value:

i) If ],''',0[ θθθ =∈ the bank will not finance through PE2, and thus chooses between

financing through PE1 and financing directly:

a) If ,'2

1

2

2

1

2

<

γ

γ

γ

γ BB the bank finances through PE1. This achieves the first best

venture value.

b) If ,''''2

1

2

2

1

2

2

1

2

<<

γ

γ

γ

γ

γ

γ BBB the bank continues to finance through PE1. This

achieves second-best value. First-best value would have been achieved by

financing directly.

c) If ,'''2

1

2

2

1

2

γ

γ

γ

γ BB <

the bank finances directly, and this achieves first-best

value.

ii) If ,''' θθθ => the bank will not finance through PE1, and thus chooses between

financing through PE2 and financing directly:

a) If ,''2

1

2

2

1

2

<

γ

γ

γ

γ BB the bank finances through PE2. This achieves the first-best

value.

b) If ,'''''2

1

2

2

1

2

2

1

2

<<

γ

γ

γ

γ

γ

γ BBB the bank will finance directly. This achieves the

second-best value.

If ,'''2

1

2

2

1

2

γ

γ

γ

γ BB <

the bank will finance directly. This achieves the first-best value.

Proof:

In proposition 10: i), we consider the case of low PE2-empathy: ].''',0[ θθθ =∈

From proposition 5 (and diagram 1), we note that the bank prefers to finance through PE1 compared to PE2. Therefore, for empathy in this interval, we only need to compare the bank’s choice between PE1 and financing directly. Consideration of the relative ability parameters in (22) and (24) provides the results in 9: i) a) – c).

In proposition 9: ii), we consider the case of high PE2-empathy: '.'' θθθ => From proposition 5 (and diagram 1), we note that the bank prefers to finance through PE2 compared to PE1. Therefore, for empathy in this interval, we only need to compare

32

the bank’s choice between PE2 and financing directly. Consideration of the relative ability parameters in (23) and (25) provides the results in 9: ii) a) – c). We clarify these results by referenced to the following diagram. In this diagram, we take our previous numerical example (and diagram 1), and we incorporate the bank’s

choice to finance directly37, with }.7.5,5{∈Bγ Note that, given our previous

numerical values, it is the case that 12 γγγ << B for both of the numerical values that

we consider for the bank’s operational ability. That is, in our numerical example, the bank has higher value-creating ability than PE238, but lower than PE1.

Bank's choice of PE and effect on venture value

0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

40.00

45.00

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Empathy

Bank's payoff/venture value

37 See footnote 25. 38 Given this feature of the relative abilities between PE2 and the bank, the question may arise, why would the bank ever choose to finance through PE2? The answer is that, the PE2 is able to create empathy/trust with the E, which is value-enhancing.

33

The thin lines are reproduced from diagram 1 (the TSMH case). The thick solid lines represent the B’s payoff, and the dashed solid lines represent the venture value, under direct financing, with the lower thick lines representing the B’s payoff/venture value

when ,5=Bγ and the upper thick lines represents B’s payoff/venture value when

.7.5=Bγ

We note the following (see proposition 10). When ],''',0[ θθθ =∈ then, for ,5=Bγ

the bank chooses to finance through PE1, and this provides the first-best value. When

the bank’s operational ability increases to .7.5=Bγ the bank continues to finance

through the PE1, but this provides second-best value. First-best value would have been achieved if the bank had financed directly39.

When ,''' θθθ => the bank finances through PE2. In our example, if empathy is less

than 0.7, then, when ,5=Bγ the bank finances through PE2, and this provides first-

best value. When the bank’s ability increases to ,7.5=Bγ the bank continues to

finance through PE2, but this gives second-best value. First-best venture value would be achieved if the bank financed directly. Hence, an interesting result in this section is the following. There may be cases where the bank’s operational value-adding abilities would suggest that direct financing is first-best, but the bank still prefers to finance through the PE-sector. This is because a) the bank only obtains part of the equity of the venture, and b) the bank has to exert effort when financing directly. 6. Policy implications We have considered a development bank’s decision to finance an entrepreneurial venture in an emerging economy, either financing through the entrepreneur’s local private-equity sector, or financing the entrepreneur directly. In our first case, the bank has no value-creating ability at the operational stage (although it has political risk-mitigating ability). The bank’s focus in this case is on the characteristics of the private equity managers. The bank considers the PE-manager’s economic (value-creating abilities) and behavioural characteristics (whether the manager can create empathetic and trusting relationships with the E). The bank may choose the lower-ability PE-manager if his behavioural characteristics are higher. Furthermore, we have demonstrated that, in considering the behavioural characteristics, the bank must attempt to remain objective in its decision-making. If the bank becomes ‘too attached’ to the PE-manager, it may make an inefficient decision. In the second case, the bank is able to add value at the operational stage. Now the bank chooses between financing through the PE-sector or financing the E directly. In this case, we have a comparison between a triple-sided and double-sided moral hazard problem. When financing through the PE-sector, the bank must share the equity with two other players (the PE-manager and the E). When financing directly, the bank avoids paying a layer of fees and profit share to the PE-manager. On the other hand,

39 Of course (not shown on the diagram), if the bank’s ability continues to increase, then, at the critical value, the bank switches to financing directly.

34

the bank needs to be sufficiently skilled to make direct investment worthwhile. Furthermore, by investing directly, the bank may lose the behavioural benefits provided by a PE-sector that can build empathetic and trusting relationships with its local entrepreneurs. De Bettignies and Brander (2007) and Fairchild (2011) emphasise that we can consider these models at a positive (descriptive) or a normative (prescriptive) level. The positive approach attempts to use the model to explain real-world observed phenomena. Thus, on a positive level, our model would explain the development bank’s real-world approach to choosing how to finance entrepreneurs in emerging economies. It would suggest that, when appraising potential PE-managers, these banks carry out a rational calculus of their economic abilities and behavioural characteristics, and arrive at an optimal decision particuarly in complex economic and political environments where cultural and linguistic attributes can have a material impact on the ability of a fund manager to source, execute and help build successful companies. The model would suggest that banks do not always choose the highest-ability entrepreneurs, but also consider whether they can ‘work with’ these PE-managers, and, more importantly, whether these PE-mangers can build good, empathetic working relationships with entrepreneurs, hence developing empathy and trust. Further, our model explains at a positive level, how these banks make the decision whether to finance development entrepreneurs directly. The observation that most development bank financing occurs through the PE-sector suggests that rational banks recognise that the PE-sector has superior operational value-creating skills. On the other hand, behavioural economists recognise that agents are not fully rational, and that, in the real world, they do not always make the optimal decisions suggested by the economic models. Indeed, according to Settel et al (2009), “given that transparency is one of the major issues facing emerging countries, one of the challenges for the multilateral development finance institutions is how to assess the trustworthiness of the parties with which they wish to work.” Now, the model can be considered at the normative (prescriptive) level. Development banks can use the model to understand that both economic and behavioural factors are important when considering which private-equity teams to involve in financing development entrepreneurs. This knowledge may help to improve the bank’s decision-making process, hence enhancing value-creation and impact in the developing economies40. Furthermore, PE-managers may use the model to understand that they need to work on both their economic (ability) and behavioural (human) skills when ‘pitching’ to development banks. At the same time, entrepreneurs can use the model to understand the importance of building trust and empathy with the PE-manager.

40 Indeed, in a practitioner paper, Botelho and Harper (2008) discuss how institutions should formalise their approach to considering both economic and behavioural factors when choosing PE-fund investments. They state that “Most private equity fund investors spend half of their diligence time assessing sponsors’ teams .. yet… limited partners view ‘people mistakes’ as the main cause of underperforming funds …. People mistakes are largely driven by lack of structure and over-reliance on gut feel.”

35

An additional implication is that our model may help DBs to better understand the factors relevant to portfolio management resource allocation issues. It may help DBs assess whether it is better to monitor and manage their PE-relationships and entrepreneurial relationships locally (through a local office and/or with local staff) where they may be able to better develop empathetic relationships, or remotely (e.g. through New York/London or perhaps even from regional centres) where investment decisions may be more objectively assessed based on economic abilities. The balance to be drawn will clearly lay between building value through empathy and between managing risks whereby excessive local empathy results in a critical loss of DB objectivity.

6. Conclusion.

We have developed a behavioral game-theoretic analysis to consider a development bank’s (DB’s) investment decision (whether to invest directly or through a local PE-fund) when investing into entrepreneurial ventures in emerging economies. If the DB decides to invest through the PE-sector, then it must decide which PE to invest with. In doing so, the DB considers two dimensions: economic (what are the value-adding capabilities of the PE manager?) and behavioral (will the PE manager be able to develop an empathetic and trusting relationship with its entrepreneur to enable the manager to access the best investment opportunities and build value collaboratively?) In addition to considering both economic and behavioral factors, an important aspect of our model is that we compare triple-sided (when the bank involves the PE-sector) and double-sided moral hazard problems (when the bank invest directly). Our analysis forms the basis for future research into development banks’ investment choices. Firstly, in terms of theoretical development, we have only considered the DB’s choice of financier. It would be useful to develop the model to consider the PE’s choice of entrepreneur, and also the entrepreneur’ choice of PE or the effects of “excess empathy” between the PE and entrepreneur. As the permutations increase, the model could become very rich. Second, we have taken the allocation of the cashflows to the parties as exogenously given (equal equity-stakes). For future research, it is desirable to develop a model that incorporates bargaining over the cashflows. Third, we have focused on the parties’ cashflow rights. An important step is to extend the analysis to include control rights. Fourth, we could extend the behavioural analysis to consider other aspects, such as negative reciprocity/retaliation. Fifth, we could extend the analysis to explicitly consider the effects of market and institutional development in emerging markets. Sixth, we have focused on moral hazard problems. We should develop our analysis to consider the effect of asymmetric information and adverse selection. This is particularly relevant to emerging economies, where entrepreneurial lack of track record and reputation is a key issue. Finally, at the empirical level, we need to be able to access data such that we can test the importance of economic and behavioral factors on the DB’s decision, and on the resulting performance of the entrepreneurial venture.

36

Overall, our analysis should provide a framework for scholars to analyse the complex economic and behavioral factors affecting the performance of development bank/private equity backed entrepreneurial ventures in emerging economies.

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