Islamic profit and loss sharing contracting versus regular equity in entrepreneurial finance: Risk sharing and managerial incentives

Hadizada, Abdulali; Nippel, Peter Article Islamic profit and loss sharing contracting versus regular equity in entrepreneurial finance: Risk sharing and managerial incentives The Journal of Entrepreneurial Finance (JEF) Provided in Cooperation with: The Academy of Entrepreneurial Finance (AEF), Los Angeles, CA, USA Suggested Citation: Hadizada, Abdulali; Nippel, Peter (2022) : Islamic profit and loss sharing contracting versus regular equity in entrepreneurial finance: Risk sharing and managerial incentives, The Journal of Entrepreneurial Finance (JEF), ISSN 2373-1761, Pepperdine University, Graziadio School of Business and Management and The Academy of Entrepreneurial Finance (AEF), Malibu, CA and Los Angeles, CA, Vol. 24, Iss. 2, pp. 209-247, https://doi.org/10.57229/2373-1761.1449 This Version is available at: https://hdl.handle.net/10419/306241 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc/4.0/ The Journal of Entrepreneurial Finance The Journal of Entrepreneurial Finance Volume 24 Issue 2 Winter 2022, Issue 2 Article 9 2022 Islamic Profit and Loss Sharing Contracting versus Regular Equity Islamic Profit and Loss Sharing Contracting versus Regular Equity in Entrepreneurial Finance: Risk Sharing and Managerial in Entrepreneurial Finance: Risk Sharing and Managerial Incentives Incentives Abdulali Hadizada University of Kiel Peter Nippel University of Kiel Follow this and additional works at: https://digitalcommons.pepperdine.edu/jef Part of the Corporate Finance Commons, Entrepreneurial and Small Business Operations Commons, and the Finance and Financial Management Commons Recommended Citation Recommended Citation Hadizada, Abdulali and Nippel, Peter (2022) "Islamic Profit and Loss Sharing Contracting versus Regular Equity in Entrepreneurial Finance: Risk Sharing and Managerial Incentives," The Journal of Entrepreneurial Finance : Vol. 24: Iss. 2, pp. 209-247. DOI: https://doi.org/10.57229/2373-1761.1449 Available at: https://digitalcommons.pepperdine.edu/jef/vol24/iss2/9 This Article is brought to you for free and open access by the Graziadio School of Business and Management at Pepperdine Digital Commons. It has been accepted for inclusion in The Journal of Entrepreneurial Finance by an authorized editor of Pepperdine Digital Commons. For more information, please contact bailey[email protected]. Islamic Profit and Loss Sharing Contracting versus Regular Equity in Entrepreneurial Finance: Risk Sharing and Managerial Incentives Abdulali Hadizada Christian-Albrecht University of Kiel, Kiel, Germany [email protected] Peter Nippel Christian-Albrecht University of Kiel, Kiel, Germany [email protected] Abstract: An entrepreneur shares business risk with the investors providing capital for her firm. Risk sharing is per se beneficial, but also results in an agency problem from diminished incentives for the entrepreneur. This classical trade-off depends on the financial contracting between the entrepreneur and the financier. As an alternative to debt or equity, we consider musharaka financing, an Islamic profit and loss sharing contract. First, we show that debt is inferior to equity or musharaka even though debt financing ensures first best efforts in our model. Whether financing with equity or by use of musharaka results in higher utility for the entrepreneur depends on how the firm’s risks are related and on the structure of the costs the entrepreneur has to bear when extending effort. Keywords: Entrepreneurial finance; Islamic finance; Equity; Musharaka; Partnership; Profit and loss sharing; Risk sharing; Managerial incentives JEL Classification: D25; D81; D82; G32; L26 209 Hadizada and Nippel: Islamic PLS versus Equity: Risk Sharing and Managerial IncentivesPublished by Pepperdine Digital Commons, 2022 1. Introduction An entrepreneur needs capital and has to provide effort to advance the success of their business. Capital can be raised primarily as debt or equity, however, hybrid instruments might also be available. In this paper, we focus on a near-equity financial instrument known as musharaka in Islamic finance. 1 A musharaka contract results in profit and loss sharing not unlike a partnership with an equity investor. Musharaka is, however, more similar to project financing in which the investor provides capital to be invested in some particular tangible assets or a joint venture (Jobst, 2017), and the profits and losses from this particular project are shared. In contrast, providing equity capital results in co-ownership of the entire business, and the equity holders share all profits or losses and any increase or decrease in total value of the firm. Therefore, musharaka and equity financing differ with respect to risk sharing and result in different incentives for the entrepreneur. We compare the alternative financial contracts in an agency-theoretic model with risk sharing and managerial incentives for the entrepreneur as the main determinants of the entrepreneur’s utility. We start with debt financing and then consider musharaka and equity financing from the perspective of an entrepreneur in a principal-agent relationship. In our model, although (risk-free) debt financing results in first best effort of the entrepreneur, this alternative of raising capital turns out to be always inferior to musharaka and equity financing; with debt financing, the entrepreneur foregoes the benefits of risk sharing, which cannot be compensated for by the effect of higher incentives. The direct comparison of musharaka and equity financing reveals no definite ranking. Which of the alternative financial instruments results in higher utility for the entrepreneur depends on the structure of the risks from the entrepreneurial business and on the structure of the costs the entrepreneur has to bear when spending effort. The partial profit and loss sharing via musharaka financing, that is, the sharing of profits and losses arising not from the whole business, but from a particular project or certain assets only, results in suboptimal risk sharing. On the other hand, musharaka comes with better incentives for the entrepreneur and results in a higher increase in expected firm value net of (private) costs under certain conditions. We consider this trade-off analytically and present a simple numerical example for illustration. The rest of this paper is structured as follows. In the next section, we provide a short introduction into Islamic (corporate) finance and compare musharaka and equity financing with respect to contractual matters. Section 3 provides the review of the literature on agency relationships and risk sharing pertaining to Islamic mode of 1 Prohibition of activities deemed sinful by Islam governs Islamic banking and finance. From a financial perspective, such prohibitions apply to interest, speculation, excessive uncertainty, and short selling (Iqbal and Mirakhor, 2011). 210The Journal of Entrepreneurial Finance, Vol. 24, Iss. 2 [2022], Art. 9 https://digitalcommons.pepperdine.edu/jef/vol24/iss2/9 DOI: 10.57229/2373-1761.1449 financing. In section 4, we present the theoretical model used for our analyses. Section 5 explores debt financing in this theoretical framework while musharaka financing is analyzed and compared to debt in section 6. In section 7, we apply our model to equity financing. We then compare equity with musharaka in section 8. The insights of this theoretical comparison are illustrated by means of a numerical analysis in section 9. Section 10 provides concluding remarks. 2. Profit and Loss Sharing in Islamic Finance Islamic methods of financing include “synthetic loans”, lease contracts, and profit sharing contracts (Jobst, 2017). The profit sharing contracts adhere the most to the three principles underlying Islamic finance: principle of equity (wealth distribution), principle of participation (risk sharing), and principle of ownership (asset-based financing) (Hussain et al., 2015). Two types of profit sharing contracts are “profit sharing and loss bearing” mudaraba contracts and “profit and loss sharing” (PLS) musharaka contracts (Hussain et al., 2015). In a mudaraba transaction, an investor provides capital for a project or an investment whereas an entrepreneur plays the role of a manager. The investor is not entitled to take part in the management process, and the profits generated from the investment are distributed between the investor and the entrepreneur based on a preagreed ratio while only the investor bears any losses unless they result from the negligence of the entrepreneur (Jobst, 2017). Mudaraba financing is used mostly by banks, where the bank can act both as an investor (on the assets side) and as an entrepreneur (on the liabilities side). Musharaka can be defined as “an equity partnership agreement with one or more partners to jointly finance an investment project” (Jobst, 2017). In a musharaka transaction, both the investor and the entrepreneur provide capital to finance a project or an investment. Musharaka financing can be used for corporate financing by non-financial companies, and it is a preferred way of Islamic financing due to its features of profit-and-loss and risk sharing. Profit and loss sharing with a musharaka contract is between an entrepreneur starting or managing a small or medium-sized business and an investor/partner as a financier, who is not necessarily a bank. Financing with regular equity, as well as by means of a musharaka contract, results in a partnership relationship between an entrepreneur and investor(s) (for musharaka as partnership, see, e.g., Usmani (1999), Mirakhor and Zaidi (2007), or Jobst (2017)). One of the parties to the partnership, the entrepreneur, is running a business or planning to start one. The other party invests in the business and shares profits and losses. With regular equity, the investment is open-ended, and all the partners hold a share in the whole business and participate in the firm’s profits and the increase (or decrease) in its value. Unlike equity, musharaka contracts are not 211 Hadizada and Nippel: Islamic PLS versus Equity: Risk Sharing and Managerial IncentivesPublished by Pepperdine Digital Commons, 2022 necessarily open-ended or can be terminated by notice of one partner. However, if one of the partners wishes to terminate his/her participation, the remaining partners may buy him/her out of the partnership (Usmani, 1999). Both types of partnership entail the right, but not the obligation of the investor(s) to take part in the management process. The main difference between equity and musharaka financing is, or at least can be, in the extent of profit and loss sharing. Equity capital is used for financing the entire business of a firm, and each of the equity partners holds a share in the success of that business in total. On the other hand, musharaka financing can be used for financing a specific project or investment, fixed assets, real estate, commodities, working capital, or other tangible assets to be used in production or trade (see Usmani (1999), Habib (2018), Rahman et al. (2020)). Yildirim (2021) identifies musharaka as a project specific instrument that does not entitle the investors as the owners of the entire firm. Jobst (2017) considers a musharaka contract being similar to a joint venture. While a share in the firm’s equity entitles the financier to a claim on all of the firm’s assets, a musharaka contract would allow a claim only on the profit generated by the investment being financed (Bacha et al., 2015). Then a musharaka investor does not profit from an increase in firm value in total, but only from the revenues and the increase in value of the financed assets or projects. This kind of partnership with sharing of profits and losses from specific assets requires identifiability and measurability, which are least problematic for tangible assets. Therefore, in our analysis, we make a distinction between tangible and intangible assets, wherein the musharaka contract involves an investment in tangible assets only and, consequently, sharing the profits and losses from only those assets. The profits from the increase in the value of intangible assets or growth opportunities are not shared between the musharaka investor and the entrepreneur. 3. Literature on Agency Aspects and Risk Sharing in (Islamic) Finance We consider a principal-agent relationship between a risk-averse entrepreneur and a risk-averse external financier (investor/partner). The entrepreneur as the manager of the firm can extend effort to increase its future value. The effort comes at private costs for the entrepreneur. In that case, the contract between the principal and the agent determines not only the allocation of risk, but also the managerial incentives and hence the agent’s effort. This principal-agent setting is similar to those in the seminal papers by Holmström (1979), Shavell (1979), and Grossman and Hart (1983). In corporate finance, principal-agent relationships between managers (agents) and shareholders or bondholders as principals have been extensively explored, with Jensen and Meckling (1976) as one of the most influential papers. In that literature, 212The Journal of Entrepreneurial Finance, Vol. 24, Iss. 2 [2022], Art. 9 https://digitalcommons.pepperdine.edu/jef/vol24/iss2/9 DOI: 10.57229/2373-1761.1449 external shareholders and bondholders are assumed to be largely diversified, hence interested in the market value of their claims. Then the optimal capital structure mainly has to trade off the agency costs of debt and equity, tax benefits, and bankruptcy costs. The allocation of risk by financial contracting and the firm’s capital structure are per se not important if all investors manage their portfolio risk via buyor-sell transactions on a broad capital market. 2 This is different for small and medium sized enterprises (SME), i.e., in entrepreneurial context. The entrepreneur often has a considerable share of their wealth invested in their firm and, therefore, cares for the direct impact of the risk on their utility and not only for the (risk-dependent) market value of the firm. Similarly, the investor’s utility depends directly on the risk he/she has to bear as financier if his/her financial claims are not traded on a frictionless capital market. This kind of financial relation between an individual entrepreneur and a financier, both risk-averse and both with a future uncertain wealth that depends primarily on the firm’s performance, is what we are going to analyze. Such a principal-agent relationship within the framework of Islamic financial transactions is seldom represented in literature even though there has been an extensive amount of research in the field of Islamic finance and banking. Most of this research, however, consists of various ways of comparing Islamic and conventional banks with respect to their financial characteristics and performance using econometric methods (e.g., Čihák and Hesse (2010), Beck et al. (2013), Johnes et al. (2014), Pappas et al. (2016), Alabbad and Schertler (2022)). The theoretical framework of Islamic financing instruments, especially, PLS contracts, with consideration for risk sharing and managerial incentives is hardly explored, with a few notable exceptions outlined below. Mirakhor et al. (2007) classify and describe Islamic financial instruments, including the profit sharing contracts of mudaraba and musharaka. They define mudaraba financing as “financing by way of trust” and musharaka financing as a “partnership”. They also refer to moral hazard problems in the context of musharaka and hint to the issue that risk aversion of individual entrepreneurs may reduce the efficiency of outcome-based incentive systems, which force them to absorb the risk that their income may vary owing to factors beyond their control. The authors qualitatively infer that high-powered incentives and efficient allocation of risk are, therefore, in conflict. In support of such conflict, Dar (2007) claims that the profit and loss sharing contracts in Islamic financing such as mudaraba and musharaka contracts lead to an incentive incompatibility between the entrepreneur and the 2 With investor’s unlimited access to frictionless secondary markets, a firm’s capital structure is irrelevant for the ultimate allocation of its business risk. Therefore, the assumption of unlimited access to frictionless secondary markets is one of the building blocks of the Modigliani and Miller (1958) theorem. 213 Hadizada and Nippel: Islamic PLS versus Equity: Risk Sharing and Managerial IncentivesPublished by Pepperdine Digital Commons, 2022 investor. Our model thoroughly analyzes this conflict and compares musharaka financing with debt or equity with respect to the entrepreneur’s utility. Formal models of musharaka financing with agency conflicts can be found in, e.g., Yousfi (2013), Elfakir and Tkiouat (2015), and Arbi (2021). Yousfi (2013) considers PLS financing in a double-sided moral hazard problem with risk neutrality. Hence, risk sharing is not an issue. Nevertheless, the first best solution is not reachable under musharaka financing since PLS implies partially externalizing the marginal returns of each agent’s effort. Elfakir et al. (2015) examine musharaka financing in an agency model, where either effort is assumed to be observable or the assumed distribution of output allows for a forcing contract. With all parties assumed to be risk neutral, Arbi (2021) analyzes diminishing musharaka contracts, which resemble leasing contracts. He considers a moral hazard problem when asset maintenance is not observable and concludes that if the lessor plans to buy out the lessee at the end of the contract, he/she purposefully neglects the maintenance of the asset. Different from our problem of unobservable effort in combination with risk sharing is the moral hazard problem that may result if output or the state of nature under which production takes place is unobservable for the principal (costly state verification). That kind of moral hazard problems with contracts as revelation mechanisms are considered by, e.g., Haque and Mirakhor (1986), Presley and Sessions (1994), Yustiardhi et al. (2020), and Ajmi et al. (2020). In overview, the existing theoretical literature mostly focuses on mudaraba financing when it comes to Islamic profit sharing contracts and the informational asymmetries inherent in such contracts. Musharaka financing has not been compared to other forms of financing with a consideration for risk sharing and effort-based moral hazard problem in a theoretical framework. Our analysis contributes to the existing literature by theoretically deriving the implications of risk sharing and incentives in a partnership relationship between an entrepreneur and a musharaka investor. 4. The Model We employ the LEN (Linear-Exponential-Normal) model, which is wellknown from agency theoretic frameworks dating back to seminal papers by Holmstrom and Milgrom (1987), Spremann (1988), and Holmstrom and Milgrom (1991). For the entrepreneur E (she) seeking financing of her business, as well as for potential financiers, we assume an exponential utility function: 214The Journal of Entrepreneurial Finance, Vol. 24, Iss. 2 [2022], Art. 9 https://digitalcommons.pepperdine.edu/jef/vol24/iss2/9 DOI: 10.57229/2373-1761.1449 Assumption 1: ( ) ( ) 1, 1, W ii i U W e  − =− , (1) where 1,i W is the future uncertain wealth of individual i (i.e., the entrepreneur or a financier) in 1t= , and 0 i   is i ’s (constant) absolute risk aversion (Pratt, 1964). The future wealth 1,E W of the entrepreneur depends on the outcome of her business and on how that outcome is divided between herself and an outside investor/partner (he) as a financier. This division depends on the financial contract between the entrepreneur and the financier. The financier’s future wealth also depends on the firm’s success and how it is shared. The entrepreneur’s business needs an initial investment of capital C . We assume that this investment is in tangible assets and intangible assets or provides for growth opportunities. The tangible assets are of value a in 1t= , and the value of the intangible assets or growth opportunities in 1t= is b . Both values depend on the entrepreneur’s unobservable effort. With efforts a e and b e , respectively, she can shift the distributions of a and b to the right: Assumption 2: Asset values depend on the entrepreneur’s effort and are jointly normal distributed: aa a x e  = + + (2) and bb b y e  = + + , (3) where 0x and 0y are constants, a e and b e indicate the entrepreneur’s effort, and a  and b  are jointly normal distributed random variables with ( ) 0 a E  = , ( ) 0 b E  = , ( ) 0 a Var   , and ( ) 0 b Var   . The constants, x and y , and the distributions of the error terms, a  and b  , are common knowledge to all the involved parties. 215 Hadizada and Nippel: Islamic PLS versus Equity: Risk Sharing and Managerial IncentivesPublished by Pepperdine Digital Commons, 2022 the other hand, b e is higher than with debt financing if 0   (vice versa for 0   ). But the total effort ( ) ab ee+ is less than under debt financing for all 0 I   : 22 11 I ab ee   − + =  ++ . (18) In this respect, a dilution of overall incentives by musharaka financing is to be observed. If the investor correctly anticipates the entrepreneur’s efforts based on his share I  , we can substitute for I S from the investor’s participation constraint (14) and the efforts from (17) in (16): ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 0, 2 2 21 1 121 11 1 1 , 22 E f E I I IE I E E I xy Var a Var b Cov a b CE r C W         + + − − +− = + −  + −−  − − − . (19) Now our last step (in fact, the entrepreneur’s first decision) is to find the optimal share I  that maximizes her certainty equivalent in (19). This maximization leads to ( ) ( ) ( ) ( ) * 2 , 1 1 E I EI Var a Cov a b Var a      +  = ++ − . (20) Since we want to make sure that this inner solution lies in the economically sensible interval   0;1 , i.e., * 01 I   , we state 4 Assumption 7: ( ) ( ) ,Cov a b Var a− (21) and 4 Otherwise, we would have to continue with the boundary solution of either 0 I  = or 1 I  = . 222The Journal of Entrepreneurial Finance, Vol. 24, Iss. 2 [2022], Art. 9 https://digitalcommons.pepperdine.edu/jef/vol24/iss2/9 DOI: 10.57229/2373-1761.1449 ( ) ( ) 2 1 1 ,I E Var a Cov a b    + −  . (22) From condition (21) follows *0 I   . This condition holds for any positive covariance and even with a negative covariance if the variance ( ) Var a of the value of the tangible assets is not “small” compared to the variance ( ) Var b of the value of the other (intangible) assets. 5 From condition (22) follows *1 I   . Note that * I  takes the maximum value for 0  = . In that case, the effort b e (from (17)) is independent of I  . Hence, there is no effort distortion in that area. That allows for more risk sharing, that is, a higher value of I  . But since the total effort ( ) ab ee+ decreases in I  (see (18)), the choice of I  always has to trade off this incentive effect against the benefits of risk sharing. With the optimal share * I  from (20), the entrepreneur’s maximized certainty equivalent from (19) is ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 0, * 1 12 , 1 1 , 1 1 21 fE E EI EE E I b C r C W Var a b Va VC r a Co E x y ar a ov a b V aa var        = + + − +  +  + − + + − +  ++  −  . (23) As in (11), we now compare this certainty equivalent from (23) with her future wealth in case she refrains from the business. Under the musharaka financing, the entrepreneur gains if 5 If ( ) ( ) ( ) 2 ,ab Var a Var b   , then ( ) ( ) 2 ,, a a a bb a b a b           . Adding the covariance to both sides results in ( ) ( ) ( ) ( ) ( ) 2 , , , 0, a a a bb a b a b a b Var a Cov a b          + =  +    + . Therefore, ( ) ( ) ( ) 2 ,ab Var a Var b   suffices for ( ) ( ) ( ) ( ) , 0 ,Var a Cov a b Cov a b Var a+    − . 223 Hadizada and Nippel: Islamic PLS versus Equity: Risk Sharing and Managerial IncentivesPublished by Pepperdine Digital Commons, 2022 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 0, 0, 1 1 , 1 1 1 1 21 2 ,1 E E f E E fE I E x w v r C W Var ay Var a Co a b V b Var a Cov a b r aW ar       + − − +  + + − +  +   + + + + + + −  (24) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 0 2 , 2 1 12 1 11 11 , 1 21 f E EI f E E xy r Var a Cov a b Cw r C W Var aa a Vr b      + −++ + −  ++    +  +   + ++  − − . (25) The LHS of condition (25) is again a risk-adjusted present value, given that the entrepreneur optimally chooses the terms of the musharaka contract and individually optimizes her effort. If this present value exceeds the total investment needed plus the present value of her alternative wage, the business has a positive NPV adjusted for risk. More importantly, we address the question which of the so far considered financing contracts results in a higher utility for the entrepreneur. To answer this question, we have to compare certainty equivalent in (23) under the optimal musharaka contract with the certainty equivalent in (10) in case of debt financing. This comparison reveals Proposition 1: Musharaka financing is always more advantageous for the entrepreneur compared to debt since the certainty equivalent in (23) exceeds the certainty equivalent in (10) if ( ) ( ) ( ) ( ) 2 2 2 ,0 1 1 E EI Var a Cov a b Var a     +   ++ − , (26) which holds for all parameters compatible with our assumptions. 224The Journal of Entrepreneurial Finance, Vol. 24, Iss. 2 [2022], Art. 9 https://digitalcommons.pepperdine.edu/jef/vol24/iss2/9 DOI: 10.57229/2373-1761.1449 Therefore, despite diluted incentives to extend effort, musharaka financing always results in a higher certainty equivalent for the entrepreneur than debt financing due to the benefits from risk sharing. It might even be the case that the business is not advantageous for the entrepreneur if financed with debt (i.e., condition (12) does not hold), but it is advantageous with musharaka financing (i.e. condition (25) holds). In this case, risk sharing increases investment activity. 7. Equity Financing Instead of financing with capital from an investor by means of a musharaka profit and loss sharing contract as considered above, we now analyze financing with regular equity capital. Equity capital comes from a partner P who provides capital in amount of P S and then holds a share P  in the firm, i.e., he becomes a regular shareholder. Therefore, as opposed to the musharaka investor, the partner P does not profit from the returns of some (tangible) assets only, but from the overall increase or decrease in firm value. This difference affects the incentives for the entrepreneur to spend effort and results in an optimal value for the partner’s share P  that differs from the musharaka investor’s share I  (in (20)) and, consequently, different allocation of risk. We will now analyze how financing with equity capital affects the entrepreneur’s utility and then compare the results with those from debt financing and musharaka profit and loss sharing. For the partner P , we assume that he is also risk-averse with an exponential utility function and a risk aversion factor of 0 P   (see assumption 1). Therefore, the certainty equivalent P CE of his future wealth depending on the share P  and the capital P S invested in the firm is ( ) ( ) ( ) ( ) 2 0, 1 1S 2 P P f P P P P CE E a b r W Var a b    = + − + − − + , (27) with 0,P W for the partner’s initial wealth in 0t= , and ( ) ( ) 1S P f P E a b r  + − + for his expected economic profit or loss. We assume (similarly to assumption 6) that the equity partnership results in a certainty equivalent for the partner exactly as high as with his outside option. 225 Hadizada and Nippel: Islamic PLS versus Equity: Risk Sharing and Managerial IncentivesPublished by Pepperdine Digital Commons, 2022 Assumption 8: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 0, 0, 2 1 1 S 1 2 11S 2 P f P P P P f P P P P f P E a b r W Var a b r W E a b Var a b r       + − + − − + = +  + − + = + . (28) The reason for this assumption is again that none of the considered financiers should earn more (on a risk-adjusted basis) than with their outside option. Without this similarity, differences in risk sharing and incentive effects would be contaminated with differences in distribution of wealth. With the partner P providing capital P S and holding a share P  in the firm, the entrepreneur’s certainty equivalent is ( ) ( ) ( ) ( ) ( ) ( ) ( ) 0, 2 ,1 1 1 1 2 E a b f E P P P E C b E c e e r CE a b Vr W a S a   − + − −− − = + − − + . (29) Again, for ( ) 0, 0 EP C W S− −  , the entrepreneur additionally requires some debt financing with an interest rate f r . On the other hand, if ( ) 0, 0 EP C W S− −  , she invests the remaining capital at the risk-free rate, f r (see the discussion of (15) above). With (2) and (3) for the asset values from assumption 2 and (4) for the cost function from assumption 3 follows: ( )( ) ( ) ( ) ( ) ( ) ( ) 22 2 0, 1 2 11 1 2 1 E P fa b a b a E PE Pb x e y e e e e e Var a b CE r C W S    + + + − + − − −− = − + − − + . (30) This is the entrepreneur’s certainty equivalent to be maximized by the choice of efforts a e and b e after the partnership contract has been signed, that is, with given P  and P S . For the entrepreneur, the following efforts are optimal: 11 , 11 PP ab ee   −− == ++ . (31) 226The Journal of Entrepreneurial Finance, Vol. 24, Iss. 2 [2022], Art. 9 https://digitalcommons.pepperdine.edu/jef/vol24/iss2/9 DOI: 10.57229/2373-1761.1449 Note that the equity financing results in the same effort ( ab ee= ) in both of the entrepreneur’s tasks. This is the result of the fact that the entrepreneur evenly shares the fruits of all her efforts with the partner, so that the incentives for providing effort a e and effort b e are evenly diluted. And a larger share P  of the equity partner results in higher dilution of incentives and hence in lower effort in both tasks. These efforts in (31) fall short of the first best efforts (see (9)) for any 0 P   . If the partner correctly anticipates the entrepreneur’s efforts based on his share P  , we can substitute P S from the partner’s participation constraint (28) and the efforts from (31) in (30): ( ) ( ) 2 2 2 11 1 1 1 2 EPE P p PVar a bCE x y     + − − − +  + =+ + + . (32) The first-order condition for the maximization of (32) determines the optimal share P  : ( ) ( ) ( ) *2 1 E EP P Var a b Var a b     + = + + + + . (33) Note that * P  increases in  . The reason is that * P  has a negative impact on effort; 1 1 ab PP de de dd    = = − + , but the larger  , the smaller this negative marginal effect in absolute terms. Consequently, with larger values of  , it becomes marginally less costly to choose higher values for * P  to improve on risk sharing. With this optimal share * P  from (33), the entrepreneur’s certainty equivalent from (32) is ( ) ( ) ( ) ( ) ( ) ( ) ( ) , * 0 1 1 1 1 1 2 2 1 2 f E E E E E EP P CE x y Var a b Var a b Var a b Var a W b rC         = + + − + + + + − + + + + − + + . (34) 227 Hadizada and Nippel: Islamic PLS versus Equity: Risk Sharing and Managerial IncentivesPublished by Pepperdine Digital Commons, 2022 In order to render the business with equity partnership advantageous for the entrepreneur, this certainty equivalent (34) must exceed her future wealth in case she refrains from the business: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 0, 0, 1 12 1 1 1 21 1 2 f E E E E EP fE w x y Var a b Var a b b r C W rVar a b Var a W        + + − + + + + −  + + + + +− + + + (35) ( ) ( ) ( ) ( ) 2 2 1 11 1 1 1 1 22 2 f E EP E x y Var a b r Var a b Cw Var a b       + + − +  ++    +  ++   + + +  + . (36) The LHS of (36) is again a risk-adjusted present value, given that the entrepreneur optimally chooses the terms of the partnership and individually optimizes her effort. If this present value exceeds the total investment needed plus the present value of her alternative wage, the business has a positive NPV adjusted for risk. By comparing the certainty equivalent of the entrepreneur under equity partnership with a shareholder from (34) with the result for debt (10), we find Proposition 2: Equity financing results in a higher utility for the entrepreneur compared to debt since the certainty equivalent in (34) exceeds the certainty equivalent in (10) if ( ) ( ) ( ) 2 2 0 2 1 E EP Var a b Var a b     +   + + + + , (37) which holds for any 1  − . 228The Journal of Entrepreneurial Finance, Vol. 24, Iss. 2 [2022], Art. 9 https://digitalcommons.pepperdine.edu/jef/vol24/iss2/9 DOI: 10.57229/2373-1761.1449 Therefore, as in the case with musharaka financing, despite diminished incentive to exert effort, equity financing dominates debt financing. Again, it might even be the case that the business is not advantageous for the entrepreneur if financed with debt (i.e., condition (12) does not hold), but it is advantageous with equity financing (i.e., condition (36) holds). Musharaka and equity financing differ in how risk is shared. But with both financial alternatives, the entrepreneur benefits from the risk sharing to an extent that compensates for the losses from diminished effort incentives. 8. Musharaka versus Equity Both musharaka and equity financing are variants of profit and loss sharing contracts and, consequently, result in risk sharing. But the terms of risk sharing and incentive effects are different. For the optimal value of I  in musharaka financing (see (20)), we calculated the entrepreneur’s certainty equivalent in (23). For the optimal value of P  in partnership with equity financing (see (33)), we calculated the entrepreneur’s certainty equivalent in (34). For the sake of comparability, we further assume Assumption 9: The equity partner and the musharaka investor are equally risk-averse: PI    = . This assumption ensures that none of the alternative financial contracts leads to more (or less) benefits from risk sharing only because of lower (or higher) risk aversion of the financier with whom the entrepreneur shares risk. Comparing the certainty equivalent of the entrepreneur under partnership with an equity shareholder from (34) with the certainty equivalent under the musharaka contract (23) by applying assumption 9, we find Proposition 3: Musharaka financing may or may not result in higher utility for the entrepreneur compared to financing with regular equity depending on the structure of risks and the effort cost function. Musharaka results in a higher certainty equivalent for the entrepreneur than financing with equity, i.e., musharaka is more advantageous, iff 229 Hadizada and Nippel: Islamic PLS versus Equity: Risk Sharing and Managerial IncentivesPublished by Pepperdine Digital Commons, 2022 ( ) () ( )( ) ( )   ( ) ( ) ( ) ( ) ( ) 2 , 1 1 2 2 1 E ab Var a b Var a b Var a b Var a Var b       ++  − + + + +  − −   , (38) with ( ) ,ab  for the correlation between the two components of the firm’s value. 6 If condition (38) holds, that is, if musharaka financing results in a higher utility for the entrepreneur than equity financing, it must be because of better incentive effects overcompensating for the disadvantage in how risk is shared. If incentives are not relevant and moral hazard problems do not exist, equity financing with linear sharing of total business risk 7 dominates musharaka financing as considered here, with sharing of risk in only a : Lemma 1: If the financial structure does not have an impact on the entrepreneur’s effort (i.e., in the absence of agency problems), and the first best efforts, 1 1 ab ee  == + , are implemented, risk sharing with equity is superior to risk sharing under musharaka financing: ( ) ( ) EE CE CEequity musharaka for all ( ) ,1 ab   . Proof: see appendix B. In that case, only for ( ) ,1 ab  = , both alternatives of raising capital result in the same certainty equivalent for the entrepreneur since with perfect positive or negative correlation, there is, in fact, only one risk. The entrepreneur can, therefore, optimally share total business risk with the musharaka investor via his share in a . A certain share of the investor in a only results in the same risk for the entrepreneur as the optimal share in both a and b of an equity partner if the risks are perfectly correlated. Then no advantage of equity financing with respect to risk sharing remains. For all non-perfectly correlated risks in a and b , i.e., ( ) ,1 ab   , sharing total business risk ( ) Var a b+ with an equity partner, ceteris paribus, dominates partial risk sharing with musharaka financing. And the relative advantage of equity with respect 6 The formal comparison of the certainty equivalents from (34) and (23) to deduce (38) is a straightforward, but lengthy task. A step-by-step illustration by the authors is available upon request. 7 The optimal division of the sum of two risky assets, independently of the specific distributions, was already determined in Borch (1960). For the optimality of linear sharing rules, see also Borch (1968), Wilson (1968), Drèze (1990), and Lemaire (1990). 230The Journal of Entrepreneurial Finance, Vol. 24, Iss. 2 [2022], Art. 9 https://digitalcommons.pepperdine.edu/jef/vol24/iss2/9 DOI: 10.57229/2373-1761.1449 to risk sharing increases in the ratio ( ) ( ) Var a b Var a + . The higher ( ) Var a b+ is compared to ( ) Var a , the more important it is for the entrepreneur to share total risk instead of only ( ) Var a (see appendix C). The ratio ( ) ( ) Var a b Var a + of total business risk to the variance ( ) Var a is lowest if the risk in b is negligible. If the risk in b , i.e., ( ) Var b , is negligible (and so is the covariance), the entrepreneur does not benefit much from sharing this risk with a partner instead of bearing it alone under musharaka financing under which only the risk in a is shared. As a counterbalance to the suboptimal risk sharing, musharaka financing comes with superior incentive effects under certain conditions, which can be determined through the comparison of the profits from effort net of the entrepreneur’s costs under musharaka and equity financing. ( ) 2 2 2 22 2 2 2 2 2 11 11 1 1 1 1 1 21 1 1 1 1 1 21 II I I I I I NPM                      − − − + =+ −−         − − − + − − − + − + −         − − − −          = − +− (39) is the net profit from extending effort under musharaka, and 22 2 11 11 1 1 1 1 1 1 1 2 1 1 11 1 P P p P P P P NPE              −− =+ ++         − − − − − + −         + + +  =− + +         +  (40) is the net profit from extending effort under equity financing. Comparing those net profits from effort in (39) and (40), we find 231 Hadizada and Nippel: Islamic PLS versus Equity: Risk Sharing and Managerial IncentivesPublished by Pepperdine Digital Commons, 2022 larger  is, the smaller the ratio ( ) ( ) Var a b Var a + should be to result in indifference for reasons explained above. But in the range of very small values of ( ) Var b , total risk ( ) Var a b+ is decreasing in ( ) Var b if ( ) ,0 ab   . So, a decrease in ( ) Var b and, consequently, a decrease in ( ) ( ) Var b Var a results, ceteris paribus, in a higher total risk ( ) Var a b+ which makes equity financing more preferable. Therefore, for large values of  and very small ( ) Var b , below the branch of the indifference curve bending backwards, equity financing dominates musharaka. To sum up, we observe that musharaka contracting is more advantageous for the entrepreneur if the risk ( ) Var b from intangible assets or growth opportunities is small relative to the risk ( ) Var a in tangible assets. The higher the cross derivative  of the entrepreneur’s effort costs, the smaller the range of ( ) ( ) Var b Var a for which musharaka contracting is more advantageous. Furthermore, the correlation ( ) ,ab  between the risks has an impact on the relative advantage of musharaka over equity. For given individual risks ( ) Var a and ( ) Var b , the total risk ( ) Var a b+ increases in ( ) ,ab  . And a higher total risk implies a higher importance of comprehensive risk sharing. Hence, equity becomes, ceteris paribus, more favorable. 10. Conclusion The principal-agent relationship between an entrepreneur (the agent) and a financier (the principal) is explored for different financial contracts. The type of financial contract used has an impact on the extent of risk sharing, and the benefits thereof, and on managerial incentives. We considered a model where all the parties involved are assumed to be riskaverse, and the entrepreneur can influence the outcome of her business by extending managerial effort at a private cost. An entrepreneur seeking funding for a business opportunity is faced with three alternatives: (i) taking out a loan; (ii) financing a project via musharaka, an Islamic profit and loss sharing (PLS) contract; (iii) raising regular equity form a financier who subsequently becomes a co-owner in the firm. 238The Journal of Entrepreneurial Finance, Vol. 24, Iss. 2 [2022], Art. 9 https://digitalcommons.pepperdine.edu/jef/vol24/iss2/9 DOI: 10.57229/2373-1761.1449 A musharaka contract can be used to finance a specific project or investment, the acquisition of some real estate, commodities, working capital, or other tangible assets to be used in production or trade. In that case, only the profits and the risk of this particular project or investment are shared by the parties to the contract. In this paper, the above-mentioned investment is assumed to be in tangible assets. Financing with regular equity results in co-ownership of the whole firm instead. Therefore, all profits and losses from all tangible and intangible assets are shared, and so is the total business risk. The theoretical analyses in this paper show that the entrepreneur can achieve a higher utility if she uses equity or musharaka financing instead of debt only. That is, both musharaka and equity financing are superior to debt financing for the entrepreneur. The benefits from risk sharing with an equity partner or a musharaka investor compensate for the losses from lower managerial incentives compared to debt financing. Comparison of musharaka and equity financing shows no definite ranking. Both alternative financial contracts result in profit and loss sharing and hence in risk sharing, even though in various modes. The entrepreneur shares either total business risk with an equity partner or some particular risk with a musharaka investor. In both cases, the entrepreneur benefits from risk sharing, yet to varying degrees. On the other hand, both considered alternative financial contracts negatively affect the entrepreneur’s incentives to work, but also differently. We analyzed the trade-offs between risk sharing and incentives for both financial contracts. As the main determinants, we identified the risks of the firm’s tangible and intangible assets or growth opportunities, the correlation between those risks, and the entrepreneur’s effort cost function. Equity financing is preferable with respect to risk sharing, considering the entrepreneur’s utility. Musharaka also results in risk sharing, although to a lesser extent. This disadvantage is compensated for by better incentives for the entrepreneur in case of musharaka financing, albeit only under certain conditions. Particularly, the risk in the firm’s intangible assets or growth opportunities must not be high compared to the risk in tangible assets. Furthermore, the smaller the correlation between those risks, the better with the alternative of musharaka financing. And the entrepreneur’s marginal costs of spending effort aiming to raise the value of tangible (intangible) assets must not increase much in the cost of effort for intangible (tangible) assets for musharaka financing to be more beneficial (i.e., the cross derivative of the cost function must not be large). However, raising capital by means of regular equity is definitely more advantageous if the risk in the firm’s tangible assets is smaller than the risk in intangible assets or growth opportunities. If the latter risk is not shared with an outside investor as with, e.g., the musharaka financing considered in our model, this disadvantage in risk sharing cannot be compensated for by better incentives. 239 Hadizada and Nippel: Islamic PLS versus Equity: Risk Sharing and Managerial IncentivesPublished by Pepperdine Digital Commons, 2022 The considerations in this paper can be extended in various ways. Since a musharaka investor, as well as an equity partner, is entitled to also take part in the management process, the effects of them also extending effort on managing either one particular project or the firm in general, respectively, could also be explored within the theoretical framework considered in this paper. Another possible extension would be applying the same assumptions and theoretical model in case the entrepreneur has the opportunity to raise capital from both an equity partner and a musharaka investor. In this case, the entrepreneur could, for example, finance tangible assets with musharaka besides external equity financing of the firm in total. Furthermore, in a more general setting, a scenario in which the entrepreneur finances a project with funding from two or more investors with different levels of risk aversion could also be analyzed within the theoretical framework applied in this paper. In such a scenario, the extent of profit-and-loss and risk sharing with different investors would depend on their individual risk preferences. The theoretical approach of this paper can be applied to analyze the use of multiple external sources of funding that are not limited to Islamic financial instruments. Other hybrid financial instruments could be considered in a similar manner. The model might also be modified and extended to account for other informational asymmetries, e.g., when the financier is unaware of the prospects of the project the entrepreneur wishes to undertake, or of the ability of the entrepreneur to manage the project. Adverse selection in such scenarios involving financing with a musharaka or a mudaraba contract could be explored. 240The Journal of Entrepreneurial Finance, Vol. 24, Iss. 2 [2022], Art. 9 https://digitalcommons.pepperdine.edu/jef/vol24/iss2/9 DOI: 10.57229/2373-1761.1449 References Ajmi, H., Aziz, H. A., & Kassim, S. (2020). Does venture capital substitute Islamic profit and loss sharing contracts? Theoretical analysis on musharakah and venture capital. International Journal of Economics and Management, 14(1), 111-127. Alabbad, A., & Schertler, A. (2022). COVID-19 and bank performance in dualbanking countries: An empirical analysis. Journal of Business Economics, 92(9), 1511-1557. Arbi, L. H. (2021). 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When the entrepreneur’s efforts are a e and b e , the net return from spending effort can be expressed as 22 22 ab a b a b ee e e e e  + − − − . From the first-order condition, we find the first best levels of effort that maximize this return to be 1 1 ab ee  == + , which leads to a net return of 1 1  + . If 1  =− , the net return from extending effort is 22 22 ab a b a b ee e e e e+ − − + , and the optimal levels of a e and b e do not exist simultaneously. Only after arbitrarily deciding on a e (or b e ) can the entrepreneur determine the optimal effort b e (or a e ). For 1  = , the net return from extending effort is ( ) ( ) 2 1 2 a b a b e e e e+ − + . The entrepreneur can choose any efforts a e and b e that add up to 1 to maximize the net return. If 1   , the entrepreneur could instead choose arbitrarily to spend either no effort a e or no effort b e and yet earn a higher (or equal) net return in optimum than if the efforts 1 1 ab ee  == + are chosen. With 1   , the optimal efforts are 1 a e= and 0 b e= or 1 b e= and 0 a e= . Then the net return is 1 2 . Only for 11  −   , we find that the net return in optimum, 1 1  + , exceeds the net return under the arbitrary constraint 0 b e= (or 0 a e= ), i.e., 11 12   + . Therefore, we restrict  to the interval   1;1− to rule out nonsensical results. Appendix B Here we prove that if the financial structure does not affect the entrepreneur’s effort, and the first best efforts are implemented, risk sharing with equity is superior to risk sharing under musharaka financing. 244The Journal of Entrepreneurial Finance, Vol. 24, Iss. 2 [2022], Art. 9 https://digitalcommons.pepperdine.edu/jef/vol24/iss2/9 DOI: 10.57229/2373-1761.1449 In the absence of agency problems, that is, with the first best efforts, the certainty equivalent of the entrepreneur is ( ) ( ) ( ) ( ) 2 0, 2 11 1 1 (2 )1 EPE f E P P x y Var a bCE r C W    + + − − − − +  =+ ++equity (44) and ( ) ( ) ( ) ( ) ( ) ( ) ( ) 0 22 , 11 1 1 2 () 2 11, 1EI E E I E f E I I x y Var a Var b Cov a b CE r C W      − = + − +  + + − − −  + −− musharaka (45) under equity and musharaka financing, respectively. With given (first best) efforts, the optimal shares are *E EP P   =+ for equity financing and ( ) ( ) ( ) ( ) *, E I EI Var a Cov a b Var a    +  =+ with musharaka. Inserting these shares in (44) and (45), respectively, and applying assumption 9, PI    = , we find ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 2 2 , 2 , , 11 22 , ,1 ( ) ( ) 1 equity musharaka E E EE a b a EE b C o E CE V C ar r a Va a Cov a b Var a b Var a b Var a Var a v a b Cov a b Var a Var b       +   +   +  +     ++   . (46) Q.e.d. Appendix C Here we show that the higher ( ) ( ) Var a b Var a + is, the more important it is for the entrepreneur to share total risk instead of only ( ) Var a . 245 Hadizada and Nippel: Islamic PLS versus Equity: Risk Sharing and Managerial IncentivesPublished by Pepperdine Digital Commons, 2022 The risk premium borne by the entrepreneur is ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 , 11 ,1 22 1 E EE E Var a Cov a b RPM Var a Cov a b Var a Var a b      +   = − +  + ++ − (47) and ( ) ( ) ( ) ( ) ( ) 112 22 1 E EE E Var a b Var a b Var a b Var a b RPE     =− + ++ ++ + + (48) under musharaka and equity financing, respectively. The relative advantage of risk sharing under equity financing can be represented by the difference between these risk premia: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 22 2 2 , 11 0 21 22 11 E E EE V RVar a b ar a Cov a b PM RPE Vara aV r a b         +  − = −  + + + + + + +− . (49) With given levels of ( ) Var a and ( ) ,ab  , the relationship between the risks being shared under the two alternatives depends on ( ) Var b . We can show that ( ) RPM RPE− increases in ( ) Var b and hence in ( ) ( ) Var a b Var b + for any given values of ( ) Var a and ( ) ,ab  : ( ) ( ) ( ) ( )( ) ( )   ( )( ) ( )   2 2 1 4 1 0 2 2 1 EE E dVar a b Var R bb RPM P V E r daa         + + + + − + = + + + + . (50) Therefore, as ( ) ( ) Var a b Var a + increases, it becomes more important for the entrepreneur to share the total risk instead of only ( ) Var a . 246The Journal of Entrepreneurial Finance, Vol. 24, Iss. 2 [2022], Art. 9 https://digitalcommons.pepperdine.edu/jef/vol24/iss2/9 DOI: 10.57229/2373-1761.1449