Ownership concentration, risk aversion and the effect of financial structure on investment decisions

European Economic Review 42 (1998) 1751—1778

Ownership concentration, risk aversion and the effect of financial structure on investment decisions Guochang Zhang* Department of Accounting, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong Received 1 November 1995; accepted 1 June 1997

Abstract This paper examines the effect of capital structure on investment decisions when the firm is controlled by a large, risk-averse shareholder. Because of under-diversification, the controlling shareholder is more averse to risky projects than atomistic shareholders whose portfolios are fully diversified, and hence the former may under-invest by rejecting projects which are desirable for the latter. We show that this under-investment problem can be mitigated by issuing risky debt because of the ‘risk-shifting’ effect of debt. The paper demonstrates a unique equilibrium capital structure, involving both risky debt and equity, which is directly linked to the ownership structure. The analysis leads to empirical predictions about how ownership and capital structure are interrelated, and how capital structure is affected by such exogenous factors as the identity of the controlling shareholder and project risk. The existing empirical studies generally support these predictions.  1998 Elsevier Science B.V. All rights reserved. JEL classification: G32 Keywords: Large shareholder; Risk aversion; Under-investment; Capital structure; Risk shifting

* Tel.: (852) 2358 7569; fax: (852) 2358 1693; e-mail: [email protected]. 0014-2921/98/$ — see front matter  1998 Elsevier Science B.V. All rights reserved. PII: S 0 0 1 4 - 2 9 2 1 ( 9 7 ) 0 0 1 0 6 - 2

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1. Introduction In practice, the ownership of a publicly held firm is typically partially concentrated and partially diverse. In spite of the general characteristic of investor risk aversion, few firms have their shares fully spread out without a significantly large shareholder. Recent studies, most notably Shleifer and Vishny (1986), Admati et al. (1994) and Huddart (1993), have provided theoretical arguments for the need for concentrated ownership, suggesting that the existence of a large shareholder helps mitigate agency conflicts between a firm’s shareholders and its management. Less well-understood in the literature, however, is the relationship between a firm’s financial structure and its ownership structure. In this paper, we use a theoretical model to study this relationship and to explore factors which cause variations in this relationship across firms. We focus on the problem of a risk-averse entrepreneur who makes a public offering of his company’s shares for the purpose of risk diversification. At some point after the initial offering, an investment opportunity becomes available, which the firm may either accept or reject. The investment decision can be improved if one of the shareholders spends private resources to acquire information about the investment opportunity. The entrepreneur faces a trade-off between the need for risk diversification and the need for information acquisition. Due to the free-rider problem, complete diversification of the firm’s risk, where each shareholder holds just a tiny fraction of the equity, leaves no one willing to acquire information. In the interest of making a more accurate investment decision, the entrepreneur finds it necessary to maintain a suitable equity position in the firm. While retaining a large position is important for ensuring information acquisition, it also causes conflicts between the entrepreneur (who later becomes the controlling shareholder) and atomistic shareholders. Because of underdiversification, the controlling shareholder is subject to both the systematic and unsystematic risk of the firm, compared with fully diversified shareholders who bear no unsystematic risk. The difference in diversification leads to different risk preferences, and the more risk-averse controlling shareholder has the tendency to reject too many projects from the standpoint of atomistic shareholders. With rational expectations, the cost of under-investment accrues to the entrepreneur as the share price at the initial offering reflects future investment decisions. Therefore, the entrepreneur has an interest in committing to less risk-averse investment behaviour. In our model, this commitment is made by

 Shleifer and Vishny (1986) find that for a sample of 456 Fortune 500 firms in the US, 354 have at least one shareholder owning at least 5% of the firm. For smaller firms and firms in many other economies, ownership is generally more concentrated.

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issuing risky debt prior to the investment decision. Here, debt creates a riskshifting effect which offsets the under-investment incentive of the under-diversified entrepreneur. We establish a sequentially rational equilibrium where the entrepreneur issues both equity and risky debt to the public but retains a large equity position, and he later acquires information for the investment decision. Our model generates a number of empirical predictions (based on numerical simulations). First, a firm’s financial leverage is shown to increase with the controlling ownership, and this relation becomes stronger the more risk-averse the controlling shareholder is. Second, firms in high-risk businesses tend to have lower financial leverage, but their debt still tends to have a lower credit rating. Third, the model predicts higher ownership concentration and greater leverage in industries where it is more costly to acquire investment-related information (such as high-tech and newly emerging industries). Our model also suggests that firm value can be negatively related to controlling ownership but for reasons other than management entrenchment suggested by Morck et al. (1988). This study is related to two strands of existing research. One strand concerns the role of a large shareholder in resolving managerial moral hazard problems (via monitoring); examples include Huddart (1993) and Admati et al. (1994). As in our model, ownership concentration matters in these papers because investors are risk-averse and have the need to diversify. The key difference of these papers is that they do not consider capital structure issues. The other strand of research concerns the role of capital structure in the presence of agency conflicts and/or information asymmetry (see Harris and Raviv (1991) for a survey). Generally speaking, there are two major differences between this strand of research and our paper. First, most of the papers in this area focus on conflicts between shareholders and debt-holders but not on those between different types of shareholders. In the few papers which do recognize the latter type of conflict, the cause of the conflict is perk consumption by the shareholder-manager, rather than differences in risk attitude between diversified and undiversified shareholders. Second, existing papers typically assume shareholder risk-neutrality. Because of risk neutrality, the issue of ownership structure is often left unaddressed in these papers. In our model, investors are all assumed to be intrinsically risk-averse. The condition of risk aversion allows us to forge a meaningful link between ownership structure and capital structure.

 One of the exceptions is Leland and Pyle (1977). The difference is that Leland and Pyle consider the signalling role of capital structure; in our paper, the capital structure decision has no signalling effect.  Investors of all types generally exhibit aversion to risk. Corporations and institutions may be less risk averse, relative to individuals, because of their large asset bases and greater ability to diversify. Nonetheless, diversification does not lead to risk neutrality in the strict sense.

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The risk-shifting effect of debt was first demonstrated by Jensen and Meckling (1976). In Jensen and Meckling, as well as in later models such as Barnea et al. (1985), risk shifting appears as a form of agency cost of debt, and this agency cost is weighed against the agency cost of external equity, caused by the inside shareholder’s desire for perk consumption, to determine the optimal capital structure. In contrast, in our model, debt helps restore the investment efficiency and, hence, plays a positive role in mitigating agency conflicts. Myers (1977) illustrates another type of debt-related effect, that debt may cause shareholders to ‘under-invest’ in situations where shareholders bear all the cost of the investment but debt-holders capture most of the return. A number of studies (including John and Senbet, 1988; Heinkel and Zechner, 1990; Titman, 1984) subsequently demonstrate that such under-investment incentives related to debt can be useful for improving the investment efficiency in a variety of situations where shareholders would have the incentive to over-invest if no debt were issued. In our paper, this type of ‘debt overhang’ problem does not exist, because the investment project at the intermediate point is financed with internal funds. Debt is also shown to be useful for offsetting the problem of over-investment and reducing perk consumption when the firm is controlled by a professional manager who owns little or no equity of the firm (see, for example, Jensen, 1986; Stulz, 1990; Hart, 1995). These papers, however, typically assume that investment decisions are controlled by a professional manager; hence, they ignore any active role of large shareholders in corporate control. Our paper does not consider managerial moral hazard problems in the form of overinvestment or perk consumption; here, the decision maker himself is a large shareholder. The remainder of this paper is organized as follows. Section 2 presents the model and discusses the form of ownership structure. Section 3 examines the investment decision under all-equity financing and shows that full-equity financing leads to socially inefficient under-investment. Section 4 examines the role of debt in correcting the under-investment problem. Section 5 discusses the robustness of our results. Section 6 provides empirical implications of the model and concludes the paper.

2. The model There are three dates in the model, denoted by t , t and t , respectively. At    the outset, t , a firm is established by an entrepreneur, the owner. The firm then  goes public. In the process, the owner decides the firm’s capital structure, represented by a mixture of debt and equity, and the fraction of equity he retains. At t , a new investment project becomes available, which the firm either  accepts or rejects. At t , the firm is liquidated. 

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2.1. Investment opportunities At date t when the firm is established, an initial asset is acquired. This asset  produces a cash flow, x , at the intermediate date t , and zero cash flow   thereafter. At t , a new project becomes available. If accepted, the project requires an  investment capital of I, and produces a stochastic cash flow XI at t which equals  either I#x, with probability p, or I!x with probability 1!p. Assume I5x so that the gross cash flow of the project is non-negative in all states. For simplicity, we also assume that the systematic risk of the project is zero. If the project is rejected at t , the firm’s intermediate cash flow (x ) is reinvested in   a riskless asset with zero interest. At time t , the firm is liquidated, and its cash flow is distributed to stake holders. To focus on the effect of existing capital structure on the investment decision and avoid information asymmetry problems associated with t -financing, we  assume that the investment at t is fully internally financed. Furthermore, we set  x "I.  2.2. Preferences The owner’s preference is represented by u(w)"!(1/c) e\AU, where w denotes the owner’s total wealth which consists of the proceeds from selling securities at t and the pay-off at t to his retained ownership, and c'0 is the   degree of the owner’s risk aversion. All other investors are intrinsically risk-averse, and have increasing, concave utility functions. Since these investors may fully diversify their portfolios, they ignore the firm’s unsystematic risk. Given that the firm’s systematic risk is zero, investors holding fully diversified portfolios effectively become neutral to the firm’s risk. 2.3. Information structure At t , all individuals (including the owner) hold identical prior beliefs about  the quality of the upcoming project. The quality of the project is characterized

 Internal financing is a realistic assumption. Masulis (1988) documents that for non-farm, non-financial firms in the US as a group, internally funded investment constitutes 40% of the total investment from 1946 to 1986. The advantages of internal financing include avoidance of flotation cost and possibly the cost of underpricing arising from issuing external equity as demonstrated by Heinkel and Zechner (1990).

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by probability p. The prior beliefs are that p is uniformly distributed over interval [0, 1], and these beliefs are common knowledge. Before the investment decision at t , an investor has the option to discover the  exact value of p at a private cost c. Since the activity of information acquisition is private and cannot be directly verified by other investors, it is not possible for the firm, or individual shareholders, to reimburse the information-acquiring investor for this cost. All cash flows of the firm are publicly observed. 2.4. The emergence of a large shareholder The firm’s investment decision can be improved if one of the shareholders acquires project-related information. Because of rational expectations, the price that the investors are willing to pay for the firm’s shares at t depends on how  the investment decision is made at t . Consequently, the benefits of information  acquisition accrues to the original owner. To demonstrate to investors his intention to acquire information, the owner needs to maintain a large equity position so that his share of the benefit from the improvement of the investment decision outweighs the cost of information acquisition. Hence, the original owner evolves to become a large shareholder after the initial public offering. On the other hand, investors who do not participate in the investment process are free to diversify their holdings completely. Consequently, the firm’s ownership becomes partially concentrated and partially diverse. In this model, the large shareholder plays the unique role of acquiring information and controlling the investment decision. We call him the ‘controlling shareholder’. From now on, the terms ‘controlling shareholder’ and ‘owner’ refer to the same individual and are used interchangeably. Whether the existence of a large shareholder can be sustained in equilibrium depends on the size of acquisition cost relative to the incremental benefit of information acquisition. To make the analysis meaningful, we focus on the set of problems where the acquisition cost can be recovered by the incremental benefit which the controlling shareholder receives. (The simulations later verify the existence of such situations.)

 One reason why the original owner becomes the controlling shareholder may be that the cost of information acquisition is lower for him than for other investors because of his prior knowledge of the business.  This type of ownership structure prevails as long as there is some form of information acquisition; the assumption that acquisition leads to perfect (as opposed to noisy) information about p is not essential.

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In the analysis below, the following equilibrium is considered: The owner becomes the controlling shareholder after the initial financing decision, and then he acquires information and decides whether or not to accept the project, and investors have rational expectations about the owner’s decisions. We examine the characteristics of the optimal ownership structure and leverage in this equilibrium.

3. The case of all-equity financing The case of all-equity financing provides a benchmark for examining the effect of financial leverage. With the restriction to all-equity financing, the owner’s decision at t is to determine a, the fraction of equity he retains.  The total wealth of the owner consists of the proceeds from external equity offering at time t , P , and the pay-off to his retained equity at t minus the cost  W  of information acquisition. Since the firm’s cash flow at t is either I!x, I,  or I#x, the owner’s contingent wealth is either ¼ ,P #a(I!x)!c,  W ¼ ,¼ #ax, or ¼ ,¼ #2ax.     3.1. The controlling shareholder+s investment decision with information acquisition The controlling shareholder learns the exact value of p if he acquires information (a). If the project is accepted (i), the utility that the controlling shareholder expects to receive is E(u " a, i, p)"u(¼ )#p[u(¼ )!u(¼ )]. (1)    On the other hand, if the project is rejected (ni), the intermediate cash flow at t (which equals I) is reinvested in a risk-free asset, and his expected utility  becomes E(u " a, ni)"u(¼ ), ∀p3[0, 1]. (2)  Conditional on information acquisition, the project is accepted if and only if E(u " a, i, p)5E(u " a, ni).

(3)

Since E(u " a, i, p) is increasing in p and E(u " a, ni) is independent of p (given that the controlling shareholder has already received P at the time of the investment W decision), there exists a cut-off probability, denoted by pL , such that the project is accepted if p3(pL , 1] and rejected if p3[0, pL ]. This cut-off probability is defined by º(¼ )!º(¼ )  . pL " º(¼ )!º(¼ )  

(4)

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With u(w)"!(1/c) e\AU, pL can be expressed more specifically as eA?V pL " . eA?V#1

(5)

3.2. The controlling shareholder+s investment decision without information acquisition We now examine the controlling shareholder’s out-of-equilibrium strategy of not acquiring information after selling (1!a) fraction of equity. This is a necessary step for deriving conditions under which the proposed equilibrium is sustained. Note that the discussion here is still conditional on the market’s equilibrium belief that the controlling shareholder will acquire information (we are not considering ‘no information acquisition’ as an equilibrium strategy here). If the controlling shareholder deviates from information acquisition, the investment decision will be based on the prior beliefs about p. It is easy to show that the ex ante unconditional expected (net) return of the project is zero. Therefore, the optimal decision for the (risk-averse) controlling shareholder is to reject the project, and the intermediate cash flow (I) is thus reinvested in a riskless asset. If the controlling shareholder decides not to acquire information after he has retained a, he may choose to diversify his portfolio further at t . We assume that  the controlling shareholder cannot trade anonymously and the market has rational expectations about the investment decision. Then, the value of the retained equity equals aI whether or not he sells off the retained equity holding. The expected utility of the controlling shareholder, conditional on his out-ofequilibrium strategy na, is E(u " na)"u(P #aI)"u(¼ #c). W 

(6)

3.3. The incentive to acquire information The ex ante expected utility of the controlling shareholder conditional on decision a is



E(u " a)"



NL  E(u " a, ni) dp# E(u " a, i, p) dp  NL

(1!pL ) (1!pL ) " u (¼ )#pL u (¼ )# u(¼ ).    2 2

(7)

This is compared with his conditional expected utility without acquisition, E(u " na). The controlling shareholder has the incentive to acquire information if

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and only if E(u " a)5E(u " na), or (1!pL ) (1!pL ) u(¼ )#pL u(¼ )# u(¼ )5u(¼ #c).     2 2

(8)

Eq. (8) is referred to as the incentive-for-acquisition constraint. It specifies that the benefit from acquiring information must be sufficient to cover the risk premium arising from portfolio under-diversification and the cost of information acquisition. So long as Eq. (8) is satisfied, the controlling shareholder has no incentive to sell off the retained ownership a and to avoid information acquisition, subsequent to the initial offering. 3.4. The financing decision at time t



Assume that external investors behave perfectly competitively among themselves. Together with previous assumptions that atomistic shareholders fully diversify their portfolios and that the systematic risk of the firm is zero, this implies that the equity price equals its expected pay-off. If Eq. (8) is satisfied, and thus the market believes that information acquisition will take place, the proceeds which the owner receives equal p "(1!a)[I#pL (1!pL )x]. (9) W The owner’s problem is to maximize E(u " a), as is given by Eq. (7), subject to the incentive-for-acquisition constraint (8). Before determining the optimal financing decision for the owner, we first examine the effect of ownership concentration (a) on the investment decision and on the owner’s utility. ¸emma 1. (i) dpL /da'0, and (ii) dEu/da(0. Proof. See Appendix A. The retained ownership (a) measures the extent of portfolio under-diversification. An increase in a reduces the owner’s riskless income (P ) and increases his W share of the risky income (the final cash flow), thereby reducing the owner’s utility. Furthermore, an increase in a makes the risky project less desirable for the controlling shareholder (owner) because he has to absorb a larger proportion of the firm’s risk. Consequently, the project is rejected by the controlling shareholder within a wider range of p. This induced change in the investment criterion further affects the owner’s utility. Although we formally prove Lemma 1(i) with negative exponential utility functions, this result holds for the whole class of decreasing absolute risk aversion utility functions (the proof is available upon request).

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Part (ii) of Lemma 1 shows that the owner’s utility is inversely related to the extent of his ownership concentration, indicating that under-diversification is costly. However, to maintain the incentive for information acquisition, the owner cannot completely diversify his holding. For example, if a is close to zero, constraint (8) will be violated because the benefit captured by the owner from information acquisition becomes negligible — too small to compensate for the cost he bears (c). As long as c is strictly positive, a must be positive and bounded away from zero. In other words, the controlling shareholder must hold a nonnegligible amount of equity in order to maintain the incentive for information acquisition. The following lemma shows that the owner never holds more equity than required by the incentive-for-acquisition constraint. ¸emma 2. ¹he optimal size of controlling ownership, denoted by (a*), is the smallest a to satisfy the incentive-for-acquisition constraint. Proof. See Appendix A. 3.5. Conflicts among shareholders We now discuss the difference in investment preference between the controlling shareholder and atomistic shareholders. But, first, we give the following definition. Definition. The first-best investment criterion is the one characterized by pL "0.5. The first-best investment occurs in the ideal case where the value of p is known publicly and costlessly. In this case, no large shareholder is needed to acquire information. As all shareholders fully diversify, they unanimously accept the project whenever the project’s net return is positive. It can be shown that for a given p, the expected net return of the project is (2p!1)x, which is positive if and only if p'0.5. Therefore, the first-best cut-off probability is pL "0.5. In our model, the cut-off probability adopted by the controlling shareholder is given by Eq. (4), where ¼ !¼ "¼ !¼ "ax. For any positive c, the     optimal holding (a*) must be strictly positive. Thus, concavity of function u implies pL '0.5. Atomistic shareholders are essentially neutral to the firm’s risk. For them, the project is acceptable whenever the expected (net) return is positive. Thus, their acceptance region is p3(0.5, 1], which is the same as in the first-best scenario.

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Within the region 0.5(p(pL , the controlling shareholder’s interest differs from the interests of atomistic shareholders; the former rejects the project that is desirable for the latter, leading to the problem of under-investment. On the other hand, if p5pL , shareholders are unanimous in preferring to accept the project. 3.6. The effect of information acquisition cost A key factor in the determination of the optimal ownership structure (a*) is the size of information acquisition cost (c). When c is small, the controlling shareholder needs to hold only a small amount of equity to satisfy the incentivefor-acquisition constraint. As c increases, the controlling ownership must increase accordingly. From part (ii) of Lemma 1, the expected utility of the controlling shareholder strictly decreases with a, and, from Lemma 2, the incentive-for-acquisition constraint is binding at the optimum. Therefore, a* must be increasing in c. Together with Lemma 1(i), this implies that the cut-off probability increases with c, dpL dpL da* " '0. dc da* dc ¸emma 3. da*/dc'0; dpL /dc'0; dEu/dc(0. An increase in c affects the owner’s expected utility in the following ways: First, it increases the direct out-of-pocket cost for information acquisition. Second, a greater cost requires a larger controlling ownership (a*) in order to satisfy the incentive-for-acquisition constraint, which leads to a greater loss from risk-bearing. And third, a higher cost c results in a higher cut-off probability pL , causing more severe under-investment. All these effects reduce the owner’s utility. The analysis for the all-equity case is summarized as follows. Summary 1. ºnder all-equity financing, (i) the controlling shareholder underinvests from the viewpoint of atomistic shareholders, and (ii) the under-investment problem is more severe the higher the information acquisition cost.

4. The impact of risky debt on the investment decision In this section, we show that issuing debt prior to the investment decision can mitigate the under-investment problem which exists with all-equity financing. The debt contract specifies a fixed amount of payment, the face value, to debtholders when the debt matures. Due to limited liability, shareholders can

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either pay the face value or hand over the whole firm if the specified payment cannot be met. Effectively, a debt contract limits the amount of down-side risk borne by shareholders. As a result, issuing debt increases shareholders’ desire for undertaking risky projects; this is commonly known as the risk-shifting effect. In the present context, this risk-shifting effect counterbalances the controlling shareholder’s under-investment incentive, which improves the investment efficiency. The following debt structure is employed: (a) debt is issued at time t and  matures at time t , i.e., debt is long term, and (b) the firm is prohibited from  paying any dividends at t ; therefore, if the project is rejected, the time t cash   flow is reinvested in a riskless asset. Condition (a) is necessary for debt to produce the desired risk-shifting effect, and condition (b) is required to protect the interests of debt-holders since, otherwise, debt would become worthless. Let F be the debt face value, a the fraction of the leveraged equity retained by the owner, and P and P the market prices of debt and equity, respectively. # The total proceeds received by the owner from selling securities at t now  become P "P #(1!a)P . As before, P and P equal their respective exW # # pected cash flows. Given limited liability, the final pay-off to debtholders is either the face value of the debt or the total cash flow of the firm, whichever is less. Thus, P depends on both F and the probability distribution of cash flow at t .  As in the all-equity case, the owner’s problem is: Maximizing Eq. (7) subject to Eq. (8), but the contingent wealth levels now become ¼ "P #  W a max+0, I!x!F,!c, ¼ "P #a max+0, I!F,!c, and ¼ "P #  W  W a max+0, I#x!F,!c. The expression for P is given later. W Due to mathematical complexity, it is difficult to obtain the closed-form expressions of F and a. As a result, we examine the properties of the optimal capital structure indirectly by deriving a sequence of lemmas. 4.1. The cut-off probability decreases as leverage increases The cut-off probability pL is still defined by Eq. (4), but pL now is a function of F since ¼ , ¼ , and ¼ all are affected by F.    When F4I!x, debt is riskless. In this case, both pL and the controlling shareholder’s wealth become independent of F, and the owner’s problem becomes equivalent to all-equity financing. Clearly, riskless debt has no effect on the investment decision. On the other hand, if F5I, then ¼ "¼ (¼ . In this case, the control   ling shareholder becomes fully insured for the down-side risk of the project, and he always accepts the project (i.e., pL "0). However, if pL "0 were a desirable investment criterion, no information acquisition would be needed as the investment decision could be made independently of p. Hence, we can also rule out this possibility for the class of problems under consideration.

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Thus, the relevant range of F we need to focus on is I!x4F(I. It can be shown that, within this range of F, the proceeds to the owner at t is    1!pL 1!pL P "I#pL (1!pL )x!a(I!F) pL # !a x. (10) W 2 2






With the exponential utility function, the cut-off probability can be simplified as 1!e\A?'\$ pL " . 1!e\A?'>V\$

(11)

Differentiating pL with respect to F yields dpL cae\A?'\$(1!e\A?V) "! (0, (1!e\A?'>V\$) dF

(12)

suggesting that the controlling shareholder is more likely to accept the project when the firm is more highly leveraged. 4.2. Optimal leverage never leads to over-investment When F increases to a certain level, the cut-off probability falls below 0.5. In this case, the controlling shareholder over-invests (relative to the first-best criterion of pL "0.5). However, we show below that over-investment never occurs in equilibrium. ¸emma 4. ºnder debt-equity financing, the equilibrium investment decision implies pL 50.5. Proof. See Appendix A. This result appears intuitive. The under-investment inefficiency in all-equity financing is caused by risk-aversion of the controlling shareholder. If debt is issued prior to the investment decision, it produces a risk-shifting effect which offsets the under-investment incentive. However, an over-correction by risky debt should never occur since there is no benefit associated with over-investment. Given that external investors have rational expectations about the investment decision, security prices equal expected cash flows; any inefficiency associated with over-investment will be reflected in the initial security prices and will be borne by the owner. Therefore, the controlling shareholder can never benefit from accepting a risky project with a negative expected return. It is possible to achieve first-best investment (pL "0.5) in some special cases (although pL "0.5 is not likely to hold in general). We give an intuitive explanation below.

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The controlling shareholder is basically averse to his wealth risk; i.e. u(¼) is concave in ¼. In the all-equity case, ¼"P #aXI , wealth is linear in cash flow W XI . Hence, concavity of u in ¼ implies concavity of u in XI . As a result, the controlling shareholder is also averse to project risk, which causes underinvestment. When the firm is leveraged, ¼ is transformed into a piecewise linear, convex function of XI . In our specific setting, the risk of the project is represented by either a gain of x or a loss of x relative to cash flow I. In terms of the controlling shareholder’s wealth, the effect of the project is either a gain of ¼ !¼ "ax   or a loss of ¼ !¼ "a(I!F). Thus, for shareholders of a leveraged firm,   the wealth gain and the loss resulting from the project are no longer symmetric. With debt being risky, F'I!x, so the possible wealth gain is greater than the possible loss. Furthermore, the magnitudes of the loss and the gain are endogenously determined by financing variables (a, F). For a concave function u, with three possible wealth levels (¼ , ¼ , and ¼ ) and two    choice variables (a and F), it is possible to adjust the locations of ¼ , ¼ , and   ¼ such that u(¼ )!u(¼ )"u(¼ )!u(¼ ). At this point, the three relevant      utility points lie on one straight line in the two-dimensional space defined by utility (u) and firm cash flow (X), in which case the controlling shareholder becomes neutral to the risk of the project and the cut-off point becomes pL "0.5. Thus, in determining whether or not first-best investment can be achieved, the key issue is whether the financing decision has enough flexibility to transform the owner’s utility into a linear function of project cash flows. In general, when there are more than three possible values of cash flows, two choice variables are not sufficient to align all possible utility levels along a linear line. Then, the controlling shareholder cannot be transformed to become neutral towards project risk, and the first-best investment cannot be achieved. 4.3. Optimal capital structure must involve risky debt Our next step is to show that financing with both debt and equity strictly dominates pure equity financing. Let F* be the face value that maximizes the owner’s expected utility at time t . We have the following lemma.  ¸emma 5. I!x(F*(I. Proof. See Appendix A.

 Detailed analysis of the equilibrium investment behaviour in general requires more complicated mathematical derivations, and is left for future research.

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From Lemma 4, we have p*50.5, which implies F*(I. This rules out the possibility of all-debt financing. What needs to be shown is that issuing some amount of risky debt strictly dominates issuing riskless debt. In the proof, we start with a benchmark case of F"I!x, where the investment decision and the owner’s utility are the same as in all-equity financing. A marginal increase of F from F"I!x makes debt risky, and changes both pL and P . And the overall W effect of a small increase in F is to increase the owner’s expected utility. Furthermore, if the increase in F is not too large, the incentive-for-acquisition constraint is not violated. This shows that the owner’s utility can be increased by issuing some risky debt at t .  Since atomistic investors always break-even in trading with the owner at t ,  their ex ante utilities are unaffected by the choice of capital structure. Given Lemma 5 that the controlling shareholder is strictly better off with risky debt, we can conclude that the equilibrium with debt-equity financing is Pareto superior to that produced by all-equity financing. Based on the above results, it will be natural to conjecture that debt-equity financing improves the investment decision in equilibrium, compared with the case of all-equity financing. This is verified by Lemma 6. ¸emma 6. ¸et the optimal financing decision be a* in the all-equity case and  (a*, F*) in the leverage case, then 0.54(pL (a*, F*)(pL (a*).    Proof. See Appendix A. The effect of financial leverage is summarized below. Summary 2: ¹he optimal capital structure is characterized by an interior debtequity combination. Compared with all-equity financing, using financial leverage improves both the investment decision and Pareto-efficiency. 4.4. Comparative static analysis Due to the mathematical complexity of the model structure, we rely on numerical simulations to perform comparative static analysis. Refer to figures for the discussion below. For convenience, the complete description of the owner’s problem used for simulations is given in Appendix B. The effect of the controlling shareholder’s risk aversion (c) on leverage (represented by debt face value F) is shown in Fig. 1a, and its effect on ownership

 Although the figures presented here are based on specific sets of parameter values, the qualitative relations described by these figures appear as general results of our model based on a wide range of parameter values with which we experimented.

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Fig. 1. (a) The relationship between the firm’s leverage (F) and the controlling shareholder’s risk aversion (c) at various levels of information acquisition cost (c). (b) The relationship between ownership concentration (a) and the controlling shareholder’s risk aversion (c) at various levels of information acquisition cost (c). The values of other parameters are: I"60 and x"45.

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concentration (a) is shown in Fig. 1b, where each curve corresponds to a particular value of information acquisition cost c. The result shows that leverage increases with the degree of risk aversion. The more risk averse the controlling shareholder is, the less tolerant he becomes towards risky projects, and therefore more debt is needed to correct the under-investment incentive. Increases in risk aversion also cause increases in controlling ownership, as is shown in Fig. 1b. In equilibrium, the cost borne by the controlling shareholder includes both c and the risk premium. For a given c, a greater c leads to a greater risk premium, and hence the controlling shareholder needs to hold a larger position to justify information acquisition. Fig. 1a and Fig. 1b also show that both ownership concentration and leverage increase with c. The greater the information acquisition cost, the more ownership concentration is required to overcome the free-rider problem, and hence the more severe the under-investment becomes. As a result, more debt is needed to counter-balance the under-investment incentive. Fig. 2a, Fig. 2b and Fig. 2c present the effect of project risk (measured by x) on F, F and a, where F ,F!(I!x) is the amount of debt repayment which is   unfulfilled in the event of financial default. The total amount of debt can be divided into two parts. One part is riskless, equal to I!x. The other part (F ) is  risky; it measures the extent to which debt is exposed to the default risk. We refer to F as the amount of ‘risky debt’. We normalize x, F, F by I in the figures so   that projects of different sizes can be shown together. As project risk increases, the total amount of debt decreases (Fig. 2a), but the amount of risky debt (F ) increases (Fig. 2b). This phenomenon can be explained  as follows. The effect of risky debt can be viewed as an insurance to the controlling shareholder for the down-side risk of the project. When a loss occurs on the project, this insurance offers shareholders a compensation of F!(I!x)"F ,  which is the difference between the promised payment and the actual payment to debt-holders. For a given I, the larger the value of x, the riskier the project, and hence the greater the amount of risky debt needed to offset the risk-averse behaviour; this explains positive relations between F and x shown in Fig. 2b.  Intuitively, this means that more insurance should be provided to shareholders when project risk increases. However, Fig. 2a suggests that increases in insurance compensation (F ) are  always smaller than increases in the level of risk (x). From Fig. 2a, dF/dx(0, then dF /dx"1#dF/dx(1. In other words, at every point, for an incremen tal increase in the size of potential loss, dx, the corresponding increase in insurance represents only a partial coverage for dx; shareholders bear some residual risk themselves. This result makes economic sense. If complete insurance were provided (which is the case when dF/dx50), the controlling shareholder would be fully compensated for any loss on the project. Then, the controlling shareholder would have a strict incentive to accept all risky projects

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Fig. 2. (a) The relationship between leverage (F) and project risk (x), (b) the relationship between the default risk of debt (F ,F!(I!x)) and project risk (x), and (c) the relationship between  ownership concentration (a) and project risk (x). The values of the other parameters are as follows. Series I: I"40, c"0.5, c"0.2; Series II: I"60, c"0.75, c"0.2; and Series III: I"80, c"1.0, c"0.2.

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except those which would lose money in every possible state. And, in our model, this would drive the cut-off probability to virtually zero. Clearly, complete insurance is not desirable. The controlling ownership is shown to decrease with x (Fig. 2c). As the potential cash flows of the project become more dispersed, there is a greater benefit from acquiring project information, and hence less equity position is required for the controlling shareholder to recover the cost of information acquisition.

5. Robustness of the results 5.1. On the feasibility of duplicating the effect of financial structure by direct compensation In this model, we use ownership structure and leverage to create an incentive for the controlling shareholder to acquire information and make a proper investment decision. Can the same incentive be produced by a direct compensation contract? In a perfect world, this might be possible; we could design a compensation contract, which mimics the net pay-off schedule for the controlling shareholder of our model, for a professional manager (who owns no equity in the firm). However, in an imperfect world where complete contracting is not possible or cannot be costlessly enforced, the effect of financial structure may not, in general, be replaced by a direct compensation contract. To be the controlling shareholder in our model, the individual must have personal wealth invested in the firm before the investment decision is made. With the uncertainty on the project’s cash flow, there is no guarantee that this individual, as a shareholder, can fully recoup his initial investment. In fact, there is a strictly positive probability that he ends up with a loss. To have a professional manager replace the large shareholder and use a compensation contract to mimic the exact pay-off schedule for the large shareholder, the contract must contain negative compensation to the manager (for the states when the corresponding large shareholder suffers a loss). As state-contingent compensation is settled only ex post, negative compensation (i.e., requiring the manager to make a payment to shareholders after the outcome is known) can be difficult to enforce as a practical matter. In the real world, the manager would have a strong incentive to avoid making such a payment, say, by transferring, hiding or even spending his personal assets when he foresees a bad outcome.

 One possible way of getting around this enforcement problem is to require the professional manager to set aside his personal wealth ex ante as a bond and leave it to an independent third party. But, then, requiring the manager to hold equity may just be a simple way of achieving the same effect.

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Another reason why it might not be possible to duplicate the effect of financial structure by an incentive contract is that information acquisition may be performed by a shareholder who is not at the same time a manager of the firm. It may be that the large shareholder who acquires information also owns stakes in other firms, such as an institutional investor, and thus has information from other industries, which makes his information acquisition more cost-effective. In this case, it is not feasible to use an incentive contract to motivate the large shareholder. 5.2. On the type of controlling shareholder In this model, the entrepreneur who founds the firm evolves to become the controlling shareholder. Do the general results on the role of ownership structure and financial leverage hold when the large shareholder is of an alternative type, such as a corporation or a financial institution? Our general results about corporate ownership structure and leverage can still hold when a firm is controlled by a corporation or an institution. The existence of a corporate or institutional large shareholder may result either from the sale of the controlling position to a corporation/institution by the firm’s original founder or from a hostile takeover, which involves tendering of shares by atomistic shareholders. In either case, the new corporate/institutional large shareholder inherits the firm’s financial and ownership structure from its predecessor. The cost—benefit trade-off faced by the new large shareholder on information acquisition is similar to what the controlling shareholder at t faces in  our model. The equilibrium strategy of the original controlling shareholder will continue to be played by the new large shareholder, since if there is any deviation in strategy which makes the new shareholder better off, it will make the original large shareholder better off and thus will unravel the original equilibrium. Of course, the new large shareholder may adjust the controlling ownership and leverage for possible differences in risk attitude from its predecessor. However, to the extent that the new shareholder is also risk averse, the qualitative results of our model still hold. A corporate large shareholder also may exist if the firm in question was originally a wholly owned subsidiary of a corporation, and subsequently part of its equity was sold to other investors. In this case, the parent corporation is interested in increasing the proceeds, just as the entrepreneur in our model, and our analysis becomes directly applicable. In practice, very often, large equity positions are passed on in blocks from one investor to another through either inheritance or transactions. Creation of a large shareholder solely by gathering atomistic shares through secondary trading seems difficult in theory, due to the free-rider problem, and is not commonly observed in practice. Our analysis is valid only to the extent where conditions indeed support the existence of a large shareholder.

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5.3. On the form of large shareholder control In this model, the activities carried out by the controlling shareholder are to acquire project information and then to make an investment decision. This particular feature of the model is intended to capture a generic situation where a large shareholder spends personal resources/effort to carry out a valueenhancing activity which benefits all shareholders of the firm. In this situation, there exists the free-rider problem, and a large shareholder is needed to resolve this problem. Some examples of large shareholder activities, to which our analysis has potential relevance, are takeover attempts, proxy fights, monitoring of management decisions, and so on, provided that these activities are expected to increase the total value of equity. A common feature is that the incentives for the large shareholder to carry out these types of activities are all described by a constraint similar to Eq. (8).

6. Empirical implications and conclusions 6.1. Empirical implications Our analysis above leads to a number of empirical predictions regarding ownership structure and leverage, to which we now turn. ¸everage and ownership concentration: The analysis predicts a positive relationship between firm leverage and ownership concentration. The higher the position owned by the controlling shareholder, the higher the firm’s leverage. Furthermore, for a given level of ownership concentration, leverage is higher for firms of which the controlling shareholder is more risk-averse. One way to measure risk aversion is to see whether the investor is an individual or a company. Typically, because of differences in wealth base, portfolio under-diversification is generally more severe when an individual investor controls a firm as opposed to when a large corporation or institution has control. Hence, the former type of controlling shareholder is generally more risk-averse than the latter types. An implication, then, is that the link between ownership concentration and leverage predicted above is, on average, stronger for firms which are controlled by individual investors compared to firms controlled by corporations/institutions. The existing empirical studies are consistent with these predictions. Mehran (1992) finds that the ratio of debt to equity is positively related to the equity ownership of the largest investor. Moreover, this relationship is statistically significant when the largest shareholder is an individual investor but not significant when the largest shareholder is an institution. Friend and Lang (1988) show that firms with a major shareholder have higher total-debt-to-asset ratios than those without a major shareholder.

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¸everage and project risk: As project risk increases, the total amount of debt decreases but the default risk of debt increases. This suggests that there are systematic differences in both leverage level and debt ratings between industries. Firms in more volatile industries, such as mining, instruments, and electronics, are likely to have lower leverage than those in stable industries such as retail and utilities. This prediction is supported by existing empirical findings (see the survey by Harris and Raviv (1991)). The prediction about the relationship between the debt credit rating and business risk needs to be tested in further research. ¸everage and the information acquisition cost: Increases in the cost of carrying out control-related activities (such as information acquisition in this model) lead to increases in ownership concentration and higher leverage. The difficulties in testing this prediction lie in the measurement of this cost. We leave it to future research for developing feasible ways of testing this prediction. Ownership structure and firm value: Since the role of the large shareholder is to enhance firm value, one might conjecture a positive relation between ownership concentration and firm efficiency. However, as this model suggests, the level of ownership concentration is determined by, among other things, the cost of performing a desired level of information acquisition or other controlling activities. Thus, high ownership concentration may be an indication of an environment where it is costly to conduct control-related activities. If Tobin’s Q is used as a measure of efficiency, as in Morck et al. (1988), then it is not clear that higher ownership concentration necessarily leads to a higher Tobin’s Q. In Morck et al. this relationship is empirically shown to be non-monotonic. 6.2. Summary In this paper, we assume that a shareholder is needed to acquire investment information and to control the firm’s investment decision. Under the condition that investors are intrinsically risk-averse, the paper provides an explanation for the simultaneous existence of a partially concentrated, partially diverse ownership structure and an interior debt-equity capital structure, which conforms to the corporate financial structure in practice. The analysis suggests that allequity financing can cause inefficient under-investment, but adopting a capital structure with a combination of debt and equity can mitigate the underinvestment problem and improve Pareto-efficiency. The model provides a number of empirical predictions about corporate ownership and financial structure. The existing empirical results mostly support these predictions.

Acknowledgements This article is based on my doctoral dissertation completed at the University of British Columbia. I thank Sudipto Dasgupta, Paul Fischer, Robert Heinkel,

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Alan Kraus, Josef Zechner, three anonymous referees and the Editor for valuable comments and suggestions on earlier versions of the paper. I also thank Yu Guang for providing capable programming assistance. I am solely responsible for all remaining errors. Financial support provided by the University of British Columbia for my doctoral study is gratefully acknowledged.

Appendix A. Proofs of lemmas Proof of ¸emma 1. (i) Since pL "eA?V/(eA?V#1), then dpL /da"cxeA?V/ (eA?V#1)'0. (ii) The owner’s expected utility is given by Eq. (7). Differentiating, and rearranging by using the definition of pL , we have





dE(u " a) (1!pL ) dpL " u(¼ ) (1!2pL ) (1!a) x !(1#pL !pL )x  da 2 da





dpL #pL u(¼ ) (1!2pL ) (1!a) x !(pL !pL )x  da





1!pL  dpL # u(¼ ) (1!2pL )(1!a) x #(1!pL #pL )x  2 da (1!pL ) ( u (¼ )[!1!pL #pL ]x  2 1!pL  #pL u(¼ ) [!pL #pL ]x# u(¼ )[1!pL #pL ]x   2 (u(¼ )x 



(1!pL ) (!1!pL #pL )#p(!pL #pL ) 2



1!pL  (1!pL #pL ) "0, # 2 where the first inequality follows since pL '0.5, a(1 and dpL /da'0, and the second inequality follows because u(¼ )'u(¼ )'u(¼ ) given ¼ (     ¼ (¼ . 䊐   Proof of ¸emma 2. With the exponential utility function, the constraint (8) can be rewritten in the form of G(a)4e\AA, with G(a) being a continuous function of a. Therefore, from part (ii) of Lemma 1, the constraint must be binding at the optimum.

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Proof of ¸emma 4. The cut-off probability with financial leverage is pL "(1!e\A?'\$)/(1!e\A?'>V\$). Let t be a control variable which alters decision variables a and F in the following way: a(t)'0, F(t)'0 and a(t) (I!F(t)) independent of t. Suppose that, contrary to Lemma 4, pL (0.5 in equilibrium. We will show that we can increase the expected utility and preserve the incentive-for-acquisition constraint by decreasing t, i.e., by decreasing a and F simultaneously while keeping a(I!F) unchanged. Differentiating pL and ¼ (which equals P !c) with respect to t, and simplify W ing, we have dpL pL cxe\A?'\$a(t) "! (0, dt 1!e\A?'\$>V and d¼ dpL dpL "(1!2pL ) x #( pL (I!F#x)!(I!F)) a dt dt dt 1 da ! (1!pL ) x . 2 dt With these two differentiations, we can show that



dE(u " a) " dt

(1!pL ) 1!pL  u(¼ )#pu(¼ )# u(¼ )    2 2



[(1!2pL )x#apL (I!F#x)!a(I!F)]

 

# !



dpL dt

1!pL  (1!pL ) u(¼ )#pL u(¼ )# u(¼ )    2 2

#u(¼ ) 





(1!pL ) da x . 2 dt

By supposition, pL (0.5. Given that the owner is risk-averse, the definition of pL implies pL (I#x!F)'I!F. Also dpL /dt(0. Therefore, the first term is negative. The second term is also negative given that u(¼ )'u(¼ )'u(¼ ).    Therefore, dE(u " a)/dt(0. The remaining part of the proof shows that the incentive-for-acquisition constraint is not violated as t decreases. Without information acquisition, the investment decision is made independently of p; the project is either always accepted or always rejected. The expected

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utilities under the alternative decisions are E(u " na, i)"E[(1!p)u(¼ #c)#pu (¼ #c)]   "(u(¼ #c)#u(¼ #c))    and E(u " na, ni)"u(¼ #c).  The supposition of pL (0.5 implies E(u " na, i)5E(u " na, ni); therefore, the controlling shareholder always accepts the project given that he does not acquire information. Information acquisition takes place if and only if E(u " a)5 E(u " na, i), or, (1!pL ) 1!pL  1 1 u(¼ )#pL u(¼ )# u(¼ )5 u (¼ #c)# u (¼ #c).      2 2 2 2 Substituting the expressions of pL , u ( ) ), ¼ , ¼ and ¼ , then rearranging, we    get (2k!1)eA?V!1 4eAA, keA?V!1 where k"eA?'\$, independent of t. It is easy to show that k'2k!1. Refer to the left-hand side of this constraint as LHS(t). Then, 2cxa(t)eA?V(k!2k#1) LHS(t)" '0. (keA?V!1) This shows that for any pL (0.5, the corresponding constraint is preserved as t decreases. This completes the proof. 䊐 Proof of ¸emma 5. To prove F'I!x, we will show that at F"I!x, the controlling shareholder can increase his expected utility by increasing the amount of debt. Differentiating E(u " a) (given by Eq. (7)) but recognizing that pL , ¼ , ¼ and   ¼ all are functions of F, and then simplifying, we get  dpL dE(u " a) "[(1!2pL )x!a(I!F)#a(I!F#x)pL ] dF dF ;





(1!pL ) 1!pL  u(¼ )#pL u(¼ )# u(¼ )    2 2

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#u(¼ ) 






!u(¼ ) 

pL (1!pL ) 1!pL  (1!pL ) a!u(¼ ) a  2 2 2

(1!pL ) 1!pL  pL # 2 2



a

'[(1!2pL ) x!a (I!F)#a (I!F#x)pL ] ;





dpL (1!pL ) 1!pL  u(¼ )#pL u(¼ )# u(¼ ) ,    dF 2 2

where the inequality follows since u(¼ )'u(¼ )'u(¼ ).    Let F"I!x#e, e50. Then, (1!2pL )x!a(I!F)#a(I!F#x)pL "(1!2pL )(1!a)x#a(1!pL )e. When e is sufficiently small, pL '0.5 as the cutoff point will be in the vicinity of the all-equity cutoff point, and, with a(1, we have (1!2pL )x!a(I!F)# a(I!F#x)pL (0. It follows that dE(u " a)/dF'0 for small values of e. The remaining issue is whether the constraint is still satisfied as F increases. Given pL 50.5 in equilibrium, the controlling shareholder would reject the project if he decides not to acquire information, in which case the the incentivefor-acquisition constraint is given by Eq. (8). Substituting the expressions for pL and u( ) ) and rearranging, the constraint becomes eA?'>V\$!(eA?V#e\A?V)/2 4e\AA. eA?'>V\$!1 Let ¸(F) represent the left-hand side of the above equation. It is easy to see that ¸(F)(1, and its derivative ca(1!¸(F)) eA?'>V\$ ¸(F)"! (0. eA?'>V\$!1 Therefore, for a given a, an increase in F does not violate the constraint. This completes the proof. 䊐 Proof of ¸emma 6. We first present the following lemma. ¸emma A.1. For any two financing choices, one with all-equity, represented by a ,  and the other with debt, represented by (a , F), which result in the same cutoff point  pL , the one with all-equity strictly dominates the other. The proof of Lemma A.1 is lengthy, which is available upon request, but the idea is straightforward. It compares the wealth distributions of the owner

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produced by the above two financing choices, and shows that, under the stated conditions, the owner’s wealth in the all-equity case second-order stochastically dominates that with debt-equity financing. We now prove Lemma 6 based on Lemma A.1. Let pL (a*) be the optimal  cut-off probability under full-equity financing. By Lemma 1, for any a greater  than a*, we have pL (a )'pL (a*) and Eu(a )(Eu(a*).      Let pL (a*, F*) be the optimal cut-off probability under debt-equity financing.  Suppose that pL (a*, F*)5pL (a*). Then, there exists an a , with a 'a*, such that      pL (a )"pL (a*, F*). Then, Lemmas 1 and A.1 together imply that   Eu (a*, F*)(Eu(a )(Eu (a*).    However, this contradicts Lemma 5. Therefore, it must be that pL (a*, F*)  (pL (a*).  Combining with Lemma 4, we have 0.54pL (a*, F*)(pL (a*).   Appendix B. Complete description of the owner’s problem with leverage



  



(1!pL ) 1 1 Maximize E (u " a), ! e\A5 #pL ! e\A5 2 c c ?$ 1!pL  1 # ! e\A5 2 c



subject to



  







1 1 1!pL  1 (1!pL ) ! e\A5 #pL ! e\A5 # ! e\A5 c c 2 c 2



1 5 ! e\A5>A , c where






1!pL  1!pL  ¼ "I#pL (1!pL )x!a(I!F) pL # !a x!c,  2 2 ¼ "¼ #a(I!F),   ¼ "¼ #a(I#x!F),   and 1!e\A?'\$ pL " . 1!e\A?'>V\$

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