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The Changing Nature of Debt and
Equity: A Hnancial Perspective
Franklin Allen*
Historically, corporations have mainly financed their activities with two securities, debt and equity. The stockholders have responsibility for the operation of the firm through the election of the board of directors; the dividends they receive in return for their subscription of capital are not guaranteed and are paid at the discretion of the board of directors. In contrast, debtholders are promised a particular rate of return; they have no rights of control unless payments by the firm are omitted, in which case they have the right to foreclose on assets or, in some cases, force bankruptcy. Dewing (1934, pp. 236-37) ascribes these differences in rights between debtholders and equityholders to the historical distinc- tion in Anglo-Saxon law between debtors and creditors. As a result of the importance of debt and equity, the focus of inquiry into firms’ choice of capital structure has traditionally been "What is the optimal debt-equity ratio?" Modigliani and Miller (1958) and subsequent authors 1 showed that if capital markets are perfect and complete and no taxes are in effect, a firm’s debt-equity ratio has no effect on its value because investors’ opportunity sets are not affected by its capital structure. If a corporate income tax is in effect, with interest deductibil- ity, Modigliani and Miller (1963) used the same logic to show firms should use entirely debt finance since this allows corporate taxes to be avoided.
*Associate Professor of Finance and Economics, the Wharton School, University of Pennsylvania. The author is grateful to Jaime Zender and to his discussants, Oliver Hart and Robert Merton, for helpful comments. Financial support from the National Science Foundation (Grant No. SES-8813719) is acknowledged. i See, for example, Hellwig (1981) and the references therein.
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This prediction of the theory did not square well with empirical evidence; despite interest deductibility and a corporate tax rate of almost 50 percent at that time, firms typically used only moderate amounts of debt. This led a number of authors^2 to point to the capital market imperfection of bankruptcy and liquidation costs. They suggested that a firm balances these costs against the tax advantage of debt and it is this trade-off that determines the optimal debt-equity ratio. The trade-off theory has been criticized on a number of grounds. Evidence on the direct costs of bankruptcy, such as lawyers’ fees, suggested they were small (Warner 1977). Direct measurement of the indirect costs of bankruptcy, such as the difficulties of running a firm while it is in bankruptcy court, are difficult to obtain; proponents of the trade-off theory suggest they are significant while detractors suggest they are small relative to the tax advantage of debt. It is widely agreed that liquidation costs, which are the costs of breaking up a firm and selling it off piecemeal, are sufficiently large to explain firms’ observed debt ratios if included with bankruptcy costs. However, Haugen and Senbet (1978) argued that liquidation costs should not be included with bankruptcy costs since liquidation was not implied by bankruptcy; if the firm was worth more as a going concern it would not be liquidated. In addition, they argued that if bankruptcy was costly it could be avoided by firms’ buying back their debt just before it became due. These arguments depend on perfect markets; a number of recent papers have investigated why bankruptcy and liquidation may be linked and why bankruptcy may be difficult to avoid by repurchasing securities when markets are imperfect. 3 The deficiencies of the trade-off theory resulted in the development of a number of alternative theories. Miller (1977) pointed to the impor- tance of personal taxes. He argued that personal taxes on equity were lower than on debt and presented a model where this personal tax disadvantage of debt entirely offset its corporate tax advantage so that in equilibrium each firm was indifferent between the use of equity and debt. De Angelo and Masulis (1980) and subsequent authors^4 developed this model to allow for bankruptcy costs and other factors; in this case again a trade-off exists between the use of debt and equity and firms have an interior optimal capital structure. Some of the alternative theories that did not rely on the inclusion of personal taxes were based on asymmetric information. Agency theories
2 See, for example, Kim (1978) and the references therein. 3 See, for example, Titman (1984); Allen (1987); Webb (1987); Giammarino (1989); and Mooradian (1989). 4 See Kim (1989) for a survey of this literature.
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ever, Miller (1986) suggests that financial innovation has proceeded at a particularly fast pace during the last twenty years. Not only have corporations started to issue new securities such as zero coupon bonds and adjustable rate bonds, but also entirely new markets such as the Chicago Board Options Exchange have been established.^6 Miller argues that much of this recent innovation is in response to features of the tax code and to regulation. A classic example of innovation in response to the tax code is zero coupon bonds. Before the Tax Equity and Fiscal Responsibility Act of 1982 (TEFRA), the tax liability on zero coupon bonds was allocated on a straight line basis; that is, the annual interest deduction was the amount to be repaid at the due date less the issue price, divided by the number of years until repayment. This rule ignored the effect of compounding of interest and created an opportunity for corporations to avoid taxes by issuing long-term zero coupon bonds to tax-exempt investors. When interest rates were high in the early 1980s, the potential tax benefits from this type of security became large and corporations issued a large amount of these bonds. Although TEFRA closed this loophole, the market for zero coupon bonds continued but now was mainly supplied by investment banks "stripping" government securities into principal and interest (Kane- masu, Litzenberger, and Rolfo 1986). An alternative rationale for financial innovation, stressed by Van Horne (1985), is that new securities may make markets more complete in the sense that they increase opportunities for risk sharing between investors. In a categorization of the primary factors responsible for the introduction of sixty-eight new types of security, Finnerty (1988) lists tax and regulatory advantages in twenty-seven cases and risk reallocation in fifty-three cases. (More than one factor is possible for each type of security.) In addition to taxes and regulation and risk reallocation, another important class of security innovation has resulted from attempts by incumbent managements to discourage takeovers. Examples of these "poison pill" defenses are preferred stock plans, flip-over plans, back- end plans and voting plans. The securities associated with these plans all have the common feature that on the occurrence of a takeover attempt not approved by the board of directors, certain rights accrue to the securityholders. For example, target shareholders may be given the right to buy the stock of the bidder at a substantial discount on completion of the takeover.^7
6 For a full account of recent innovation see Finnerty (1988). 7 See Malatesta and Walkling (1988) for a more complete description of actual poison pills.
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Tufano (1988) has constructed a data base of fifty-eight financial innovations introduced by investment banks between 1974 and 1987. These innovations, often bonds, equities or preferred stocks with novel features, can cost substantial amounts to develop. Tufano finds that the banks that create these products almost immediately face competition from rivals offering imitative products. During the brief period of monopoly before imitation, originators do not charge high prices to recoup their development costs. Moreover, once the imitative products appear, they charge a lower rather than a higher price than the imitators. The main difference between the originating bank and imita- tors is that the originating bank obtains a larger share of the market. Tufano gives a number of reasons why market share may allow originators to recoup the costs of developing the products. Sunk costs may be involved in entering the underwriting business. These may deter entry and allow positive profits; price competition may be limited by the type of noncooperative collusion considered by the threat of reverting to the single-period equilibrium. Another possibility is that the bank may make profits on related business so that it can recapture the costs in this way. The fact that debt and equity are not the only securities that firms use to finance their activities, and the constant introduction of new forms of securities, suggest that a more fundamental issue than "What is the optimal debt-equity ratio?" is "What are the optimal securities that should be issued?" Many recent studies of capital structure have taken this perspective. These studies provide some insight into the changing nature of debt and equity. This literature has two branches. The first has been concerned with trying to identify the circumstances in which debt and equity are optimal. This will be considered in the next section of this paper. The second branch has been concerned with the optimal securities that a firm should issue. The succeeding section considers this, followed by a summary and conclusions.
When Are Debt and Equity Optimal?
A number of papers have identified situations where debt contracts are optimal. Townsend (1979) considers the optimal contract between a risk-averse agent and a risk-neutral principal. In one version of the model, the agent requires funds at the beginning of the period to produce a random income at the end. The principal can observe the realization of the agent’s income only if bankruptcy is declared and the agent’s income is transferred to the principal. This bankruptcy process is cosily. Among the class of deterministic strategies, where the principal
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state by state that are contingent on the firm’s earnings will presumably prevent markets from being effectively complete. In addition to the applicability of this type of analysis to corpora- tions, another issue to be considered is the assumption by Townsend that strategies are deterministic, so that income is observed by declaring bankruptcy with probability one or zero. Mookherjee and Png (1989) show that if random strategies are possible, then the optimal contract involves randomization. To see why it is possible to do better with random strategies, consider the optimal deterministic contract, which is a debt contract. Suppose that the agent is now made to announce his income, and bankruptcy occurs with probability one whenever the announced income is less than the required payment. During bank- ruptcy, the true value of the agent’s income is revealed. By rewarding the agent when he has correctly announced his income level, it is possible to provide a strict incentive to tell the truth. This means it is no longer necessary to force bankruptcy all the time. Since the agent is risk averse and the principal is risk neutral, this change allows a Pareto improvement. The important issue here is whether randomization is possible. If a device exists that both parties know is truly random, then Townsend’s type of analysis is unable to provide a rationale for debt contracts, but if such randomization devices do not exist, it can.
Allocation of Control Rights
The papers considered above are primarily concerned with the allocation of cash flows. In a recent paper, Aghion and Bolton (1988) take a different approach by looking at the allocation of control rights among different securityholders in closely held firms. They consider a model with the sequence of events shown in Figure 1. An entrepreneur has insufficient resources of his own to finance a project he wishes to undertake. The project involves an outlay at time 0 and yields revenues at time 1 and time 2. The entrepreneur can finance the investment by issuing securities at time 0 to an outside investor who receives a portion of the firm’s profits at time 1 and time 2. Both the entrepreneur and the investor are assumed to be risk neutral, so that risk-sharing issues are not considered in the model. At time 1, the firm’s monetary profits and its prospects for future earnings, which can be either good or bad, are determined. After receiving this information, the party in control of the firm decides on which of three possible courses of action to undertake: expand the firm, continue as before, or liquidate. If the time 1 prospects for future earnings are good, expansion leads to the highest expected profits, continuing as before the next highest, and liquidating the least. If the
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Figure 1
The Sequence of Events in the Aghion
and Bolton (1988) Model
t=0 1 2
Entrepreneur issues Monetary/profits realized.^ Monetary profits a security to finance The prospects (good^ realized. an investment, or bad) for time 2 earnings revealed and the firm either expands, stays the same, or liquidates.
prospects are bad, the reverse is true. The private costs to the entrepre- neur of the three courses are different, with liquidation being the most costly, expansion the next most costly, and keeping operations the same the least costly. The magnitudes of the expected monetary profits and private costs to the entrepreneur are such that in the first-best world where all states can be contracted on, it is optimal for the firm to continue operations as before in the state where prospects are good, and liquidate in the state where prospects are bad. The critical assumption that Aghion and Bolton make is that contracting possibilities are incomplete. In particular, the earnings prospects cannot be contracted upon; the only variable that can be contracted on is monetary profits. This creates two problems. The first occurs if the entrepreneur uses securities that cede control of the firm to the investor and the good state is realized. In this case, the investor would like the firm to expand since this maximizes expected monetary profits. However, this is not optimal since it imposes large costs on the entrepreneur; when these costs are taken into account, continuing the current level of operations is optimal. The second problem occurs if the entrepreneur retains control. Now if prospects are good the efficient action of continuing operations will be chosen; however, if prospects are bad the entrepreneur may not have the correct incentives to liquidate. The entrepreneur bears high private
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Figure 2
The Sequence of Events in the Zender (1 989) Model
t=O (^1 2 3 )
Entrepreneur Effort choice that Signal Effort choice Monetary designs and sells determines realized that partially/ profits securities, time 2 signal and control determines (^) realized. Control assigned and partially assigned for time 4 for time 1. determines time 3. profits. time :4 profits.
finance the entire project would obtain the full marginal benefits of the effort choices and so would be prepared to undertake the efficient level. However, because neither investor has sufficient funds to finance the entire project, the securities must be such that both have a chance of obtaining part of the time 4 payoffs. This means that the investor in control does not get the full marginal benefit of the effort choice at times 1 and 3. Zender shows that the optimal contract involves making control at time 3 and the allocation of payoffs at time 4 contingent on the time 2 signal. If a good signal is observed at time 2, the investor in control at time 1 remains in control and retains the residual of the payoffs less a constant amount at time 4. If a bad signal is observed, then control is switched to the second investor who obtains the payoffs at time 4. This optimal contract is interpreted as the investor in control initially having equity and the other investor having debt; it ensures that the investor who is delegated control is made the residual claimant and so has incentives to make the proper decisions. Another paper that is related to Aghion and Bolton (1988) is Hart and Moore (1989). They also consider a model of an entrepreneur who wishes to raise funds to undertake a project when contracting possibil- ities are incomplete. The focus of their analysis, however, is the problem of providing an incentive for the entrepreneur to repay the borrowed funds. It is the ability of the creditor to seize the entrepreneur’s assets that provides this incentive.
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Figure 3
The Sequence of Events in the Hart and Moore (1 989) Model
t=0 1 2
Entrepreneur (^) Payoffs Payoffs raises funds realized, realized. for initial Assets can be Assets have investment, liquidated for less zero liquidation than the time 2 value. payoffs.
The sequence of events in the simplest version of their model is shown in Figure 3. A risk-neutral entrepreneur raises funds from a risk-neutral outside investor to purchase assets that can realize payoffs at times 1 and 2. If the entrepreneur does not fulfill the contract at time 1, the outside investor can renegotiate or can seize some proportion of the assets and liquidate them. Liquidation is socially inefficient, how- ever, because the liquidation value of the assets at time I is less than the present value of the time 2 payoffs. Although both the entrepreneur and the outside investor have symmetric information, third parties such as the courts cannot observe the asset payoffs so these cannot be contracted upon. The entrepreneur can appropriate the cash flows from the assets for his own use, so the problem is to design a contract that provides incentives for the entrepreneur to repay the loan. It is shown that the optimal contract is a debt contract and the incentives to repay are provided by the threat of liquidation. Since the present value of the time 2 payoffs of the assets is above their liquidation value, the entrepreneur will always want to hold on to as high a proportion of the assets as possible and will be prepared to pay up to the assets’ present value. In low payoff states, the entrepreneur will have insufficient cash to make the required payment; the outside investor therefore renegotiates the loan and liquidates a certain proportion of the assets to make the payment up to the required amount. Although this liquidation is inefficient relative to an ideal world, it is necessary because the entrepreneur cannot commit to pay any of the time 2 payoffs to the
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exists: individual shareholders do not have an incentive to carefully monitor management and vote them out when they perform badly. Monitoring of management is likely to be important when a single individual or group has a large enough ownership share to make the free-rider problem insignificant. A prime example of the type of situa- tion where this occurs is the case of a takeover bid. Grossman and Hart therefore consider a model where the allocation of voting rights and dividends to securities is determined by its effect on allowing rivals to obtain control from an incumbent management. Initially, the firm is owned by an entrepreneur who wishes to draw up a corporate charter that maximizes the value of the firm. Grossman and Hart are interested in schemes that are privately optimal for the entrepreneur. A number of different classes of shares can be created and the share of votes and the share of dividends accruing to each can be varied. The entrepreneur anticipates that these securities will be widely held and that the firm will be run by an incumbent management. At some date in the future, a rival team, which may or may not be able to manage the firm better than the incumbent team, may attempt to acquire control by bidding for the securities to which control rights are attached. The incumbent team makes a counteroffer and holders of the securities decide which offer to accept. The critical assumption of the model is that management teams can obtain private benefits from controlling the firm; the optimal allocation of voting rights and dividends depends on the absolute and relative sizes of the private benefits accruing to the incumbent management team and the rival team. If private benefits are negligible, then the allocation of control is unimportant and one share, one vote is as good as any other allocation. Grossman and Hart first consider the case where all securities of a particular class must be treated equally, so that the whole class must be purchased if the votes of that class are necessary for control. Suppose that the private benefits of control are one-sided; for example, suppose the incumbent team has no private benefits of control but the rival team does. In this case one share, one vote is optimal because it maximizes the amount the rival must pay to obtain control. If a firm has a voting structure that allows the rival to obtain control by buying securities with only a small proportion of dividends attached, then he can obtain control and the associated benefits it provides to him at a small price. This may even be worth doing when the rival cannot generate as high a dividend stream as the incumbent. In order to make sure the rival pays as much as possible for control and its associated private benefits, and in particular at least as much as the value of the dividend stream provided by the incumbent, votes must be spread as widely as possible. This
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implies one share, one vote. A similar argument holds if the incumbent team has one-sided private benefits of control. If private benefits are two-sided so that both teams value control, one share, one vote is no longer optimal. The reason is that by separating votes from dividends it is possible to get the incumbent and rival to compete for control and pay for the associated private benefits they obtain. Grossman and Hart argue that this case is of little interest empirically for large publicly owned corporations, since the extent to which management can extract benefits is limited by corporate law, which gives a corporation’s directors a fiduciary duty to all sharehold- ers. It then follows that their theory is consistent with the widespread use of one share, one vote among publicly owned corporations. Finally, Grossman and Hart consider the case where it is not necessary to treat all holders of a particular class of securities equally; it is only necessary for the rival to obtain the proportion of votes specified in the charter to obtain control. This prespecified proportion is assumed to be between 50 and 100 percent. Ignoring the case where both incumbent and rival have private benefits of control for the reasons mentioned above, the analysis of the optimal proportion is similar to before. The main difference occurs when the incumbent has one-sided benefits of control. In this case, it is optimal to set the proportion at the lowest value of 50 percent, since this minimizes the chance of the incumbent team maintaining control. Their paper thus provides some rationale for the use of a single class of equity with control requiring a majority of the votes. Harris and Raviv (1988a) also consider the optimal allocation of voting rights and dividends to securities. Although the details differ somewhat, the framework is similar. One of the main differences between the papers is in the focus of the analysis. Grossman and Hart consider arrangements that are privately optimal as far as the original entrepreneur who designs the charter is concerned; they do not consider a criterion of social optimality, which includes the private benefits accruing to the incumbent and rival management teams. In contrast, Harris and Raviv do explicitly distinguish between private and social optimality. Harris and Raviv show that one-share, one-vote majority rule is socially optimal since it ensures that the management team that gener- ates the greatest total amount (including payouts to shareholders and private benefits to managers) controls the firm. This is because the arrangement allows the team that can pay the most to gain control; any deviation gives an advantage to the incumbent or rival that may allow them to gain control even though they generate a lower total amount. The arrangement that is privately optimal for the original owner involves issuing two extreme classes of security, one with all the voting
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Blair, Golbe and Gerard (1989) consider a model similar to that of Harris and Raviv (1988a) in that they are concerned with social optimal- ity and both the rival and incumbent have private benefits of control, but these authors obtain rather different results. They are able to show that, in the absence of taxes, one-share, one-vote majority rule and extreme securities that unbundle voting rights and cash flows are equivalent and both lead to social optimality. In contrast, Harris and Raviv show that only one-share, one-vote majority rule is socially optimal; extreme secur- ities can lead to suboptimal outcomes. The reason for this difference is that Blair, Golbe and Gerard assume the rival and incumbent bid simultaneously, whereas Harris and Raviv assume they bid sequen- tially. Again, this difference in approaches and its effect on the results raises the question of which is the most appropriate way of modeling the situation. The main concern of Blair, Golbe and Gerard is to consider the effect of capital gains taxes on the allocation of voting rights and cash flows. If capital gains taxes are in effect, then welfare is improved if extreme securities are used. This is because a lock-in effect means capital gains taxes may prevent a superior rival from winning if there is one-share, one-vote majority rule; tax liabilities may be higher when the rival wins than when the incumbent wins. Allowing separate trading of votes alleviates this effect. Taking the security structure of voting equity and debt as exoge- nous, Harris and Raviv (1988b) stress the importance of capital structure for takeover contests, because high leverage allows a controlling interest to be acquired for a low outlay. Harris and Raviv (1989) combine this idea with the approaches in Grossman and Hart (1988) and Harris and Raviv (1988a) by considering the allocation of voting rights and cash flows when the firm is not restricted to issuing just equity. They use a similar model to that of Grossman and Hart. In particular they focus on privately optimal securities, only the incumbent (or the rival) is assumed to have private benefits of control, and each investor ignores any effect his actions may have on the outcome of the tender. The problem of the entrepreneur who owns the firm initially is to design securities that prevent the incumbent management that has private benefits from maintaining control when a superior rival appears. This means that the cost of resisting takeovers must be maximized. As in the papers focusing only on equity, one share, one vote among voting securities is an important component of this, since it means that control cannot be acquired cheaply by the party with private benefits. In addition, they show that nonvoting risky securities should not be sold to outside investors; if nonvoting securities are sold to outside investors, they should be risk-free debt. The reason is again that these maximize the cost of obtaining control and so tend to favor the superior rival.
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Figure 4
The Sequence of Events in the Bagwell
and Judd (1 989) Model
t=
Identical investors design a corporate charter and issue securities to finance investments.
1
Investors discover whether they are type A or B. Initial investments’ payoffs are realized and firms decide on payout and how to invest retained earnings. New firms can be set up.
2
Payoffs of investments are realized and paid out.
The private optimality of one share, one vote in Harris and Raviv (1989) again appears to depend on the assumption of asymmetric benefits of control between the incumbent and rival. If both had private benefits of control, extreme securities of some sort might be optimal as in Harris and Raviv (1988a). An interesting issue is whether debt and equity remain optimal in this case. The models to analyze the design of equity that have been consid- ered above are all concerned with the effect of voting when an incum- bent management team is challenged by a rival team. Bagwell and Judd (1989) take a different approach by considering the optimality of major- ity rule where control is concerned with payout and investment deci- sions. The sequence of events in their model is shown in Figure 4. Initially all investors are identical; they design corporate charters and issue securities to finance firms’ investments. At time 1 investors discover whether they are type A or B. Type As value consumption at time 1 and time 2 and require a minimum level of consumption at time 1. Type Bs only value consumption at time 2 and are less risk averse than type As at that time. Just after investors’ types are discovered, firms decide on how much of the cash generated by the initial investment to pay out to shareholders and whether to invest the retained earnings in a safe or a risky project. If investors have any cash remaining at time 1 they can invest it in new firms. At time 2, the final payoffs from firms’ invest- ments are realized and paid out to shareholders.
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papers mentioned require that the firm or its investors or both be risk neutral. Since it has traditionally been argued that one of the main roles of the stock market is to allow risk to be shared, this assumption is fairly restrictive. Moreover, the long history and extent of financial innovation suggest that firms’ financing needs are not satisfied by debt and equity. Rather than ask "What are the circumstances where debt and equity are optimal?" another branch of the literature has been concerned with the question "What are the optimal securities to issue?" The Modigliani and Miller result, that capital structure is irrelevant when markets are complete, suggests that the form of securities issued is also irrelevant in these circumstances. In orde’r to develop a theory of optimal securities, it is necessary that markets be incomplete. One possible reason for incompleteness that is often suggested is transaction costs. Allen and Gale (1988; 1989) have considered the implications of the transaction costs of issuing securities. Allen and Gale (1988) develop a simple model of financial innova- tion with two dates and a finite set of states of nature. Information is symmetric; the state is unknown to everybody at the first date and revealed to all at the second. A single good exists at both dates, along with a finite number of investor and firm types with a continuum of each type. Instead of assuming that firms are restricted to issuing debt and equity, however, Allen and Gale assume that firms choose the securities that they issue and this determines the transaction costs they incur. This means the market structure is endogenous and it is possible to consider the theoretical issues raised by financial innovation. The equilibrium concept used is based on that of Hart (1979) and is essentially Walrasian. Markets are perfectly competitive since there is a continuum of firms and consumers. Prices are quoted to both firms and investors for every possible security. This includes all those securities that are issued in equilibrium as in Hart’s model. It also includes all those securities that could be issued but in equilibrium are not (that is, demand and supply are both zero). This contrasts with Hart’s approach where markets for these unissued securities are closed to investors and prices are quoted only to firms. The first result obtained is that under standard assumptions equi- librium exists provided short sales are not possible. If securities can be costlessly sold short, then equilibrium may not exist because short- sellers are effectively able to expand the supply of firms’ securities more cheaply than firms can. For example, suppose a firm can issue two securities rather than one for some additional cost. In order for the firm to be willing to do this, its gross value with two securities must be larger than with one to allow it to recoup this additional cost. However, if costless short sales are possible this implies an arbitrage opportunity is available, since by going short in a two-security firm and long in a
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one-security firm, an investor can earn the difference between the two. An equilibrium where all firms issue one security may not be feasible because at the prevailing prices issuing two securities may be profitable. Thus equilibrium may not exist unless short sales are ruled out. The short sales constraint means that with incomplete markets distinct types of investor value securities differently on the margin. The price of a security, whether issued or unissued, is determined by the group that values it most. In equilibrium, the firm issues the securities that maximize its value and sells them to the groups or clienteles that value them the most. The second result obtained is that every equilibrium is constrained efficient. In other words, a planner subject to the same transaction costs for issuing securities and able to make transfers between investors at the first date cannot make everybody better off than in the market alloca- tion. This result arises because of the assumption that the prices of unissued securities are quoted to both firms and investors. If prices are only quoted to firms, then inefficient equilibria may exist because of a pecuniary externality. To see this, suppose there are two types of firm, each of which produces output in one state only. Investors have Cobb-Douglas utility functions so that consumption in one state will not have value unless consumption is positive in the other. If markets for unissued securities are closed to investors, an equilibrium exists where the firms do not issue any securities because the price quoted to them for all securities is zero. This cannot be an equilibrium if prices are quoted to investors as well, because at zero prices they would demand securi- ties that allow them to consume in both states. A third result is that debt and equity are not optimal but that the optimal securities do have a particularly simple form. To see this, suppose there are two types of investor, one type of firm and two states. When firms issue only equity, the more risk-averse investors have a lower marginal utility of consumption in the high-output state than the less risk-averse investors; in the low-output state, the reverse is true. If a firm issues debt and levered equity, the more risk-averse group will pay a premium for the debt since it allows them to smooth consumption; the levered equity will be held by the less risk-averse group since they value consumption most in the high-output state. This split is not optimal, however, because the debt allocates payoffs in the good state to the more risk-averse group that values consumption the least. The firm could obtain more for its securities by allocating all the payoffs in the good state to the security that is held by the less risk-averse group, which values consumption most in this state. In general, it can be seen that optimal securities involve allocating all the firm’s output in a particular state to the security held by the group that values consump- tion most in that state.
