Ebook The Roles of Debt, Equity and Warrants Under Asymmetric Information
Following the famous irrelevance proposition of Modigliani and Miller (1958), a vast literature has developed trying to explain the financial choices of firms when they seek outside funds. Despite this research effort, important puzzles remain. Some recent empirical studies find that neither of the two dominant theories of capital structure, the trade-off theory and the pecking-order theory, provides a satisfactory explanation for the observed financing patterns. Firms appear to issue surprisingly large amounts of equity, even after controlling for the various costs (due to financial distress, bankruptcy and agency problems between debtholders and shareholders) associated with debt issues. Moreover, although equity issue announcements are associated with stock price drops (due to adverse selection), equity dominates debt as a source of external financing. Myers and Majluf (1984) show that this adverse selection problem may lead to underinvestment and so a loss in social welfare.
Furthermore, a considerable fraction of the securities with option features issued by firms are debt-warrant (or equity-warrant) combinations rather than convertible debt. Existing models offer various explanations of why firms issue convertible debt. However, none of them justifies the necessity for the issue of warrants.
This paper abstracts from taxes, financial distress, bankruptcy and other agency costs and focuses on asymmetric information. We consider a model involving both adverse selection and (effort) moral hazard. There are two types of firms (projects): risky (R), safe (S). Given identical effort levels, the success probability of the safe project is higher but its return in case of success is lower. In the event of failure the return of both types is zero. The entrepreneur can increase the success probability by exerting costly effort. Regardless of the project’s type, if the entrepreneur exerts effort the net present value (NPV) of his project exceeds the cost of effort whereas if he shirks the project has negative NPV. That is, exerting effort is socially efficient for both types. Both the project’s type and the entrepreneur’s action are unobservable.
In this setting, we analyse the roles of debt, equity and warrants and make three contributions. First, we explain the issue of combinations of debt and equity as the outcome of the interaction between adverse selection and moral hazard. Some firms (the risky ones) issue equity even if under pure adverse selection they would have issued just debt. Second, we show that, in the presence of moral hazard, adverse selection may result in the conversion of a negative into a positive NPV project and an improvement in social welfare. Third, we provide two rationales for the use of warrants. We also show that, under certain conditions, a debt-warrant combination can implement the optimal contract as a competitive equilibrium.
n implement the optimal contract as a competitive equilibrium. Two cases are considered: i) pure adverse selection and ii) adverse selection cum moral hazard. In the former case, a combination of securities is only used to convey socially costless information about the type of the project. In the latter case, in addition to transmitting information, the securities issued are the means of providing the appropriate effort incentives. Because of this second role, the introduction of moral hazard into an adverse selection framework has significant effects both on the combinations of securities issued in equilibrium and their pricing.
Regarding the pure adverse selection case, if firms have more information about the quality of their projects than their financiers, then they have an incentive to issue overpriced securities. To the extent that firms cannot credibly signal their type, the resulting adverse-selection problem may lead firms to forego a positive NPV project. Following Myers and Majluf (1984), a great deal of reseach effort has been devoted to exploring the extent to which this problem can be overcome if firms use different combinations of financial instruments to transmit information. It has been shown that debt or equity repurchases in conjuction with the issue of some other security (e.g. equity or convertible debt respectively) may allow for the existence of fully revealing equilibria where the securities issued are correctly priced.
In this paper, we do not allow for debt or equity repurchases. Firms try to reveal their type by issuing debt-equity or debt-warrant combinations. Equity (warrant) is a convex claim and so its value increases with the variability of returns. On the other hand, debt is a concave claim and so its value falls with risk. That is, in relative terms, debt is more valuable for the safe type and equity (warrant) for the risky one. Thus, by issuing more of the less valuable for him security, an entrepreneur can credibly signal his type and reduce the underpricing of his securities. However, the existence of an equilibrium where the securities issued are fairly priced requires that debt is more valuable for the S-type and equity (warrant) for the R-type not only in relative but also in absolute terms. Otherwise, the type whose securities are more valuable can only minimise the underpricing of his securities by issuing just the relatively less valuable for him security.
If the risky projects are mean-increasing or mean-preserving spreads of the safe ones or the risky projects dominate the safe ones by first-order stochastic dominance both conditions are met. In the first case, separation requires the issue of both debt and equity (Heinkel 1982). In the two remaining cases, the adverse-selection problem can be solved (mitigated) by issuing either just equity (mean-preserving spreads) or just debt (first-order stochastic dominance). On the other hand, if the risky projects are mean-reducing spreads of the safe ones, both the debt and equity issued by the S-type are more valuable than those issued by the R-type. Thus, the S-type cannot reveal his type and inevitably subsidises the R-type through the mispricing of the relatively less valuable for him security (equity) at individual level.
The use of warrants, through the appropriate choice of their exercise price, allows for the achievement of full separation even in this case. Since the return of the R-type in case of success is greater, a given increase in the exercise price of the warrant implies that the project’s return constitutes a smaller proportion of the total payment to the financier if the warrant is issued by the S-type. That is, as the exercise price rises, the value of the warrant issued by the S-type falls faster. As a result, for a sufficiently high exercise price, the warrant issued by the R-type can be more valuable than that of the S-type even if the S-type equity is more valuable.
This mechanism provides a rationale for the use of warrants. Warrants are issued because they can serve as separation devices when other standard securities (debt, equity and/or convertible debt) cannot.
The introduction of moral hazard into an adverse selection framework has significant effects both on the combinations of the securities issued in equilibrium and their pricing. The distinguishing feature of this part of the paper is the existence of pooling equilibria involving cross subsidisation across types and the issue of both debt and equity (warrants). These pooling equilibria reflect a trade-off between information revelation and effort incentives. The securities issued by the R- and S-type are priced as a pool. Although, because of perfect competition, debt and equity (warrants) are fairly priced collectively, at individual level they are mispriced. In fact, it is precisely this mispricing that provides the more prone to shirking type with the subsidy necessary to induce him to choose the socially efficient high effort level.
Consider, for example, the case where the S-type is more prone to shirking and we restrict ourselves to debt and equity. In this case, in the pooling equilibrium the R- type subsidises the S-type through the mispricing of equity. In the absence of moral hazard, the R-type would have issued more debt and less equity. Since, in doing so, he would reduce the subsidy and increase his expected return. However, in the presence of moral hazard, the S-type always mimicks the R-type and such a deviation would destroy his effort incentives. As a result, both the collective and the R-type’s net expected return would fall. Since he cannot reveal his type, the R-type accepts to issue just enough equity to induce the S-type to exert effort because the resulting increase in his net expected return (due to the lower interest rate on debt) more than offsets the cost of the incremental subsidy (the adverse selection cost of issuing equity). That is, this pooling equilibrium involves the minimum subsidy consistent with the S-type exerting effort. In any pooling equilibrium involving more than this minimum subsidy, the R-type can still profitably deviate by issuing more debt and less equity.
That is, in the presence of both adverse selection and moral hazard, in addition to being communication devices, debt and equity play a second role. That of incentivising the more prone to shirking type through their mispricing at individual level. This double role stems from the interaction between advese selection and moral hazard and provides an explanation for the issue of combinations of debt and equity even if the issue of equity implies an adverse selection cost. What is more, in contrast with the pure adverse selection case, the cross-subsidisation is socially beneficial. It converts a negative into a positive NPV project and improves social welfare.
However, if firms can only issue debt and equity, it may be the case that, at any given debt level, the proportion of equity issued consistent with exerting effort is strictly lower for the S-type. That is, the pooling equilibrium where both types exert effort may collapse although the R-type would have exerted effort even if a higher proportion of equity was issued (more subsidy was given to the S-type). Because the warrant value falls with the exercise price faster for the S-type, the S-type is willing to increase faster the proportion of equity offered to the financier than the R-type while still exerting effort. As a result, through the appropriate choice of their exercise price, warrants allow for the implementation of the socially efficient outcome even if this is not possible when we restrict ourselves to debt, equity and/or convertible debt. This result provides a second rationale for their use. Finally, we show that, under certain conditions, a debt-warrant combination can implement the optimal contract as a competitive equilibrium.
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