Ebook Excessive Risk Taking and The Maturity Structure of Debt
The Asset substitution problem is one of the widely discussed agency problems in finance. Jensen and Meckling (1976) argue that in presence of debt, limited liability introduce convexity in the equity and consequently gives incentives to equity holders to increase their claim value at the expense of debt holders, by taking excessive risk. Several tools have been proposed to overcome this problem. One of the most popular of these tools is short term debt. Barnea and al (1980) for example suggest that shorter debt maturity will be used as risk increases. If the early literature, mainly concerned with a qualitative analysis, has demonstrated the efficiency of finite maturity debt in reducing equity holders risk shifting incentives, little attention have been devoted to the quantitative effect of finite maturity debt on asset substitution. In fact, although short term debt clearly reduces equity holders’ risk shifting incentives, it also induces a greater default risk for the firm. It is therefore not clear what is the overall effect of short term debt on the firm value.
The literature provides a series of papers that address the issue of quantifying the impact of asset substitution in presence of short term debt essentially in a framework where the capital structure decision involves trading off the tax benefits of leverage, financial distress costs and the agency costs associated with risk shifting incentives. Leland (1998) propose a model of asset substitution where equity holders can continuously choose a high or a low volatility level for the firm’s assets once debt is in place. He then studies the impact of equity holders’ ex post risk flexibility on the firm’s optimal capital structure and finds that agency costs restrict leverage, debt maturity and increase yield spreads. Similarly, Ericsson (2000) provides a quantitative illustration of how the capital structure decision is influenced by the potential for asset substitution. He shows that by ruling out asset substitution, a firm could afford to take on an additional 20% of leverage and use distinctly longer term debt maturity, but still bears a significant loss.
Our paper share several common features with the model developed by Ericsson (2000). We consider a continuous time model of asset substitution where leverage and maturity structure are chosen optimally by the firm’s management. In order to formalize the effect of short term debt on asset substitution, we assume that debt is a perpetual coupon bond, randomly renewed according to a Poisson process of constant intensity m. In such a setting, debt is comparable to a short term debt with average maturity. This modelling of short term debt, initiated in a continuous time setting by Leland (1994) was suggested by Barnea and al (1980) who argue that, in presence of asset substitution, call strategies perform the same task as short term debt in aligning the interests of stockholders with those of bondholders. Like Ericsson (2000), we assume that default is triggered whenever cash flows received by the firm are not sufficient to cover debt service, and we consider that the decision to alter the dynamics of the cash flows process is irreversible. Our paper however presents two distinctive features with respect to Ericsson (2000):
The asset substitution problem. Following Décamps and Djembissi (2006), we assume that at any time equity holders have the opportunity to change the activity of the firm and to adopt a high risk cash flows generating technology characterized by a lower risk-adjusted growth rate and a larger volatility. Hence, on the one hand equity holders are willing to switch to the riskier activity, but on the other hand risk shifting lowers the growth rate of the cash flows. The risk shifting date therefore trades off the opportunity costs of risk shifting, that is the decrease in the drift of the cash flows process, and the benefits of risk shifting, represented by the increase in the volatility of the cash flows. In Ericsson (2000), equity holders can increase, at no cost, the volatility of the cash flows. As pointed out by the author, this implies that, if debt is a perpetual coupon bond, equity holders will immediately choose the high risk activity. In our setting such behavior will not be optimal because of the opportunity costs of risk shifting.
Debt restructuring. It is widely recognized that short term debt significantly reduces risk shifting incentives. However, it is also true that this type of debt induces a heavier default risk on the firm. Actually, as shown by Childs and al (2005), short term debt does not show up a significant effect on the agency costs of asset substitution in a context of static capital structure. This implies that the choice of debt maturity will not be sufficient to tradeoff the two opposite effects of finite maturity debt. In others terms, the default cost of short term debt is only partially internalized in Ericsson (2000) when choosing debt maturity. We then propose to add to short term debt a feature that accounts for the heavier default risk induced by finite maturity debt. It consists in a downsized restructuring of debt as the situation of the firm deteriorates. Precisely, we consider the standard long term debt contract, to which we attach a new specific clause. Once cash flows drop to a specific level, the maturity of debt is reduced and set to a finite prespecified level. Both the date of restructuring and the maturity of debt after restructuring are specified in the debt contract. Intuitively, the decision to restructure debt is a threat towards equity holders.
When the cash flows of the firm are sufficiently high, debt is viewed like a perpetual coupon bond. However when the situation deteriorates, equity holders risk shifting incentives increases. However, by increasing the risk of the activity, they indirectly increase the likelihood of facing conversion of debt, which is not desirable to them because of the additional default risk associated to short term debt. The capital structure will then consists of the coupon rate and debt maturity as in Ericsson (2000), but also of the cash flows level at which equity holders are required to reduce the maturity of debt. This additional feature of debt can be implemented through a put provision on bonds whereby debt holders can force equity holders to redeem the bond at par value. In fact, debt is a perpetual coupon until the restructuring date where debt holders require the repricing of their claim. This restructuring date can be thought as the exercise date of a put option held by debt holders, with the strike price being equal to the face value of debt.
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