سرمایه گذاری غیر قابل برگشت تحت عدم قطعیت و خطر ورشکستگی

The firm-level theory of irreversible investment under uncertainty is extended to account for bankruptcy. With a sufficiently large risk of bankruptcy, firms prefer to defer their investment decision to a later date. Simulated option values reach as high as 30 percent.

The literature on firm-level investment with irreversibility and uncertainty has grown rapidly over the last decade. The standard problem, first examined by McDonald and Siegal (1986), is comprised of a firm who must decide when to invest a fixed amount P in exchange for a project with value V where V is continually changing over time. The decision to invest is irreversible and thus an option value associated with waiting normally exists. That is, P must be sufficiently less than V in order for the investment to occur. There have been many extensions of this basic model, much of which is described by Dixit and Pindyck (1994). For example, Leahy (1993) and others have examined option values in the context of a competitive equilibrium. Recent papers on irreversible investment under uncertainty and oligopoly include Fatas and Metrick (1997) and Baldursson (1998). Dixit (1991) examined the problem in the context of price ceilings and Dixit (1995) considered the role of scale economies. Sequential investment and incremental investment have also been considered in several studies. Finally, Chang (1988) examines how irreversible investment impacts the incentive for horizontal merger. Despite its importance for the decision making of most firms, bankruptcy has not yet been formally examined in the context of irreversible investment. Specifically, suppose in the standard model, the firm must borrow funds to finance the investment. If the firm is unlucky, outstanding debt may increase and exceed the value of the collateralized investment asset. At this point, the lender will foreclose by seizing the asset and the firm will lose access to the future revenue stream. Making an investment increases the probability of foreclosure. Therefore, waiting to invest may be valuable because waiting allows the firm to reduce its debt and also to avoid the investment if the risk of foreclosure increases. The purpose of this paper is to develop a simple model of irreversible investment with foreclosure risk. To isolate the option value solely attributable to foreclosure risk, the model is constructed such that an option value does not exist in the absence of bankruptcy considerations. The normal assumption is that the value of the project follows some type of Brownian motion stochastic process. Suppose instead that returns are continuously and independently normally distributed. In the standard model, there is no value from waiting if the project’s value is stationary over time. Thus, any option value arising within the current model is due to the foreclosure risk. An important assumption within the model concerns the form of the foreclosure rule. The standard rule, ‘foreclose if the firm becomes insolvent (i.e., outstanding debt exceeds the collateralized value of the assets),’ is employed. This rule is not necessarily efficient because an insolvent firm may expect to eventually become solvent if it is allowed to continue operating1. In this model, returns are stationary and the project is assumed profitable at date 0, implying that foreclosure is always inefficient/premature. However, lending without foreclosure (in which case the option value results of this paper vanish) would typically require an unbounded risk premium within the lending rate. For institutional and transaction cost reasons, lenders typically do not employ this strategy2.

The result that firms may value the option to defer investment to a later date when foreclosure is a concern has intuitive appeal. As in the existing literature, this result is consistent with the general finding that the present value rule alone may not be appropriate for investment purposes. An obvious extension of this model is to allow the firm to invest at any time between time 0 and time T, as in the standard analysis. Option values are likely to be higher in this less constrained environment. It would also be of interest to solve for the competitive equilibrium and attempt to show that the investment rule ‘invest if price exceeds long-run average cost’ no longer holds if the risk of foreclosure is sufficiently high. Another (probably more difficult) extension would allow for a non-stationary series for net returns. For example, if returns were modeled as an Ornstein-Uhlenbeck mean reverting process, it is likely that stronger results would be obtained because the foreclosure rule would be relatively less efficient in such a case.