#### Title

Bankruptcy cost and bond valuation

#### Document Type

Article

#### Publication Date

9-2008

#### Abstract

Bankruptcy costs are an important factor in valuing a firm and its debt. The Leland-Toft (1996) model is one of the most important firm valuation models that consider bankruptcy costs and corporate debt tax shields. However, it treats bankruptcy costs as a fraction of the (unobserved) endogenously determined bankruptcy threshold, making the model difficult to test empirically and implement in practice. This paper provides an approach to solve these difficulties. Our model is easier to implement and test while preserving the attractive features of the Leland-Toft model, such as endogenously determined leverage. Bankruptcy costs are an important factor in valuing a firm and its debt. While many firm valuation models built on the tradeoff theory come up with the consensus that the default likelihood and bankruptcy costs are two major factors for pricing a risky bond, how to measure bankruptcy costs and account for them in a model still pose great challenges to empirical tests and model application. For example, models by Leland (1994), and Leland and Toft (1996) (hereafter the LT model) show how to endogenously optimize capital structure and thereby predict the bond value. However, in their models bankruptcy costs are measured as a fraction of the endogenously determined bankruptcy threshold. Despite the elegance of the model, one difficulty is that the threshold is unobserved and therefore the bankruptcy costs may be difficult to accurately account for. Empirically, this makes advanced empirical methods such as Maximum Likelihood and Kalman Filter less reliable. This paper develops a model by modifying the LT model to address this issue. In particular, we measure bankruptcy costs based on bond’s face value. This allows us to incorporate bankruptcy costs more accurately in the model because of the greater availability of the data. At the same time, we preserve the desirable features of the original LT model, such as the endogeneity in optimizing the capital structure. Next we review the issues in greater details. Leland and Toft (1996) propose a tradeoff model that endogenously determines the bankruptcy boundary by maximizing equity value and firm value at the expense of bondholders. The LT model, investigating the tradeoff between the corporate tax advantages and bankruptcy costs, shows that issuing longer term debt better exploits the corporate tax advantages because bankruptcy boundary can be endogenously set at lower asset values. However, the LT model is difficult to test empirically and apply practically. This is because the endogenously determined bankruptcy boundary is unobservable and thus the bankruptcy costs cannot be accurately incorporated into the model. Due to this technical difficulty, the model performance can be questionable in some situations. For example, the model may noticeably overpredict the credit spread (see e.g., Johnson and Qi (2006)). From practical point of view, a reason to modify the LT model is the data availability. The Pacer (Public Access to Court Electronic Records) service is the most comprehensive bankruptcy database which provides the full-text source for bankruptcy documents, including debt/assets ratio, where assets recorded are right pre-bankruptcy (e.g., see Bris, Welch and Zhu (2006)). This allows us to directly infer bankruptcy costs as a simple function of debt face value. In particular, bankruptcy costs may be deduced as a fraction of the face value by using the information available in the Pacer system. This provides a good and much more reliable bankruptcy costs measurement to facilitate empirical tests of the model as well as set a benchmark to predict bond prices for similar firms. Moreover, a recent paper by Davydenko (2007) finds that for an “average firm”, the default threshold is about 72 percent of the face value of debt. Therefore, it would be desirable to modify the LT model such that the bankruptcy costs can be expressed as a fraction of the face value of debt rather than as a fraction of some unobserved endogenously chosen default boundary. From theoretical point of view, there is also a reason for our modification of the LT model. The LT model assumes that as long as the firm can raise additional capital from the equity holders to serve the debt interest payment, the bondholders have no power to force a bankruptcy even when the firm is operating with negative net worth. The rationale that a firm can possibly operate with negative net worth is that with higher asset volatility, equity holders find it more attractive to contribute new equity capital to make bond coupon payment in order to keep the firm alive. This is because with higher asset volatility, the firm has better chance of making larger profit while bondholders bear the brunt of the hit if the business runs into trouble. This can be better understood if we view the equity as a call option on firm’s asset and bond as a shorted put option with a strike price being the debt face value. The volatility of the underlying asset (firm’s asset) has a positive relationship with the corresponding option value. Therefore, with higher asset volatility, the firm will find it easier to raise new equity capital and use it to serve the debt interest payment and declare bankruptcy once the new equity capital is not enough to meet the debt service. This can result in a bankruptcy boundary lower than the face value of the firm’s debt. (1) That the firm can choose such a low bankruptcy boundary implies that the bondholders would recover very little once the firm declares bankruptcy. The lower the bankruptcy boundary, ceteris paribus, the smaller the bond value and hence the higher the credit spread. Perhaps this is why sometimes the LT model may overpredict the credit spreads on risky bonds. However, this may not be realistic since it implies that a firm can essentially drag on (till bond’s maturity) just by paying the coupons and the coupons can be much below the face value. Of course, this is not likely to be true since bondholders would not passively wait till bond’s maturity. They could force a bankruptcy before the firm value drifts too much below the face value of debt, which essentially sets a lower bound for the bankruptcy boundary. Conversely, suppose that in an ideal case, the bondholders can take immediate action once the firm value drops to the face value of bonds. Then the reasonable choice for bankruptcy threshold would be the face value. However, this is likely untrue in reality either. There is evidence that the absolute priority rule (APR) can be violated (e.g., Weiss and Capkun (2007), Eberhart, Moore and Rosenfeldt (1990), Betker (1995)). Bris, Welch and Zhu (2006) finds that APR is always followed in Chapter 7 liquidation and about 12% of the firms in their Chapter 11 reorganization samples had APR violated. Taken together, a fraction of bond’s face value (not 100 percent due to the possibility of APR) appears to be a convenient way of measuring the bankruptcy loss.

#### Publication Title

The Journal of American Academy of Business, Cambridge

#### Recommended Citation

Xie, Y. A.,
Qi, H.,
&
Huang, H.
(2008).
Bankruptcy cost and bond valuation.
*
The Journal of American Academy of Business, Cambridge,
14*(1).

Retrieved from: https://digitalcommons.mtu.edu/business-fp/25

## Publisher's Statement

© 2008 The Journal of American Academy of Business, Cambridge.