Endogenous-Dynamic

The models of Black & Cox (1976), Leland (1994), and LT assume that management make a single initial capital structure decision, with the level of debt principal remaining time homogeneous thereafter for the remaining maturity of the bond being valued. In practice, firms can be expected to adjust their level of debt over time, in particular to preserve the value of tax shields should as assets grow over time as expected. The absence of time-varying management adjustment of firm gearing is a weakness in the endogenous-static structural models. In this section we consider a group of structural models that permit the debt-ratio of the firm to adjust over time in response to asset growth and exogenous shocks to the firm’s asset value. We refer to these as endogenous- dynamic models since these models permit dynamic adjustment of the default boundary. Endogenous-dynamic capital structure models retain the same basic assumptions of Leland (1994), but assume management adjusts the firm’s debt-ratio in response to changing firm value. Depending upon the importance of transaction costs associated with adjusting the firm’s debt-ratio, the literature predicts different relationships between current firm leverage and the term structure of credit spreads. Initially we discuss models that ignore any bargaining between bondholders and equityholders.

Fischer et al. (1989) recognise that changing the firm’s capital structure is costly and will not occur until there is sufficient movement in the debt-ratio. Thus, it is hypothe- sised that firm’s have a ‘region of no recapitalisation’ bounded by an upper and lower solvency barrier. The firm capital structure policy follows a simple rule; gearing is in- creased if the firm’s ratio of asset value to debt reaches an upper boundary, but default occurs if the asset value of the firm reaches the lower default boundary. Compared with Leland (1994), the option to recapitalise at an upper boundary causes an initially lower optimal debt level and higher default risk. Importantly, Fischer et al. (1989) show that firms may allow their debt-ratios to vary over time within a set of optimal boundaries. Therefore, firms with similar recapitalisation preferences and similar default risks may exhibit different observed debt-ratios on any given balance date. The cross-sectional ob- served term structure of credit spreads may therefore be poorly explained by the use of current balance sheet debt if used to proxy for the firm’s default point in the presence of recapitalisation costs. This may be an explanation for the large firm-wise prediction error variance reported by EHH who use balance sheet debt to estimate the firm’s default boundary.

Using similar capital management rules as Fischer et al. (1989), Dangl & Zechner (2004) show that default risk is monotonically decreasing with respect to rising solvency under static analysis when incremental adjustments to capital structure are made. How- ever, with significant fixed costs of recapitalisation, the firm is assumed to leverage back to its initial optimum in the event that the upper boundary of firm value to debt-ratio is hit. Such an adjustment is only warranted if bond indentures prohibit the issuing of new

debt, therefore forcing the firm to retire existing debt and re-issuing new debt, or if rais- ing debt has significant fixed costs that encourage large scale debt issuance in preference to smaller incremental debt raisings. It follows that Dangl & Zechner (2004) predict that the probability of default, at the upper solvency boundary, is equal to the probability of default at the initial optimum solvency point. Thus, default risk is predicted to be ‘U’- shaped with respect to solvency; initially it falls with increasing asset value relative to debt, but then rises as the re-leveraging solvency boundary is approached. This hypoth- esis does not appear to be well supported empirically. For example, structural models that map a predicted distance-to-default to observed default rates, show monotonically increasing default risk with respect to increasing leverage (Sobehart & Stein 2000, Cros- bie & Bohn 2002).

Goldstein et al. (2001) provide a variation to Fischer et al. (1989) in which the state variable is not the value of the firm, but rather the firm’s earnings before interest and tax expenses. The EBIT state variable is therefore unaffected by the firm’s choice of leverage, whereas the firm value state variable in other endogenous-dynamic models must be interpreted as the pre-leverage firm value.

Like LT, endogenous-dynamic models also predict that default will occur below the face value of debt. Unless debt is immediately due, shareholders will continue to service debt until the expected value of the firm is not sufficient to warrant paying coupons. For bankruptcy costs of 5 percent, the equivalent of default boundary to face value of debt, K/F, is reported to be: Fischer et al. (1989), 57 percent; Goldstein et al. (2001, Table 2), 51 percent; Dangl & Zechner (2004), 69 percent.6 Empirical support is provided by Davydenko (2005) who finds that on averageK/Fis 65 percent, but varies widely in the cross-section, depending on balance sheet liquidity, asset volatility, and asset tangibility. An important theoretical result of the aforementioned endogenous-dynamic models is the prediction of asymmetric debt-ratio adjustments. The result arises from assuming that shareholders follow a second-best capital management policy in which they max- imise their own wealth. Fischer et al. (1989) argue under a second-best policy it is never optimal for debt to be repurchased when firm value declines. This is because the rising cost of bankruptcy is fully borne by the bondholders. The implication is that capital ad- justments are asymmetric and negative value shocks are not matched by reducing debt. Under an alternative first-best policy, shareholders maximise total firm value and may seek to reduce some debt rather than default, thereby introducing some debt reduction near the default boundary. This is only likely if there is a precommitment in the bond indenture to maintain a minimum level of solvency.

Some support for the hypothesised asymmetric recapitalisation behaviour is given by

6_{Independently Huang & Huang (2003) estimate the default boundary to be 60 percent of the face value}

of debt using the reasonable ‘back-of-the-envelope’ assumption that bond recovery is 50 percent of debt face value with 10 percent total bankruptcy costs.

Gilson (1997) who examines the behaviour of leverage ratios before and after bankruptcy proceedings. He finds that firms that proceed through Chapter 11 do experience a de- crease in leverage after recontracting with creditors, but that the leverage ratios remain well above the industry mean, and substantially above the levels five years prior to en- tering Chapter 11. He concludes that the optimal target debt-ratio has most likely in- creased. One possible reason cited is that restructured firms benefit from the additional operational discipline imposed by debt (Jensen 1986).

The predicted asymmetric capital adjustment behaviour is a consequence of assum- ing strict second-best behaviour, in the presence of bankruptcy costs, with no voluntary debt reduction agreed by bondholders. We now discuss a second group of endogenous- dynamic models that consider the potential for negotiation between stockholders and bondholders at the default boundary.

Working in discrete-time, Anderson & Sundaresan (1996) estimates the default bound- ary as an outcome from a non-cooperative game; shareholders make take-it-or-leave-it offers of debt service to bondholders. In the presence of bankruptcy costs, bondholders may accept to renegotiate a lower than contracted payment to preserve the value of their claim on the firm and avoid the costs of bankruptcy. In other words, reduction in lever- age occurs at a reorganisation boundary that is higher than the insolvency boundary in the absence of negotiation. The resultant reduction in debt, due to the threat of default, is termed strategic default. Shareholders have an incentive to offer below contracted debt payments, but not sufficiently low to force rejection by bondholders and subsequent liq- uidation. Bondholders will rationally accept a lower debt service payment up until the point at which the concessions offered equal the expected bankruptcy costs. The greater the potential bankruptcy costs the greater the concessions that will be accepted. Thus, the assumption of negotiation in the presence of bankruptcy costs implies firms contrac- tually default at a higher asset value than they otherwise would in the absence of the opportunity to negotiate.

For a given level of gearing, the potential for future strategic debt service implies higher credit spreads than predicted by Merton. Mella-Barral & Perraudin (1997) and Anderson et al. (1996) work in continuous-time and solve the value of a consol bond analytically. Fan & Sundaresan (2000) introduce taxes and assume equal bargaining power between shareholders and bondholders. They find that because shareholders have some power to exploit bondholders, the default boundary is always higher than predicted by Leland (1994) resulting in a greater probability of default.

Default may also arise from a breach of minimum cash flow covenants. Fan & Sun- daresan (2000) examine non-negotiable cash flow covenants and their influence on the bargaining process. They suggest that in the presence of cash flow covenants, sharehold- ers would rather sacrifice dividends to reinvest and avoid a premature liquidation of the firm. They reinvest the minimum amount such that the strategic default point is reached

before the cash flow covenant becomes binding.

In summary, the endogenous-dynamic models provide a rich theoretical field for predicting the relationship between dynamic capital structure choice and credit spread term structures. These are as follows:

1. In the presence of bankruptcy costs and taxes, shareholders will not allow the firm’s debt-ratio to deviate to below a desired level of gearing necessary to protect the value of tax shields. The option to increase leverage in the future results in higher predicted future credit spreads relative to the endogenous static models; 2. Where there are costs of recapitalisation, the firm will resist increasing leverage

until the benefit exceeds the cost, resulting in a region of no recapitalisation, mak- ing inference of the firm’s target debt-ratio impossible from simply observing its current debt-ratio. If the costs are largely fixed, or bond indentures prevent in- cremental debt changes, the firm will increase is predicted to change to increase its leverage sharply from an upper solvency boundary to its optimal level. The speed of mean-reversion in debt-ratios depends upon the size of recapitalisation costs, and whether it is a smooth adjustment depends upon the proportion that is variable as opposed to fixed. Slower rates of mean-reversion will result in lower future credit spread term structures more closely represented by the static models; 3. In the absence of bargaining between bondholders and equityholders, debt-ratios may not revert as a result of downward shocks in firm value since the increased potential cost of bankruptcy is passed to bondholders, when a second-best capital management strategy is followed by shareholders;

4. If bargaining is permitted, then the theory of strategic debt service suggests that default will occur at higher firm asset values, when bankruptcy costs are high and impediments to renegotiation are low. Shareholders are able to extract a negotiated debt service reduction or reduction in the amount of debt, by threatening to default. This mechanism may cause the future debt-ratio to reduce in response to negative shocks in firm value as a consequence of partial debt forgiveness by bondholders. Credit spreads are predicted to be higher than in the absence of bargaining, a consequence of the potential to default earlier, and the expected increased loss associated with debt renegotiation.

Relative to the Merton model, the theoretical extensions of the endogenous model lit- erature suggest a greater likelihood of future default and higher future credit spread. For empirical estimation, the implication is that the default boundary is not simply proxied by the current balance sheet level of debt:

1. The presence of longer tenor debt encourages shareholders to maintain debt ser- vice payments despite the firm value falling below the face value of debt;

2. If bankruptcy costs are high, the owners have bargaining strength, and the debt can be easily negotiated, shareholders will seek to offer below the contracted debt payment. Default, under the original terms of the debt contract, occurs earlier at a higher solvency threshold;

3. Default can be triggered by breach of minimum cash flow covenants, however, the influence of liquidity default is contingent upon how binding the liquidity covenant is relative to the strategic default threshold.