It is supported by the evidence reported by Bris, Ravid, and Sverdlove (2010) that 56% of the sampled firms that filed for Chapter 7 bankruptcy had both senior and junior debts. Also note that in Ju and Ou-Yang's (2006) model, the firm defaults (before the debt maturity T) the first time the expected time-7 value of its assets becomes smaller than the debt principal P.
Accordingly, in Sub-case 2.1, the time-0 values of the senior and junior debts are given (with obvious notation), respectively, by:
The following proposition provides the values of the senior and junior debts under Case 1, which realistically applies to more firms than Case 2.
One of our objectives is to identify the optimal proportions of senior and junior debts in the total debt amount that maximizes the firm's market value.
The existence of senior and junior debt has also been attributed to covenants that prohibit firms from issuing further senior debt.
The valuation of senior and junior debt has been investigated by Black and Cox (1976) and Geske (1977).
Our model predicts that low leverage firms rely more on junior debt than do more indebted firms.
Finally, we contribute to the literature by determining the default probabilities for senior and junior debt and by analyzing the ensuing senior and junior credit spreads.
The latter is the relative proportion of junior debt defined by [omega] = [P.sub.J]/[P.sub.S].
is due to the probability that no sufficient assets would be available to repay the senior debt principal (inducing the second and third terms in Equations (19) and (21)) and the junior debt principal after paying the senior one (inducing all terms but the first one in Equations (20) and (22)).
At some level of total debt, indicated by an "o" in Figure 1, the firm substitutes its junior debt, progressively or rapidly, for senior debt.