Source: Altman and Kishore (1998)

The other is to use a statistical approach, such as a probit to estimate the probability of default, based upon the firm's observable characteristics, at each level of debt.

The bankruptcy cost can be estimated, albeit with considerable error, from studies that have looked at the magnitude of this cost in actual bankruptcies. Studies that have looked at the direct cost of bankruptcy conclude that they are small25, relative to firm value. The indirect costs of bankruptcy can be substantial, but the costs vary widely across firms. Shapiro and Titman speculate that the indirect costs could be as large as 25 to 30% of firm value but provide no direct evidence of the costs.

The net effect of adding debt can be calculated by aggregating the costs and the benefits at each level of debt.

Value of Levered Firm = FCFFo (1+g)/(pu - g) + tc D - na BC We compute the value of the levered firm at different levels of debt. The debt level that maximizes the value of the levered firm is the optimal debt ratio.

24 This study estimated default rates over ten years only for some of the ratings classes. We extrapolated the rest of the ratings.

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