## Refinements on the Operating Income Approach

The operating income approach described in this section is simplistic because it is based upon historical data and the assumption that operating income changes are normally distributed. We can make it more sophisticated and robust by making relatively small changes:

2 This is the probability of defaulting on interest payments in one period. The cumulative probability of default over time will be much higher.

3 By rolling two-year periods, we mean 1980 & 1981, 1981 & 1982, 1982 & 1983 The resulting standard deviation is corrected for the multiple counting of the same observations.

• You can look at simulations of different possible outcomes for operating income, rather than looking at historical data; the distributions of the outcomes are based both upon past data and upon expectations for the future.

• Instead of evaluating just the risk of defaulting on debt, you can consider the indirect bankruptcy costs that can accrue to a firm, if operating income drops below a specified level.

• You can compute the present value of the tax benefits from the interest payments on the debt, across simulations, and thus compare the expected cost of bankruptcy to the expected tax benefits from borrowing.

With thee changes, you can look at different financing mixes for a firm, and estimate the optimal debt ratio as that mix that maximizes the firm's value.4

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