Substantial doubt and the entropy of auditors' going concern modifications

- Shannon entropy measures the information of the realization of an uncertain event.
- Shannon entropy is applied to evaluate the informational value of the audit report.
- Information content is maximized at a bankruptcy probability threshold of 0.08.

Auditors need to establish a substantial doubt threshold in order to determine the type of audit report to issue, but substantial doubt is not defined in the auditing standards. Auditors are regularly criticized for having high thresholds, which results in too few going concern reports. We apply Shannon entropy from information theory as the criterion to evaluate the informational value of the audit report. Shannon entropy provides a measure of the expected information content associated with the realization of an uncertain event. First, we estimate the client's probability of bankruptcy in our sample. Second, using the distribution of the probability of bankruptcy we calculate the entropy at each point of the probability of bankruptcy. We find that entropy is maximized at the 0.08 probability of bankruptcy.