Optimal Timing of Account Audits in Internal Control

This paper calculates the minimum required frequency between audits of a given type to meet prespecified accuracy goals for a given type of account. Both “100 percent,” as well as sampling type audits are addressed. The effectiveness of a given audit type includes the mean and standard deviation of any residual error that may remain in the account after the audit has been performed and after account balances have been adjusted. The accuracy goals consist of the maximum accumulated error that is considered by management to be tolerable between audits, and the prescribed likelihood that this tolerance level will not be exceeded. The model assumes that certain parameters of the error process have been estimated, but no distributional information is required. Closed form, easy to use, lot-size type formulae are derived which calculate the required frequency (or upper bounds) between audits. The model also provides insights as to the relative cost-effectiveness of various types of audits.