The chief audit executive (CAE) typically performs several activities following an audit engagement, including reporting follow-up activities to senior management, implementing follow-up procedures to evaluate residual risk, and evaluating the extent of improvements. These activities are crucial to ensure that audit recommendations are properly addressed and that any residual risks are managed effectively. However, determining the costs of implementing the recommendations is not typically a responsibility of the CAE. This task is usually handled by the management of the area being audited, as they have the detailed operational knowledge necessary to accurately estimate these costs. Reference:
The IIA's International Standards for the Professional Practice of Internal Auditing (Standards), specifically Standard 2500 - Monitoring Progress.
The IIA's Practice Guide on Follow-up Processes.