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As Mr. Guest Said:
Information Processing Objectives area related to controls (COSO, chapter 4 not a PwC creation), and Financial Statement Assertions are related to financial statement lines (accounts). A well done COSO implementation should use CAVR.
When you map your process and identify a control, it is easer to link to CAVR, and then link to FS assertions. I use to document both on my RCM.
The correct relation between CAVR and FS Assertions are:
Completeness - Completeness, Cut-off, Existence/Occurrence, Rights and Obligations
Accuracy - Accuracy, Classification, Valuation and Allocation
Validity - Existence/Occurrence, Cut-off, Rights and Obligations
Restricted Access - Most, except for Rights and Obligations