Your firm plans audit programs based on the following version of the audit risk model:
AR = CR x DR ,

where DR = TD [for substantive tests of routine data]
AR is audit risk,
CR is control risk,
DR is detection risk, and
TD is tests of details risk.

Inherent risk (IR) is assumed to be 100%. Thus, IR is ignored here. The planned risk of material misstatement, RMM, is CR.

The risk levels are MAXIMUM [that is, 100%], MODERATE, LOW, and VERY LOW. Assume that the audit risk AR is never greater than the risk associated with the lowest risk component [remember that low risk is good]. If the detection risk is low, then the audit risk cannot be greater than low. Nevertheless, even though control risk may be low, the auditor must still perform substantive tests [because GAAS requires substantive tests no matter how effective the controls are]. To reduce AR to LOW, at least two risk components on the right side of the audit risk model must be MODERATE or better. To reduce AR to VERY LOW, at least one risk component must be VERY LOW, or three components must be MODERATE.

The auditor has planned an audit program for testing the existence and valuation assertions of accounts receivable. Materiality is $1,000,000 and the planned AR is LOW. CR is expected to be MODERATE. Planned TD is MODERATE. The following are the only available options for testing. The audit manager's initial choices are in boldface:

•Nature of principal audit procedure: Positive confirmation and vouching of open invoices, positive confirmation only , negative confirmation.
•Extent of principal audit procedure: 50 accounts, 100 accounts, 200 accounts.
•Timing of principal audit procedure: October 31, November 30, December 31.

If the auditor confirms receivables before year-end, then analytical procedures and further tests of controls will be performed on data covering the remaining portion of the fiscal year. AP is MODERATE, regardless of when the confirmations are performed.

1. Assume that the engagement partner changes the planned AR to VERY LOW. Considering each factor independently [assuming that each one changes, but not the other two], what would be the effect on the confirmations [which are tests of details] regarding:
a. nature?
b. extent?
c. timing?
d. Does TD increase, decrease, remain the same, or is it not determinable from the information?

2. Suppose that the auditor has tested controls and has revised CR to reflect the test results. CR is now LOW. Considering each factor independently[assuming that each one changes, but not the other two], what would be the effect on the confirmations [which are tests of details] regarding:
a. nature?
b. extent?
c. timing?
d. Does TD increase, decrease, remain the same, or is it not determinable from the information?

3. Suppose the engagement partner has increased performance materiality from $1,000,000 to $1,500,000. Planned AR and CR are unchanged.
a. Briefly explain why TD remains the same.
b. If the auditor is planning to confirm accounts, does the extent increase, decrease, or remain the same?

NOTE: The difference between positive and negative confirmations is discussed in PCAOB standard AU330 (http://pcaobus.org/Standards/Auditing/Pages/AU330.aspx )