The audit risk model for planning expresses the relationship between the audit risk components as follows:

**AR = IR x CR x DR**

The symbols represent

**AR = Audit Risk****IR = Inherent Risk****CR = Control Risk****DR = Detection Risk**

The model can be used to determine the planned detection risk for an assertion.

To illustrate the use of the model, let’s assume that the auditor has made the following risk assessments for a particular assertion, such as the valuation or allocation assertion for inventories:

**IR – 50%**

**CR = 50%**

Further, let’s assume the auditor has specified an overall AR of 5%. Detection risk can be determined by solving the model for DR as follows:

**DR = AR + (IR x CR)**

**= 5% 4- (50% x 50%)**

**= 20%**

In practice, many auditors do not attempt to quantify each of the risk components, making it impossible to mathematically solve the risk model.

However, even when not solved mathematically, familiarity with the model makes the following relationship clear: to hold audit risk to a specified level, the higher the assessed levels of inherent and control risks, the lower will be the acceptable level of detection risk.

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