Audit Risk Calculator
This tool helps auditors calculate the required level of Detection Risk based on their assessments of Inherent Risk, Control Risk, and the desired level of overall Audit Risk for a specific assertion or area.
The calculation is based on the audit risk model: AR = IR × CR × DR, rearranged to solve for Detection Risk: DR = AR / (IR × CR).
Assess Risk Components & Set Target
Understanding the Audit Risk Model
The Audit Risk Formula: AR = IR × CR × DR
Audit risk (AR) is the risk that the auditor expresses an inappropriate audit opinion when the financial statements are materially misstated. The audit risk model breaks this down into three components:
- Inherent Risk (IR): The susceptibility of an assertion to a misstatement that could be material, assuming that there are no related controls. Factors like the nature of the account (cash vs. fixed assets), industry factors, and complexity of transactions influence IR.
- Control Risk (CR): The risk that a material misstatement that could occur in an assertion will not be prevented or detected and corrected, on a timely basis, by the entity's internal control. CR is assessed based on the effectiveness of the client's internal controls.
- Detection Risk (DR): The risk that the procedures performed by the auditor to reduce audit risk to an acceptably low level will not detect a misstatement that exists and that could be material, individually or when aggregated with other misstatements. DR is controlled by the auditor through the nature, timing, and extent of audit procedures.
The product of Inherent Risk and Control Risk is often referred to as the Risk of Material Misstatement (RMM = IR × CR). The audit risk model can therefore also be expressed as: AR = RMM × DR.
Auditors assess IR and CR based on their understanding of the client and its environment, including internal controls. They then set a target AR (usually low or very low) and use the model to determine the acceptable level of Detection Risk (DR = AR / (IR × CR)). This required DR level directly impacts the amount of substantive testing the auditor must perform.
Audit Risk Examples
These examples show how different assessments of Inherent Risk (IR) and Control Risk (CR), combined with a Target Audit Risk (AR), impact the Required Detection Risk (DR) and the implication for the level of substantive testing needed.
Example 1: Low RMM, Low Target AR
Scenario: Auditing a stable, simple cash account with effective controls. Target Audit Risk is Very Low.
Inputs: Inherent Risk = Low, Control Risk = Low, Target Audit Risk = Very Low.
Result: Required Detection Risk = Very High.
Implication: Minimal Substantive Testing Required.
Example 2: High RMM, Low Target AR
Scenario: Auditing a complex derivatives portfolio with weak internal controls. Target Audit Risk is Low.
Inputs: Inherent Risk = High, Control Risk = High, Target Audit Risk = Low.
Result: Required Detection Risk = Very Low.
Implication: Extensive Substantive Testing Required.
Example 3: Moderate RMM, Low Target AR
Scenario: Auditing inventory for a manufacturing company; physical existence is a risk (Moderate IR) but controls over cycle counts are effective (Moderate CR). Target Audit Risk is Low.
Inputs: Inherent Risk = Moderate, Control Risk = Moderate, Target Audit Risk = Low.
Result: Required Detection Risk = Moderate.
Implication: Moderate Substantive Testing Required.
Example 4: Mixed RMM, Low Target AR
Scenario: Auditing revenue recognition which involves complex contracts (High IR), but the company has strong IT system controls over billing and recording (Low CR). Target Audit Risk is Low.
Inputs: Inherent Risk = High, Control Risk = Low, Target Audit Risk = Low.
Result: Required Detection Risk = Moderate.
Implication: Moderate Substantive Testing Required.
Example 5: Mixed RMM, Low Target AR (Opposite of Ex 4)
Scenario: Auditing payroll, which is generally straightforward (Low IR), but the company's manual process and weak segregation of duties lead to high risk (High CR). Target Audit Risk is Low.
Inputs: Inherent Risk = Low, Control Risk = High, Target Audit Risk = Low.
Result: Required Detection Risk = Moderate.
Implication: Moderate Substantive Testing Required.
Example 6: Very High RMM, Very Low Target AR
Scenario: Auditing related party transactions (Very High IR) where management override of controls is a concern (Very High CR). Target Audit Risk is Very Low.
Inputs: Inherent Risk = Very High, Control Risk = Very High, Target Audit Risk = Very Low.
Result: Required Detection Risk = Very Low.
Implication: Extensive Substantive Testing Required.
Example 7: Very Low RMM, Moderate Target AR
Scenario: Auditing fixed assets additions (Very Low IR) with fully automated and effective controls (Very Low CR). The overall engagement strategy allows for a Moderate Target Audit Risk in this area.
Inputs: Inherent Risk = Very Low, Control Risk = Very Low, Target Audit Risk = Moderate.
Result: Required Detection Risk = Very High.
Implication: Minimal Substantive Testing Required.
Example 8: Moderate RMM, Moderate Target AR
Scenario: Auditing accruals (Moderate IR) with some effective controls but notable exceptions found in testing (High CR). The auditor has set a Moderate Target Audit Risk for this balance.
Inputs: Inherent Risk = Moderate, Control Risk = High, Target Audit Risk = Moderate.
Result: Required Detection Risk = Moderate.
Implication: Moderate Substantive Testing Required.
Example 9: High IR, Moderate CR, Moderate Target AR
Scenario: Auditing provisions involving significant estimation uncertainty (High IR) where management review controls are present but not fully robust (Moderate CR). Target Audit Risk is Moderate.
Inputs: Inherent Risk = High, Control Risk = Moderate, Target Audit Risk = Moderate.
Result: Required Detection Risk = Low.
Implication: More Substantive Testing Required.
Example 10: Very Low RMM, Low Target AR
Scenario: Auditing a simple, non-material expense account (Very Low IR) with strong, tested controls (Low CR). Target Audit Risk is Low.
Inputs: Inherent Risk = Very Low, Control Risk = Low, Target Audit Risk = Low.
Result: Required Detection Risk = High.
Implication: Less Substantive Testing Required.
Frequently Asked Questions about Audit Risk
1. What is Audit Risk?
Audit Risk is the risk that an auditor expresses an inappropriate audit opinion when the financial statements are materially misstated. Auditors aim to reduce this risk to an acceptably low level.
2. What are the main components of the Audit Risk Model?
The model is AR = IR × CR × DR, where AR is Audit Risk, IR is Inherent Risk, CR is Control Risk, and DR is Detection Risk.
3. What is Inherent Risk (IR)?
Inherent Risk is the susceptibility of an account balance or class of transactions to a material misstatement, assuming there are no related internal controls. Factors like complexity, subjectivity, and volume of transactions influence IR.
4. What is Control Risk (CR)?
Control Risk is the risk that a material misstatement will not be prevented or detected and corrected by the entity's internal control system. It is assessed based on the design and operating effectiveness of controls.
5. What is the Risk of Material Misstatement (RMM)?
RMM is the combination of Inherent Risk and Control Risk (RMM = IR × CR). It's the risk that the financial statements are materially misstated *before* considering the auditor's procedures.
6. What is Detection Risk (DR)?
Detection Risk is the risk that the auditor's procedures will not detect a material misstatement that exists. This is the only component of the audit risk model that the auditor can directly influence by changing the nature, timing, and extent of their substantive procedures.
7. How does this calculator use the Audit Risk Model?
It uses the model to solve for the required Detection Risk (DR = AR / (IR × CR)) based on your assessments of IR and CR and your chosen Target Audit Risk (AR).
8. What does the Required Detection Risk level mean for audit work?
A lower required Detection Risk means the auditor must perform *more* rigorous substantive procedures to reduce the risk of missing a misstatement. A higher required Detection Risk means *less* substantive testing is needed.
9. Why is Target Audit Risk typically set low?
Auditing standards require the auditor to reduce audit risk to an acceptably low level to be able to express an opinion. Therefore, the target AR is usually set as Low or Very Low.
10. Can the calculated Detection Risk be greater than 100%?
Theoretically, if RMM is extremely low compared to the Target AR, the calculation DR = AR / RMM might yield a value > 1. However, Detection Risk cannot exceed 100% in practice. A DR of 100% implies no testing is needed because RMM alone is lower than the target AR (or controls are so effective that IR * CR is negligible). The tool caps the numerical DR at 1.0 (representing Very High qualitative DR) and maps this to the "Minimal Testing" implication.
