(b) Tolerable Error:

Tolerable error serves as the cornerstone of any test of control. It delineates the boundary beyond which the auditor deems a control to be ineffective. Imagine a scenario where a company’s internal control mechanism is designed to ensure that all financial transactions above a certain threshold are approved by at least two authorized individuals.

The tolerable error would specify the maximum deviation from this expected process that the auditor can accept without raising concerns about the control’s effectiveness.

For instance, if the tolerable error is set at 5%, this signifies that the auditor is willing to accept a 5% error rate in the population without concluding that the control is ineffective. In other words, if the actual error rate falls below this 5% threshold, the control is considered effective.

Conversely, if the error rate exceeds this limit, the auditor will raise red flags and conduct further investigations.

The determination of the tolerable error is not arbitrary; it requires a judicious assessment of various factors. This includes an understanding of the client’s business operations, industry benchmarks, regulatory requirements, and the potential impact of control failures.

For example, in a highly regulated industry like healthcare, the tolerable error for patient billing and records might be set much lower due to the critical nature of accurate patient information.

Moreover, the tolerable error is not a fixed value applicable to all controls and all organizations. It is contingent on the specific circumstances of each audit engagement.

For instance, in an environment where financial controls are intricate and closely monitored, a lower tolerable error might be established to ensure a stringent evaluation. On the contrary, in a less regulated setting, a slightly higher tolerable error may be deemed acceptable.

(c) Expected Error:

Expected error complements the concept of tolerable error by providing a benchmark against which the actual error rate is compared. It is essentially an estimate of the error rate in the population based on the auditor’s knowledge and understanding of the client’s internal controls, historical data, and industry norms.

To put it into perspective, let’s consider an example of a retail company. The internal control in focus might be the reconciliation of cash registers at the end of each day.

Based on historical data and the effectiveness of the company’s procedures, the auditor might expect the error rate to be around 2%. This 2% serves as the anticipated level of deviation from the ideal reconciliation process.

During the testing phase, if the actual error rate aligns closely with this expected 2%, it indicates that the control is performing as anticipated. However, if the actual error rate significantly surpasses this benchmark, it raises concerns about the control’s effectiveness.

This scenario prompts the auditor to delve deeper, potentially expanding the sample size or investigating specific instances of non-compliance.

The interplay between expected error and tolerable error is crucial. If the tolerable error is set too low without considering the expected error, the auditor might be overly stringent and flag controls that are, in fact, functioning effectively.

Conversely, if the tolerable error is too lenient without factoring in the expected error, the auditor might inadvertently overlook significant control deficiencies.

In essence, the auditor seeks a balance between these two factors. The expected error provides context for what can reasonably be anticipated given the nature of the control and the organization’s operational environment. The tolerable error, on the other hand, delineates the point at which the auditor becomes concerned about the control’s effectiveness.

Explanation of Incorrect Answers:

(a) Projected Error:

This term is not commonly used in the context of determining sample size for tests of control. It might be a source of confusion, but it doesn’t have a specific meaning or role in this context. The focus is on tolerable error and expected error because they are directly related to the assessment of control effectiveness.

In conclusion, both tolerable error and expected error are pivotal in determining the sample size for tests of control. The former sets the threshold for what is acceptable, while the latter provides a benchmark for comparison.

By judiciously considering these factors, auditors can establish an appropriate sample size that enables them to effectively evaluate the controls in place, ultimately contributing to the assurance of financial statement reliability.