Question

Data relative to three MPU estimation plans are presented below.

1 2 3
Tolerable misstatement $110,000 $140,000 $170,000
Size of population 5,000 6,000 8,000
Risk of incorrect rejection 10% 5% 10%
Estimated population standard deviation $80 $105 $125
Risks that misstatements accumulating to greater than tolerable misstatements will not be detected by:
Internal control 50% 40% 40%
Other substantive procedures (excluding this test of details) 25% 50% 85%
Desired overall audit risk 5% 5% 5%
Inherent risk 100% 100% 100% Analysis: Determine an appropriate risk of incorrect acceptance for each population.

Answer 1

To determine the risk of incorrect acceptance for each MPU estimation plan, the audit risk formula is used, taking into account the inherent risk, control risk, the risk of other substantive procedures, and the desired audit risk. Detection risk is derived and adjusted by the risk of incorrect rejection to find the risk of incorrect acceptance.

Step-by-step explanation:

The question is asking to determine an appropriate risk of incorrect acceptance for each of the three MPU (Monetary Unit Sampling) estimation plans presented. The key to answering this question lies in understanding the relationship between inherent risk, control risk, and detection risk, which together make up the audit risk. Audit risk can be defined as the risk that the auditor expresses an inappropriate audit opinion when the financial statements are materially misstated.

The formula for audit risk is:

Audit Risk = Inherent Risk x Control Risk x Detection Risk

Since the question presents the inherent risk as 100% for all three plans, and the desired overall audit risk as well as the risks associated with internal controls and other substantive procedures are provided, we can rearrange the audit risk formula to solve for detection risk, which includes both the risk of incorrect rejection and the risk of incorrect acceptance.

Detection Risk = Audit Risk / (Inherent Risk x Control Risk x Risk of other substantive procedures)

For the first MPU estimation plan (Plan 1), the appropriate risk of incorrect acceptance could be calculated as follows:

Detection Risk = 0.05 / (1.00 x 0.50 x 0.25) = 0.40 or 40%

Therefore, considering that the risk of incorrect rejection is 10%, we can deduce the risk of incorrect acceptance for Plan 1 is the remaining detection risk (40% - 10%), which is 30%.

This process repeats similarly for each MPU estimation plan, taking the unique values of control risk and risk of other substantive procedures into account for each.