Audit Sampling for Tests of Details of Balances

1. Audit Sampling for Testsof Details of Balances Chapter 16

2. Learning Objective 1 Differentiate audit sampling for tests of details of balances and for tests of controls and substantive tests of transactions.

3. Tests of Details of Balances, Controls, and Substantive Transactions Tests of Controls Substantive tests of transactions Sampling for tests of details of balances

4. Learning Objective 2 Apply nonstatistical sampling to tests of details of balances.

5. Nonstatistical Sampling There are 14 steps required in audit sampling for tests of details of balance. These steps parallel the 14 steps used for sampling for tests of controls and substantive tests of transactions. There are a few differences because of the different objectives of the tests.

6. Tests of Controls and SubstantiveTests of Transactions Step 1 State the objectives of the audit test. Step 2 Decide whether audit sampling applies. Step 3 Define attributes and exception conditions. Step 4 Define the population. Step 5 Define the sampling unit.

7. Audit Sampling for Testsof Details of Balances Step 1 State the objectives of the audit test. Step 2 Decide whether audit sampling applies. Step 3 Define misstatement conditions. Step 4 Define the population. Step 5 Define the sampling unit. Difference

8. Tests of Controls and SubstantiveTests of Transactions Step 6 Specify the tolerable exception rate. Step 7 Specify acceptable risk of assessing control risk too low. Step 8 Estimate the population exception rate. Step 9 Determine the initial sample size.

9. Audit Sampling for Tests of Details of Balances Step 6 Specify tolerable misstatement. Step 7 Specify acceptable risk of incorrect acceptance. Step 8 Estimate misstatements in the population. Step 9 Determine the initial sample size. Difference

10. Tests of Controls and SubstantiveTests of Transactions Step 10 Select the sample. Step 11 Perform the audit procedures. This is the same as in “Audit Sampling for Tests of Details of Balances.”

11. Tests of Controls and SubstantiveTests of Transactions Step 12 Generalize from the sample to the population. Step 13 Analyze the exceptions. Step 14 Decide the acceptability of the population.

12. Audit Sampling for Tests of Details of Balances Step 12 Generalize from the sample to the population. Step 13 Analyze the misstatements. Step 14 Decide the acceptability of the population. Difference

13. Action When aPopulation Is Rejected • Take no action until tests of other audit areas • are completed • Perform expanded audit tests in specific areas • Increase the sample size • Adjust the account balance • Request the client to correct the population • Refuse to give an unqualified opinion

14. Learning Objective 3 Apply monetary unit sampling.

15. Monetary Unit Sampling MUS is an innovation in statistical sampling methodology that was developed specifically for use by auditors.

16. Differences between MUS and Nonstatistical Sampling The definition of the sampling unit is an individual dollar. The population size is the recorded dollar population. Preliminary judgment of materiality is used for each account instead of tolerable misstatement.

17. Differences between MUS and Nonstatistical Sampling Sample size is determined using a statistical formula. A formal decision rule is used for deciding the acceptability of the population. Sample selection is done using probability proportional to size sample selection (PPS).

18. The Auditor Generalizes from theSample to the Population Using MUS Attributes sampling tables are used to calculate the results. The attributes results must be converted to dollars. The auditor must make an assumption about the percentage of misstatement for each population item that is misstated. The statistical results when MUS is used are called misstatement bounds.

19. Generalizing from theSample to the Population Assumption 1 Overstatement amounts equal 100 percent; understatement amounts equal 100 percent; misstatement bounds at a 5 percent ARIA are: Upper misstatement bound = $1,200,000 × 3% × 100% = $36,000 Lower misstatement bound = $1,200,000 × 3% × 100% = $36,000

20. Generalizing from theSample to the Population All amounts have to be overstatements. All population items misstated have to be 100 percent misstated.

21. Generalizing from theSample to the Population Assumption 2 Overstatement amounts equal 10 percent; understatement amounts equal 10 percent; misstatement bounds at a 5 percent ARIA are: Upper misstatement bound = $1,200,000 × 3% × 10% = $3,600 Lower misstatement bound = $1,200,000 × 3% × 10% = $3,600

22. Generalizing from theSample to the Population Assumption 3 Overstatement amounts equal 20 percent; understatement amounts equal 200 percent; misstatement bounds at a 5 percent ARIA are: Upper misstatement bound = $1,200,000 × 3% × 20% = $7,200 Lower misstatement bound = $1,200,000 × 3% × 200% = $72,000

23. Appropriate Percent of Misstatement Assumption The appropriate assumption for the overall percent of misstatement in those population items containing a misstatement is an auditor’s decision.

24. Generalizing When Misstatements Are Found 1. Overstatement and understatement amounts are dealt with separately and then combined. 2. A different misstatement assumption is made for each misstatement, including the zero misstatements.

25. Generalizing When Misstatements Are Found 3. The auditor must deal with layers of the computed upper exception rate (CUER) from the attributes sampling table. 4. Misstatement assumptions must be associated with each layer.

26. Illustration of the Auditor’s Decision Rule for MUS – Tolerable Misstatement $0 Misstatement + Tolerable Misstatement LMB UMB #1 LMB UMB #2 #2 LMB UMB LMB UMB #3 #4 LMB UMB #5

27. Determining Sample SizeUsing MUS Materiality Assumption of the average percent of misstatement for population items that contain a misstatement Acceptable risk of incorrect acceptance Recorded population value

28. Determining Sample SizeUsing MUS Estimate of the population exception rate Relationship of the audit risk model to sample size for MUS Remember this? PDR = AAR ÷ (IR × CR)

29. Learning Objective 4 Describe variables sampling.

30. Frequency Distributionof Sample Means Frequency of values in percent Value of in dollars x

31. Sampling Distribution The mean value of all the sample means is equal to the population mean . (X) A corollary is that the sample mean value with the highest frequency of occurrence is also equal to the population mean. (x)

32. Sampling Distribution The shape of the frequency distribution of the sample means is that of a normal distribution (curve), as long as the sample size is sufficiently large, regardless of the distribution of the population.

33. Sampling Distribution The percentage of sample means between any two values of the sampling distribution is measurable.

34. Sampling Distribution fora Population Distribution Mean Sampling distribution – Normal Population distribution – Skewed Frequency of values in percent Value of in dollars x

35. Variables Methods Difference estimation Ratio estimation Mean-per-unit estimation

36. Stratified Statistical Methods All of the elements of the population are divided into two or more subpopulations. Each subpopulation is independently tested.

37. Sampling Risks(ARIA and ARIR) Actual State of the Population Actual Audit Materially Not Materially Decision Misstated Misstated Conclude that the Correct conclusion Incorrect conclusion population is – no risk – risk is ARIR materially misstated Conclude that the Incorrect conclusion Correct conclusion population is – risk is ARIA – no risk not materially misstated

38. Learning Objective 5 Use difference estimation in tests of details of balances.

39. Plan the Sample andCalculate the Sample Size State the objectives of the audit test. Decide whether audit sampling applies. Define misstatement conditions. Define the population. Define the sampling unit. Specify tolerable misstatement.

40. Plan the Sample andCalculate the Sample Size Specify acceptable risk. ARIA ARIR

41. Estimate Misstatementin the Population Estimate an expected point estimate. Make an advance population standard deviation estimate – variability of the population.

42. Calculate the InitialSample Size n = {[SD*(ZA + ZB)N]÷ (TM – E*)}2 where: n = initial sample size SD* = advance estimate of the standard deviation ZA = confidence coefficient for ARIA ZB = confidence coefficient for ARIR N = population size TM = tolerable misstatement for the population (materially) E* = estimated point estimate of the population misstatement

43. Select the Sample andPerform the Procedures Select the sample. Perform the audit procedures.

44. Evaluate the Results Compute the point estimate of the total misstatement. Compute an estimate of the population standard deviation. Compute the precision interval. Compute the confidence limits.

45. Effect of Changing Factors Effect on the Computed Type of ChangePrecision Interval Increase ARIA Decrease Increase the point estimate of the misstatements Increase Increase the standard deviation Increase Increase the sample size Decrease

46. Analyze the Misstatements The auditor must evaluate misstatements to determine the cause of each misstatement and decide whether modification of the audit risk model is needed.

47. Auditor’s Decision Rule for Difference Estimation – Tolerable Misstatement $0 Misstatement + Tolerable Misstatement LCL UCL #1 LCL UCL #2 #2 LCL UCL LCL UCL #3 #4 LCL UCL #5

48. End of Chapter 16