1. The Use of Audit Sampling Test of Balances
Section 2a
The Use of Audit Sampling
Test of Balances

2. Statistical Tests of Balances
Monetary Unit Sampling (MUS) or (PPS)
Involves the same previously seen 14 steps

3. Athens Corporation Case
An auditor has been assigned the responsibility of auditing the trade accounts receivable of Athens Corporation as of December 31, 200X. The total amounts to $2,400,000 and consists of 800 accounts. The auditor tested controls that relate to the existence of Athens Corporation’s trade accounts receivable during November 200X. After reviewing the work, the audit manager agreed with the auditor’s assessment that assessing control risk at 80 percent was appropriate. The manager indicated that the planned audit risk should be limited to 5 percent, inherent risk should be assessed to be 100 percent, and the risk that analytical procedures will not detect material misstatements should be assessed to be 60 percent. The manager also decided that $100,000 should be used as tolerable misstatement for purposes of confirming trade accounts receivable. During last year’s audit, the auditors found misstatements amounting to only $10,000, which the manager suggests should be used this year as an estimate of the misstatement for the purposes of determining sample size. A review of the listing of accounts indicates that it includes no accounts that have credit balances or zero balances.

4. 1. Determine the Objective of MUS Sampling
Must relate to the audit procedure
What would be the assertion in this example?

5. Decide if audit sampling applies
Why would sampling apply here?
3. Define attributes and error conditions
What is the attribute here?
Error condition?

6. 4. Define the population
What is the population in this case?
5. Define the sampling unit
The sampling unit is ?
Logical sampling unit

7. Specify Tolerable Misstatement (TM)
Summary:
For Athens Corporation, the population is all 800 customer accounts with debit balances, and the recorded book value of the accounts is $2,400,000. The audit manager decided that customers' accounts rather than individual invoices are to be confirmed. Accounts receivable has 2,400,000 sampling units and 800 logical sampling units.
Specify Tolerable Misstatement (TM)
The auditor’s planned level of materiality for the account
Thus TM is

8. 7. Specify the reliability factor (RF) for acceptable risk of incorrect acceptance (ARIA)
Can eliminate the acceptable risk of incorrect acceptance by auditing the entire population
Recall the audit risk model
AR = IR x CR x AP x ARIA DR
ARIA =

9. RF Reliability Factors for Misstatements of Overstatements Always used
Number of Overstatement Misstatements
Acceptable Risk of Incorrect Acceptance (ARIA) 1% 5%
10%
15%
20%
25%
30%
37%
50%
4.61
3.00
2.31
1.90
1.61
1.39
1.21
1.00
0.70 1
6.64
4.75
3.89
3.38
2.70
2.44
2.14
1.68 2
8.41
6.30
5.33
4.72
4.28
3.93
3.62
3.25
2.68 3
10.05
7.76
6.69
6.02
5.52
5.11
4.77
4.34
3.68 4
11.61
9.16
8.00
7.27
6.73
6.28
5.90
5.43
4.68 5
13.11
10.52
9.28
8.50
7.91
7.43
7.01
6.49
5.68 6
14.57
11.85
10.54
9.71
9.08
8.56
8.12
7.56
6.67 7
16.00
13.15
11.78
10.90
10.24
9.69
9.21
8.63
7.67 8
17.41
14.44
13.00
12.08
11.38
10.81
10.31
9.68
8.67 9
18.79
15.71
14.21
13.25
12.52
11.92
11.39
10.74
9.67 10
20.15
16.97
15.41
14.42
13.66
13.02
12.47
11.79
10.67
Always used

10. 8. Specify Anticipated Misstatement (AM) and Expansion Factor (EF)
For Athens Corporation?

11. Acceptable Risk of Incorrect Acceptance (ARIA)
The expansion factor (EF)
Expansion factor
Acceptable Risk of Incorrect Acceptance (ARIA) 1% 5%
10%
15%
20%
25%
30%
37%
50%
1.9
1.6
1.5
1.4
1.3
1.25
1.2
1.15
1.0
What is the expansion factor for anticipated misstatement and why?

12. 9. Determine the sample size
Auditors can use the following formula:
Anticipated Misstatement (AM)
Expansion factor for anticipated misstatement (EF) x -
Tolerable misstatement (TM)
Reliability factor (RF) for risk of overstatement
Book value (BV) =
Sample size
(n)
n = x -
n =

13. Component of Sample Size Equation Relationship to Sample Size
Change in a component of sample size
Component of Sample Size Equation
Relationship to Sample Size
Book value
Direct
Risk of incorrect acceptance
Inverse
Tolerable misstatement
Anticipated misstatement
Expansion factor for anticipated misstatement

14. Book value of the population (BV) Sample size (n)
10. Select Sample
Sampling interval
Systematic sampling
Sampling Interval =
Book value of the population (BV) Sample size (n)

15. The auditor decides to use systematic sampling
What is the sampling interval?
BV/n =
Must now identify customer account numbers
Also called logical sampling units

16. Customer Account Number Recorded Account Balance
Cumulative Dollar Total
1001
521
1012
8,484
9,005
1030
793
9,798
1041
8,309
18,107
1052
547
18,654
1056
28,838
47,492
1075
356
47,848
1080
74,358
122,206
1091 40
122,246
2089
2,498
2,396,787
2894
3,213
2,400,000

17. Assume auditor selects 9832 with a random stab
From where?
Which account balance should we select?
What is the sampling interval?
Thus what is the next account?

18. Customer Account Number Recorded Account Balance
Cumulative Dollar Total
Dollar Selected
1001
521
1012
8,484
9,005
1030
793
9,798
1041
8,309
18,107
$9,832
1052
547
18,654
1056
28,838
47,492
$46,755
1075
356
47,848
1080
74,358
122,206
$83,768 and $120,601
1091 40
122,246
2089
2,498
2,396,787
2894
3,213
2,400,000

19. 11. Perform the audit procedures
Appropriate procedures that are appropriate for the circumstances
What is the appropriate procedure?

20. Allowance for sampling risk
12. Generalize from the sample to the population
Upper misstatement limit
Allowance for sampling risk
Upper misstatement limit =
Projected misstatement +
Basic precision
Incremental allowance

21. (a) Computing Projected Misstatements
What is projected misstatement?
The tainting percentage

22. For logical sampling units less than the sampling interval
Tainting percentage
Book value – Audited value
Book value
Sampling interval x
Project misstatement for each audited item =
For logical sampling units greater than or equal to the sampling interval
Book value – Audited value = Projected misstatement for each audited item

23. Tainting Percentage (d)/(b) Projected Misstatement (e) x (f)
Assume that for Athens Corporation three errors were found. Customer accounts 1491 and 1794 have book values less than the sampling interval, and customer account 1225 is larger than the sampling unit
(a)
(b)
(c)
(d)
(e)
(f)
(g)
Account Number
Book Value
Audited Value
Difference (b) – (c)
Tainting Percentage (d)/(b)
Sampling Interval
Projected Misstatement (e) x (f)
Logical sampling units less than sampling interval:
1491
$40
$36 $4
10%
$36,923
$3,692
1794
$4,000
$3,800
$200 5%
$1,846
$5,538
Logical sampling units greater than or equal to sampling interval:
1225
$37,858
$37,465
$393
Projected misstatement
$5,931

24. (b) Computing Allowance for Sampling Risk
What is this allowance?
Two components
Basic precision
BP = RF x SI

25. Acceptable Risk of Incorrect Acceptance(ARIA)
Incremental allowance for sampling risk
Auditor must use reliability factors
Number of Overstatements
Acceptable Risk of Incorrect Acceptance(ARIA) 1% 5%
10%
15%
20%
25%
30%
37%
50%
4.61
3.00
2.31
1.90
1.61
1.39
1.21
1.00
0.70 1
6.64
4.75
3.89
3.38
2.70
2.44
2.14
1.68 2
8.41
6.30
5.33
4.72
4.28
3.93
3.62
3.25
2.68 3
10.05
7.76
6.69
6.02
5.52
5.11
4.77
4.34
3.68 4
11.61
9.16
8.00
7.27
6.73
6.28
5.90
5.43
4.68

26. For Athens Corporation accounts 1491 and 1794 were identified as including misstatements less than the sampling interval.
(a)
(b)
(c)
(d)
(e)
(f)
Tainting Percentage (ranked)
Account Number
Projected Misstatement
Reliability Factor
Increase in Reliability Factor
Incremental Allowance (c) x (e)
2.31 10
1491
$3,692
3.89
1.58
$5,833 5
1794
1,846
5.33
1.44
2,658
$8,491
Less: Projected misstatement for sampling units less than sampling interval
5,538
Incremental allowance for sampling risk
$2,953

27. Allowance for sampling risk
Thus upper misstatement limit (UML) is
Upper misstatement limit =
Projected misstatement +
Basic precision
Incremental allowance
Allowance for sampling risk
UML =

28. 13. Evaluating results
To evaluate results the auditor compares the estimate of upper misstatement limit with the tolerable misstatement
From the results, the auditor for Athens Corporation may conclude with a 5% risk that the $2,400,000 book value is not overstated by more than $94,176.
What was the tolerable misstatement?
What is the final evaluation?

29. When upper misstatement limit exceeds the tolerable misstatement
What does this mean to valuation?
If the sample has no misstatements
UML = PM + BP + IA

30. 14. Decide the acceptability of the population
Reaching a conclusion
Have to also look at qualitative aspects
Must evaluate whether misstatements are errors or irregularities

31. If upper misstatement limit exceeds the tolerable misstatement
Population is not acceptable
Some possible courses of action

32. Consider whether the projected amount of misstatement in the population based on the audit is greater than the amount anticipated when sample size was determined.
2. Consider whether the sample is representative of the population.

33. 3. Ask the client to perform additional work or to adjust the accounts

34. Advantages and Disadvantages of MUS Sampling
1. Increases likelihood of including high-dollar value items
2. Easy to use

35. 3. Enables auditor to state a conclusion
Disadvantages
1. Assumption is that the audited value of a sampling unit is neither less than zero nor greater then book value.
2. Upper misstatement limit.

36. Risk of Incorrect Acceptance (ARIA)
Problem 16. MUS Sampling. Edwards has decided to use MUS sampling in the audit of a client’s accounts receivable balance. Few, if any, overstatements of account balance are expected. Edwards plans to use the following MUS sampling table:
Reliability Factors for Overstatement
Number of Overstatements
Risk of Incorrect Acceptance (ARIA) 1% 5%
10%
15%
20%
25%
30%
37%
50%
4.61
3.00
2.31
1.90
1.61
1.39
1.21
1.00
0.70 1
6.64
4.75
3.89
3.38
2.70
2.44
2.14
1.68 2
8.41
6.30
5.33
4.72
4.28
3.93
3.62
3.25
2.68 3
10.05
7.76
6.69
6.02
5.52
5.11
4.77
4.34
3.68 4
11.61
9.16
8.00
7.27
6.73
6.28
5.90
5.43
4.68
Required:
Calculate the sampling interval and the sampling size Edwards should use, given the following information:
Tolerable misstatement $15,000
Risk of incorrect acceptance 5%
Number of misstatements allowed 0
Recorded amount of accounts receivable $300,000

37. Calculate the total projected misstatement if the following three misstatements were discovered in a MUS sample:
Recorded Amount Audited Amount Sampling Interval
($) ($) ($)
,000
,000
3, , ,000
Does the book value present fairly?

38. Problem 2. MUS Sampling. Tim Dolan plans to use MUS sampling in auditing the Repairs and Maintenance account for Daco International to determine whether the accounts includes items that should be capitalized rather than expensed. Daco has recorded 2,000 invoices in arriving at the $800,000 expense for the year. Tim has decided to use $4,000 as the anticipated misstatement, and $50,000 as tolerable misstatement. After reviewing Tim’s work, the audit manager agreed with him that assessing control risk at 80 percent was appropriate. The manager indicated that the planned audit risk should be limited to 2 percent, inherent risk should be assessed to be 100 percent, and the risk that analytical procedures will not detect material misstatements should be assessed to be 50 percent.
Required:
Determine the required sample size and sampling interval.
Calculate the upper misstatement limit, assuming that the auditor tested the sample and discovered the following misstatements.
Voucher Number Book Value Audited Value
$ 2, $ 0
, ,400
, ,000