Section 2a
The Use of Audit Sampling
Test of Balances
Statistical Tests of Balances
• Monetary Unit Sampling (MUS) or (PPS)
• Involves the same previously seen 14 steps
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.
1. Determine the Objective of MUS Sampling
• Must relate to the audit procedure
• What would be the assertion in this example?
2. Decide if audit sampling applies
•
Why would sampling apply here?
3. Define attributes and error conditions
– What is the attribute here?
– Error condition?
4. Define the population
•
What is the population in this case?
5. Define the sampling unit
• The sampling unit is ?
•
Logical sampling unit
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.
6. Specify Tolerable Misstatement (TM)
•
The auditor’s planned level of materiality for
the account
•
Thus TM is
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 =
Reliability Factors for Misstatements of Overstatements
RF
Number of
Overstatement
Misstatements
Always
used
Acceptable Risk of Incorrect Acceptance (ARIA)
1%
5%
10%
15%
20%
25%
30%
37%
50%
0
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
3.00
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
8. Specify Anticipated Misstatement
(AM) and Expansion Factor (EF)
• Anticipated misstatement
• For Athens Corporation?
•
The expansion factor (EF)
Acceptable Risk of Incorrect Acceptance (ARIA)
Expansion factor
•
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?
9. Determine the sample size
•
Auditors can use the following formula:
Book value (BV)
Sample size
(n)
= Tolerable
misstatement (TM)
x
-
Anticipated
Misstatement (AM)
x
n=
-
n=
Reliability factor (RF) for risk of overstatement
x
x
Expansion factor for
anticipated misstatement
(EF)
• 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
Inverse
Anticipated misstatement
Direct
Expansion factor for anticipated misstatement
Direct
10.Select Sample
• Sampling interval
• Systematic sampling
Sampling
Interval
=
Book value of the population (BV)
Sample size (n)
•
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
Customer
Recorded
Account Number Account Balance
Cumulative
Dollar Total
1001
$521
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
•
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?
Customer
Recorded
Account Number Account Balance
Cumulative
Dollar Total
1001
$521
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
1091
$40
122,246
2089
$2,498
2,396,787
2894
$3,213
2,400,000
Dollar Selected
$9,832
$46,755
122,206 $83,768 and $120,601
11. Perform the audit procedures
• Appropriate procedures that are appropriate
for the circumstances
• What is the appropriate procedure?
12. Generalize from the sample to the population
• Upper misstatement limit
Allowance for sampling
risk
Upper
=
misstatement limit
Projected
+
misstatement
Basic
+
precision
Incremental
allowance
(a) Computing Projected Misstatements
• What is projected misstatement?
• The tainting percentage
• For logical sampling units less than the sampling interval
Tainting percentage
Book value – Audited value
Book value
x
Sampling
interval
=
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
•
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)
Account
Number
Book
Value
(c)
(d)
Audited Difference
Value
(b) – (c)
(e)
(f)
(g)
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%
$36,923
$1,846
$5,538
Logical sampling units greater than or equal to sampling interval:
1225
$37,858
Projected misstatement
$37,465
$393
$393
$5,931
(b) Computing Allowance for Sampling Risk
• What is this allowance?
• Two components
1. Basic precision
BP = RF x SI
2. 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%
0
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
3.00
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
•
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
Incremental allowance for sampling risk
5,538
$2,953
Thus upper misstatement limit (UML) is
Allowance for sampling
risk
Upper
=
misstatement limit
UML
=
Projected
+
misstatement
Basic
+
precision
Incremental
allowance
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?
• When upper misstatement limit exceeds the
tolerable misstatement
• What does this mean to valuation?
• If the sample has no misstatements
• UML = PM + BP + IA
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
• If upper misstatement limit exceeds the
tolerable misstatement
Population is not acceptable
• Some possible courses of action
1. 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.
3. Ask the client to perform additional work or to adjust the
accounts
Advantages and Disadvantages of MUS
Sampling
Advantages
1. Increases likelihood of including highdollar value items
2. Easy to use
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.
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%
0
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
3.00
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:
a.
Calculate the sampling interval and the sampling size Edwards should use, given the
following information:
i.
Tolerable misstatement
$15,000
ii.
Risk of incorrect acceptance
5%
iii.
Number of misstatements allowed
0
iv.
Recorded amount of accounts receivable
$300,000
b.
Calculate the total projected misstatement if the following three misstatements were
discovered in a MUS sample:
Recorded Amount
($)
c.
Audited Amount
($)
Sampling Interval
($)
400
320
1,000
500
0
1,000
3,000
2,500
1,000
Does the book value present fairly?
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:
1.
Determine the required sample size and sampling interval.
2.
Calculate the upper misstatement limit, assuming that the auditor tested the sample
and discovered the following misstatements.
Voucher Number
Book Value
Audited Value
0220-01
$ 2,400
0615-31
50
48
0714-09
3,600
2,400
1119-22
15,000
14,000
$
0