Section 2a The Use of Audit Sampling Test of Balances.
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Transcript of Section 2a The Use of Audit Sampling Test of Balances.
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 =
Number of Overstatement Misstatements
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
Reliability Factors for Misstatements of Overstatements
Always used
RF
8. Specify Anticipated Misstatement (AM) and Expansion Factor (EF)
• Anticipated misstatement• For Athens Corporation?
• 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?
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 overstatementxBook value (BV)
=Sample size
(n)
n = x
- x
n =
• 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 Account Number
Recorded 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 Account Number
Recorded Account Balance
Cumulative Dollar Total
Dollar Selected
1001 $521 521
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
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
Upper misstatement limit
= Projected misstatement
+ Basic precision
+ Incremental allowance
Allowance for sampling risk
(a) Computing Projected Misstatements
• What is projected misstatement?
• The tainting percentage
Book value – Audited value
Book value
Sampling intervalx
Project misstatement for each audited item=
• For logical sampling units less than the sampling interval
Tainting percentage
• 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) (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% $36,923 $1,846
$5,538
Logical sampling units greater than or equal to sampling interval:
1225 $37,858 $37,465 $393 $393
Projected misstatement $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
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
•Auditor must use reliability factors
• 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
Thus upper misstatement limit (UML) is
Upper misstatement limit
= Projected misstatement
+ Basic precision
+ Incremental allowance
Allowance for sampling risk
UML =
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?
• What does this mean to valuation?
• If the sample has no misstatements
• UML = PM + BP + IA
• When upper misstatement limit exceeds the tolerable misstatement
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
Population is not acceptable
• Some possible courses of action
• If upper misstatement limit exceeds the tolerable misstatement
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 high-dollar 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 $300,000
b. Calculate the total projected misstatement if the following three misstatements were discovered in a MUS sample:
Recorded Amount Audited Amount Sampling Interval
($) ($) ($)
400 320 1,000
500 0 1,000
3,000 2,500 1,000
c. 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 $ 0
0615-31 50 48
0714-09 3,600 2,400
1119-22 15,000 14,000