Section 2a

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Section 2a

• The Use of Audit Sampling
• Test of Balances

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Statistical Tests of Balances

• Monetary Unit Sampling (MUS) or (PPS)
• Involves the same previously seen 14 steps

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• 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 Corporations trade
accounts receivable during November 200X. After
reviewing the work, the audit manager agreed with
the auditors 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 years 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.
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• 1. Determine the Objective of MUS Sampling

• Must relate to the audit procedure
• What would be the assertion in this example?

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• Decide if audit sampling applies
• Why would sampling apply here?

• 3. Define attributes and error conditions
• What is the attribute here?
• Error condition?

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• 4. Define the population
• What is the population in this case?

• 5. Define the sampling unit
• The sampling unit is ?
• Logical sampling unit

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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 auditors planned level of materiality for
  the account
• Thus TM is

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• 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

• ARIA

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Reliability Factors for Misstatements of
Overstatements
Number of Overstatement Misstatements Acceptable Risk of Incorrect Acceptance (ARIA) Acceptable Risk of Incorrect Acceptance (ARIA) Acceptable Risk of Incorrect Acceptance (ARIA) Acceptable Risk of Incorrect Acceptance (ARIA) Acceptable Risk of Incorrect Acceptance (ARIA) Acceptable Risk of Incorrect Acceptance (ARIA) Acceptable Risk of Incorrect Acceptance (ARIA) Acceptable Risk of Incorrect Acceptance (ARIA) Acceptable Risk of Incorrect Acceptance (ARIA)
Number of Overstatement Misstatements 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
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• 8. Specify Anticipated Misstatement (AM) and
  Expansion Factor (EF)
• Anticipated misstatement
• For Athens Corporation?

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• The expansion factor (EF)

Expansion factor Acceptable Risk of Incorrect Acceptance (ARIA) Acceptable Risk of Incorrect Acceptance (ARIA) Acceptable Risk of Incorrect Acceptance (ARIA) Acceptable Risk of Incorrect Acceptance (ARIA) Acceptable Risk of Incorrect Acceptance (ARIA) Acceptable Risk of Incorrect Acceptance (ARIA) Acceptable Risk of Incorrect Acceptance (ARIA) Acceptable Risk of Incorrect Acceptance (ARIA) Acceptable Risk of Incorrect Acceptance (ARIA)
Expansion factor 1 5 10 15 20 25 30 37 50
Expansion factor 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?

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• 9. Determine the sample size
• Auditors can use the following formula

n
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• 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
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• 10. Select Sample
• Sampling interval
• Systematic sampling

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• 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

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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
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• 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?

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

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• 12. Generalize from the sample to the population

• Upper misstatement limit

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(a) Computing Projected Misstatements

• What is projected misstatement?
• The tainting percentage

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• For logical sampling units less than the sampling
  interval

• For logical sampling units greater than or equal
  to the sampling interval

Book value Audited value Projected
misstatement for each audited item
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• 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 Logical sampling units less than sampling interval Logical sampling units less than sampling interval Logical sampling units less than sampling interval Logical sampling units less than sampling interval Logical sampling units less than sampling interval 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 Logical sampling units greater than or equal to sampling interval Logical sampling units greater than or equal to sampling interval Logical sampling units greater than or equal to sampling interval Logical sampling units greater than or equal to sampling interval Logical sampling units greater than or equal to sampling interval Logical sampling units greater than or equal to sampling interval
1225 37,858 37,465 393 393
Projected misstatement Projected misstatement Projected misstatement Projected misstatement Projected misstatement Projected misstatement 5,931
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(b) Computing Allowance for Sampling Risk

• What is this allowance?
• Two components
• Basic precision
• BP RF x SI

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1. Incremental allowance for sampling risk

• Auditor must use reliability factors

Number of Overstatements Acceptable Risk of Incorrect Acceptance(ARIA) Acceptable Risk of Incorrect Acceptance(ARIA) Acceptable Risk of Incorrect Acceptance(ARIA) Acceptable Risk of Incorrect Acceptance(ARIA) Acceptable Risk of Incorrect Acceptance(ARIA) Acceptable Risk of Incorrect Acceptance(ARIA) Acceptable Risk of Incorrect Acceptance(ARIA) Acceptable Risk of Incorrect Acceptance(ARIA) 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
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• For Athens Corporation accounts 1491 and 1794
  were identified as including misstatements less
  than the sampling interval.

(a) (a) (b) (c) (d) (e) (f)
Tainting Percentage (ranked) Tainting Percentage (ranked) Account Number Projected Misstatement Reliability Factor Increase in Reliability Factor Incremental Allowance (c) x (e)
2.31
10 1491 1491 3,692 3.89 1.58 5,833
5 1794 1794 1,846 5.33 1.44 2,658
8,491
Less Projected misstatement for sampling units less than sampling interval Less Projected misstatement for sampling units less than sampling interval Less Projected misstatement for sampling units less than sampling interval Less Projected misstatement for sampling units less than sampling interval Less Projected misstatement for sampling units less than sampling interval Less Projected misstatement for sampling units less than sampling interval 5,538
Incremental allowance for sampling risk Incremental allowance for sampling risk Incremental allowance for sampling risk Incremental allowance for sampling risk Incremental allowance for sampling risk Incremental allowance for sampling risk 2,953
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Thus upper misstatement limit (UML) is
UML
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• 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?

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• When upper misstatement limit exceeds the
  tolerable misstatement

• What does this mean to valuation?
• If the sample has no misstatements
• UML PM BP IA

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• 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

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• If upper misstatement limit exceeds the
  tolerable misstatement

• Population is not acceptable
• Some possible courses of action

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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.
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3. Ask the client to perform additional work or
to adjust the accounts
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• Advantages and Disadvantages of MUS Sampling

Advantages 1. Increases likelihood of including
high-dollar value items 2. Easy to use
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• 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.
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Problem 16. MUS Sampling. Edwards has decided to
use MUS sampling in the audit of a clients
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) Risk of Incorrect Acceptance (ARIA) Risk of Incorrect Acceptance (ARIA) Risk of Incorrect Acceptance (ARIA) Risk of Incorrect Acceptance (ARIA) Risk of Incorrect Acceptance (ARIA) Risk of Incorrect Acceptance (ARIA) Risk of Incorrect Acceptance (ARIA) 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
• 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

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• 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
• Does the book value present fairly?

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• 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 Tims 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
• 0220-01 2,400 0
• 0615-31 50 48
• 0714-09 3,600 2,400
• 1119-22 15,000 14,000