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