audchap9.htm

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CHAPTER 9

AUDIT SAMPLING: AN APPLICATION TO

SUBSTANTIVE TESTS OF ACCOUNT BALANCES

Answers to Review Questions

9-1 The steps in a statistical sampling application for substantive testing include (by phases):

Planning:1. Determine the test objectives.2. Define the population characteristics:o Define the population.

o Define the sampling unit.

o Define a misstatement.

3. Determine sample size, using the following inputs:

o Desired confidence level or risk of incorrect acceptance.

o Tolerable misstatement.

o Expected misstatement.o Population size.

Performance:4. Select sample items.5. Perform the audit procedures:

o Understand and analyze any misstatements observed

Evaluation:6. Calculate the projected misstatement and the upper limit on misstatement.7. Draw final conclusions.

9-3 The following table shows how the desired confidence level, tolerable misstatement, and expectedmisstatement are related to sample size:

Factor Relationship to Sample Size

Desired confidence level Direct

Tolerable misstatement Inverse

Expected misstatement Direct

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9-4 The advantages and disadvantages of MUS are:

Advantages:

When the auditor expects no misstatements, MUS will normally result in a smaller sample size thanclassical variables sampling.

The calculation of sample size and the evaluation of the sample results are not based on the variation(that is, the standard deviation) between items in the population.

MUS, when applied using a probability proportional to size sample selection procedure as outlined inthe text, automatically results in a stratified sample because sampled items are selected in proportion totheir monetary amount.

Disadvantages:

Selection of a zero or negative balance generally requires special design consideration.

The general approach to MUS assumes that the audited amount of the sample item is not in error bymore than 100 percent.

When more than one or two misstatements are detected using a MUS approach, the sample resultscalculations may overstate the allowance for sampling risk.

9-6 The decision rule for determining the acceptability of sample results when MUS is used compares thetolerable misstatement (TM) to the upper misstatement limit (UML). If UML is less than TM, theevidence supports the fair presentation of the account. If UML is greater than TM, the evidence does notsupport the fair presentation of the account balance.

9-9 The advantages and disadvantages of classical variables sampling are:

Advantages:

When the auditor expects a large number of differences between book and audited values, classicalvariables sampling will normally result in a smaller sample size than MUS.

Classical variables sampling techniques are effective for both overstatements and understatements. No

special evaluation considerations are necessary if the sample data include both types of misstatements. The selection of a zero balance generally does not require special sample design considerations since

the sampling unit will not be an individual dollar but rather an account, a transaction, or a line item.

Disadvantages:

In order to determine sample size, the auditor must estimate the standard deviation of the audited valueor differences.

If few misstatements are detected in the sample data, the true variance tends to be underestimated andthe resulting projection of the misstatements to the population is not likely to be reliable.

Answers to Multiple-Choice Questions

9-11 D 9-16 B9-12 D 9-17 A9-13 B 9-18 A9-14 A 9-19 C9-15 C 9-20 C

Solutions to Problems

9-21 a. The advantages of MUS over classical variables sampling are as follows:


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MUS sampling is generally easier to use than is classical variables sampling.

The calculation of sample size in a MUS sample is not based on an estimate of the standarddeviation in the population.

MUS sampling in conjunction with probability-proportional-to-size selection results in a stratifiedsample.

Individually significant items are automatically identified.

If no misstatements are expected, MUS will usually result in a smaller sample size than classicalvariables sampling.

b. Using Table 8-5 in the text with a desired confidence level = 95%, tolerable misstatement = 5%

($15,000 $300,000), and expected misstatement = 2%, ($6,000 $300,000) sample size is equal to

181 items. The sampling interval is $1,657 ($300,000 181).

Using ACL with a desired confidence level = 95%; population = $300,000; tolerable misstatement =$15,000; and expected misstatement = $6,000; the sample size is equal to 161 items. The samplinginterval is $1,853.93.

c. The total projected misstatement for the three misstatements identified is calculated by firstcomputing the tainting factor as follows:

MisstatementNumber

BookValue

AuditValue

TaintingFactor

1 $400 $320 .20

2 500 0 1.00

3 3,000 2,500Not applicable, since book valueexceeds sampling interval.


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The upper misstatement limit is calculated as follows:

Misstatement

Number

Tainting

Factor

Sampling

Interval

Projected

Misstatement

(column 2 x 3)

95% Upper

Limit

Increment

(from Table

8-8*)

Upper

Misstatement

(column 2 x 3 x

5)

Basic Precision 1.0 $1,657 NA 3.0 $4,971

2 1.0 1,657 1,657 1.7 (4.7-3.0) 2,817

1 .20 1,657 331 1.5 (6.2-4.7) 497Add

misstatements

detected in logical

units greater than

the sampling

interval:

Misstatement

3

NA 1,657 NA NA 500

Upper Misstatement Limit $8,785NANot Applicable* Using sample size 100, see footnote 3 in chapter 9.

Since the UML ($8,785) is less than the TM ($15,000), the evidence supports the fair presentation of theaccount balance.

Using ACL and the ACL sampling interval calculated by ACL in part b, the Upper Error Limit (UML) is$9,881.10 and the Most Likely Error is $2,724.72. Since the UML ($9,881.10) is less than the TM($15,000), the evidence supports the fair presentation of the account balance. The ACL output follows:

Command: EVALUATE MONETARY CONFIDENCE 95 ERRORLIMIT 400, 80,500, 500,3000, 500INTERVAL 1853.93 TO SCREEN

Confidence: 95, Interval: 1854

Item Error Most Likely Error Upper Error Limit

Basic Precision 5562.00

500.00 500.00 1853.93 3244.38

400.00 80.00 370.79 574.72

3000.00 500.00 500.00 500.00

Totals 2724.72 9881.10

9-23 a. Using Table 8-5 with a desired confidence level of 95% (risk of incorrect acceptance = 5%), tolerable

misstatement = 4% ($360,000 $9,000,000), and expected misstatement = 1% ($90,000

$9,000,000), sample size is equal to 156. The sampling interval is $57,692 ($9,000,000 156).

Using ACL with a desired confidence level = 95%; population = $9,000,000; tolerable misstatement= $360,000; and expected misstatement = $90,000; the sample size is equal to 130 items. Thesampling interval is $68,906.25.

b. The upper misstatement limit is calculated as follows:


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Overstatement Errors

ErrorNumber

Book Value Audit Value Tainting Factor

1 10,000 7,500 .25

2 9,000 6,000 .33

3 60,000 0 Not applicable, since the book valueexceeds the sampling interval

4 800 640 .20

Error Number Tainting

Factor

Sampling

Interval

Projected

Misstatement

(column 2 x 3)

95% Upper

Limit

Increment

(from Table

8-8*)

Upper

Misstatement

(column 2 x 3 x

5)

Basic Precision 1.0 $57,692 NA 3.0 $173,076

2 .33 57,692 19,038 1.7 (4.7-3.0) 32,365

1 .25 57,692 14,423 1.5 (6.2-4.7) 21,635

4 .20 57,692 11,538 1.4 (7.6-6.2) 16,153

Add

misstatements

detected in logical

units greater than

the sampling

interval:

Error 3

NA 57,692 NA NA 60,000

Upper Misstatement Limit $303,229NANot Applicable* Using sample size 100, see footnote 3 in chapter 9.

Since the UML ($303,229) is less than the tolerable misstatement ($360,000), Nancy Van Pelt canaccept the inventory account as being fairly stated since there is only a 5 percent risk that theaccount contains a misstatement greater than $360,000.

Using ACL and the sampling interval calculated by ACL in part a, the Upper Error Limit (UML) is$407,351.03 and the Most Likely Error is $122,882.81. The ACL output follows:

Command: EVALUATE MONETARY CONFIDENCE 95 ERRORLIMIT

10000.00,2500.00,9000.00,3000.00,60000.00,60000.00,800.00,160.00 INTERVAL 68906.25 TOSCREEN




60000.00 60000.00 68906.25 120585.94

9000.00 3000.00 22968.75 35601.56

10000.00 2500.00 17226.56 25150.78

800.00 160.00 13781.25 19293.75


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Totals 122882.81 407351.03

Since the UML ($407,351.03) is greater than the tolerable misstatement ($360,000), Nancy Van Pelt

cannot accept the inventory account as being fairly stated. The difference in the evaluation betweenthe manual calculation using the tables and ACL is driven by the difference in the size of thesampling interval. The larger sampling interval increases the UML for the Basic Precision and theother errors detected in the sample. Because the $60,000 item is smaller than the sampling interval inthe ACL calculation, there is an error projection (most likely error) and an upper error limit or

allowance for sampling risk added on. When using the tables the sample size is larger and thesampling interval is $57,692 and all items greater than the interval will be tested and therefore theerror associated with the $60,000 item is not projected when the tables are used and requires noadditional margin for sampling risk.

c. The calculation of the adjustment for the understatement errors is as follows:

Understatement Errors

Error Number Book Value Audit Value Tainting Factor

5 6,000 6,500 -.083

6 750 800 -.067

Adjustment for Understatement Errors

Tainting

Factor

Sampling

Interval

Projected

Misstatement

-.083 57,692 -4,788

-.067 57,692 -3,865

Adjustment to UML -8,653

Using ACL and the results from parts a and b, the Adjustment to the Most Likely Error is -10,335.94(112,546.87-122,882.81. The ACL output follows:

Command: EVALUATE MONETARY CONFIDENCE 95 ERRORLIMIT10000.00,2500.00,9000.00,3000.00,60000.00,60000.00,800.00,160.00,6000.00,-500.00,750.00,-50.00INTERVAL 68906.25 TO SCREEN




60000.00 60000.00 68906.25 120585.94

9000.00 3000.00 22968.75 35601.56

10000.00 2500.00 17226.56 25150.78

800.00 160.00 13781.25 19293.75

750.00 -50.00 -4593.75 0.00

6000.00 -500.00 -5742.19 0.00

Totals 112546.87 407351.03

9-27 The incorrect assumptions, statements, and inappropriate applications of sampling are as follows:


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Classical variables sampling is not designed for tests of controls.

MUS sampling uses each dollar in the population, not each account, as a separate sampling unit.

MUS sampling is not efficient if many misstatements are expected because the sample size canbecome larger than the corresponding sample size for classical variables sampling as the expectedamount of misstatement increases.

Each account does not have an equal chance of being selected; the probability of selection of theaccounts is proportional to the account's dollar amount.

MUS sampling requires special consideration for negative (credit) balances.

Tolerable misstatement was not considered in calculating sample size.

Expected misstatement was not considered in calculating sample size.

The standard deviation of the dollar amounts is not required for MUS sampling.

The three selected accounts with insignificant balances should not have been ignored or replacedwith other accounts.

The account with the $1,000 difference (recorded amount of $4,000 and audited amount of $3,000)was incorrectly projected as a $1,000 misstatement; the projected misstatement for this differencewas actually $2,500 ($1,000/$4,000 x $10,000 sampling interval).

The difference in the understated account (recorded amount of $1,900 and audited amount of$2,000) should not have been omitted from the calculation of projected misstatement.

The reasoning (the comparison of projected misstatement with the allowance for sampling risk)concerning the decision that the receivables balance was not overstated was erroneous.


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