chapter 09 international

7/29/2019 Chapter 09 International

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Copyright 2006 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

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Chapter Nine

Audit Sampling:

An Application to Substantive Tests

of Account Balances


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Substantive Tests of Details of Account

Balances

The statistical concepts we discussed in the last

chapter apply to this chapter as well. Three important

determinants of sample size are

1. Desired confidence level.

2. Tolerable misstatement (error).

3. Estimated misstatement (error).

Misstatements discovered in the audit sample mustbe projected to the population, and there must be an

allowance for sampling risk.


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Balances

Consider the following information about the inventory

account balance of an audit client:

The ratio of misstatement in the sample is 2%

(2,000 100,000)

Applying the ratio to the entire population produces a best

estimate of misstatement of inventory of60,000.(3,000,000 2%)

Book value of inventory account balance 3,000,000

Book value of items sampled 100,000Audited value of items sampled 98,000

Total amount of overstatement observed in audit sample 2,000


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Balances

The results of our audit test depend

upon the tolerable error associated with

the inventory account. If the tolerable

error is50,000, we cannot concludethat the account is fairly stated because

our best estimate of the projected error

is greater than the tolerable error.


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Monetary-Unit Sampling (MUS)

MUS uses attribute-sampling theory toexpress a conclusion in monetary amounts

(e.g. in euros or other currency) rather than

as a rate of occurrence. It is commonly usedby auditors to test accounts such as

accounts receivable, loans receivable,

investment securities and inventory.

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MUS uses attribute-sampling theory to

estimate the percentage of monetary units in

a population that might be misstated and then

multiplies this percentage by an estimate ofhow much the euros are misstated.

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7/55Copyright 2006 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

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Advantages of MUS

1. When the auditor expects no misstatement, MUS

usually results in a smaller sample size than classical

variables sampling.

2. The calculation of the sample size and evaluation of

the sample results are not based on the variation

between items in the population.

3. When applied using the probability-proportional-to-size

procedure, MUS automatically results in a stratified

sample.

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Disadvantages of MUS

1. The selection of zero or negative balances generally

requires special design consideration.

2. The general approach to MUS assumes that the

audited amount of the sample item is not in error by

more than 100%.

3. When more than one or two misstatements aredetected, the sample results calculations may

overstate the allowance for sampling risk.

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Steps in MUS Sampling ApplicationSteps in MUS Sampling Application

Planning1. Determine the test objectives.

2. Define the population characteristics.

Define the population.

Define the sample unit.

Define a misstatement.

3. Determine the sample size, using the following inputs:

The desired confidence level or risk of incorrect acceptance.

The tolerable misstatement.

The expected population misstatement.

Population size.

Performance4. Select sample items.

5. Perform the auditing procedures.

Evaluation

6. Calculate the projected misstatement and the upper limit on misstatement.

7. draw final conclusions.

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Steps in MUS Sampling Application

Steps in MUS Sampling ApplicationPlanning

1. Determine the test objectives.





Sampling may be used for substantive testing to:

1. Test the reasonableness of assertions about a

financial statement amount.

2. Develop an estimate of some amount.

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For MUS the population is defined as the

monetary value of an account balance,

such as accounts receivable, investmentsecurities or inventory.

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An individual euro represents the sampling unit.

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A misstatement is defined as the difference between

monetary amounts in the clients records andamounts supported by audit evidence.

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Steps in MUS Sampling Application3. Determine the sample size, using the following inputs:

The desired confidence level or risk of incorrect acceptance.

The tolerable misstatement.

The expected population misstatement.

Population size.

Factor

Relationship

to Sample Size

Change

in Factor

Effect on

Sample

Lower Decrease

Higher Increase

Lower IncreaseHigher Decrease

Lower Decrease

Higher Increase

Lower Decrease

Higher Increase

Desired confidence level

Tolerable mistatement

Expected mistatement

Population size

Direct

Inverse

Direct

Direct

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Steps in MUS Sampling ApplicationPerformance

4. Select sample items.


Evaluation

6. Calculate the projected misstatement and the upper limit on misstatement

7. Draw final conclusions.

The auditor selects a sample for MUS by using a

systematic selection approach called probability-

proportionate-to-size selection. The sampling intervalcan be determined by dividing the book value of the

population by the sample size. Each individual euro in

the population has an equal chance of being selected.

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Assume a clients book value of accounts receivable is 2,500,000, and theauditor determined a sample size of 93. The sampling interval will be

26,882(2,500,000 93). The random number selected is 3,977theauditor would select the following items for testing:

Cumulative Sample

Account Balance Euros Item1001 Ace Emergency Center 2,350 2,350

1002 Admington Hospital 15,495 17,845 3,977 (1)

1003 Jess Base 945 18,780

1004 Good Hospital Corp. 21,893 40,673 30,859 (2)

1005 Jen Mara Corp. 3,968 44,641

1006 Axa Corp. 32,549 77,190 57,741 (3)

1007 Green River Mfg. 2,246 79,436

1008 Bead Hospital Centers 11,860 91,306 84,623 (4)

1213 Andrew Call Medical - 2,472,032

1214 Lilly Health 26,945 2,498,977 2,477,121 (93)

1215 Janyne Ann Corp. 1,023 2,500,000

Total Accounts Receivable 2,500,000

3,977

26,882

30,859

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Steps in MUS Sampling ApplicationPerformance

4. Select sample items.


Evaluation



After the sample items have been selected,

the auditor conducts the planned audit

procedures on the logical units containingthe selected euro sampling units.

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Steps in MUS Sampling ApplicationEvaluation



The misstatements detected in the sample

must be projected to the population.

Book value 2,500,000

Tolerable misstatement 125,000

Sample size 93Desired confidence level 5%

Expected amount of misstatement 25,000

Sampling interval 26,882

Example Information

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Basic PrecisionIf no misstatements are found in the sample,

the best estimate of the population

misstatement would be zero euros.

SampleSize 0 1 2 3

65 4.6 7.1 9.4 11.5

70 4.2 6.6 8.8 10.8

85 4.0 6.2 8.2 10.1

80 3.7 5.8 7.7 9.5

90 3.3 5.2 6.9 8.4100 3.0 4.7 6.2 7.6

125 2.4 3.8 5.0 6.1

Actual Number of Deviations Found

26,882 3.0 = 80,646upper misstatement limit

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Misstatements DetectedIn the sample of 93 items the following misstatements

were found:

3,284 21,893 = 15%Because the Axa balance of32,549 is greater than theinterval of26,882, no sampling risk is added. Since allthe euros in the large accounts are audited, there is no

sampling risk associated with large accounts.

Customer Book Value Audit Value Difference

Tainting

Factory

Good Hospital 21,893 18,609 3,284 15%Marva Medical Supply 6,705 4,023 2,682 40%

Axa Corp. 32,549 30,049 2,500 NA

Learn Heart Centers 15,000 - 15,000 100%

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Compute the Upper Misstatement LimitWe compute the upper misstatement limit by calculating basic

precision and ranking the detected misstatements based on

the size of the tainting factor from the largest to the smallest.

(0.15 26,882 1.4 =5,645)

Customer

Tainting

Factor

Sample

Interval

Projected

Misstatement

95% Upper

Limit

Upper

Misstatement

Basic Precision 1.00 26,882 NA 3.0 80,646

Learn Heart Centers 1.00 26,882 (26,882) 1.7 (4.7 - 3.0) 45,700

Marva Medical 0.40 26,882 (10,753) 1.5 (6.2 - 4.7) 16,130

Good Hospital 0.15 26,882 (4,032) 1.4 (7.6 - 6.2) 5,645

Add misstatments greater

that the sampling interval:

Axa Corp. NA 26,882 NA 2,500

Upper Misstatement Limit 150,621

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Steps in MUS Sampling ApplicationEvaluation



We compare the tolerable misstatement to the upper

misstatement limit. If the upper misstatement limit is lessthan or equal to the tolerable misstatement, we conclude

that the balance is not materially misstated.

In our example, the final decision is

whether the accounts receivable balance

is materially misstated or not.

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In our example the upper misstatement limit of150,621is greater than the tolerable misstatement of125,000, so

the auditor concludes that the accounts receivable

balance is materially misstated.

When faced with this situation, the auditor may:

1. Increase the sample size.

2. Perform other substantive procedures.

3. Request the client adjust the accounts receivable balance.

4. If the client refuses to adjust the account balance, the

auditor would consider issuing a qualified or adverse

opinion.

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Risk When Evaluating Account Balances

Auditor's Decision Based

on Sample Evidence Not Materially Misstated Materially Misstated

Supports the fairness of

the account balanceCorrect decision

Risk of incorrect

acceptance (Type II)Does not support the

fairness of the account

balance

Risk of incorrect

rejection (Type I)

Correct Decision

True State of Financial Statement Account


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Effect of Understatement Misstatements

MUS is not particularly effective at detecting

understatements. An understated account is less likely to be

selected than an overstated account.

The most likely error will be reduced by2,688( 0.10 26,882)

CustomerBookValue

AuditValue Difference

TaintingFactor

Wayne County Medical 2,000 2,200 (200) -10%


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Identifying Individually Significant Items

The items to be tested individually are items that may

contain potential misstatements that individually exceed

the tolerable misstatement. These items are tested

100% because the auditor is not willing to accept any

sampling risk.

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Determining the Sample Size

Sample

Size=

Population book value

Tolerable misstatement Assurance factor

Combined Assessment of Slightly Below

Inherent and Control Risk Maximum Maximum Moderate LowMaximum 3.0 2.7 2.3 2.0

Slightly below maximum 2.7 2.4 2.0 1.6

Moderate 2.3 2.1 1.6 1.2

Low 2.0 1.6 1.2 1.0

Risk That Other Substantive Procedures Will Fail to

Detect Material Misstatements

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Selecting Sample Items

Auditing standards require that the sample items be

selected in such a way that the sample can be expected

to represent the population.

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Calculating the Sample Results

One way of projecting the sampling results to the

population is to apply the misstatement ratio in the

sample to the population.

If the population

total is200,000,the projected

misstatement would

be20,000(200,000 10%)

Assume the auditor

finds1,500 inmisstatements in a

sample of15,000.

The misstatementratio is 10%.

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Calculating the Sample Results

A second method is the difference estimation. This

method projects the average misstatement of each item

in the sample to all items in the population.

The projected

misstatement would

be30,000, (300

100 =3 10,000).

Assume

misstatements in a

sample of 100 items

total300, and the

population contains10,000 items.

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Non-statistical Sampling Example

The auditors of Calabro Paging Service have decidedto use non-statistical sampling to examine the accounts

receivable balance. Calabro has 11,800 accounts with

a balance of3,717,900. The auditors stratify theaccounts as follows:


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The auditor sent positive confirmations to each of the 110

(95 + 15) accounts selected. Either the confirmations were

returned or alternative procedures were successfully

used. Four customers indicated that their accounts were

overstated and the auditors determined that themisstatements were the result of unintentional error by

client personnel. Here are the results of the audit testing:

Amount of

Book Value Audit Value Over-

Stratum Book Value of Sample of Sample Statement

>25,000 550,000 550,000 549,500 500

>3,000 850,500 425,000 423,000 2,000


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As a result of the audit procedures, the following

projected misstatement was prepared:

The total projected misstatement of10,800 is less thanthe expected misstatement of15,000, so the auditors

may conclude that there is a low riskthat the true

misstatement exceeds the tolerable misstatement.

Amount of Projected

Stratum Misstatement Misstatement

>25,000 500 500

>3,000 2,000 4,002


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Why Did Statistical Sampling Fall Out Of

Favor?

1.Firms found that some auditors were

over relying on statistical sampling

techniques to the exclusion of good

judgment.

2.There appears to be poor linkage

between the applied audit setting and

traditional statistical sampling

applications.

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Classical Variable Sampling

Classical variables sampling uses normal distribution

theory to evaluate the characteristics of a population

based on sample data. Auditors most commonly use

classical variables sampling to estimate the size of

misstatement.

Sampling distributions are formed by plotting the

projected misstatements yielded by an infinite

number of audit samples of the same size takenfrom the same underlying population.


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Classical Variables Sampling

In classical variables sampling, the sample mean is

the best estimate of the population mean.

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Advantages

1. When the auditor expects a large number of

differences between book and audited values, this

method will result in smaller sample size thanMUS.

2. The techniques are effective for both

overstatements and understatements.

3. The selection of zero balances generally does not

require special sample design considerations.

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Disadvantages

1. To determine sample size, the auditor must

estimate the standard deviation of the audited

value or differences.

2. If few misstatements are detected in the sample

data, the true variance tends to be

underestimated, and the resulting projection of the

misstatements to the population is likely not to bereliable.

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Applying Classical Variables Sampling

Defining the Sampling Unit

The sampling unit can be a customer account,

an individual transaction, or a line item. In

auditing accounts receivable, the auditor candefine the sampling unit to be a customers

account balance or an individual sales invoice

included in the account balance.

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Determining the Sample Size

where

ZIA = One-tailed Z value for the specified

level of the risk of incorrect acceptance.SD = Estimated standard deviation.

Sample

Size

=Population size ZIA SD

Tolerable misstatement Estimated misstatement

2

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The risk of incorrect acceptance is the risk that the

auditor will mistakenly accept a population as fairly

stated when the true population misstatement is greater

than tolerable misstatement.

Risk of Incorrect

Acceptance Z Value

2.5% 1.96

5.0% 1.65

10.0% 1.2815.0% 1.04

20.0% 0.84

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The year-end balance for accounts receivable contains 5,500accounts with a book value of5,500,000. The tolerable

misstatement for accounts receivable is set at50,000. Theexpected misstatement has been judged to be20,000. The

risk of incorrect acceptance is 2.5%. Based on workcompleted last year, the auditor estimates the standard

deviation at31. Lets calculate sample size.

SampleSize 5,500 1.96 3150,00020,000

2

= = 125


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The mean misstatement must beprojected to the population.

= 5,500 2.65 =14,575

Population size Mean misstatementper sampling item

Projected

populationmisstatement

= (in sampling units)

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Point estimate of accounts receivable balance . . .

Accounts receivable

point estimate

Book

value

Projected population

misstatement=

= 5,500,00014,575 =5,485,425

The sum of the audited differences squared is

equal to36,018.32. We will use this value tocalculate the standard deviation.

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The formula for the standard deviation is . . .

Total audit

differences squared

Mean difference

per sampling item2

Sample

Size

Sample size 1

SD =

= 36,018.32 (125 2.652)124

=16.83

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Confidence

bound

Population

size ZIASD

Sample size =

= 5,500 1.96 16.83125 =16,228

Confidence

interval

Population

point estimate

Confidence

bound=

= 5,485,425 16,228

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Lowerbound5,469,197

Pointestimate5,485,425

Upperbound5,501,652

Book

value5,500,000

Confidence interval

If theprecision intervalincludes the book value, the

evidence supports the conclusion that the account is not

materially misstated.

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Applying Classical Variables


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Applying Classical Variables

Sampling

Lowerbound5,469,197

Pointestimate5,485,425

Upperbound5,501,652

Book

value5,508,000

Confidence interval

When the evidence indicates that the account may be materially

misstated the auditor might consider(1) increasing sample size, (2)

performing additional substantive procedures, (3) adjusting the

account, or(4) issue a qualified or adverse opinion.

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End of Chapter 9

chapter 09 international

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