Substantive Tests of Details of Account Balances

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Chapter 9

Audit Sampling: An Application to Substantive Tests of

Account Balances

Substantive Tests of Details of

Account Balances

The statistical concepts we discussed in the last The statistical concepts we discussed in the last chapter apply to this chapter as well. Three important chapter apply to this chapter as well. Three important determinants of sample size are

determinants of sample size are 1.

1. Desired confidence level.Desired confidence level. 2

2 T lT l blbl ii t tt t tt

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2.

2. Tolerable misstatement.Tolerable misstatement. 3.

3. Estimated misstatement.Estimated misstatement.

Population plays a bigger role in some of the sampling Population plays a bigger role in some of the sampling techniques used for substantive testing.

techniques used for substantive testing.

Misstatements discovered in the audit sample must be Misstatements discovered in the audit sample must be projected to the population, and there must be an projected to the population, and there must be an allowance for sampling risk.

allowance for sampling risk.

Substantive Tests of Details of

Account Balances

Consider the following information about the inventory account balance of an audit client:

Book value of inventory account balance $ 3,000,000 Book value of items sampled $ 100,000

A dit d l f it l d 98 000

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Audited value of items sampled 98,000 Total amount of overstatement observed in audit sample $ 2,000

The ratio of misstatement in the sample is 2% The ratio of misstatement in the sample is 2%

($2,000

($2,000 ÷÷ $100,000)$100,000)

Applying the ratio to the entire population produces a best estimate of misstatement of inventory of $60,000.

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Account Balances

The results of our audit test depend upon

the tolerable misstatement associated

with the inventory account. If the tolerable

misstatement is $50 000 we cannot

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misstatement is $50,000, we cannot

conclude that the account is fairly stated

because our best estimate of the

projected misstatement is greater than

the tolerable misstatement.

Monetary-Unit Sampling (MUS)

MUS uses attribute

MUS uses attribute--sampling theory to

sampling theory to

express a conclusion in dollar amounts rather

than as a rate of occurrence. It is commonly

used by auditors to test accounts such as

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accounts receivable

,

loans receivable

,

investment securities

, and

inventory

.

Monetary-Unit Sampling (MUS)

MUS uses attribute

MUS uses attribute--sampling theory (used

sampling theory (used

primarily to test controls) to estimate the

percentage of monetary units in a population

that might be misstated and then multiplies

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g

p

g

p

this percentage by an estimate of how much

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Monetary-Unit Sampling (MUS)

Advantages of MUS

1.

1. When the auditor expects no misstatement, MUS When the auditor expects no misstatement, MUS usually results in a smaller sample size than classical usually results in a smaller sample size than classical variables sampling.

2. The calculation of the sample size and evaluation of The calculation of the sample size and evaluation of the sample results are not based on the variation the sample results are not based on the variation between items in the population.

between items in the population.

3.

3. When applied using the probabilityWhen applied using the probability--proportionalproportional--toto--size size procedure, MUS automatically results in a stratified procedure, MUS automatically results in a stratified sample.

1. The selection of zero or negative balances generally The selection of zero or negative balances generally requires special design consideration.

requires special design consideration.

2

2 The general approach to MUS assumes that theThe general approach to MUS assumes that the LO# 2

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2.

2. The general approach to MUS assumes that the The general approach to MUS assumes that the audited amount of the sample item is not in error by audited amount of the sample item is not in error by more than 100%.

more than 100%.

3.

3. When more than one or two misstatements are When more than one or two misstatements are detected, the sample results calculations may detected, the sample results calculations may overstate the allowance for sampling risk. overstate the allowance for sampling risk.

Steps in MUS Sampling

Steps in MUS Sampling Application Planning

1. 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:

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4. Select sample items. 5. Perform the auditing procedures.

• Understand an alayzye any missstatements observed.

Evaluation

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Sampling may be used for substantive testing to: 1. Test the reasonableness of assertions about a

financial statement amount (i.e., is the amount fairly stated). This is the most common use of sampling for substantive testing.

2. Develop an estimate of some amount.

Steps in MUS Sampling

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For MUS the population is defined as the monetary value of an account balance, such as accounts receivable, investment

securities, or inventory.

Steps in MUS Sampling

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Steps in MUS Sampling

1. Determine the test objectives. 2. Define the population characteristics. • Define the population. • Define the sample unit.

• Define a misstatement

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9-13 • Define a misstatement.

A misstatement is defined as the difference between monetary amounts in the client’s records and

amounts supported by audit evidence.

Steps in MUS Sampling

Steps in MUS Sampling Application

3. Determine the sample size, using the following inputs: • The desired confidence level or risk of incorrect acceptance. to Sample Size

Change

Steps in MUS Sampling

Steps in MUS Sampling Application Performance

Evaluation

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

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9-15 7. Draw final conclusions.

The auditor selects a sample for MUS by using a systematic selection approach called probability-proportional-to-size selection. The sampling interval can

be determined by dividing the book value of the population by the sample size. Each individual dollar in

the population has an equal chance of being selected and items or “logical units” greater than the interval will

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Assume a client’s book value of accounts receivable is $2,500,000, and the auditor determined a sample size of 93. The sampling interval will be

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

Cumulatvie Sample

Account Balance Dollars Item

1001 Ace Emergency Center $ 2,350 $ 2,350

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1001 Ace Emergency Center $ 2,350 $ 2,350

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

1003 Jess Base, Inc. 945 18,780

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

1005 Jen Mara Corp. 3,968 44,641

1006 Zippy 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 Heather, Inc. 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 $

Steps in MUS Sampling

Steps in MUS Sampling Application Performance

Evaluation

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

7 D fi l l i

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After the sample items have been selected, the auditor conducts the planned audit procedures on the logical units containing

the selected dollar sampling units.

Steps in MUS Sampling

Steps in MUS Sampling Application Evaluation

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

The misstatements detected in the sample t b j t d t th l ti

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must be projected to the population.

Book value $ 2,500,000 Tolerable misstatement $ 125,000 Sample size 93 Desired confidence level 95% Expected amount of misstatement $ 25,000 Sampling interval $ 26,882

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Steps in MUS Sampling

Basic Precision using the Tables

If no misstatements are found in the sample, the best estimate of the population misstatement would be zero dollars.

Sample

Size 0 1 2 3

Actual Number of Deviations Found

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$26,882 ×× 3.0 = 3.0 = $80,646$80,646upper misstatement limitupper misstatement limit

Steps in MUS Sampling

Misstatements Detected

In the sample of 93 items, the following misstatements were found:

Customer Book Value Audit Value Difference Tainting Because the Axa balance of $32,549is greater than the interval of $26,882, no sampling risk is added. Since all the dollars in the large accounts are audited, there is no

sampling risk associated with large accounts.

Steps in MUS Sampling

Computed Upper Misstatement Limit using Tables Computed Upper Misstatement Limit using Tables

We 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.

Tainting Sample Projected 95% Upper Upper

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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 Application Evaluation

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

In our example, the final decision is whether the accounts receivable balance

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We compare the tolerable misstatement to the upper We compare the tolerable misstatement to the upper misstatement limit. If the upper misstatement limit is misstatement limit. If the upper misstatement limit is less less than or equal to

than or equal tothe tolerable misstatement, we conclude the tolerable misstatement, we conclude that the balance is

that the balance is not materially misstatednot materially misstated. .

whether the accounts receivable balance is materially misstated or not.

Steps in MUS Sampling

In our example, the upper misstatement limit of $150,621

is greater than the tolerable misstatement of $125,000, so the auditor concludes that the accounts receivable

balance is materially misstated. When faced with this situation, the auditor may: When faced with this situation, the auditor may:

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, y

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.

, y

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.

Risk When Evaluating Account

Balances

Auditor's Decision Based

on Sample Evidence Not Materially Misstated Materially Misstated Supports the fairness of

the account balance Correct decision

Risk of incorrect acceptance (Type II)

D t t th

True State of Financial Statement Account

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Does not support the fairness of the account

balance

Risk of incorrect rejection (Type I)

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Why is the Sampling Interval

Rather than the Sample Size Used

in Evaluating MUS Results?

Due to simplifying assumptions about accounting populations, the misstatement factors used in most MUS evaluation approaches are nearly identical to the misstatement factors associated with a sample size of 100, regardless of the actual

l i d b th dit Al th f t

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sample size used by the auditor. Always use these factors:

Number of Misstatement Incremental Misstatement Incremental

Errors Factor Increase Factor Increase

0 3.0 2.3

1 4.7 1.7 3.9 1.6

2 6.2 1.5 5.3 1.4

3 7.6 1.4 6.6 1.3

4 9.0 1.4 7.9 1.3

95% Confidence Level 90% Confidence Level

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.

C t

Book V l

Audit

V l Diff

Tainting F t

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Customer Value Value Difference Factor

Wayne County Medical $ 2,2002,000 $ (200)$ -10%

The most likely error will be reduced by The most likely error will be reduced by $2,688$2,688

((–– 0.10 0.10 ×× $26,882)$26,882)

Nonstatistical Sampling for Tests

of Account Balances

The sampling unit for nonstatistical sampling is normally a customer account, an individual transaction, or a line item on a transactions. When using nonstatistical sampling, the

following items must be considered:

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o

oIdentifying individually significant items.Identifying individually significant items.

o

oDetermining the sample size.Determining the sample size.

o

oSelecting sample items.Selecting sample items.

o

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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

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sampling risk.

Determining the Sample Size

Sample Size =

Sampling Population book value

Tolerable – Expected misstatement× Assurance factor

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Assessment of Risk of Slightly Below

Material Misstatement Maximum Maximum Moderate Low

Maximum 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

Desired Level of Confidence

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

If the population If the population total is $200,000, total is $200,000, the projected

Assume the auditor Assume the auditor finds $1,500 in finds $1,500 in misstatements in a misstatements in a sample of $15,000. sample of $15,000. The misstatement The misstatement ratio is 10%. ratio is 10%.

Calculating the Sample Results

A second method is the difference estimation. This method projects the averagemisstatement of each item

in the sample to all items in the population.

Assume misstatement would be misstatement would be $30,000 (

$30,000 ($3 $3 ×× 10,000). 10,000).

Assume Assume

misstatements in a misstatements in a sample of 100 items sample of 100 items total $300 (for total $300 (for average average

misstatement of $3), misstatement of $3), and the population and the population contains 10,000

The auditor’s of Calabro Wireless Service have decided to use nonstatistical sampling to examine the

accounts receivable balance. Calabro has a total of

11,800 (15 + 250 + 11,535) accounts with a balance of$3 717 900 The auditor’s stratify the

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balance of $3,717,900. The auditor s stratify the accounts as follows:

Number and Size Book

of Accounts Value

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Example

The auditor’s decide . . .

o

o There is a low assessment for inherent and control risk.There is a low assessment for inherent and control risk.

o

o The tolerable misstatement is $40,000, and the expected The tolerable misstatement is $40,000, and the expected misstatement is $15 000

misstatement is $15 000

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misstatement is $15,000. misstatement is $15,000.

o

o There is a moderate risk that other auditing procedures There is a moderate risk that other auditing procedures will fail to detect material misstatements.

will fail to detect material misstatements.

o

o All customer account balances greater than $25,000 are All customer account balances greater than $25,000 are to be audited.

Sampling population book value

Tolerable - Estimated misstatement × Assurance factor

$3,717,900 $3,717,900 –– $550,000$550,000

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Combined Assessment of Slightly Below

Inherent and Control Risk Maximum Maximum Moderate Low

Maximum 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 Fail to Detect Material Misstatement

$ , , $ , , $$ ,,

$55,000 $55,000 –– $15,000$15,000

Nonstatistical Sampling

Example

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 the

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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 <$3,000 2,317,400 92,000 91,750 250

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Nonstatistical Sampling

Example

As a result of the audit procedures, the following projected misstatement was prepared:

Amount of Projected

Stratum Misstatement Misstatement

>$25,000 $ 500 $ 500

Ratio of Misstatement in Stratum Tested

Not Applicable--100% Tested

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>$3,000 2,000 4,002 <$3,000 250 6,298 Total projected misstatement $ 10,800

$250 ÷ 92,000 × $2,317,400 $2,000 ÷ 425,000 × $850,500

The total projected misstatement of $10,800 is less than The total projected misstatement of $10,800 is less than the expected misstatement of $15,000, so the auditors the expected misstatement of $15,000, so the auditors

may conclude that there is an acceptably

may conclude that there is an acceptably low risklow riskthat that the true misstatement exceeds the tolerable the true misstatement exceeds the tolerable

misstatement. misstatement.

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

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judgment.

2.There appears to be poor

linkage between the applied audit

setting and traditional statistical

sampling applications.

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

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misstatement.

Sampling distributions are formed by plotting the Sampling distributions are formed by plotting the projected misstatements yielded by an infinite projected misstatements yielded by an infinite number of audit samples of the same size taken number of audit samples of the same size taken

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A sampling distribution is useful because it allows us to estimate the probability of observing any single

sample result.

Classical Variables Sampling

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In classical variables sampling, the sample mean is the best estimateof the population mean.

Classical Variables Sampling

1.

1. When the auditor expects a large number of When the auditor expects a large number of differences between book and audited values, this differences between book and audited values, this method will result in smaller sample size than method will result in smaller sample size than

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Advantages

MUS. MUS.

2.

2. The techniques are effective for both The techniques are effective for both overstatements and understatements. overstatements and understatements.

3.

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Classical Variables Sampling

1.

1. Does not work well when little or not misstatement Does not work well when little or not misstatement is expected in the population.

is expected in the population.

2

2 To determine sample size the auditor mustTo determine sample size the auditor must

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Disadvantages

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2.

2. To determine sample size, the auditor must To determine sample size, the auditor must estimate the standard deviation of the audited estimate the standard deviation of the audited value or differences.

value or differences.

3.

3. If few misstatements are detected in the sample If few misstatements are detected in the sample data, the true variance tends to be

data, the true variance tends to be

underestimated, and the resulting projection of the underestimated, and the resulting projection of the misstatements to the population is likely not to be misstatements to the population is likely not to be reliable.

reliable.

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 can

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auditing accounts receivable, the auditor can define the sampling unit to be a customer’s account balance or an individual sales invoice

included in the account balance.

Applying Classical Variables

Sampling

Determining the Sample Size

Sample Size =

Population size (in sampling units)× CC × SD Tolerable misstatement – Estimated misstatement

2

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Sampling

The Confidence Coefficient (CC) is associated with the desired level of confidence. The desired level of confidence is the complement of the risk that the auditor will mistakenly accept a population as fairly stated when the true population

misstatement is greater than tolerable misstatement

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misstatement is greater than tolerable misstatement.

Desired Level of

Confidence CC Value 95.0% 1.96 90.0% 1.65 80.0% 1.28 70.0% 1.04

Applying Classical Variables

Sampling

The year-end balance for accounts receivable contains 5,500 accounts with a book value of $5,500,000. The tolerable misstatement for accounts receivable is set at $50,000. The expected misstatement has been judged to be $20,000. The desired confidence is 95%. Based on work completed last

th dit ti t th t d d d i ti t $31 L t’ LO# 6

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year, the auditor estimates the standard deviation at $31. Let’s calculate sample size.

Sample Size

5,500 × 1.96 × $31 $50,000 – $20,000

2

= = 125125

Applying Classical Variables

Sampling

Calculating the Sample Results

The sample selection usually relies on random-selection techniques. Upon completion, 30 of the customer accounts selected contained misstatements that totaled $330 20

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contained misstatements that totaled $330.20. Our first calculation is the mean misstatement in an individual account which is calculated as follows:

Mean misstatement per sampling

item

= Total audit difference_{Sample size}

= $330.20 125

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Applying Classical Variables

Sampling

The mean misstatement must be projected to the population

Population size × Mean misstatement li it Projected

population =

(i li it)

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$14,575

$14,575 = 5,500 × $2.65 per sampling item p p

misstatement (in sampling units)

Applying Classical Variables

Sampling

The formula for the standard deviation is . . .

Total audit differences squared–

Mean difference per sampling item2 Sample

Size ×

SD =

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Sample size – 1

= $36,018.32 – (125 × 2.652₎

124 = $16.83$16.83

Applying Classical Variables

Sampling

Confidence bound

Population

size CC

SD

Sample size

× × =

16.83

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= 5,500 × 1.96 ×

_√

₁₂₅

Confidence interval

Projected misstatement

Confidence bound

±

=

= $14,575 = $14,575 ±±$16,228$16,228

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Sampling

Lower limit ($1,653)

Projected misstatement

$14,575

Upper limit $30,803

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If both limitsare within the bounds of tolerable misstatement, the evidence supports the conclusion

that the account is not materially misstated.

($50,000) $0 $50,000

Tolerable Misstatement