Audit Sampling: An Application to Substantive Tests of Account Balances

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Chapter Nine. 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 chapter apply to this chapter as well. Three important determinants of sample size are: - PowerPoint PPT Presentation

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Chapter 9Audit Sampling: An Application to Substantive Tests of Account Balances
Chapter Nine
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:
Desired confidence level.
Tolerable misstatement.
Expected misstatement.
Population plays a bigger role in some of the sampling techniques used for substantive testing.
Misstatements discovered in the audit sample must be projected to the population, and there must be an allowance for sampling risk.
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Substantive Tests of Details of Account 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 of €60,000.
(€3,000,000 × 2%)
3,000,000
100,000
98,000
2,000
Substantive Tests of Details of 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 conclude that the account is fairly stated because our best estimate of the projected misstatement is greater than the tolerable misstatement.
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Monetary-Unit Sampling (MUS)
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Monetary-Unit Sampling (MUS)
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Monetary-Unit Sampling (MUS)
Advantages of MUS
When the auditor expects no misstatement, MUS usually results in a smaller sample size than classical variables sampling.
The calculation of the sample size and evaluation of the sample results are not based on the variation between items in the population.
When applied using the probability-proportional-to-size procedure, MUS automatically results in a stratified sample.
*
Monetary-Unit Sampling (MUS)
Disadvantages of MUS
The selection of zero or negative balances generally requires special design consideration.
The general approach to MUS assumes that the audited amount of the sample item is not in error by more than 100%.
*
Planning
• Define the population.
• The tolerable misstatement.
Evaluation
6. Calculate the projected misstatement and the upper limit on misstatement.
7. Draw final conclusions.
$ 775,000,000
40%
$ 310,000,000
800,000,000
40%
320,000,000
Cash
1,800
25,000,000
40%
10,000,000
$ 320,000,000
Sampling may be used for substantive testing to:
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.
Develop an estimate of some amount.
Table 1
Planning
• Define the population.
$ 775,000,000
40%
$ 310,000,000
800,000,000
40%
320,000,000
Cash
1,800
25,000,000
40%
10,000,000
$ 320,000,000
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Steps in MUS Sampling
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Planning
• Define the population.
$ 775,000,000
40%
$ 310,000,000
800,000,000
40%
320,000,000
Cash
1,800
25,000,000
40%
10,000,000
$ 320,000,000
*
Planning
• Define the population.
$ 775,000,000
40%
$ 310,000,000
800,000,000
40%
320,000,000
Cash
1,800
25,000,000
40%
10,000,000
$ 320,000,000
© The McGraw-Hill Companies 2010
Steps in MUS Sampling
*
Planning
• Define the population.
$ 775,000,000
40%
$ 310,000,000
800,000,000
40%
320,000,000
Cash
1,800
25,000,000
40%
10,000,000
$ 320,000,000
3. Determine the sample size, using the following inputs:
• The desired confidence level or risk of incorrect acceptance.
• The tolerable misstatement.
$ 775,000,000
40%
$ 310,000,000
800,000,000
40%
320,000,000
Cash
1,800
25,000,000
40%
10,000,000
$ 320,000,000
$ 775,000,000
40%
$ 310,000,000
800,000,000
40%
320,000,000
Cash
1,800
25,000,000
40%
10,000,000
$ 320,000,000
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Steps in MUS Sampling
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Performance
Evaluation
6. Calculate the projected misstatement and the upper limit on misstatement
7. Draw final conclusions.
$ 775,000,000
40%
$ 310,000,000
800,000,000
40%
320,000,000
Cash
1,800
25,000,000
40%
10,000,000
$ 320,000,000
© The McGraw-Hill Companies 2010
Steps in MUS Sampling
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 €3,977 the auditor would select the following items for testing:
Cumulative
Sample
Account
Balance
Euros
Item
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Steps in MUS Sampling
*
Performance
Evaluation
6. Calculate the projected misstatement and the upper limit on misstatement.
7. Draw final conclusions.
$ 775,000,000
40%
$ 310,000,000
800,000,000
40%
320,000,000
Cash
1,800
25,000,000
40%
10,000,000
$ 320,000,000
© The McGraw-Hill Companies 2010
Steps in MUS Sampling
The misstatements detected in the sample must be projected to the population. Let’s look at the following example:
Book value
Evaluation
6. Calculate the projected misstatement and the upper limit on misstatement.
7. Draw final conclusions.
$ 775,000,000
40%
$ 310,000,000
800,000,000
40%
320,000,000
Cash
1,800
25,000,000
40%
10,000,000
$ 320,000,000
Basic Precision using the Table
If no misstatements are found in the sample, the best estimate of the population misstatement would be zero euros.
€26,882 × 3.0 = €80,646 upper misstatement limit
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Misstatements Detected
In the sample of 93 items the following misstatements were found:
€3,284 ÷ €21,893 = 15%
Because the Axa balance of €32,549 is greater than the interval of €26,882, no sampling risk is added. Since all the euros in the large accounts are audited, there is no sampling risk associated with large accounts.
Customer
Compute the Upper Misstatement Limit
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.
(0.15 × €26,882 × 1.4 = €5,645)
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Steps in MUS Sampling
We compare the tolerable misstatement to the upper misstatement limit. If the upper misstatement limit is less than or equal to the tolerable misstatement, we conclude that the balance is not materially misstated.
*
Evaluation
6. Calculate the projected misstatement and the upper limit on misstatement.
7. Draw final conclusions.
$ 775,000,000
40%
$ 310,000,000
800,000,000
40%
320,000,000
Cash
1,800
25,000,000
40%
10,000,000
$ 320,000,000
© The McGraw-Hill Companies 2010
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:
Increase the sample size.
Perform other substantive procedures.
Request the client adjust the accounts receivable balance.
*
Auditor's Decision Based
on Sample Evidence
Not Materially Misstated
Correct decision
Does not support the fairness of the account balance
Risk of incorrect rejection (Type I)
Correct Decision
$ 775,000,000
40%
$ 310,000,000
800,000,000
40%
320,000,000
Cash
1,800
25,000,000
40%
10,000,000
$ 320,000,000
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 by €2,688
(– 0.10 × €26,882)
Tests of Account Balances
The sampling unit for non-statistical sampling is normally a customer account, an individual transaction, or a line item on a transaction. When using non-statistical sampling, the following items must be considered:
Identifying individually significant items.
Determining the sample size.
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Identifying Individually Significant Items
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Sample
Size
× Confidence factor
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. This approach is known as ratio projection.
Assume the auditor finds €1,500 in misstatements in a sample of €15,000. The misstatement ratio is 10%.
If the population total is €200,000, the projected misstatement would be €20,000 (€200,000 × 10%)
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Calculating the Sample Results
A second method is the difference projection. This method projects the average misstatement of each item in the sample to all items in the population.
The projected misstatement would be €30,000 (€3 × 10,000).
Assume misstatements in a sample of 100 items total €300 (for an average misstatement of €3), and the population contains 10,000 items.
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Example
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The auditor decides . . .
Based on the results of the tests of controls, the risk of material misstatement is assessed as low.
The tolerable misstatement is €55,000, and the expected misstatement is €15,000.
The desired level of confidence is moderate based on the other audit evidence already gathered.
All customer account balances greater than €25,000 are to be audited.
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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 misstatements were the result of unintentional error by client personnel. Here are the results of the audit testing:
Amount of
Book Value
Audit Value
€2,000 ÷ 425,000 × €850,500
As a result of the audit procedures, the following projected misstatement was prepared:
*
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Why Did Statistical Sampling
Fall Out Of Favour?
Firms found that some auditors were over relying on statistical sampling techniques to the exclusion of good judgement.
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Classical Variables 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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Classical Variables Sampling
A sampling distribution is useful because it allows us to estimate the probability of observing any single sample result.
In classical variables sampling, the sample mean is the best estimate of the population mean.
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Advantages
When the auditor expects a relatively large number of differences between book and audited values, this method will normally result in smaller sample size than MUS.
The techniques are effective for both overstatements and understatements.
*
Disadvantages
Does not work well when little or no misstatement is expected in the population.
To determine sample size, the auditor must estimate the standard deviation of the audit differences.
*
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Applying Classical Variables Sampling
Defining the Sampling Unit
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Tolerable misstatement – Estimated misstatement
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Applying Classical Variables 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.
Table 1
$ 775,000,000
40%
$ 310,000,000
800,000,000
40%
320,000,000
Cash
1,800
25,000,000
40%
10,000,000
$ 320,000,000
© The McGraw-Hill Companies 2010
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 year, the auditor estimates the standard deviation at €31.
Let’s calculate sample size.
5,500 × 1.96 × €31
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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 totalled €330.20. Our first calculation is the mean misstatement in an individual account which is calculated as follows:
€330.20
125
Mean
misstatement
€14,575 = 5,500 × €2.65
SD =
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Applying Classical Variables Sampling
If both limits are within the bounds of tolerable misstatement, the evidence supports the conclusion that the account is not materially misstated.
(€50,000)
€50,000
Lower
limit
(€1,653)
Projected
misstatement
€14,575
Upper
limit
€30,803
€0
Planning
• Define the population.
• The tolerable misstatement.
Evaluation
6. Calculate the projected misstatement and the upper limit on misstatement.
7. Draw final conclusions.
Planning
• Define the population.
Planning
• Define the population.
Planning
• Define the population.
Planning
• Define the population.
3. Determine the sample size, using the following inputs:
• The desired confidence level or risk of incorrect acceptance.
• The tolerable misstatement.
Performance
Evaluation
6. Calculate the projected misstatement and the upper limit on misstatement
7. Draw final conclusions.
Performance
Evaluation
6. Calculate the projected misstatement and the upper limit on misstatement.
7. Draw final conclusions.
Evaluation
6. Calculate the projected misstatement and the upper limit on misstatement.
7. Draw final conclusions.
Evaluation
6. Calculate the projected misstatement and the upper limit on misstatement.
7. Draw final conclusions.
Supports the fairness of
Desired Level of
Confidence CC Value