Lecture Auditing and assurance services (Second international edition) Chapter 9 Audit sampling An application to substantive tests of account balances

In this chapter, the learning objectives are Understand the similarities and differences between audit sampling for tests of controls and substantive tests of details of account balances, learn to apply monetaryunit sampling, work through an extended example of monetary unit sampling,…

Audit 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:

1 Desired confidence level.

allowance for sampling risk.

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.

Substantive Tests of Details of Account

(€3,000,000 × 2%)

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

Total amount of overstatement observed in audit sample € 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.

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.

Monetary-Unit Sampling (MUS)

MUS uses attribute-sampling theory to express a conclusion in monetary amounts (e.g in euros or other currency) rather than

as a rate of occurrence It is commonly used

by auditors to test accounts such as accounts

receivable, loans receivable, investment

securities and inventory

MUS uses attribute-sampling theory to express a conclusion in monetary amounts (e.g in euros or other currency) rather than

as a rate of occurrence It is commonly used

by auditors to test accounts such as accounts

Monetary-Unit Sampling (MUS)

MUS uses attribute-sampling theory (used primarily to test controls) to estimate the percentage of monetary units in a population that might be misstated and then multiplies this percentage by an estimate of how much the euros are misstated.

MUS uses attribute-sampling theory (used primarily to test controls) to estimate the percentage of monetary units in a population that might be misstated and then multiplies this percentage by an estimate of how much the euros are misstated.

Monetary-Unit Sampling (MUS)

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

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

Monetary-Unit Sampling (MUS)

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

are detected, the sample results calculations may overstate the allowance for sampling

risk

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

are detected, the sample results calculations may 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:

• The desired confidence level or risk of incorrect acceptance.

• The tolerable misstatement.

• The expected population misstatement.

• Population size.

Performance

4 Select sample items.

5 Perform the auditing procedures.

Evaluation

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

7 Draw final conclusions.

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.

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

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

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.

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

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.

An individual euro represents the sampling unit

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.

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.

• The tolerable misstatement.

• The expected population misstatement.

Lower Decrease Higher Increase Lower Increase Higher Decrease Lower Decrease Higher Increase Lower Decrease Higher Increase

Desired confidence level Tolerable mistatement Expected mistatement Population size

Direct Inverse Direct Direct

Steps in MUS Sampling

Steps in MUS Sampling Application

Performance

4 Select sample items.

5 Perform the auditing procedures.

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 interval can 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 and items or ‘logical units’ greater than the interval will always be

selected.

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:

1001 Ace Emergency Centre € 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

30,859

€

Steps in MUS Sampling

Steps in MUS Sampling Application

Performance

4 Select sample items.

5 Perform the auditing procedures.

Evaluation

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

7 Draw final conclusions.

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

euro 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 must be projected to the population Let’s look at the following

example:

Tolerable misstatement € 125,000 Sample size 93 Desired confidence level 95%

Expected amount of misstatement € 25,000

Example Information

Steps in MUS Sampling

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

Steps in MUS Sampling

sampling risk associated with large accounts.

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 Book Value Audit Value Difference

Tainting Factor

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 Centres 15,000 - 15,000 100%

Steps in MUS Sampling

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

Sample Interval

Projected Misstatement

95% Upper Limit

Upper Misstatement Basic Precision 1.00 € 26,882 NA 3.0 € 80,646 Learn Heart Centres 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

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.

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

We compare the tolerable misstatement to the upper misstatement limit If the upper misstatement limit is

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

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:

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.

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.

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)

Does not support the fairness of the account

balance

Risk of incorrect rejection (Type I)

Correct Decision

True State of Financial Statement Account

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 by €2,688

Audit Value Difference

Tainting Factor

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

Non-Statistical Sampling for 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.

• Identifying individually significant items.

• Determining the sample size.

• Selecting sample items.

• Calculating the sample results.

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

Determining the Sample Size and

Selecting the Sample

SampleSize =

Sampling Population book value Tolerable – Expected misstatement × 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.

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.

If the population total is

€200,000, the projected misstatement would be

€20,000 (€200,000 × 10%)

Assume the auditor finds

€1,500 in misstatements in

a sample of

€15,000 The misstatement ratio is 10%

Assume the auditor finds

€1,500 in misstatements in

a sample of

€15,000 The misstatement ratio is 10%

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)

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

Assume misstatements in a sample of 100 items total €300 (for an average

misstatement of €3), and the population contains 10,000 items