Chapter 11

Audit Sampling ConceptsAudit Sampling Concepts

Discussion of Audit ProceduresNatureNature

Technique (eg. computation, observation, Technique (eg. computation, observation, confirmation etc.)confirmation etc.)

Type of evidence (eg. Internal, external..)Type of evidence (eg. Internal, external..)TimingTiming

when procedures are performedwhen procedures are performedExtentExtent

the amount of work done when the the amount of work done when the procedures are performed. Many audit procedures are performed. Many audit techniques are applied on a test basis (on techniques are applied on a test basis (on only a sample of the population)only a sample of the population)

Sampling Defined: SAS No 39 = application of an audit procedure to less than 100 percent of the items within an account balance or class of transactions for the purpose of evaluating some characteristic of the balance or class (AU 350.01).

Population

Sample

Audit Sampling Does Not Include:

Tracing several transactions through the accounting system Tracing several transactions through the accounting system to gain an understanding internal control structure to gain an understanding internal control structure ((walk-walk-through);through);

Complete or 100%Complete or 100% examination of population items examination of population items Examining all itemsExamining all items exceeding some dollar amount, and exceeding some dollar amount, and

testing the remaining items by analytical procedures or, in testing the remaining items by analytical procedures or, in some cases, not at all because they are immaterial; andsome cases, not at all because they are immaterial; and

Observing employeesObserving employees who are performing a control who are performing a control procedure that does not leave an audit trail, such as procedure that does not leave an audit trail, such as observing the physical inventory count. observing the physical inventory count.

Enquiry, written representations, and internal control Enquiry, written representations, and internal control questionnaires questionnaires

Analytical ProceduresAnalytical Procedures

Two purposes for audit sampling

Purpose:Obtain evidence about client’s control objective compliance:

OccurrenceOccurrenceAuthorizationAuthorizationCompletenessCompletenessAccuracy (valuation)Accuracy (valuation)Posting, Classification, TimingPosting, Classification, Timing

Sample:Usually from a class of transactions (populations), such as:

Cash ReceiptsCash disbursementsPurchases (inventory additions)Inventory issuesSales on creditExpense details

Test of controls

Examples of tests of controls For a sample of recorded sales invoices, compare to For a sample of recorded sales invoices, compare to

bill of lading, price list, quantity shipped, shipping bill of lading, price list, quantity shipped, shipping date and recalculate amountsdate and recalculate amounts

Trace a sample of shipping documents to invoicesTrace a sample of shipping documents to invoices For a sample of cash receipts compare to deposit For a sample of cash receipts compare to deposit

slips, check for approval, recalculate cash, trace to slips, check for approval, recalculate cash, trace to daily report, compare dates, trace postingsdaily report, compare dates, trace postings

Trace daily reports to cash receiptsTrace daily reports to cash receipts

Two purposes for audit sampling

PurposePurposeObtain evidence about Obtain evidence about assertions related to financial assertions related to financial statement balances:statement balances: Existence / OccurrenceExistence / Occurrence CompletenessCompleteness ValuationValuation OwnershipOwnership Presentation and disclosurePresentation and disclosure

Sample:Sample:Usually from items in an asset Usually from items in an asset or liability balance (population) or liability balance (population) such as:such as: Accounts ReceivableAccounts Receivable Loans receivableLoans receivable InventoryInventory Fixed assetsFixed assets Accounts payableAccounts payable

Test of Details

Tests of Details: Examples Confirm a sample of the receivables, investigate exceptions and Confirm a sample of the receivables, investigate exceptions and

follow up non-respondents by vouching sales charges and cash follow up non-respondents by vouching sales charges and cash receipts to supporting documents receipts to supporting documents (evidence of existence, rights (evidence of existence, rights

and valuationand valuation)) Obtain an aged trial balance of the receivables. Audit the aging Obtain an aged trial balance of the receivables. Audit the aging

accuracy on a sample basis. Calculate and analyze the age status accuracy on a sample basis. Calculate and analyze the age status of the accounts and the allowance for uncorrectable accounts in of the accounts and the allowance for uncorrectable accounts in the light of current economic conditions and the company’s the light of current economic conditions and the company’s collection experience collection experience (evidence of valuation)(evidence of valuation)

Vouch a sample of receivable balances to cash received after the Vouch a sample of receivable balances to cash received after the cutoff data cutoff data (evidence of existence, rights and valuation)(evidence of existence, rights and valuation)

Audit Sampling: Key Decisions Which population should be tested and for what Which population should be tested and for what

((population)population)??

How many items should be included in the sample How many items should be included in the sample ((sample sample sizesize)?)?

Which items should be included Which items should be included ((selectionselection)?)?

What does the sample information tell about the population What does the sample information tell about the population as a whole as a whole ((evaluationevaluation)?)?

Non-sampling and Sampling Risk An auditor can fail to reduce audit risk to an acceptably low level because of:An auditor can fail to reduce audit risk to an acceptably low level because of:

Non sampling Risk:Non sampling Risk:improper assessment of inherent and/or control riskimproper assessment of inherent and/or control risk failed to apply audit procedures carefully, loss of control failed to apply audit procedures carefully, loss of control

over audit evidenceover audit evidenceInappropriate proceduresInappropriate proceduresLack of professional skepticismLack of professional skepticism

Sampling Risk:Sampling Risk:the probability that an auditor’s conclusion based on a sample the probability that an auditor’s conclusion based on a sample

might be different from the conclusion based on an audit of might be different from the conclusion based on an audit of the entire population.the entire population.

Non-sampling Risk Non-sampling risk cannot be quantified. It can Non-sampling risk cannot be quantified. It can

only be guarded against. only be guarded against. Public accounting firms attempt to minimize non-Public accounting firms attempt to minimize non-

sampling risk by :sampling risk by :Implementing good quality control practices Implementing good quality control practices

of hiring, training, and supervising of hiring, training, and supervising competent personnel, competent personnel,

Carefully designing audit program Carefully designing audit program procedures, and procedures, and

Assigning appropriately qualified auditors Assigning appropriately qualified auditors to each audit.to each audit.

Sampling Terminology

How to select sample:How to select sample: Random selectionRandom selection

All sampling units have equal chance of All sampling units have equal chance of selectionselection. Good, but time-consuming. Good, but time-consuming

Systematic random selectionSystematic random selectionRandom starting pointRandom starting point. Less timc-consuming. . Less timc-consuming.

Beware of systematically recurring errors in Beware of systematically recurring errors in popn.popn.

Directed sample selectionDirected sample selection Block sample selectionBlock sample selection Haphazard selectionHaphazard selection

Sampling Terminology

Whether to subdivide population or notWhether to subdivide population or not Stratified vs. non-stratified sampleStratified vs. non-stratified sample

How to evaluate resultsHow to evaluate results Statistical vs. non-statisticalStatistical vs. non-statistical

How to define sampling unit /what item to selectHow to define sampling unit /what item to select Physical unitsPhysical units Dollar units (= proportionate to size sampling)Dollar units (= proportionate to size sampling)

Sampling Techniques

By Physical attribute:By Physical attribute: physical units are physical units are

sampling unitssampling units each unit has equal each unit has equal

chance of selectionchance of selection may need to may need to

compensate for compensate for high variability eg. high variability eg. By stratificationBy stratification

By Dollar Unit:By Dollar Unit: dollars are sampling dollars are sampling

unitsunits larger $ units have larger $ units have

greater chance of greater chance of selectionselection

no need to no need to compensate for high compensate for high variability or stratify variability or stratify population by valuepopulation by value

Sampling Terminology

What to look at once sample is identifiedWhat to look at once sample is identified Attribute sampling (yes/no)Attribute sampling (yes/no) Variables samplingVariables sampling

Statistical vs. Non-statistical

Either Either either statistical or non-statistical either statistical or non-statistical methods are permitted under GAASmethods are permitted under GAAS..

Objective of both is to enable the auditor to reach a Objective of both is to enable the auditor to reach a conclusion about an entire set of data by examining conclusion about an entire set of data by examining only a part of it. only a part of it.

Statistical sampling methods allow the auditor to Statistical sampling methods allow the auditor to express sampling risk in mathematical terms. In express sampling risk in mathematical terms. In non-statistical sampling, the auditor gives non-statistical sampling, the auditor gives “thoughtful attention” to this risk“thoughtful attention” to this risk

Statistical samplingStatistical sampling = audit sampling Statistical sampling = audit sampling

that uses the laws of probability for that uses the laws of probability for selectingselecting and and evaluatingevaluating a sample a sample from a population for the purpose of from a population for the purpose of reaching a conclusion about the reaching a conclusion about the population.population. selected at randomselected at random statistical calculations used to measure statistical calculations used to measure

and express the resultsand express the results does not require that laws of does not require that laws of

probability be used to determine probability be used to determine sample sizesample size

Statistical vs. Non-statistical

Statistical:Statistical: --precise, definite, precise, definite,

objective description objective description of resultsof results

-requires -requires quantification of risk quantification of risk and materialityand materiality

-requires a random -requires a random samplesample

-costly, training of -costly, training of staffstaff

Non-Statistical:Non-Statistical: Less rigid approach to Less rigid approach to

unique problemsunique problems Permits auditors to be Permits auditors to be

vague about risk and vague about risk and materialitymateriality

Permits auditors to be Permits auditors to be more subjective, more subjective, consider outside consider outside factorsfactors

Sampling Steps

1. State the objectives of the audit test1. State the objectives of the audit test TOC: To ensure key control is operating TOC: To ensure key control is operating

effectively, as documented, throughout period effectively, as documented, throughout period of relianceof reliance

TD: To determine amount of misstatements TD: To determine amount of misstatements related to assertion being addressedrelated to assertion being addressed

In both cases, must carefully specify procedure In both cases, must carefully specify procedure to be applied and popn that it applies toto be applied and popn that it applies to

Sampling Steps

2. Define error or exception conditions2. Define error or exception conditions TOC: Normally an attribute. TOC: Normally an attribute.

define exceptions advance of test so that the define exceptions advance of test so that the auditors doing the test will know one when they see auditors doing the test will know one when they see it. Should be related to the key control, and should it. Should be related to the key control, and should be important enough that its exception could lead to be important enough that its exception could lead to material errors.material errors.

TD: Normally an error amount, or audited TD: Normally an error amount, or audited value which is compared to book value.value which is compared to book value.

Sampling Steps

3. Define the population 3. Define the population =The set of all elements in the account or =The set of all elements in the account or

class of transactions. class of transactions. Consider objective (eg. Direction of test) Consider objective (eg. Direction of test) Ensure all items in population are subject to Ensure all items in population are subject to

selection (timing, physical location, proper selection (timing, physical location, proper stratification if population is stratified)stratification if population is stratified)

4. Define the sampling unit4. Define the sampling unit Physical unit or dollar units?Physical unit or dollar units?

Sampling Steps

5. Specify your tolerances 5. Specify your tolerances TOC: Tolerable exception rateTOC: Tolerable exception rate

Depends on significance of transactions, Depends on significance of transactions, significance of control, and consequences of non-significance of control, and consequences of non-control control

TD: Tolerable misstatement (related to materiality)TD: Tolerable misstatement (related to materiality)

These are your benchmarks: if your test results lead you These are your benchmarks: if your test results lead you to conclude that your “problems” (control to conclude that your “problems” (control deviations/exceptions in TOC, errors in TD) exceed deviations/exceptions in TOC, errors in TD) exceed these amounts, you will act accordingly. these amounts, you will act accordingly.

Sampling Steps

6. Specify your sampling risk6. Specify your sampling risk TOC: Acceptable risk of assessing control risk TOC: Acceptable risk of assessing control risk

too low (ARACR)too low (ARACR)The lower your control risk, the higher the The lower your control risk, the higher the

reliance on internal controls, the lower this reliance on internal controls, the lower this risk must be risk must be

TD: Acceptable risk of incorrect acceptance TD: Acceptable risk of incorrect acceptance (ARIA)(ARIA)

From equation: AAR=IR*CR*DRFrom equation: AAR=IR*CR*DR AAR=IR*CR*APR*ARIAAAR=IR*CR*APR*ARIA

Sampling Steps

7. Estimate rate of problems in population7. Estimate rate of problems in population TOC: Expected population exception rateTOC: Expected population exception rate

As this rate increases and approaches your As this rate increases and approaches your tolerable exception rate, your sample size tolerable exception rate, your sample size will have to increasewill have to increase

TD: Expected population error rateTD: Expected population error rateSame as aboveSame as above

Sampling Steps

7. Determine sample size7. Determine sample size TOC: TOC:

TERTER ARACRARACR EPEREPER Population size if less than 1000Population size if less than 1000

TD: TD: Tolerable misstatement (relates to materiality)Tolerable misstatement (relates to materiality) ARIA (relates to other components in risk model)ARIA (relates to other components in risk model) Expected errors in populationExpected errors in population Population Size (book is incorrect!!)Population Size (book is incorrect!!) Some methodologies adjust for popn. Variability: Some methodologies adjust for popn. Variability:

unncessary if DUS is usedunncessary if DUS is used

Sampling Steps

88. . Select sample and perform audit Select sample and perform audit proceduresprocedures

9. Generalize from sample to the 9. Generalize from sample to the populationpopulation TOC: TOC:

Compare sample exception rate to tolerable Compare sample exception rate to tolerable exception rate. Consider ARACR. exception rate. Consider ARACR.

TD: TD: Compare errors in sample and extrapolate Compare errors in sample and extrapolate

to populationto population

MisstatementsType Definition Calculation

Known Actual errors found in thesample

=sum of errors foundin sample

MostLikely

Best estimate of errors inpopn, assuming sample isrepresentative

-see next slide

Possible Possible amount of errors inpopn, given risk that sampleis not representative

Non stat sampling: -use judgment

Stat sampling:-use tables orcomputers

Sampling Techniques

By Physical attribute:By Physical attribute: each unit has equal each unit has equal

chance of selectionchance of selection may need to may need to

compensate for high compensate for high variabilityvariability

MLE = MLE = $ amount of error in $ amount of error in sample sample / # of units in / # of units in sample * # of units sample * # of units in popn.in popn.

By Dollar Unit:By Dollar Unit: larger $ units have greater larger $ units have greater

chance of selectionchance of selection no need to compensate for no need to compensate for

high variabilityhigh variability MLE = MLE = $ recorded amount of $ recorded amount of

popn / popn / # of units in sample # of units in sample * sum of proportionate * sum of proportionate amounts of error in dollar amounts of error in dollar units in sample in errorunits in sample in error

Sampling Steps

10.10. Analyze exceptions or misstatementsAnalyze exceptions or misstatements TOC: consider:TOC: consider:

Pervasive ?Pervasive ? Deliberate?Deliberate? Misunderstanding ?Misunderstanding ? Related to FS balances ? Related to FS balances ?

TD:TD:misunderstanding of GAAP?misunderstanding of GAAP?Isolated?Isolated? intentional irregularityintentional irregularitymanagement override of controlsmanagement override of controls

Sampling Steps

11.11. Determine acceptabilty of populationDetermine acceptabilty of population TOC: if results are unsatisfactory:TOC: if results are unsatisfactory:

Increase sample size (will decrease Increase sample size (will decrease ARACR)ARACR)

Set control risk higher, reduce reliance on Set control risk higher, reduce reliance on internal controlinternal control

TD:TD:Increase sample size (will decrease ARIA)Increase sample size (will decrease ARIA)Have client correct (careful: just correcting Have client correct (careful: just correcting

known errors will not affect MLE)known errors will not affect MLE)Qualify audit reportQualify audit report