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MANUAL AUDIT SAMPLINGSampling is the application of an audit procedure to less than 100% of the items within an account balance orclass of transactions for the purpose of evaluating some characteristic of all the items within the balance orclass of transactions.Much of the information included in this manual was taken from the Statement on Auditing Standards No. 39on Audit Sampling which provides guidance on the use of sampling in an audit of financial statements. Thisinformation has been adapted to fit the circumstances most often encountered in tax auditing.HISTORYThe Department has used sampling in its audit procedures for many years. That sampling, for the most part,has been block sampling. That is, taking a period of time and testing 100% of the records during that time.Until 1990, the Department's policy on sampling was to take 100% samples from three test months per yearselected for being the high, low and average months of the year. From 1990 forward the Department hasadopted other systematic or random sampling techniques.Random sampling techniques are both convenient and accurate when performed properly, for these reasonssampling is the rule rather than the exception in most audits performed by the Department. The convenienceand accuracy extends to taxpayers as well. Audits based on sampling have been challenged. When challengedwe have allowed the taxpayer to present detailed information to refute the results of the sample.PURPOSE OF AUDIT SAMPLINGSampling is performed because it is more efficient than testing 100% of a population. In tax audits, if thetaxpayer and the Department can agree on a representative sample, it can save both parties time and money.By definition, any procedure that does not examine 100% of the items in question is a sampling procedure.WHEN NOT TO SAMPLEThere are many audit procedures which do not involve sampling.Inquiry and Observation:Reviewing records for the method of accounting and other information.Observing accounting procedures.Discussing methods of accounting and reporting with taxpayer.Scanning documents for possible issues.Analytical Review Procedures:Comparing records reports and other information.Recomputing or estimating amounts.Reviewing trends in reporting.Comparing similar businesses.One-Hundred Percent Examination:Reviewing all fixed asset purchases, where appropriate.Examining all contracts, where there are a small number.Reconciling each years gross receipts to CIT A sales factors or Schedule C receipts.Zero Percent Examination:Page 1 of 15

This occurs when the auditor determines that a type of receipt, deduction, exemption or otheritem does not need to be tested.Note: Even though 100% examination may be done where appropriate. It is not mandatory for anyparticular taxpayers or tax programs. Sampling procedures discussed below may be more cost effective.SAMPLING RISKOverall tax audit risk is made up of the risk of inaccurate records and the risk of misapplication of the tax law.Both of these risks are made up of two components as well.1.2.Risk that there are errors (inherent risk).Risk that procedures will not find errors (audit risk).Audit risk, in turn is made up of two components, the risk that a procedure is not effective and sampling risk.Sampling risk is the probability that the sample results are not representative of the entire population. Ingeneral, factors that may lessen sampling risk include:1.2.3.4.5.6.7.Taking larger size samplesUsing random sample selection methodsStratifying the sampleProperly defining the test objectiveProperly defining a deviationExclusion of non-recurring, non-systematic errors.Properly evaluating errors.STATISTICAL VS. NON-STATISTICAL SAMPLINGThe difference between statistical and non-statistical sampling is that statistical sampling allows the user tomeasure the sampling risk associated with the procedure. Statistical sampling applies the laws of probability todetermine the percent likelihood that the sample does not accurately reflect the population.In essence, the laws of probability say that large, relatively homogeneous populations have similardistributions and other features so that if a random sample is taken, it will consistently reflect the populationwithin certain limits. In order for the sample to be a “statistical" sample, the results must be evaluated and twocalculations made. These calculations tell the user how likely it is that the sample results are within a givenrange of the actual population.For instance, a statistical sample would not only tell you that disallowed deductions are estimated at 5,000,but that you have a 95% likelihood (confidence) of being within 50 (precision) of the actual disalloweddeductions.A properly designed and applied non-statistical sample can provide results that are accurate and effective, butwill not measure the sampling risk.Generally, the decision to apply a statistical or non-statistical sampling application to a particular audit test is amatter of cost effectiveness. Statistical applications usually require more training for auditors and more time toapply. The department utilizes non-statistical random sampling procedures.Many audit programs in both the public and private sector have developed standard sampling approacheswhich use predetermined allowances for acceptable sampling risk, expected and tolerable error. Theseapproaches reduce the time and effort required to determine the sample size and evaluate results. The cost ofthese approaches is that they usually generate sample sizes somewhat larger than necessary to allow a marginfor variance. The New Mexico Taxation and Revenue Department has elected to use fixed sample sizes of 250and 500 items of interest for variable sampling. The sample sizes apply to homogeneous and nonPage 2 of 15

homogeneous populations respectively. Stratification of a population can reduce sample size in most cases.Provisions for sampling units based on time periods is also provided.In any sampling approach, the auditor must evaluate the population that is being tested, must determine if anystratification should be done, must evaluate the cause of any exceptions and must apply the results from thesample to the remaining portion of the population.DESIGNING A SAMPLING APPLICATIONThere are several steps in designing a sampling application for an audit or investigation. The steps arediscussed in detail in the next pages.1.2.Define the objectives of the testDetermine the type of test to be performeda.Variables Samplingb.Attribute Sampling3.Define the deviation conditions4.Define the populationa.Decide what period will be covered by the testb.Define the sampling unitc.Consider the completeness of the populationd.Consider how the error rate will be extrapolated5.Determine the method of selecting the samplea.Random-Number samplingb.Systematic samplingc.Other sampling6.Determine the sample sizea.Variables Samplingb.Attribute Sampling7.Perform the samplea.Compare the sample to the population before completing the sample8.Evaluate the sample resultsa.Interpret resultsb.Extrapolate resultsC. Consider the qualitative aspects of the deviationsd.Reaching an overall conclusion about the population9. Document the sampling procedureDEFINE THE OBJECTIVES OF THE TEST-STEP 1The auditor must have a definite question to be answered by the test. Examples of questions to be answeredare.1.2.3.4.5.6.7.8.Does the Sales Summary contain all invoices and is information recorded accurately?How often are invoices voided without explanation?Does the taxpayer record all supplies pulled from inventory in the inventory log?Does the sales supervisor correctly batch sales by destination so that they can be recorded bystate in the summary journal?What is the amount of deductions not supported by NTTC's?What is the percentage of sales of services to the government relative to total sales?What percentage of supplies are pulled from inventory held for sale each month?What percentage of supplies purchased outside NM have not had tax paid or accrued?Auditors should record the objective of the test within the audit narrative and/ or other workpapers. Not onlydoes that help the reviewer, but it also clarifies the objective for the auditor so that the proper audit procedureand sampling application can be defined. If the auditor can create a one sentence question, like the ones above,Page 3 of 15

to be answered, he or she is less likely to perform an inappropriate procedure or use the wrong samplingapplication.DETERMINE THE TYPE OF TEST TO BE PERFORMED-STEP 2The type of sampling application, whether statistical or non-statistical, is usually defined by the conclusionwhich the auditor is attempting to reach. "Variables sampling" is used to reach a conclusion about a populationin terms of an amount. Variables sampling is commonly used to determine the dollar size of a population or todetermine if the stated dollar size is correct."Attribute sampling" is used when the auditor is only concerned with acceptance or rejection of a hypothesis.It is used to reach a yes or no answer about a question.The reason that defining the type of application is so important is that sample size is dependent on which typeof application is being performed. Below is the same list of questions given on the previous page, and anexplanation of the type of application required for each.SAMPLING APPLICATION ANALYSISQUESTION TO BE ANSWEREDDoes the Sales Summary contain allinvoices and is information recordedaccurately?How often are invoices voided withoutexplanation?Does the taxpayer record all suppliespulled from inventory in the inventorylog?Does the sales supervisor correctlybatch sales by destination so that theycan be recorded by state in the summaryjournal?What is the amount of deductions notsupported by NTTC’s?What is the percentage of sales ofservices to the government relative tototal sales?What percentage of supplies are pulledfrom inventory held for sale eachmonth?What percentage of supplies purchasedoutside NM have not had tax paid teAttributeVariablesOFEXPLANATIONThe auditor doesn’t want to knowwhat percentage or how much, onlyyes or no.Here, the auditor wants to know aspecific amount.Presumably, if there are supplies notrecorded, the auditor will not“accept” the inventory record.This is a yes or no question, whichwill result in accepting or rejectingthe data in the summary journal.VariablesThe auditor needs to know a specificdollar amount.If the auditor asked the question, “Isthe percentage 20%,” attributesampling could be used. But here theauditor wants to know the exact rate.Same as aboveVariablesSame as aboveVariablesSampling applications can also be classified by the type of audit procedure in which they are used.“Compliance tests” are tests which determine whether controls are being complied with. The answer to acompliance test is yes or no. “Substantive tests” are tests which determine the amount of some class of items.Attribute sampling is most often used in compliance tests and variables sampling is most often used insubstantive tests.Page 4 of 15

COMPLIANCE TESTSCompliance tests are most often used by tax auditors to determine if controls which ensure theaccuracy of records are in place and working correctly. These tests can be performed directly on thecontrol feature itself or indirectly on the outcome of the control.An example of a direct test would be a test to determine that invoices are pre-numbered, used insequence and accounted for by those issuing the invoices. Such a test would be helpful in assuringthe auditor that all invoices issued in a period are used or voided.An example of an indirect test would be a tracing of a sample of invoices to a summary journal todetermine that the controls over recording invoices in the summary journal are working. In this case,the controls themselves are not actually tested, but the results of those controls are examined, and thequestion of whether the summary record is reliable will be answered yes or no.Note that tax auditors do not use formal compliance testing as frequently as other types of auditors.However, tax auditors do make judgments about the level of risk of incorrect records and the risk ofmisapplication of the tax law. These are the types of judgments that can be backed up by compliancetests.The decision to test controls or the accuracy of records is based on auditor judgement and thecircumstances of the audit. The decision should be documented. Compliance testing may help to limitthe scope of the audit to areas of higher risk or point out problems with records that may haveotherwise appeared reliable.The main reason for performing compliance tests is to reduce the amount of substantive tests thatneed to be performed. Therefore, the decision of whether to perform compliance tests should weighthe possible compliance tests against the possible substantive tests that could be performed todetermine which test will be most efficient and effective.For instance, if an auditor decides that he can either test the taxpayer's summary records and use themto perform the audit, or, rely on comparing reports to bank statements, then he or she shoulddetermine which method will be more efficient. If a compliance test of the summary records isperformed and the records prove to be unreliable, then the auditor may still have to rely on bankstatements. However, it may be that using the summary records will be much more efficient thanusing bank statements. Therefore, testing those records is worth the time needed and the risk that thetest results will be negative. Before relying on the summary records the auditor should perform a testof transactions to determine the records are reliable.SUBSTANTIVE TESTSSubstantive tests are used to determine the amount, usually the dollar amount, of a specific group ofitems. If the auditor seeks to determine the amount of disallowed deductions, for instance, the resultof the sample will be a dollar figure of disallowed deductions found in the sample. The assumption isthat the same proportion of disallowed deductions will exist in the population. Therefore, the finalresult of the test will be a dollar amount of disallowed deductions for the population which will beused as a basis for assessment.Often, samples can be designed to serve both compliance and substantive tests. When it is likely that recordswill be needed for both types of applications, the auditor should strive to pull one sample. This is called dualpurpose testing.DEFINE THE DEVIATION CONDITIONS-STEP 3If you are performing a direct test of controls, such as checking for supervisor approval before selling goodsfree of tax, a deviation will be any noted lapse in the control. In this case if the control is documented insome way, such as with initials of the supervisor on the invoice, a deviation would be the lack of initials. IfPage 5 of 15

the control is not documented, you will have to rely on direct observation of the control being performed, oron indirect evidence.If you are testing controls indirectly, you would look at the error which the control is intended to prevent andwould base your deviation on what defines that error. In the case above, the control in place is intended toprevent salesmen from not charging tax on sales that should be taxed. A deviation would therefore bedefined as an invoice that did not have tax and should have.If you are performing a substantive test, the item(s) you are picking up might not necessarily be thought of asdeviations. For instance, you may be trying to determine the average New Mexico inventory value over aperiod for testing the CIT property factor. However, the same principle applies. You need to define whichitems meet the criteria necessary to reach the objective of the test. In this example, that might be inventorycontrol log entries backed up by shipping and receiving reports.Auditors should be careful not to include factors in the deviation, which do not affect the objective of thetest. For instance, in the first test described above, invoices where the customer name was misspelled wouldnot affect the objective of the test and should not be treated as deviations. On the other hand, auditors shouldalso be careful to include all factors, which may affect the objective of the test. For instance, if an invoicecontains the initials of a supervisor from another Department who is not familiar with the customers whohave Non Taxable Transaction Certificates (NTTC’s) on file, the invoice should be picked up as a deviation,even though it contains a supervisor's initials.Some of the most common problems faced by auditors performing any kind of test come from not properlydefining the deviation, and finding out after the test has been performed that there were other conditions thatshould have been considered.DEFINE THE POPULATION-STEP 4The auditor should determine if the population from which the sample is selected is appropriate for the specificaudit objective, because sample results can be projected to only the population from which the sample wasselected. If a change in the business results in more than one distinct population, then each needs to be testedseparately. The auditor should also evaluate the reliability of the data presented as the population. The datashould be complete and should also tie to other records such as CRS-1s, journals, summary reports, etc.Analysis may reveal that the taxpayer changed a specific control procedure during the period under audit. Theauditor needs to decide whether to design one sample and test both controls or do two separate samples. Theauditor might also discover that the non-taxable sales do not match the CRS-1 reports due to the exclusion of aparticular type of sale or due to the inclusion of non-New Mexico sales.DECIDE WHAT PERIOD WILL BE COVERED BY THE TESTGenerally, a sample should be drawn from the entire period to which the test results will be applied. However,there are many situations when this is not practical. In any test where the auditor decides to limit the periodfrom which the sample will be drawn, the auditor should evaluate sample results, as well as the period outsidethe sample, and determine the following:1. What were the results of the sample and could they reasonably be expected to apply to the periodnot sampled.2. What is the nature of the remaining period, does it have similar characteristics to the period tested?3. How large is the remaining period? Ideally, the period from which the sample is drawn should beas large as possible. Limiting the period to a day out of each year or a week from the total auditperiod is not a sound basis for extrapolating results to the period not sampled. The more the sample isspread throughout the audit period, the more reliable the results will be.4. What is the nature and amount of the transactions involved? The more homogeneous thepopulation and the greater the size, the more likely a sample taken from only part of the period underaudit will be representative.5. What tests can be done of the remaining period to further substantiate the sample results?Page 6 of 15

6. What other matters are relevant to the sample results? Have conditions which might affect theresults changed in the remaining period?DEFINE THE SAMPLING UNITA sampling unit is any of the individual elements constituting the population. The auditor should define thesampling unit in light of what is being tested and the type of records kept by the taxpayer. A sampling unitmay be, for example, a document, an entry in a journal, a line item, or a single transaction.It is possible to sample based on time period representations such as days, weeks, or months. The departmenthas set minimums of 30, 25, and 9 respectively. The days, weeks, or months should be randomly selected fromthe entire audit period. Random sampling within the selected days, weeks, or months is encouraged.Regardless of the type of time period selected the number of items of interest (invoices, line items,transactions, etc) must be achieved for the population type. In most time period samples the items of interestwill exceed the minimum required.CONSIDER THE COMPLETENESS OF THE POPULATIONThe population is physically represented by some form of record. For instance, sales invoices, entries in asales journal or summary entries in a ledger may represent total sales. The auditor actually selects samplingunits from this physical representation and so must confirm that all sample units from this record are includedin the entire population. If the physical representation differs from the actual population, the auditor mightmake erroneous conclusions about the population. A simple example of this is testing a depreciation schedulewhere a page of the schedule is missing.Therefore, the auditor should be careful to determine that the records used to draw the sample are complete andreflect the actual population being tested. One means of doing this is comparing different records andreconciling differences found.DETERMINE THE METHOD OF SELECTING THE SAMPLE-STEP 5Sample items should be selected in such a way that the sample can be expected to be representative of thepopulation. Therefore, all items in the population should have an equal opportunity to be selected.RANDOM-NUMBER SELECTIONThe auditor may select a random sample by corresponding random numbers generated by a computer orselected from a random number table with document numbers. The random number generating softwareprograms utilized by the department provide seed numbers which can be used to duplicate a specific list ofrandom numbers. The seed number should be documented within the audit workpapers.Examples of random selection:When a listing is available, even if the items are unnumbered or have non-continuous or non-systematicnumbering systems, the random number sampling can be accomplished by making use of the page and linenumber.For instance, the auditor might want to obtain a random number sample of items sold to one customer.Assume that a computer listing is available which consists of pages containing a total of 20,000 items. Thepages of the listing can be easily numbered or their numbers determined by counting. There may be the samenumber of lines on most pages, with perhaps fewer on some.Assume that there are 400 pages in the listing with 50 lines on most pages. The auditor would draw two listsof random numbers, one for three digit numbers between 1 and 400 and one for two digit numbers between 1and 50. Items would then be selected by pairing numbers from the first and second list to identify the page andline on which the item to be selected is located.Page 7 of 15

SYSTEMATIC SELECTIONFor this method, the auditor determines a uniform interval by dividing the number of physical units in thepopulation by the sample size then rounding up. A starting point is randomly selected and each item after thatis selected at the uniform interval. If the population is arranged randomly, systematic selection is essentiallythe same as random number selection. However, if the population is not randomly arranged, for instance, ifsales are listed by item, rather than in the order made, there may be problems with this method.One way to ensure more randomness in a systematic sample is to re-compute the interval each time by use of arandom-number table. In this approach the auditor would select a list of random numbers. The first numberwould be the starting point. The second number would tell the auditor the interval to count to the next item tobe selected. For instance, if the first two random numbers are 503 and 219, the auditor would select item 503to start, then item 722 (503 219). In this approach, the auditor might have to go through the population morethan once to finish drawing all the items. The number of digits to be used for the random numbers shouldmake intervals that are large enough to go through the entire population a least once.DETERMINE THE SAMPLE SIZE STEP 6ATTRIBUTE SAMPLING (YES/NO)To perform an attribute test, sample size should be determined as follows:1.2.3.If the sample is drawn from the entire audit period, use an initial sample of 50 items. If the sample isdrawn from a block, or if the population is limited in some other way, the initial sample should be 100items.If one or more deviations are found in the sample, the auditor must either reject the item being tested, ormay expand the sample. If the auditor chooses to expand the sample, an additional number of items equalto the initial sample should be tested.If one or more additional deviations are found, the auditor must either reject the item being tested, or mayexpand the sample to the appropriate variables sample size and use the results to estimate the amount oferror in the item being tested.See the section on evaluating the sampling results to determine whether qualitative aspects of a deviation maydetermine whether a deviation can be overlooked in an attribute sample.VARIABLES SAMPLING (NUMBERS)A critical question must be answered before the sample size for a variables sample can be computed. Is thepopulation relatively homogeneous?Homogeneous populations can be tested using smaller size samples since there are fewer exceptional items toskew the results. Non-homogeneous populations require larger size samples.Homogeneity is the tendency of items in a population to be similar, or closer to the same dollar value. Forinstance, a population containing sales of three kinds of mid-priced property will be far more homogeneousthan a population containing all sales of a Department store.If a population is non-homogeneous, the auditor can reduce the sample size through stratification andidentifying individually significant items. See Step 7 on performing the sample for an explanation of howstratification should be done.The Audit Sampling Workpaper, AUD-21, can be used to document whether a population is homogeneous ornot. Whether or not this workpaper used, the auditor should document why the population was eitherdetermined to be homogeneous or non-homogeneous.Page 8 of 15

SAMPLING SIZE TABLEThis table gives sample sizes for any population over 500 items where variables testing is performed.Populations smaller than 500 items should be examined in detailLIMITEDUNLIMITEDSELECTIONMETHODPOPULATION TYPE (see flow chart for determination of population type)NON-HOMOGENEOUSHOMOGENEOUS1 INDIVIDUALITEM500 items of interest250 items of interest1 INDIVIDUALITEMSTRATIFIED100 items per strata (5 strata max)75 items per strata (5 strata max)2 DAY *3 WEEK *30 days (1000 items of interest)25 weeks (1000 items of interest)30 days (500 items of interest)25 weeks (500 items of interest)4 MONTH *9 months (1000 items of interest)9 months (500 items of interest)(Note: the number to the left of the selection method is the order of preference for selection methods. A 1indicates the most preferred methods and a 4 indicates the least preferred)*LIMITED Month, week, and day samples should examine two times the minimum required items of interestfor the population type being tested, whenever possible. Random sampling of items of interest within the timeperiod selected is encouraged. When using the month selection method the auditor must evaluate all monthsthat have unusual balances and determine the circumstances for variance before including the months in thesample or in the extrapolation procedure. LIMITED SAMPLING IS ALWAYS OUR LAST CHOICEAND THE REASON FOR ITS USE SHOULD BE ADEQUETLY DOCUMENTED.If the auditor determines that the population to be sampled is diluted with transactions that are not of interestthen the sample size should be increased. In the case of a test of deductions where taxable and non-taxablesales are commingled the auditor would first need to determine the percentage of non-taxable sales in thepopulation and then use this percentage to compute the increased sample size.(non –taxable sales total sales) x 100 % of non-taxable sales250 ( % of non-taxable sales) sample sizePERFORM THE SAMPLE-STEP 7After the sampling plan has been designed, the auditor selects the sample and examines the selected items todetermine if they contain deviations. Test the viability of the sample plan using approximately 25% of theitems you intended to select. If the planned procedures work and the results meet your expectations continueto sample the balance of the units. The sample should also be evaluated to determine if it is representative ofthe population. The average value of the sample should be similar to the average value of the population. Ifexpectations are not met or if the average values are not similar to the sample the plan may need to be modifiedor a new sample may need to be selected.The following problems may arise during the sample procedure.VOIDED DOCUMENTS: If an auditor randomly or otherwise selects a voided item to be included in thesample, and has reasonable assurance that the item was properly voided, it should be replaced with anotheritem selected in accordance with the sampling procedure. The rule here is not absolute, the auditor orsupervisor may make a judgement decision based on the circumstances associated with the voided transaction.Page 9 of 15

CREDITS: Most populations will contain credits. It may be possible in certain situations to remove thecredits prior to sampling, but care should be taken to avoid inflating the population’s total value. If the creditsoffset debits it is important to remove both. When stratifying a population it is necessary to use absolutevalues in order to keep credits and matching debits within the same strata. A credit will generally not producea reduction in the exception total (the numerator in the error calculation). One example of a credit that mightgenerate a reduction in a compensating tax exception total is the return of an item which had compensating taxaccrued and paid at the t

The Department has used sampling in its audit procedures for many years. That sampling, for the most part, has been block sampling. That is, taking a period of time and testing 100% of the records during that time. Until 1990, the Department's policy on sampling