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**CHAPTER** **19** AUDIT SAMPLING FOR SUBSTANTIVE TESTS I Review Questions An incorrect acceptance decision directly impairs the effectiveness of an audit Auditors wrap up the work and the material misstatement appears in the financial statements An incorrect rejection decision impairs the efficiency of an audit Further investigation of the cause and amount of misstatement provides a chance to reverse the initial decision error The two methods of projecting the known misstatement to the population are the average difference method and the ratio method Refer to **Chapter** **19** for formula expressions of each The important thing is to audit all the sample units You cannot simply discard one that is hard to audit in favor of adding to the sample a customer whose balance is easy to audit This action might bias the sample If considering the entire balance to be misstated will not alter your evaluation conclusion, then you not need to work on it any more Your evaluation conclusion might be to accept the book value, as long as the account counted in error is not big enough to change the conclusion Your evaluation conclusion might already be to reject the book value, and considering another account to be misstated just reinforces the decision If considering the entire balance to be misstated would change an acceptance evaluation to a rejection evaluation, you need to something about it Since the example seems to describe a dead end, you may need to select more accounts (expand the sample) and perform the procedures on them (excluding confirmation) and reevaluate the results Two main reasons for stratifying a population when sampling for variables (peso) measurement: a b Some units may be individually significant (e.g., large) and taking sampling risk with respect to them is not a good idea Auditors may want to achieve audit coverage of a large proportion of pesos in the balance **by** choosing the largest units (a protective sampling objective, which is closely related to avoiding sampling risk) 19-2 Solutions **Manual** - Assurance Principles, Professional Ethics… The tolerable misstatement (judged for the audit of a particular account balance) must be less than the monetary misstatement considered material to the overall financial statements Also, the aggregation of multiple tolerable misstatement amounts for several different balances under audit must be equal to or less than the amount of monetary misstatement considered material to the overall statements The appropriate general set of objectives is the objective(s) of obtaining evidence about each of the client’s assertions in the financial balance In general, the assertions are about: Existence (and cutoff) Occurrence (and cutoff) Completeness (and cutoff) Rights and obligations (ownership, owership) Valuation Measurement Presentation and disclosure Influence on sample size: Sample Size Relationships: Audit of Account Balances Sample Size Influence Risk of incorrect acceptance Risk of incorrect rejection Tolerable misstatement Expected misstatement Population variability Population size Predetermined Sample Size Will Be: High Rate or Low Rate or Large Amount Small Amount Smaller Larger Sample Size Relation Inverse Smaller Larger Inverse Smaller Larger Inverse Larger Smaller Direct Larger Smaller Direct Larger Smaller Direct The three basic steps in quantitative evaluation are these: Figure the total amount of actual misstatement found in the sample This amount is called the known misstatement Project the known misstatement to the population The projected amount is called the likely misstatement Compare the likely misstatement (also called the projected misstatement) to the tolerable misstatement for the account, and consider the Audit Sampling for Substantive Tests a b 19-3 Risk of incorrect acceptance that likely misstatement could be less than tolerable misstatement even though the actual misstatement in the population is greater, or the Risk of incorrect acceptance that likely misstatement could be greater than tolerable misstatement even though the actual misstatement in the population is smaller Nonstatistical measurements described in **Chapter** **19** (page 718) leave only one avenue for “accounting for further misstatement”: Apply experience and professional judgment to decide if further misstatement could be large enough to prevent an acceptance decision If the projected likely misstatement is a great deal less than the amount considered material, an auditor could judge that further misstatement, if known, would not affect acceptance If projected likely misstatement is close to the amount considered material, maybe acceptance is not warranted 10 Account balances also can be audited, at least in part, at an interim date When account balance audit work is done before the company’s year-end date, auditors must extend the interim-date audit conclusion to the balance-sheet date The process of extending the audit conclusion amounts to nothing more (and nothing less) than performing substantive-purpose audit procedures on the transactions in the remaining period and on the year-end balance to produce sufficient competent evidence for a decision about the year-end balance Additional considerations include: a b c If the company’s internal control over transactions that produce the balance under audit are not particularly strong, you should time the substantive detail work at year-end instead of at interim If control risk is high, then the substantive work on the remaining period will need to be extensive If rapidly changing business conditions might predispose managers to misstate the accounts (try to slip one **by** the auditors), the work should be timed at year-end In most cases, careful scanning of transactions and analytical review comparisons should be performed on transactions that occur after the interim date As an example, accounts receivable confirmation can be done at an interim date Subsequently, efforts must be made to ascertain whether controls continue to be strong You must scan the transactions of the remaining period, audit any new large balances, and update work on collectibility, especially with analysis of cash received after the year-end 11 Classical variables sampling estimates the value of a population **by** calculating the mean and standard deviation of a sample and imputing the results to the population Probability proportional to size sampling uses the results of 19-4 Solutions **Manual** - Assurance Principles, Professional Ethics… sampling to calculate an estimated upper error limit and compares this with a preset tolerable error limit Although used for substantive testing purposes, PPS sampling is actually a variation for attribute sampling 12 Detection (or beta) risk affects sample size inversely for substantive testing purposes That is, the higher the acceptable detection risk, the smaller the sample size; and the lower the acceptable detection risk, the larger the sample size 13 Precision is the range + – within which the true answer most likely falls It is set **by** the auditor as a function of materiality and those levels of beta and alpha risk deemed acceptable Reliability is the likelihood that the sample range contains the true value Also referred to as the confidence level, reliability is set **by** the auditor on the basis of overall audit risk 14 PPS sampling is restricted to populations for which the auditor suspects a few errors of overstatement only 15 Several statistical software packages are available to facilitate audit sampling applications In addition to calculating sample size and evaluating sample results, these packages can also assist in the following sampling areas: a b c Stratify populations for sampling purposes; Generate random numbers to facilitate sample selection; Draw the sample, given computerized data bases II Multiple Choice Questions b a c&d b c b b d 10 11 12 Supporting Computations: Audited Value 47,520 c Book Value 48,000 d P480 120 = 1,200 x P4 P 17,500 P500,000 d a a c = 13 14 15 16 P4,800 = 3.5% P450,000 x 3.5% = 17 18 **19** 20 d b c d 490,000 x 0.99 = 485,100 0.99 ; 490,000 – 485,100 = P4,900 P4 = a a c d P157,500 Audit Sampling for Substantive Tests 19-5 III Comprehensive Cases Case a Alpha risk is the risk of rejecting a population that is essentially correct Beta risk is the risk of accepting a population that is materially incorrect Alpha risk affects audit efficiency because overauditing results from incorrectly rejecting a population Beta risk impacts audit effectiveness because underauditng results from incorrectly accepting a population Collectively, alpha and beta risk comprise sampling risk, defined as the probability that the auditor will draw erroneous conclusions about a population b Attention to, and quantification of, alpha and beta risk assist the auditor in applying an audit risk approach to substantive testing During the audit planning stage, the auditor identifies areas of high audit risk and sets detection (beta) risk low for these areas The result is that more substantive testing is devoted to the high risk areas relative to the lower risk areas This approach enhances both audit efficiency and audit effectiveness c Because it is closely related to the basis for the auditor’s opinion, alpha risk is usually set equal to overall audit risk Beta risk is set on the basis of the auditor’s evaluation of inherent risk and control risk The greater these risk factors, as determined **by** the auditor during the audit planning stages, the lower the beta risk set **by** the auditor The lower the acceptable beta risk, the larger the sample sizes for substantive testing purposes Alpha and beta risk, therefore, provide the necessary link between audit risk analysis and substantive audit testing Case a (1) Mean-per-unit estimates the total value of a population **by** (1) using the sample mean as an estimate of the true population mean, and (2) extending this estimated population mean **by** the number of items in the population The computations are as follows: (1) Estimated population mean = P582,000 / 200 lots = P2,910 per lot (2) Estimated total value = P2,910 per lot x 2,000 lots = P5,820,000 (2) Ratio estimation estimates total population value **by** (1) using the ratio of the sample audited values to book values as an estimate of the ratio of population audited value to book value, and (2) applying the estimated ratio to the population book value The computations are as follows: 19-6 Solutions **Manual** - Assurance Principles, Professional Ethics… (1) Estimated ratio of audited to book value = P582,000 / P600,000 = 97% (2) Estimated total value = 97% x P5,900,000 = P5,723,000 (3) Difference estimation estimates total population values **by** (1) using the average difference between the audited and book values of sample items as an estimate of the average difference for all population items, (2) extending the estimated average difference **by** the number of items in the population, and (3) using the resulting estimate of the total difference between audited and book value to compute the estimated total value The computations are as follows: (1) Estimated average difference in audit and book values: (P582,000 - P600,000) / 200 lots = - P90 per lot (2) Estimated total difference = - P90 per lot x 2,000 lots = - P180,000 (3) Estimated total value = P5,900,000 - P180,000 = P5,720,000 b The sample contains an element of sampling error with respect to the average peso value of production lots The mean book value of the population is P2,950 (P5,900,000 / 2,000 lots), while the mean book value in the sample is P3,000 (P600,000 / 200 lots) Mean-per-unit estimation uses the mean value of the sample as the basis for estimating total value Thus, if the sample contains a disproportionate number of higher (or lower) priced items, this sampling error will affect the estimate of the total population value The estimate of total value developed in ratio estimation is based upon the ratio of audited values to book values, rather than upon mean peso value If this ratio has no tendency to vary with the peso value of the lot, the estimate of total value is not affected **by** the mean value of items in the sample However, sampling error may still be present if the sample lots are not representative of the population with respect to the ratio of audited values to book values Audit Sampling for Substantive Tests 19-7 Case The auditors would project the misstatement found in the sample to the population using either the ratio or difference approach The ratio approach would result in a projected misstatement of P65,500 This may be computed **by** first calculating the ratio of the audited to book value as 1.0131 [P23,100 / P22,800 (since there is a net understatement of P300, the audited value is P23,100)] and estimating the audited value of the population as: 1.0131 x P5,000,000 = P5,065,500 (rounded) The projected misstatement is thus P65,500 under the ratio method The difference approach results in an average difference of P1.50 (P300 net difference divided **by** 200 items) Multiplying **by** the 100,000 invoices indicates a projected misstatement of P62,400 (P1.50 x 41,600) Case The audit risk (ultimate risk) of material misstatement in the financial statements (AR) is the product of: (1) Inherent risk (IR), the risk of material misstatement in an assertion, assuming there were no related internal controls (2) Control risks (CR), the risk of material misstatement occurring in an assertion, and not being prevented or detected on a timely basis **by** the internal control structure (3) Detection risk (DR), the risk that the auditors’ procedures will lead them to conclude an assertion is not materially misstated, when in fact such misstatement does exist In equation form, this relationship is expressed as follows: AR = IR x CR x DR This equation may be restated to solve for the allowable detection risk as follows: DR = AR / (CR x IR) Using the risk levels set forth in the problem, the allowable risk of reliance upon substantive tests is computed as illustrated below: DR = 02 / (.2 x 5) = 20 Thus the risk of incorrect acceptance should be limited to 20 percent if the auditors are to achieve their objective of holding audit risk to percent 19-8 Solutions **Manual** - Assurance Principles, Professional Ethics… Case a (1) Required sample size is calculated as follows: Sample size = Recorded amount of population x Reliability factor Tolerable misstatement – (Expected misstatement x Expansion factor) Sample size = P500,000 x P25,000 – (P2,000 x 1.6) = 69 Note: The reliability factor is from the zero misstatements row of the PPS sampling table given in the case (2) The sampling interval is calculated simply **by** dividing the book value of receivables **by** the sample size, as follows: Sampling interval = Recorded receivables / Sample size = P500,000 / 69 = P7,246 b The results may be evaluated as follows: (1) Projected misstatement = Book Value Audite d Value P 50 800 8,500 P 47 760 8,100 (2) Basic precision Misstatemen t P 40 400 = Tainting % 6% 5% NA Samplin g Interval P7,246 7,246 NA Projected Misstatemen t P 435 362 400 P1,197 Reliability factor x Sampling interval = 3.0 x P7,246 = P21,738 (3) Incremental allowance = Reliability Factor 3.00 4.75 6.30 Projected Incremen (Increment – 1) Misstatement 1.75 1.55 75 55 P435 362 Incremental Allowance P326 199 Audit Sampling for Substantive Tests 19-9 P525 (4) Upper limit on misstatement = P1,197 + P21,738 + P525 = P23,460 NOTES: Projected misstatement (a) Tainting percentages are calculated as the difference between book and audited value divided **by** book value (e.g., (P50 – P47) / P50 = 6%) (b) No tainting percentage is calculated for items in excess of the sample interval and the actual misstatement is extended to projected misstatement (as for the third error) Basic precision is always the reliability factor for zero misstatements multiplied times the sampling interval Incremental allowance (a) Reliability factors are read from the PPS sampling table given in the case, starting at zero misstatements (b) “Increment – 1” is the difference in the two adjacent reliability factors minus (e.g., 4.75 – 3.00 – 1.00 = 75) (c) Misstatements in excess of the sampling interval are not considered in the incremental allowance This is because the nature of the process requires that all items in excess of the sampling interval be included in the sample – therefore no allowance for items not in the sample is necessary c The results obtained in part b would indicate that the auditors may accept the population as not containing a tolerable misstatement at the percent level of risk of incorrect acceptance The auditors would also consider the results obtained in conjunction with other audit tests Case a The advantages of probability-proportional-to-size (PPS) sampling over classical variables sampling are as follows: PPS sampling is generally easier to use than classical variables sampling The size of a PPS sample is not based on the estimated variation of audited amounts PPS sampling automatically results in a stratified sample Individually significant items are automatically identified 19-10 Solutions **Manual** - Assurance Principles, Professional Ethics… b If no misstatements are expected, PPS sampling will usually result in a smaller sample size than classical variables sampling A PPS sample can be easily designed and sample selection can begin before the complete population is available Sampling interval = Recorded receivables / Sample size = c P300,000 / 60 = P5,000 Projected misstatement = Book Value Audite d Value P 400 500 3,000 P 320 2,500 Misstatemen t P 80 500 NA Tainting % 20% 100% NA Samplin g Interval P1,000 1,000 NA Projected Misstatemen t P 200 1,000 500 P1,700 ... population by calculating the mean and standard deviation of a sample and imputing the results to the population Probability proportional to size sampling uses the results of 19-4 Solutions Manual. ..19-2 Solutions Manual - Assurance Principles, Professional Ethics… The tolerable misstatement (judged for... control risk The greater these risk factors, as determined by the auditor during the audit planning stages, the lower the beta risk set by the auditor The lower the acceptable beta risk, the larger

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