Using Materiality in Audit Planning.

10
USING MATERIALITY IN AUDIT PUNNING A practicai way to relate the auditor's materiality estimate to the design of audit procedures. hy George R. Zuher. Robert K. Elliott, William R. Kitmey, Jr., and James J. Leisenring John Smith. CPA, is the auditor ofAjax. Inc. Recetitly. Smith had listened to another CPA describe how a careful consideration of mate- riality during the planning phase improved the coordination and efficiency of an audit. In planning his cutrent examination of Ajax. Inc.'s.. financial statements (see exhibit 1. page 44). Smith decided to apply some of those materiality concepts in the design of audit procedures. Auditors like Smith, who are engaged to examine financial statements, seek to deter- mine whether the financial statements taken as a whole are materially misstated. Material- ity has been defined over the years by. among others, accounting standard-setting bodies, courts, regulatory agencies and auditors. Gen- erally, these definitions indicate that an omis- sion or misstatement is material if knowledge of the omission or misstatement would influ- Authors' ntilL-: The Amcriciin Institute of CPAs audiling stan- dards board has exposed a proposed statement on auditing standards entitled MateriuUty mid Audit Risk in Coiitttatiiig tin Audit (New York: AICPA. Deecmber 6, 1982), This article isn't an interpretation or digest ot the exposure draft, although the methods discussed in this article would be. in the authors' view, one method ot complying with certain provisions of the exposure draft. ence the judgment of a reasonable person. Although the determination of what is materi- al to financial statements is necessarily an ac- counting concept, materiality also is a basic consideration in the audit process. An objec- tive of an audit is to search for errors that, either individually or in the aggregate, would be material to the financial statements. Be- cause Smith will have to decide if he is satis- fied that the financial statements aren't mate- rially misstated, it is essential that he plan his audit to obtain sufficient evidential matter to make that evaluation. This article will describe how Smith, and other auditors, can use a preliminary estimate of materiality in planning an effective—and efficient—audit. What Is a Preliminary Estimate of Materiality? According to Statement on Auditing Stan- dards no. 22. Planning and Supervision.^ the auditor considers, among other things, pre- liminary estimates of materiality levels when he plans an audit of financial statements. SAS no. 22 doesn't explicitly require an auditor to quantify, either as a specific or an approxi- mate amount, his preliminary estimate of ma- teriality. However, quantification is the most practical way to consider such an estimate in audit planning. Because financial statement*^ are used to assess an entity's current position and performance and to predict an entity's future flow of cash, changes in the amount, timing or uncertainty of the entity's cash flow are matters that would be expected to affect the judgment of a reasonable person. Because 'statement on Auditing Standards no 22. Phinniiif; ami Su- pervision (New York; AICPA. 197H). See also AfCPA Profes- sional Standards, vol. 1 (Chicago; Commerce Clearing House). AU section .^11, GEORGE R, ZUBER, CPA. now a diKtoral student at the L'niversity of Michigan. Ann ,'\rbor. was a manager in the American Institute of CPAs auditing standards division when this article was written. Mr, Zuher is a member of the AICP,'\ statistical sampling subcommittee. ROBERT K. ELLIOTT, CPA. is a partner of Peat. Marwick. Mitchell & Co,, New York. A former chairman of the staiistieal sampling subcom- mittee. Mr. Elliott is ;t member of the Institute's auditing standards board (ASR) and tbe materiality and audit risk task force, WILLIAM R. KINNEY, JR., CPA. Ph,D,, is the John F. Murray Professor of Accounting and the director of the Insti- tute t)f Aecouniing Research at the I'niversity of Iowa. Iowa City. He is u member of the .ASB and a former member of (he statistical sampling subcommittee. JAMES J. LHISENRING, CPA. is director of research and technical aciivities at the Financial Accounting Standards Board. Stamford. Connecti- cut, Mr. Leisenring is immediate past chairman of the ASB. 42 Journal of ,^ceoun(ancy. Mareh

Transcript of Using Materiality in Audit Planning.

Page 1: Using Materiality in Audit Planning.

USINGMATERIALITYIN AUDITPUNNINGA practicai way torelate the auditor'smateriality estimateto the design ofaudit procedures.hy George R. Zuher. Robert K. Elliott,William R. Kitmey, Jr., and James J. Leisenring

John Smith. CPA, is the auditor ofAjax. Inc.Recetitly. Smith had listened to another CPAdescribe how a careful consideration of mate-riality during the planning phase improved thecoordination and efficiency of an audit. Inplanning his cutrent examination of Ajax.Inc.'s.. financial statements (see exhibit 1.page 44). Smith decided to apply some ofthose materiality concepts in the design ofaudit procedures.

Auditors like Smith, who are engaged toexamine financial statements, seek to deter-mine whether the financial statements takenas a whole are materially misstated. Material-ity has been defined over the years by. amongothers, accounting standard-setting bodies,courts, regulatory agencies and auditors. Gen-erally, these definitions indicate that an omis-sion or misstatement is material if knowledgeof the omission or misstatement would influ-

Authors' ntilL-: The Amcriciin Institute of CPAs audiling stan-dards board has exposed a proposed statement on auditingstandards entitled MateriuUty mid Audit Risk in Coiitttatiiig tinAudit (New York: AICPA. Deecmber 6, 1982), This articleisn't an interpretation or digest ot the exposure draft, althoughthe methods discussed in this article would be. in the authors'view, one method ot complying with certain provisions of theexposure draft.

ence the judgment of a reasonable person.Although the determination of what is materi-al to financial statements is necessarily an ac-counting concept, materiality also is a basicconsideration in the audit process. An objec-tive of an audit is to search for errors that,either individually or in the aggregate, wouldbe material to the financial statements. Be-cause Smith will have to decide if he is satis-fied that the financial statements aren't mate-rially misstated, it is essential that he plan hisaudit to obtain sufficient evidential matter tomake that evaluation.

This article will describe how Smith, andother auditors, can use a preliminary estimateof materiality in planning an effective—andefficient—audit.

What Is a PreliminaryEstimate of Materiality?According to Statement on Auditing Stan-dards no. 22. Planning and Supervision.^ theauditor considers, among other things, pre-liminary estimates of materiality levels whenhe plans an audit of financial statements. SASno. 22 doesn't explicitly require an auditor toquantify, either as a specific or an approxi-mate amount, his preliminary estimate of ma-teriality. However, quantification is the mostpractical way to consider such an estimate inaudit planning. Because financial statement*^are used to assess an entity's current positionand performance and to predict an entity'sfuture flow of cash, changes in the amount,timing or uncertainty of the entity's cash floware matters that would be expected to affectthe judgment of a reasonable person. Because

'statement on Auditing Standards no 22. Phinniiif; ami Su-pervision (New York; AICPA. 197H). See also AfCPA Profes-sional Standards, vol. 1 (Chicago; Commerce ClearingHouse). AU section .^11,

GEORGE R, ZUBER, CPA. now a diKtoral student at theL'niversity of Michigan. Ann ,'\rbor. was a manager in theAmerican Institute of CPAs auditing standards division whenthis article was written. Mr, Zuher is a member of the AICP,'\statistical sampling subcommittee. ROBERT K. ELLIOTT,CPA. is a partner of Peat. Marwick. Mitchell & Co,, NewYork. A former chairman of the staiistieal sampling subcom-mittee. Mr. Elliott is ;t member of the Institute's auditingstandards board (ASR) and tbe materiality and audit risk taskforce, WILLIAM R. KINNEY, JR., CPA. Ph,D,, is the John F.Murray Professor of Accounting and the director of the Insti-tute t)f Aecouniing Research at the I'niversity of Iowa. IowaCity. He is u member of the .ASB and a former member of (hestatistical sampling subcommittee. JAMES J. LHISENRING,CPA. is director of research and technical aciivities at theFinancial Accounting Standards Board. Stamford. Connecti-cut, Mr. Leisenring is immediate past chairman of the ASB.

42 Journal of ,^ceoun(ancy. Mareh

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these assessments and predictions are ex-pressed in quantitative terms, the definition ofmateriality must relate to these quantities. Inaddition, some quantification of "allowableerror" is essential to communicating withstaff assistants about the design and perfor-mance of audit procedures.

SAS no. 22 suggests that there may. in fact,be more than one level of materiality for tbefinancial statements taken as a wbole to beconsidered by an auditor. For example. Smithbelieves that $125,000 may be material if theerror affects Ajax. Inc.'s. net income.^ whilean error of up to $200,000 may be immaterialif the error affects only classification. Thevarious levels of materiality result from thevarying significance of different errors to theuser's assessments and predictions of futurecash flow.

Although there may be more than one levelof materiality, it is practical to design auditprocedures using only one preliminary esti-mate of materiality for the financial state-ments taken as a whole. The selection of onepreliminary estimate results from the inabilityof an auditor to simultaneously plan the na-ture, timing and extent of an audit procedurewith different sensitivities to error. For exam-ple, it isn't practical for Smith to try to designone inventory test which would find pricingerrors that aggregate to $ 10.000 and extensionerrors that aggregate to $20,000. Because in-come is frequently considered the most sensi-tive predictor of future cash flow for a busi-ness entity, auditors often establish aspreliminary estimates of materiality tbe aggre-gate level of errors affecting income that theywould consider to be material.^ Accordingly,Smith decided that $125,000 is a reasonablepreliminary estimate of financial statementmateriality to use in planning the audit ofAjax, Inc.

Numerous factors would likely influence anauditor's evaluation of the results of his audit

Virtually all errors in Ajax. Inc ' s . financial statements thataffect income are mitigated by a lax effect. If the marginal laxrale (federal and state) is 50 percent, the aftertax effect of$125.00(1 of error would be about 6 percent of net income,

^Tie fact that income is often considered the most sensitivepredictor of future cash fitws doesn't mean that an auditorcan't develop a preliminary estimate of materiality until thenet income for the period is known. Because materiality gen-erally relates to a notion of longer-run expected income oraverage income, some auditors use total assets or averagesales in eonjunetion with average income rates to estimatemateriality.

procedures when he decides whether the fi-nancial statements include material error. Inmaking a preliminary estitTiate of materiality,an auditor can anticipate many of those fac-tors. For example, by <ibtaining an under-standing of the client's business, an auditorhas a reasonable understanding of the size ofthe entity (for example, total assets, equity.sales and average earnings) and the nature ofthe client's operations and related transac-tions. Those factors would ordinarily be con-sidered in developing a preliminary estimateof materiality. As a result, those factorswouldn't be likely to cause the preliminaryestimate of materiality to differ from the mate-riality standard used in evaluating the finan-cial statement presentation after the audit iscomplete. Certain factors, however, maycause the auditor's preliminary estimate ofmateriality to differ from the materiality stan-dard used for evaluation. Those factors in-clude significant changes in the circumstancesconsidered in making the preliminary estimate(such as a merger or a disposal of a segment ofthe business) and information disclosed by theapplication of audit procedures that couldn't

Journal of Accountancy, March I9X.1 4.1

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Exhibit 1

Financial statements for Ajax,

Balance sheet(as of December 31. J9XX)

CashAccounts receivableInventoryProperty, plant and equipmentOther assets

Current installments oflong-term debt

Accounts payableAccrued liabilitiesLong-term debtDeferred income taxesCommon stockRetained earnings

Statement of earnings(for the vear endedDecember 31. I9XX)

SalesCost of goods soldSelling and administrative

expenseInterest expenseProvision for taxes

Net income

Inc.

$ 1.830.0002.627.0005.155.0004.573.000

205.000$14,390,000

S 257.0001,419.0001.996.0003,115.000

755.0001.679.0005.169.000

$14,390,000

$22,425,00018.407,000

2.096.000254.000672.000

S 996.0(K)

be anticipated in the design of audit proce-dures.

The latter group includes errors that aresmaller, either individually or in the aggre-gate, than the auditor's preliminary estimateof materiality but that could be expected, be-cause of their nature, to affect the judgment ofa reasonable person relying on the financialstatements. Matters that may be material be-cause of qualitative factors include fraudulenttransactions, improper payments for the pur-pose of obtaining favorable trade concessionsand errors that may intluence compliance witha working capital requirement under a debtcovenant. Since qualitative factors may relateto transactions or accounts that involve rela-tively small amounts, it would be prohibitive-ly expensive to plan audit procedures suffi-cient to search for them. For example, Ajax,

44 Journal of Accountancy. March 19S3

Inc., sells a significant portion of its productsto a foreign country that prohibits any form ofpayment to governmental officials in ex-change for favorable trade arrangements. If anAjax. Inc , agent would pay SI.000 to an offi-cial of that country, the future cash flow ofAjax, Inc., might be materially affected bythe loss of trade. Although such a paymentcould lead to a material effect on Ajax, Inc.'s,financial statements, it would be impracticalfor Smith to plan for. and Ajax, Inc., to payfor, an audit that could be expected to revealany improper payments as small as SI,000.As a result, while such factors—if discoveredduring the audit—are ordinarily considered inevaluating the financial statement presenta-tion after the application of audit procedures,they can't effectively be considered when theauditor makes a preliminary estimate of mate-riality.

We believe materiality is essentially aquantitative consideration of what is impor-tant to the presentation of a company's finan-cial statements. Both quantitative and qualita-tive matters, while not necessarily all preciseamounts, can be considered either in terms ofhistorical dollar values or in terms of the pres-ent value of their future effects on the com-pany's financial statements. Any matters thatwould have no quantitative effect on currentor future financial statements, including tbenotes and statement of accounting policies,are outside the scope of an auditor's responsi-bilities.

Relating Materiality to AuditProcedures for FinancialStatement ComponentsThe auditor's preliminary estimate of materi-ality for the financial statements taken as awhole influences the appropriate nature, tim-ing and extent of audit procedures for particu-lar account balances and classes of transac-tions. As stated earlier, the auditor should usehis preliminary estimate of materiality to planthe audit in a manner that will provide himwith sufficient evidential matter to make areasonable evaluation of the extent of errors,if any. in the financial statements. Holding oth-er planning considerations equal, as the totalamount of enror that would be considered mate-rial decreases, the scope of appropriate auditprocedures to be applied to financial statementcomponents increases and vice versa.

Two examples of extreme situations illus-trate this point. If Smith considered SI to bematerial to Ajax. Inc,"s, financial statements,the scope of audit procedures sufficient to de-

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tect material errors would require Smith toexamine and evaluate virtually every transac-tion and balance composing the financialstatements. On the other hand, if Smith esti-mated materiality to be $20 million for thefinancial statements of Ajax, Inc.. he couldconclude, virtually without performing anyaudit procedures, that it was unlikely that thefinancial statements include material error.Because the threshold of what constitutes amaterial error is never at either extreme, it isnecessary to devise some means of translatingan auditor's preliminary estimate of material-ity into the selection of appropriate proce-dures, the determination of the extent of thoseprocedures and the selection of suitable timesfor applying the procedures.

Without some method of using his prelimi-nary estimate of materiality to design auditprocedures, an auditor incurs the risk of inad-vertently underauditing. In such circum-stances, an auditor is precluded from express-ing an opinion on the financial statements, or,if he does express an opinion, he violates pro-fessional auditing standards because the opin-ion isn't based on sufficient evidential matter.

One way in which an auditor might planprocedures that will be sufficient to detect ma-terial errors is to overaudit. This approachwould cause an auditor to use procedures thatcould be expected to delect errors that aresignificantly smaller than any amounts thatcould be expected to aggregate to a materialamount. This approach isn't practical as ageneral policy because more resources wouldbe used in reaching an opinion on the presen-tation of Ihe financial statements than neces-sary. If Smith used this approach. Ajax, Inc.,would pay unnecessarily large audit fees. Be-cause Smith wouldn't be competitive in themarketplace, it would be reasonable to expectAjax. Inc., to eventually engage a differentauditor. Inefficient use of resources isn't aprofessionally desirable method of achievingan auditor's objective of detecting materialerror. An auditor needs a better way to incor-porate his preliminary estimate of materialityinto planning audit procedures.

A Practical Approach toRelating Materiality to FinancialStatement ComponentsOne practical approach is to break down, orallocate, the preliminary estimate of material-ity to components of the financial statements.In essence, the auditor would establish a pre-liminary estimate of allowable error for indi-

46 Journal of Accountancy, March 198.

vidual components of the financial statementsbased on his preliminary estimate of material-ity for the financial statements taken as awhole. Examples of such components wouldbe account balances, classes of transactions,locations and divisions. SAS no. 39, AuditSampling,* refers to such a measure of al-lowable error for planning substantive tests ofdetail as tolerable error. According to SASno. 39, tolerable error is the maximum "mon-etary error in the related account balance orclass of transactions [thatl may exist withoutcausing the financial statements to be materi-ally misstated." Furthermore, tolerable error•'is related to the auditor's preliminary esti-mates of materiality levels in such a way thattolerable error, combined for the entire auditplan, does not exceed those estimates."^While SAS no. 39 discusses tolerable erroronly in the context of audit sampling, thatconcept of allowable error in a financial state-ment component is applicable to all audit pro-cedures.

Tolerable error, as discussed in SAS no.39, can be thought of as including two ele-ments: (1) the auditor's expectation of likelyerror that will remain uncorrected in the finan-cial statements after the audit is complete and(2) an allowance for the risk of possible fur-ther error that might not be detected or indicat-ed by the audit procedures.

Assessing Expected ErrorSeveral factors influence an auditor's expecta-tion of error in the financial statements. Whenplanning the audit, an auditor can generallyestimate the amount of error that is likely toexist in the financial statements based on hisunderstanding of the entity's business and hisexperience in auditing the client in prioryears. For example. Smith knows from prioryears' experience that there are generally amoderate number of adjustments necessary toAjax, Inc.'s, financial statements because of anumber of weaknesses in related internal ac-counting controls. Smith's preliminary esti-mate is that the Ajax, Inc., financial state-ments will include approximately $30,000 oferrors that overstate net income.

*SAS no. 39. AHt/i/S(/m/7//«^ (New York: AICPA. 1981). SecProfessional Standiints. AU sec. .150.

id.. par. 18. See dho A!CPA Professional Stundards. AU. 350.18.

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An auditor also might be aware tbat an errorexists in tbe financial statements because tbaterror was first identified during the audit of aprior period's financial statements, Tbe errorwasn't corrected in prior periods because itwas considered immaterial to the financialstatements for those periods. It may be materi-al, however, to tbe current financial state-ments if, when added to other errors tbat areidentified in the current period, the sum is

"The auditor's expectationof error that will remain uncorrected

is influenced by the likelihoodthat the client will adjust the

financial statements for the auditor'sbest estimate of error."

material. Even though the auditor first ob-tained information about the error before theaudit of the current financial statements be-gan, he would still consider that informationin planning audit procedures. For example,during tbe prior year's audit. Smith identifieda machine recorded in Ajax. Inc.'s, financialstatements that had been scrapped, Ajax.Inc.'s, management didn't adjust the prioryear's financial statements because the ma-chine had only a two-year remaining life.Smith had atireed that the error was immateri-al. The related overstatement of machinery inthe current year's financial statements, net ofdepreciation, is $2,000, resulting in a totalexpected error in the financial statements of$32,000.

Tbe auditor's expectation of error that willremain uncorrected is intluenced by the likeli-hood that tbe client will adjust the financialstatements for the auditor's best estimate oferror. An auditor is generally able to antici-pate tbe likelihood that the client will be will-ing to adjust the financial statements forsome, or all, of the auditor's best estimate oferror. For example. Smith knows from expe-rience tbat some of his clients don't believe itis cost justified to adjust financial statementsfor the immaterial errors he brings to theirattention. The more an entity is willing toadjust the financial statements for the audi-tor's estimate of error, the less the auditorneeds to consider expected uncorrected cn'or

in relation to tbe preliminary estimate of mate-riality. If a client agrees to adjust the financialstatement for all errors identified or projectedby the auditor, no portion of the preliminaryestimate of materiality will need to be re-served for expected uncorrected error. Be-cause Ajax. Inc 's . management generally ad-justs for a substantial portion of the errorsidentified by the audit procedures. Smith be-lieves it is likely that only about $4,000 of the$32,000 in errors he expects in the financialstatements won't be adjusted.

Because it may be difficult for an auditor toidentify the specific accounts in which expect-ed error is likely to occur and remain uncor-rected, it is often practical for an auditor tosimply reduce his preliminary estimate of ma-teriality by expected uncorrected error in thefinancial statements taken as a whole ratherthan to estimate the expected uncorrected er-ror for each component of tbe financial state-ments. As a result. Smith will have $121,000of the $ 125.000 preliminary estimate of mate-riality available to be allocated to tbe tolerableerrors for components of the financial state-ments. In a sense, this $121.(KX) is a "cush-ion" or an allowance for the imprecision in-herent in tbe application of audit procedures.

Determining Toierable ErrorsThe need to allow for possible further errorthat may not be detected or indicated byplanned audit procedures arises from tbe im-precision inherent in audit procedures. Anauditor performs audit procedures related tospecific assertions about a component of thefinancial statements to estimate the amount oferror in that component. When an auditor de-signs audit procedures, be recognizes that hisbest estimate of error in a component of thefinancial statements will in fact likely begreater or less than tbe true, but unknown,actual amount of error in the component. Be-cause an auditor is primarily concerned witbtbe possibility tbat his best estimate of errorfor all components of the financial statementsmay underestimate the actual error in the fi-nancial statements, the auditor allows forsome cushion in the design of audil proce-dures.

To be conservative, an auditor might al-ways plan to evaluate tbe results of his auditprocedures by adding an estimate, given theaudit procedures he performed, of the maxi-mum error that he believes might reasonablyexist for each of tbe components of the finan-cial statements. That approach, however.

Journiil o! Accountanc\. Marth

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would be overly conservative because anymistake in the auditor's best estimate of erroris equally likely to be an underestimate or anoverestimate. Although some of the best esti-mates might underestimate the actual error inthe component, it is extremely unlikely thatall best estimates are underestimates. A goodanalogy would be to consider the results onemight expect from flipping 10 coins. Al-though it is possible to flip 10 coins and get 10heads, it is very unlikely. In a similar manner,it is unlikely that an auditor would underesti-mate the error in all components of the finan-cial statements. As a result, an auditor wouldordinarily plan audit procedures so that thesum of the individual allowances, or tolerableerrors, for each component of the financialstatements would be larger than the desiredallowance for possible further error for thefinancial statements taken as a whole. Howmuch larger will be illustrated below.

Several factors influence the auditor's de-termination of tolerable error for a componentof the financial statements. One factor is themagnitude of the component relative to thefinancial statements taken as a whole. Anauditor generally allocates a greater portion ofhis preliminary estimate of materiality for thefinancial statements to larger components ofthose financial statements. For example, it isgenerally reasonable to allow for the possibil-ity of more error in an accounts receivablebalance of $30 million than in a marketablesecurities balance of $2 million. The unit costto audit an individual element making up acomponent of the financial statements also in-fluences the determination of tolerable errorfor that component. For example, greater tol-erable error might be allocated to compo-nents, such as inventory, that are expected tobe relatively difficult and costly to audit pre-cisely when compared with components suchas cash and long-term debt. An auditor alsomay consider the variability of the values in a

component of the financial statements whenhe determines an appropriate tolerable errorfor the component. As the variability of theitems within a component increases, it is moredifficult to estimate the amount of error in thecomponent. As a result, some auditors wouldallocate a relatively larger tolerable error tocomponents with high variability. Further, theauditor would consider user needs for preci-sion in financial statement components andnot select a tolerable error for a component(for example, receivables or current assets)that would result in an insufficiently precisedetermination of the amount of the compo-nent.

Smith used as a decision aid for determin-ing tolerable errors for components of the fi-nancial statements a simplified mathematicalformula. One such formula is illustrated inexhibit 2, this page. Smith used the formula toobtain "first pass" estimates of tolerable er-rors for all the account balances that make upAjax, Inc.'s, financial statements. These esti-mates are shown in exhibit 3, page 52. Smithcalculated his first pass estimates for all ac-counts to be audited. He didn't calculate toler-able error for net income or retained earningsbecause net income is the residual of the otheraccounts and retained earnings is the sum ofprior net income (less dividends, which can beaudited with precision).

The formula in exhibit 2 includes only aconsideration of the relative magnitude of thecomponents of the financial statements. Amore comprehensive model also would in-clude the other factors that influence the ap-propriate allocation of the preliminary esti-mate of materiality for the financialstatements to the individual components. Al-though a more comprehensive model mightresult in a more efficient allocation, the cost todevelop such a complex model mightoutweigh the savings.

A less formal method of determining toler-

Exhibit 2

Illustrative formula for allocating tolerable error

Tolerable errorfor acomponent

Preliminary estimate ofmateriality less expecteduncorrected error xin the financial statements

Amount of component

Total amount of all components thatmake up the financial statements towhich materiality is being allocated

50 Journal of Accountancy, March 1983

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able errors would be for the auditor to use hisjudgment to assess a tolerable error for eachcomponent of the financial statements andthen consider whether those tolerable errors,in the aggregate, are reasonable in relation tothe preliminary estimate of materiality for thefinancial statements taken as a whole. Be-cause of the nonadditive nature of tolerableerror discussed earlier, the sum of tolerableerrors would ordinarily be larger than theauditor's preliminary estimate of materialityfor the financial statements taken as a whole.*

Smith decided to use a judgmental alloca-tion of tolerable error to the financial state-ment components. He started with the firstpass estimates of the formula but adjustedthem for other factors he considered relevant.As an example, he allocated less tolerable er-ror to cash than the formula did because heknew that the audit costs to achieve a tightprecision in cash are very reasonable. Some ofhis other reasons are indicated in exhibit 3.Smith allocated no tolerable error to those ac-counts he planned to audit 100 percent.

After Smith allocated tolerable error to thefinancial statement components by using hisjudgment, he considered whether the com-bined tolerable error was within his adjustedpreliminary estimate of materiality. His finalallocations and the combined amount areshown in exhibit 3.

The objectives described in this article canbe achieved without an explicit allocation ofthe auditor's preliminary estimate of material-ity. The most common approach is an exten-sive use of dollar-unit sampling. The auditorwho uses dollar-unit sampling essentiallythinks of the financial statements as one largepopulation to be sampled. Therefore, ratherthan determine tolerable errors for the compo-nents of the financial statements, that auditoruses his preliminary estimate of materialityfor financial statements directly in the calcula-tion of appropriate sample sizes for the com-ponents. Auditors who use dollar-unit sam-pling would, of course, still need to (1) deductan allowance for expected unadjusted errorfrom their preliminary estimates of material-ity, (2) consider errors arising in prior years

MTie combined tolerable error couid be estimaled by Ihe use ofa slatislical formula that takes into account the nonadditivenature of tolerable error. The aggregate tolerable error wouldhcthesquarerootofthesumof the squared tolerahle errors forthe components. Using this formula, the combined tolerableerrors forthe "firstpass" column in exhibit 3. page52, wouldbe $121,083. which is approximately equal to Smith's adjust-ed preliminary estimate of materiality.

that affect the current financial statements and(3) establish tolerable errors for componentsof the financial statements that are tested byaudit procedures other than dollar-unit sam-pling.

How Tolerable Error Is UsedAfter Smith used his judgment to determinethe tolerable error for various components ofAjax, Inc.'s, financial statements, he de-signed audit tests that he expected to achievethose levels of precision. Other things beingequal, the smaller the tolerable error Smithassigned to a component, the stronger the re-quired procedures to achieve that precision.Stronger tests would, in general, be (1) teststhat, by their nature, are more likely to detecterror (a test of detail, for example, versus ananalytical review procedure), (2) tests usinglarger sample sizes or (3) tests performedcloser to the balance sheet date.

For certain tests. Smith could use his esti-mate of tolerable error explicitly in designingthe tests. For example, he planned to use sta-tistical sampling for accounts receivable andinventory; thus tolerable error for those ac-counts would be used in the statistical formulato determine sample size. Also, Smithplanned to use a multiple regression analyticalreview procedure for cost of goods sold, andhe could use the tolerable error explicitly inthat test. Even in the areas that Smith plannedto use nonstatistical sampling, he could usetolerahle error to design his tests using themethods described in a recent article on auditsampling' and in the American Institute ofCPAs guide entitled Audit Sampling.^

However, Smith's consideration of the con-cept of tolerable error isn't meant to suggestthat the scope of all audit procedures can hedetermined using mathematical formulas. Infact. Smith will still be unable to directlycompute the scope of his other audit proce-dures by using a formula. However, evenwithout the ability to directly translate toler-able error into the scope of most audit proce-

Carl S. Warren. Stephen V. N. Yates and George R. Zuber."Audit Sampling: A Practical Approach." JofA, Jan.82. pp.62-72.

^Statistical Sampling Subcommittee. Audit Sampling (NewYork; AICPA. 1983).

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dures by formula, the consideration of toler-able error still assists Smith in making deci-sions about the nature, timing and extent ofprocedures appropriate for testing compo-nents of the financial statements. For exam-ple, if Smith is deciding whether to visit awarehouse location with $100,000 of inven-tory, an assignment of $80,000 of tolerableerror to that location may assist him in decid-ing that he doesn't need to visit the ware-house. Instead, he may perform limited testsof the warehouse records or analytical reviewprocedures. Conversely, if an account balanceis assigned a very small tolerable error relativeto the total balance. Smith would generally

need to perform procedures sufficient to de-tect even small amounts of error.

Summary

When an auditor examines financial state-ments, he looks for errors that could be mate-rial to those statements. Unless an auditormakes a preliminary estimate of what is mate-rial to the financial statements under examina-tion and uses that estimate in designing appro-priate audit procedures, he isn't likely to findmaterial errors if they exist. This article hasdescribed some of the factors that influence anauditor's consideration of a preliminary esti-mate of materiality for financial statementsand a praetica! way to relate that estimate tothe design of appropriate audit procedures. •

Advice to directors:avoid the rubber stamp

When Penn Central collapsed more than a decade ago. many of its direc-tors were surprised and dismayed to find themselves sued by stockholderswho alleged that the directors had failed to meet their responsibilities.Subsequently, under prodding from the Securities and Exchange Com-mission, the New York Stock Exchange and litigious stockholders . . .corporate boards began adding more outside directors, forming directoraudit committees to monitor corporate affairs and enlarging director in-volvement in corporate policjes.

But memories are short, and , . . directors of many corporations haveagain slid back into the clubby atmosphere that tempts them to rubber-stamp management decisions with few questions. At the least, directorsshould keep in mind that if serious company troubles break into the open,shareholders and the public will want to know, and have a right to know,what the board of directors was doing, or not doing, to serve the bestinterests of the corporation and its owners.

From an editorial inBusiness Week, August 23. 1982

54 Journal of Accountancy. March 1983

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