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By William R. Kinney, Jr. and
Linda S. McDaniel

In a healthy business, certain relations among data are expected. For example, gross profit should bear a close relation to pricing policies, revenues and receivables should reflect a reasonable collection period, and payables should reflect both resource acquisition and cash management objectives. Presence of these expected relations among preaudit "book values" (BVs) can be evidence of both the health of the company, and the lack of material accounting misstatement.

To assess possible misstatement, the auditor applying SAS No. 56, Analytical Procedures, uses the knowledge of data relations to form an expectation about the true (audited 100%) account balance. Then, the expectation is compared to the current year's BV. For a small difference, the BV may be accepted as "not materially misstated." Large differences warrant consideration of possible cause(s) including misstatement. How should expected account balances be determined? As to book value and expectation, how close is close enough? How much reliance can be safely placed on substantive analytical procedure results?

Expectation Formation

The expectation of an audited account value (EV) can be based on the auditor's general knowledge of business relations, specific knowledge of the client, and analysis of related financial and nonfinancial data within the firm. EVs can be the result of subjective judgments by experienced auditors based on a wide array of information or statistical regression models based on objective, but limited data series. There is no one best approach, but expectation formation methods differ as to their precision (closeness-of-expected-to-audited), the data used, and their cost to apply.

The simplest method uses very little data. It asks, "What has changed from last year?" In effect, the "change from last year" approach uses last year's audited values (AV) as EVs for this year. If the client's business for last year was similar to this year, this is a good approach. It is not a good approach in the presence of business operation or accounting changes, unusual events, or changes in factors such as interest rates. Often the auditor knows (or could easily know) about current factors that should cause values to change from those observed last year. Examples are new products, new equipment, labor strikes, and supply problems.

To illustrate, an auditor with knowledge of a retailer's midyear supply shortage of a popular product might quantify the shortage and mentally adjust last year's sales and cost of sales in forming EVs for this year. This would lead to a lowered EV for sales and cost of sales as well as lowered inventory and receivables turnover ratios. If book values (BVs) for sales and cost of sales are close to last year's AVs adjusted for the expected changes due to the shortage, the auditor might accept the book values without detailed auditing.

On the other hand, suppose the client covered the reduced sales by entering fictitious charge sales. The inflated BV for sales would be higher than expected, and receivables turnover lower than expected. The auditor would investigate these differences from expectation to determine whether material misstatement might exist. In contrast, an auditor who simply compared BV with last year's AV might accept the small differences as "reasonable." Thus, the auditor may accept materially misstated BVs if explicit knowledge-based expectations are not formed.

Some auditors don't use their knowledge to form explicit expectations. But recent auditing research shows that auditors are sensitive even to the instruction to form and document their expectations. One study by the authors shows that the auditor's ability to find a material misstatement in quarterly financial statements is doubled by the mere instructions to form and document EV before considering BV.

Auditors in the study were given real world 10-Qs and related client background data from a small entity that had materially misstated its third quarter balance sheet by failing to accrue the current portion of long-term debt. Only 29% of auditors who were given the third quarter BVs and told to "apply analytical procedures" noticed the material misstatement. Auditors in another group were not given the current BVs initially, but were told to form and document EV's for the balance sheet and income statement accounts based on the prior 10-Qs, 10-Ks, and client background data. After documenting expectations, these auditors were given the BV's. Sixty-two percent of these latter auditors correctly identified the under-reporting of current long-term debt.

In practice, valid expectation formation requires experience, data, and thoughtful analysis. And, it is difficult to ignore BVs in forming expectations. However, expectations are important if the guidance of SAS No. 56 is to be applied and analytical procedures made effective.

Assessing Expectation Precision

SAS No. 56 directs the auditor to consider the "precision of the expectation." The auditor is to consider the dollar magnitude of possible variation in an account's value that could exist even if there were no misstatement. How can this be done? The answer varies depending upon three factors. One factor is the inherent precision in the underlying accounting process. For example, processes that develop accounting estimates are naturally highly varied, and any value in a wide range could be correct (i.e., wide precision). On the other hand, the range for composite depreciation is narrow as is the range of cost of sales as a percentage of sales.

The second and third factors are the analytical methods applied, and the data used to determine the expectation. A mere calculation of year-end trial balance ratios and comparison with last year's ratios using AVs involves simplistic data analysis and no data collection. Use of last year's values as "expectations" are likely to have a wide range of possible AVs (wide precision). They do not provide much assurance for the auditor.

In contrast, an auditor may form an expectation of quarterly or monthly balances at the product line or segment level of detail. EVs might be based on financial data that have been audited, nonfinancial data, data provided by outside sources, or data prepared from independent processes within the firm under conditions of good internal control. Thoughtful analyses using more data lead to "high precision" of expectations. High precision (a narrow range for expectations) justifies a higher level of assurance from analytical procedures by the auditor.

As to method, auditors using regression analysis to develop EV will automatically have a measure of precision. The statistical standard error of the regression provides such a measure. However, auditors also use subjective or judgmental methods to form expectations. How can these auditors evaluate the imprecision in their methods?

A relatively simple way to subjectively evaluate precision can be used on any audit. It begins with the planning assessment of financial statement materiality, as required by SAS No. 47, Audit Risk and Materiality in Conducting an Audit. Call this magnitude of misstatement "M*." For example, for a small company, two percent of revenues for the year might be a useful first pass estimate of M*. The accompanying figure diagrams the steps in the procedure.

Before obtaining data and actually applying analytical procedures, the auditor considers the likelihood that the methods and data he or she plans to use would yield an account balance expectation within plus or minus a "material amount" of the account's true value (100% audited). For example, assume the auditor believes a material amount for the financial statements as a whole is $100,000, i.e., M*=$100,000. The auditor would ask himself or herself, "Given my planned analytical procedures, how likely is it that the true value (TV) of inventory will be within plus or minus $100,000 of its EV?"

If the client's business and inventory processes are stable, and the auditor plans appropriate analytical methods using reliable disaggregated data to determine EV, the EV should be "precise." To be specific, assume "precise" means the auditor believes it is "as likely as not" that TV would be within plus or minus $100,000 of the EV. Part of the auditor's subjective assessment or self-examination of expectation precision is consideration of whether the EV could be defended to outsiders, such as jurors deciding a lawsuit. Would jurors believe the analytical procedures applied would lead to a 50/50 chance of detecting a $100,000 error in the account being audited? If the answer is yes, it is probably sufficiently precise.

After determining the planned procedures should lead to a "precise" expectation, the auditor applies his or her knowledge, information, and professional judgment to actually determine the EV. An auditor reviewing for possible overstatement of the BV of inventory would proceed to see whether the book value minus the expected amount (BV­EV) is less than one-half of materiality. (One-half materiality is used by at least one large firm as a "material amount" or "unacceptable amount" for each account under audit.) If BV­EV is less than M*/2, the auditor is justified in accepting the book value as materially correct at a "risk of incorrect acceptance" for analytical procedures equal to about .4, or 40% (see sidebar).

If BV­EV is greater than M*/2, the auditor must investigate the difference by considering alternative explanations for the difference. Especially important to consider are misstatement-based explanations. After review of the appropriateness of the method used to form the expectation and after possible misstatements are ruled out, the auditor might question client management.

This "analytical" investigation should include consideration of the possibility of error or fraud as well as possible non-error causes. Some auditors "quantify" the dollar impact of all tentative explanations of differences. Research shows that auditors who quantify the likely magnitude of client management explanation of a difference between BV and EV are more likely to correctly conclude whether material misstatement exists than an auditor who does not quantify an explanation.

The auditor may decide that the EV was incorrect--for example, a nonerror cause was omitted from the auditor's initial expectation. In this case, the auditor would revise the expectation by adding or subtracting the omitted factor amount, and proceed through the steps in the figure using the revised EV. If, on the other hand, the model appears to be right, the auditor would reject the book value as fairly stated, and apply other substantive auditing procedures.

Better to Think Ahead

Auditors applying the above procedures can have an audit process that will be more effective, on average, because auditors form better justified expectations and will be more consistent in their reliance on analytical procedures. First, by forming expectations before examining book values, the auditor will bring to bear more of his or her knowledge about the client and will more readily recognize book values that are far from a reasonable expectation. This focus is more likely to uncover client explanations that are based on incorrect nonerror causes. Second, by considering the inherent precision in the auditor's expectations, the auditor will be less likely to overrely on book values that are close to expectations even though material misstatement exists.

The approach suggested here is subjective, and therefore results will differ somewhat across even experienced and expert auditors. However, the structure imposed by having each auditor consider "what would reasonable persons think is reasonable under these circumstances" should avoid excessive reliance (i.e., overreliance) on procedures that, in fact, do not warrant much reliance. It is better to think about reasonable expectations and the inherent imprecision in an analytical procedure at the time of the audit,
rather than several years later in a
courtroom. *

William R. Kinney, Jr., PhD, CPA, is a professor at the University of Texas, a member of the AICPA Special Committee on Assurance Services, and a past member of the Auditing Standards Board. Linda S. McDaniel, PhD, CPA, is an assistant professor at the University of North Carolina and a member of the AICPA's Analytical Procedures Task Force.





Douglas R. Carmichael, PhD, CPA

Baruch College

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