# The audit strategy: analytical procedures as substantive tests.

An audit strategy involves the evaluation of internal controls and
the performance of substantive tests. Substative tests may be derived
from test of details, analytical procedures or any combination of the
two. Tests of details involve examining details of an account in an
attempt to reconstruct and draw conclusions about the reported account
balance, while analytical procedures involve drawing conslusions based
on expected amounts calculated by the auditor. Generally, it is easy to
obtain the necessary data to perfrom the analytical analysis regardless
of the size or complexity of a company's accounting system.

Auditor objectives usually can be accomplished with less time and cost by applying analytical procedures rather than tests of details. In addition, the auditor may need to rely on analytical procedures when detailed evidence is not readily available for a particular item. Therefore, the auditor should be more aware of this part of the audit since it may not only be more cost effective but may provide evidence when other procedures would be ineffective.

Types of Analytical

Procedures

The recent accounting standard states that the analytical procedures range from simple comparisons to the use of complex models involving many relationships and elements of data." Data used to help determine expected amounts for account balances can be obtained from sources such as results of prior periods, budgets, forecasts, industry data and current financial and operative data. There is not given set of analytical procedures for use by all auditors on all audits. The analytical procedures available for use are limited only by the availability of reliable data and the creativity of the auditor. However, the more common procedures may be classified into four types: trend analysis, reasonable tests, ratio analysis and strutural modeling.

Trend Analysis

Trend analysis is the most commonly used analytical procedure. The auditor may choose either a diagnostic or a causal approach. Applying the diagnostic approach, the auditor would evaluate whether the current balance of an account is out of line with the trend establish with previous balances for that account. Alternately, the causal approach calculates an expected balance for the account based on an understanding of factors that cause the account to change. This expected amount is then compared to the actual amount recorded in the books and the difference is judged as to reasonableness. Those differences indicated as unreasonable are signaled for additional audit attention.

The causal approach is generally preferable according to SAS No. 56, "Analytical Procedures". However, this procedure requires more effort than the diagnostic approach. The auditor should consider the higher costs involved with application of the causal approach in relation to the additional benefits received in determinig which approach should ultimately be used.

Generally trend analysis relies on the balance of the account under audit consideration for prior periods. Different methods of applying trend analysis would include an expected amount based on:

1. Last year's balance;

2. Last year's balance plus the change between the two prior years;

3. Average change in the account balance over a given number of previsous years added to last year's balance;

4. Simple average of the account balance over a given number of previous years;

5. Last year's balance plus the percentage change in the account between the two prior years; or

6. Last year's balance plus the average percentage change in the account balance over the past several years.

Other methods could be developed based on the auditor's knowledge of factors that would affect the change in the account.

Trend analysis is more useful for expense and revenue accounts than it is for assets and liabilities. Because trend analysis focuses on the change in account balances from prior periods, it is not as useful with balance sheet accounts which are relatively unpredictable.

Reasonable Tests

Reasonable tests involve the calculation of an expected amount for the account balance based on nonfinancial data for the current period. Unlike trend analysis, this analytical procedure does not rely on events of past periods, but only operating data for the audit period under consideration. For example, revenue from renting apartments would be related to average occupancy rate and average rent per apartment. Although the exact calculation of total rent revenue would rely on knowing the number of months each individual apartment was rented and the rent per month for each apartment, an estimate could be calculated by multiplying the average number of months per year the apartments were rented times the total number of apartments times the average rent per apartment. This estimate would then be compared to the recorded amount of revenue, and unreasonably large discrepancies would need further investigation and justification.

Tests of reasonableness use operating data to establish expected amounts and operating data typically measure flows; therefore, these procedures are generally more applicable to income statements accounts rather than balance sheet accounts. Since information for current periods may be easier to obtain than data of prior years, reasonable tests may be easily applied.

Ratio Analysis

Ratio analysis involves comparing the relationships among account balances. Unlike trend analysis which has only limited usefulness in the examination of balance sheet accounts, ratio analysis is useful for examining assets and liabilities as well as income statement accounts. Individual asset and liability account balances are often difficult to predict. However, the relationship to other account balances is more predictable.

Ratio analysis may be performed on a time series or a cross sectional basis. Applying time series analysis, ratios are compared over time. Since relationships often remain stable over time, significant differences would be signaled for further investigation.

Cross sectional analysis compares a company's ratios of account balances with ratios of other companies and of the industry for a given time period. The acquisition of data for cross-sectional analysis may require more effort than time series analysis since data external to the company is necessary.

Ratios that may be analyzed include financial liquidity, leverage, activity or profitability ratios. Common-sized balance sheets or income statements may also be compared over time or cross sectionally. When analysis is performed cross-sectionally using either ratios or common-sized statements, care should be exercised when different accounting principles are used by various companies such as FIFO versus LIFO for inventory costing. Use of different account principles as well as different demographics, technologies and financial leverage may result in noncomparable ratio analysis.

Structural Modeling

This type of precedure constructs a statistical model from financial and/or nonfinancial data of past accounting periods to predict current account balances. Three potentially useful models to the auditor or linear regression, autoregressive integrated moving average (ARIMA) and the X-11 model.

Linear Regression. A statistical model discussed in accounting literature and used to a limited extent in practice is linear regression. A regression model is developed based on a linear relationship between an account balance under audit cosideration and one or more financial and/or nonfinancial variables over pasts months. The linear regression model is of the form:

Y = A + B1X1 + B2X2 + ... +

BiXi where Y is the account of audit interest, Xi are the variables theoretically related to Y, and Bi are the coefficients determined by the best model developed from the past data points.

The model is then used to provide an expected amount for the current account balance assuming that the same relationship continues to exist for the current audit period.

The regression model is generally constructed for income statement accounts using monthly data for the previous three years for each of the variables. The use of 36 monthly observations provides enough data to establish a relationship without the data being so far removed from the current audit period so as not to be representative of the current underlying relationship. This expected amount is compared to the recorded amount, and the difference is evaluated as to reasonableness.

ARIMA. Another statistical technique with potential use as an analytical procedure is ARIMA. This method develops a model based on past data of the account under audit consideration. The model is developed by using patterns of the data within each year and patterns of the data over several years. It is generally suggested that a minimum of 50 observations be used in order to establish this pattern although limited research has indicated that use of fewer than 50 observations would still provide a useful model. Being a time series technique, AIRMA is more applicable to income statement accounts.

X-11 Model. The X-11 model has been suggested as a potential analytical procedure for auditing theory and practice. The model statistically decomposes a time series of data into three components (trend-cyle, seasonal and irregular), each of which possesses an underlying economic interepretation. The trend-cycle component includes the long-term trend inherent in the series and any effects of the business cycle on the data. The seasonal component reflects an intrayear pattern of variation that is repeated consistently from year to year. The irregular component consists of residual variations in the data that reflect any random or unexplained events in the time series. Accordingly, the X-11 model may be used to decompose a time series and to determine the relative (i.e., percentage) contribution of the trend-cycle, seasonal and irregular components to changes that occur in the series.

The time series decomposed would be the balance of the account under the audit consideration for prior periods. Since this procedure deals with account balances overtime, the X-11 model is more applicable to income statement accounts.

Computer software is available for these statistical models. Although training is necessary in order to interpret results or to identify when use of the models may not provide good results, these methods are viable alternatives to less sophisticated analytical procedures.

Efficiency and Effectiveness

The auditor is interested in developing models which will provide accurate predictions. As the predicted amounts become more precise, the range of expected differences between actual and expected amounts becomes narrower and the more likely significant differences are due to misstatements in the account balance. Numerous research studies have been performed evaluating the relative predictive abilities of various analytical procedures. Simple ratios and trends have been acceptable analytical procedures over the years, but recent research revealed a change in the use of analytical procedures toward the use of quantitative procedures. The results of a questionnaire showed an overall increase in the use of analytical procedures in audits and suggested an increase in the use of quantitative procedures with a corresponding decrease in the use of nonquantitative procedures. Other researchers have suggested that two statistical procedures, regression analysis and autoregressive integrated moving average (ARIMA), were superior in predictive ability to simpler nonquantitative techniques.

Auditors are also interested in the model's ability to detect material misstatements. When the auditor uses analytical procedures as substantive tests, he/she is exposed to two potential errors. An incorrect rejection (Type I error) occurs when the model signals an account balance as having a material misstatement when, in fact, the account balance is correctly stated. An incorrect acceptance (Type II error) occurs when the model indicates that the account balance is correctly stated when, in fact, a material error exists in the account balance. If an auditor commits a Type I error, he/she will spend unnecessary additional audit time on an account that is correctly stated. This will result in additional audit costs. If an auditor commits a Type II error, he/she will sign a statement attesting to the account balances as fairly presented with no material misstatement when, in fact, material misstatement exists. A lawsuit against the auditor potentially exists if this material misstatement is later uncovered. So the auditor desires a low Type I error rate (efficiency) and a low Type II error rate (effectiveness). Since a lawsuit causes Potentially higher costs with both liability costs and loss of image for the firm, auditors are probably more concerned with effectiveness.

Research has shown that nonstatistical as well as statistical analytical procedures increased audit effectiveness relative to an audit strategy that did not use analytical procedures. However, additional research testing three types of models commonly used in practice (trend analysis, ratio models and regression models) with simulated data indicates that statistical models are more efficient and effective than the nonstatistical methods. Many of the nonstatistical techniques had high levels of Type I and Type II errors. Subsequent research with actual data has supported those results by indicating that statistically oriented models and decision rules are more effective than nonstatistical approaches and that the regression and X-11 models dominate the naive methods.

Conclusion

The issuance of Statement on Auditing Standards No. 56 - Analytical Procedures has placed greater emphasis on the use of analytical procedures by auditors. The use of analytical procedures with tests of details provides the auditor with evidence to draw audit conclusions. The more reliance an auditor can place on analytica procedures, the less time he needs to spend on tests of details.

There is no given list of acceptable techniques. Analytical procedures include any method an auditor can develop to help predict account balances which are unusual. However, analytical procedures generally fall into four groups:

1. Trend analysis

2. Reasonable tests,

3. Ratio analysis, and

4. Structural models.

Although most of the procedures used will supply the auditor with some helpful information, research over the past few years has shown statitical models to be more efficient and effective.

Arlette C. Wilson, Phd, CPA, CMA, CIA, is associate professor of accounting at Auburn University, Alabama. She has published in various academic and practitioner journals.

Janet L. Colbert, Phd, CPA, CIA, is an associate professor of accounting at Auburn University, Alabama. She has worked in public accounting and in industry and has published in various accounting journals.

Auditor objectives usually can be accomplished with less time and cost by applying analytical procedures rather than tests of details. In addition, the auditor may need to rely on analytical procedures when detailed evidence is not readily available for a particular item. Therefore, the auditor should be more aware of this part of the audit since it may not only be more cost effective but may provide evidence when other procedures would be ineffective.

Types of Analytical

Procedures

The recent accounting standard states that the analytical procedures range from simple comparisons to the use of complex models involving many relationships and elements of data." Data used to help determine expected amounts for account balances can be obtained from sources such as results of prior periods, budgets, forecasts, industry data and current financial and operative data. There is not given set of analytical procedures for use by all auditors on all audits. The analytical procedures available for use are limited only by the availability of reliable data and the creativity of the auditor. However, the more common procedures may be classified into four types: trend analysis, reasonable tests, ratio analysis and strutural modeling.

Trend Analysis

Trend analysis is the most commonly used analytical procedure. The auditor may choose either a diagnostic or a causal approach. Applying the diagnostic approach, the auditor would evaluate whether the current balance of an account is out of line with the trend establish with previous balances for that account. Alternately, the causal approach calculates an expected balance for the account based on an understanding of factors that cause the account to change. This expected amount is then compared to the actual amount recorded in the books and the difference is judged as to reasonableness. Those differences indicated as unreasonable are signaled for additional audit attention.

The causal approach is generally preferable according to SAS No. 56, "Analytical Procedures". However, this procedure requires more effort than the diagnostic approach. The auditor should consider the higher costs involved with application of the causal approach in relation to the additional benefits received in determinig which approach should ultimately be used.

Generally trend analysis relies on the balance of the account under audit consideration for prior periods. Different methods of applying trend analysis would include an expected amount based on:

1. Last year's balance;

2. Last year's balance plus the change between the two prior years;

3. Average change in the account balance over a given number of previsous years added to last year's balance;

4. Simple average of the account balance over a given number of previous years;

5. Last year's balance plus the percentage change in the account between the two prior years; or

6. Last year's balance plus the average percentage change in the account balance over the past several years.

Other methods could be developed based on the auditor's knowledge of factors that would affect the change in the account.

Trend analysis is more useful for expense and revenue accounts than it is for assets and liabilities. Because trend analysis focuses on the change in account balances from prior periods, it is not as useful with balance sheet accounts which are relatively unpredictable.

Reasonable Tests

Reasonable tests involve the calculation of an expected amount for the account balance based on nonfinancial data for the current period. Unlike trend analysis, this analytical procedure does not rely on events of past periods, but only operating data for the audit period under consideration. For example, revenue from renting apartments would be related to average occupancy rate and average rent per apartment. Although the exact calculation of total rent revenue would rely on knowing the number of months each individual apartment was rented and the rent per month for each apartment, an estimate could be calculated by multiplying the average number of months per year the apartments were rented times the total number of apartments times the average rent per apartment. This estimate would then be compared to the recorded amount of revenue, and unreasonably large discrepancies would need further investigation and justification.

Tests of reasonableness use operating data to establish expected amounts and operating data typically measure flows; therefore, these procedures are generally more applicable to income statements accounts rather than balance sheet accounts. Since information for current periods may be easier to obtain than data of prior years, reasonable tests may be easily applied.

Ratio Analysis

Ratio analysis involves comparing the relationships among account balances. Unlike trend analysis which has only limited usefulness in the examination of balance sheet accounts, ratio analysis is useful for examining assets and liabilities as well as income statement accounts. Individual asset and liability account balances are often difficult to predict. However, the relationship to other account balances is more predictable.

Ratio analysis may be performed on a time series or a cross sectional basis. Applying time series analysis, ratios are compared over time. Since relationships often remain stable over time, significant differences would be signaled for further investigation.

Cross sectional analysis compares a company's ratios of account balances with ratios of other companies and of the industry for a given time period. The acquisition of data for cross-sectional analysis may require more effort than time series analysis since data external to the company is necessary.

Ratios that may be analyzed include financial liquidity, leverage, activity or profitability ratios. Common-sized balance sheets or income statements may also be compared over time or cross sectionally. When analysis is performed cross-sectionally using either ratios or common-sized statements, care should be exercised when different accounting principles are used by various companies such as FIFO versus LIFO for inventory costing. Use of different account principles as well as different demographics, technologies and financial leverage may result in noncomparable ratio analysis.

Structural Modeling

This type of precedure constructs a statistical model from financial and/or nonfinancial data of past accounting periods to predict current account balances. Three potentially useful models to the auditor or linear regression, autoregressive integrated moving average (ARIMA) and the X-11 model.

Linear Regression. A statistical model discussed in accounting literature and used to a limited extent in practice is linear regression. A regression model is developed based on a linear relationship between an account balance under audit cosideration and one or more financial and/or nonfinancial variables over pasts months. The linear regression model is of the form:

Y = A + B1X1 + B2X2 + ... +

BiXi where Y is the account of audit interest, Xi are the variables theoretically related to Y, and Bi are the coefficients determined by the best model developed from the past data points.

The model is then used to provide an expected amount for the current account balance assuming that the same relationship continues to exist for the current audit period.

The regression model is generally constructed for income statement accounts using monthly data for the previous three years for each of the variables. The use of 36 monthly observations provides enough data to establish a relationship without the data being so far removed from the current audit period so as not to be representative of the current underlying relationship. This expected amount is compared to the recorded amount, and the difference is evaluated as to reasonableness.

ARIMA. Another statistical technique with potential use as an analytical procedure is ARIMA. This method develops a model based on past data of the account under audit consideration. The model is developed by using patterns of the data within each year and patterns of the data over several years. It is generally suggested that a minimum of 50 observations be used in order to establish this pattern although limited research has indicated that use of fewer than 50 observations would still provide a useful model. Being a time series technique, AIRMA is more applicable to income statement accounts.

X-11 Model. The X-11 model has been suggested as a potential analytical procedure for auditing theory and practice. The model statistically decomposes a time series of data into three components (trend-cyle, seasonal and irregular), each of which possesses an underlying economic interepretation. The trend-cycle component includes the long-term trend inherent in the series and any effects of the business cycle on the data. The seasonal component reflects an intrayear pattern of variation that is repeated consistently from year to year. The irregular component consists of residual variations in the data that reflect any random or unexplained events in the time series. Accordingly, the X-11 model may be used to decompose a time series and to determine the relative (i.e., percentage) contribution of the trend-cycle, seasonal and irregular components to changes that occur in the series.

The time series decomposed would be the balance of the account under the audit consideration for prior periods. Since this procedure deals with account balances overtime, the X-11 model is more applicable to income statement accounts.

Computer software is available for these statistical models. Although training is necessary in order to interpret results or to identify when use of the models may not provide good results, these methods are viable alternatives to less sophisticated analytical procedures.

Efficiency and Effectiveness

The auditor is interested in developing models which will provide accurate predictions. As the predicted amounts become more precise, the range of expected differences between actual and expected amounts becomes narrower and the more likely significant differences are due to misstatements in the account balance. Numerous research studies have been performed evaluating the relative predictive abilities of various analytical procedures. Simple ratios and trends have been acceptable analytical procedures over the years, but recent research revealed a change in the use of analytical procedures toward the use of quantitative procedures. The results of a questionnaire showed an overall increase in the use of analytical procedures in audits and suggested an increase in the use of quantitative procedures with a corresponding decrease in the use of nonquantitative procedures. Other researchers have suggested that two statistical procedures, regression analysis and autoregressive integrated moving average (ARIMA), were superior in predictive ability to simpler nonquantitative techniques.

Auditors are also interested in the model's ability to detect material misstatements. When the auditor uses analytical procedures as substantive tests, he/she is exposed to two potential errors. An incorrect rejection (Type I error) occurs when the model signals an account balance as having a material misstatement when, in fact, the account balance is correctly stated. An incorrect acceptance (Type II error) occurs when the model indicates that the account balance is correctly stated when, in fact, a material error exists in the account balance. If an auditor commits a Type I error, he/she will spend unnecessary additional audit time on an account that is correctly stated. This will result in additional audit costs. If an auditor commits a Type II error, he/she will sign a statement attesting to the account balances as fairly presented with no material misstatement when, in fact, material misstatement exists. A lawsuit against the auditor potentially exists if this material misstatement is later uncovered. So the auditor desires a low Type I error rate (efficiency) and a low Type II error rate (effectiveness). Since a lawsuit causes Potentially higher costs with both liability costs and loss of image for the firm, auditors are probably more concerned with effectiveness.

Research has shown that nonstatistical as well as statistical analytical procedures increased audit effectiveness relative to an audit strategy that did not use analytical procedures. However, additional research testing three types of models commonly used in practice (trend analysis, ratio models and regression models) with simulated data indicates that statistical models are more efficient and effective than the nonstatistical methods. Many of the nonstatistical techniques had high levels of Type I and Type II errors. Subsequent research with actual data has supported those results by indicating that statistically oriented models and decision rules are more effective than nonstatistical approaches and that the regression and X-11 models dominate the naive methods.

Conclusion

The issuance of Statement on Auditing Standards No. 56 - Analytical Procedures has placed greater emphasis on the use of analytical procedures by auditors. The use of analytical procedures with tests of details provides the auditor with evidence to draw audit conclusions. The more reliance an auditor can place on analytica procedures, the less time he needs to spend on tests of details.

There is no given list of acceptable techniques. Analytical procedures include any method an auditor can develop to help predict account balances which are unusual. However, analytical procedures generally fall into four groups:

1. Trend analysis

2. Reasonable tests,

3. Ratio analysis, and

4. Structural models.

Although most of the procedures used will supply the auditor with some helpful information, research over the past few years has shown statitical models to be more efficient and effective.

Arlette C. Wilson, Phd, CPA, CMA, CIA, is associate professor of accounting at Auburn University, Alabama. She has published in various academic and practitioner journals.

Janet L. Colbert, Phd, CPA, CIA, is an associate professor of accounting at Auburn University, Alabama. She has worked in public accounting and in industry and has published in various accounting journals.

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Author: | Wilson, Arlette C.; Colbert, Janet L. |
---|---|

Publication: | The National Public Accountant |

Date: | May 1, 1991 |

Words: | 2265 |

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