4.3 Analytical Procedures, Trend Analysis & Audit Sampling

Analytical Procedures, Trend Analysis & Audit Sampling

1. Substantive Analytical Procedures (ISA 520)

Under ISA 520 (Analytical Procedures), analytical procedures consist of evaluations of financial information through analysis of plausible relationships among both financial data (e.g., revenue, gross margin, operating expenses) and non-financial data (e.g., headcount, square footage of retail space, volume of goods produced).

Analytical procedures also encompass investigating identified fluctuations or relationships that are inconsistent with other relevant information or that differ from expected values by a significant amount.

The Three Stages of Analytical Procedures in an Audit

ISA standards mandate or permit analytical procedures at three distinct stages of an audit engagement:

1. Planning / Risk Assessment Stage (Mandatory under ISA 315): Used to gain an understanding of the entity and its environment, and to identify areas of unusual transactions or high risk of material misstatement.
2. Substantive Testing Stage (Optional under ISA 520): Used as a substantive procedure to obtain evidence regarding specific assertions when analytical procedures are more efficient and effective than tests of details.
3. Final Overall Review Stage (Mandatory under ISA 520): Formulating an overall conclusion near the end of the audit as to whether the financial statements are consistent with the auditor's understanding of the entity.

Four Primary Analytical Techniques

• Trend Analysis: Examining changes in account balances over time (e.g., comparing monthly sales revenue across the current and preceding 3 years).
• Ratio Analysis: Analyzing relationships between financial statement line items (e.g., Gross Profit Margin, Current Ratio, Inventory Turnover Days, Receivables Collection Period).
• Reasonableness Testing: Modeling expected financial results based on non-financial metrics (e.g., multiplying room count × average occupancy rate × average daily room rate to project hotel room revenue).
• Structural / Regression Analysis: Using statistical models to evaluate relationships between key economic variables and financial performance.

Factors Governing Suitability of Substantive Analytics

When designing substantive analytical procedures, the auditor must evaluate:

• Predictability of the Relationship: Income statement accounts (routine transactions) are generally more predictable than balance sheet accounts (point-in-time balances).
• Availability and Reliability of Data: Data from independent external sources or generated under effective internal controls is more reliable.
• Precision of Expectations: Finer expectations (e.g., monthly broken down by division) yield more precise results than broad annual aggregates.
• Tolerable Misstatement: The threshold of acceptable variance established by the auditor.

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2. Audit Sampling Fundamentals (ISA 530)

ISA 530 (Audit Sampling) applies when the auditor decides to use audit sampling in performing audit procedures. Audit sampling is defined as the application of audit procedures to less than 100% of items within a population of audit relevance such that all sampling units have a chance of selection in order to provide the auditor with a reasonable basis on which to draw conclusions about the entire population.

Testing Strategies: 100% Examination vs. Specific Item Selection vs. Sampling

• 100% Examination: Appropriate for small populations of high-value items or when risk is extremely high and automated testing allows complete coverage.
• Selecting Specific Items: Testing items over a specific monetary threshold (e.g., all items > BDT 1,000,000) or key high-risk items. Note: Selecting specific items is NOT audit sampling, because unselected items have zero chance of selection and conclusions cannot be projected to the remainder of the population.
• Audit Sampling: Used when the auditor intends to draw inferences about the whole population from a representative sample.

Sampling Risk vs. Non-Sampling Risk

Detection Risk is affected by:  Sampling Risk  +  Non-Sampling Risk
(Audit Risk = Inherent Risk x Control Risk x Detection Risk)

Note the relationship carefully: sampling risk and non-sampling risk are the two sources of detection risk — the risk that the auditor's procedures fail to detect a misstatement that exists. They are not additional components of audit risk alongside inherent and control risk.

• Sampling Risk: The risk that the auditor's conclusion based on a sample may be different from the conclusion if the entire population were subjected to the same procedure. Sampling risk gives rise to two types of erroneous conclusions:
  • Type I Error (Risk of Incorrect Rejection / Under-Reliance): Concluding controls are less effective or balances are materially misstated when they are not. Affects audit efficiency (causes unnecessary work).
  • Type II Error (Risk of Incorrect Acceptance / Over-Reliance): Concluding controls are more effective or balances are not materially misstated when they are in fact misstated. Affects audit effectiveness and leads to an inappropriate audit opinion!
• Non-Sampling Risk: The risk that the auditor reaches an erroneous conclusion for any reason not related to sampling risk (e.g., using inappropriate audit procedures, misinterpreting evidence, or failing to recognize a misstatement).

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3. Statistical vs. Non-Statistical Sampling

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4. Sample Selection Methods under ISA 530

Auditors must select items for the sample in such a way that each sampling unit in the population has a chance of selection. Key methods include:

1. Random Selection: Applied through random number generators or tables (ensures every item has equal selection probability).
2. Systematic Selection: The number of sampling units in the population is divided by the sample size to give a sampling interval ($I = N / n$). Starting point is selected randomly within the first interval. $\text{Sampling Interval } (I) = \frac{\text{Total Population Units } (N)}{\text{Target Sample Size } (n)}$
3. Monetary Unit Sampling (MUS) / Value-Weighted Selection: A statistical sampling method where sample selection, amount, and evaluation result in a conclusion expressed in monetary amounts. Larger monetary items have a higher probability of selection.
4. Haphazard Selection: The auditor selects the sample without following a structured technique, but avoiding deliberate bias or predictability. (Cannot be used in statistical sampling!).
5. Block Selection: Involves selecting contiguous items from within a population. Block selection is rarely appropriate in audit sampling because items in a block tend to share similar characteristics.

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5. Projecting Sample Misstatements & Evaluating Results

When substantive audit sampling reveals misstatements, ISA 530 requires the auditor to project the sample misstatements to the population to obtain a broad view of the scale of misstatement.

Projection Formula for Ratio Method

$\text{Projected Misstatement} = \text{Sample Monetary Misstatement} \times \left( \frac{\text{Total Population Value}}{\text{Total Sample Value}} \right)$

Worked Example:
An auditor samples trade receivables with a total population book value of BDT 10,000,000.

• Sample size book value = BDT 2,000,000 (20% of population value).
• Audit testing reveals monetary errors in the sample totaling BDT 50,000.
• Projected Misstatement = BDT 50,000 × (BDT 10,000,000 / BDT 2,000,000) = BDT 250,000.

If the total projected misstatement (plus any anomalous misstatements) exceeds tolerable misstatement, the sample does not provide a reasonable basis for conclusions about the population, and the auditor must request management to investigate, perform additional audit procedures, or adjust the accounting records.