Auditing & Assurance Services, 6e

Auditing & Assurance Services, 6e

Variables Sampling USA Today has come out with a new survey – apparently, three out of every four people make up 75 percent of the population. David Letterman, American comedian and television host Module G

Module G Objectives • Define variables sampling and understand when it is used in the audit. • Understand the basic process underlying monetary unit sampling (MUS) and when to use it. • Identify the factors affecting the size of an MUS sample and calculate the sample size for an MUS application. • Evaluate the sample results for an MUS by calculating the projected misstatement, incremental allowance for sampling risk, and basic allowance for sampling risk. • Understand the basic process underlying classical variables sampling and the use of classical variables sampling in the audit. • Understand the use of nonstatistical sampling for variables sampling.

Variables Sampling • Variables sampling is used to estimate the amount (or value) of a population • Substantive procedures • Estimate account balance or misstatement • Compare estimated account balance or misstatement to recorded amount or tolerable misstatement • Approaches • Monetary unit sampling (MUS) • Classical variables sampling

Major Topics • Monetary Unit Sampling (MUS) • Basics of MUS • Determining Sample Size • Selecting and Measuring Sample Items • Evaluating Sample Results • Classical Variables Sampling • Nonstatistical Sampling

Monetary Unit Sampling (MUS) • Defines the sampling unit as an individual dollar (or other monetary unit) in an account balance • Auditor will select individual dollars (or monetary units) for examination • Auditor will verify the entire “logical unit” containing the selected dollar (or monetary unit) • Accounts receivable: Customer account • Inventory: Inventory item

Advantages of MUS • Results in more efficient (smaller) sample sizes • Selects transactions or components reflecting larger dollar amounts • Effective in identifying overstatement errors • Asset and revenue accounts • Generally simpler to use than classical variables sampling

Disadvantages of MUS • Provides a conservative (higher) estimate of misstatement • Not effective for understatement or omission errors • Liabilities and expenses • Expanding sample is difficult if initial conclusion is to reject the account balance • Requires special consideration for accounts with zero or negative balances

Effect of Factors on Sample Size

Summary: Sampling Risks Under Variables Sampling Decision Based on Population Decision Based on Sample AM = Actual misstatement TM = Tolerable misstatement ULM = Upper limit on misstatements

Using MUS Tables • See Exhibit G.2 for Sample Size Table • Inputs • Risk of incorrect acceptance • Expected misstatement • Tolerable misstatement • Population size

Example • Parameters • Risk of incorrect acceptance = 5% • Expected misstatement = $100,000 • Tolerable misstatement = $500,000 • Population size = $1,000,000 • Calculations • Ratio of expected to tolerable misstatement: $100,000 ÷ $500,000 = 0.20 • Tolerable misstatement as a percentage of population: $500,000 ÷ $1,000,000 = 50%

Step 3: Select column for TM as % of population = 50% Step 1: Select entries for risk of incorrect acceptance = 5% Step 4: Read sample size at junction of row and column Step 2: Select row for ratio of EM to TM = 0.20

MUS: Selecting Sample Items • Use systematic random sampling • Calculate sampling interval as: Population size ÷ Sample size • Process • Identify random start • Skip number of items equal to sampling interval • Select item (dollar in account) and examine entire logical unit containing that item (customer account) • May select same logical unit multiple times

MUS: Measuring Sample Items

MUS: Evaluating Sample Results • Determine the upper limit on misstatements, which has a (1 – Risk of incorrect acceptance) of equaling or exceeding the true amount of misstatement • Components: • Projected misstatement • Incremental allowance for sampling risk • Basic allowance for sampling risk

Projected Misstatement • Assumes entire sampling interval contains same percentage of misstatement as the logical unit examined by auditors • Calculated for each misstatement as: Sampling interval x Tainting % • Do not project misstatements if the logical unit > sampling interval

Incremental Allowance for Sampling Risk • Adjusts the projected misstatement to control exposure to risk of incorrect acceptance • Allows for the possibility that the remainder of the sampling interval might be misstated by a higher percentage than the logical unit • Procedure: • Rank all projected misstatements in descending order • Determine incremental confidence factor for each misstatement • Multiply projected misstatement by (incremental confidence factor – 1)

Basic Allowance for Sampling Risk • Provides a measure of the misstatement that might exist in sampling intervals in which a misstatement was not detected • Calculated as: Sampling interval x Confidence factor

MUS: Evaluating Sample Results 1 2 3

Upper Limit on Misstatements • If ULM = $50,000 and risk of incorrect acceptance = 5% $50,000 $0 95% probability (1 – risk of incorrect acceptance) 5% probability (risk of incorrect acceptance)

MUS: Making the Decision Upper Limit on Misstatement Tolerable Misstatement Account balance is not misstated ≤ Account balance is misstated Upper Limit on Misstatement Tolerable Misstatement >

Decisions under MUS • Account balance is not misstated • Suggest correction of identified misstatements • Investigate cause of misstatements • Account balance is misstated • Increase sample size to attempt and reduce upper limit on misstatements • Recommend adjustment to reduce misstatement below tolerable misstatement

Classical Variables Sampling • Uses normal distribution theory and the central limit theorem to provide an estimated range of • Recorded account balance or class of transactions • Misstatement in an account balance or class of transactions • Basic methodology • Determine estimated range of account balance or misstatement • Evaluate using tolerable misstatement

Additional Considerations in Classical Variables Sampling • Consider the following additional factors in determining sample size • Risk of incorrect rejection • Population variability • To reduce population variability, auditors may choose to stratify the population

Example • Assume • Recorded balance = $300,000 • Tolerable misstatement = $10,000 • Estimated balance = $292,500 • Precision = $2,275 • Risk of incorrect acceptance = 10% • Risk of incorrect rejection = 15%

Example (continued) • Estimate ± Precision $292,500 ± $2,275 = $290,225 to $294,775 $290,225 $294,775 $300,000 90% probability of including true recorded balance Difference between recorded balance and far end of interval < Tolerable misstatement

Classical Variables Sampling Approaches • Mean-per-unit: • Assumes each item in population (component of account) has similar balance • Estimates recorded balance by multiplying number of components by average audited value • Difference estimation: • Assumes each item in population (component of account) has similar difference between recorded and audited value • Estimates the amount of misstatement by multiplying number of components by average misstatement • Estimates recorded balance using estimated misstatement • Ratio estimation: • Assumes a constant percentage misstatement in population • Estimates recorded balance by multiplying recorded balance by ratio of audited value to recorded balance

Sampling Methods

Nonstatistical Sampling • Permissible under GAAS • Does not permit auditors to control exposure to sampling risk • Major differences in: • Determining sample size • Selecting sample items • Evaluating sample results

Auditing & Assurance Services, 6e