Auditing & Assurance Services, 6e

1. Auditing & Assurance Services, 6e

2. 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

3. 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

4. Effect of Factors on Sample Size

5. 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

6. 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

7. MUS: Measuring Sample Items

8. 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

9. 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)

10. 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 >

11. 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

12. 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

13. 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

14. Sampling Methods

15. 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