In this chapter, the learning objectives are Understand the similarities and differences between audit sampling for tests of controls and substantive tests of details of account balances, learn to apply monetaryunit sampling, work through an extended example of monetary unit sampling,…
Chapter Nine Audit Sampling: An Application to Substantive Tests of Account Balances McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Substantive Tests of Details of Account Balances The statistical concepts we discussed in the last chapter apply to this chapter as well Three important determinants of sample size are: Desired confidence level Tolerable misstatement Expected misstatement Population plays a bigger role in some of the sampling techniques used for substantive testing Misstatements discovered in the audit sample must be projected to the population, and there must be an allowance for sampling risk McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Substantive Tests of Details of Account Balances Consider the following information about the inventory account balance of an audit client: Book value of inventory account balance Book value of items sampled € 3,000,000 € 100,000 Audited value of items sampled 98,000 Total amount of overstatement observed in audit sample € 2,000 The ratio of misstatement in the sample is 2% (€2,000 ÷ €100,000) Applying the ratio to the entire population produces a best estimate of misstatement of inventory of €60,000 (€3,000,000 × 2%) McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Substantive Tests of Details of Account Balances The results of our audit test depend upon the tolerable misstatement associated with the inventory account If the tolerable misstatement is €50,000, we cannot conclude that the account is fairly stated because our best estimate of the projected misstatement is greater than the tolerable misstatement McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Monetary-Unit Sampling (MUS) MUS MUS uses uses attribute-sampling attribute-sampling theory theory to to express express aa conclusion conclusion in in monetary monetary amounts amounts (e.g (e.g in in euros euros or or other other currency) currency) rather rather than than as as aa rate rate of of occurrence occurrence ItIt is is commonly commonly used used by by auditors auditors to to test test accounts accounts such such as as accounts accounts receivable, receivable, loans loans receivable, receivable, investment investment securities securities and and inventory inventory McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Monetary-Unit Sampling (MUS) MUS uses attribute-sampling theory (used primarily to test controls) to estimate the percentage of monetary units in a population that might be misstated and then multiplies this percentage by an estimate of how much the euros are misstated McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Monetary-Unit Sampling (MUS) Advantages of MUS When the auditor expects no misstatement, MUS usually results in a smaller sample size than classical variables sampling The calculation of the sample size and evaluation of the sample results are not based on the variation between items in the population When applied using the probabilityproportional-to-size procedure, MUS automatically results in a stratified sample McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Monetary-Unit Sampling (MUS) Disadvantages of MUS The selection of zero or negative balances generally requires special design consideration The general approach to MUS assumes that the audited amount of the sample item is not in error by more than 100% When more than one or two misstatements are detected, the sample results calculations may overstate the allowance for sampling risk McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Steps in MUS Sampling McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Steps in MUS Sampling Sampling may be used for substantive testing to: Test the reasonableness of assertions about a financial statement amount (i.e is the amount fairly stated) This is the most common use of sampling for substantive testing Develop an estimate of some amount McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Why Did Statistical Sampling Fall Out Of Favour? 1.Firms found that some auditors were over relying on statistical sampling techniques to the exclusion of good judgement 2.There appears to be poor linkage between the applied audit setting and traditional statistical sampling applications McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Classical Variables Sampling Classical variables sampling uses normal distribution theory to evaluate the characteristics of a population based on sample data Auditors most commonly use classical variables sampling to estimate the size of misstatement Sampling distributions are formed by plotting the projected misstatements yielded by an infinite number of audit samples of the same size taken from the same underlying population McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Classical Variables Sampling A sampling distribution is useful because it allows us to estimate the probability of observing any single sample result In classical variables sampling, the sample mean is the best estimate of the population mean McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Classical Variables Sampling Advantages When the auditor expects a relatively large number of differences between book and audited values, this method will normally result in smaller sample size than MUS The techniques are effective for both overstatements and understatements The selection of zero balances generally does not require special sample design considerations McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Classical Variables Sampling Disadvantages Does not work well when little or no misstatement is expected in the population To determine sample size, the auditor must estimate the standard deviation of the audit differences If few misstatements are detected in the sample data, the true variance tends to be underestimated, and the resulting projection of the misstatements and the related confidence limits are not likely to be reliable McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Applying Classical Variables Sampling Defining the Sampling Unit The sampling unit can be a customer account, an individual transaction, or a line item In auditing accounts receivable, the auditor can define the sampling unit to be a customer’s account balance or an individual sales invoice included in the account balance McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Applying Classical Variables Sampling Determining the Sample Size Sample = Size Population size (in sampling units) × CC × SD Tolerable misstatement – Estimated misstatement where CC = Confidence coefficient SD = Estimated standard deviation of audit differences McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Applying Classical Variables Sampling The Confidence Coefficient (CC) is associated with the desired level of confidence The desired level of confidence is the complement of the risk that the auditor will mistakenly accept a population as fairly stated when the true population misstatement is greater than tolerable misstatement McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Applying Classical Variables Sampling The year-end balance for accounts receivable contains 5,500 accounts with a book value of €5,500,000 The tolerable misstatement for accounts receivable is set at €50,000 The expected misstatement has been judged to be €20,000 The desired confidence is 95% Based on work completed last year, the auditor estimates the standard deviation at €31 calculate sample size Sample Let’s 5,500 × 1.96 × €31 = 125 = Size €50,000 – €20,000 McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Applying Classical Variables Sampling Calculating the Sample Results The sample selection usually relies on random-selection techniques Upon completion, 30 of the customer accounts selected contained misstatements that totalled €330.20 Our first calculation is the mean misstatement in an individual account which is calculated as follows: Mean Total audit difference misstatement = Sample size per sampling item €2.65 = €330.20 125 McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Applying Classical Variables Sampling The mean misstatement must be projected to the population Projected population =Population size × Mean misstatement (in sampling per sampling item misstatement units) 14,575 McGraw-Hill/Irwin = 5,500 â The McGraw-Hill Companies 2010 ì €2.65 Applying Classical Variables Sampling The formula for the standard deviation is SD = Sample Mean difference Total squared – Size ×per sampling item2 audit differences Sample size – = McGraw-Hill/Irwin €36,018.32 – (125 × 2.652) = €16.83 125 – © The McGraw-Hill Companies 2010 Applying Classical Variables Sampling Confidence bound €16,228 = Population size SD × CC × Sample size €16.83 = 5,500 × 1.96 × √ 125 Confidence = interval Projected misstatement ± = €14,575 ± €16,228 McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Confidence bound Applying Classical Variables Sampling Lower Projected Upper limit misstatement limit (€1,653) (€50,000) €14,575 €0 €30,803 €50,000 Tolerable Misstatement If both limits are within the bounds of tolerable misstatement, the evidence supports the conclusion that the account is not materially misstated McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 End of Chapter McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 ... unit can be a customer account, an individual transaction, or a line item In auditing accounts receivable, the auditor can define the sampling unit to be a customer’s account balance or an individual... inventory account balance of an audit client: Book value of inventory account balance Book value of items sampled € 3,000,000 € 100,000 Audited value of items sampled 98 ,000 Total amount of overstatement... McGraw-Hill Companies 2010 Substantive Tests of Details of Account Balances The results of our audit test depend upon the tolerable misstatement associated with the inventory account If the tolerable