Question

What is MUS? What steps do auditors follow to execute a MUS? How does an auditor evaluate the results of a MUS? What issues should auditors address before concluding that the auditee’s balances are misstated?

Answer 1

What is MUS? What steps do auditors follow to execute a MUS?

Monetary-unit sampling (MUS) is a method of statistical sampling used to assess the amount of monetary misstatement that may exist in an account balance. The method, also known as dollar-unit sampling or probability-proportional-to-size sampling, has been used for many years and is widely accepted among auditors.In the MUS approach, the underlying idea is to treat the population as consisting of individual dollars, each of which may or may not be misstated. It is, therefore, essentially an attribute sampling application. Its use in practice is nevertheless subject to a wide range of variants.

Suppose that an invoice for $1,000 is selected for audit by virtue of its 750th dollar being randomly selected, and that the audited value of the invoice turns out to be only $800; i.e..., there is a $200 overstatement. In original formulation, for example, the 200 overstated dollars might be allocated to be the first $200 dollars of the invoice, or the final $200; depending on this choice, the 750th dollar may be classified as overstated or not. This leads to obviously undesirable variability in audit applications and proposed instead that each of the 1000 dollars in the invoice be considered as 20% overstated.

Using MUS involves three key steps:

• Determining the proper sample size;
• Selecting the sample and performing the audit procedures; and
• Evaluating the results and arriving at a conclusion about the recorded population value.

1. Determining the proper sample size;

Although MUS is used for variables sampling, it is actually based on attribute sampling techniques. Attribute sampling is often used for tests of controls and is most appropriate when each sample item can be placed into one of two classifications: “exception” or “no exception.” When a monetary balance is the object of interest, however, there are varying degrees of exceptions; for example, the balance of a $5,000 receivable may be overstated by $50, $500, or even $5,000. An auditor is obviously more concerned with larger misstatements. There are mainly four inputs are required to determine the sample size,the first two are discussed together ;

• Population dollar value and tolerable misstatement. The population dollar value is the amount recorded on the books for the account being audited. Tolerable misstatement is the maximum monetary misstatement in an account balance that can exist, when combined with misstatement in other accounts, without causing the financial statements to be materially misstated.The actual input needed to determine the sample size is the tolerable rate of misstatement (TR), which equals the tolerable misstatement divided by the population dollar value. Because tolerable misstatement is usually expressed as a dollar amount.There is an inverse relationship between TR and required sample size.
• Expected population exception rate (EPER). EPER is the exception rate anticipated to exist in the population. For example, if the auditor uses 2% for EPER and the recorded population value is $100,000, the implication is that the auditor expects the recorded value to be misstated by $2,000. If the auditor’s estimate of the expected misstatement is a dollar amount, it should be converted to a percentage. EPER is directly related to sample size and must be significantly less than TR. As EPER approaches TR, the sample size will become prohibitively large.Determining EPER requires auditor judgment. In making this estimate, the auditor might consider prior audit findings, recent changes in client personnel, or other information that might shed light on the likelihood of misstatement. If no misstatement is expected, zero may be used. To allow a margin for error, using some small value for EPER might be prudent even if no misstatement is expected.
• Acceptable risk of incorrect acceptance (ARIA). ARIA is the maximum risk the auditor is willing to accept of incorrectly concluding that the population is not materially misstated when, in fact, the true misstatement in the population exceeds tolerable misstatement. Although ARIA should be set at a low level, the exact value used may be affected by several factors, including overall acceptable audit risk and the results of tests of controls and other substantive tests (e.g.., analytical procedures) performed on the account.There is an inverse relationship between ARIA and required sample size.

Selecting the sample and performing the audit procedures

•Use systematic random sampling

•Calculate sampling interval as:

•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

Evaluating the results and arriving at a conclusion about the recorded population value.

•Determine the upper limit on misstatements which has a (1 – Risk of incorrect acceptance) of equaling or exceeding the true amount of misstatement.The various components of misstatements are;

–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 * Taintiong %

•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 * Confidence Factor

Evaluating Sample Results
Projected Misstatement	$ XX,XXX
Incremental allowance for sampling risk	XX,XXX
Basic allowance for sampling risk	XX,XXX
Upper limit on misstatements	$ XXX,XXX

if Uppper limit on misstatement is less than or equal to Tolerable Misstatement , " The account balance is not misstated"

if Uppper limit on misstatement is greater than or equal to Tolerable Misstatement , " The account balance is misstated"

What issues should auditors address before concluding that the auditee’s balances are misstated?

•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