When using monetary unit sampling reliability factors are used in calculating

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MUS provides a conclusion in terms of monetary value i.e. “Based on the sample results, the amount of misstatement in the account balance would not exceed $X (tolerable misstatement). It is used in auditing for “substantive tests” of account balances (e.g. accounts receivable, investments, inventory) to determine if the financial statements are fairly stated.

The development of MUS was pioneered in the early 1960’s by Kenneth W. Stringer of Haskins & Sells with Frederick F. Stephan (Professor of Statistics) Princeton University.

Determine MUS sample size

The sample size can be determined by using MUS sample size tables (e.g. AICPA tables) or statistical audit software. The inputs required are:

• Population Value (PV): the book value or monetary value of the population.
• Expected Misstatement (EM): the expected amount of misstatement in the population.
• Tolerable Misstatement (TM): the maximum amount of misstatement that can be accepted in the population (margin of error).
• Confidence Level (CL): the desired level of assurance (complement of risk of incorrect acceptance). High (90-95%), moderate (80-86%), low (50-75%).

Example:
PV=94,613,131  EM=300,000  TM=3,000,000  CL=75%

• Determine the Confidence Factor from the MUS sampling table below:
  ⇒ Ratio of Expected-to-Tolerable Misstatement (EM/TM) = 0.10
  ⇒ Match to the Confidence Level of 75% (i.e. 25% Risk of Incorrect Acceptance)
  ⇒ Confidence Factor = 1.61

• Calculate the sample size using the MUS formula:
  ⇒ Confidence Factor / Tolerable Misstatement Rate
  ⇒ 1.61 / (3,000,000/94,613,131)
  ⇒ 1.61 / 0.0317
  ⇒ n= 51

If statistical audit software is used (e.g. AuditSampler), the confidence factor for the MUS sample size calculation would be computed numerically based on the Poisson Distribution.

Select Sample Items

Samples are selected from the population based on a sampling interval which is obtained by dividing the population value with the sample size. The samples are selected by cumulatively adding the sampling interval to pick every nth dollar unit in the population after an initial random start. The random start would be a value between $1 and the sampling interval.

• Any amount larger than the sampling interval is selected at least once and very large amounts may be selected more than once. Therefore, the number of sampled records may be less than the sample size.

For example, if the population value is $94,613,131 and the required sample size is 51, the sampling interval would be $1,855,159 (i.e. 94,613,131/51). Each amount in the population is added to a “cumulative total”. The amount which causes the cumulative total to equal or exceed the random start ($668,048) is selected as the first sample. The remaining samples are selected from subsequent amounts which cause the cumulative total to equal or exceed each increment of the sampling interval (i.e. $2,523,207; $4,378,366; $6,233,525 etc).

• Zero and Negative value amounts are not included in the cumulative total and would not be selected. The auditor may choose to review these items separately.

Evaluate Sample Results

Sample results are evaluated by comparing the Upper Misstatement Bound (UMB) and Lower Misstatement Bound (LMB) to the tolerable misstatement (TM). The upper and lower misstatement bounds equals the upper error limit for overstatements and understatements¹.

• If UMB and LMB ≤ TM, the sample results indicate that the account balance is not materially misstated.

• If UMB or LMB > TM, the sample results indicate that the account balance is materially misstated.

In the evaluation above three (3) overstatements were detected in the sample, LMB = $1,863,878 and UMB = $3,473,238. As the upper misstatement bound exceeds the tolerable misstatement by $473,238 (i.e. 3,473,238 – 3,000,000), there is risk that the account balance is materially misstated (overstated).

In evaluating the sample results, the preliminary assessment of risks may need to be revised upward if misstatements are detected. The auditor may need to increase the sample size and re-evaluate the results.

What is monetary unit sampling used for?

Which of the following factors would indicate that monetary unit sampling should be used rather than other statistical sampling techniques?

When using monetary unit sampling is the recorded Dollar population?

What is the advantage of monetary unit sampling relative to random sampling?