The MUS formula and the factors behind it
AU-C 530 leaves the sampling method to the auditor. The AICPA Audit Guide Audit Sampling sets out the formula approach used here: n = BV × RF ÷ (TM − EM × EF), where BV is the population book value, RF the reliability factor, TM tolerable misstatement, EM expected misstatement and EF the expansion factor. The sampling interval is (TM − EM × EF) ÷ RF.
The reliability factor is the Poisson upper limit for zero misstatements at the chosen confidence: 3.00 at 95%. Expansion factors come from Appendix C of the guide: 1.90 at 1% risk of incorrect acceptance, 1.60 at 5%, 1.50 at 10%, 1.40 at 15%, 1.30 at 20%, 1.25 at 25%, 1.20 at 30%, 1.15 at 37% and 1.10 at 50%.
Evaluating misstatements
Each overstatement found is expressed as a tainting (misstatement ÷ book value) and projected over the interval. The upper misstatement limit adds basic precision (RF × interval), the projected misstatement and an incremental allowance that weights each tainting, largest first, by the step in the Poisson factor. If the upper limit is within tolerable misstatement, the sample supports the recorded balance. Carry the projected amount to the summary of uncorrected misstatements (AU-C 450).
Common questions
What is monetary unit sampling?
Monetary unit sampling (MUS), also called probability-proportional-to-size (PPS) sampling, treats each dollar in a population as a sampling unit. Larger items are more likely to be selected, which suits tests for overstatement of balances such as receivables or inventory.
How is the MUS sample size calculated?
Sample size = population book value × reliability factor ÷ (tolerable misstatement − expected misstatement × expansion factor). With no expected misstatement at 95% confidence the reliability factor is 3.00, so a $1,000,000 population with $50,000 tolerable misstatement needs 60 items.
What is the reliability factor for 95% confidence?
For zero expected misstatements it is 3.00 (the Poisson factor, −ln 0.05 = 2.996, rounded up). It is 2.31 at 90% and 4.61 at 99%. The factors rise with each misstatement found: 4.75 for one and 6.30 for two at 95%.
How do I select items using the sampling interval?
Pick a random start between $1 and the interval, then select the item containing every interval-th dollar through the cumulative balance. Any item larger than the interval is selected with certainty and evaluated as a top stratum.
When is MUS a poor choice?
When understatement is the main risk (zero or small balances have little chance of selection), when many misstatements are expected (the bound becomes conservative and samples balloon), or when the population has many negative or zero balances that need separate treatment.
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