Monetary unit sampling (MUS, also called dollar-unit or probability-proportional-to-size sampling) treats each dollar in the population as a sampling unit. Larger items are more likely to be selected, which fits tests for overstatement of balances such as receivables, inventory and fixed assets. This post runs one test from design through conclusion, with the arithmetic the reviewer will follow. See audit sampling methods for choosing between methods.
When MUS fits
MUS is efficient when you expect few misstatements and want to detect overstatement of recorded amounts. It selects large items automatically, needs no population standard deviation and is easy to document. It handles understatements poorly, since an understated item has a lower chance of selection, and it is awkward with zero or credit balances. If you expect a large amount of misstatement, the GAO Financial Audit Manual points to classical variables sampling, with an audit sampling specialist, instead of MUS.
Step 1: Set tolerable misstatement and the interval
Tolerable misstatement for the test is set from performance materiality for the account. The sampling interval is tolerable misstatement divided by the statistical risk factor for your assurance level and expected misstatement. The GAO manual's illustration uses performance materiality of $3 million, no expected misstatement and 95 percent assurance, and arrives at a sampling interval of $1 million, so the factor in that case is 3 (the Poisson value is 3.00 at 95 percent with no misstatements). The preliminary sample size is the population divided by the interval.
Our example: trade receivables of $4,800,000. Tolerable misstatement is $240,000. No expected misstatement, 95 percent assurance, factor 3.
- Sampling interval = $240,000 ÷ 3 = $80,000.
- Preliminary sample size = $4,800,000 ÷ $80,000 = 60 items.
Items larger than the interval are automatically selected, and a single large item can account for several "hits."
Step 2: Prepare the population
Obtain the aged receivables listing. Confirm completeness by tying it to the ledger total. Handle credit balances separately: test them as a separate population or stratum. Decide how to treat zero and negative items before selecting.
Step 3: Select with a random start
Choose a random start between 1 and 80,000, say 31,500. Accumulate the dollar amounts down the list. Each time the running total crosses the start or the start plus a multiple of the interval, the customer balance containing that dollar is selected.
| Cumulative balance | Customer | Balance | Selected? |
|---|---|---|---|
| 0 to 28,400 | Alder Supply | 28,400 | No |
| 28,400 to 61,900 | Birch Works | 33,500 | Yes (31,500 falls here) |
| 61,900 to 189,300 | Cedar Foods | 127,400 | Yes (111,500 falls here; the balance exceeds the interval, so it is selected for certain) |
| 189,300 to 205,000 | Dunn Tools | 15,700 | Yes (191,500 falls here) |
Any single balance of $80,000 or more is selected for certain, because the band it occupies is wider than the interval. Cedar Foods ($127,400) is one such item; report these as top-stratum items.
Step 4: Test each selected item
Send positive confirmations on the selected balances or perform alternative procedures: agree to invoices, shipping documents and subsequent cash receipts. See confirmation exceptions and alternative procedures for non-responses. Record the audited amount for each item and the misstatement, if any.
Step 5: Project the misstatements
The FAM shows the arithmetic. For a sample item with a recorded amount at or above the sampling interval, the projected misstatement equals the actual misstatement. For an item below the interval, the projected misstatement is the tainting (misstatement divided by recorded amount) multiplied by the sampling interval.
Illustration from the manual, sampling interval $300,000:
- A $50,000 misstatement in a $500,000 item: the item exceeds the interval, so projected misstatement is $50,000.
- A $100 misstatement in a $1,000 item: tainting 10 percent, projected misstatement is 10 percent of $300,000, which is $30,000.
- Aggregate projected misstatement: $80,000.
Our example results, interval $80,000:
| Item | Recorded | Audited | Misstatement | Tainting | Projected |
|---|---|---|---|---|---|
| Birch Works | 33,500 | 30,150 | 3,350 | 10% | 8,000 |
| Hemlock Co | 54,000 | 54,000 | 0 | 0 | 0 |
| Cedar Foods | 127,400 | 127,400 | 0 | 0 | 0 |
| Lark Partners | 22,000 | 17,600 | 4,400 | 20% | 16,000 |
| Others (56 items) | 0 | 0 | 0 | ||
| Total projected misstatement | 24,000 |
The projected misstatement is the best estimate of the overstatement of the population: $24,000, or 0.5 percent of the $4,800,000 balance.
Step 6: Compute the upper limit and conclude
The projected misstatement is only part of the picture. The upper limit adds an allowance for sampling risk, made of basic precision and incremental precision. Basic precision is the risk factor times the interval: 3.00 × $80,000 = $240,000, which equals tolerable misstatement because the sample was sized for zero expected misstatement.
Incremental precision applies to each misstatement found in an item below the interval. A common hand method is the Stringer bound with Poisson risk factors at 95 percent assurance: 3.00 for no misstatements, 4.75 for one and 6.30 for two. Rank the misstatements by tainting, largest first, and for each multiply its projected misstatement by the step in the factor less 1.
| Rank | Projected misstatement | Factor step | Step less 1 | Incremental precision |
|---|---|---|---|---|
| 1 (Lark, 20%) | 16,000 | 4.75 - 3.00 = 1.75 | 0.75 | 12,000 |
| 2 (Birch, 10%) | 8,000 | 6.30 - 4.75 = 1.55 | 0.55 | 4,400 |
Upper limit = projected misstatement $24,000 + basic precision $240,000 + incremental precision $16,400 = $280,400.
The upper limit exceeds tolerable misstatement of $240,000. An upper limit below tolerable misstatement supports the conclusion that the population is not misstated by more than tolerable misstatement at the desired confidence level. Here it does not, so the sample alone does not support the receivables balance. The auditor has three options: ask management to investigate and correct the pricing error across the population, perform additional procedures with a specialist, or conclude on a different basis. Do not add sample items and reuse the original table.
If the sample had many misstatements, bring in a sampling specialist rather than relying on this hand calculation.
Step 7: Carry the results forward
- Unless management books them, the misstatements go on the summary of uncorrected misstatements: $7,750 of factual misstatements (Birch $3,350 and Lark $4,400) and $16,250 of further projected misstatement, which together make the $24,000 projection. The FAM notes that management can book a projected misstatement through a general journal entry that reverses the following year.
- The upper limit goes into the audit exposure evaluation.
- Investigate the cause of each misstatement (here, assume a pricing error on two customer accounts) and whether it points to a control deficiency or to similar errors outside the sample.
Common mistakes
- Not reselecting after changing the population.
- Treating a nonresponse as correct.
- Netting understatements against overstatements in the projection.
- Ignoring items above the interval.
- Using the hand calculation on a sample that had many misstatements.
Documentation checklist
- Objective, population definition and tie to the ledger.
- Tolerable misstatement, risk factor, interval and sample size.
- Random start and selection listing.
- Results with tainting and projection.
- Upper limit calculation or software output.
- Conclusion and link to the summary of uncorrected misstatements.
CORAA prepares ready-to-review audit files for US CPA firms; the firm keeps the client, the review and the signature. See /us.
Sources
- AICPA, AU-C Section 530, Audit Sampling; AU-C Section 450, Evaluation of Misstatements Identified During the Audit
- U.S. Government Accountability Office, Financial Audit Manual, Volume 1 (GAO-26-108577), June 2026, sections 295 C, 480 and 495 D (sampling interval, projected misstatement for monetary unit samples): gao.gov
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