Monetary unit sampling for tests of details

In this lesson you will

Compute a monetary unit sample size and sampling interval.
Select a sample using systematic probability-proportional-to-size selection.
Compute projected misstatement and the upper misstatement limit.
Identify when monetary unit sampling is a poor fit.

What it is

Monetary unit sampling (MUS) treats each dollar in a population as a sampling unit. AU-C 530.A5 notes sampling units can be monetary units, and AU-C 530.A16 lists probability-weighted selection, including monetary unit selection, as a random selection technique. Larger items have a higher chance of selection, which concentrates testing where dollars are.

When it fits

MUS works well for testing overstatement, such as existence of receivables or occurrence of revenue, when few misstatements are expected. It is weak for:

understatement, because unrecorded or understated items have few or no dollars to be selected;
zero and negative balances, which need separate treatment; and
populations with many expected misstatements, where the upper limit grows quickly.

Sample size

Statistical MUS uses Poisson-based confidence factors. For zero expected misstatement, the factor at a given risk of incorrect acceptance is the negative natural log of the risk. At 5% risk, that is about 3.0.

Sample size = (population book value x confidence factor) / tolerable misstatement.

When you expect some misstatement, the formula reduces the denominator by an allowance for expected misstatement, using an expansion factor published in sampling tables such as those in the AICPA Audit Guide Audit Sampling. The MUS calculator handles that case.

Sampling interval = book value / sample size.

AU-C 530.A13 lists the same inputs for tests of details: desired assurance, tolerable misstatement, expected misstatement, stratification and, for some methods, the number of sampling units in each stratum.

Selection

Use systematic selection with a random start between 1 and the interval. Every item larger than the interval is certain to be selected; treat those as key items and evaluate them separately. AU-C 530.A8 points to AU-C 500.08: you must obtain evidence that the population is complete before you select.

Evaluation

For each misstatement in an item smaller than the interval:

Tainting = misstatement / book value of the item.
Projected misstatement = tainting x sampling interval.

Items at or above the interval are not projected; their actual misstatement is added.

The upper misstatement limit adds three parts:

Basic precision = confidence factor for zero misstatements x interval.
Projected misstatement, summed.
Incremental allowance: for the misstatements, ranked by tainting from largest, each one's projected misstatement multiplied by the increase in the confidence factor at that rank minus 1. At 5% risk, the Poisson factor for one misstatement is about 4.75, so the first misstatement's increment is 4.75 - 3.0 - 1 = 0.75.

Compare the upper limit with tolerable misstatement. If it is lower, the sample supports the conclusion that the population is not misstated by more than tolerable misstatement at the chosen risk. If higher, see projecting and evaluating results.

Common findings

Understatement objectives tested with MUS.
Key items above the interval projected instead of evaluated separately.
Tainting computed on the wrong base.
Upper limit omitted, with only projected misstatement compared with tolerable misstatement.
No evidence that the population used for selection was complete and agreed to the ledger.

Keep the selection file, random start and interval in the workpaper so a reviewer can reproduce every selected item.

The MUS worked example guide and MUS workpaper follow the steps above.

Worked example

Receivables existence with MUS

Coastal Ridge Electrical Supply, Inc. has receivables of $2,400,000 with no individual balance over $16,000. Tolerable misstatement is $60,000; risk of incorrect acceptance 5%; expected misstatement zero.

Minimum size: $2,400,000 x 3.0 / $60,000 = 120. To allow room for a misstatement, the team selects 150 items. Interval: $2,400,000 / 150 = $16,000. No balance exceeds the interval. Random start: $7,412; selections at $7,412, $23,412, $39,412 and so on.

Results: one confirmation exception. A customer balance of $5,000 should be $4,000; the $1,000 relates to a credit memo recorded in January for December goods returned.

Tainting: $1,000 / $5,000 = 20%. Projected misstatement: 20% x $16,000 = $3,200. Basic precision: 3.0 x $16,000 = $48,000. Incremental allowance: $3,200 x (4.75 - 3.0 - 1) = $3,200 x 0.75 = $2,400. Upper misstatement limit: $48,000 + $3,200 + $2,400 = $53,600.

$53,600 is below tolerable misstatement of $60,000. The team concludes receivables are not overstated by more than $60,000 at 5% risk, records likely misstatement of $3,200 (the $1,000 known error plus $2,200 projected to the rest of the population), and investigates the credit memo cutoff.

Self-check

Answer each question before you open the answer.

Why is MUS weak for testing completeness?
Show answer
Selection is proportional to recorded dollars, so understated or unrecorded items have little or no chance of selection.
How do you treat items larger than the sampling interval?
Show answer
They are certain to be selected and are evaluated as individually tested items. Their actual misstatement is added without projection.
A $2,000 item is misstated by $500 and the interval is $10,000. What is the projected misstatement?
Show answer
Tainting is $500 / $2,000 = 25%, so projected misstatement is 25% x $10,000 = $2,500.
What three components make up the upper misstatement limit?
Show answer
Basic precision, projected misstatement, and the incremental allowance for sampling risk on the misstatements found.

Sources

Back to the syllabus

Standards are paraphrased from the primary sources listed above; read the source before relying on a requirement. This lesson is training material, not professional advice. Report an error