What is a projected misstatement?
ISA 530.14 requires the auditor to project misstatements found in a sample to the population. For classical variables sampling, you multiply the error rate by the population value. For monetary unit sampling (MUS), you use the tainting percentage approach: calculate the percentage error (tainting) for each sample item, then multiply by the sampling interval.
The projected amount goes onto the summary of uncorrected misstatements. It is not a known error but a statistical estimate of the likely total error in the population, based on what the sample revealed.
Projection applies only to populations tested by sampling. Items tested 100% (such as items exceeding the sampling interval in MUS) produce factual misstatements, not projected ones. Mixing the two categories inflates or deflates the summary and produces an incorrect evaluation against materiality.
Key Points
- Applies only to populations tested by sampling, not 100%-tested items or specific high-value items.
- Projection method depends on sampling approach: MUS uses a different formula than classical variables sampling.
- Most inspection findings relate to teams failing to project at all, not getting the projection wrong.
- Projected misstatements are accumulated on the summary alongside factual and judgmental misstatements.
Why it matters in practice
Teams also frequently forget the second comparison: the projected misstatement versus the expected misstatement used to design the sample. If the projected amount significantly exceeds the expected amount, the sample design assumptions were wrong, and the auditor should reconsider whether the sample was sufficient.
Worked example: Van den Berg Machinebouw B.V.
Client: Dutch manufacturer, FY2024, revenue €47M, Dutch GAAP (RJ) reporter.
Population
Trade receivables, €6.2M, 1,840 items. Performance materiality €310,000.
MUS parameters
Sample of 40 items. Sampling interval €155,000.
Error 1
Invoice #2289, recorded €12,400, confirmed at €11,100. Overstatement €1,300. Tainting: €1,300 / €12,400 = 10.48%. Projected misstatement: 10.48% × €155,000 = €16,250.
Error 2: Invoice #3741, recorded €185,000, confirmed at €181,200. This item exceeds the sampling interval (€155,000), so it was selected with certainty and tested individually. The €3,800 difference is a factual misstatement, not projected.
Summary
Projected misstatement €16,250 + factual misstatement €3,800 = total €20,050 vs performance materiality €310,000. No further action required.
Projected vs factual misstatement
| Dimension | Projected misstatement | Factual misstatement |
|---|---|---|
| Source | Extrapolation from sample | Direct observation |
| Certainty | Statistical estimate | Known error |
| Applies when | Audit sampling used | Any testing approach |
| Calculation | Yes: depends on method | No: error amount = misstatement |
| Management pushback | High | Low |
Key standard references
- ISA 530.14 : Requires projecting misstatements found in a sample to the population.
- ISA 450 .A1: Classifies projected misstatements alongside factual and judgmental on the summary.
- ISA 530 .A18–A19: Application guidance on projection methods for different sampling approaches.
Related terms
Related tools
Related tools
Related reading
Frequently asked questions
Do you project errors found in items tested 100%?
No. Items tested individually (e.g., items exceeding the sampling interval in MUS) are recorded as factual misstatements. Projection applies only to the sampled portion of the population.
What happens if the projected misstatement exceeds tolerable misstatement?
The sample fails. The auditor must either expand the sample, perform alternative procedures, or conclude that the population may be materially misstated.