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Projected Misstatement vs Tolerable Misstatement Calculator (AU-C 530)

What do these figures come to once the work is shown?

Project sample misstatements to the population by ratio or difference, add key item misstatements, and compare the total with tolerable and expected misstatement.

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Your figures
Example figuresIllustrative only. Type over them with your own.
Total projected misstatement
$34,800
Best estimate of misstatement in the population
Book value of the sampled population
$3,600,000
Misstatement rate in the sample
0.80%
Drawn to one scale
Book value of the sampled population$3,600,000
Projected misstatement in the sampled population$28,800
Total projected misstatement$34,800
Room to tolerable misstatement$55,200
All results
MeasureResult
Book value of the sampled population$3,600,000
Misstatement rate in the sample0.80%
Projected misstatement in the sampled population$28,800
Total projected misstatement
Projected sample misstatement plus key item misstatement
$34,800
Room to tolerable misstatement$55,200
Total as % of tolerable38.67%
Conclusion
Below tolerable, but the projection in the sampled population is above the planning expectation: sampling risk is too high, extend testing or ask management to investigate
How this was worked out
Work shownrecomputed as you type
Ratio: projected = sample misstatement / sample book value x (population book value - key items)
Difference: projected = sample misstatement / items in sample x items in the sampled population
Total projected = projected + misstatement found in key items
Compare the total with tolerable misstatement, and the projection in the sampled population with the expected misstatement used to size the sample

Illustrative arithmetic on the figures you enter. Check the result against your firm's methodology before relying on it.

The formulas

  • Ratio: projected = sample misstatement / sample book value x (population book value - key items)
  • Difference: projected = sample misstatement / items in sample x items in the sampled population
  • Total projected = projected + misstatement found in key items
  • Compare the total with tolerable misstatement, and the projection in the sampled population with the expected misstatement used to size the sample

How it works

AU-C 530 paragraph .13 requires the auditor to project the results of audit sampling to the population. For tests of details paragraph .A24 says the projection gives the likely misstatement, which paragraph .A27 calls the auditor's best estimate of misstatement in the population. Key items tested 100% are not sampled, so their misstatements are added at face value rather than projected.

The ratio method suits populations where misstatements grow with book value. The difference method suits populations where misstatements are about the same size per item. When the total approaches or exceeds tolerable misstatement, actual misstatement is more likely to exceed it. When the projection is above the misstatement you expected when you sized the sample, AU-C 530 .A27 says you can conclude sampling risk is unacceptable.

Illustrative figures only. Check the result against your firm's methodology before relying on it.

Common questions

Should understatements offset overstatements?

Enter the net figure here for the projection, and keep the gross amounts in your workpaper. Large offsetting errors are a qualitative matter under AU-C 450.

Is the projected misstatement the amount to record?

Not by itself. AU-C 530 .A24 notes that because of sampling risk the projection is not enough on its own to set an amount to record.

What goes into the summary of uncorrected misstatements?

The key item misstatement is factual. The projected part is a projected misstatement. Carry both to the summary.

Sources

Runs in your browser. The figures you type are not sent to CORAA or stored. Check the result against your firm's methodology before relying on it.

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