Projecting Misstatements on Population (Audit Sampling)
## Projecting Misstatements on Population
### Why Projection Matters
When an auditor tests a sample, any misstatement found is not confined to that sample — it is an indicator of error across the entire population. Before concluding whether a population is materially misstated, the auditor must scale up (project) the sample result to the full population.
This step is required by SA 530 – Audit Sampling.
---
### The Core Formula
For value-based (monetary) sampling:
$$\text{Projected Misstatement} = \frac{\text{Misstatement in Sample}}{\text{Book Value of Sample}} \times \text{Book Value of Population}$$
Equivalently expressed as a factor (ratio) approach:
$$\text{Projection Factor} = \frac{\text{Misstatement in Sample}}{\text{Book Value of Sample}}$$
$$\text{Total Projected Misstatement} = \text{Projection Factor} \times \text{Population Book Value}$$
For attribute (rate-based) sampling:
$$\text{Projected Error Rate} = \frac{\text{Number of Errors in Sample}}{\text{Sample Size}} \times 100$$
---
### Step-by-Step Process
1. Identify misstatements found within the tested sample.
2. Compute the projection factor = misstatement ÷ sample book value.
3. Multiply by population book value to get total projected misstatement.
4. Add known misstatements (items tested 100%) if any.
5. Compare total projected misstatement with tolerable misstatement (materiality).
If projected misstatement < tolerable misstatement → population is likely acceptable.
If projected misstatement ≥ tolerable misstatement → consider additional procedures or conclude the population is misstated.
---
### SA 530 Requirement
SA 530 para 14 requires the auditor to project misstatements found in a sample to the population AND evaluate whether the projected misstatement, together with anomalous misstatements, exceeds tolerable misstatement.
> Anomalous misstatement: A misstatement arising from an isolated event that is not representative of the population. These are excluded from projection but must still be considered separately.
Step 3: If tolerable misstatement = ₹25,000 → Projected (₹30,000) > Tolerable (₹25,000) → Auditor should perform additional procedures or qualify.
### Example 2
Example 2 – Attribute Sampling Projection
An auditor tests 100 purchase invoices for approval signature:
Sample size = 100
Errors found (missing signature) = 4
Step 1: Projected error rate = 4 ÷ 100 × 100 = 4%
Step 2: If tolerable deviation rate = 5% → Projected (4%) < Tolerable (5%) → Control is operating effectively.
Step 3: If tolerable deviation rate = 3% → Projected (4%) > Tolerable (3%) → Control cannot be relied upon; extend substantive procedures.
### Example 3
Example 3 – Handling an Anomalous Misstatement
During debtor testing:
Projected misstatement from sample = ₹18,000
One item in sample: ₹9,000 error due to a one-off data entry error (confirmed isolated event)
Step 1: Remove the anomalous item before projecting: adjusted sample misstatement = ₹18,000 − ₹9,000 = ₹9,000 (for projection purposes)
Step 2: Project ₹9,000 to population normally.
Step 3: Add back the anomalous ₹9,000 as a separate known misstatement when comparing with tolerable misstatement.
Note: Anomalous misstatements are NOT projected but must still be considered in the overall evaluation.
⚠️ Common exam mistakes
Projecting the misstatement amount without using the correct base — use book value of sample, not sample size (units), when dealing with monetary amounts.
Forgetting to add known (100%-tested) misstatements to the projected figure before comparing with tolerable misstatement.
Treating anomalous misstatements as zero — they must still be included separately in the final evaluation even though they are excluded from projection.
Confusing 'projected misstatement' with 'tolerable misstatement' — projection is the estimate of actual error; tolerable misstatement is the threshold set by the auditor.
Using population count (number of items) instead of population value in a monetary-unit projection formula, leading to an incorrect projected figure.
Bare-Act text Paragraph 14 · SA 530 – Audit Sampling (ICAI) · click to expand
14. Projecting Misstatements — For monetary unit sampling, the auditor shall project misstatements found in the sample to the population. When a misstatement has been established as an anomalous misstatement, it may be excluded from the projection of misstatements to the population. However, the effect of any such misstatement, if uncorrected, still needs to be considered in addition to the projection of the non-anomalous misstatements.