Application 2: Introduction to ACL
Application 2: Introduction to ACL
1.
i) Sample Size using Attribute Sampling:-
Where, N = Population size,
M = {(Z-score at the desired confidence level) 2 * P (1-P)} / E2,
P = Proportion of the Sample, and
E = Expected Error Rate
Thus, M = {(1.65)2 * 0.5 (1-.05)} / (0.05)2
= {2.7225 * 0.5* 0.5} / 0.0025
= 272.25
And, Sample Size = (217 * 272.25) / (272.25 + 217 – 1)
= 59078.25 / 488.25
= 121
ii) Tolerable errors for the Selected Sample:-
Tolerable errors are the maximum errors which can be tolerated by the auditors. In this case, tolerable errors are 5% of the population size i.e. 10.85.
iii)
a) Increase in confidence level to 95% -
M = {(1.96)2 * 0.5 (1- 0.5)} / (0.05)2
= {3.8416 * 0.5 *0.5} / 0.0025
= 384.16
Sample Size = (384.16 * 217) / (384.16 + 217 – 1)
= 138.90 samples
The sample size increases from 121 to 139 by increasing the confidence level to 95%.
b) Increase in upper error limit to 25% -
M = {(2.7225 * 0.5 * 0.5)} / 0.0025
= 272.25
Sample Size = (272.25 * 217) / (272.25 + 217 – 1)
= 121 samples
The sample size remains same on increasing the upper error limit to 25%.
c) Increase in expected error rate to 10% -
M = {(2.7225 * 0.5* 0.5)} / (0.1)2
= 68.0625
Sample Size = (68.0625 * 217) / (68.0625 + 217 - 1)
= 14769.56 / 284.0625
= 51.99406
The sample size decreases from 121 to 52 on increasing the expected error rate to 10%.
2. Sample Size using MUS Sampling:-
Sample Size = MUS Confidence Factor x (Population Value / Materiality)
= 3.41 x (5000, 000 / 500,000)
= 34.10 samples
Where, MUS Confidence Factor will be determined from the ratio of Expected Total Errors to Materiality. Thus, confidence factor of 90% will be matched with the ratio which comes to (100,000 / 500,000) = 0.20. Hence, the MUS confidence factor from the confidence factor table is 3.41.
Note: - The Population value has been assumed to be 5 million.
3. “The sample's confidence level refers to the reliability the auditor places on the sample results” (Applegate, 2010). It is the rate of confidence which the auditor places on the sample that the results of sampling will be reliable. Confidence level and sample size has a linear relationship with each other. As the confidence level increases, the sample size also increases and as the confidence level decreases the sample size decreases. This is because as more confidence is placed on the sample results, a greater sample size would be required to compensate for the increased confidence levels. Upper error limit refers to the maximum limit upto which the auditor can tolerate errors and misstatements in the sample. Sample size and tolerable error rate have an inverse relationship with each other because when the upper limit is quite high , the auditor can place reliance on a smaller sample and vice versa. Expected error rate is the rate at which errors are expected to occur in a sample. This rate is also inversely related to the sample size. Decreasing the expected error rate would mean auditing a larger sample in order to balance out the reduction in expected errors and conclude that actual errors do not exceed the tolerable error rate. Materiality refers to the limit of tolerable misstatements which the auditor places on a sample. It is “a monetary amount set by the auditor in respect of which the auditor seeks to obtain an appropriate level of assurance that the monetary amount set by the auditor is not exceeded by the actual misstatement in the population” (Audit Sampling, 2009). Materiality has a direct relationship with the sample size. When materiality levels are high, a larger sample is required since greater number of entities reduce the risk of material misstatements. Expected total errors or expected misstatements are the total errors the auditor expects to be present in the selected sample. When the auditor expects total errors to be high, the sample size is increased in order to reduce the detection risk.
References
Applegate, D. (2010). Attribute Sampling Plans. Iaonline.theiia.org. Retrieved 5 March 2016, from https://iaonline.theiia.org/attribute-sampling-plans
Audit Sampling. (2009) (p. 3). Retrieved from https://frc.org.uk/OurWork/Publications/APB/ISA-530-Audit-sampling.pdf
