Question

You are the auditor for a company and need to review the company’s accounts receivable using probability proportional to size (PPS) sampling. In addition, the board of directors has requested that you and your team present an explanation of your PPS process at its next monthly meeting.

Individual Portion:

Use the following company data and the PPS Sampling Tables 1 & 2:

• The recorded book value of these accounts is $3,460,000.
• The company has a tolerable error of $63,460.
• The anticipated error is $13,000.
• The risk of incorrect acceptance is 5%.
• The acceptable number of overstatements of misstatements is 2.

Use probability proportional to size (PPS) sampling to do the following:

1. Determine the reliability factor.
2. Determine the correct expansion factor.
3. Determine the sample size you should use.
4. Determine the sampling interval you should use.

Please add your file.

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Group Portion:

With your team of analysts, create a PowerPoint presentation of 7–10 slides to explain the following to the board of directors:

5. The objective of using probability proportional to size sampling (PPS) to test account balances
6. Specifically, how you used PPS to test this company's account balances
7. The purpose of the sample size and the sampling interval

Answer 1

A) Reliability Factor is determined using a reliability factor table, with a risk of incorrect acceptance of 5% and 0 overstatements (for the purposes of determining sample size and sampling interval)

Reliability factor = 3.0

B) Expansion Factor is determined using an expansion factor table, given risk of incorrect acceptance of 5% Expansion factor = 1.6

C) Sample size = (Book value of population * Reliability Factor)/(Total misstatement - (Expected misstatement*Expansion factor))

where:Book value of population = $3,460,000

Reliability Factor = 3.0 (from part A)

Total misstatement (or tolerable error) = $63,460

Expected misstatement (or anticipated error) = $13,000

Expansion factor = 1.6 (from part B)

Sample Size = ($ 3,460,000 *3.0) / {$63,460 - ($13,000 * 1.6)}

= $ 10,380,000/$ 42,660

= $ 243.31

D) Sampling interval = Book value of population/Sample size

where: Book value of population = $3,460,000

Sample size = answer from part C

Sampling interval = $ 3,460,000/$ 243.31

$ 14220.541

E) Objective Of Using Probability Proportional to Size (PPS) Sampling In Account Balances

• Dollar-based sampling approach where the population is the number of dollars in the account balance examined
• Using dollars as sampling units means larger dollar items in the account balance are more likely to be selected in the sample
• PPS is an effective sampling approach when the auditor is testing for overstatements
• Appropriate when few misstatements are expected and individual book values are available

F) Probability Proportional Sample size ( PPS) sampling – mainly dollar based sampling approach where the population is te number of dollars in the account balance examined

PPS is an effective sampling approach when the auditors is testing for overstatement

To use PPS , auditor must determine the allowable risk of the sample falling to detect a material misstatement

Test of detail risk

Detection risk is the risk that the substantive audit procedures will fail to detect material misstatement

High Inherent risk mean the auditor is examining transactions that are susceptible to misstatement

Auditor want to be more careful while determining sample procedures

To achieve the lower risk of failing to detect , the sample size mist be increased

PPS sample are usually selected using a fixed interval sampling approach

G) The purpose of the Sample size (n) is to determine the Sampling interval (k). The Sample size is collection of consecutive integers that is a part of the Population (N) used for analysis having resembling characteristics.

Sampling interval (k) can be defined as length of string of the consecutive integers. This length of string of sample collection is determined through Population and the Sample Size through formula (k =N/n). Thus, the purpose of the Sampling Interval is essential to know the sampling length to cover the Population. The sampling interval does partitions of the Population into n (Sample size) zonal blocks.

Example:

Population : 1 – 200 numbers

Sample size : 10 numbers ie. 1-10, 11-20, 21-30,……

Sampling interval : 200 / 10 = 20