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:
Determine the reliability factor.
Determine the correct expansion factor.
Determine the sample size you should use.
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:
The objective of using probability proportional to size sampling (PPS) to test account balances
Specifically, how you used PPS to test this company's account balances
The purpose of the sample size and the sampling interva

A.Reliability factor = 3.0

B Expansion factor =1.6

C.$ 243.31

D.$ 14220.541

E.Using dollars as a sampling units means that the larger dollar items in the account balance are more and most likely to be selected in the sample

F.To use PPS , the auditor must determine the allowable risk of the sample falling to in order to easily and effectively detect a material misstatement.

G.The purpose of the Sample size (n) is to help determine the Sampling interval (k

The purpose of the Sampling Interval is important to know the sampling length to cover the Population

Explanation:

A) Reliability Factor can be determined by using a reliability factor table which has a risk of incorrect acceptance of let say 5% and 0 overstatements for the aim of determining sample sizes as well as the sampling interval

Hence,

Reliability factor = 3.0

B) Expansion Factor can be determined by using an expansion factor table by given risk of incorrect acceptance of 5% the Expansion factor will be :

= 1.6

C) The formula for Sample size is:

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

Let plug in the formula

where,

Book value of population = $3,460,000

Reliability Factor = 3.0

The misstatement total = $63,460

The misstatement expected= $13,000

Expansion factor = 1.6

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

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

= $ 243.31

D) Formula for Sampling interval

Sampling interval= Book value of population/Sample size

Let plug in the formula

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

Hence:

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

=$ 14220.541

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

The Dollar-based sampling approach where the population is said to be the number of dollars in the account balance has been examined.

Therefore when the dollars is been used as a sampling units it can be said to means that the larger dollar items in the account balance are more and most likely to be selected in the sample.

PPS can be seen as a reliable sampling approach in a situation where the auditor is testing for overstatements.

Therefore Appropriate when few misstatements are expected as well as when individual book values are available

F) The Probability Proportional sampling is a reliable sampling approach when the auditors is testing for overstatement.

Therefore in order to use PPS , the auditor must determine the allowable risk of the sample falling to in order to easily and effectively detect a material misstatement

Test of detail risk

Detection risk can be defined as the risk in which the substantive audit procedures will fail to detect material misstatement

High Inherent risk cannbe defined as the way in which the auditor is examining transactions that are susceptible to misstatement.

Therefore Auditor want to be more careful while determining sample procedures

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

PPS sample are usually been selected using a fixed interval sampling approach

G) The aim of the Sample size (n) is to help determine the Sampling interval (k) which is why the Sample size is can be seen as the collection of consecutive integers which are is part of the Population (N) used for analysis having resembling characteristics.

Sampling interval (k) can therefore be defined as length of string of the consecutive integers and the length of string of sample collection is determined through Population and the Sample Size through formula (k =N/n).

Therefore the purpose of the Sampling Interval is important to know the sampling length to cover the Population.

Example:

Population : 1 – 300 numbers

Sample size : 10 numbers ie. 1-20, 21-30, 31-40,……