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.

-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:

a. Determine the reliability factor.

b. Determine the correct expansion factor.

c. Determine the sample size you should use.

d. Determine the sampling interval you should use.

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