Chapter G, Problem 70EP

a.

To determine

Indicate the factors DM should consider while ascertaining sample size, and explain the way in which these factors could be evaluated.

Explanation of Solution

Sample size: The number of individual samples or items that an auditor examines to make a decision regarding the population, is referred to as sample size.

The sample size is determined on the basis of the following factors:

• Sampling risk or risk of incorrect acceptance.
• Tolerable misstatement.
• Expected misstatement.
• Population size.

The following are the factors DM should consider while ascertaining sample size:

• Balance of accounts receivable recorded in the customer accounts.
• Acceptable level of risk of incorrect acceptance.
• Tolerable misstatement.
• Expected misstatement.

These factors would be evaluated in the following ways:

• Balance of accounts receivable recorded in the customer accounts: The balances of accounts receivable would be evaluated by referring the accounting records of Company C.
• Acceptable level of risk of incorrect acceptance: The risk of incorrect acceptance is evaluated by application of audit risk models, evaluation of audit risk, evaluation of risk of material misstatement, and evaluation of audit risk by applying the analytical procedures.
• Tolerable misstatement: The tolerable misstatements would be evaluated by taking into account the recorded balances, class of transactions, relationship between the balances in accounts and class of transactions like total assets, or total sales.
• Expected misstatement: The expected misstatements would be evaluated by considering the previous engagements of DM with Company C, or considering the pilot samples, in case the engagement with the client is for the first time.

b.

To determine

Compute the sample size and sampling interval that would be used by DM for auditing Company C.

Explanation of Solution

Sampling interval: This is the frequency at which the auditor selects the samples or items from the population, based on the size of the population.

Compute the sample size.

Step 1: Compute the risk of incorrect acceptance.

In the give case, risk of incorrect acceptance is given as 5%.

Step 2: Compute the ratio of expected misstatement to tolerable misstatement.

$\begin{array}{c}\begin{array}{l}\text{Ratio of expected misstatement }\\ \text{to tolerable misstatement}\end{array}\}\text{ =}\frac{\text{Expected misstatement}}{\text{Tolerable misstatement}}\\ \text{=}\frac{\text{\$24,000}}{\text{\$120,000}}\\ \text{= 0}\text{.20}\end{array}$

Step 3: Compute the ratio of tolerable misstatement to the size of population.

$\begin{array}{c}\begin{array}{l}\text{Ratio of tolerable misstatement }\\ \text{to size of population}\end{array}\}\text{ =}\frac{\text{Tolerable misstatement}}{\text{Size of population}}\\ \text{=}\frac{\text{\$120,000}}{\text{\$2,000,000}}\\ \text{= 0}\text{.06 or 6\%}\end{array}$

Step 4: Ascertain the sample size from Exhibit GA-1 by selecting the sample size at the intersection of ratios computed in Step 2 and Step 3.

The ratio of expected misstatement to tolerable misstatement, 0.20, intersects the ratio of tolerable misstatement to the size of population, 6%, for a risk of incorrect acceptance of 5%, at 78. Hence, the sample size is 78.

Compute the sampling interval.

$\begin{array}{c}\text{Sampling interval = }\frac{\text{Population size or Recorded balance}}{\text{Sample size}}\\ \text{=}\frac{\text{\$2,000,000}}{\text{78}}\\ \text{=\$25,641}\end{array}$

c.

To determine

Explain the way in which DM would select the accounts receivable sample while auditing Company C’s accounts receivable ledger.

Explanation of Solution

DM would select the accounts receivable sample by identifying a random amount between $0 and $25,641, the sampling interval, and selecting an accounts receivable ledger corresponding to the identified random sample. This process continues for every interval of 25,641, until 78 samples are selected.

d.

To determine

Ascertain the projected misstatement.

Explanation of Solution

Projected misstatement: This is an assumption that a similar percentage of misstatement can be projected for whole sampling interval.

Ascertain the projected misstatement.

Step 1: Compute difference between the recorded balance and the audited value for the given misstatements.

Recorded Balance	˗	Audited Value	=	Difference
$45,000	˗	$40,000	=	$5,000
8,000	˗	6,000	=	2,000
12,000	˗	9,000	=	3,000

Table (1)

Step 2: Compute the tainting percentage (Refer to Table (1) for the difference values).

Difference	÷	Recorded Balance	=	Tainting Percentage
$5,000	÷	$45,000	=	11%
2,000	÷	8,000	=	25%
3,000	÷	12,000	=	25%

Table (2)

Step 3: Compute the projected misstatement (Refer to Table (2) for the tainting percentage values).

Tainting Percentage	×	Sampling Interval	=	Projected Misstatement
	×	$5,000	=	$5,000
25%	×	13,000	=	3,250
25%	×	13,000	=	3,250
				$11,500

Table (3)

Note: Since the recorded balance of $45,000 is higher than the sampling interval of $13,000, the misstatement is not projected.

e.

To determine

Compute the upper limit on misstatements assuming a 5% risk of incorrect acceptance.

Explanation of Solution

Upper limit on misstatements (ULM): ULM is the total of projected misstatement, incremental allowance for sampling risk, and basic allowance for sampling risk. ULM is the amount that has a probability of risk of incorrect acceptance percentage to exceed or equal the true amount of misstatement.

Compute the upper limit on misstatements assuming a 5% risk of incorrect acceptance.

Step 1: Compute the incremental allowance for sampling risk.

Projected Misstatement	×	Incremental Coincidence Factor	=	Incremental Allowance For Sampling Risk
3,250	×	0.75 ((4.75–3.00)–1.00)	=	$2,438
3,250	×	0.55 ((6.30–4.75)–1.00)	=	1,788
				$4,226

Table (4)

Note: Refer to Exhibit-GA-2 for confidence factors at a risk of incorrect acceptance level of 5%.

Step 2: Compute the basic allowance for sampling risk.

$\begin{array}{c}\begin{array}{l}\text{Basic allowance }\\ \text{for sampling risk}\end{array}\}\text{ = Sampling interval }\times \text{ Confidence factor}\\ \text{=\$13,000}\times \text{3}\text{.00}\\ \text{=\$39,000}\end{array}$

Step 3: Compute the ULM (Refer to the previous computations for all the values).

Components of ULM	Amount ($)
Projected Misstatement	$11,500
Incremental Allowance For Sampling Risk	4,226
Basic Allowance For Sampling Risk	39,000
Upper limit on misstatements	$54,726

Table (5)

f.

To determine

Provide concluding statements from the computations of part (e), regarding Company C’s accounts receivable.

Explanation of Solution

Comparing the ULM of $54,726 with the tolerable misstatement of $120,000, DM can conclude that the accounts receivable of Company C were fairly stated.