Chapter G, Problem 58EP

a)

To determine

Compute the necessary sample size for the audit of Company S’s accounts receivable.

Explanation of Solution

Sample size: Sample size indicates the number of items that the audit team inspects within a population of interest

Compute the necessary sample size for the audit of Company S’s accounts receivable:

The required sample size for the audit of Company S’s inventory is as follows:

Particulars	Sample size	Workings
Risk of incorrect acceptance	10%
Ratio of expected to tolerable misstatement	40%	$\left(\frac{\$10,000}{\$25,000}\times 100\right)$
Tolerable misstatement as a percentage of population	8.30%	$\left(\frac{\$25,000}{\$300,000}\times 100\right)$

Table (1)

Note: The tolerable misstatement as a percentage of population is 8.3 % which ranges from 8% (sample size 72) to 10% (sample size 58).

Calculate the sample size for the audit of Company S’s accounts receivables:

Step 1: Calculate the difference in sample size for an 8% tolerable misstatement and a 10% tolerable misstatement $\left(72\text{–}58\text{=14items}\right)\text{.}$

 Step 2: As the actual tolerable misstatement (8.3 percent) is one-third of the difference above $\left[\frac{\left(8.3\%-\text{8}.00\%\right)}{\left(10.00\%–\text{ 8}.00\%\right)}\right]$ and multiply the difference calculated in step 1 (14 items) by one-third $\left[\text{0}\text{.15×14 items = 2}\text{.1}\text{item}\right]$.

Note: Refer to EXHIBIT E.4.

Step 3: Adjust the sample size for the 8 percent tolerable misstatement by the result in step 2 to determine a sample size of 70 items$\left[\text{72 items –}\text{2}\text{.1item = 70 items}\left(\text{Rounded}\right)\right]$ . As a quick validation, note that because the tolerable misstatement is closer to 8 percent than 10 percent, the final sample size is closer to that shown for the 8 percent tolerable misstatement than the 10 percent tolerable misstatement.

Therefore, according to the above explanation, sample size is 70.

Note: Refer to exhibit GA.1.

b)

To determine

Identify the suitable sampling interval based on the sample size computed in requirement (a).

Explanation of Solution

Sampling interval: The samples units from a larger population are picked corresponding to an arbitrary beginning point however with a fixed interval. This fixed interval is referred as sampling interval.

Sampling interval is calculated as follows:

$\text{Sampling}\text{interval}\text{=}\frac{\text{Population}\text{size}}{\text{Required}\text{sample}\text{size}}$

The sample interval computed by Person CP is as follows:

$\begin{array}{c}\text{Sampling}\text{interval}\text{=}\frac{\text{Population}\text{size}}{\text{Required}\text{sample}\text{size}}\\ =\frac{\$300,000}{70}\\ =\$4286\left(\text{rounded off}\right)\end{array}$

Therefore, the sampling interval is $4286.

c)

To determine

Explain the manner Person CP could choose the sample from computerized customer list that Company S maintains.

Explanation of Solution

Person CP might arbitrarily choose a beginning point between 0 and 4,286 and pick a dollar in the computerized accounts receivable list related to that dollar. He could then pick every 4,286th dollar in the accounts receivables list till an entire 70 dollar units were picked.

d)

To determine

Analyze the impact on the sample size and sampling interval due to the changes in Person CP’s sampling plan.

Explanation of Solution

1. Compute the necessary sample size for the audit of Company S’s accounts receivable:

The required sample size for the audit of Company S’s inventory is as follows:

Particulars	Sample size	Workings
Risk of incorrect acceptance	5%
Ratio of expected to tolerable misstatement	40%	$\left(\frac{\$10,000}{\$25,000}\times 100\right)$
Tolerable misstatement as a percentage of population	8.30%	$\left(\frac{\$25,000}{\$300,000}\times 100\right)$

Table (2)

Note: The tolerable misstatement as a percentage of population is 8.3 % which ranges from 8% (sample size 102) to 10% (sample size 81).

Calculate the sample size for the audit of Company S’s accounts receivables:

Step 1: Calculate the difference in sample size for an 8% tolerable misstatement and a 10% tolerable misstatement $\left(102\text{–}81\text{=}\text{21items}\right)\text{.}$

 Step 2: As the actual tolerable misstatement (8.3 percent) is one-third of the difference above $\left[\frac{\left(8.3\%-\text{8}.00\%\right)}{\left(10.00\%–\text{ 8}.00\%\right)}\right]$ and multiply the difference calculated in step 1 (21 items) by one-third $\left[\text{0}\text{.15×}\text{21 items = 3}\text{.15}\text{item}\right]$.

Note: Refer to EXHIBIT E.4.

Step 3: Adjust the sample size for the 8 percent tolerable misstatement by the result in step 2 to determine a sample size of 99 items$\left[\text{102 items –}3.\text{15item = 99 items}\left(\text{Rounded}\right)\right]$ . As a quick validation, note that because the tolerable misstatement is closer to 8 percent than 10 percent, the final sample size is closer to that shown for the 8 percent tolerable misstatement than the 10 percent tolerable misstatement.

Therefore, according to the above explanation, sample size is 99.

Note: Refer to exhibit GA.1.

The sample interval computed by Person CP is as follows:

$\begin{array}{c}\text{Sampling}\text{interval}\text{=}\frac{\text{Population}\text{size}}{\text{Required}\text{sample}\text{size}}\\ =\frac{\$300,000}{99}\\ =\$3030\left(\text{rounded off}\right)\end{array}$

Therefore, the sampling interval is $3030.

2. Compute the necessary sample size for the audit of Company S’s accounts receivable:

The required sample size for the audit of Company S’s inventory is as follows:

Particulars	Sample size	Workings
Risk of incorrect acceptance	10%
Ratio of expected to tolerable misstatement	50%	$\left(\frac{\$12,500}{\$25,000}\times 100\right)$
Tolerable misstatement as a percentage of population	8.30%	$\left(\frac{\$25,000}{\$300,000}\times 100\right)$

Table (3)

Note: The tolerable misstatement as a percentage of population is 8.3 % which ranges from 8% (sample size 100) to 10% (sample size 80).

Calculate the sample size for the audit of Company S’s accounts receivables:

Step 1: Calculate the difference in sample size for an 8% tolerable misstatement and a 10% tolerable misstatement $\left(100\text{–}80\text{=}\text{20}\text{items}\right)\text{.}$

 Step 2: As the actual tolerable misstatement (8.3 percent) is one-third of the difference above $\left[\frac{\left(8.3\%-\text{8}.00\%\right)}{\left(10.00\%–\text{ 8}.00\%\right)}\right]$ and multiply the difference calculated in step 1 (20 items) by one-third $\left[\text{0}\text{.15×}\text{20 items = 3}\text{item}\right]$.

Note: Refer to EXHIBIT E.4.

Step 3: Adjust the sample size for the 8 percent tolerable misstatement by the result in step 2 to determine a sample size of 97items$\left[\text{100 items –}3\text{item = 97 items}\left(\text{Rounded}\right)\right]$ . As a quick validation, note that because the tolerable misstatement is closer to 8 percent than 10 percent, the final sample size is closer to that shown for the 8 percent tolerable misstatement than the 10 percent tolerable misstatement.

Therefore, according to the above explanation, sample size is 97.

Note: Refer to exhibit GA.1.

The sample interval computed by Person CP is as follows:

$\begin{array}{c}\text{Sampling}\text{interval}\text{=}\frac{\text{Population}\text{size}}{\text{Required}\text{sample}\text{size}}\\ =\frac{\$300,000}{97}\\ =\$3,093\left(\text{rounded off}\right)\end{array}$

Therefore, the sampling interval is $3,093.

3. Compute the necessary sample size for the audit of Company S’s accounts receivable:

The required sample size for the audit of Company S’s inventory is as follows:

Particulars	Sample size	Workings
Risk of incorrect acceptance	10%
Ratio of expected to tolerable misstatement	50%	$\left(\frac{\$10,000}{\$20,000}\times 100\right)$
Tolerable misstatement as a percentage of population	6.7%	$\left(\frac{\$20,000}{\$300,000}\times 100\right)$

Table (4)

Note: The tolerable misstatement as a percentage of population is 6.7 % which ranges from 8% (sample size 100) to 6% (sample size 134).

Calculate the sample size for the audit of Company S’s accounts receivables:

Step 1: Calculate the difference in sample size for an 8% tolerable misstatement and a 6% tolerable misstatement $\left(100\text{–}134\text{=}\text{34}\text{items}\right)\text{.}$

 Step 2: As the actual tolerable misstatement (8.3 percent) is one-third of the difference above $\left[\frac{\left(6.7\%-6.00\%\right)}{\left(8.00\%–\text{ 6}.00\%\right)}\right]$ and multiply the difference calculated in step 1 (34 items) by one-third $\left[\text{0}\text{.35×}\text{34 items = 11}\text{.9}\text{item}\right]$.

Note: Refer to EXHIBIT E.4.

Step 3: Adjust the sample size for the 8 percent tolerable misstatement by the result in step 2 to determine a sample size of 122 items$\left[\text{134 items –}11.9\text{item = 122 items}\left(\text{Rounded}\right)\right]$ . As a quick validation, note that because the tolerable misstatement is closer to 8 percent than 10 percent, the final sample size is closer to that shown for the 8 percent tolerable misstatement than the 10 percent tolerable misstatement.

Therefore, according to the above explanation, sample size is 122 items.

Note: Refer to exhibit GA.1.

Conclusion

The analysis in (1) through (3) specifies that the risk of incorrect acceptance and the tolerable misstatement has an inverse relationship with sample size. The expected misstatement has a direct relationship with sample size.