1 chapter 17 audit sampling for tests of details of balances accounts receivable

1

Chapter 17

Audit Sampling for

Tests of Details of Balances

Accounts Receivable

2

Aaron

Tests of Controls

What do they measure

The operating effectiveness of internal controls

3

The introduction

… when all the confirmation replies were received or alternate procedures were completed ….. Bob called Barbara to do some statistical evaluation.

4

Kelly Mc

Substantive Tests of Balances

What do Substantive Tests measure

calculate the dollar misstatements in account balances

5

Sampling Methods

Non statistical samplingStatistical sampling

monetary unit sampling

variables sampling

difference estimation

ratio estimation

Mean-per-Unit

6

Work Paper 2

College Business Computer performed by: Tad

Sales Collection cycle date: 1/27/2009

Sales

nature of test Substantive tests of transactionsobjective The objective of this procedure is to determine if the sales account is overstated.assertion(s) Occurrence and Accuracy

invoiceship doc

sales order

customerinvoice

amount

audited amount

difference

1 6523 4973 10153 Trusco Tank 9,182.00 9,182.00 0.001 6526 4975 10155 San Luis Ready Mix 22,546.00 22,546.00 0.001 6532 4981 10161 Copeland's Sports Superstoresds 4,188.00 4,188.00 0.001 6537 4985 10165 Standard Motor Co. 4,538.00 4,538.00 0.001 6542 4990 10170 Airport Auto Center 12,664.00 12,664.00 0.001 6545 Flora Design Studio 3,432.00 0.00 (3,432.00)1 6552 4998 10178 F. McLintocks 18,908.00 18,908.00 0.001 6560 5006 10186 Foothill Cyclery 12,446.00 11,572.00 (874.00)1 6562 5008 10188 Sinsheimer, Schiebelhut & Baggett -PC11,982.00 11,982.00 0.001 6565 5011 10191 Hind Inc. 16,576.00 0.00 (16,576.00)

sample average 9,558.00 -2,088.20projected value 430,110.00 -93,969.00

Book Value 489,029.00projected error -58,919.00

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Page 413 Test of Details - sampling

Objective ---- derived from management assertions

Define a misstatement“ population“ sampling unit

Specify tolerable misstatement ---- a dollar amount

risk of incorrect acceptance βeta risk

Determine sample size

Select the samplePerform the procedure

Project the sample results to the population

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Test of Details – samplinginventory handout

Objective all recorded inventory exist as of 12/31physical quantities on hand agree INV recordscosts used to value INV are correct

Define misstatement incorrect cost or quantity

population items in parts inventorysampling unit SKU or part number

Specify tolerable misstatement $200,000 risk of incorrect acceptance 5%

Determine sample size 387

Select the sample

Perform the procedure


9

Grace

what is the audit risk model ?

10

Audit Risk Model

Tests eSubstantiv extensive low PDR if

Tests eSubstantiv limited high PDR if

)(

rearrange

CR

cCRfPDR

RoMM

AARPDRPDRRoMMARPDRCRIRAAR

11

Ishrak

pretend GAAS requires AAR ≤ .05

Controls are effective, we assess CR as 0.03

Which audit approach will we take ?

12

Mackenzie


Controls are effective, we assess CR as 0.03

We will take the Reduced Level of Control Risk Approach

What is the Planned Detection Risk ?

13

Sami


Controls are ineffective, we assess CR as MAX

Which audit approach are we going to take ?

14

Catherine


Controls are ineffective, we assess CR as MAX (1.00)

We are taking the Primarily Substantive Approach


15

Melissa


Controls are effective, not great but

Somewhat effective and

we assess CR as 0.25


16

Anne


Controls are effective, not great but

somewhat effective and

we assess CR as 0.25

Which audit approach will we take?

17

Tori

is Detection Risk

risk of incorrect rejection Type I or risk

risk of incorrect acceptance Type II or risk

18

Applying what we know about Hypothesis Tests and Confidence Intervals

The risk of incorrectly concluding the book value of the inventory is incorrect when it is correct is Alpha risk or a Type I error. This is the risk of incorrect rejection. The risk of incorrectly concluding inventory is fairly presented when the book value is materially overstated is Beta risk or a Type II error. This is the risk of incorrect acceptance.

In the previous examples the critical value of the hypothesis test and the lower limit of the interval were arbitrarily set to equal to the midpoint between the hypothetical mean and the book value. This will result in Alpha risk that is twice as large as Beta risk because the hypothesis test is a one-tail test while intervals have two tails.

For planning purposes assume that tolerable error for the parts inventory has been set as $200,000, which is approximately 10% of the $1,965,560 balance. Statistical sampling cannot prove that the balance is correct. But auditing standards do not require balances to be exact. Auditing standards require auditors to “obtain reasonable assurance about whether the financial statements are free of material misstatement.” Auditing standards require auditors obtain “sufficient, appropriate evidence” the financial statements “present fairly, in all material respects.” Auditors are typically concerned that asset accounts, such as inventory, are overstated. If tolerable error is $200,000, we need evidence that the actual balance of the parts inventory is greater than $1,765,560.

The interval between the hypothetical mean $1,036.74 ($1,765,560 / 1,703) and the average book value $1,154.17 ($1,965,560 / 1,703) is $117.44 ($200,000 / 1,703). This will remain the same regardless of how we allocate risk between Alpha Risk and Beta Risk. The interval is comprised of two elements: the upper portion of the hypothesis test and the lower tail of the confidence interval. Together these two elements comprise the tolerable error.

19

type

II

type I

21

Test of Details - sampling


you must project sample results to the population

plus

appropriate consideration for sampling risk

22

projected error + allowance for sampling risk

must be less than

tolerable error

23

cv

allowance for sampling

risk

Accept

24

Also notice that the critical value will change because it now 1.645 standard deviations to the right of the hypothesized mean.

Later, during the audit we will select and audit a random sample of 387 inventory line items. If everything goes exactly as planned and the sample mean of the audited values exceeds $1,108.78, we will accept the hypothesis that the parts inventory balance is not materially overstated.

The attached work sheet shows the results of our sample. We found two types of errors in our sample. We observed instances where the actual quantity on hand differed from the quantity in the client’s accounting records. We also observed on instance where the cost per the invoice was different than the cost used to determine the inventory balance. The sum of the extended audited balances for the 387 part lines in the sample came to $441,567.00. The sample mean of $1,141.00 lies in the acceptance region. However, the standard deviation of the sample exceeded the standard deviation used to calculate the original critical value.

25

allowance for sampling risk

Accept

C V

BVtolerable error

$200,000 or$117.44

error

$1,110.32

26

Test of Details - sampling


you must project sample results to the population

appropriate consideration for sampling risk

is the projected error too close to tolerable error

How close is too close?

27

Applying what we know about Hypothesis Tests and Confidence Intervals

The risk of incorrectly concluding the book value of the inventory is incorrect when it is correct is Alpha risk or a Type I error. This is the risk of incorrect rejection. The risk of incorrectly concluding inventory is fairly presented when the book value is materially overstated is Beta risk or a Type II error. This is the risk of incorrect acceptance.

In the previous examples the critical value of the hypothesis test and the lower limit of the interval were arbitrarily set to equal to the midpoint between the hypothetical mean and the book value. This will result in Alpha risk that is twice as large as Beta risk because the hypothesis test is a one-tail test while intervals have two tails.

For planning purposes assume that tolerable error for the parts inventory has been set as $200,000, which is approximately 10% of the $1,965,560 balance. Statistical sampling cannot prove that the balance is correct. But auditing standards do not require balances to be exact. Auditing standards require auditors to “obtain reasonable assurance about whether the financial statements are free of material misstatement.” Auditing standards require auditors obtain “sufficient, appropriate evidence” the financial statements “present fairly, in all material respects.” Auditors are typically concerned that asset accounts, such as inventory, are overstated. If tolerable error is $200,000, we need evidence that the actual balance of the parts inventory is greater than $1,765,560.

The interval between the hypothetical mean $1,036.74 ($1,765,560 / 1,703) and the average book value $1,154.17 ($1,965,560 / 1,703) is $117.44 ($200,000 / 1,703). This will remain the same regardless of how we allocate risk between Alpha Risk and Beta Risk. The interval is comprised of two elements: the upper portion of the hypothesis test and the lower tail of the confidence interval. Together these two elements comprise the tolerable error.

28

n = Mean N = Projection

Book value 1,154.18 1703 1,965,560.03

Sample total 441,567.00 387 1,141.00 1703 1,943,123.00

overstatement 13.18 22,437.03

Allowance for Zβ for 0.05 sampling risk

1.645 73.59 1703 125,323.77

error plus allowance 86.77 147,760.80

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29

What if the Sample Mean is less than the Critical Value? Assume the sum of the 387 lines that were audited came to $423,412.83; the standard deviation of the sample was $880.00 and the sample mean was $1,094.09. The sample mean would not lie in the acceptance region. However, the sample mean is larger than the hypothetical mean of $1,036.74. The

projected balance would be $1,863,235.27 . The

projected discrepancy is $102,324.73 ($1,965,560 - $1,863,235) which is less than tolerable error.

The sample does not provide sufficient evidence to state that the parts inventory is not materially overstated with 95% confidence. However, the sample does not provide evidence that the parts inventory is materially overstated. We can modify the equation used to calculate the critical value and determine the level of confidence the sample results do provide.

Let’s assume the sample mean was $1,094.09

30

allowance for sampling risk

Accept

C V

BVtolerable error

$200,000 or$117.44

error

$1,110.32

31

n = Mean N = Projection

Book value 1,154.18 1703 1,965,560.03

Sample total 441,567.00 387 1,094.09 1703 1,863,235.27

overstatement 60.09 102,324.76

Allowance for Zβ for 0.05 sampling risk

1.645 73.59 1703 125,323.77

error plus allowance 133.68 227,648.53

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32

Chris

Which assertions relate to Inventory and Accounts Receivable?

33

Page 153

34

Valuation & allocation

35

Valuation & allocation

36

V&T what we didCollege Business Computer performed by: Tad


Sales

nature of test Test of details of transactionsobjective The objective of this procedure is to determine if the sales account is overstated.assertion(s) Existence/Occurrence and Valuation

invoiceship doc

sales order

customerinvoice

amount

audited amount

difference


sample average 9,558.00projected value 430,110.00

37

Page 436-437 Difference Estimation


Sales

nature of test Test of details of transactionsobjective The objective of this procedure is to determine if the sales account is overstated.assertion(s) Existence/Occurrence and Valuation

invoiceship doc

sales order

customerinvoice

amount

audited amount

difference


sample average -2,088.20projected value -93,969.00sample std deviation 5,203.64

38

customer salesinvoice name to date

6521 Hind Inc. 12,376.00 12,376.00

6522 Foster's Freeze 14,314.00 26,690.00 25,000.006523 Trusco Tank 9,182.00 35,872.006524 Foothill Cyclery 1,344.00 37,216.006525 Performing Arts Center 10,020.00 47,236.006526 San Luis Ready Mix 22,546.00 69,782.00 25,000.00

6527 Copeland's Sports Superstoresds32,807.00 102,589.00 73,902.90 + 48,902.906528 Madonna Inn 7,688.00 110,277.006529 Trusco Tank 8,076.00 118,353.00 73,902.90

6530 Foster's Freeze 6,482.00 124,835.00 122,805.80 + 48,902.906531 Apple Farm Inn 11,020.00 135,855.006532 Copeland's Sports Superstoresds 4,188.00 140,043.006533 Barbich, Longcrier, Hooper & King Accountancy10,426.00 150,469.006534 Flora Design Studio 4,476.00 154,945.006535 First Presbyterian Church 1,344.00 156,289.006536 Kimball Motor Co. 4,188.00 160,477.006537 Standard Motor Co. 4,538.00 165,015.006538 Performing Arts Center 4,834.00 169,849.00 122,805.80

6539 Pacific Conservatory of the Performing Arts2,594.00 172,443.00 171,708.70 + 48,902.906540 Barbich, Longcrier, Hooper & King Accountancy1,344.00 173,787.006541 Hind Inc. 4,188.00 177,975.006542 Airport Auto Center 12,664.00 190,639.006543 Foster's Freeze 9,182.00 199,821.006544 Madonna Inn 15,976.00 215,797.006545 Flora Design Studio 3,432.00 219,229.006546 Copeland's Sports Superstoresds 1,344.00 220,573.00 171,708.70

6547 Apple Farm Inn 39,340.00 259,913.00 220,611.60 + 48,902.90

6548 Barbich, Longcrier, Hooper & King Accountancy12,314.00 272,227.00 269,514.50 + 48,902.906549 Performing Arts Center 19,970.00 292,197.006550 Barbich, Longcrier, Hooper & King Accountancy5,214.00 297,411.006551 Neal-Truesdale Insurance 19,970.00 317,381.00 269,514.50

6552 F. McLintocks 18,908.00 336,289.00 318,417.40 + 48,902.906553 San Luis Ready Mix 8,376.00 344,665.006554 Apple Farm Inn 18,102.00 362,767.00 318,417.40

6555 Standard Motor Co. 5,832.00 368,599.00 367,320.30 + 48,902.906556 Sinsheimer, Schiebelhut & Baggett -PC 1,990.00 370,589.006557 Airport Auto Center 28,628.00 399,217.006558 Trusco Tank 3,432.00 402,649.00 367,320.30

6559 San Luis Ready Mix 19,970.00 422,619.00 416,223.20 + 48,902.906560 Foothill Cyclery 12,446.00 435,065.006561 Barbich, Longcrier, Hooper & King Accountancy1,344.00 436,409.006562 Sinsheimer, Schiebelhut & Baggett -PC 11,982.00 448,391.00 416,223.20

6563 San Luis Medical Center 19,370.00 467,761.00 465,126.10 + 48,902.906564 Kimball Motor Co. 4,692.00 472,453.006565 Hind Inc. 16,576.00 489,029.00

sample size = 10 48,902.90

Page 420-29 MUS

1 chapter 17 audit sampling for tests of details of balances accounts receivable

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