Completing the Tests in the Sales and Collection Cycle: Accounts Receivable

Completing the Tests in the Sales and Collection Cycle: Accounts Receivable

Designing Tests of Details of Balances

• Audit Risk Model

• Thus need to consider– Inherent risk

– Control risk

– Detection risk

– Audit risk

Accounts Receivable-2

Types of Audit Tests and Audit Risk Model

Risk Assessment Procedures

Procedures to understand internal control

Test of control

Inherent Risk

Control Risk

Analytical Procedures

Test of details

Detection Risk

Audit Risk

=

x

x

Sufficient Appropriate Audit Evidence

=

+

+

+

+


The Audit of Accounts Receivable

Set materiality.Assess Audit Risk for A/R.

Conduct analytical procedures for planning purposes

Assess Control Risk for sales and collections cycle

Identify assertions where substantive testing is insufficient,

and/or there is risk of material misstatement

Design and perform test of control. Assess control risk

Design and perform analytical procedures as substantive tests for

accounts receivable balance.

The type of audit procedures?What is the sample size?

Items to be selected? Timing – when to do the procedures?

Design tests of accounts receivable balance to satisfy balance-related

audit objectives.


Effects of Inherent and Control Risks

High Inherent or Control Risk

Greater chance of missing material

misstatement

Thus a lot of substantive

testing

Low Inherent or Control Risk

Material misstatement will be caught by the

system

Thus substantivetesting can be

reduced, but not eliminated


Materiality Considerations

• Accounts receivable may be one of the largest amounts on the balance sheet.

• Sales and accounts receivable balances are normally significant.


Inherent Risk Considerations

• Inherent risk tends to be moderate to low for all assertions – What are the risk associated with Accounts Receivable?

– High risk areas:


Balance-Related Audit Objectives

• Help auditor decide appropriate audit evidence– Accounts receivable exist

– Accounts receivable are owned and have not been sold or discounted

– There are no unrecorded accounts receivables

– Stated at NRV

– Accounts receivable are appropriately recorded and disclosed

• Properly classified

• Aged trial balance agrees with the general ledger

• Accounts receivable are recorded in the correct period


Disclosure-Related Audit Objectives

• Presentation and disclosure in the financial statements– Accounts receivable transactions actually occurred

– Accounts receivable are amounts collectible by the client

– Disclosures for accounts receivables are fully included

– Accounts receivable in the financial statements are materially correct

– Shown at amounts that are collectible

– Correctly shown as current and long-term

– Both financial and non-financial is clearly disclosed


Relationship Between Transaction-Related and Balance-Related Audit Objectives


• Occurrence transaction-related audit objective for sales and the Existence balance-related audit objective

– For sales, the audit objective occurrence shows that

– For accounts receivable, the audit object of existence shows that

– From the point of control risk

• If auditor concludes that control risk over sales is low

– Also, by performing accounts receivable confirmations


• Completeness transaction-related audit objective for cash receipts and the Existence balance-related audit objective

– For cash receipts the audit objective completeness shows that

– For accounts receivable the audit object shows that

– From the point of control risk

• If auditor concludes that control risk over cash receipts is low

– Thus by performing subsequent payments


Analytical Procedures

• Analytical procedures are important

• But remember that analytical procedures are used during three main phases of the audit:1. Planning

2. As part of substantive testing

3. As part of completing the audit engagement


Using Analytical Review to Target Detailed Tests

• Helpful analyses could include comparing:– Sales by month– Sales returns and allowances– Individual customer balances– Bad debt expense to gross sales– Number of days in A/R– Aging categories– Allowance for uncollectible accounts

• To what would these items be compared?

• What is the auditor looking for?


The Audit Objective and the Audit Procedure

• Existence and accuracy: – Confirm accounts receivable balances

– performing alternative procedures for discrepancies and non-replies.


• Rights and obligations:– Could also say the ownership of the asset

– But what is done about pledged or factored accounts receivable?


• Valuation: – What is the important valuation account in relation to

accounts receivable?

– Thus pertinent procedures for valuation?


• Completeness:

• Classification:


• Cut-off: – Select the last 40 sales transactions from the current year’s

sales journal and the first 40 from the subsequent year’s

• Detail tie-in:– Foot the customer master file

• Presentation and disclosure: – Ensure full and complete disclosure in the financial

statements


The Power of Confirmations

• A very important audit procedure– McKesson & Robbins 1937

• Useful for existence

• A/R confirmations come in two forms:– Negative

– PositiveAccounts Receivable-20

Positive vs. Negative Confirmations

• Positive confirmations– A more reliable form of evidence for A/R

– if not answered

• When are they used?– Individual balances are

– And/or .


ABC Company Letterhead

ABC Company

1234 Main Street

Winnipeg, Manitoba

R3R 3R3

15 January, 201Y

To Whom it May Concern:

Please examine the accompanying statement carefully and either confirm its correctness or report any differences directly to our auditors

Black & White, LLP

P.O. Box 789

Hamilton, Ontario

L8C 2H5

Your prompt attention to this request will be appreciated. An stamped envelope is enclosed for your reply.

Sincerely,

……………………………………Jean Fellows, Controller

Confirmation

The balance receivable from us for $2,987.50 as of December 31, 201X is correct except as noted below:

___________________________________________________________________________________________________________

___________________________________________________________________________________________________________

___________________________________________________________________________________________________________

ABC Company

Date ………………………………………. By …………………………………………..


• Negative confirmations– Failure to reply

• Negative confirmation requires a response only if there is a

discrepancy.

• When are they used?


ABC Company Letterhead

ABC Company

1234 Main Street

Winnipeg, Manitoba

R3R 3R3

15 January, 201Y

To Whom it May Concern:

Please examine the accompanying statement. If it does NOT agree with your records, please report any differences directly to our auditors

Black & White, LLP

P.O. Box 789

Hamilton, Ontario

L8C 2H5

Your prompt attention to this request will be appreciated. An stamped envelope is enclosed for your reply. Please do not send your payments to the auditors.

Sincerely,

……………………………………Jean Fellows, Controller

Differences

___________________________________________________________________________________________________________

___________________________________________________________________________________________________________

___________________________________________________________________________________________________________

ABC Company

Date ………………………………………. By …………………………………………..


Controlling and Managing the Confirmation Process

Look at the following points:1. Controlling the sending of confirmations2. Procedures for those accounts the client does not want

confirmed3. Handling returned confirmations4. Timing of alternative procedures and second requests


1. Controlling the Sending of Confirmations

• The client may assist in preparing the confirmations

• If the client stuffs and stamps the envelopes

• Return envelopes


2. Procedures for those Accounts the Client does not want Confirmed

• If it has been selected by the auditor


3. Handling Returned Confirmations

• Confirmations should be returned directly

• Differences between the client’s records and the confirmation reply


Types of differences between client and customer

• Differences between the client records and the confirmation could be due to:1. Payment already made by the client

2. Goods were not received

3. Goods were returned

4. Amounts are in dispute


4. Timing of alternative procedures and second requests

• Second requests can be sent

• Control of such follow-up requests

• Alternative procedures


Nature of Alternative Procedures

• Review of subsequent cash receipts

• Examination of duplicate sales invoices

• Examination of shipping documentation

• Review of correspondence between the client and the customer


Sampling and Accounts Receivable

• Sampling is always used to determine which accounts receivable will be selected

• Statistical sampling could be used to select accounts receivable for confirmation

• Or directed sampling


How Does Monetary Unit Sampling Work?

Auditors use monetary unit sampling, also called probability-proportional-to-size or dollar-unit sampling , to determine the accuracy of financial accounts. With monetary unit sampling, each dollar in a transaction is a separate sampling unit. A transaction for $40, for example, contains 40 sampling units. Auditors usually use monetary unit sampling to sample and test accounts receivable.

Here’s an example of how monetary unit sampling works The audit client’s accounts receivable book value is $300,000, and the sample size is set at 96 records.

1.Figure the sampling interval by dividing book value by sample size• (300,000/96) = 3125

2.Arrange the client’s accounts receivable in an ordered list using some sort of ordering sequence.•For example, you can arrange them alphabetically by customer name or numerically by customer number.

3.Pick a random number between 1 and 3,125.• For this method to work correctly, the random number has to be less than the sampling interval and greater than the smallest

sampling unit. Auditors usually use a random-number-generator computer program to pick the random number. The sampling unit and sampling interval limits are programmed into the software before the task is run. In this case, say the software selects the random number 556.

Monetary Unit Sampling Table

Customer Name Customer Balance Cumulative Balance Sampling Item

ABC Electric $435 $435

Best Friend Cat Care $785 $1,220 (1) $556

Brandy’s Grill $1,510 $2,730

Buddy’s Gas Station $5,000 $7,730 (2) $556 + $3,125 = $3,681


First, pick the records to test: Take the alphabetically ordered list shown in the Customer Name column, which lists every customer balance by dollar amount, and count each dollar until getting to $556. The random number generator gives the number 556 in Step 3 in the previous slide. The cumulative dollar amount for ABC Electric is under $556.

That shows that the first sampling item is Best Friend Cat Care, which at a cumulative total of $1,220 is the first customer in the list with a cumulative balance over $556. Best Friend Cat Care becomes the first customer in the sample.

Secondly, select the next invoice to sample: Add the sampling interval of $3,125 to the random number of $556. This equals $3,681, which is the next sampled item dollar amount. Brandy’s Grill at $2,730 cumulatively is under $3,681, thus Brandy’s is skipped. Buddy’s Gas Station has the 3,681st dollar.

To pick the next sampling item: Add the sampling interval of $3,125 to the prior sampling item of $3,681, which equals $6,806, and so on until the last name in the customer list is reached. This will give the total sample size of 96.

When sampling, misstatements are being looked for. If a selected customers invoice should have been entered for $986, for example, and it was entered as $896, there is a misstatement. If the total misstatements exceed the tolerable level, there may be a material misstatement.


Problem 13-25, p. 446

You have been assigned to the confirmation of aged accounts receivable for the audit of Blank Paper Company Ltd. You have tested the trial balance and selected the accounts for confirmation. Before the confirmation requests are mailed, the controller asks to look at the accounts you intend to confirm in order to determine whether she will permit you to send them.

She reviews the list and informs you that she does not want you to confirm six of the accounts on your list. Two of them have credit balances, one has a zero balance, two of the other three have a fairly small balance, and the remaining balance is highly material. The reason she gives is that she feels the confirmations will upset these customers because they are “kind of hard to get along with.” She does not want the credit balances confirmed because it may encourage the customers to ask for a refund.

In addition, the controller asks you to send an additional 20 confirmations to customers she has listed for you. She does this as a means of credit collection for “those who won’t know the difference between a public accountant and a credit collection agency.”

REQUIRED:

a.Is it acceptable for the controller to review the list of account you intend to confirm? Discuss.

b.Discuss the appropriateness of sending 20 additional confirmations to the customers.

c.If the auditor complies with the controller’s request, what additional audit work is required?

d.Assuming the auditor complies with all of the controller’s requests, what is the effect on the auditor’s opinion?


Problem 13-28, p. 447

You intend to use MUS as a part of the audit of several accounts for Roynpower Manufacturing Inc. You have done the audit for the past several years, and there has rarely been an adjusting entry of any kind. Your audit tests of all tests of controls for the transaction cycles were completed at an interim date, and control risk has been assessed as low. You therefore decide to use an ARIA of 10 percent for all tests of details of balances.

You intend to use MUS in the audit of three of the most material asset balances: accounts receivable, inventory, and marketable securities. You feel justified in using the same ARIA for each audit area because of the low assessed control risk.

The recorded balances and related information for the three accounts are as follows:

Recorded Value

Accounts receivable $3,600,000

Inventory 4,800,000

Marketable securities 1,600,000

$10,000,000

Net earnings before taxes for Roynpower are $2,000,000. You decide that materiality will be $100,000 for the client


The audit approach will be to determine the total sample size needed for all three accounts. A sample will be selected from all $10 million, and the appropriate testing for a sample item will depend on whether the item is a receivable, inventory, or marketable security. The audit conclusions will pertain to the entire $10 million, and no conclusion will be made about the three individual accounts unless significant misstatements are found in the sample.

REQUIRED

a.Evaluate the audit approach of testing all three account balances in one sample.

b.Calculate the required sample size for each of the three accounts assuming you decide that the tolerable misstatement in each account is $100,000. (Recall that tolerable misstatement equals preliminary judgement about materiality for MUS.)

c.How would you identify which sample item in the population to the audit for the number 4,627,817? What audit procedures would you perform?

d.Assume you select a sample of 100 sample items for testing and you find one misstatement in inventory. The recorded value is $987.12, and the audit value is $887.12. Calculate the misstatement bounds for the three combined accounts, and reach the appropriate audit conclusions.


Some Key Terms for Testing Balances

Estimated Population Error Expected Population Error Rate

• A judgmental estimate based on knowledge of client.• Used to determine appropriate sample size.• Low Error => low sample size • As Expected Error approaches Tolerable misstatement, more precision is needed and larger sample

size is needed.

Acceptable Risk of Incorrect Acceptance ARIA

• The risk that the auditor is willing to take of accepting a balance as correct when the true misstatement is greater than the tolerable misstatement.

• In other words it could be materially misstated

ARIA is equivalent to ARACR• ARACR is the risk the auditor is willing to take of accepting a control as effective (or monetary

amount as tolerable) when the true population exception rate is greater than TER. • Again, materially misstated• ARIA is inversely related to sample size

Tolerable Misstatement TER on the tables

• The misstatement that the auditor will permit in the population before concluding that the balance is materially misstated.

• Result of auditor judgment.


Estimated Population Deviation Rate (EPDR)

(in percentage)

Tolerable Exception Rate / Tolerable Misstatement (in percentage)

2 3 4 5 6 7 8 9 10 15 20

5-Percent ARIA

0.00 149 99 74 59 49 42 36 32 29 19 14

0.25 236 157 117 93 78 66 58 51 46 30 22

0.50 . 157 117 93 78 66 58 51 46 30 22

0.75 . 208 117 93 78 66 58 51 46 30 22

1.00 . . 156 93 78 66 58 51 46 30 22

1.25 . . 156 124 78 66 58 51 46 30 22

1.50 . . 192 124 103 66 58 51 46 30 22

1.75 . . 227 153 103 88 77 51 46 30 22

2.00 . . . 181 127 88 77 68 46 30 22

2.25 . . . 208 127 88 77 68 61 30 22

2.50 . . . . 150 109 77 68 61 30 22

2.75 . . . . 173 109 95 68 61 30 22

3.00 . . . . 195 129 95 84 61 30 22

3.25 . . . . . 148 112 84 61 30 22

3.50 . . . . . 167 112 84 76 40 22

3.75 . . . . . 185 129 100 76 40 22

4.00 . . . . . . 146 100 89 40 22

5.00 . . . . . . . 158 116 40 30

6.00 . . . . . . . . 179 50 30

7.00 . . . . . . . . . 68 37


EPDR2 3 4 5 6 7 8 9 10 15 20

10–Percent ARIA

0.00 114 76 57 45 38 32 28 25 22 15 11

0.25 194 129 96 77 64 55 48 42 38 25 18

0.50 194 129 96 77 64 55 48 42 38 25 18

0.75 265 129 96 77 64 55 48 42 38 25 18

1.00 . 176 96 77 64 55 48 42 38 25 18

1.25 . 221 132 77 64 55 48 42 38 25 18

1.50 . . 132 105 64 55 48 42 38 25 18

1.75 . . 166 105 88 55 48 42 38 25 18

2.00 . . 198 132 88 75 48 42 38 25 18

2.25 . . . 132 88 75 65 42 38 25 18

2.50 . . . 158 110 75 65 58 38 25 18

2.75 . . . 209 132 94 65 58 52 25 18

3.00 . . . . 132 94 65 58 52 25 18

3.25 . . . . 153 113 82 58 52 25 18

3.50 . . . . 194 113 82 73 52 25 18

3.75 . . . . . 131 98 73 52 25 18

4.00 . . . . . 149 98 73 65 25 18

4.50 . . . . . 218 130 87 65 34 18

5.00 . . . . . . 160 115 78 34 18

5.50 . . . . . . . 142 103 34 18

6.00 . . . . . . . 182 116 45 25

7.00 . . . . . . . . 199 52 25

7.50 . . . . . . . . . 52 25

8.00 . . . . . . . . . 60 25

8.50 . . . . . . . . . 68 32

Tolerable Misstatement


Solution The audit approach of testing all three account balances is acceptable. This approach is also desirable when the following conditions are present:

• The auditor can obtain valid, reliable information to perform the required tests in all of the areas.• Internal control for each of the three areas is comparable.• Misstatements are expected to occur evenly over the entire population. For instance, the auditor does not expect a large number

of misstatements in accounts receivable and very few, if any, in inventory.

a.The required sample sizes if each account is tested separately are:

Account Tolerable Misstatement as a % Approximate Sample Size (Table 14-9)

Accounts receivable n = 100,000 / 3,600,000 = 0.028 76Inventory n = 100,000 / 4,800,000 = 0.021 114Marketable securities n = 100,000 / 1,600,000 = 0.063 38

c. The population would be arranged so that all accounts receivable would be first, followed by inventory and marketable securities. The items would be identified by the cumulative totals. In the example, the number 4,627,871 would relate to an inventory item since it is between the cumulative totals of $3,600,000 and $8,400,000. Accordingly, for this number the inventory audit procedures would be performed.

d. The misstatement data are as follows:

Recorded Amount

(a)

Audited Amount

(b)

Difference(c)

Misstatement / Recorded

Amount (c/a)

$987.12 $887.12 $100.00 10.1%

Now need to extend the misstatement to the population.Do this by calculating the Upper and Lower limits, not a point estimate.


Generalizing Misstatements to the Population

• The auditor wants to determine the maximum amount of overstatements and understatements

– While still providing a sample with no misstatements– In other words, the auditor did not miss any misstatements in the sample

• These are the upper misstatement bound and the lower misstatement bound• Use the Upper & Lower Misstatement Limits tables for 5% or 10% ARIA and the

number of misstatements• In this example there is one misstatement and the sample size is 114• From the table at an ARIA of 10% on slide 46

– The percentage is between 3.8% (Note for future 2.3 + 1.5 = 3.8) and 3.2% (1.9 + 1.3)– See next slide for the calculation. Calculated percentage = 3.38%– This percentage represents both upper and lower bounds as a percentage

• Based on this:– At a 10% sampling risk, there are no more than 3.38% of the dollar units in the

population that are misstated.– The auditor must make an assumption about the average percent of

misstatement for population dollars that contain a misstatement, but which the auditor has not examined.

• i.e. what is the average misstatement rate for those items that contain a misstatement• This called the Percent of Misstatement Assumption, see Slide 46• In our example the misstatement rate for one misstatement in 10.1% - see previous page.• The auditor is trying to estimate it for those misstatements not found.• This estimate significantly affects the misstatement bounds


Generalizing from the Sample to the Population

Calculating Misstatement Percentage

Sample size for inventory was 114Actual number of deviations was 1ARACR is 10%

From table on page 45, Misstatement Percentage = between 3.8 an 3.2

Sample size of 100 = % of 3.8Sample size of 120 = % of 3.2

Thus a sample size of 114:

100 = 3.8114 = x120 = 3.2

Thus (114 – 100)/(120 – 100) = (x – 3.8)/3.2 – 3.8

x = 3.38

This percentage can be used in calculating the upper and lower bounds (i.e. $ balances)

But note in our example, Part d, we are using a sample size of 100. Thus we will use 3.8%


SAMPLE SIZEACTUAL NUMBER OF DEVIATIONS FOUND

0 1 2 3 4 5 6 7 8 9 10

5 PERCENT RISK OF OVER RELIANCE

25 11.3 17.6 . . . . . . . . .

30 9.5 14.9 19.5 . . . . . . . .

35 8.2 12.9 16.9 . . . . . . . .

40 7.2 11.3 14.9 18.3 . . . . . . .

45 6.4 10.1 13.3 16.3 19.2 . . . . . .

50 5.8 9.1 12.1 14.8 17.4 19.9 . . . . .

55 5.3 8.3 11.0 13.5 15.9 18.1 . . . . .

60 4.9 7.7 10.1 12.4 14.6 16.7 18.8 . . . .

65 4.5 7.1 9.4 11.5 13.5 15.5 17.4 19.3 . . .

70 4.2 6.6 8.7 10.7 12.6 14.4 16.2 18.0 19.7 . .

75 3.9 6.2 8.2 10.0 11.8 13.5 15.2 16.9 18.4 20.0 .

80 3.7 5.8 7.7 9.4 11.1 12.7 14.3 15.8 17.3 18.8 .

90 3.3 5.2 6.8 8.4 9.9 11.3 12.7 14.1 15.5 16.8 18.1

100 3.0 4.7 6.2 7.6 8.9 10.2 11.5 12.7 14.0 15.2 16.4

125 2.4 3.7 4.9 6.1 7.2 8.2 9.3 10.3 11.3 12.2 13.2

150 2.0 3.1 4.1 5.1 6.0 6.9 7.7 8.6 9.4 10.2 11.0

200 1.5 2.3 3.1 3.8 4.5 5.2 5.8 6.5 7.1 7.7 8.3


Sample size ACTUAL NUMBER OF DEVIATIONS FOUND

0 1 2 3 4 5 6 7 8 9 10


20 10.9 18.1 . . . . . . . . .

25 8.8 14.7 19.9 . . . . . . . .

30 7.4 12.4 16.8 . . . . . . . .

35 6.4 10.7 14.5 18.1 . . . . . . .

40 5.6 9.4 12.8 15.9 19.0 . . . . . .

45 5.0 8.4 11.4 14.2 17.0 19.6 . . . . .

50 4.5 7.6 10.3 12.9 15.4 17.8 . . . . .

55 4.1 6.9 9.4 11.7 14.0 16.2 18.4 . . . .

60 3.8 6.3 8.6 10.8 12.9 14.9 16.9 18.8 . . .

70 3.2 5.4 7.4 9.3 11.1 12.8 14.6 16.2 17.9 19.5 .

80 2.8 4.8 6.5 8.3 9.7 11.3 12.8 14.3 15.7 17.2 18.6

90 2.5 4.3 5.8 7.3 8.7 10.1 11.4 12.7 14.0 15.3 16.6

100 2.3 3.8 5.2 6.6 7.8 9.1 10.3 11.5 12.7 13.8 15.0

120 1.9 3.2 4.4 5.5 6.6 7.6 8.6 9.6 10.6 11.6 12.5

160 1.4 2.4 3.3 4.1 4.9 5.7 6.5 7.2 8.0 8.7 9.5

200 1.1 1.9 2.6 3.3 4.0 4.6 5.2 5.8 6.4 7.0 7.6


Appropriate Percent of Misstatement Assumption

• This is an auditor decision

• Many auditors assume that it is desirable to assume 100% for both overstatements and understatements

• Using MUS, upper and lower misstatement bounds are used rather than maximum likely misstatement attached to a confidence level

• In other words, the misstatement is likely somewhere in between the max and the min

• The following example uses 50% instead of 100%

• The single overstatement percentage amount for this problem is 10.% as calculated below

Recorded Amount

Audited Amount

Difference Misstatement / Recorded Amount

$987.12 $887.12 $100.00 10.1%Accounts Receivable-46

Number of Misstatements

(1)

Upper Precision Limit

Portion(2)

Recorded Value

(3)

Misstatement Unit Error Assumption

(4)

Bound Portion2x3x4

Overstatements

0 0.023 10,000,000 0.50 115,000

1 0.015 10,000,000 0.101 15,150

Upper Precision Limit 0.038

Initial Misstatement Bound

130,150


(1)


Portion(2)

Recorded Value

(3)

Misstatement Unit Error Assumption

(4)

Bound Portion2x3x4

Understatements

0 0.023 10,000,000 0.50 115,000



115,000

Also remember in this example the auditor makes the assumption that the average percent of misstatement for population dollars that contain a misstatement is a 50% misstatement unit error. These will be items that the auditor has not examined.

Note that there may be both overstatements and understatements in the population. Thus the following tables look at the Precision Limits for both over and understatements. Also remember that there was only one misstatement found, and this was an overstatement.



Misstatement Unit Error

Assumption(a)

Sample Size(b)

Recorded Population

(c)

Point Estimatea(c/b)

Bounds

Initial Overstatement

Bound

130,150

Understatement Misstatements

0

Adjusted Overstatement Bound

130,150

Initial Understatement

Bound

115,000

Overstatement Misstatements

1 0.101 100 10,000,000 10,100 (10,100)

Adjusted Understatement Bound

105,000

Thus the likely misstatement is between $105,000 and $130,050. Since materiality is $100,000, more work needs to be done

There must be adjustments made to the over and understatement bounds because an understatement offsets and over statement, and vice-versa


49

Alternatively: Calculate point estimate for the overstatement.

Sum of Unit Misstatement Assumptions

Sample Size

XRecorded Population

Value = Point Estimate

Overstatement Point Estimate:

0.101

100X 10,000,000 = 10,100

Initial understatement bound 115,000Less overstatement point estimate (10,100)Adjusted understatement bound (LMB) 105,000

Calculate adjusted upper and lower misstatement bounds.

The adjustment of bounds for offsetting amounts is made by reducing each bound by the opposite point estimate.

Initial overstatement bound 130,150Less understatement point estimate (0)Adjusted overstatement bound (UMB) 130,150

The MUS Decision Rule

If both the lower misstatement bound (LMB) and upper misstatement bound (UMB) fall between the understatement and overstatement tolerable misstatement amounts, accept the conclusions that the book value is not misstated by a material amount.

Otherwise, conclude that the book value is misstated by a material amount.

Reject

Tolerable misstatement

($-35,000)


$35,000

($25,000)

LMB

($40,000)

UMB

For Example:

Reject


($-100,000)


$100,000

($105,000)

LMB

($130,000)

UMB

Our Example:

Another example

• Assume that there are the following misstatements with a sample size of 100 and an ARIA of 10%

Recorded Amount

(a)

Audited Amount

(b)

Misstatement(c)

Misstatement Percentage

c/a

9987.12 9887.12 100.00 1.0%

3350.75 3340.75 10.00 0.3%

2167.34 2267.34 (100.00) 4.6%

65.43 64.53 0.90 1.4%

775.45 757.45 18.00 2.3%



(1)

Upper Precision

Limit Portion

(2)

Recorded Value

(3)


Assumption (4)

Bound Portion2x3x4

Overstatements

0 0.023 10,000,000 0.500 115,000

1 0.015 10,000,000 0.023 3,450

2 0.014 10,000,000 0.014 1,960

3 0.014 10,000,000 0.010 1,400

4 0.012 10,000,000 0.003 360


0.078


122,170

Note in the following table, the conservative approach is to associate the lowest misstatement limit (2) portion with the highest misstatement unit error (4) .The amount of error is thus maximized

Overstatements

*

* These amounts come from the previous slide. Only overstatements.


Sample size ACTUAL NUMBER OF DEVIATIONS FOUND

0 1 2 3 4 5 6 7 8 9 10


20 10.9 18.1 . . . . . . . . .

25 8.8 14.7 19.9 . . . . . . . .

30 7.4 12.4 16.8 . . . . . . . .

35 6.4 10.7 14.5 18.1 . . . . . . .

40 5.6 9.4 12.8 15.9 19.0 . . . . . .

45 5.0 8.4 11.4 14.2 17.0 19.6 . . . . .

50 4.5 7.6 10.3 12.9 15.4 17.8 . . . . .

55 4.1 6.9 9.4 11.7 14.0 16.2 18.4 . . . .

60 3.8 6.3 8.6 10.8 12.9 14.9 16.9 18.8 . . .

70 3.2 5.4 7.4 9.3 11.1 12.8 14.6 16.2 17.9 19.5 .

80 2.8 4.8 6.5 8.3 9.7 11.3 12.8 14.3 15.7 17.2 18.6

90 2.5 4.3 5.8 7.3 8.7 10.1 11.4 12.7 14.0 15.3 16.6

100 2.3 3.8 5.2 6.6 7.8 9.1 10.3 11.5 12.7 13.8 15.0

120 1.9 3.2 4.4 5.5 6.6 7.6 8.6 9.6 10.6 11.6 12.5

160 1.4 2.4 3.3 4.1 4.9 5.7 6.5 7.2 8.0 8.7 9.5

200 1.1 1.9 2.6 3.3 4.0 4.6 5.2 5.8 6.4 7.0 7.6



(1)

Upper Precision

Limit Portion

(2)

Recorded Value

(3)


Assumption (4)

Bound Portion2x3x4

Understatements

0 0.023 10,000,000 0.500 115,000

1 0.015 10,000,000 0.046 6,900


0.038


121,900

Understatements


Number of Misstatements Misstatement Unit Error

Assumption(a)

Sample Size(b)

Recorded Population

(c)

Point Estimatea(c/b)

Bounds

Initial Overstatement Bound 122,170

Understatement Misstatements

1 0.046 100 10,000,000 4,600 (4,600)

Adjusted Overstatement Bound 117,570

Initial Understatement Bound

Overstatement Misstatements 121,900

1 0.023 100 10,000,000 2,300 (2,300)

2 0.014 100 10,000,000 1,400 (1,400)

3 0.010 100 10,000,000 1,000 (1,000)

4 0.003 100 10,000,000 300 (300)

Adjusted Understatement Bound 116,900

Offsetting Adjustments


58

Calculate point estimate for the overstatements and understatement.


Sample Size

X Recorded Population Value = Point Estimate


0.023+0.014+0.010+0.003

100X 10,000,000 = 5,000

Understatement Point Estimate:

0.046

100X 10,000,000 = 4,600



Initial understatement bound 121,900Less overstatement point estimate (5,000)Adjusted understatement bound (UMB) 116,900

Initial overstatement bound 122,170Less understatement point estimate (460)Adjusted overstatement bound (LMB) 117,570

Since both LMB and UMB are above the materiality (tolerable misstatement) of $100,000 – reject the population because it is misstated by a material amount.

Alternatives When a Population is Rejected

1. Take no action until tests of other audit areas are completed

2. Perform expanded audit tests

3. Increase the sample size

4. Adjust the account balance

5. Request the client to correct the population

6. Refuse to give an unqualified opinion

1. Take no action until tests of other audit areas are completed

2. Perform Expanded Audit Tests in Specific Areas

3. Increase the Sample Size

4. Adjust the Account Balance

5. Request the Client to Correct the Population

6. Refuse to Give an Unqualified Opinion


(1)

Upper Precision

Limit Portion

(2)

Recorded Value

(3)


Assumption (4)

Bound Portion2x3x4

Overstatements

0 0.023 4,800,000 0.50 55,200

1 0.015 4,800,000 0.023 1,656

2 0.014 4,800,000 0.014 941

3 0.014 4,800,000 0.010 672

4 0.012 4,800,000 0.003 173


0.078


58,642

Now: Assume that we did not combine Accounts Receivable, Inventory and Marketable Securities together as one population. The misstatements would have to be allocated to the population from which they came. In this example, lets assume they all came from Inventory. N = $4,800,000

Overstatements

*

* These amounts come from the previous slide. Only overstatements.63


(1)

Upper Precision

Limit Portion

(2)

Recorded Value

(3)


Assumption (4)

Bound Portion2x3x4

Understatements

0 0.023 4,800,000 0.500 55,200

1 0.015 4,800,000 0.046 3312


0.038


58,512

Understatements

64

65

Calculate point estimate for the overstatements and understatement.


Sample Size

X Recorded Population Value = Point Estimate


0.023+0.014+0.010+0.003

100X 4,800,000 = 2,400

Understatement Point Estimate:

0.046

100X 4,800,000 = 2208

or: (0.05/100) x 4,800,000



Initial understatement bound 58,512Less overstatement point estimate (2,400)Adjusted understatement bound (LMB) 56,112

Initial overstatement bound 58,642Less understatement point estimate (2,208)Adjusted overstatement bound (UMB) 56,434

Problem 13-19, p. 443

During his interim audit visit, Charles Ai determined that one of the subsidiary companies of Mega Big Limited had experienced some very serious problems with respect to the credit management and collection of trade accounts receivable. During the first six months of the year, the accounts receivable of this subsidiary had almost doubled, the number of days’ sales in accounts receivable had increased from 39 to 64 days, and bad-debt expense had risen sharply.

REQUIRED

Prepare an outline of the steps that should be taken to investigate the nature and causes of the credit and collection problems. (Do not consider the possibility of fraud.)


Documents

Completing the Tests in the Sales and Collection Cycle: Accounts Receivable