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MISCELLANEOUS STATISTICAL SAMPLING PROBLEMS THE POPULATION, THE FRAME AND THE SAMPLING UNIT The following problems are based on the material in the ELEMENTS OF SAMPLING: THE POPULATION, THE FRAME AND THE SAMPLING UNIT folder. The problems refer to the Revised Sales-AR-Receipts Manual System flowchart, which is in INTERNAL CONTROL > SALES-ACCOUNTS RECEIVABLE > MANUAL SYSTEM. For each of the following test objectives, identify: The assertion The population The frame The sampling unit Supporting document[s] 1. Recorded sales are posted timely 2. Shipments are billed 3. Recorded sales occured 1 MISCELLANEOUS STATISTICAL SAMPLING PROBLEMS INTERPRETING SAMPLE RESULTS The following problems are based on the material in the INTERPRETING CONFIDENCE INTERVALS IN AUDIT SAMPLES folder. Your best approach to proper interpretation is to sketch the results on a 1-dimensional graph. 1. An auditor has selected and evaluated a statistical sample of accounts receivable to assess collectibility on an account-by-account basis, and then project the finding of uncollectible amounts to the population. Several accounts were found in the examination to be partly or entirely uncollectible. The test results showed that, at 95% confidence, uncollectible receivables total between 800,000 and 4,200,000 (overstatement). a. What should be the auditor's conclusion if the maximum tolerable misstatement is $1,800,000? b. Propose an appropriate adjusting journal entry. c. Suppose that, prior to this test, the client's allowance for uncollectible accounts is $1,000,000. What would you recommend? 2. You are performing an obsolescence review of a 22,000 item parts inventory. The book value of the inventory is $10,515,000. You decide to select a random sample for dollar value estimation. The maximum tolerable misstatement is $500,000 and the planned confidence level is 95% (2-sided). Pricing errors were disclosed in the sample. What would be your conclusions/recommendation in each of the following situations? a. Overstated by an estimated $320,000, with a lower confidence limit [LCL] of $30,000 and an upper confidence limit [UCL] of $610,000. b. Overstated by an estimated $240,000, with LCL = $90,000 and UCL=$390,000. $ VALUE ESTIMATION - DESIGN AND EVALUATION The following problems are based on the material in the VARIABLES ESTIMATION IN EQUAL PROBABILITY SAMPLES folder. 2 MISCELLANEOUS STATISTICAL SAMPLING PROBLEMS 1. An equal probability random sample of 432 items was selected from a population of 11,487 items. The average value of the sample was $127.09, and its standard deviation was $42.08. Calculate the 99% confidence interval. 2. An equal probability random sample of 110 items was selected from a population of 5,230 items. The sample disclosed six misstated items, and 104 items with $0.00 misstatement. The amounts of the misstatements are as follows: Misstatement $ 235.30 (147.33) 24.35 101.21 ( 18.04) 92.55 $ 288.04 net overstatement Calculate the 95% two-sided confidence interval on the total misstatement in the population. [Hint: Do not ignore the items with $0 misstatement] 3. If a population has a total value of $5,724,300, a standard deviation of $840, and a population size of 15,000 items, what is the probability that a simple random sample of 1,500 items will yield an estimate of the population's total value that is within 10% of the actual total value? 4. If a population has 94,000 items and an estimated standard deviation of $235, how large a sample would be required to estimate the population's total value to within $2,000,000 of its value? Assume a 90% two-sided confidence level. ANSWERS 1. Lower limit Upper limit $1,399,712 $15,20053 [without finite population correction] 2. Lower limit Upper limit ($15,643) $43,033 [without finite population correction] 3. Within +/- 10%, probability = 0.9364 4. Within +/- $2,000,000, sample size = 331 HYPOTHESIS TESTING The following problems are based on the materials in the AUDIT SAMPLING AND HYPOTHESIS TESTING folder. 3 MISCELLANEOUS STATISTICAL SAMPLING PROBLEMS 1. A random sample is to be selected from a population of 22,000 items. The standard error the estimate of the population's total value [ T^ ] is $78,500. If the chosen confidence level [1 is 95%, what is the risk [] of failing to detect misstatement amounting to $100,000? (Hint: First, calculate the precision [A]) 2. Given that the maximum tolerable misstatement is $750000 and the risk of incorrect rejection (estimation risk) is 20%, calculate the required precision for the following detection risks []: 10%, and 50%. 3. Given that materiality is $700000, planned precision is $500000, and confidence level is 90%, calculate the risk of accepting a materially misstated book value. ANSWERS: 1. 75.4% risk of failing to detect $100,000 2. Risk Precision 10% $277,479 50% $700,000 3. Probability of accepting materially misstated book value is 25.5% 4 SALES-ACCOUNTS RECEIVABLE MANUAL SYSTEM CREDIT NOTE: ALL DOCUMENTS ARE PRENUMBERED. SALES NOTE: ALL DOCUMENTS ARE PRENUMBERED. CUSTOMER G CUSTOMER PO CHECK CUST LIST OR OBTAIN CREDIT INFO CUSTOMER LIST APPROVED CUSTOMER P/O C2 INVENTORY LIST * SALES ORDERS Account history [previous customers] Credit information Bank information Other financial information Report prepared, if new customer PREPARED ONLY FOR COMPLETEABLE ORDERS. OTHERS NOT DESCRIBED HEREIN CHECK INVENTORY* & PRICES. PREPARE SALES ORDER LOG ORDER PRICE LIST SALES ORDER LOG YES IS CUSTOMER APPROVED ? NO CUSTOMER PREPARE REJECTION NOTICE COPY & APPROVE P/O. UPDATE CUST. LIST , IF NEW CUST L B 2 1 NEW CUST CREDIT REPORT # 1 2 REJECTION NOTICE CUSTOMER PURCHASE ORDER G ORIG APPROVED CUST P/O A TO CUSTOMER A BY CUSTOMER A BY CUSTOMER SALES INVOICE P/O COPY COPY 2 COPY 1 1 1 2 SALES ORDER 1 3 1 4 1 A EVERY SALE BY S/O D SALES-ACCOUNTS RECEIVABLE MANUAL SYSTEM SHIPPING NOTE: ALL DOCUMENTS ARE PRENUMBERED. BILLING NOTE: ALL DOCUMENTS ARE PRENUMBERED. ORIG APPROVED CUSTOMER P/O SALES ORDER 3 1 PRICE LIST SHIPPING DOC 2 1 3 A C SHIPPER SALES ORDER LOG SALES ORDER SHIPPING LOG ASSEMBLE, PACKAGE GOODS. PREPARE SHIPPING DOC & LOG ENTRY INVENTORY LIST C L A B WITH GOODS CUSTOMER PRICE LISTS 1 2 SHIPPING DOC 3 4 COMPARE DOCS, CHECK ARITH PREPARE INVOICE. POST TO INVOICE LOG SALES ORDER 3 1 # INVOICE LOG SALES ORDER 2 1 BY SHIPPING DOCUMENT CUSTOMER NOTE: INVENTORY ACTIVITY IS NOT DESCRIBED HERE 1 1 2 SALES INVOICE 1 3 1 4 1 D BATCH WITH OTHER BILLS END OF DAY D E EVERY SALE # BY SALES INVOICE SHIPPING DOC 3 APPROVED CUSTOMER P/O BILLING ACCOUNTING 1 POST DRs TO ACCOUNTS/CRs TO SA F E BATCHED INVOICES 3 CONTROL TAPE BATCHED INVOICES 3 TOTAL THE INVOICES. PRAPARE TAPE D A I L Y BATCHED INVOICES 3 CONTROL TAPE MAKE COPIES OF INVOICES POST SALES CUST A/Cs. TOTAL & COMPARE CONTROL TAPE D A C T I V I T I E S F BATCHED INVOICE COPIES 3 J CCOUNTING 1 ACCOUNTS/CRs TO SALES POST CASH F ATCHED NVOICES CONTROL TAPE PASSWORD PROTECTED ACCESS TO COMPANY LAN POST SALES CUST A/Cs. TOTAL & COMPARE A/R LEDGER A/R LEDGER SALES JL APPLICATION NOTE 1 SEE NOTES 1 AND 2 K BATCHED INVOICES 3 # ACCOUNT NUMBER SALES JOURNAL ATCHED VOICE OPIES PASSWORD PROTECTED ACCESS TO COMPANY LAN NOTE 2 NOTES: 1. ACCESS ONLY TO POST DRs TO CUSTOMER ACCOUNTS Customer and invoice information entered: Cust name, a/c #, invoice #, date $ amt. Appl tests for existing customer [new customers entered by credit dept. App charges customer a/c and updates balance 2. ACCESS ONLY TO POST CRs TO CUSTOMER ACCOUNTS Customer and invoice information entered: Cust name, a/c # Invoice #, date billed, $ amt. billed, $ amt, paid,. Remittance advice #, date received, App tests for existing customer, matches data entered by Acct 2 to Acct 1 App credits customer a/c for amt paid and updates balance. App maintains A/R aging. ACCOUNTING 2 POST CASH CRs TO ACCOUNTS J TREAS. OFF BATCHED INVOICE COPIES 3 # PRENUMBERED A/C , INVOICE# AMT PAID CUSTOMER REMITTANCE ADVICES OPEN INVOICE FILE, BY ACCOUNT NUMBER PLACE R/As IN AN IN-BOX ON DESK AS D RECEIVED. REMOVE FIRST-IN-FIRST-OUT REMOVE PAID INVOICE FROM FILE INVOICE COPY 3 CUSTOMER REMITTANCE ADVICE COMPARE DOCUMENTS, POST AMOUNT PAID TO CUST A/C RETURN TO OPEN INVOICE FILE INVOICE COPY PAID IN FULL? 3 NO YES CUSTOMER REMITTANCE ADVICE K DO FOR EACH PAID INVOICE INVOICE COPY 3 CUSTOMER REMITTANCE ADVICE # PD IN FULL INVOICE FILE, BY ACCOUNT NUMBER Purpose: To document key controls around the Revenue Cycle: INTERNAL CONTROL CHECK SALES-ACCOUNTS RECEIVABLE MAN Location: Item # Control Objective: Control strength 1 Sales are inititated only upon receipt of a customer order. S1 2 Customer is approved for credit prior to executing a sale. S2 3 Prices are based on current price lists or policies S3 4 Goods are shipped only upon receipt of approved sales order S4 5 Shipped orders are checked for accuracy prior to invoicing the customer S5 6 Invoices are properly supported by evidence that an arrangement exists. S5 7 Shipped orders are billed and posted in a timely manner. S5 8 Revenue is recorded in the proper time period. S5 9 Invoices are posted to accounts receivable in a timely manner. S6 10 Segregation of Duties: Authorization and custody Authorization and recording Custody and recording G G G Supporting Documentation 11 Documents are prenumbered S0 12 Customer orders are properly documented and retained S7 13 Customer credit documentation exists and is up-to-date S8 14 Sales orders are prepared and copies retained S9 15 Shipping documents are prepared and copies retained S10 16 Customer invoices ae prepared and copies retained S11 G = objective is ach G = objective is not NTERNAL CONTROL CHECKLIST COUNTS RECEIVABLE MANUAL SYSTEM Supported Assertions Control weakness N/A Existence or Occurrence Completeness Accuracy Cutof G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G Valuation or Allocation G G G G G G G G G = objective is achieved or assertion is supported = objective is not achieved or assertion is not supported. G G G G G G Presentation and disclosure Rights and obligations G G G G G G G G G G G G SALES NOTE: ALL DOCUMENTS ARE PRENUMBERED. S0 CUSTOMER S1 S2 I APPROVED CUSTOMER P/O CUSTOMER P/O S8 RECEIVED DAILY FROM CREDIT CHECK CUST LIST FOR APPROVAL CUSTOMER LIST CUSTOMER P/O NO CUST APPROVED ? YES G APPROVED CUSTOMER P/O * SALES ORDERS PREPARED ONLY FOR COMPLETEABLE ORDERS. OTHERS NOT DESCRIBED HEREIN CHECK INVENTORY* & PRICES. PREPARE SALES ORDER COPY CUST PO INVENTORY LIST PRICE LIST S3 PRENUMBERED CUSTOMER 1 1 2 SALES ORDER 1 3 1 4 1 A P/O COPY APPROVED CUSTOMER P/O B SALES INVOICE 2 1 P/O COPY APPROVED CUSTOMER P/O SALES INVOICE 2 1 # BY S/O S7 S9 1 REJECTION NOTICE A H D S0 CREDIT NOTE: ALL DOCUMENTS ARE PRENUMBERED. G CUSTOMER PO OBTAIN CREDIT INFORMATION Account history [previous customers] Credit information Bank information Other financial information S2 YES NO IS CUSTOMER APPROVED ? PREPARE REJECTION NOTICE S8 PREPARE APPROVAL UPDATE CUST. LIST 1 2 H COPY 3 REJECTION NOTICE CUSTOMER LIST APPROVED CUST P/O DELIVER UPDATED CUSTOMER LIST TO SALES DAILY TO CUSTOMER A I A I SHIPPING NOTE: ALL DOCUMENTS ARE PRENUMBERED. S0 B SALES ORDER S4 S10 3 1 SHIPPING LOG ASSEMBLE, PACKAGE GOODS. PREPARE SHIPPING DOC & LOG ENTRY ous customers] C SHIPPER WITH GOODS CUSTOMER 1 2 SHIPPING DOC 3 4 SALES ORDER 3 1 # PREPARE REJECTION NOTICE BY SHIPPING DOCUMENT NOTE: INVENTORY ACTIVITY IS NOT DESCRIBED HERE CUSTOMER PURCHASE ORDER S8 A S0 BILLING NOTE: ALL DOCUMENTS ARE PRENUMBERED. C A SALES ORDER 2 1 S0 SHIPPING DOC APPROVED CUSTOMER P/O 3 SHIPPING LOG A S3 S5 PRICE LISTS COMPARE DOCS, CHECK ARITH PREPARE INVOICE. POST TO SALES JL SALES ORDER 3 1 SALES JOURNAL CUSTOMER END OF DAY 2 1 SHIPPING DOC 3 APPROVED CUSTOMER P/O 1 1 2 SALES INVOICE 1 3 1 4 1 D BATCH WITH OTHER BILLS SALES ORDER D E # S7 BY SALES INVOICE S9 S10 S11 BILLING ACCOUNTING F E BATCHED INVOICES 3 S6 BATCHED INVOICES 3 CONTROL TAPE TOTAL THE INVOICES. PREPARE TAPE BATCHED INVOICES 3 CONTROL TAPE POST CUST A/Cs. TOTAL & COMPARE CONTROL TAPE D F ACCOUNTING F ATCHED NVOICES CONTROL TAPE POST CUST A/Cs. TOTAL & COMPARE ACCTS RECV SUB-LEDGER BATCHED INVOICES 3 # S11 ACCOUNT NUMBER