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Section Topics

Sampling Statistical analyses Data gathering tools Analytical review techniques Observation. Section Topics. Problem solving Risk and control self-assessment Computerized audit tools and techniques Process mapping, including flowcharting. Part 2, Section E. When to use.

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Section Topics

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  1. Sampling Statistical analyses Data gathering tools Analytical review techniques Observation Section Topics • Problem solving • Risk and control self-assessment • Computerized audit tools and techniques • Process mapping, including flowcharting Part 2, Section E

  2. When to use To estimate the number of times a certain characteristic may occur in a population Size of sample Based on judgment about probability that errors (or other characteristics) will occur or based on statistical tables Statistical table specifications • Population size • Confidence level • Precision • Expected error rate Attributes Sampling Part 2, Section E, Topic 1

  3. Variables Sampling When to use variables sampling Specifications for statistical tables When size matters; e.g., amount of a discrepancy • Population size • Confidence level • Precision • Standard deviation Reminder: Use attributes sampling when number matters, not size. Reminder: For attributes sampling, error rate is a specification, not standard deviation. Part 2, Section E, Topic 1

  4. Case example Population: 1,500 accounts Total book value: US $1 million Sample size: 100 accounts Sample book value: US $66,666.67 Sample audit value: US $69,350.00 Step 1: Calculate average audit value (i.e., mean-per-unit value for audited samples). $69,350.00 / 100 = $693.50 / acct. Step 2: Multiply mean/unit value by number of accounts in the population. $693.50  1,500 accounts = $1,040,250.00 Undercount = $40,250.00 ($1,040,250.00 – $1,000,000.00) Variables Sampling: Mean-per-Unit Estimation Part 2, Section E, Topic 1

  5. Case example Population: 1,500 accounts Total book value: US $1 million Sample size: 100 accounts Sample book value: US $66,666.67 Sample audit value: US $69,350.00 Variables Sampling: Difference Estimation Step 1: Calculate average difference between audit value and book value for the sample. $69,350.00 – $66,666.67 / 100 accounts = $26.83 Step 2: Determine the difference estimate for the population. $26.83  1,500 accounts = $40,245.00 Step 3: Estimate actual value by adding the difference estimate and book value for the population. $40,245.00 + $1,000,000 = $1,040,245.00 Book value is understated by $40,245.00. Part 2, Section E, Topic 1

  6. Case example Population: 1,500 accounts Total book value: US $1 million Sample size: 100 accounts Sample book value: US $66,666.67 Sample audit value: US $69,350.00 Variables Sampling: Ratio Estimation Step 1: Audit value for sample = $69,350.00 Step 2: Book value for sample = $66,666.67 Step 3: Find ratio of sample audit value/book value: $69,350.00 / $66,666.67 = 1.04 Step 4: To estimate actual population value, multiply ratio by population book value: 1.04  $1,000,000 = $1,040,000.00 Book value is understated by $40,000. Part 2, Section E, Topic 1

  7. When an internal auditor reports the results of statistical sampling in the form “We are 95% confident that the error rate in the population is 6%, plus or minus 3%,” what exactly does that mean? Discussion Question Answer: This means that a randomly selected sample from an entire population (e.g., a group of transactions) contained a number of errors indicating that there is a 95% chance that the error rate in the total population is between 3% and 9%. Part 2, Section E, Topic 1

  8. Which of the following considerations would necessitate an increase in sample size? Which would allow for a smaller sample? Discussion Question Answer: Larger Smaller 1. Increase confidence level from 90% to 95%. X 2. Increase range of error from  2.5% to  5%. X 3. Increase population size from 150,000 to 500,000. X Part 2, Section E, Topic 1

  9. What are some of the advantages and disadvantages of statistical sampling? Discussion Question Sample answer: • Advantages • May yield desired results from the minimum sample size • Yields quantified data • Includes measures of sampling risk, confidence level, and precision • Is adaptable to computer testing • Lends credibility to audit conclusions • Disadvantages • Requires cost and time to perform • Requires training and software costs • May preclude experienced auditors’ insights Part 2, Section E, Topic 1

  10. What are the differences, if any, between unsystematic (haphazard) sampling and judgmental sampling? Discussion Question Sample answer: Some, but not all, judgmental sampling is unsystematic. Unsystematic sampling makes no attempt either to randomize samples (such as picking every tenth item from the population) or to select samples according to the auditor’s best judgment (such as excluding certain items as obviously unrepresentative). Part 2, Section E, Topic 1

  11. What are some advantages and disadvantages of nonstatistical sampling? Discussion Question Sample answer: • Advantages • Flexibility • Use of internal auditor’s judgment • Allows reasonable reliability at reasonable cost • Disadvantages • Results not statistically valid • No objective measure of sampling risk provided • Chance of wrong sample size • Effectiveness depends upon the auditor’s skill Part 2, Section E, Topic 1

  12. Random Numbers Discussion Question Which random number matches a population number? Answer: Population Numbers 96 97 98 99 100 101 102 103 104 105 106 85 86 87 88 89 90 92 93 93 94 95 107 108 109 110 111 112 113 114 115 116 117 Part 2, Section E, Topic 1

  13. Stratified Random Sampling Widely varied populations can be grouped into like strata with random sampling of each to reduce the chances of missing a significant item in a small but important segment. Stratum 2 Billionaires Stratum 1 Ordinary accounts Part 2, Section E, Topic 1

  14. Discussion Question Interval sampling selects items a set distance apart, such as every third item. What is a potential problem and a safeguard? Sampling interval = 3; Starting point = 2 Sample answer: The population may use the same interval for identical items. Run the selection more than once from different random starting points. Part 2, Section E, Topic 1

  15. Cluster Sampling Samples made up of pre-existing clusters such as file drawers, boxes, rooms, etc. A–Z A–Z A–Z taxes A–Z A–Z Size 9 A–Z A–Z taxes A–Z A–Z Part 2, Section E, Topic 1

  16. Discussion Question When is it appropriate to use the two types of attribute sampling below? Answer: Use discovery sampling when: Use stop-and-go sampling when: You need to find only one instance; e.g., suspected fraud. You think you may get reasonable results from a small sample. Part 2, Section E, Topic 1

  17. Dollars 1–500,000 Dollar-Unit Discovery Sampling (DUDS) All confirmations #1 = $1,000 #2 = $876 #3 = $58 *** #28 = $9,999 *** #1012 = $1,350 Dollar #824 Dollar #221, #422 Dollar #1173 Dollar #23 Dollar #500,000 Click again to show random selections. $500,000 total Part 2, Section E, Topic 1

  18. Population Dollar units Sample Outcome $1 $1 $1 $1 $1 $1 $1 $1 $1 $1 $1 $1 $1 $1 $1 $1 $1 $1 Account 1 = $2 Estimate of maximum error at confidence level Account 2 = $3 Acct. 2 Acct. 4 Account 3 = $4 Account 4 = $9 Dollar-Unit Sampling: A Hybrid Part 2, Section E, Topic 1

  19. Discussion Question What is the difference between descriptive and inferential statistics? Answer:Descriptive statistics provides tools and vocabulary to shape raw data in such a way that inferential statisticscan be used to draw conclusions about the meaning of the data (as in the preceding section). Part 2, Section E, Topic 2

  20. Normal Distributions and the Bell Curve The individual values in any large-scale population tend to be distributed symmetrically around a midpoint (m) unless a force other than chance distorts the distribution. -3s -2s -1s m +1s +2s +3s Part 2, Section E, Topic 2

  21. 29% Tosses 28% 17% 20% 4% 2% 5h,0t 4h,1t 3h,2t m 4h,1t 4t,1h 5t,0h Discussion Question Can you get a normal curve when you toss 5 pennies 100 times? Answer: Not quite; it’s a small sample. Part 2, Section E, Topic 2

  22. Mode = Most Frequent m 1 2 3 3 3 4 5 ... ... ... ... ... ... Median = Midpoint Mean = Average 1 + 2 + 3 + 3 + 3 + 4 + 5 7 = 3 -3s -2s -1s +1s +2s +3s m Measures of Central Tendency: Mean, Median, and Mode Part 2, Section E, Topic 2

  23. 3 5 1 2 3 3 4 ... ... ... ... ... ... Impact of an Outlier (Change 5 to 15) Mode = Most Frequent Mode = Most Frequent 15 3 1 2 3 3 4 ... ... ... ... ... ... Median = Midpoint Median = Midpoint Mean = Average Mean = Average 1 + 2 + 3 + 3 + 3 + 4 + 5 7 1 + 2 + 3 + 3 + 3 + 4 + 15 7 = 3 = 4.43 Part 2, Section E, Topic 2

  24. 13.59% 13.59% 0.1% 0.1% 2.14% 2.14% Discussion Question The standard deviation, represented by the Greek letter sigma (s), measures variabilityof the sample—the percentage of items falling with equal segments on both sides of the mean. What % of area lies between –1 and +1 sigmas? 34.13% 34.13% Answer: About 68% -3s -2s -1s m +1s +2s +3s Part 2, Section E, Topic 2

  25. Range The wider the range from “tail” to “tail,” the larger the standard deviation—because there is more variability in the sample of items. Left tails Right tails Range Part 2, Section E, Topic 2

  26. MAD = Average deviation of sample items from the mean without regard to direction of the deviation MAD example: mileage for 10 cars MPG MPG – Mean = Absolute deviation 1—20.0 2—21.5 3—19.5 4—25.0 5—42.5 6—14.0 7—8.0 8—23.0 9—17.5 10—28.0 20.0 – 21.9 = 1.9 21.5 – 21.9 = 0.4 19.5 – 21.9 = 2.4 25.0 – 21.9 = 3.1 42.5 – 21.9 = 20.6 14.0 – 21.9 = 7.9 8.0 – 21.9 = 13.9 23.0 – 21.9 = 1.1 17.5 – 21.9 = 4.4 28.0 – 21.9 = 6.1 61.8 deviation 10 mpg items 6.18 MAD Total = 219.0 Deviation = 61.8 MAD (Mean Absolute Deviation) Part 2, Section E, Topic 2

  27. Variance (s2)measures dispersion and so is similar to MAD—except that it uses the square of each deviation from the mean. Squares of MPG deviations (previous slide) Variance (s2) 1.92 = 3.61 0.42 = 0.16 2.42 = 5.76 3.12 = 9.61 20.62 = 424.36 7.92 = 62.41 13.92 = 193.21 1.12 = 1.21 4.42 = 19.36 6.12 = 37.21 756.9 10 s2 = 75.69 Note: Square root of variance (s2) is standard deviation (s). Total = 756.9 Variance Part 2, Section E, Topic 2

  28. Discussion Question If this C chart tracks account errors per batch for batches 1 through 10, which batches (if any) would likely be selected for review? Assignable variation UCL 6 Mean 4 Natural variation Answer: Batches 3 and 7, which are “out of control.” LCL 2 Assignable variation 1 2 3 4 5 6 7 8 9 10 Part 2, Section E, Topic 2

  29. Discussion Question If this P chart measures percentage of errors committed by tellers 1–10, is it measuring variables or attributes? Assignable variation UCL 4.5% Mean 3.75% Natural variation Answer: P charts measure attributes in percentage terms. LCL 3.0% Assignable variation 1 2 3 4 5 6 7 8 9 10 Part 2, Section E, Topic 2

  30. Discussion Question This R chart is used to measure the dollar amount of overcounting in 10 branches. Is it measuring attributes or variables? Assignable variation UCL $500 Mean $450 Natural variation Answer: R charts are used to track variables, such as ranges of counting error. LCL $400 Assignable variation 1 2 3 4 5 6 7 8 9 10 Part 2, Section E, Topic 2

  31. Preparation Production Review • Planning • Opening • Conducting • Closing • Documenting • Evaluating Elements of the Audit Interview Part 2, Section E, Topic 3

  32. Discussion Question What are some steps to take when planning the audit interview? Sample answer: Obtain background information. Define purpose and specific objectives. Prepare open and closed questions. Organize questions in logical sequence. Prepare a written agenda. Tailor objectives and questions to the person. Schedule a convenient, agreed-upon time. Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Part 2, Section E, Topic 3

  33. Step 1 Step 2 Step 3 Step 4 Step 5 Discussion Question What are some effective ways to open an audit interview? Sample answer: Start on time. Build rapport with a warm introduction. Get the interviewee’s name right. After the warm-up, state objectives and purpose. Continue building rapport, if possible. Part 2, Section E, Topic 3

  34. Discussion Question What are some do’s and don’ts for conducting the interview? Sample answers: • Be confident but not intimidating. • Avoid offensive or confusing language, humor, etc. • Watch the interviewee’s body language/behavior; don’t focus on note-taking. • Stay focused; prompt for feelings as well as facts. • Question, summarize, and rephrase for clarity. • Don’t confuse opinion with fact. • Bring a second interviewer if necessary. • Be professional in action and appearance. • Take appropriate notes. Part 2, Section E, Topic 3

  35. Closing the Interview Stop at the promised time. Ask for permission to return if questions remain. Summarize key points from notes. Describe the next step. Provide contact information. Thank the interviewee. Part 2, Section E, Topic 3

  36. Interview notes After the Interview Document the interview. Evaluate your performance. • Put notes in final written form. • Do it right away. • Surprises? • Right balance of open and closed questions? • Organized and logical process? • Right time and place? • Rapport? • Objectives and purpose explained? Part 2, Section E, Topic 3

  37. Branch: Supervisor: Area: Date completed: Yes Question No Comments 1. Are all credit sales approved by the Credit Department before shipping? 2. Is the Credit Department independent of the sales department? 3. Are sales priced on the basis of approved price lists? 4. Are prenumbered sales invoice forms used? 5. Are all sales invoice forms properly controlled? 6. Are prenumbered shipping orders used to authorize shipments to customers? Discussion Question What are some advantages and disadvantages of using questionnaires? Sample answer: Advantages—Easy to administer; uniform information for comparison; can go to large numbers of informants anywhere Disadvantages—Not appropriate for some situations; not good for in-depth information; can’t observe informants Part 2, Section E, Topic 3

  38. As a reminder of questions to ask As a data sheet for respondents to fill out quickly Discussion Question What are some appropriate ways to use a checklist for data-gathering? Sample answer: As a control to ensure complete audit Part 2, Section E, Topic 3

  39. Asks recipients to respond regardless of whether or not they believe the information is correct Asks recipients to respond only when they believe the information is incorrect Third-party Confirmation Obtains direct written verification of the accuracy of information from independent third parties Positive confirmation Negative confirmation Part 2, Section E, Topic 3

  40. yes Analyze data to explain finding Recommend action Gather data Unexpected finding? • Period—period comparison • Results—budget comparison • Financial—nonfinancial relationship • Element—element relationship • Unit—unit comparison • Organization—industry comparison Analytical Review Techniques Part 2, Section E, Topic 4

  41. Discussion Question (Variance Analysis) What are the unreasonable relationships in the chart? Budgeted expense Actual expense Period January $9,000 $8,500 February 10,000 8,500 March 10,500 8,500 April 10,500 9,500 May 10,500 10,500 June 10,000 12,000 July 10,000 16,000 August 12,500 13,000 September 13,000 11,000 October 12,500 9,000 November 9,500 8,000 December 9,000 12,500 Answer: Divergence is especially large in July and December. Total 127,000 127,000 Part 2, Section E, Topic 4

  42. Model Y—Convertible Model X—SUV Monthly auto sales Jan Feb Mar Apr May Jun Trend Analysis Trend analysis looks for unreasonable changes in a series of historical data. A typical use of trend analysis is to track changes in financial data through periods of time—monthly, quarterly, and annually. Part 2, Section E, Topic 4

  43. Ratio Analysis By definition,ratio analysis is the measurement of relationships between quantities, such as debt to equity or all statement items to gross revenue. A B Ratio of A to B where A is any quantity of interest and B is any other related quantity. Part 2, Section E, Topic 4

  44. Discussion Question What is the main benefit of common-size statement analysis? Sample Common-Size Statement Revenue Net sales$3,000,000 = 100.00% Rent revenue 35,000 = 5.46% Interest revenue 9,000 = 0.03% Total revenue 3,044,000 = 101.47% Expenses Cost of goods sold 1,750,000 = 58.33% Selling expenses 400,000 = 13.33% Administrative expenses 325,000 = 10.83% Interest expense 40,000 = 0.01% Total expenses 2,515,000 = 83.83% Income before taxes 429,000 = 14.30% Income taxes 127,700 = 0.04% Net income $302,000 = 10.07% Answer: Expressing all items as percentages of sales enables comparison with statements of any size. Part 2, Section E, Topic 4

  45. How They Work General Types Users By comparing relationships of various financial statement items to assess organizational or unit performance • Activity ratios • Liquidity ratios • Leverage (debt) ratios • Profitability ratios • Auditors • Investors • Lenders • Managers Financial Ratios Part 2, Section E, Topic 4

  46. Discussion Question What do activity ratios measure? Answer: Ratio Calculation What It Measures Inventory Turnover Number of times during the year inventory is replaced Cost of Goods Average Inventory Effectiveness in collecting receivables (small is good) Days’ Sales Outstanding Accounts Receivable Sales / 360 Days Accounts Payable Turnover Effectiveness in managing all obligations to creditors Accounts Payable Purchases / 360 Days Fixed Assets Turnover Sales Efficiency in use of fixed assets to generate sales Average Net Fixed Assets Total Assets Turnover Effectiveness in using total assets to produce revenues Sales Average Total Assets Part 2, Section E, Topic 4

  47. Liquidity Ratios Ratio Formula What It Measures Measures potential to pay down current liabilities; larger number = more assets available to pay debts Current Assets Current Ratio Current Liabilities Like current ratio except current assets exclude inventory as least liquid (least available) current asset Current Assets – Inventory Quick Ratio Current Liabilities Not a ratio; subtracts current liabilities from current assets to gauge potential to pay debts Net Working Capital Current Assets – Current Liabilities Part 2, Section E, Topic 4

  48. Discussion Question: Leverage (Debt) Ratios Ratio Formula Is Higher or Lower Better? Debt Ratio Answer: Lower. A higher ratio generally indicates greater debt relative to assets and more risk. Total Liabilities Total Assets Debt to Equity Ratio Answer: Lower, generally. But the organization should carry some reasonable debt relative to equity. Long-term Debt Total Equity Answer: Higher. A higher ratio indicates greater ability to cover obligations with earnings (EBIT). Times Interest Earned Ratio Earnings Before Interest and Taxes (EBIT) Interest Fixed Payment Coverage Ratio Answer: Higher. A higher ratio indicates greater ability to cover fixed obligations within a set time. Earnings Before Interest and Taxes (EBIT) Interest + (Principal + Preferred Dividends) × [1 / (1 – Taxes)] Part 2, Section E, Topic 4

  49. Operating Profits Sales Net Profits Sales ROE 1 + Debt/Equity Ratio Total Earnings No. of Shares Outstanding Profitability Ratios What It Measures Ratio Calculation Sales – Cost of Goods Sold Effectiveness of pricing and cost control Gross Profit Margin Sales Operating Profit Margin Operational efficiency and effective pricing Effective managing of pricing, cost, operations, debt, and taxes Net Profit Margin Return on Investment (ROI) Total Asset Turnover × Net Profit Margin Effective use of assets to generate profit Return on Equity (ROE) Net Profits Success in generating net profits relative to equity Shareholders’ Equity Ability to use equity and debt to generate profits Return on Capital Organization’s value to investors Earnings per Share Part 2, Section E, Topic 4

  50. Discussion Question Regression analysis traces the impact of one condition (independent variable) on another condition (dependent variable). Which is the independent variable in the scatter diagram? Scatter diagram 90,000 75,000 60,000 Fraud Losses (USD 000) 45,000 30,000 15,000 Answer: Security expenditures (x axis) is the independent variable. 0 200 400 600 800 1000 1200 Security expenditures (USD 000) Part 2, Section E, Topic 4

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