ACCT: 742-Advanced Auditing SAS 56-Analytical Procedures (AU 329) Regression Analysis and Other Analytical Procedures

SAS 56: ANALYTICAL PROCEDURES (AU 329) “Analytical procedures are an important part of the audit process and consist of evaluation of financial information made by a study of plausible relationships among both financial and non-financial data. Analytical procedures range from simple comparisons to the use of complex models involving many relationships and elements of data. A basic premise underlying the application of analytical procedures is that plausible relationships among data may reasonably be expected to exist and continue in the absence of known conditions to the contrary.” [AU 329.02]

Analytical procedures are used for the following purposes: To assist the auditor in planning the nature, timing, and extent of other auditing procedures As a substantive test to obtain evidential matter about particular assertions related to account balances or classes of transactions As an overall review of the financial information in the final review stage of the audit

Timing and Purposes of Analytical Procedures-Planning Phase (Required) Purpose Understand client’s industry and business Primary purpose Assess going concern Secondary purpose Indicate possible misstatements (attention directing) Primary purpose Reduce detailed tests Secondary purpose

Timing and Purposes of Analytical Procedures-Testing Phase (Recommended) Understand client’s industry and business Assess going concern Indicate possible misstatements (attention directing) Secondary purpose Reduce detailed tests Primary purpose

Timing and Purposes of Analytical Procedures-Completion Phase (Required) Understand client’s industry and business Assess going concern Secondary purpose Indicate possible misstatements (attention directing) Primary purpose Reduce detailed tests

Five Types of Analytical Procedures Compare client and industry data. Compare client data with similar prior period data. Compare client data with client-determined expected results. Compare client data with auditor-determined expected results. Compare client data with expected results, using non-financial data.

Some Specific Examples of Analytical Procedures Ratio Analysis (Financial and Non-financial data) Common-Size Statements Trend Analysis Regression Analysis Time Series Regression Cross-Sectional Regression Discriminant Analysis Bankruptcy Models (Altman Z-factor) Digital Analysis Intelligent Agents and Expert Systems Non-financial ratios: number of units produces vs. production costs, miles traveled (gross tonnage hauled) by a trucking company vs. fuel expenses. Time Series Regression: Prediction of the current year sales by month based on a two-or three year history of the monthly relationship of sales to cost of sales. Cross-Sectional Regression: Prediction of an amount, such as account balance, based on independently predicting variables from the same period: data from other firms, the industry, or across different units of the client’s business, such as sales branches or inventory locations. For example, auditor cannot economically observe inventory at each location of a client that has 600 retail outlets. Regression analysis can be used to identify locations that seem out of line with the other stores. Inventory amounts at each store may be predicted base on the sales, floor space, and price-level index at each location.

Altman Z-factor Z = 1.2*X1 + 1.4*X2 + 3.3*X3 + 0.6*X4 + 1.0*X5 Z = discriminant or credit score X1 = (working capital)/(total assets) X2 = (retained earnings)/(total assets) X3 = (earnings before interest and taxes)/(total assets) X4 = (market value of equity)/(book value of total debt) X5 = sales/(total assets) Z < 1.81: Company will go bankrupt within a year or two. 2.675 > Z>1.81: Company will probably go bankrupt, but there is a chance it will not. 2.676 <Z< 2.99: Company will probably not go bankrupt, but there is a chance it will. Z > 2.99: Company will not go bankrupt.

Altman Z-factor Calculation Use this website for a company's data: http://www.sec.gov/edgar.shtml Use 10-K from SEC and stock price for the day from http://finance.yahoo.com/ You may have to go to Google to search for the sicker symbol of your company In millions except stock price QualComm Inc. (QCOM) Delta Ailines (DAL) AAPL (Apple Computers)   2009 Stock Price (March 22, 2010) $ 40.28 $ 13.07 $ 224.72 Number of Common Shares 1,674 794.873058 899.804500 Current Assets 13,574 7,741 36,265 Current Liabilites 2,948 9,797.00 19,282 Working Capital 10,626 (2,056) 16,983 Total Assets 28,903 43,539 53,851 MValue of Equity 67,429 10,389 $ 202,204.07 BV of Total Debt 7,550 43,294 26,019 Retained Earnings 11,792 (10,019) 19,538 EBIT 1,052 (1,581) 7,984 Sales 2,670 28,063 36,537 Z-factor 6.58 0.29 6.72

Regression Analysis Regression analysis is a statistical technique used to describe the relationship between the account being audited and other possible predictive factors. Regression analysis helps Determine whether there is a relationship between the dependent and independent variables Determine whether a “significant difference” has occurred Simple Linear Regression (Time-series & Cross-Sectional Analysis) Multiple Regression (Time-series & Cross-Sectional Analysis)

Regression Analysis: Data Requirements Accuracy and honesty in recording data Accounting transactions should be properly accrued Data should be adjusted for economies of scale or learning effects. Changes in the nature of production process should be properly taken into consideration. Variable level of activity is required.

Some Examples of Regression Analysis Applications Monthly sales based on cost of sales and selling expense Airline and truck company fuel expense based on miles driven and fuel cost per gallon Maintenance expense based on production levels Overhead cost based on machine hours and labor hours used Inventory at each location of a retail company based on store sales, store square footage, regional economic data, and type of store location

Linear Regression Model yi = a + bxi + ei yi = dependent variable at time ‘i’ or location ‘i’ xi = independent variable at time ‘i’ or location ‘i’ ei = Error term that incorporates (1) the effects of omitted variables, and (2) model errors caused by nonlinear relationships between x and y. ‘a’ and ‘b’ are estimated by minimizing the sum of the squared terms (Ordinary Least Squares, OLS, technique) Minimize: (ei)2= (yi – a - bxi)2

Regression Line: y = a + bx Scatter Graph ei = (yi-y) Minimize variance S(ei)2 a

Assumptions Linear relationship between the dependent variable and the independent variable(s). E(ei) = 0, i.e., Sei = 0. Variance of ei is constant for all t, and does not depend on the independent variables. Covariance(ei, ej) = 0, for all i, j where i  j. The independent variables are uncorrelated. ei ~ N(0, se).

E(ei) = 0, i.e., Sei = 0. Sei = 0 ei

Variance of ei is constant for all i

Four Criteria For Evaluating Regression Results Plausibility of relationship between the dependent variable and the independent variables. Goodness of fit measured by R2 (Coefficient of determination) and F statistic. Confidence placed on the parameters of the regression model. Specification Tests – Critical assumptions have been met.

Goodness of fit Measured by Coefficient of Determination R2 (Coefficient of Determination) represents the percentage of variance explained in the dependent variable through the independent variables. Value: 1>R2>0 If R2 = 0.85, it means 85% of variance is explained by the independent variable(s)

Significance of the Coefficients Y = a + bx Is ‘a’ different from zero? Determines if there is a constant term. Is ‘b’ different from zero? Determines if there is a linear relationship. We use t-statistics to test for their significance ta = (a – 0)/sa, sa is the standard deviation of ‘a’ tb = (a – 0)/sb , sb is the standard deviation for ‘b’ As a rule of thumb, for a large sample size, if t is greater than 2 then we consider the coefficient to be different from zero.

Standard Error of the Regression and Standard deviations of a and b The standard error of the regression where n is the number of data points and k is number of unknown parameters in the model. The standard deviation of b, the coefficient of the independent variable:

Standard Deviation of the parameter a The standard error of the constant term, a:

Predictions from the Regression Equation Prediction: yf from regression line = a + bxf. The standard error Sf for yf is given by: The t statistic for the test of significance is:

95% Confidence Intervals Confidence interval for coefficient a: = [ a ± t.95 sa] Confidence interval for coefficient b: = [ b ± t.95 sb] Confidence interval for the predicted value : = [ ± t.95 sf]