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Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng F. Lee Rutgers University Chapter 4 Application of Discriminant Analysis and Factor Analysis in Financial Management 1

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Outline 4.1Introduction 4.2Credit analysis 4.3Bankruptcy and financial distress analysis 4.4Applications of factor analysis to select useful financial ratios 4.5Bond ratings forecasting 4.6Bond quality ratings and the change of quality ratings for the electric utility industry 4.7Ohlson’s and Shumway’s methods for Estimating Default Probability 4.8Summary Appendix 4A. Jackknife method and its application in MDA analysis Appendix 4B. Multi-period Logistic Regression 2

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4.2Credit analysis (4.1) where Y i = Index value for the ith account; = ith firm’s quick ratio; = ith firm’s total sales/inventory ratio; and A and B are the parameters or weights to be determined. 3

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4.2Credit analysis (4.2) (4.3) (4.4a) 4

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4.2Credit analysis (4.4b) Where = Variance of X 1 ; = Variance of X 2 ; = Covariance between X 1 and X 2 ; = Difference between the average of X 1 ’s for good accounts and the average of X 1 ’s for bad accounts; and = Difference between the average of X 2 for good accounts the average of X 2 for bad accounts. 5

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4.2Credit analysis TABLE 4.1 Status and index values of the accounts Account NumberAccount StatusYiYi 7Bad0.81 10Bad0.89 2Bad1.30 3Bad1.45 6Bad1.64 12Good1.77 11Bad1.83 4Good1.96 1Good2.25 8Good2.50 5Good2.61 9Good2.80 6

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4.2Credit analysis 7

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4.3Bankruptcy and financial distress analysis Discriminant Model (Y is the value of z-score) (4.5) TABLE 4.2 Mean ratios of bankrupt / nonbankrupt firms From Altman, E. I., “Financial ratios, discriminant Analysis, and the prediction of corporate bankruptcy,” Journal of Finance 23 (1968), p. 596, Table I. Reprinted by Permission of Edward I. Altman and Journal of Finance. Z-score >2.99 : non-bankrupt sector; Z-score < 1.81 : bankruptcy; Z-score between 1.81 and 2.99 : gray area. Ratio Definition Bankrupt Group Mean Nonbankrupt Group Mean X1X1 Working capital / total assets -0.0610.414 X2X2 Retained earnings / total assets -0.6260.355 X3X3 EBIT/ total assets -0.3180.153 X4X4 Market value of equity / book value of total debt 0.4012.477 X5X5 Sales / total assets 1.5001.900 9

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Empirical When we apply Equation (4.5) to calculate financial Z- score, the model should be defined as Here we use JNJ in 2005 as an example, Then, the z-score for JNJ is 1.2(0.3233)+1.4(0.7147)+3.3(0.2353)+0.6(8.8683)+1.0(0.8 706) =8.3567 10 Ratio Definition JNJ X1X1 Net Working capital / total assets ( current asset –current liability ) / total assets 0.3233 X2X2 Retained earnings / total assets 0.7147 X3X3 EBIT/ total assets 0.2353 X4X4 Market value of equity / book value of total debt 8.8683 X5X5 Sales / total assets 0.8706

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4.3Bankruptcy and financial distress analysis ClassSize of SampleDefinition 1. PPO2(1.8%) Serious problem-potential payoff. An advanced problem bank that has at least 50 percent chance of requiring financial assistance in the near future. 2. SP14(12.7%) Serious problem. A bank whose financial condition threatens ultimately to obligate financial outlay by the FEIC unless drastic changes occur. 3. OP94(85.5%) Other problem. A bank with some significant weakness, with vulnerability less than class 2, but still calling for aggressive supervision and extraordinary concern by the FEIC. Total110(100%) From Sinkey, J.F., “A multivariate statistical analysis of the characteristics of problem banks,” Journal of Finance 30 (1975), Table 2. Reprinted by permission. 11

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4.3Bankruptcy and financial distress analysis TABLE 4.3 Profile analysis for problem banks From Sinkey, J.F., “A multivariate statistical analysis of the characteristics of problem banks,” Journal of Finance 30 (1975), Table 3. Reprinted by permission. This paper was written while the author was a Financial Economics at the Federal Deposit Insurance Corporation, Washington, D.C. He is currently Professor of Banking and Finance at College of Business Administration, University of Georgia. Financial Ratio1969197019711972 Loans/Assets 1. Problem bank53.955.456.956.0 2. Nonproblem bank49.348.947.8 Loans/Capital plus Reserves 1. Problem bank648.3692.2768. 9838.6 2. Nonproblem bank564.5 562.5562.4577.5 Operating Expense/Operating Income 1. Problem bank83.985.589.394.1 2. Nonproblem bank78.578.681.882.4 Loan Revenue/Total Revenue 1. Problem bank64.765.868.869.8 2. Nonproblem bank59.359.259.959.6 Other Expenses/Total Revenue 1. Problem bank15.816.016.316.4 2. Nonproblem bank12.313.0 13.213.7 12

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4.3Bankruptcy and financial distress analysis Year Type I Error Type II Error Total Error 196946.36%25.45%35.91% 197042.73%27.27%35.00% 197138.18%24.55%31.36% 197228.15%21.36%24.76% 13

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4.3Bankruptcy and financial distress analysis (4.6) where = 0: Unsecured loan, 1: Secured loan; = 0: Past interest payment due, 1: Current loan; = 0: Not audited firm, 1: Audited firm; = 0: Net loss firm 1: Net profit firm = Working Capital/Current Assets; = 0: Loan criticized by bank examiner, 1: Loan not criticized by bank examiner. 14

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4.3Bankruptcy and financial distress analysis (4.7) where = Agents’ balances/Total assets; a measure of the firms’ accounts receivable management; = Stocks at cost (preferred and common)/Stocks at market (preferred and common); measures investment management; = Bonds at cost/Bonds at market; measures the firm’s age; = (Loss adjustment expenses paid + underwriting expenses paid) / Net premiums written; a measure of a firm’s funds flow from insurance operations; = Combined ratio; traditional measure of underwriting profitability; and = Premiums written direct/Surplus; a measure of the firm’s sales aggressiveness. 15

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4.4Applications of factor analysis to select useful financial ratios TABLE 4.4a Cross-sectional comparison of financial ratios and factor loadings defining eight financial ratio categories for industrial firms Factor Loadings 19721974 Primary Ratio NumberRatio NameMfg.RetailMfg.Retail Factor 1 Return on Investment 4Earnings/Sales.88.63*.75.81* 7Earnings/Net Worth.79.94*.95.95* 12Earnings/Total Assets.93.89*.85.87* 13Cash Flow/Total Assets.92.85*.84.84* 14Cash Flow/Net Worth.50.88*.79.93* 15EBIT/Total Assets.89.85*.77.84* 16EBIT/Sales.89.61*.70.77* 17Cash Flow/Total Capital.94.90*.85.93* 16

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4.4Applications of factor analysis to select useful financial ratios TABLE 4.4a Cross-sectional comparison of financial ratios and factor loadings defining eight financial ratio categories for industrial firms (Cont.) Factor Loadings 19721974 Primary Ratio NumberRatio NameMfg.RetailMfg.Retail Factor 1 Return on Investment 18Earnings/Total Capital.94.90*.88.94* 19Cash Flow/Sales.79.59*.87.74* 41EBIT/Net Worth.79 a.92*.95.97* 47Cash Flow/Total Debt.81.73*.84.70* 48Earnings/Total Debt.87.78*.86.73* 53Operating Funds/Total Assets.88.82*.45.82* 54Operating Funds/Net Worth.25.75.63 a.86 55Operating Funds/Total Capital.83.81.33.88 17

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4.4Applications of factor analysis to select useful financial ratios TABLE 4.4a Cross-sectional comparison of financial ratios and factor loadings defining eight financial ratio categories for industrial firms (Cont.) Factor Loadings 19721974 Primary Ratio NumberRatio NameMfg.RetailMfg.Retail Factor 2 Financial Leverage 2Net Worth/Total Assets-.80-.85*-.82-.69 a * 5Long-Term Debt/Total Assets.87.85.87 11Long-Term Debt/Net Worth.88.90.91.93 29Long-Term Debt/Net Plant.85.81.80.81 30Long-Term Debt/Total Capital.89.92.94.91 31Total Debt/Net Worth.79.85.83.71 a 32Total Debt/Total Assets.81.85*.79.74* 50Total Debt and Preferred Stock/Total Assets.79.85*.78.68* 18

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4.4Applications of factor analysis to select useful financial ratios TABLE 4.4a Cross-sectional comparison of financial ratios and factor loadings defining eight financial ratio categories for industrial firms (Cont.) Factor Loadings 19721974 Primary Ratio NumberRatio NameMfg.RetailMfg.Retail Factor 3 Capital Intensiveness 3Sales/Net Worth.66.85*.70a.78* 6Sales/Total Assets.78 a.81*.75.79* 19Cash Flow/Sales-.44-72 a * 20Current Liabilities/Net Plant.81.49*.81.43 a 22Current Assets/Total Assets.88.46*.84.41 26Sales/Net Plant.94.78*.91.79* 27Sales/Total Capital.85.91*.86.83* 19

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4.4Applications of factor analysis to select useful financial ratios TABLE 4.4a Cross-sectional comparison of financial ratios and factor loadings defining eight financial ratio categories for industrial firms (Cont.) Factor Loadings 19721974 Primary Ratio NumberRatio NameMfg.RetailMfg.Retail Factor 4 Inventory Intensiveness 1Working Capital/Sales.72 a.44*.69 a.81* 20Current Liabilities/Net Plant.33.71* 21Working Capital/Total Assets.40.76.46.85 22Current Assets/Total Assets.39.83*.45.84 24Current Assets/Sales.92.74*.92.74 25Cost of Goods Sold/Inventory-.91-.92*-.94-.93* 28Inventory/Sales.87.93*. 94.93* 20

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4.4Applications of factor analysis to select useful financial ratios TABLE 4.4a Cross-sectional comparison of financial ratios and factor loadings defining eight financial ratio categories for industrial firms (Cont.) Factor Loadings 19721974 Primary Ratio NumberRatio NameMfg.RetailMfg.Retail Factor 5 Cash Position 42Cash/Total Assets.91.93.89.81 43Cash/Current Liabilities.84.88.83.87 44Cash/Sales.93.86*.88.89* 46Cash/Fund Expenditures.91.86*.88.89* 21

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4.4Applications of factor analysis to select useful financial ratios TABLE 4.4a Cross-sectional comparison of financial ratios and factor loadings defining eight financial ratio categories for industrial firms (Cont.) Factor Loadings 19721974 Primary Ratio NumberRatio NameMfg.RetailMfg.Retail Factor 6 Receivables Intensiveness 23Quick Assets/Total Assets.52.89*.68 a.89* 33Receivables/Inventory.94.84*.80 a.82* 34Inventory/Current Assets-.75 a -.70*-.64-.76* 35Receivables/Sales.72 a.83*.81.83* 37Quick Assets/Sales.58.86*.78.88* 40Quick Assets/Current Liabilities.40.76*.46.81* 45Quick Assets/Fund Expenditures.55.85*.75.87* 22

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4.4Applications of factor analysis to select useful financial ratios TABLE 4.4a Cross-sectional comparison of financial ratios and factor loadings defining eight financial ratio categories for industrial firms (Cont.) Factor Loadings 19721974 Primary Ratio NumberRatio NameMfg.RetailMfg.Retail Factor 7 Short-Term Liquidity 21Working Capital/Total Assets .73-.35 36Inventory/Working Capital -.79.16* 38Current Liabilities/Net Work -.55 a.80 39Current Assets/Current Liabilities.91.64*.90-.61 40Quick Assets/Current Liabilities.77.37*.76-.31* 49Current Liabilities/Total Assets -.64 a.78* 51Net Defensive Assets/Fund Expenditures.55.74*.75-.52 a * 23

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4.4Applications of factor analysis to select useful financial ratios TABLE 4.4a Cross-sectional comparison of financial ratios and factor loadings defining eight financial ratio categories for industrial firms (Cont.) From Johnson, W.B., “The cross-sectional stability of financial ratio patterns,” Journal of Financial and Quantitative Analysis 14 (1979), Table 2. Reprinted by permission of W. Bruce Johnson and JFQA. a Indicates variables having a within-sample cross-loading of between 0.50 and 0.70 on one other factor. *t-test of untransformed data significant at p 0.05. Factor Loadings 19721974 Primary Ratio NumberRatio NameMfg.RetailMfg.Retail Factor 8 Decomposition Measures 56Asset Decomposition.68.74 58Equity Decomposition.84.86.87 60Noncurrent Items Decompostion.83.78.87.85 61Time Horizon Decompostion .62.70 24

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4.5Bond ratings forecasting TABLE 4.4b Cross-sectional congruency coefficients for eight financial-ratio dimensions for 1974 Factor: Retail Firms Factor: Primary Manufacturing FirmsOneTwoThreeFourFiveSixSevenEight One Return on Investment.95 .41 .13 .05.14.05 .25 .26 Two Financial Leverage .40.95.11 .17 .05.45.07 Three Capital Intensiveness .15 .00.84.28 .14 .16.55.04 Four Inventory Intensiveness .13 .02 .27.87 .01.15.08 Five Cash Position.20 .15 .21.00.88.46 .29.15 Six Receivables Intensiveness.01 .06 .42.11.29.92 .24.10 Seven Short-term Liquidity.19 .34 .17.30.38.39.76 .01 Eight Decomposition Measures .20.16.06.01.05.27.84 From Johnson, W.B., “The cross-sectional stability of financial ratio patterns,” Journal of Financial and Quantitative Analysis 14 (1979), Table 3. Reprinted by permission of W. Bruce Johnson and JFQA. 25

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4.5Bond ratings forecasting Ratio found useful in study; (X) Ratio mentioned in study; (1) Net Income plus Depreciation, Depletion, Amortization; (2) No Credit Interval = Quick Assets minus CL/Operating Expense minus Depreciation, Depletion, Amortization; (3) Quick Flow = C + MS + AR + (Annual Sales divided by 12)/[CGS = Depreciation + Selling and Administration + Interest] divided by 12]; (4) Cash Interval = C + MS/Operating Expense minus Depreciation, Depletion, Amortization; 26

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4.5 Bond ratings forecasting (5) Defensive Interval = QA/Operating Expense Minus Depreciation, Depletion, Amortization; (6) Capital Expenditure/Sales; (7) Nonoperating Income before Taxes/Sales. From Chen, K. H., and T. A. Shimerda, “An empirical analysis of useful financial ratios,” Financial Management (Spring 1981), Exhibit 1. Reprinted by permission. 27

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4.5Bond ratings forecasting From Chen, K. H., and T. A. Shimerda, “An empirical analysis of useful financial ratios,” Financial Management (Spring 1981), Exhibit 5. Reprinted by permission. * Ratio not included in the final factors of the PEMC studies. ** Ratio not in the 48 ratios included in the PEMC study. 28

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4.5Bond ratings forecasting 29

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4.5Bond ratings forecasting TABLE 4.7 Variable means, test of significance, and important ranks Bond RatingFunction Ranks VariableAAABAABABF-RatioOneTwoThree X1X1 0.0000.0770.5201.000 162 X2X2 1.6341.5811.2601.0580.48625.45***225 X3X3 1.8691.6571.2751.3541.25013.97***331 X4X4 1.1380.6060.5600.5110.7076.05***616 X5X5 0.0910.1620.1540.1510.2154.06**544 KX 6 0.0990.0750.0660.0750.0692.68*453 From Pinches, G.E., and K.A. Mingo, “A multivariate analysis of industrial and bond ratings,” Journal of Finance 28 (March 1973), Table 3. Reprinted by permission. ***Significant at 0.001 level **Significant at 0.01 level *Significant at 0.05 level. 30

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4.6Bond quality ratings and the change of quality ratings for the electric utility industry The multivariate-analysis technique developed by Pinches and Mingo for analyzing industrial bond ratings has also been used to determine bond quality ratings and their associated changes for electric utilities. Pinches, Singleton, and Jahakhani (1978) (PSJ) used this technique to determine whether fixed coverages were a major determinant of electric utility bond ratings. Bhandari, Soldofsky, and Boe (1979) (BSB) investigate whether or not a multivariate discriminant model that incorporates the recent levels, past levels, and the instability of financial ratios can explain and predict the quality rating changes of electric utility bonds. PSJ (1978) found that fixed coverage is the only (and not the dominant) financial variable that apparently influences the bond ratings assigned to electric utility firms. Other important variables are the climate of regulation, total assets, return on total assets, growth rate or net earnings, and construction expenses/total assets.2 The major finding of BSB’s study is that the MDA method can be more successful in predicting bond rating changes than it had been predicting the bond ratings themselves. These results have shed some light for the utility regulation agency on the determinants of bond ratings and the change of bond ratings for electric utility industries. 31

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4.7Ohlson’s and Shumway’s methods for Estimating Default Probability X 1 = Natural log of (Total Assets/ GNP Implicit Price Deflator Index). The index assumes a base value of 100 for 1968; X 2 = (Total Liabilities/Total Assets); X 3 = (Current Assets – Current Liabilities)/Total Assets; X 4 = Current Assets/ Current Liabilities; X 5 = One if total liabilities exceeds total assets, zero otherwise; X 6 = Net income/total assets; X 7 = Funds provided by operations/total liabilities; X 8 = One if net income was negative for the last two years, zero otherwise; and X 9 = (Net income in year t – Net income in t–1) / (Absolute net income in year t + Absolute net income in year t–1). 32

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4.7Ohlson’s and Shumway’s methods for Estimating Default Probability (4.8) Where, P = the probability of bankruptcy. 33

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4.7Ohlson’s and Shumway’s methods for Estimating Default Probability (4.9) Where, P = the probability of bankruptcy; X 1 = Net Income/Total Assets; X 2 = (Total Liabilities/Total Assets); X 3 = The logarithm of (each firm’s market capitalization at the end of year prior to the observation year / total market capitalization of NYSE and AMEX market); X 4 = Past excess return as the return of the firm in year t-1 minus the value-weighted CRSP NYSE/AMEX index return in year t - 1; and X 5 = idiosyncratic standard deviation of each firm’s stock returns. It is defined as the standard deviation of the residual of a regression which regresses each stock’s monthly returns in year t – 1 on the value-weighted NYSE/AMEX index return for the same year. 34

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4.8Summary In this chapter, we have discussed applications of two multivariate statistical methods in discriminant analysis and factor analysis. Examples of using two-group discriminant functions to perform credit analysis, predict corporate bankruptcy, and determine problem banks and distressed P-L insurers were discussed in detail. Basic concepts of factor analysis were presented, showing their application in determining useful financial ratios. In addition, the combination of factor analysis and discriminant analysis to analyze industrial bond ratings was discussed. Finally, Ohlson’s and Shumway’s methods for estimating default probability were discussed. In sum, this chapter shows that multivariate statistical methods can be used to do practical financial analysis for both managers and researchers. 35

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Appendix 4A. Jackknife method and its application in MDA analysis (4.A.1) (4.A.2) (4.A.3) 36

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Appendix 4A. Jackknife method and its application in MDA analysis TABLE 4.A.1 Original and jackknifed (standardized) discriminant functions Discriminant Function 123 VariableCoefficient Jackknifed* Coefficient Coefficient Jackknifed* Coefficient Coefficient Jackknifed* Coefficient X1X1 .936 .882**.131.102 .365 .361** X2X2.528.461** 1.073.863** .216 .017 X3X3.360.352** .758 .541 .493 .516** X4X4.023.041 1.284 .888**.006.012 X5X5 .283 .171 .529 .544**.335.421** X6X6.327.302** .280 .067 .340 .320** 37

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