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Financial Analysis, Planning and Forecasting Theory and Application Chapter 4 Application of Discriminant Analysis and Factor Analysis in Financial Management By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng F. Lee Rutgers University 1 Outline v 4.1 Introduction v 4.2 Credit analysis v 4.3 Bankruptcy and financial distress analysis v 4.4 Applications of factor analysis to select useful financial ratios v 4.5 Bond ratings forecasting v 4.6 Bond quality ratings and the change of quality ratings for the electric utility industry v 4.7 Ohlson’s and Shumway’s methods for Estimating Default Probability v 4.8 Summary v Appendix 4A. Jackknife method and its application in MDA analysis v Appendix 4B. Multi-period Logistic Regression 2 4.2 Credit analysis (4.1) where Yi = 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 4.2 Credit analysis (4.2) (4.3) (4.4a) 4 4.2 Credit analysis (4.4b) Where = Variance of X1; = Variance of X2; = Covariance between X1 and X2; = Difference between the average of X1’s for good accounts and the average of X1’s for bad accounts; and = Difference between the average of X2 for good accounts the average of X2 for bad accounts. 5 4.2 Credit analysis TABLE 4.1 Status and index values of the accounts Account Number Account Status Yi 7 Bad 0.81 10 Bad 0.89 2 Bad 1.30 3 Bad 1.45 6 Bad 1.64 12 Good 1.77 11 Bad 1.83 4 Good 1.96 1 Good 2.25 8 Good 2.50 5 Good 2.61 9 Good 2.80 6 4.2 Credit analysis 7 4.2 Credit analysis 8 4.3 Bankruptcy and financial distress analysis v Discriminant Model (Y is the value of z-score) (4.5) TABLE 4.2 Mean ratios of bankrupt / nonbankrupt firms Ratio Definition Bankrupt Group Nonbankrupt Mean Group Mean X1 Working capital / total assets -0.061 0.414 X2 Retained earnings / total assets -0.626 0.355 X3 EBIT/ total assets -0.318 0.153 X4 Market value of equity / book 0.401 2.477 value of total debt X5 Sales / total assets 1.500 1.900 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. 9 Empirical v When we apply Equation (4.5) to calculate financial Z- score, the model should be defined as v Here we use JNJ in 2005 as an example, Ratio Definition JNJ X1 Net Working capital / total assets 0.3233 ( current asset –current liability ) / total assets X2 Retained earnings / total assets 0.7147 X3 EBIT/ total assets 0.2353 X4 Market value of equity / book 8.8683 value of total debt X5 Sales / total assets 0.8706 v 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 4.3 Bankruptcy and financial distress analysis Class Size of Sample Definition Serious problem-potential payoff. An advanced problem bank that has at least 1. PPO 2(1.8%) 50 percent chance of requiring financial assistance in the near future. Serious problem. A bank whose financial condition threatens ultimately to obligate 2. SP 14(12.7%) financial outlay by the FEIC unless drastic changes occur. Other problem. A bank with some significant weakness, with vulnerability 3. OP 94(85.5%) less than class 2, but still calling for aggressive supervision and extraordinary concern by the FEIC. Total 110(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 4.3 Bankruptcy and financial distress analysis TABLE 4.3 Profile analysis for problem banks Financial Ratio 1969 1970 1971 1972 Loans/Assets 1. Problem bank 53.9 55.4 56.9 56.0 2. Nonproblem bank 49.3 48.9 47.8 47.8 Loans/Capital plus Reserves 1. Problem bank 648.3 692.2 768. 9 838.6 2. Nonproblem bank 564.5 562.5 562.4 577.5 Operating Expense/Operating Income 1. Problem bank 83.9 85.5 89.3 94.1 2. Nonproblem bank 78.5 78.6 81.8 82.4 Loan Revenue/Total Revenue 1. Problem bank 64.7 65.8 68.8 69.8 2. Nonproblem bank 59.3 59.2 59.9 59.6 Other Expenses/Total Revenue 1. Problem bank 15.8 16.0 16.3 16.4 2. Nonproblem bank 12.3 13.0 13.2 13.7 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 12 Administration, University of Georgia. 4.3 Bankruptcy and financial distress analysis Type I Type II Total Year Error Error Error 1969 46.36% 25.45% 35.91% 1970 42.73% 27.27% 35.00% 1971 38.18% 24.55% 31.36% 1972 28.15% 21.36% 24.76% 13 4.3 Bankruptcy 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 4.3 Bankruptcy 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 4.4 Applications 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 1972 1974 Primary Primary Ratio Number Ratio Name Mfg. Retail Mfg. Retail Factor 1-Return on Investment 4 Earnings/Sales .88 .63* .75 .81* 7 Earnings/Net Worth .79 .94* .95 .95* 12 Earnings/Total Assets .93 .89* .85 .87* 13 Cash Flow/Total Assets .92 .85* .84 .84* 14 Cash Flow/Net Worth .50 .88* .79 .93* 15 EBIT/Total Assets .89 .85* .77 .84* 16 EBIT/Sales .89 .61* .70 .77* 17 Cash Flow/Total Capital .94 .90* .85 .93* 16 4.4 Applications 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 1972 1974 Primary Primary Ratio Number Ratio Name Mfg. Retail Mfg. Retail Factor 1-Return on Investment 18 Earnings/Total Capital .94 .90* .88 .94* 19 Cash Flow/Sales .79 .59* .87 .74* 41 EBIT/Net Worth .79a .92* .95 .97* 47 Cash Flow/Total Debt .81 .73* .84 .70* 48 Earnings/Total Debt .87 .78* .86 .73* 53 Operating Funds/Total Assets .88 .82* .45 .82* 54 Operating Funds/Net Worth .25 .75 .63a .86 55 Operating Funds/Total Capital .83 .81 .33 .88 17 4.4 Applications 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 1972 1974 Primary Primary Ratio Number Ratio Name Mfg. Retail Mfg. Retail Factor 2-Financial Leverage 2 Net Worth/Total Assets -.80 -.85* -.82 -.69a* 5 Long-Term Debt/Total Assets .87 .85 .85 .87 11 Long-Term Debt/Net Worth .88 .90 .91 .93 29 Long-Term Debt/Net Plant .85 .81 .80 .81 30 Long-Term Debt/Total Capital .89 .92 .94 .91 31 Total Debt/Net Worth .79 .85 .83 .71a 32 Total Debt/Total Assets .81 .85* .79 .74* 50 Total Debt and Preferred Stock/Total Assets .79 .85* .78 .68* 18 4.4 Applications 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 1972 1974 Primary Primary Ratio Number Ratio Name Mfg. Retail Mfg. Retail Factor 3-Capital Intensiveness 3 Sales/Net Worth .66 .85* .70a .78* 6 Sales/Total Assets .78a .81* .75 .79* 19 Cash Flow/Sales -.44 -72a* ¾ ¾ 20 Current Liabilities/Net Plant .81 .49* .81 .43a 22 Current Assets/Total Assets .88 .46* .84 .41 26 Sales/Net Plant .94 .78* .91 .79* 27 Sales/Total Capital .85 .91* .86 .83* 19 4.4 Applications 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 1972 1974 Primary Primary Ratio Number Ratio Name Mfg. Retail Mfg. Retail Factor 4¾Inventory Intensiveness 1 Working Capital/Sales .72a .44* .69a .81* 20 Current Liabilities/Net Plant .33 .71* ¾ ¾ 21 Working Capital/Total Assets .40 .76 .46 .85 22 Current Assets/Total Assets .39 .83* .45 .84 24 Current Assets/Sales .92 .74* .92 .74 25 Cost of Goods Sold/Inventory -.91 -.92* - .94 -.93* 28 Inventory/Sales .87 .93* . 94 .93* 20 4.4 Applications 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 1972 1974 Primary Primary Ratio Number Ratio Name Mfg. Retail Mfg. Retail Factor 5¾Cash Position 42 Cash/Total Assets .91 .93 .89 .81 43 Cash/Current Liabilities .84 .88 .83 .87 44 Cash/Sales .93 .86* .88 .89* 46 Cash/Fund Expenditures .91 .86* .88 .89* 21 4.4 Applications 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 1972 1974 Primary Primary Ratio Number Ratio Name Mfg. Retail Mfg. Retail Factor 6¾Receivables Intensiveness 23 Quick Assets/Total Assets .52 .89* .68a .89* 33 Receivables/Inventory .94 .84* .80a .82* 34 Inventory/Current Assets -.75a -.70* -.64 -.76* 35 Receivables/Sales .72a .83* .81 .83* 37 Quick Assets/Sales .58 .86* .78 .88* 40 Quick Assets/Current Liabilities .40 .76* .46 .81* 45 Quick Assets/Fund Expenditures .55 .85* .75 .87* 22 4.4 Applications 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 1972 1974 Primary Primary Ratio Number Ratio Name Mfg. Retail Mfg. Retail Factor 7¾Short-Term Liquidity 21 Working Capital/Total Assets ¾ ¾ .73 -.35 36 Inventory/Working Capital ¾ ¾ -.79 .16* 38 Current Liabilities/Net Work ¾ ¾ -.55a .80 39 Current Assets/Current Liabilities .91 .64* .90 -.61 40 Quick Assets/Current Liabilities .77 .37* .76 -.31* 49 Current Liabilities/Total Assets ¾ ¾ -.64a .78* 51 Net Defensive Assets/Fund Expenditures .55 .74* .75 -.52a* 23 4.4 Applications 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 1972 1974 Primary Primary Ratio Number Ratio Name Mfg. Retail Mfg. Retail Factor 8¾Decomposition Measures 56 Asset Decomposition .68 .74 ¾ ¾ 58 Equity Decomposition .84 .84 .86 .87 60 Noncurrent Items Decompostion .83 .78 .87 .85 61 Time Horizon Decompostion ¾ ¾ .62 .70 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. 24 4.5 Bond ratings forecasting TABLE 4.4b Cross-sectional congruency coefficients for eight financial-ratio dimensions for 1974 Factor: Retail Firms Factor: Primary Manufacturing Firms One Two Three Four Five Six Seven Eight One ¾ Return on Investment .95 -.41 -.13 -.05 .14 .05 -.25 -.26 Two ¾ Financial Leverage -.40 .95 .11 -.17 -.17 -.05 .45 .07 Three ¾ Capital Intensiveness -.15 -.00 .84 .28 -.14 -.16 .55 .04 Four ¾ Inventory Intensiveness -.13 -.02 -.27 .87 -.01 .15 .08 .08 Five ¾ Cash Position .20 -.15 -.21 .00 .88 .46 -.29 .15 Six ¾ Receivables Intensiveness .01 -.06 -.42 .11 .29 .92 -.24 .10 Seven ¾ Short-term Liquidity .19 -.34 -.17 .30 .38 .39 .76 -.01 Eight ¾ Decomposition Measures -.20 .16 .06 .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 4.5 Bond 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 26 + 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; 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 4.5 Bond 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 4.5 Bond ratings forecasting 29 4.5 Bond ratings forecasting TABLE 4.7 Variable means, test of significance, and important ranks Bond Rating Function Ranks Variable AA A BAA BA B F-Ratio One Two Three X1 0.000 0.077 0.520 1.000 1.000 ¾ 1 6 2 X2 1.634 1.581 1.260 1.058 0.486 25.45*** 2 2 5 X3 1.869 1.657 1.275 1.354 1.250 13.97*** 3 3 1 X4 1.138 0.606 0.560 0.511 0.707 6.05*** 6 1 6 X5 0.091 0.162 0.154 0.151 0.215 4.06** 5 4 4 KX6 0.099 0.075 0.066 0.075 0.069 2.68* 4 5 3 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 30 *Significant at 0.05 level. 4.6 Bond 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 4.7 Ohlson’s and Shumway’s methods for Estimating Default Probability X1 = Natural log of (Total Assets/ GNP Implicit Price Deflator Index). The index assumes a base value of 100 for 1968; X2 = (Total Liabilities/Total Assets); X3 = (Current Assets – Current Liabilities)/Total Assets; X4 = Current Assets/ Current Liabilities; X5 = One if total liabilities exceeds total assets, zero otherwise; X6 = Net income/total assets; X7 = Funds provided by operations/total liabilities; X8 = One if net income was negative for the last two years, zero otherwise; and X9 = (Net income in year t – Net income in t–1) / (Absolute net income in year t + Absolute net income in year t–1). 32 4.7 Ohlson’s and Shumway’s methods for Estimating Default Probability (4.8) Where , P = the probability of bankruptcy. 33 4.7 Ohlson’s and Shumway’s methods for Estimating Default Probability (4.9) Where , P = the probability of bankruptcy; X1 = Net Income/Total Assets; X2 = (Total Liabilities/Total Assets); X3 = 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); X4 = 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 X5 = 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 34 value-weighted NYSE/AMEX index return for the same year. 4.8 Summary 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 Appendix 4A. Jackknife method and its application in MDA analysis (4.A.1) (4.A.2) (4.A.3) 36 Appendix 4A. Jackknife method and its application in MDA analysis TABLE 4.A.1 Original and jackknifed (standardized) discriminant functions Discriminant Function 1 2 3 Jackknifed* Jackknifed* Jackknifed* Variable Coefficient Coefficient Coefficient Coefficient Coefficient Coefficient X1 -.936 -.882** .131 .102 -.365 -.361** X2 .528 .461** 1.073 .863** -.216 -.017 X3 .360 .352** - .758 -.541 -.493 -.516** X4 .023 .041 -1.284 -.888** .006 .012 X5 -.283 -.171 -.529 -.544** .335 .421** X6 .327 .302** -.280 -.067 -.340 -.320**37

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