# Financial Analysis_ Planning and Forecasting Theory and Application

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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
12                      Good          1.77
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

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.)

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.)

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.)

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.)

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.)

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.)

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.)

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.)

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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