Transcript PowerPoint for Chapter 4

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










4.1
4.2
4.3
4.4
Introduction
Credit analysis
Bankruptcy and financial distress analysis
Applications of factor analysis to select useful financial
ratios
4.5 Bond ratings forecasting
4.6 Bond quality ratings and the change of quality ratings for
the electric utility industry
4.7 Ohlson’s and Shumway’s methods for Estimating Default
Probability
4.8 Summary
Appendix 4A. Jackknife method and its application in MDA
analysis
Appendix 4B. Multi-period Logistic Regression
2
4.2 Credit analysis
YI  AX1i  BX 2i
(4.1)
where
Yi = Index value for the ith account;
X 1i = ith firm’s quick ratio;
X 2i = ith firm’s total sales/inventory ratio;
and A and B are the parameters or weights to be determined.
3
4.2 Credit analysis
S11 A  S12 B  D1
(4.2)
S12 A  S 22 B  D2
(4.3)
S22 D1  S12 D2
A
2
S22 S11  S12
(4.4a)
4
4.2 Credit analysis
S11 D2  S12 D1
B
S22 S11  S122
(4.4b)
Where
S11
= Variance of X1;
S 22
= Variance of X2;
S12
= Covariance between X1 and X2;
D1 =
Difference between the average of X1’s for good accounts
and the average of X1’s for bad accounts; and
D2 =
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

Discriminant Model (Y is the value of z-score)
Yi  0.012X 1  0.014X 2  0.033X 3  0.006X 4  0.999X 5 (4.5)
TABLE 4.2 Mean ratios of bankrupt / nonbankrupt firms
Ratio
Definition
Bankrupt 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
value of total debt
0.401
2.477
X5
Sales / total assets
1.500
1.900
Nonbankrupt
Group Mean
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

When we apply Equation (4.5) to calculate financial Zscore, the model should be defined as
Yi  1.2 X1  1.4 X 2  3.3 X 3  0.6 X 4  1.0 X 5


Here we use JNJ in 2005 as an example,
Ratio
Definition
JNJ
X1
Net Working capital / total assets
( current asset –current liability )
/ total assets
0.3233
X2
Retained earnings / total assets
0.7147
X3
EBIT/ total assets
0.2353
X4
Market value of equity / book
value of total debt
8.8683
X5
Sales / total assets
0.8706
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
1. PPO
2. SP
Size of Sample
2(1.8%)
14(12.7%)
3. OP
94(85.5%)
Total
110(100%)
Definition
Serious problem-potential payoff. An
advanced problem bank that has at least
50 percent chance of requiring financial
assistance in the near future.
Serious problem. A bank whose financial
condition threatens ultimately to obligate
financial outlay by the FEIC unless drastic
changes occur.
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.
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
1. Problem bank
53.9
55.4
56.9
56.0
2. Nonproblem bank
49.3
48.9
47.8
47.8
1. Problem bank
648.3
692.2
768. 9
838.6
2. Nonproblem bank
564.5
562.5
562.4
577.5
1. Problem bank
83.9
85.5
89.3
94.1
2. Nonproblem bank
78.5
78.6
81.8
82.4
1. Problem bank
64.7
65.8
68.8
69.8
2. Nonproblem bank
59.3
59.2
59.9
59.6
1. Problem bank
15.8
16.0
16.3
16.4
2. Nonproblem bank
12.3
13.0
13.2
13.7
Loans/Assets
Loans/Capital plus Reserves
Operating Expense/Operating Income
Loan Revenue/Total Revenue
Other Expenses/Total Revenue
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
12
Insurance Corporation, Washington, D.C. He is currently Professor of Banking and Finance at College of Business
Administration, University of Georgia.
4.3 Bankruptcy and financial distress analysis
Year
Type I
Error
Type II
Error
Total
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
Z i  1.1018 0.1017X 1i  0.3966X 2i  0.0916X 3i  .1573X 4i  0.0199X 5i  0.4533X 6i
(4.6)
where
X 1 = 0: Unsecured loan,
1: Secured loan;
X 2 = 0: Past interest payment due,
1: Current loan;
X 3 = 0: Not audited firm,
1: Audited firm;
X 4 = 0: Net loss firm
1: Net profit firm
X 5 = Working Capital/Current Assets;
X 6 = 0: Loan criticized by bank examiner,
1: Loan not criticized by bank examiner.
14
4.3 Bankruptcy and financial distress
analysis
Z  11.08576 X1  1.50752 X 2  3.53606 X 3
 2.49824 X 4  2.45352 X 5  0.24492 X 6
(4.7)
where
X 1 = Agents’ balances/Total assets; a measure of the firms’
accounts receivable management;
X 2 = Stocks at cost (preferred and common)/Stocks at market
(preferred and common); measures investment management;
X 3 = Bonds at cost/Bonds at market; measures the firm’s age;
X 4 = (Loss adjustment expenses paid + underwriting expenses
paid) / Net premiums written; a measure of a firm’s funds flow
from insurance operations;
X 5 = Combined ratio; traditional measure of underwriting profitability;
and
X 6 = 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
Ratio
Number
Ratio Name
1972
1974
Primary
Primary
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
Ratio
Number
Ratio Name
1972
1974
Primary
Primary
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
Ratio
Number
Ratio Name
1972
1974
Primary
Primary
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
Ratio
Number
Ratio Name
1972
1974
Primary
Primary
Mfg.
Retail
Mfg.
Retail
.66
.85*
.70a
.78*
Factor 3Capital Intensiveness
3
Sales/Net Worth
6
Sales/Total Assets
.78a
.81*
.75
.79*
19
Cash Flow/Sales
-.44
-72a*


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
Ratio
Number
Ratio Name
1972
1974
Primary
Primary
Mfg.
Retail
Mfg.
Retail
Working Capital/Sales
.72a
.44*
.69a
.81*
20
Current Liabilities/Net Plant
.33
.71*


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*
Factor 4Inventory Intensiveness
1
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
Ratio
Number
Ratio Name
1972
1974
Primary
Primary
Mfg.
Retail
Mfg.
Retail
Factor 5Cash 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
Ratio
Number
Ratio Name
1972
1974
Primary
Primary
Mfg.
Retail
Mfg.
Retail
Factor 6Receivables 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
Ratio
Number
Ratio Name
1972
1974
Primary
Primary
Mfg.
Retail
Mfg.
Retail
Factor 7Short-Term Liquidity
21
Working Capital/Total Assets


.73
-.35
36
Inventory/Working Capital


-.79
.16*
38
Current Liabilities/Net Work


-.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


-.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
Ratio
Number
Ratio Name
1972
1974
Primary
Primary
Mfg.
Retail
Mfg.
Retail
Factor 8Decomposition Measures
56
Asset Decomposition
.68
.74


58
Equity Decomposition
.84
.84
.86
.87
60
Noncurrent Items Decompostion
.83
.78
.87
.85
61
Time Horizon Decompostion


.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.
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.
a
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
.95
.41
.13
.05
.14
.05
.25
.26
Two  Financial Leverage
.40
.95
.11
.17
.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
.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
.06
.01
.05
.27
.84
One  Return on Investment
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
+ 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
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
27
financial ratios,” Financial Management (Spring 1981), Exhibit 1. Reprinted by permission.
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
Y1  0.329X 1  0.107X 2  0.100X 3  0.005X 4  0.270X 5  0.893X 6
Y2  0.046X 1  0.218X 2  0.212X 3  0.264X 4  0.505X 5  0.762X 6
Y3  0.128X 1  0.044X 2  0.138X 3  0.001X 4  0.320X 5  0.928X 6
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

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
30
**Significant at 0.01 level
*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
Y  1.32  0.407 X1  6.03 X 2  1.43 X 3  0.0757 X 4  2.37 X 5  1.83 X 6  0.285 X 7
 1.72 X 8  0.521X 9
(4.8)
Where Y  log[P /(1  P)], P = the probability of bankruptcy.
33
4.7 Ohlson’s and Shumway’s methods for
Estimating Default Probability
Y  13.303 1.982X 1  3.593X 2  0.467X 3  1.809X 4  5.79X 5
(4.9)
Where Y  log[P /(1  P)], 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
Ji ( )  M  (M 1)i
(i  1,..., M ).
 M J i ( ) 
J ( )  
 M  (M  1) i 

 i 1 M 
  ( N k  1) S

  ( N k  1)
2
k



(4.A.1)
(4.A.2)
1/ 2
(4.A.3)
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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
1
2
3
Variable
Coefficient
Jackknifed*
Coefficient
Coefficient
Jackknifed*
Coefficient
Coefficient
Jackknifed*
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