Debt covenant selection: an empirical examination.

Carter, Fonda L. ; Hadley, Linda H. ; Hogan, Patrick T. 等

ABSTRACT

How are debt covenants selected? Which firm and industry factors are significant in the covenant selection process? Previous research by the current authors examined individual debt covenants to determine if identifiable patterns exist and if there is a significant difference in debt covenant utilization among industry classifications. The evidence suggested that not only are there identifiable patterns, but that debt covenants are systematically grouped into packages. A theory of debt covenant utilization was offered to explain the theoretical significance of each of the independent variables that appear to influence selection. This paper offers additional insight. It develops a model to test the significance of the independent variables and the patterns and predictability of use. After identifying the significant variables, the authors explain the implications of their findings to current financial management.

INTRODUCTION

Equity investors enjoyed years of a bull market from 1982 to early 2000, when the value of U. S. common stocks peaked at approximately $17 trillion in market value of the Wilshire 5000 index. The stock market slide began in the year 2000, and this downward trend continued in the days following the September 11, 2001 terrorist attacks on the United States' homeland. Throughout 2002, as equity markets struggled to stage several comeback rallies, the market's bad news shifted to huge business failures and bankruptcies, due to deceit and outright fraud in Fortune 100 companies such as Enron, Tyco, and Worldcom. The Wilshire 5000 index further declined during 2002 to end the year at a market value of only about $10 trillion, a stunning paper loss approximating $7 trillion over the three year period (Browning, 2003). Indeed, investor confidence in equities has deteriorated so much, that one major Canadian investment broker recently stated that "investors have totally lost faith in the stock market" (Wahl, 2002).

For many of these stock-shy investors, both corporate and individuals, investing in corporate bonds is becoming an increasingly attractive alternative, despite historically low interest rates. The increased attractiveness of bonds is due not only to the recent volatility of equity markets, but also to the reduced transactions costs and increased liquidity of corporate bonds for individual investors. Previously, corporate bond issues were funneled through only a few Wall Street dealers, resulting in bond prices being controlled by this small group. In recent years, more bonds are being issued in smaller increments without substantially increasing transactions costs, thus making them more attractive to individual purchasers. Additionally, research and analysis on thousands of bond issues has recently become available to the investing public on the Internet (Updegrave, 2001). The combined result of these factors is that non-institutional bond investors can buy investment grade corporate bond issues more easily and at more competitive prices than before.

With many investors fleeing equity markets seeking to preserve their investment capital, perceived risk will be a critical factor in bond selection. Spurned equity investors are likely to examine bond covenants more now than at any other time in recent decades. In addition to the usual decisions made with new debt offerings, financial managers may need to be particularly attentive to bond covenant selection. While they may be more important to investors still reeling from equity portfolio shrinkage and corporate fraud scandals, covenants can be quite costly to issuers. The challenge to management will be to include only those covenants which are necessary to make the issue marketable, and no more. The number and characteristics of the necessary covenants will vary considerably by issuer and by issue at any given point in time.

This study provides insight into debt covenant selection for financial managers of companies considering new debt offerings. The study includes a large sample covering a period that includes the stock market Crash of 1929, the Great Depression that ensued, the World Wars, and the prosperity that followed. The sample period spans recession, depression and prosperity, thus increasing its relevance and applicability.

BACKGROUND

Prior to the actual issuance of bonds, companies negotiate with the bond trustee specifically on which financial covenants are to be included in the debt contract. The trustee, acting on behalf of the bondholders, requires specified covenants be included in debt contracts in order to restrict management behavior that may be harmful to bondholders (Jensen and Meckling, 1976). In the absence of these covenants, a firm's management may be free to employ strategies that serve to expropriate wealth from bondholders to the benefit of the shareholders of the firm. The benefit of restrictive covenants is readily apparent; however, this benefit must be weighed against the costs associated with their selection, inclusion and enforcement.

Smith and Warner (1979) explained in their costly contracting hypothesis that a tradeoff is often made between the increase in firm value from including the covenants and the additional costs associated with the writing and monitoring of the contracts and the indirect costs resulting from reduction of management discretion related to management decisions. These costs may be offset by the higher prices bondholders are willing to pay for the firm's debt given the added protection afforded by the covenants. As a result, the value of the firm increases. In an effort to reduce contracting costs, thus producing a net increase in the value of the firm through the use of covenants, Smith and Warner suggested that systematic patterns of debt covenants would exist across debt covenants. At the time the bond contract is developed, the bondholders make predictions regarding the investment, financing and dividend policies available to the stockholders. Based on these predictions, bondholders propose the inclusion of selected covenants to control potential wealth transfers from the bondholders to the stockholders. The potential increase in firm value resulting from higher bond prices serves as the incentive for stockholders to oblige. The firm is then faced with making decisions concerning the number and type of covenants to include. Once it becomes evident which covenants are effective in reducing the varying levels of perceived conflict, systematic patterns of covenant use will evolve to reduce contracting costs. Identifying these covenant packages and the variables that influence their inclusion could provide valuable information to the manager in the negotiation process.

THE IDENTIFICATION OF DEBT COVENANT PACKAGES

Previous research by the authors (2000) examined the type and incidence of restrictive covenants used in debt contracts. The sample surveyed consisted of 327 public debt issues for 28 different companies. The issues were chosen from the time period of the early 1920s to 1993. Five industries were represented in the sample: petroleum, food, steel, paper and plastics. These industries were chosen because they represent companies in existence during the time period studied. The industry factor was included in the survey to later analyze whether it was a significant variable in the determination of debt covenant selection. Only companies with at least three public issues of non-convertible, senior debt in at least three decades over the period of study were included.

It was noted that very few debt agreements contained a covenant for merger restriction, a covenant requirement for maintenance of assets, a covenant for a restriction on investments, a covenant for a restriction on disposition of assets, or a covenant for an indirect investment restriction. The results support the premise that some covenants are more efficient in controlling sources of conflict than others.

This initial analysis led to the elimination of several covenants from further study of the patterns of covenant grouping. The callable provision was eliminated because it was present in 76.1% of the packages and further analysis revealed that the debt agreements that did not contain this covenant were primarily short-term agreements. The rights on default condition was also eliminated since it was included in 85.9% of the covenants. The sales/lease restriction was eliminated because further analysis revealed it was included only in the more recently written debt agreements. Other covenants were excluded from further analysis (merger restriction, requirement for maintenance of assets, restriction on investment, restriction on disposition of assets, and indirect investment restriction) due to the small number of debt agreements containing these covenants. The covenants that were included for further analysis of debt covenant package existence were the sinking fund covenant, the debt priority restriction, the security requirement, and the dividend restriction. As previously reported by the authors (2002), four different but systematic covenant packages were identified. The covenants included specifically protect assets for the bondholder in terms of claim dilution, asset substitution, dividend payout and under-investment. These covenants are among a subset of covenants that appear consistently in public debt contracts over the time period of the study as determined by a review of the literature and a preliminary study. The analysis also showed that the covenants are ordered in the amount of protection they offer the bondholder.

The first covenant package (PACK A) includes none of the four covenants that are the focus of the study and offers no protection to the bondholder in the event of default. The second covenant package (PACK B) offers only a sinking fund covenant out of the four covenants studied, adding one additional layer of protection. The third covenant package (PACK C) includes a sinking fund covenant and a direct security covenant and/or a direct debt priority covenant. This package adds a second layer of protection. The fourth and final package (PACK D) includes a dividend covenant to the previous package of covenants, adding a third layer of protection. The packages were ordered in this manner based on observations from a survey of the sample and the theorized level of benefit that each covenant provides to the bondholder.

The survey of 327 packages of covenants from the study supports the theory that the covenants are ordered. Table 2 illustrates that out of 208 issues including covenants in their debt contracts, all but 21 include a sinking fund covenant. Of the 65 issues including a dividend covenant, only nine issues include this covenant without a related sinking fund and security or debt priority covenant. Of the 93 issues including either a security covenant or debt covenant, only four issues do not include a sinking fund covenant.

A THEORY OF DEBT COVENANT UTILIZATION

Previous research had clearly explained the desirability of covenant inclusion and the current authors' 2000 study identified patterns of individual and packaged covenant use. In an effort to further develop the field of research in this area, Carter, Hadley and Thomson (2001) developed a model to explain both the existence and ordering (ranking) of patterns of debt covenant packages. Toward this end, a model was developed to identify independent variables that have been observed to influence debt covenant package selection. These include, the size of the firm, financial leverage of the firm, the firm's trend in profitability, the firm's industry, and the length of the debt contract.

THE VARIABLES

Size of the firm (SIZE). The literature in this area suggests that larger, well-established firms have reputations in the market and hence are subject to more analysis than smaller firms. Their investment opportunity set is considered to be available public information. The market has shown trust in the firm by allowing it to grow. If the firm had caused any of the sources of conflict to be realized in the past, the firm's ability to raise funds in the future would be altered (Malitz 1986). The size of the firm was measured by the natural log of total assets.

Financial leverage of the firm (LEV). It is hypothesized that the closer a firm is to bankruptcy, the more likely the bondholders will include a covenant to protect against claim dilution (i.e. secured debt covenant). Therefore, firms with higher financial leverage are theorized to have a greater probability of issuing bond packages with higher levels of protection than firms with lower financial leverage. The financial leverage variable of the firm was measured by the ratio of total debt to total assets determined by issue year numbers.

Rate of Return (ROR). In the event of declining earnings, the firm has an incentive to maintain dividend payouts at the expense of new investment, thus creating an underinvestment conflict. Firms with higher levels of earnings are not impacted by this conflict because the earnings are available for dividends. Firms with positive profitability trends have a greater probability of issuing bonds with covenant packages that have lower levels of protection than firms with lower average rates of return. The rate of return variable was measured by the average rate of return of the issuing firm for the three years prior to year of issue.

Time to Maturity (MAT). Time to maturity is predicted to be a significant factor in debt covenant selection. The longer the contract, the greater the need will be to control possible sources of conflict. Therefore, the longer the contract, the greater the probability of including a debt covenant package with a higher level of protection. The time to maturity variable was divided into three categories: long term (15 years or longer), medium term (10-14 years), and short term (less than 10 years).

Industry of the issuing firm (IND). While it is not clear which covenant packages will be attractive to particular industries, it is clear that industry is likely to be a significant variable due to the nature and desirability of the firm's assets. The industry of the firm is particularly related to the need to control the conflict related to asset substitution. The more specialized a firm's resources, the less likely the firm will benefit from asset substitution (Smith and Warner). The industries included petroleum, paper, plastic, steel, and food. Table 3 summarizes the independent variables and the type of measurement variable.

THEORETICAL MODEL

The theoretical model is displayed in Figure 1, setting forth the proposed relationships between each independent variable and the issuing company's covenant packet membership. The figure shows that two propositions (P2 and P5) should be positively related to more restrictive covenant membership, since these two variables are perceived to increase risk. On the other hand, three propositions (P1, P3, and P4) should be negatively related to more restrictive covenant membership, since these three variables are perceived to reduce risk. This model does not imply cause and effect; it only indicates the proposed positive or negative relationship.

[FIGURE 1 OMITTED]

METHODOLOGY

After initial descriptive statistics were obtained, the issues in the sample were segregated into four groups for the testing of the theory of the factors significant in debt covenant selection using an ordered probit model. The issues were segregated into PACK A, those issues that did not contain any of the covenants in questions; PACK B, those issues with only a sinking fund covenant; PACK C, those issues with the sinking fund covenant, a direct debt/priority covenant and/or a direct security covenant; PACK D, a sinking fund covenant, a dividend covenant, and either a direct debt priority covenant or a direct security covenant.

Ordered probit was used to construct the model indicating the significance of the independent variables in covenant package selection. It is similar to OLS regression analysis where independent variables are used to explain the dependent variables and the independent variable can be continuous, discrete, or ordered. However, with an ordered probit model the dependent variable is a discrete choice rather than a continuous intervally scaled variable as it is in OLS regression analysis. The dependent variable is scored as selected or not selected based on a function of the independent variables. Ordered probit is preferable to multinomial logit as multinomial logit yields multiple equations that can be difficult to interpret. Also multinomial logit ignores the natural ranking of the dependent variables.

The model estimated to test the hypotheses was specified by the equation that follows. The significance of the individual independent variables was measured by the p statistic.

Package of Covenants = [b.sub.1](SIZE) + [b.sub.2](LEV) + [b.sub.3](ROR) + [b.sub.4](MAT) + [b.sub.5](IND)

The dependent variable is a dummy variable representing the levels of covenant packages and was coded "0" for PACK A, "1" for PACK B, "2" for PACK C, and "3" for PACK D. The independent variables utilized to test the hypotheses table are outlined along with their measurement base in Table 3.

Alternatively, the model can be stated in terms of probability with PACK A, where y=0 going to PACK D, where y = 3.

The general form of the model is as follows:

[[PHI].sup[..sub.1]([p.sub.1]) = [[alpha].sub.1] + [[beta].sub.'x] [[PHI].sup.1] ([p.sub.1] + [p.sub.2)] = [[alpha].sub.2] + [[beta].sub.'x] [[PHI].sup.1] ([p.sub.1] + [p.sub.2 ... + [p.sub.k]) = [[alpha].sub.k] + [[beta].sub.'x] and [p.sub.1] + [p.sub.2] ... + [p.sub.k] + 1 = 1

The equation can also be stated equivalently, as follows:

[p.sub.1] = [PHI]([[alpha].sub.1] + [[beta].sub.'x]) [p.sub.1] = [PHI]([[alpha].sub.2] + [[beta].sub.'x]) - [PHI]([[alpha].sub.1] + [[beta].sub.'x]) [p.sub.k] = [PHI]([[alpha].sub.k] + [[beta].sub.'x]) - [PHI]([[alpha].sub.k-1] + [[beta].sub.'x]) [p.sub.k-1] = 1 - [PHI]([[alpha].sub.k] + [[beta].sub.'x)]

In the equation, [[PHI].sup.1] is in the inverse of the cumulative standard normal distribution function, also referred to as the probit. The [PHI] denotes the cumulative standard normal distribution function. The probit model used (LIMDEP7) produced, in addition to the coefficients, an intercept and two additional cut points that are thresholds between the levels of the ordered dependent variables. There are four dependent variables, one constant term and two thresholds (Mu).

SIGNIFICANCE OF THE OVERALL MODEL

Since ordered probit analysis does not produce a measure analogous to the r2 statistic of traditional regression models, the log likelihood ratio statistic is utilized to test the overall significance of the models. This ratio is based on the theory that the coefficients of the model are not significantly different than zero, with the exception of the constant. The ratio follows a chi-square distribution and the number of degrees of freedom is equal to the number of parameters tested. An additional consideration of the significance of the overall model is the calculation of a classification table as seen in Table 6. The table shows frequencies of predicted and actual outcomes for the four categories of the dependent variable. From this table, the percentage of outcomes accurately predicted can be calculated.

THE RESULTS

The first step in the statistical analysis was to eliminate from the original sample of 327 issues those issues that did not contain either PACK A, PACK B, PACK C, or PACK D covenants in their debt contract. This resulted in the elimination of 23 issues from the sample reducing it to 304 issues. Table 4 reports the statistics for each of the independent variables.

The first hypothesis predicted that packages of covenants with higher levels of protection are more likely the smaller the size of the issuing firm. This hypothesis was supported by the model. The coefficient for size (the log of total assets) was significant at the 0.001 level. Also, the coefficient was negative indicating that as the size of the firm increases, the probability of including a package of covenants with higher levels of protection decreases.

The second hypothesis predicted that the packages of covenants with higher levels of protection are more likely the higher the leverage ratio of the issuing firm. The leverage ratio, measured by total assets to total debt in the issue year, was significant in the model. However, this ratio did not act in the direction predicted. This may be the result of having used actual debt ratios. Long-term debt to total capitalization and total debt to total assets may not have appropriately captured the leverage of the firm. A better ratio may have been long-term debt to the market value of the equity of the firm. The contrary performance may also have been the result of the other variables for size, industry, and maturity of the debt being more significant predictive factors, thus outweighing the leverage factor.

The third hypothesis predicted that packages of covenants with higher levels of protection are more likely the lower the prior average rate of return of the issuing firm. The independent variables measuring the average three prior year rate of return (ROR) was significant at the .10 level in the revised model (as measured by the p statistic). However, this variable also acted in the opposite direction predicted. It was predicted that as the average prior rate of return increases, the probability of selecting a package of covenants with a higher level of protection should decrease producing a negative coefficient. Additionally, based on correlation analysis, this variable was significantly correlated with the LEV4 variable. When the LEV4 variable was dropped from analysis, this variable (ROR) was no longer significant. The effect of this variable on the hypothesis is inconclusive.

There are several possible reasons that the prior three year average rate of return did not behave as predicted. First of all it is an average number and may not necessarily represent a trend in the rate of return. A better measure of the effect of rate of return on probability of default on the debt may be a variable measuring the volatility of earnings rather than the average rate of return. Additionally, the variable for size may be a better indicator of the probability of default on debt since it is a significant variable in the model. Also, the factors for industry and length to maturity were significant variables for the four packages of debt covenants.

The fourth hypothesis predicted that covenants with higher levels of protection were more likely for issues with longer maturities than issues with medium or short-term issues. This hypothesis was supported by the model. The coefficient for maturity of the debt was dummy coded based on long term (coded 0), medium term (coded 1), and short term (coded 2). The coefficient was negative in the model supporting the theory that medium term and short -term issues are less likely to include covenant packages with a higher level of protection.

The final hypothesis predicted that the industry of the issuing firm was a significant factor in the selection of debt covenant packages. The industry factors were significant in the model. The coefficient for petroleum was zero indicating that this industry was not as likely to issue packages with higher levels of covenants. The coefficients for paper and plastic were less than 1.0 indicating also that these industries were not as likely to issue packages with higher protection. The coefficients for the food industry and the steel industry were greater than the petroleum coefficient indicating that these industries were more likely to include covenant packages with higher levels of protection than the other industries.

REVISED MODEL

The revised model, after the statistical analysis, is displayed in Figure 2. All five variables were found to be significantly related to covenant packet membership: size of the firm, financial leverage, rate of return, time to maturity, and industry of the issuing firm.

[FIGURE 2 OMITTED]

CONCLUSION

Overall, the model (Table 5) provided a good fit for the data. The log likelihood ratio statistic supports the model's significance. The Chi2 was 312.227 at the .0000 significance level. Additionally, the table comparing predicted and actual outcomes (Table 6) indicated a correct classification percentage of 68.75%.

The results of this study provide valuable information to managers when negotiating which debt contracts are to be included in a debt agreement. As noted above, each of the five variables was statistically significant at the .10 level, or better. The following section addresses what these findings may mean to financial managers who are contemplating new debt offerings.

MANAGERIAL IMPLICATIONS

Of the findings made by this study, the one with the most significant implications for financial managers is the tendency of bond covenants in actual debt offerings to be grouped together in packages. The results of this research show that debt covenants tend to cluster into four packages, beginning with the least restrictive number of covenants in package one, ranging through progressively more restrictive covenants in packages two and three, to the most restrictive covenants contained in package four. It is important to note that covenants are not necessarily negotiated individually. Investors tend to require clusters of covenants based, at least in part, on the factors noted below.

Size does matter. The larger the firm the less likely it is that it will need to include covenant packages with higher levels of protection in the debt agreement. This finding is partly intuitive. Large firms project an image of greater stability. While this has been the case in the past, the recent collapse of Fortune 100 companies such as Enron, Tyco and Worldcom, may serve to result in large firms being held up to greater scrutiny in the future. So while size does matter, we predict that it might matter less in the future. Debt ratio will likely become a more significant determinant of investors' debt covenant expectations than firm size.

Profitability plays a part. Clearly the lack of earnings or declining earnings will increase both the number and cost of the covenants required. It might be important to note, however, that since debt is not serviced by profits, profitability will be more significant for those firms with high or long-standing dividend expectations.

Time matters as well. Since time increases uncertainty and risk, as the maturity is extended, it becomes more likely that the firm will need to include covenant packages with high degrees of protection.

Covenant expectations will vary by industry. Although this study did not attempt to predict covenant package requirements by industry, the findings do suggest that industry differences exist. While further examination is needed, industry differences are likely the result of the level of investment and marketability of firm assets.

Debt covenants may be costly to the issuing firms, but they provide protection that investors require. Careful analysis of covenant selection patterns will assist financial managers in maximizing their control over firm assets and minimizing covenant costs.

REFERENCES

Browning, E.S. (2003). Year-end review of markets and finance, 2002, Wall Street Journal, January 2, 2003.

Carter, F. & L. Hadley. (2002). An empirical examination of the determinants of covenants in public debt contracts: An examination of accounting and non-accounting factors. Conference Proceedings of the Academy of Accounting and Financial Studies, 31-36.

Carter, F. & L. Hadley. (2001). A theory of debt covenant utilization in public debt contracts. Conference Proceedings of the Academy of Accounting and Financial Studies, 36-40.

Carter, F., L. Hadley & N. Thomson. (2000). A survey of debt covenants in public debt contracts. Conference Proceedings of the Academy of Accounting and Financial Studies, 82-86.

Jensen, M. C. & W.H. Meckling. (1976). On financial contracting: An analysis of bond covenants. Journal of Financial Economics, 3, 305-360.

Malitz, I. (1986). Financial contracting: The determinants of bond covenants. Financial Management, 15(1), 18-25.

Smith, C. W. Jr. & J. B. Warner. (1979). On financial contracting: An analysis of bond covenants. Journal of Financial Economics, 7, 117-161.

Wahl, A. (2002). Balancing act, Canadian Business, 75(19), Oct. 2002.

Fonda L. Carter, Columbus State University

Linda H. Hadley, Columbus State University

Patrick T. Hogan, Columbus State University

Table 1: Incidence of Individual Covenant Use

Individual % Issues
Restrictive Covenant Containing

Rights on Default 85.9%
Callable Covenant 76.1%
Sinking Fund Requirement 59.3%
Security Requirement 17.1%
Dividend Restriction 22.6%
Debt/Priority Restriction 26.9%
Sales/Lease Restriction 53.2%

Table 2: Priority Levels of Covenants Packages

PACKAGE FREQUENCY PERCENTAGE

PACK A--No covenants 119 36.4%
PACK B--Sinking Fund Only 98 30.0%
PACK C--Sinking fund/Security 4 0.2%
 --Sinking fund/Security
 & Debt Priority 13 4.0%
 --Sinking fund/Debt Priority 16 33 4.9% 10.1%
PACK D--Sinking fund/
 Security & Dividend 25 7.6%
 --Sinking fund/Dividend
 & Debt Priority 3 0.9%
 --Sinking fund/Dividend/ 2 56 8.6% 17.1%
 Debt Priority &
 Security

ALL OTHER
 Dividend Only 9 2.8%
 Security/Dividend/
 Debt Priority 4 1.2%
 Other 8 2.4%
TOTAL ALL ISSUES 327 100.0%

Table 3: Independent Variable Measurement

 Type of
 Variable Measurement
 Measurement Variable Name Variable

[H.sub.1] The size of the issuing SIZE Continuous
 firm as measured by
 natural log of total
 assets

[H.sub.2] Alternative leverage LEV4 Continuous
 ratios of the issuing
 firm as measured by (4)
 Current year ratio
 of total debt/
 total assets

[H.sub.3] The average rate of ROR Continuous
 return of the issuing
 firm for the three years
 prior to year of issue

[H.sub.4] Maturity or type MAT Dummy Variable:
 measured by length in 0 = long term
 years of issue (15 years
 or more)
 1 = medium term
 (10-14 years)
 2 = short term
 (less than
 10 years)

[H.sub.5] Industry of the IND Dummy Variable:
 issuing firm 0 = Petroleum
 1 = Paper
 2 = Plastic
 3 = Steel
 4 = Food

Table 4: Statistics for the Independent Variables

Variable Mean Std. Dev. Minimum Maximum

LEV4 44.94 13.62 14.57 83.92
ROR 11.81 06.30 00.00 36.18
SIZE 11319 20786 140 304578
MAT 00.43 00.75 00.00 02.00

Table 5
Ordered Probit Model

 Coefficient
Variable (p Statistic)

Constant 5.051 (0.000) **
Food Industry 1.740 (0.000) **
Steel Industry 1.851 (0.000) **
Paper Industry 0.299 (0.223)
Plastic Industry 0.568 (0.013) **
Medium Term -2.167 (0.000) **
Short Term -2.409 (0.000) **
LEV4 -0.16E-01 (0.009) **
Prior Rate of Return 0.232 (0.068) *
Size -0.469 (0.000) **
 Dependent Variable
 Cutoff Points
MU(1) Threshold 1.737 (0.000) **
MU(2)Threshold 2.426 (0.000) **

Statistics: ** significant Statistics: **
 at the .05 level significant at
 the .10 level
Log likelihood -234.370
Restricted Log Likelihood -390.484
Chi-squared $312.227
Significance level 0.000

Table 6: Classification Table for Final Model

 PREDICTED OUTCOME

ACTUAL PACK A PACK B PACK C PACK D TOTAL
OUTCOME

PACK A 91 27 0 0 118
 (38.8)
PACK B 12 78 0 7 97
 (31.9)
PACK C 0 11 0 22 33
 (10.9)
PACK D 1 15 0 40 56
 (18.4)
TOTAL 104 131 0 69 304
 (34.2) (43.1) 0.00 (22.7) (100.0)