transferred to capital. In essence, then, that amount of capital which represents funds
contributed by the owners of the firm is the only part of equity that is not considered
in the Brazilian equivalent to retained earnings. X 2 was calculated as:
A more precise expression of the numerator would be the cumulative yearly retained
earnings plus the cumulative reserves created over the life of the firm, but this infor-
mation is very difficult to obtain outside the firm and was not available to the authors.
Since most Brazilian firms’ equity was not traded, there cannot be a variable which
measures the market value of equity (number of shares outstanding times the latest
market price). To derive the new values for X 4 , the book value of equity (patrimonio
liquido) was substituted and divided by the total liabilities. The remaining three vari-
ables were not adjusted, although we are aware of the fact that certain financial ex-
penses are also adjusted for inflation in Brazilian accounting.
(b) Empirical Results. The empirical results will be discussed in terms of two sepa-
rate but quite similar models. The first model, referred to as Z 1 , includes variables X 2
to X 5 (four measures) of the original Z-Score model. Model Z 1 does not include X 1
because the stepwise discriminant program indicated that it did not add any explana-
tory power to the model and the sign of the coefficient was contrary to intuitive logic.
Once again, as so often is found in multivariate failure classification studies, the liq-
uidity variable is not found to be particularly important. The second model, referred
to as Z 2 , does not include X 2 , because X 2 is quite difficult to derive with just one set
of financial statements and it is similar to X 4. Model Z 2 can therefore be applied with-
out supplementary data.
The models are as follows:
In both cases, the critical cutoff score is zero. That is, any firm with a score greater
than zero is classified as having a multivariate profile similar to that of continuing en-
tities and those with a score less than zero are classified as having characteristics sim-
ilar to those of entities that experienced serious problems.
Results from the two models are essentially identical based on one year prior data.
Model Z 1 performed better for Years 2 and 3; therefore, only the results of that model
are discussed. Of the 58 firms in the combined two samples, seven are misclassified,
yielding an overall accuracy of 88%. The Type I error (that of classifying a serious-
problem firm as a continuing entity) was 13% (3 out of 23 misclassified) and the Type
II error (that of misclassifying a continuing entity) was slightly lower at 11.4% (4 of
35). These results are impressive since they indicate that published financial data in
Brazil, when correctly interpreted and rigorously analyzed, do indeed possess im-
portant information content.
Due to the potential upward bias involved in original sample classification results,
further tests of the models were performed with several types of holdout or valida-
tion samples. The accuracy of the SP sample is unchanged after applying the Lachen-
bruch test. Several replication tests also showed high accuracy levels. Finally, the ac-
Z 2 1.840.51X 1 6.23X 3 0.71X 4 0.56X 5Z 1 1.444.03X 2 2.25X 3 0.14X 4 0.42X 51 Total equityCapital contributed by shareholders 1 CCS22>Total assets10 • 34 BUSINESS FAILURE CLASSIFICATION MODELS