# Predicting Corporate Bankruptcy: The Z-Score Model1

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**Part III**Risk

Appendix 30A Predicting Corporate Bankruptcy:

The Z-Score Model1

Many potential lenders use credit scoring models to assess the creditworthiness of prospec-

tive borrowers. The general idea is to ﬁ nd factors that enable the lenders to discriminate be-

tween good and bad credit risks. To put it more precisely, lenders want to identify attributes

of the borrower that can be used to predict default or bankruptcy.

Edward Altman has developed a model using ﬁ nancial statement ratios and multiple

discriminant analyses to predict bankruptcy for publicly traded manufacturing ﬁ rms. The

resultant model is of the form

EBIT

New working capital

Z 3.3

__________

_________________

1.2

Total assets

Total assets

Sales

Market value of equity

1.0

__________

___________________

.6

Total assets

Book value of debt

Accumulated retained earnings

1.4

__________________________

Total assets

where Z is an index of bankruptcy.

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A score of Z less than 2.675 indicates that a ﬁ rm has a 95 percent chance of becoming

bankrupt within one year. However, Altman’s results show that in practice scores between

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1.81 and 2.99 should be thought of as a gray area. In actual use, bankruptcy would be pre-

dicted if Z 1.81 and nonbankruptcy if Z 2.99. Altman shows that bankrupt ﬁ rms and

nonbankrupt ﬁ rms have very different ﬁ nancial proﬁ les one year before bankruptcy. These

different ﬁ nancial proﬁ ts are the key intuition behind the Z-score model and are depicted in

Table 30A.1.

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**Table 30A.1**

**Average Ratios One Year before**

**Financial Statement**

**Bankruptcy of**

**Ratios One Year**

**Bankrupt Firms**

**Nonbankrupt Firms**

**before Bankruptcy:**

Net working capital

**Manufacturing Firms**

_________________

6.1%

41.4%

Total assets

Accumulated retained earnings

__________________________

62.6%

35.5%

Total assets

EBIT

__________

31.8%

15.4%

Total assets

Market value of equity

___________________

40.1%

247.7%

Total liabilities

Sales

______

150%

190%

Assets

SOURCE: Edward I. Altman,

*Corporate Financial Distress and Bankruptcy*(New York: John Wiley & Sons,

1993),Table 3.1, p. 109.

1Edward I. Altman,

*Corporate Financial Distress and Bankruptcy*(New York: John Wiley & Sons, 1993), Chapter 3.

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Altman’s

original

*Z*-score model requires a ﬁ rm to have publicly traded equity and be

a manufacturer. He uses a revised model to make it applicable for private ﬁ rms and non-

manufacturers. The resulting model is this:

Net working capital

Accumulated retained earnings

*Z*6.56

__________________________

________________

3.26

Total assets

Total assets

Book value of equity

EBIT

1.05

__________

_________________

6.72

Total assets

Total liabilities

where Z 1.23 indicates a bankruptcy prediction,

1.23 Z 2.90 indicates a gray area,

and Z 2.90 indicates no bankruptcy.

U.S. Composite Corporation is attempting to increase its line of credit with First National State

Bank. The director of credit management of First National State Bank uses the Z-score model to de-

termine creditworthiness. U.S. Composite Corporation is not a publicly traded ﬁ rm, so the revised

Z-score model must be used.

**EXAMPLE**

The balance sheet and income statement of U.S. Composite Corporation are in Tables 2.1 and

2.2 (Chapter 2).

The ﬁ rst step is to determine the value of each of the ﬁ nancial statement variables and apply

them in the revised Z-score model:

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(in millions)

Net working capital

275

_________________

_____

0.146

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Total assets

1,879

Accumulated retained earnings

390

__________________________

_____

0.208

Total assets

1,879

EBIT

219

__________

_____

0.117

Total assets

1,879

Book value of equity

805

_________________

____

1.369

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Total liabilities

588

The next step is to calculate the revised Z-score:

*Z*6.56 0.146 3.26 0.208 1.05 0.117 6.72 1.369

10.96

Finally we determine that the Z-score is above 2.9, and we conclude that U.S. Composite is a good

credit risk.

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