Chapter 9
Forecasting Bankruptcy

Learning objectives

  • Identify the ratios to be used in both of Altman’s models for bankruptcy prediction.
  • Recognize how a Z-score determines the likelihood of bankruptcy.

Introduction

The purpose of this section is to provide you with a way to forecast bankruptcy using five simple ratios to determine a Z-score for any firm. The ratios used to determine the Z-score are working capital to total assets, retained earnings to total assets, E.B.I.T. to total assets, the market value of the firm’s equity to the book value of its debt, and sales to total assets. The Z-score is a measure of overall financial health.

Altman’s bankruptcy prediction formula

Z = .012X1 + .014X2 + .033X3 + .006X4 + .999X5

X1 = working capital/total assets

X2 = retained earnings/total assets

X3 = earnings before interest and taxes/total assets

X4 = total equity/total debt

X5 = sales/total assets

Z = overall index

Altman’s suggested Z-score cutoff

If Z is This indicates
Less than 1.81 A problem
Between 1.81 and 2.99 Concern
Greater than 2.99 No problem

The Z-score was developed using a statistical procedure called discriminant analysis. This procedure allows the statistician to find variables that distinguish between groups. In this case the procedure found five ratios that distinguish between bankrupt and non-bankrupt companies. The coefficients in front of the X variables come from the statistical procedure.

Computational note

Variables X1 to X4 are to be computed as a percent, not as a decimal. For example, if X1 is 21.8 percent, put it in the model as 21.8, not as 0.218.

Usage notes

The Z-score is a good measure of overall health. Do not become too hung-up on Altman’s 1.81 cutoff. Observe how the Z-score varies across time. I would be less worried about a company whose Z-score remains between 1.70 and 1.85 for the last 10 years than about a firm that dropped from 2.8 to 1.95 in 1 year. Use your judgment regarding this ratio.

Knowledge check

  1. A company’s liquidity is considered in the Altman Z-score in variable
    1. X1.
    2. X2.
    3. X3.
    4. X4.
  2. Suppose retained earnings were $4,000 and total assets were $100,000. Variable X2 would be 4 percent. If written as a decimal, it would be 0.04. Which 2 numbers would you multiply by the coefficient 0.014?
    1. 4.0.
    2. 0.04.
    3. 400.
    4. 4,000.

Bankruptcy prediction example

Crystal Brands, Inc. selected financial data (in 000)
  20X5 20X6 20X7 20X8 20X9
Net sales $857,241 $868,465 $826,876 $486,893 $444,302
EBIT 84,758 84,393 (19,345) 1,103 (87,379)
Current assets 351,726 363,880 350,048 245,744 155,245
Current liabilities 167,558 172,179 199,761 77,165 313,392
Total assets 682,528 688,138 659,437 486,309 248,437
Total debt 444,779 421,963 465,946 362,128 340,556
Retained earnings 47,161 74,235 1,019 (66,801) (282,917)
Number of shares 9,078 9,098 9,116 9,117 9,117
Market price/share 33.03 21.06 14.00 4.03 1.07
X1 26.98% 27.86% 22.79% 34.66% (63.66%)
X2 6.91% 10.79% 0.15% (13.74%) (113.88%)
X3 12.4% 12.2% (2.9%) (0.2%) (35.17%)
X4 67.41% 45.41% 27.39% 10.15% 2.86%
X5 1.26 1.26 1.25 1.00 1.79
Z 2.49 2.42 1.59 1.29 (1.71)

Knowledge check

  1. A Z-score of 3.66 implies _______ financial health.
    1. Good.
    2. Poor.
    3. Average.
    4. Decreasing.
  2. Suppose that the Perfect Company’s Z-score dropped from 3.55 to 1.45 over a 3-year period. What could we conclude?
    1. Prefect’s overall financial health had deteriorated.
    2. Perfect is too deeply in debt.
    3. Both of the above.
    4. Neither of the above.

Altman’s second model

In 1983 Altman developed a second model that is, perhaps, more useful for small companies (service companies and manufacturers). Each variable is computed as a percent, not as a decimal.

images

Where

Y1 = working capital to total assets

Y2 = retained earnings to total assets

Y3 = earnings before interest and taxes to total assets

Y4 = net worth to total liabilities

Critical values

Z′ ≤ 1.1 Concern
1.1 < Z′ < 2.6 Grey Area
2.6 ≤ Z′ Strong Company

Several other bankruptcy prediction models have been proposed. Altman’s models may work as well as most others. However, if you would like an additional model to choose from, we recommend the following:

  • Fulmer, J.G, J.E. Moon, T.A. Gavin, and J.M. Erwin, “A Bankruptcy Classification Model for Small Firms.” The Journal of Commercial Bank Lending, July 1984, pp. 25–37.
  • Altman, E.I, R.G. Haldeman, and P. Narayanan, “Zeta Analysis: A New Model to Identify Bankruptcy Risk of Corporations.” Journal of Banking and Finance, June 1977, pp. 29–54.

Review questions

  1. Outline the procedure for calculating and using a Z-score to forecast bankruptcy.

     

     

     

  2. What ratios are used in a Z-score analysis? Why is each ratio used? What does each ratio indicate that helps to forecast bankruptcy?

     

     

     

  3. What are the decision criteria used in a Z-score analysis? How were they determined?