Altman s Z-Score Discriminant Function Algorithm

Altman's Z-Score Discriminant Function Algorithm

In order to attempt to determine the early onset of an inflection point, we are fortunate to have available to us the pioneering work of Edward I. Altman, a professor at the Stern School of Business at New York University.^[19] While Altman was looking for a means to predict bankruptcy, his algorithm also works extremely well in determining inflection points and is the basis of the inflection point analysis discussed herein. That is, inflection points as discussed in this work are only used to highlight changes in business condition (positive or negative) not to predict bankruptcy, as Altman envisioned.

Altman used empirical data and regression analysis in order to formulate an algorithm comprised of fractions to which predetermined weights were applied. Scores above or below certain measures indicated the likelihood one would fall into bankruptcy. Altman's tool was found to have a correlation factor of 95% in predicting companies that would file for bankruptcy some 12 months prior to such actual filing, 72% 24 months prior to such a happening, and 48% 36 months before—highly accurate by most measures.

There are some shortcomings. Altman developed the algorithm presented herein for mid-sized manufacturing companies. However, this algorithm works exceedingly well for capital-intensive, infrastructure-laden enterprises—telecom service providers and telecom equipment manufacturers. But, as Altman based his research on mid-sized companies, Altman's time line to business failure is perturbed by the asset-rich nature of the telecom enterprise. That is, the larger the entity (the more assets it has), the more time it has to fix its problems, as it has assets it can borrow against or sell off. This is the AT&T case we see today, with the break up of AT&T and the spin-out of its wireless and cable entities.

Nevertheless, we are only using Altman's algorithm to sense improvement or degradation in business condition (an inflection point), one period to the next. Hence, in our application of Altman's model, the degree of change in score is significantly more important than the score itself.

So, how does Altman's algorithm work?

Altman's Z-Score—A Discriminant Function Algorithm

Z = 1.2X1 + 1.4X2 + 3.3X3 + 0.6X4 + 1.0X5

where:

• X1 = working capital divided by total assets;

• X2 = retained earnings divided by total assets;

• X3 = earnings before interest and taxes (EBIT) divided by total assets;

• X4 = market value divided by total debt;

• X5 = sales divided by total assets; and

• Z = overall index of corporate fiscal health.

According to Altman, financially strong small- to mid-sized manufacturing companies have a Z-score above 2.99. Companies in serious trouble have Z-scores below 1.81, and companies with scores in between can go either way.

In this case, we can again look to AT&T to see what was happening with its Z-score in the 1998 and 1999 time period (Table 11). Here, numbers were taken from AT&T's Web site, except for the price per share, which came from a financial site.

Table 11: AT&T's Abridged Financials (Unaudited)

Category	1999	1998
Current assets	$14B	$14B
Current liabilities	28B	15B
Working capital	(14B)	(1B)
Total assets	131B	60B
Retained earnings	9B	8B
EBIT	10B	9B
Equity at market	161B	134B
Total debt	82B	34B
Sales	62B	53B
Shares outstanding	3,196,436,757@$50	2,630,391,784@$51
Gross margin	53.2%	51.5%

Applying Altman's algorithm to the AT&T numbers in Table 11, we see the outcomes shown in Table 12.

Table 12: AT&T's Z-Score Calculation

Factor	1999	Score		1998	Score
X1	($14B/131B)	-0.107		(1B)/60B	-0.107
X2	$9B/131B	0.069		$8B/60B	0.133
X3	$10B/131B	0.076		$9B/60B	0.150
X4	$161B/82B	1.960		$134B/34B	3.940
X5	$62B/131B	0.473		$53B/60B	0.883

Solution

Using the information gathered, we arrive at the following solutions:

• 1999:

• (1.2 -0.107) + (1.4 0.069) + (3.3 0.076) + (0.6 1.96) + (1 0.473) = 1.87Z

• 1998:

• (1.2 -0.017) + (1.4 0.133) + (3.3 0.150) + (0.6 3.940) + (1 0.883) =3.91Z

As we can see from the above calculations, AT&T's Z-score declined by over half in a single year. Clearly, AT&T reached a major inflection point—a major negative inflection point. In fact, if you calculate AT&T's Z-score for 1997, when AT&T Wireless was still a subsidiary, you will find that the Z-score was higher still than 3.91.

As an investor in or creditor or supplier to AT&T, such an early warning that things were heading south would have been helpful in determining your future actions relative to AT&T. For instance, AT&T primarily only agreed to hold unsecured debt. If you were a creditor of AT&T and calculated such a degradation in Z-scores, you might have wanted to lessen your exposure, or raise fees to better offset risk. If you were a supplier to AT&T, for instance, such as Lucent, Nortel, or Ericsson, as AT&T was a large customer, such analysis and determination of a degrading Z-score might have changed your sales strategy relative to this key account. For instance, one of the companies above, if calculating a Z-score for AT&T, might have wanted to offer a discount for large purchases made early, in order to induce AT&T to advance capital equipment purchases. This strategy might have given one supplier a "first grab" at AT&T cash assets long before others realized (perhaps AT&T itself) that capital expenditures might have to be curtailed in future periods. In a moment, we will see how Altman's Z-score algorithm was modified based on negative changes in gross margin.

Hence, Z-scores, and adjusted Z-scores, can be used to determine inflection points and gain competitive advantage from both offensive and defensive perspectives.

However, as we do not seek to determine the likelihood of bankruptcy but rather only to determine changes in condition (inflections points), it is recommended that an adjusted Altman's Z-score model be used. This adjusted model puts more emphasis on debt as gross margin declines. This is because as an entity becomes less operationally efficient, debt becomes more onerous and increases relative risk for the entity.

Reflected in Table 13 is a suggested adjustment to Altman's Z-score model as gross margins diverge in order to highlight significant inflection points.

Table 13: Adjusted Altman's Z-Score Based on Gross Margin Divergence

Annual Decline in Gross Margin %	Reduction in X$ weighting (0.6)	X4 Adjusted Value (0.6)
3 < 10	100%	0
>10<20	150%	-0.3
>20<30	300%	-1.8
>30<40	600%	-3.6
>40	1000%	-6.0

As we can see in the AT&T Corp. case examined above, as AT&T's gross margin improved for the periods under examination, there would be no need to adjust the X4 factor. But other cases may require such an adjustment.

^[19]Altman, E. I. (1983). Corporate financial distress: A complete guide to predicting, avoiding, and dealing with bankruptcy. New York: John Wiley & Sons. The author does not apply Altman's algorithm in its pure form; rather, he uses decimal representations of Altman's weighting functions.