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:
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.
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