Given the ongoing panic in coal shares, I decided to do a series which will look at several coal stocks using the Altman Z-score. The purpose will be to get a feel of the relative risk with each coal stock. I will start with **Arch Coal** (NYSE:ACI). The Altman Z-score, as defined by Wikipedia, is:

The Z-score formula for predicting bankruptcy was published in 1968 by Edward I. Altman, who was, at the time, an Assistant Professor of Finance at New York University. The formula may be used to predict the probability that a firm will go into bankruptcy within two years. Z-scores are used to predict corporate defaults and an easy-to-calculate control measure for the financial distress status of companies in academic studies. The Z-score uses multiple corporate income and balance sheet values to measure the financial health of a company.

The Z-score is a linear combination of four or five common business ratios, weighted by coefficients. The coefficients were estimated by identifying a set of firms which had declared bankruptcy and then collecting a matched sample of firms which had survived, with matching by industry and approximate size (assets).

**Inputs**

The Z-score has 5 inputs:

- T1 = Working Capital / Total Assets.
- T2 = Retained Earnings / Total Assets.
- T3 = Earnings Before Interest and Taxes / Total Assets.
- T4 = Market Value of Equity / Book Value of Total Liabilities.
- T5 = Sales / Total Assets.

**Formula**

Which then come together using the following formula:

Z = 1.2T1 + 1.4T2 + 3.3T3 + 0.6T4 + .999T5

**Calculation for Arch Coal**

The following data, obtained from Arch Coal's latest 10-Q, is necessary to make the Z-score calculation:

- Current assets: $1179 million.
- Current liabilities: $763 million.
- Total assets: $10165 million.
- Retained earnings: $600 million.
- EBIT (ttm): $420 million.
- Total liabilities: $6581 million.
- Market capitalization: $1520 million.
- Revenues: $4450 million.

Using this data we get the following parcels:

1.2 * T1 = 0.049

1.4 * T2 = 0.083

3.3 * T3 = 0.136

0.6 * T4 = 0.139

0.999 * T5 = 0.437

This gives us an Altman Z-score of **0.84.**

**Interpretation**

The Altman Z-scores are interpreted according to the following ranges (source: Creditworthy.com):

3.0 or more,

Most likely safe based on the financial data. Of course, mismanagement, fraud, economic downturns, and other factors may cause an unexpected reversal.

2.7 to 3.0,

Probably safe to predict survival, but this is a portion of the gray area and is below the threshold of relative safety.

1.8 to 2.7

Likely to be bankrupt within two years. This is the lower portion of the gray area and dramatic action may be required to effect survival.

Below 1.8

Highly likely headed for bankruptcy. Rarely would a firm be expected to recover from a financial condition generating this or lower scores.

**Conclusion**

Arch Coal's Z-score does imply there's considerable risk of bankruptcy with Arch Coal. This is a measure taken at a very unfavorable timing in the coal cycle, but still its implications cannot be ignored. Arch Coal can only be held as a very speculative bet on the short-term recovery of coal prices.

The Altman Z-score doesn't give much thought to the coal companies' ability to generate a large cash flow, from the fact that depreciation and depletion of coal reserves is a large non-cash cost that these companies have. This large non-cash cost might mean ACI's ability to survive is somewhat higher than implied by the Altman Z-score, but it's now a certainty that ACI will have to cut capex to the bone, if it wants to have a chance.

**Disclosure: **I am long ACI.