Altman Z score

Introduction

Altman [@Altman1968] was a ground-breaking study that overcame many of the limitations of univariate analysis, and was the next step in the bankruptcy prediction evolution at the time. The study by Altman was the first study to utilise Multiple Discriminant Analysis in predicting signs of financial distress.

Altman found that the previously-used methodology was essentially univariate in nature and emphasis was placed on individual signs of future problems. Altman used an initial sample of 66 manufacturing companies, with 33 corporations in each of the two groups. Group 1 consisted of 33 bankrupt companies from 1946-1965 and Group 2 consisted of 33 live companies still in existence in 1966.

In assessing predictive variables, they were classified into 5 groups: liquidity, profitability, solvency, leverage and activity ratios. Out of the 20 ratios assessed, five were selected, based on the one from each classification perceived as doing the best job in the prediction of corporate bankruptcy. The final discriminant function using five variables is known as the Altman Z-score model.

Private Companies

The original Z-Score Model was based on the market value of the firm and was thus applicable only to publicly traded companies. Altman [@Altman1983] emphasized that the Z-Score Model is a publicly traded firm model and ad hoc adjustments are not scientifically valid. Therefore, Altman advocated a complete re-estimation of the model substituting the book value of equity for the market value in the ratio. Altman [@Altman1983] assigned score cut-offs specific for private firms.

Non-manufacturing

In 2006 Altman, improving upon his previous work by developing a four-variable Z-Score model in collaboration with [@Hotchkiss2006] for non-manufacturing firms. He excluded the ratio from this revised model, because of a potential industry effect. He concluded the industry effect is more likely to take place when this kind of industry-sensitive variable (asset turnover) is included into the model (Altman 1983).

Developing and Emerging Markets

Altman, developed a four-variable Z-Score model in collaboration with [@Hotchkiss2006] for non-manufacturing firms. He excluded the ratio from this revised model because of a potential industry effect. He concluded the industry effect is more likely to take place when this kind of industry-sensitive variable (asset turnover) is included into the model (Altman 1983).

However, this model did not cater to the needs of the emerging markets. Recognizing this need, Altman tweaked the model equation by adding a constant of 3.25 to its existing equation -- the constant term of +3.25 was added to standardize the scores with a score of zero equated to a D (default) rated bond. However, the set of cut off limits remain the same as above.

Calculation

Not all factors are used in all models, some of the parameters are zero which eliminates the influence of those factors, the following table summarises the parameters used in the model for each industry:

Input selection

Input	Description	Selection
Total Assets	Total assets refers to the total amount of assets owned by a person or entity. Assets are items of economic value, which are expended over time to yield a benefit for the owner. If the owner is a business, these assets are usually recorded in the accounting records and appear in the balance sheet of the business.
Total Liabilities	Total liabilities are the combined debts that an individual or company owes. They are generally broken down into three categories: short-term, long-term, and other liabilities. On the balance sheet, total liabilities plus equity must equal total assets
Sales	Total sales revenue, also known as gross sales, is the combined value of goods and services a business delivers to its customers during a specific reporting period.
Earnings before interests and taxes	Earnings before interest and taxes (EBIT) is a common measure of a company's operating profitability. As its name suggests, EBIT is net income excluding the effect of debt interest and taxes. Both of these costs are real cash expenses, but they're not directly generated by the company's core business operations.
Retained earnings	Retained earnings are the amount of profit a company has left over after paying all its direct costs, indirect costs, income taxes and its dividends to shareholders.
Market value of equity	Market value of equity represents how much investors think a company is worth today. Market value of equity is the same as market capitalization and both are calculated by multiplying the total shares outstanding by the current price per share.
Book value of equity	The book value of equity, or “Shareholders' Equity”, is the amount of cash remaining once a company's assets have been sold off and if existing liabilities were paid down with the sale proceeds.
Working capital	Net working capital is the difference between a business's current assets and its current liabilities. Net working capital is calculated using line items from a business's balance sheet. Generally, the larger your net working capital balance is, the more likely it is that your company can cover its current obligations.

Altman Z-Score Results

The calculated score is which results in a rating of .

References

Altman, E. I. 1968. “Financial Ratios, Discriminant Analysis And The Prediction Of Corporate Bankruptcy.” Journal of Finance 23 (4): 589–609. https://doi.org/j.1540-6261.1968.tb00843.
Altman, E. I. 1983. Corporate Financial Distress and Bankruptcy : A Complete Guide to Predicting & Avoiding Distress and Profiting from Bankruptcy. Wiley Finance. Wiley.
Altman, E. I., and E. Hotchkiss. 2006. Corporate Financial Distress and Bankruptcy: Predict and Avoid Bankruptcy, Analyze and Invest in Distressed Debt. Wiley Finance. Wiley.