Standard mathematics formula sheet

Altman Z-scoreThe Z-score formula for predicting bankruptcywas 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.Contents1Estimation of the formula2Precedents3Accuracy and effectiveness4Original Z-score Component Definitions Variable Definition Weighting Factor5Z-score estimated for private firms6Z-score estimated for Non-Manufacturer Industrials & Emerging Market Credits7See also8References9Further readingEstimation of the formulaThe 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 sampleof firms which had survived, with matching by industry and approximate size (assets).Altman applied the statistical method of discriminant analysisto a dataset of publicly held manufacturers. The estimation was originally based on data from publicly held manufacturers, but has since been re-estimated based on other datasets for private manufacturing, non-manufacturing and service companies.The original data sample consisted of 66 firms, half of which had filed for bankruptcy under Chapter 7. All businesses in the database were manufacturers, and small firms with assets of <$1 million were eliminated.The original Z-score formula was as follows: Z = 0.012T1+ 0.014T2+ 0.033T3+ 0.006T4+ 0.999T5.
T1= Working Capital / Total Assets. Measures liquid assets in relation to the size of the company.T2= Retained Earnings / Total Assets. Measures profitability that reflects the company's age and earning power.T3= Earnings Before Interest and Taxes / Total Assets. Measures operating efficiency apart from tax and leveraging factors. It recognizes operating earnings as being important to long-term viability.T4= Market Value of Equity / Book Value of Total Liabilities. Adds market dimension that can show up security price fluctuation as a possible red flag.T5= Sales/ Total Assets. Standard measure for sales turnover (varies greatly from industry to industry).Altman found that the ratio profile for the bankrupt group fell at -0.25 avg, and for the non-bankrupt group at +4.48 avg.PrecedentsAltman's work built upon research by accounting researcher William Beaverand others. In the 1930s and on, Mervyn and others had collected matched samples and assessed that various accounting ratios appeared to be valuable in predicting bankruptcy. Altman's Z-score is a customized version of the discriminant analysis technique ofR.A. Fisher (1936).William Beaver's work, published in 1966 and 1968, was the first to apply a statistical method, t-teststo predict bankruptcy for a pair-matched sample of firms. Beaver applied this method to evaluate the importance of each of several accounting ratios based on univariate analysis, using each accounting ratio one at a time. Altman's primary improvement was to apply a statistical method, discriminant analysis, which could take into account multiple variables simultaneously.Accuracy and effectivenessIn its initial test, the Altman Z-Score was found to be 72% accurate in predicting bankruptcy two years prior to the event, with a Type II error (false positives) of 6% (Altman, 1968). In a series of subsequent tests covering three different time periods over the next 31 years (up until 1999), the model was found to be approximately 80-90% accurate in predicting bankruptcy one year prior to the event, with a Type II error (classifying the firm as bankrupt when it does not go bankrupt) of approximately 15-20% (Altman, 2000).[1]