Z-Score Formula

Z-Score Formula

The Altman Z-Score contains five performance ratios that are clubbed into a single score.

Z-Score = 1.2A + 1.4B + 3.3C + 0.6D + 1.0E

Where,

A = Working Capital ÷ Total Assets

B = Retained Earnings ÷ Total Assets

C = Earnings before interest & taxes ÷ Total Assets

D = Market value of equity ÷ Total Liabilities

E = Sales ÷ Total Assets

When evaluating Z-score of a company, lesser the value higher will be the chances that company is going towards bankruptcy. The rules for interpreting firm’s Z-score are given below:

1.  Below 1.8 shows a firm going for bankruptcy.

2.  Above 3.0 shows a firm that is unlikely to enter bankruptcy.

3.  Between 1.8 to 3.0 is a statistical gray area.

Components of Z-Score

1.  Working Capital to Total Assets: Working Capital calculates company’s liquidity and its short term financial health. Positive working capital shows strong liquidity, ability to meet short term obligations. Negative working capital implies that current assets of the company are not sufficient to meet its current liabilities. The company could face problems while paying back its creditors and ultimately leading to bankruptcy.

2.  Retained Earnings to Total Assets: The ratio of retained earnings to total assets assist in calculating the extent to which a company relies on debt or leverage. The lesser the ratio, the more a company’s assets are funded by borrowings instead of retained earnings, which again increases the risk of bankruptcy.

3.  Earnings before interest and taxes to total assets: This evaluates the ability of a company to produce profits before reducing interest and taxes.

4.  Market Value of Equity to Total Liabilities: This ratio evaluates how much a company’s market value could decrease before liabilities exceeded assets. Market capitalization is regarded as market’s confidence in financial position of a company. Higher market capitalization implies higher chances of survival.

5.  Sales to Total Assets: It calculates the amount of sales produced by every dollar of asset invested. It shows how efficiently a firm uses its assets to generate sales. High number is better while a low number poses danger for company.

Financial Data (in 000's) / GAP / H & M / TJX
Sales / $ 15,651,000.00 / $ 120,799,000.00 / $ 25,878,372.00
Earnings Before Interest & Taxes / $ 1,950,000.00 / $ 21,754,000.00 / $ 3,112,010.00
Current Assets / $ 4,132,000.00 / $ 37,232,000.00 / $ 5,711,543.00
Total Assets / $ 7,226,000.00 / $ 58,549,000.00 / $ 9,511,855.00
Current Liabilities / $ 2,344,000.00 / $ 14,010,000.00 / $ 3,760,596.00
Total Liabilities / $ 4,332,000.00 / $ 14,714,000.00 / $ 5,845,918.00
Retained Earnings / $ 13,259,000.00 / $ 45,528,000.00 / $ 3,155,427.00
Market Value of Equity / $ 14,371,520.00 / $ 53,638,813.03 / $ 30,729,639.94
Z-Score Ratios / GAP / H & M / TJX / Z-Score Weighting
Working Capital ÷ Total Assets / 0.25 / 0.40 / 0.21 / 1.2
Retained Earnings ÷ Total Assets / 1.83 / 0.78 / 0.33 / 1.4
Earnings Before Interest & Taxes ÷ Total Assets / 0.27 / 0.37 / 0.33 / 3.3
Market Value of Equity ÷ Total Liabilities / 3.32 / 3.65 / 5.26 / 0.6
Sales ÷ Total Assets / 2.17 / 2.06 / 2.72 / 1.0
Z-Score / 7.91 / 7.04 / 7.66

The Z score for all the three companies is above 3. It is 7.91, 7.04 and 7.66 for GAP, H & M and TJX respectively. It shows that these firms are unlikely to enter bankruptcy. Thus, solvency position of all the companies is strong and reliable.

Tobin’s Q Ratio

Tobin’s Q Ratio also known by the name Q Ratio is an instrument formulated by James Tobin of Yale University, Nobel laureate in Economics. It is dependent on the assumption that combined market value of all the companies on the stock market should be equivalent to their replacement costs. The Q ratio is computed as the division between market value of company and replacement value of firm’s assets.

Q Ratio = Total Market Value (Market Capitalization) / Total Asset Value

A lower Q ratio (between 0 to 1) shows that cost of replacing the firm’s assets is larger than value of its stock. This indicates that stock is undervalued. The market value of firm should be equivalent to worth of their assets. A high Q ratio (higher than 1) indicates that stock of firm is expensive than replacement cost of its assets. This shows that stock is overvalued. This technique of stock valuation is driving factor behind investment in Tobin’s model. Q Ratio gives information on how well a company’s investments pay off.

Financial Data (in 000's) / GAP / H & M / TJX
Total Market Value / Market Capitalization / $ 14,371,520.00 / $ 53,638,813.03 / $ 30,729,639.94
Total Assets / $ 7,226,000.00 / $ 58,549,000.00 / $ 9,511,855.00
Q Ratio / 1.99 / 0.92 / 3.23

The Q ratio for GAP, H & M and TJX are 1.99, 0.92 and 3.23 respectively. The ratio for GAP and TJX is greater than 1. It implies that stock of GAP and TJX is expensive than replacement cost of its assets. The ratio for H&M is 0.92 i.e. less than 1. It indicates that cost of replacement of assets is greater than value of its stock. Thus it can be concluded that stock of H&M is undervalued and stock of GAP and TJX is overvalued.

References

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