# is there a mapping from Altman Z-score for private companies to bond ratings or probability of default?

On wikipedia, there is a formula to calculate the Altman Z-score for private companies:

Z-score estimated for private firms:

T1 = (Current Assets − Current Liabilities) / Total Assets
T2 = Retained Earnings / Total Assets
T3 = Earnings Before Interest and Taxes / Total Assets
T4 = Book Value of Equity / Total Liabilities
T5 = Sales/ Total Assets

Z' Score Bankruptcy Model:

Z' = 0.717T1 + 0.847T2 + 3.107T3 + 0.420T4 + 0.998T5


Zones of Discrimination:

Z' > 2.9 -“Safe” Zone
1.23 < Z' < 2. 9 -“Grey” Zone
Z' < 1.23 -“Distress” Zone

Is there a mapping from this Z', a dimensionless number, to something like, "BBB" or "12% of default in one year"?

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why not calculate the altman z-score for non-private companies with ratings and come up with your own mapping? –  phubaba Feb 11 '13 at 19:04