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How do you calculate the Altman Z-score, and which version applies?

The three versions of the Altman Z-score worked on one private borrower, with the cut-offs that go with each and the ratio that quietly carries the score.

Julian R. Sterling · from Credit Analysis

The Altman Z-score is a weighted sum of five ratios: working capital, retained earnings, EBIT, equity and sales, each over total assets or liabilities. There are three versions with different weights and cut-offs, and choosing the wrong one moves a borrower between zones. On one illustrative private manufacturer the scores are 2.18 on the original Z, 1.67 on the private-company Z' and 2.44 on Z'': grey on all three, but Z' read against the original 1.81 cut-off would call it distressed.

Worked in full in Credit Analysis by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →

The borrower

A privately owned packaging manufacturer, last audited year, figures in millions. All figures are illustrative. A market value of equity is shown only so the original model can be run; a private company does not have one, which is the point of the second version.

Balance sheet and income inputs, millions

Input	Value
Total assets	250.0
Current assets	95.0
Current liabilities	60.0
Working capital	35.0
Retained earnings	40.0
EBIT	22.0
EBITDA (not used by the model)	34.0
Revenue	250.0
Book equity	70.0
Total liabilities	180.0
Market value of equity, if it were listed	150.0

Step 1: the five ratios

The ratios are the same in every version, except that X4 changes from market to book equity. What changes between versions is the weights, and with them the cut-offs.

Step 2: three versions, three scores

Weighted terms and totals

Term	Z	Z'	Z''
X1, working capital	0.1680	0.1004	0.9184
X2, retained earnings	0.2240	0.1355	0.5216
X3, EBIT	0.2904	0.2734	0.5914
X4, equity	0.5000	0.1633	0.4083
X5, asset turnover	1.0000	0.9980
Score	2.18	1.67	2.44
Distress below	1.81	1.23	1.10
Safe above	2.99	2.90	2.60

The result

All three scores sit in their grey zones. For a private manufacturer the right test is Z', and at 1.67 the borrower is 0.44 above the distress line of 1.23. The original Z needs a market value of equity, and the 150.0 used here is hypothetical. Z'' was built for non-manufacturers and emerging market issuers, and drops asset turnover because it varies too much between industries. Some practitioners add a constant of 3.25 to Z'' for emerging market issuers, which takes it to 5.69 and changes the scale again: one more reason never to quote a Z-score without saying which one.

Look at where the score comes from. Asset turnover carries 0.9980 of the 1.67, or 60 per cent of Z'. EBIT, the ratio a credit analyst would expect to matter most, contributes 0.2734. Set EBIT to zero and Z' falls only to 1.40, still grey. A company that earns nothing and turns its assets once a year is not, on this model, in distress. That is a property of the weights, and it is why the Z-score is a screen rather than a credit decision.

What if the borrower weakens?

Sensitivity of Z' and Z''

Case	Z'	Change	Z''
Base	1.67	0.00	2.44
EBIT down 30% to 15.4	1.59	−0.08	2.26
Revenue down 10% to 225.0, EBIT down 30%	1.49	−0.18	2.26
Dividend recap: 30.0 of new debt paid out	1.49	−0.18	1.84
Working capital drawn to 15.0	1.61	−0.06	1.91
EBIT zero	1.40	−0.27	1.85

A 30 per cent fall in EBIT moves Z' by less than a tenth. A dividend recapitalisation, which leaves the operating business untouched, moves it more than twice as far, because it hits retained earnings and book equity at once and adds to liabilities. Holding everything else, revenue would have to fall 44.2 per cent, to 139.6, before Z' reached 1.23. Z'', without the turnover term, is far more sensitive to earnings and leverage: the same recap takes it from 2.44 to 1.84.

The common mistakes

• Book equity in the original formula. Replacing market value with book value in Z gives 1.92 here. It is not Z and it is not Z': the 0.6 weight was estimated on market values, so the number has no valid cut-offs.
• The wrong cut-offs. Z' of 1.67 read against the original 1.81 line reads as distress. Against its own 1.23 line it is 0.44 clear.
• EBITDA for EBIT. Using 34.0 instead of 22.0 lifts X3 to 0.1360 and Z' to 1.82. The model never saw EBITDA, and the uplift is the depreciation line, nothing else. The temptation is the same one that runs through every adjusted earnings figure in a credit paper.

The Z-score was estimated on historical samples of failed and surviving companies. It is a quick screen of a balance sheet, not a probability of default, and it knows nothing about the maturity of the debt, the covenants or the cash. A borrower is repaid from cash, which no ratio of this model measures.

Takeaway

• Compute the five ratios once; apply the weights and cut-offs of the version that fits the borrower.
• For a private manufacturer use Z': 1.67 here, grey, with the distress line at 1.23.
• Check what drives the score: asset turnover is 60 per cent of this one, and EBIT at zero still leaves it grey.
• Pair it with leverage and cover on a defined EBITDA, as in net debt to EBITDA for a credit analysis.

The book's own borrower is analysed on four EBITDAs, from the statutory figure to cash, in the free workbook for this case.

Questions readers ask

What is a good Altman Z-score?

On the original model, above 2.99 is the safe zone and below 1.81 the distress zone. The private-company Z' uses 2.90 and 1.23, and the four-ratio Z'' uses 2.60 and 1.10. A score is only good or bad against the cut-offs of its own version: the illustrative borrower here scores 1.67 on Z', comfortably grey, which on the original scale would read as distress.

Can you use the Altman Z-score for a private company?

Yes, but use Z', which replaces the market value of equity with book equity and re-estimates every weight: 0.717, 0.847, 3.107, 0.420 and 0.998. Putting book equity into the original formula instead gives 1.92 on the borrower here, a number that belongs to no model and has no cut-offs.

Why does the Z-score use EBIT and not EBITDA?

Because the model was estimated on EBIT over total assets, and its weight of 3.107 in Z' is calibrated to that ratio. Substituting EBITDA of 34.0 for EBIT of 22.0 lifts Z' from 1.67 to 1.82 for the same company, an improvement that comes entirely from the depreciation line.

Also on this site

• How do you calculate net debt to EBITDA for a credit analysis?Debt less usable cash over EBITDA on the same basis: one borrower reads 3.69x on a covenant definition and 4.50x once leases, pension and trapped cash are counted.
• How do you calculate the interest coverage ratio: EBIT or EBITDA?Earnings over interest, but which: one borrower reads 2.06x on EBIT, 2.94x on EBITDA and 3.65x on its covenant, and breaks 3.00x after 161 bp of rates.
• What probability of default does a loan margin break even at?Margin over loss given default: 400 bp against an LGD of 26.52 per cent breaks even at a 15.08 per cent PD, and at 8.91 per cent if the exit multiple is 3.0x.
• How many years does it take to repay debt from free cash flow?Solve for the year the debt hits zero as interest falls: 120,000,000 at 4.22x leverage takes 9.12 years from 9,680,000 of free cash flow, not four.
• How does operating leverage amplify a lender's downside case?Twice: an 8 per cent revenue fall at 2.2x operating leverage cuts EBITDA 17.6 per cent and cash for debt service 26.99 per cent, taking cover from 1.25x to 0.91x.
• How do you calculate a company's debt capacity from EBITDA?Take the lower of the leverage limit and the cover limit, both on the lender's EBITDA: 120,955,000 here, 955,000 above the debt the borrower already has.

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