One borrower, one soft year, and the two multipliers between the top line and the cash that services the debt.
Operating leverage multiplies a revenue fall twice before it reaches the lender. With a degree of operating leverage of 2.2, an 8 per cent fall in revenue cuts EBITDA by 17.6 per cent; because capital expenditure, working capital and tax do not shrink with it, cash available for debt service falls 26.99 per cent, an amplification of 3.37 times. On the fictional Halstead Packaging loan that takes cover from 1.25x to 0.91x and leverage from 4.22x to 5.12x: both covenants broken by a soft year.
Worked in full in Credit Analysis by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Halstead Packaging is the borrower in Credit Analysis: a sponsor-owned maker of rigid packaging with revenue of 285.0 million and EBITDA, as adjusted by the lender, of 28.46 million. It borrows 120 million of senior net debt at 7.40 per cent, amortising 5.00 per cent a year. Two maintenance covenants apply: leverage of at most 4.25x and cover of at least 1.20x. All figures are illustrative.
| Input | Value |
|---|---|
| Revenue | 285.0 |
| EBITDA, lender's adjusted | 28.46 |
| Maintenance capital expenditure | 6.2 |
| Increase in working capital | 1.6 |
| Cash tax | 2.1 |
| Cash available for debt service | 18.56 |
| Debt service: interest 8.88 plus amortisation 6.00 | 14.88 |
| Degree of operating leverage | 2.2 |
| Revenue fall in the downside | 8% |
At closing, leverage is 120 / 28.46 = 4.22x and cover is 18.56 / 14.88 = 1.25x. Both pass.
First amplification: the fixed cost base. The degree of operating leverage is the percentage change in EBITDA for each percentage change in revenue. It comes from costs that do not move with volume: rent, salaried staff, plant overheads. At 2.2, the 8 per cent revenue fall becomes a 17.6 per cent EBITDA fall.
Downside EBITDA = 28.46 × (1 − 2.2 × 8%) = 23.45
Leverage = 120 / 23.45 = 5.12x against 4.25x
Second amplification: the deductions that do not shrink. Maintenance capex, working capital and cash tax total 9.9 million in the base case, and in the first year of a downturn they are held at that level. Cash falls by the same money as EBITDA, but from a smaller base. The second multiplier is EBITDA over cash, 28.46 / 18.56 = 1.53.
Downside cash = 23.45 − 9.9 = 13.55, a fall of 26.99% from 18.56
Cover = 13.55 / 14.88 = 0.91x against 1.20x; shortfall 1.33 million, about 110,747 a month
Amplification = 26.99% / 8% = 2.2 × 1.53 = 3.37
Excel: =(EBITDA*(1-DOL*Fall)-Capex-WC-Tax)/(Debt*(Rate+Amort))
The business has not failed. It has lost 22.8 million of revenue, which a board would call a soft year. The lender has gone from a covenant pass to a payment shortfall.
| Revenue fall | EBITDA | EBITDA fall | Cash | Cash fall | Leverage | Cover |
|---|---|---|---|---|---|---|
| 2% | 27.21 | 4.4% | 17.31 | 6.7% | 4.41x | 1.16x |
| 4% | 25.96 | 8.8% | 16.06 | 13.5% | 4.62x | 1.08x |
| 6% | 24.70 | 13.2% | 14.80 | 20.2% | 4.86x | 0.99x |
| 8% | 23.45 | 17.6% | 13.55 | 27.0% | 5.12x | 0.91x |
| 10% | 22.20 | 22.0% | 12.30 | 33.7% | 5.41x | 0.83x |
Run the thresholds backwards and the room is smaller still. Leverage breaks on a revenue fall of 0.36 per cent, 1.02 million or 1.3 days of sales. Cover breaks on a fall of 1.12 per cent, 3.20 million or 4.1 days. Cash stops covering debt service at all, cover below 1.00x, at a fall of 5.88 per cent. Every one of these is inside normal forecasting error for a packaging business.
None of them brings the amplification back to one. The second stage exists as long as some deductions do not scale with revenue, and in the first year of a downturn they rarely do.
The frequent error is to apply the revenue fall straight to EBITDA and leave the rest of the model alone. On Halstead that gives EBITDA of 26.18 million, leverage of 4.58x and cover of 1.09x. It still shows a breach, which makes it look conservative, but it understates leverage by 0.53 turns and overstates cover by 0.18. A lender negotiating a covenant reset on those numbers would set the new level too tight and be back at the table within a year.
The related error is to stop the downside at EBITDA. Leverage covenants are measured there, so the analyst who stops there sees a leverage problem. Cover is measured on cash, and cash is where the second amplification sits. The analysis of what an add-back bridge is worth in leverage turns shows how much of the starting EBITDA is itself argued rather than audited, which makes the base of this calculation softer still.
Both amplifications, the curve, the softeners and the recovery on the downside EBITDA are live formulas in the free workbook for this case. For the coverage side of a direct loan with a rate shock instead of a revenue shock, see how to calculate a fixed charge coverage ratio.
Divide the percentage change in EBITDA by the percentage change in revenue, or equivalently contribution over EBITDA. A degree of 2.2 means each 1 per cent of revenue lost removes 2.2 per cent of EBITDA because fixed costs stay. In the Halstead case an 8 per cent revenue fall takes EBITDA from 28.46 to 23.45 million, a 17.6 per cent fall.
Because maintenance capex, working capital and cash tax are deducted after EBITDA and do not shrink in the first year of a downturn. Cash loses the same money as EBITDA from a smaller base, so the fall is multiplied by EBITDA over cash, 1.53 on Halstead. The 17.6 per cent EBITDA fall becomes a 26.99 per cent fall in cash available for debt service.
It understates the damage. On Halstead, passing the 8 per cent fall straight through gives leverage of 4.58x and cover of 1.09x; carrying operating leverage through gives 5.12x and 0.91x. The shortcut understates leverage by 0.53 turns and overstates cover by 0.18, enough to set a covenant reset at the wrong level.
This article is one calculation from Credit Analysis. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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