Leverage in turns of EBITDA is not a repayment period. The years come from cash after interest, compounded as the debt falls, and they are more than twice the multiple.
Divide debt by free cash flow after interest for a first answer, then correct for the interest that falls as debt is repaid: years = ln(CADS / (CADS − r × Debt)) / ln(1 + r). On Halstead, the borrower of Credit Analysis, 120,000,000 of debt at 7.4 per cent against 18,560,000 of cash available for debt service takes 9.12 years to repay. Leverage on the lender's EBITDA is 4.22x; the gap between the two is what capital expenditure, working capital, tax and interest take out of EBITDA before any debt is repaid.
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Halstead Packaging, the borrower the book analyses from four angles. Its EBITDA, the three deductions from earnings to cash and its debt are the book's; the payback is this article's. Every figure assumes the year repeats unchanged and that all free cash flow goes to debt.
| Line | Amount |
|---|---|
| EBITDA as adjusted by the lender | 28,460,000 |
| Less maintenance capital expenditure | −6,200,000 |
| Less increase in working capital | −1,600,000 |
| Less cash tax | −2,100,000 |
| Cash available for debt service (CADS) | 18,560,000 |
| Less interest, 120,000,000 at 7.4% | −8,880,000 |
| Free cash flow available to repay debt | 9,680,000 |
The loan's scheduled amortisation of 5.0% is 6,000,000 a year, so debt service is 14,880,000 and the borrower covers it with 3,680,000 to spare. The question here is different: how long until the debt is gone if every spare unit of cash goes to it?
Debt / free cash flow = 120,000,000 / 9,680,000 = 12.40x, or a free cash flow to debt ratio of 8.07%.
12.4 years overstates the period, because it assumes interest stays at 8,880,000 for ever. Each repayment cuts next year's interest, and the saving goes to debt as well. The repayment grows every year.
With constant CADS of C and rate r, the debt follows Dt+1 = Dt(1 + r) − C. That is a loan amortised by a level payment of C, and the number of payments that clears it is the familiar annuity formula solved for n.
n = ln(C / (C − r × D)) / ln(1 + r)
= ln(18,560,000 / 9,680,000) / ln(1.074) = ln(1.9174) / ln(1.074) = 9.12 years
Excel: =NPER(7.4%,-18560000,120000000) returns the same 9.12.
| Year | Opening debt | Interest | Repaid | Closing debt |
|---|---|---|---|---|
| 1 | 120,000,000 | 8,880,000 | 9,680,000 | 110,320,000 |
| 2 | 110,320,000 | 8,163,680 | 10,396,320 | 99,923,680 |
| 3 | 99,923,680 | 7,394,352 | 11,165,648 | 88,758,032 |
| 4 | 88,758,032 | 6,568,094 | 11,991,906 | 76,766,127 |
| 5 | 76,766,127 | 5,680,693 | 12,879,307 | 63,886,820 |
| 6 | 63,886,820 | 4,727,625 | 13,832,375 | 50,054,445 |
| 7 | 50,054,445 | 3,704,029 | 14,855,971 | 35,198,474 |
| 8 | 35,198,474 | 2,604,687 | 15,955,313 | 19,243,161 |
| 9 | 19,243,161 | 1,423,994 | 17,136,006 | 2,107,155 |
| 10 | 2,107,155 | 155,929 | 2,107,155 | 0 |
At the end of year seven, the tenor of a typical leveraged loan, 35,198,474 is still outstanding, 29 per cent of the original debt. To repay in full over seven years Halstead would need CADS of 22,577,867, which is 4,017,867 or 21.6% more than it generates. The loan is a refinancing risk from the day it is signed, and a leverage of 4.22x does not show it.
As interest falls, taxable profit rises. At an illustrative 25.0% tax rate, each unit of interest saved returns only three quarters to debt. The level payment becomes CADS less tax on the starting interest, 16,340,000, and the effective rate becomes 5.55%. The payback lengthens to 9.69 years. The formula is unchanged; only its two inputs move.
| Case | CADS | Rate | Free cash flow | Debt / FCF | Payback |
|---|---|---|---|---|---|
| Base | 18,560,000 | 7.4% | 9,680,000 | 12.4 | 9.1 |
| Rates +200 bp | 18,560,000 | 9.4% | 7,280,000 | 16.5 | 10.4 |
| Rates −200 bp | 18,560,000 | 5.4% | 12,080,000 | 9.9 | 8.2 |
| CADS +10% | 20,416,000 | 7.4% | 11,536,000 | 10.4 | 8.0 |
| CADS −10% | 16,704,000 | 7.4% | 7,824,000 | 15.3 | 10.6 |
| CADS −20% | 14,848,000 | 7.4% | 5,968,000 | 20.1 | 12.8 |
Two hundred basis points of rate add 1.3 years. A 10 per cent fall in cash adds 1.5, and a 20 per cent fall adds 3.6. The payback is more sensitive to cash than to rates on this borrower, because interest is less than half of CADS; at higher leverage the order reverses, and as interest approaches CADS the payback goes to infinity.
Reading leverage as years. "4.2 turns, so the debt is repaid in about four years" is said in credit committees more often than it should be. EBITDA is before capital expenditure, working capital, tax and interest, and on Halstead those take 18,780,000 of the 28,460,000. The figure that converts into years is debt over cash after interest, compounded.
Which EBITDA starts the walk matters as much. With the same three deductions, management's 37,600,000 gives free cash flow of 18,820,000 and a payback of 5.4 years; the statutory 24,600,000 gives 5,820,000 and 13.0 years. The same company, the same debt, and a repayment period that varies by a factor of more than two depending on which number is believed. On headline leverage the same three readings are 3.19x, 4.22x and 4.88x.
The payback assumes the business stands still and that a lender can take all of the free cash flow. In practice a sweep takes a share, and distributions, acquisitions and growth capital expenditure take the rest. The figure is a ceiling on how fast the debt can go, not a forecast.
NPER in Excel.The walk from audited EBITDA to cash available for debt service, with every adjustment on a switch, is in the free workbook for this case. For the leverage side of the same borrower see net debt to EBITDA for a credit analysis.
There is no universal level, but the ratio converts directly into a repayment period. At 12.40x, as here, simple division says 12.4 years; because interest falls as debt is repaid, the true payback at 7.4 per cent is 9.12 years. A lender with a seven-year loan needs cash available for debt service of 22,577,867, 21.6 per cent more than this borrower generates, for the debt to amortise fully.
No. EBITDA is before capital expenditure, working capital, tax and interest. On this borrower 4.22x leverage on the lender's EBITDA becomes 6.47x on cash available for debt service, 12.40x on free cash flow after interest, and a 9.12-year payback once the falling interest is counted.
Yes, through free cash flow. With 200 basis points more on 120,000,000, free cash flow falls from 9,680,000 to 7,280,000 and payback lengthens from 9.1 to 10.4 years. A 10 per cent fall in cash available for debt service does more damage: 10.6 years.
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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