A term loan and a part-drawn revolver: exposure with a conversion factor, a recovery built from the default case, and the shortcut that compounds two errors.
Expected loss is the probability of default times the loss given default times the exposure at default: EL = PD × LGD × EAD. On an illustrative borrower with a €100.0m term loan and a €30.0m revolver of which €10.0m is drawn, a 2.5 per cent PD, an LGD of 52.2 per cent and an EAD of €125.0m give an expected loss of €1.63m a year, 1.48 per cent of the drawn balance. Taking EAD as the drawn balance and LGD undiscounted would report €1.02m, 37.1 per cent too little.
Worked in full in Credit Analysis by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
A sponsor-backed borrower with a senior term loan and a committed revolving credit facility, both secured and ranking equally. The default scenario is the one a lender should model: EBITDA already down to the level at which the company fails, not the level it was lent against. All figures are illustrative, in € millions.
| Input | Value |
|---|---|
| Term loan, drawn | 100.0 |
| Revolver: limit / drawn | 30.0 / 10.0 |
| Credit conversion factor on the undrawn revolver | 75% |
| One-year probability of default | 2.5% |
| EBITDA in default | 15.0 |
| Enterprise value multiple in default | 5.0x |
| Enforcement and advisory costs | 8% of value |
| Time from default to recovery | 1.5 years |
| Discount rate over the workout | 10% |
Borrowers draw their revolvers on the way into default, because the revolver is the cheapest liquidity they have left. EAD therefore adds a share of the undrawn commitment, the credit conversion factor, to what is drawn today.
EAD = drawn + CCF × undrawn = (100.0 + 10.0) + 75% × 20.0 = 110.0 + 15.0 = 125.0
LGD is one minus the recovery rate, and the recovery has to be built from the default scenario, net of costs and discounted for the time a workout takes.
Enterprise value in default = 15.0 × 5.0 = 75.0; net of 8% costs = 69.0
Present value = 69.0 / 1.101.5 = 69.0 × 0.8668 = 59.81
Recovery = 59.81 / 125.0 = 47.8%; LGD = 52.2%
Excel: =1-MIN(1,EBITDA_D*Multiple*(1-Costs)/(1+Disc)^Years/EAD)
Undiscounted, the same recovery would read 55.2 per cent and the LGD 44.8 per cent. The 7.4 point difference is the cost of waiting eighteen months for the money, which a lender's funding does not do for free.
EL = PD × LGD × EAD = 2.5% × 52.2% × 125.0 = 1.63
As a share of EAD: 1.30%; of the drawn balance: 1.48%, or 148 basis points
Against a 4.00 per cent margin, the expected loss absorbs 37.0 per cent of the spread, before the cost of capital that unexpected loss requires. Where the margin stops covering the loss altogether is worked in what probability of default a loan margin breaks even at.
The quick version uses the drawn balance as the exposure and the undiscounted recovery on that smaller balance. Both choices lower the loss, and the second is made worse by the first: dividing the same 69.0 of value by 110.0 instead of 125.0 lifts the recovery rate.
| Method | EAD | LGD | Expected loss |
|---|---|---|---|
| Drawn balance, undiscounted recovery | 110.0 | 37.3% | 1.02 |
| Full EAD, undiscounted recovery | 125.0 | 44.8% | 1.40 |
| Full EAD, discounted recovery | 125.0 | 52.2% | 1.63 |
The shortcut understates expected loss by 0.60, or 37.1 per cent. On a portfolio priced from that number, the pricing is light by the same proportion in every name with an undrawn revolver.
PD gets most of the attention in a credit paper, but for a secured lender LGD and EAD often move expected loss as much. Hold PD at 2.5 per cent and vary the two:
| Exit multiple in default | CCF 50% | CCF 75% | CCF 100% |
|---|---|---|---|
| 4.0x | 1.80 | 1.93 | 2.05 |
| 5.0x | 1.50 | 1.63 | 1.75 |
| 6.0x | 1.21 | 1.33 | 1.46 |
One turn of exit multiple moves expected loss by about 0.30, more than the full range of drawdown assumptions. For comparison, doubling PD from 2.5 to 5.0 per cent doubles expected loss to 3.26, and cutting it to 1.0 per cent gives 0.65: PD scales the loss linearly, while the multiple works through the recovery, and stops mattering only once the discounted recovery covers the whole exposure. A lender that argues for weeks about the default probability and accepts the sponsor's exit multiple has spent its time on the wrong input.
The default EBITDA matters as much as the multiple. A recovery computed on the EBITDA the loan was sized against, rather than the EBITDA at which the borrower actually defaults, overstates recovery systematically, because nobody defaults at their underwriting EBITDA.
Recovery computed on the downside EBITDA rather than the sized one, with the exit multiple solved for, is built in the free workbook for this case. A liquidation-based recovery, the other route to LGD, is worked in how to calculate recoveries in a liquidation analysis.
It is the share of an undrawn commitment assumed to be drawn by the time the borrower defaults. Distressed borrowers draw revolvers to fund losses, so EAD is the drawn balance plus the CCF times the undrawn amount. With 110.0 drawn and 20.0 undrawn at an illustrative 75 per cent, EAD is 125.0.
Yes, for an economic view. Recoveries arrive after a workout, often a year or more after default. In the example 69.0 of net value received 1.5 years later at 10 per cent is worth 59.81 at default, so LGD is 52.2 per cent rather than the 44.8 per cent an undiscounted calculation gives.
Expected loss is linear in each, but for a secured loan the recovery inputs are often less certain. In the worked case moving the default multiple from 5.0x to 4.0x raises expected loss from 1.63 to 1.93, while the whole range of drawdown assumptions from 50 to 100 per cent moves it only from 1.50 to 1.75.
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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