A worked first-out and last-out split: the formula, the sensitivity to size and price, and the loss the extra spread pays for.
The last-out spread in a split unitranche is whatever spread is left once the first-out lender has been paid: total spread dollars less first-out spread dollars, divided by the last-out amount. On an illustrative $150M unitranche at S+600, a 60 per cent first-out at S+400 leaves the last-out at S+900. The last-out earns 300 basis points more than the whole loan, and loses 2.5 times as much per turn of enterprise value lost.
Worked in full in The Private Credit Investor by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
A direct lender arranges a $150M unitranche for a business with $30M of EBITDA, so 5.0x leverage, at the reference rate plus 600 basis points. The borrower sees one loan, one price and one set of documents. Behind it, an agreement among lenders splits the loan in two: a bank or senior fund takes the first-out piece and is paid first from any recovery; the arranger keeps the last-out. The borrower's coupon does not change. Only its allocation does.
| Input | Value |
|---|---|
| Unitranche | 150 |
| Borrower spread | 600 bp |
| EBITDA | 30 |
| Reference rate | 4.00% |
| First-out share | 60% |
| First-out spread agreed with the senior lender | 400 bp |
Work in spread dollars, because that is what the borrower actually pays and what the lenders actually divide. The borrower pays 600 basis points on $150M: $9.00M a year above the reference rate. The first-out lender takes 400 basis points on $90M: $3.60M. Everything else, $5.40M, goes to the $60M last-out.
Last-out spread = (blended spread × total loan − first-out spread × first-out amount) / last-out amount
= (600 × 150 − 400 × 90) / 60 = (9.00 − 3.60) / 60 = 900 bp
Excel: =(Spread*Loan-FO_Spread*FO_Amount)/(Loan-FO_Amount)
All-in, at a 4.00 per cent reference rate, the first-out earns 8.00 per cent, the unitranche 10.00 per cent and the last-out 13.00 per cent. In leverage terms the first-out covers the first 3.0x of EBITDA and the last-out sits from 3.0x to 5.0x. The last-out holder is, economically, a second-lien lender that shares documents and a security package with the senior.
Every basis point conceded to the first-out lender is paid by the last-out at a multiple of the first-out to last-out ratio. At a 60/40 split, each 25 basis points cut from the first-out spread adds 37.5 basis points to the last-out. Negotiating the first-out price is negotiating the last-out return.
The last-out spread is highly sensitive to both terms, and the arranger usually controls neither alone: the size of the first-out is set by what the senior lender will take at a given attachment point, and its spread by that lender's cost of capital.
| First-out share (last-out $M) | FO at 350 bp | FO at 400 bp | FO at 450 bp |
|---|---|---|---|
| 50% (75) | 850 | 800 | 750 |
| 60% (60) | 975 | 900 | 825 |
| 70% (45) | 1183 | 1067 | 950 |
A larger first-out raises the last-out spread on both counts: more of the loan is priced cheaply, and the remaining spread is concentrated in a thinner piece. At 70 per cent and S+350, the last-out earns 1183 basis points over the reference rate on the same borrower and the same documents.
A higher spread on a thinner tranche is not free income. It is the same credit risk with the first loss concentrated. Set the recovery against enterprise value on a default, ignoring costs for clarity:
| EV / EBITDA | EV | Unitranche | First-out | Last-out |
|---|---|---|---|---|
| 5.0x | 150 | 100% | 100% | 100.0% |
| 4.5x | 135 | 90% | 100% | 75.0% |
| 4.0x | 120 | 80% | 100% | 50.0% |
| 3.5x | 105 | 70% | 100% | 25.0% |
| 3.0x | 90 | 60% | 100% | 0.0% |
Each turn of enterprise value lost below 5.0x costs the unitranche 20 points and the last-out 50: a ratio of 2.5x, which is simply the total loan divided by the last-out. At 4.0x, a sale that leaves the whole loan with 80 cents leaves the last-out with 50. That loss of 50 points equals about 16.7 years of the last-out's extra 300 basis points over the unitranche, on a loan that will rarely be outstanding for more than five.
The shortcut often heard is that the last-out earns the unitranche spread plus whatever discount the first-out accepted: 600 plus 200, or S+800. It treats the split as symmetric, which it is only when the two pieces are the same size. At 60/40 the right answer is S+900, and the shortcut understates it by 100 basis points; at 70/30 the gap widens further.
The second mistake is comparing the last-out spread with the unitranche spread on a return basis without changing the loss assumption. A last-out at S+900 should be underwritten against second-lien loss rates on the attachment point from 3.0x to 5.0x, not against the default and recovery assumptions used for the unitranche as a whole. The agreement among lenders also matters: payment waterfalls, standstill periods and who controls enforcement often decide the last-out's recovery as much as enterprise value does.
The book's Aster unitranche is split the same way, and the third case in the free workbook for this case follows its last-out through two quarters of margin compression to a sale. For how the fulcrum moves through a capital structure as value falls, see does the fulcrum security move when enterprise value changes.
It is a single loan to the borrower, at one price, that the lenders split privately under an agreement among lenders. The first-out piece is repaid first from any recovery and accepts a lower spread; the last-out takes the residual. In the worked example a $150M loan at S+600 is split into $90M first-out at S+400 and $60M last-out at S+900.
Because the spread given up on the larger first-out piece is concentrated in the smaller last-out. At a 60/40 split, the 200 basis point discount on $90M becomes 300 basis points on $60M, so the last-out is at S+900, not the S+800 a symmetric shortcut gives. Each 25 basis points cut from the first-out adds 37.5 to the last-out.
Per turn of enterprise value lost below the total loan, the last-out loses the total loan divided by its own size times what the unitranche loses. At 150 over 60, that is 2.5x: at 4.0x EBITDA the unitranche recovers 80 cents and the last-out 50, and at 3.0x the last-out recovers nothing while the first-out is still whole.
This article is one calculation from The Private Credit Investor. 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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