A second lien is a levered position in the house, and its price starts with one line: net value less the first lien's payoff.
A non-performing second lien is priced on the equity behind the first lien, not on its own balance: what the house nets after selling costs, less everything the first lien will be owed, capped at the second's total debt, run through each path and weighted by its probability. On an illustrative $60,000 second behind a $285,000 first on a $360,000 house, there is $46,200 of equity for $68,000 of debt, and at a 20.0 per cent target yield the bid is $22,858, 38.1 per cent of the balance. A 10 per cent fall in the house price takes it to 21.7 per cent.
Worked in full in The Mortgage Note Investor by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Second liens sell at low prices for a reason. The first lien is paid before them in any sale, it can foreclose and wipe them out, and every dollar of change in the house's value lands on the second first. Pricing one is the same exercise as pricing a first lien, with one extra line at the top.
| Input | Value |
|---|---|
| House value | $360,000 |
| Selling costs | 8.0% |
| First lien payoff at resolution, with interest and arrears | $285,000 |
| Second lien balance / arrears / total debt | $60,000 / $8,000 / $68,000 |
| Foreclosure: months to cash, legal and holding costs | 18, $6,000 |
| Modification: rate, term, first payment | 6.0%, 240 months, month 4 |
| Probability: modification / foreclosure / wiped out by the first | 40.0% / 40.0% / 20.0% |
| Target yield | 20.0% |
Equity behind the first = value × (1 − selling costs) − first lien payoff
Bid = Σ probabilitypath × PVpath at the target yield
In Excel: =MIN(MAX(Value*(1-Sell)-First,0),Debt) for the recovery, =PV(20%/12, 240, -Payment)/(1+20%/12)^3 for the modification, whose first payment arrives in month 4, and =SUMPRODUCT(Probabilities,PVs) for the bid.
1. The equity. $360,000 × 92% = $331,200, less the first lien's $285,000, leaves $46,200. That covers 67.9 per cent of the second's $68,000. The combined loan-to-value is 98.1 per cent: the house is barely worth the two loans before any costs.
2. Foreclosure path. The second forecloses, takes the house subject to the first, sells and pays the first off. It nets $46,200 less $6,000 of costs, $40,200, in month 18. At 20.0 per cent the discount factor is 0.7427, so the path is worth $29,855.
3. Modification path. The borrower keeps the house on a new payment: $68,000 at 6.0 per cent over 240 months is $487 a month, starting in month 4. The annuity factor at 20.0 per cent is 58.86, so the path is worth $27,290 today. The borrower has a reason to keep paying only while there is equity to protect, which is why this path sits next to the foreclosure path rather than replacing it.
4. Wiped out. If the first lien forecloses and the sale does not cover it, the second is extinguished and recovers nothing. This path is worth $0.
5. The bid. 40.0% × $27,290 + 40.0% × $29,855 + 20.0% × $0 = $10,916 + $11,942 = $22,858, which is 38.1 per cent of the balance and 33.6 per cent of the total debt.
The second's foreclosure recovery is zero below a house price of $309,783, where the first lien takes everything, leaving only the modification path, and it is covered in full only above $383,696. Between those two points it behaves like a levered equity position in the house: around the base case the bid moves about 4.3 times as fast as the house price.
| House value | Change | Equity behind the first | Foreclosure PV | Bid | % of UPB |
|---|---|---|---|---|---|
| $324,000 | −10.0% | $13,080 | $5,258 | $13,019 | 21.7% |
| $342,000 | −5.0% | $29,640 | $17,556 | $17,938 | 29.9% |
| $360,000 | 0.0% | $46,200 | $29,855 | $22,858 | 38.1% |
| $378,000 | +5.0% | $62,760 | $42,153 | $27,777 | 46.3% |
| $396,000 | +10.0% | $79,320 | $46,044 | $29,334 | 48.9% |
The upside is capped: once the equity exceeds the $68,000 of debt, more value adds nothing. The downside is not. That is the shape of a second lien, and it is why the house value deserves more diligence than the borrower's payment history. The table also flatters the low-value rows, because a smaller equity cushion raises the chance of being wiped out. With the wipe-out probability at 30.0 per cent instead of 20.0, the base bid falls to $20,001, 33.3 per cent; at 10.0 per cent it rises to $25,715.
The first lien's payoff is a moving number. Every month the first goes unpaid, its arrears, default interest and fees grow, and every dollar of that comes out of the second's equity. Order the first lien's payoff figure before bidding, and project it to the month you expect to resolve.
The common mistake is to compare the second's debt with the house value, $68,000 against $360,000, an 18.9 per cent loan-to-value, and conclude the note is well secured. The second's security is what is left after the first, and here that is 67.9 per cent of its debt before costs. The second mistake is to forget the wipe-out path: a bid that assumes the second always gets to foreclose or modify overstates the value by 25.0 per cent here, $28,572 against $22,858.
The same path-weighted method is used for first liens in modify or foreclose, where the timeline is the main input; for a second, as above, it is the equity.
Start every second lien with one line: net value less the first lien's payoff. Here $46,200 against $68,000 of debt supports a bid of $22,858, 38.1 per cent of the balance, and a 10 per cent fall in the house price cuts that by 43 per cent. The free workbook for this case takes a tape with second liens in it apart loan by loan, down to the bid.
The second is extinguished and recovers only any surplus from the sale after the first lien is paid. If the house nets less than the first lien's payoff, it recovers nothing. In the illustrative case the second has value only above a house price of $309,783 and is covered in full only above $383,696.
Because they absorb every change in house value first and can be wiped out. The illustrative note with a $60,000 balance supports a bid of 38.1 per cent at a 20.0 per cent yield, falling to 21.7 per cent if the house is worth 10.0 per cent less, while a 10.0 per cent rise only lifts it to 48.9 per cent.
House value times one minus selling costs, less the first lien's full payoff at the date you expect to resolve, including arrears and default interest. In the example $360,000 times 92 per cent is $331,200, less $285,000, leaving $46,200, which covers 67.9 per cent of the second's $68,000 of debt.
This article is one calculation from The Mortgage Note 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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