Is the debt worthless?

A number of readers have sent me notes saying that a debt for equity swap would help re-capitalize insolvent (and illiquid) financial institutions, contra my assertions here and here. I've outlined my thinking below -- let me know what I'm missing.

Here's an example (riffing on a simple model by Hussman)

Take a simple balance sheet for a hypothetical bank called, say, GS. It's 20x levered, and suffered losses of 5x equity.

--ASSETS

Good assets: $75

Assets gone bad: $25 (but not yet written off)

TOTAL ASSETS: $100

--LIABILITIES & EQUITY

Liabilities to customers/counterparties: $80

Debt to bondholders of company: $15

Shareholder equity: $5

TOTAL LIABILITIES AND EQUITY: $100

So, they are leveraged 20x (floating $100 of assets on $5 of equity), and they have losses 5x equity ($25 of assets that are actually worth zero, but have not yet been marked to zero).

Say they do that writedown, and bad assets are now zero. Their balance sheet shrinks to $75. The liabilities side shrinks by equity going from $5 to -$20. This bank is insolvent. Here's the new balance sheet.

--ASSETS

Good assets: $75

Assets gone bad: $0 (written off)

TOTAL ASSETS: $75

--LIABILITIES & EQUITY

Liabilities to customers/counterparties: $80

Debt to bondholders of company: $15

Shareholder equity: -$20

TOTAL LIABILITIES AND EQUITY: $75

The Paulson plan takes those $25 of bad assets, and substitutes them for $25 of good assets (or maybe $20 of good assets). The point is, for the bank to re-capitalize, he *HAS* to pay more than the assets are worth. By swapping good for bad, the balance sheet does not have to contract, and part of the Paulson/Bernanke plan is to combat deflation, and keep balance sheets from shrinking so lenders can keep borrowing.

Zingales, to my understanding, says that instead of public gifts of cash, bondholders should have their debt converted to equity. If shareholder equity was say, -$10 (GS did not lose that much money) then this would work, and such a debt to equity conversion would reduce debt to $5, bring equity to $0, and debtholders would take an immediate 67% haircut and now have participation in any upside. I can see how this works if debt was larger than negative equity, but I don't think that's the case as firms were so leveraged, and floated on equity cushions that were so tiny. At any rate, I can see how that *might* be the case, which, to my understanding, would render the Zingales option as not feasible.

I also cannot see GS reducing liabilities by going after that "counterparty" line item, as that would trigger exactly the kind of contagion that Paulson & Co. wants to avoid.

Finally, to keenly illustrate how bank runs work, look at the Good Assets line item at $75. In maturity transformation stops working, the value of these fall to pennies on the dollar -- remember, maturity transformed long term debt has two stable prices. Pure liquidity interventions work by bringing this back up to the "maturity transformation working" price, rendering the firm solvent.

Please let me know if I'm getting something wrong.