Question
Three businesses must settle six invoices on the same day (amounts in dollars): A owes B 90 and C 30; B owes A 50 and C 80; C owes A 40 and B 20. They can use (i) gross settlement, paying every invoice separately; (ii) bilateral netting, cancelling opposite invoices between each pair; or (iii) an enforceable multilateral clearing agreement, replacing all invoices with each business's single net obligation to or from the clearing pool.
If B is solvent, everyone pays in full. If B defaults, a contractual insolvency rule applies after the chosen netting: creditors collect only 50% of each remaining positive payment owed by B. All A and C obligations are paid in full, with no secondary defaults. Payments made to B enter its insolvency estate and cannot be redirected to cure these shortfalls because senior claims have priority. Compare total promised settlement payments and aggregate creditor losses in the solvent and default states. Count cash settled once per obligation; under multilateral clearing, report money paid into the pool, not that same money again as it is distributed out. If B defaults with probability 20%, what is expected creditor loss under each arrangement?
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Hint 1
For each method, establish the legally enforceable payment obligations before applying the 50% recovery. Gross, pairwise and clearing-wide offsets are not equivalent.
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Solution
Gross invoices. The six amounts total \(90+30+50+80+40+20=310\). If B defaults, its outgoing amounts 50 to A and 80 to C suffer 50% shortfalls, so creditor loss is \(25+40=65\). The other invoices are still due and paid.
Bilateral netting. Opposite flows cancel pairwise: A owes B \(90-50=40\); B owes C \(80-20=60\); C owes A \(40-30=10\). Promised cash volume is \(40+60+10=110\). B's one remaining debt is 60 to C; at 50% recovery, C loses \(30\). A's separate 40 obligation to B still settles.
Multilateral clearing. Before default, A owes 120 and is owed 90, so pays net 30. B owes 130 and is owed 110, so pays net 20. C owes 60 and is owed 110, so receives net 50. The clearing pool receives \(30+20=50\) and pays 50; nominal cash volume counted as payer-to-pool contributions is 50, not 100 (which would double-count the pool's redistribution). If B defaults, it pays 10 instead of 20, and C receives 40 instead of 50, a creditor loss of 10.
When B is solvent, creditor losses are zero under all three methods. With default probability \(0.2\), expected loss is respectively \(0.2(65)=13\), \(0.2(30)=6\) and \(0.2(10)=2\). Netting reduces the legally exposed amount but cannot conjure the missing $10 when B's final net debt is only half recovered. The specified bankruptcy priority is essential: absent an enforceable netting and recovery order, amounts due to and from B could be treated differently.
Assumptions
All figures are nominal dollars and obligations are enforceable under the specified settlement method.
Only B may default; its 50% recovery applies to positive obligations after legal netting.
Receipts paid to B cannot be used to make up the 50% unpaid creditor claims in this stylized priority arrangement.
The multilateral cash volume counts contributions into the pool once, not both sides of clearing.
Final Answer
Solvent gross payment volumes: $310, $110, $50 (gross, bilateral, multilateral). When B defaults, creditor losses: $65, $30, $10; expected losses at 20% default: $13, $6, $2, respectively.