A bank loan sale occurs when a bank originates a loan and sells it either with or without recourse to an outside buyer $($another bank, shadow bank or some other entity$).$ If the loan is sold without recourse, not only is it removed from the selling bank$$s balance sheet, but also the selling bank has no explicit liability if the loan eventually goes bad. Thus, the buyer $($and not the bank that originated the loan$)$ bears all the credit risk. If$,$ however, the loan is sold with recourse, under certain conditions, the buyer can put the loan back to the selling bank; therefore, the bank retains a contingent credit risk liability. In practice, most loan sales are without recourse because a loan sale is only technically removed from the balance sheet when the buyer has no future credit risk claim on the selling bank.

A bank has made a $3-$year $$10$ million dollar loan that pays annual interest of $8\%.$ The principal is due at the end of the third year.

A$.$ The bank is willing to sell this loan with recourse at $8\mathrm{.}5\%$ discount rate. What should it expect for selling this loan?

B$.$ It also has the option of selling this loan without recourse at a discount rate of $8\mathrm{.}75\%.$ What should it expect for selling this loan?

C$.$ If the bank expects a $(1)/(2)\%$ probability of default on this loan, is it better off selling this loan with or without recourse? It expects to receive no interest payments or principal if the loan is defaulted.

D$.$ Why do you think that the interest rate in part A is different from the interest rate in part B$?$