Bank issues two loans. Each loan yields a return R with probability p and $0$ otherwise. Probabilities of success of individual loans are independently and identically distributed $($i$.$i$.$d$.).$ The bank finances the loan with equity $($k$)$ and debt $($d$).$ Debt has a net cost of $0($bank debtors breakeven in expectation$).$ Equity is costly$,$ where $1$ unit of bank equity costs c $>1.$ Suppose the bank keeps the loans on its balance sheet. Expected return from each loan is pR$.$ For each loan, bank needs to hold equity k and d$=1-$k$,$ where the cost of equity is ck$.$ Hence, the expected profit for the bank from holding the loans on its balance sheet is given as: E$($Profit$)=2$pR $2(1-$k$)2$ck $=2$pR $22$k$($c$-1).$ For the rest, suppose that R $=4,$ p $=0\mathrm{.}5,$ k $=0\mathrm{.}5$ and c $=2\mathrm{.}5.$ a$)$ What is the expected profit of the bank in this case from holding the loans on its balance sheet? b$)$ Suppose the bank wants to avoid capital costs and securitizes the two loans. Bank sells the loans individually to risk$-$averse investors with utility functions u$($x$)=$ x $1/2.$ What is the revenue that the bank would get if it sold $2$ loans to two risk$-$averse investors?