A bank is near insolvency $$ its assets are worth $1,000$million, only a fraction more

than its debt liabilities of $999\mathrm{.}5$ million. As a result, the true value of its equity is

small. The bank is able to take $100$ million more deposits from the public in return

for a promise to pay $6\%$ return. The bank considers two possible uses to which the

new deposits can be put. The safe option is to lend at a rate of $8\%.$ There is a $95\%$

chance that such a loan will be repaid in full. There is a $5\%$ chance that for each

dollar loaned the bank will simply get its money back $($no interest$).$ The alternative

loan is very risky. There is a $60\%$ chance that the bank can make the risky loan at

an interest rate of $40\%$ and be paid back in full $($receiving $1\mathrm{.}40$ for each $1).$

There is a $40\%$ chance that it will be repaid nothing.

Which loan has the higher expected return?

Which loan would the shareholders, who have limited liability prefer the bank to

make?