There is a large number of banks in a country. Each bank holds a portfolio of corporate loans that will pay off $100M next year as well a portfolio of mortgage loans. Half of the banks have made good mortgage loans; these good banks will receive a payoff from their mortgage loans of $80M next year. The other half have made bad mortgage loans; these bad banks will receive a payoff from their mortgage loans of $20M next year. Neither the corporate loan nor mortgage loan portfolios generate any payoff after next year. Banks have no cash and no other assets.

Each bank owes $90M of debt that it must pay off today by raising $90M of cash. It can do so in one of two ways. It can issue $90M of equity to new investors or it can sell off its corporate loan portfolio for $90M (a $10M discount to its true value of $100M). A bank cannot sell its mortgage portfolio. The bank owes no other debt. Existing shareholders receive a payoff of $0 if the bank defaults on its debt, so the bank will not default. A banks manager knows whether her bank is a good bank or a bad bank, but outside investors only know that there is an equal probability that any bank is a good bank or a bad bank. Outside investors are also aware of each banks need to pay off its loan. In making decisions, bank managers maximize value for their existing shareholders. Assume no discounting and no taxes.

1a) Describe how each type of bank will choose to pay off its debt, i.e., by issuing equity or by liquidating loans. Support your answers with calculations. (Hint: A good bank will be averse to issuing equity because of concerns about dilution, and the cost of liquidating the loan portfolio (i.e., the discount) is small, so it makes sense to believe that a good bank will prefer to liquidate its corporate loan portfolio. The bad bank does not face concerns about dilution. Given the cost of liquidating its corporate loan portfolio, it makes sense to believe that a bad bank will prefer to issue equity.)

1b) Suppose that each bank has one million shares outstanding. Given your answer to part a, compute the per share stock price of a bank under three circumstances: right before it announces how it will pay off its debt, right after announcing that it will issue equity to pay off its debt, and right after announcing that it will liquidate corporate loans to pay off its debt.