QUESTION 4: BANKS (30 points)

In this question, you will be asked to consider a bank that faces THREE balance sheet requirements.

1.A reserve requirement: its reserves are required to be no less than 10% of its deposits.

2.An unweighted capital requirement: its capital is required to be no less than 10% of its total assets.

3.A risk-weighted capital requirement: its capital is required to be no less than 15% of its assets other than its reserves.

The bank's balance sheet takes the following form:

ASSETS

LIABILITIES

Reserves: $10 million

Deposits: $85 million

Mortgages: $50 million

Bank Capital: $15 million

Long-term Gov't Securities: $40 million

a.Verify that the bank is satisfying all three of its requirements.Show your work.

reserve requirement: $85 million*10%=$8.5million $8.5million<$10 million(reserves) so the bank is satisfying the reserve requirement.

unweighted capital requirement:

risk-weighted capital requirement:

Now suppose that the bank receives $150 million in additional deposits, so it has a total of $235 million in deposits.

b.Suppose that the bank keeps $75 million of the new deposits as reserves and uses the remaining $75 million to buy securities.Which of the three requirements is the bank violating? Which of the three requirements is the bank not violating? Justify your answer.

c.As in part (b), suppose that the bank keeps $75 million of the new deposits as reserves and uses the remaining $75 million to buy securities.What is the smallest amount of new equity that it would have to issue in order to satisfy all three of the requirements?Show all of your work. (Hint: assume that the bank keeps all of the funds raised by the equity issue as reserves.)