Question

A commercial bank has $800 of deposits as the only liabilities (excluding capital). Its desired reserve ratio is 20% and it does not want to hold any excess reserves. The financial regulatory authority requires it to have a minimum capital of 20% of assets. The commercial bank holds 30% of its assets as government securities. Assets that are not held as reserves or securities are lent out.

a) Assume the bank does not hold any capital in excess of the minimum required by the regulator. Calculate the amount of assets. And write down the balance sheet of the commercial bank.
b) Suppose there is a deposit withdrawal of $100. Assuming the bank cannot further change any of its liabilities (including capital), and it still holds 30% of its assets as government securities, write down the new balance sheet after the desired reserve ratio is satisfied again.

c) Given the situation in b), how much of bad loan loss would cause bankruptcy?

Answer 1

a)                                             Initial Balance Sheet

Assets	Amount ($)	Liabilities	Amount ($)
Required Reserves	160	Deposits	800
G-Secs	240
Minimum Capital Requirement	160
Loans	240
Total	800	Total	800

b)                                             Final Balance Sheet

Assets	Amount ($)	Liabilities	Amount ($)
Required Reserves	140	Deposits	700
G-Secs	210
Minimum Capital Requirement	140
Loans	210
Total	700	Total	700

c) Thus, a bad loan loss of $210 will result in bankruptcy.