Question

Assume that a bank has been affected by several defaults on its mortgage loans and became insolvent. Suppose that this bank has the following balance sheet (the required reserve ratio is 8%): Assets Liabilities Checking Deposits $130 million Required Reserves $10.4 million Excess Reserves $28.6 million Loans $75.0 million Bank Capital -$16 million To avoid insolvency, regulators decide to provide the bank with $25 million in bank capital. However, the bad news about the mortgages is featured in the local newspaper, causing a bank run. As a result, $30 million in deposits is withdrawn. Show the effects of the capital injection and the bank run on the balance sheet. Was the capital injection enough to stabilize the bank? If the bank regulators decide that the bank needs a leverage ratio of 10% to prevent further runs on the bank, how much of an additional capital injection is required to reach a 10% leverage ratio?

Answer 1

1.  Injection of 25 Million of Bank capital -

Required Reserves - 10.4 million Checking Deposits - 130 million

Excess Reserves - 28.6 million Bank Capital - 9 million

Loans - 75 million

Bank Run and withdrawal of 30 million from deposits @ 8% Required Reserve Ratio

Required Reserves - 8 million Checking Deposits - 100 million

Excess Reserves - 26 million Bank Capital - 9 million

Loans - 75 million

The capital injection will stabilize the bank

2. Bank Run and withdrawal of 30 million from deposits @ 10% Required Reserve Ratio

Required Reserves - 10 million Checking Deposits - 100 million

Excess Reserves - 24 million Bank Capital - 9 million

Loans - 75 million

Current Leverage Ratio - Capital / Total Assets = 9/109 = 8.2%

Required Leverage Ratio = 10%

With Injection of 28 million Bank can achieve leverage ratio of 10 as follows -

Required Reserves - 10 million Checking Deposits - 100 million

Excess Reserves - 24 million Bank Capital - 12 million

Loans - 75 million

Leverage Ratio - 12/112 = 10.71%

Even for 10% Reserve ratio 25 million capital injection is sufficient