Question

A bank starts its first day of operations with $9 million in capital. A total of $130 million in checkable deposits is received. The bank makes a $25 million commercial loan and another $50 million in mortgages with the following terms: 200 standard, 30-year, fixed-rate mortgages with a nominal annual rate of 5.25%, each for $250,000. Assume that required reserves are 8%. a. Show the bank balance sheet. b. How well capitalized is the bank? c. Calculate the risk-weighted assets and risk-weighted leverage ratio (known as the capital adequacy ratio) after the bank's first day.

Answer 1

a) Bank Balance Sheet

Assets		Liabilities
Required Reserves	$ 10.40 million	Checkable Deposits	$130.00 million
Excess Reserves	$ 53.60 million	Bank Capital	$   9.00 million
Loans	$ 75.00 million
	$139.00 million		$139.00 million

Checkable Deposits = $ 130 million (given)

Bank Capital = $ 9 million (given)

Required Reserve =Checkable deposits * Required reserve ratio = $ 130 million * 8% = $ 10.40 million

Loans = Commercial loans + Mortgages = $ 25 million + $ 50 million = $ 75 million

Excess Reserve = Checkable deposits + Bank capital - Required reserves - Loans

Excess Reserve= $ 130 million + $ 9 million -10.4 million - 75 million = $ 53.6 million

b)How well capitalized is the bank

It is calculated as

Bank Capital / Total Assets = $9 million /139 million = 0.0647 or 6.47%

The bank is well capitalized at 6.47%

c) Calculation of Risk Weighted Assets

Reserves have no weight i.e 0 weight . So $ 64 million has no weight.

Commercial Loans have 100% weight . So Risk Weighted Asset = $ 25 million

and Mortgages have 50% weight . So Risk weighted Asset = $50 million * 50% = $ 25 million

So, Total Risk Weighted Assets are = $ 25 million + $ 25 million = $ 50 million.

Calculation of Risk Weighted Leverage Ratio or Capital Adequacy Ratio

It is calculated by dividing bank capital funds and the risk weighted assets. This ratio indicate the risk of becoming insolvent and abilities of the bank to discharge its liabilities. If the Bank have good CAR there will be chances of insolvency.

Capital Adequacy Ratio = Bank Capital / Risk Weighted Assets

= $ 9 million / $ 50 million = 0.18 or 18%