Question

Τhe bank has the following balance sheet

Assets	Liabilities
Available: 20	Deposits: 190
Loans: 180	Clean seat: 10

The deposit interest rate is 1%, while the loan interest rate is 3%. For ease of calculation, you assumed that the bank's operating and other expenses are 0.
a) calculate the return on assets ROA, and the return on equity ROE.
b) if the capital adequacy rule is imposed

clean seat / total assets > or equal to 0.1 (10%)
how much will be the maximum ROA and ROE if the available and the clean seat do not change?

Answer 1

Interest Income = Loans * Interest Rate = 180 * 3% = 5.40

Interest Expense = Deposits * Interest Rate = 190 * 1% = 1.9

Net Income = Interest Income -  Interest Expense = 5.40 - 1.90 = 3.50

Return on Assets (ROA) = Net Income / Total Assets = 3.50 / (Available + Loans)

= 3.50 / ( 180 + 20) = 3.50 / 200 = 1.75%

Return on Equity (ROE) =   Net Income / Equity =  Net Income / Clean seat =3.5 / 10 = 35%

Ans a : ROA of the bank = 1.75%

ROE of the bank = 35%

Now,

if the capital adequacy rule is imposed

clean seat / total assets > or equal to 0.1 (10%)

Maximum Total Assets will be = clean seat / 0.1 = 10 / 0.1 = 100

So banks balance sheet will reduce by a fctor of 02 [ Previous Total Assets / Current Total Assets ] = [ 200 /100]

New Balance Sheret :

Assets Liabilities
Available: 10 Deposits: 90
Loans: 90 Clean seat: 10

Note = Deposit = Total Liabilities - Clean seat = 100 - 10 = 90

Interest Income = Loans * Interest Rate = 90* 3% = 2.70

Interest Expense = Deposits * Interest Rate = 90 * 1% = 0.9

Net Income = Interest Income -  Interest Expense = 2.70 - 0.90 = 1.80

Return on Assets (ROA) = Net Income / Total Assets = 1.80 / (Available + Loans)

= 1.80 / ( 90+ 10) = 1.80 / 100 = 1.80%

Return on Equity (ROE) =  Net Income / Equity = 1.80 / 10 = 18%

Ans b : Maximum , ROA of the bank = 1.80%

Maximum. ROE of the bank = 18%