Question

Consider a bank that has the following assets and liabilities:

Loans of $100 million with a realized rate of 5%

Security holdings of $50 million earning 10% interest income

Reserves of $10 million

Savings accounts of $100 million interest of 2.5%

Checking deposits of $30 million which pay no interest

Set up the balance sheet for this bank. (Hint: Remember that assets + liabilities = equity or net worth!)

Determine the profits for this bank. (Hint: The bank earns income, or revenues, not only from its loans but also from any securities it holds!)

Determine ROA for this bank.

Determine ROE for this bank.

Suppose that this bank calls in $10 million of its good loans and writes off another $10 million of loans that turn out to be in default. What happens to this bank’s ROA and ROE? (Hint: Examine very carefully the Notes on Bank Management which you received this past April 16 in your student webmail via Canvas!)

Do you see any problems for this bank as a result of the actions in part E above? Explain carefully and fully! (Hint: Same as for part E above!)

G. Carefully explain what the impact would be on a bank’s ROA and ROE from increased use by a bank of off-balance sheet (OBS) activities.

Answer 1

Balance Sheet

Asset

Loan : 100

Security holding : 50

Reserves : 10

Total Asset: 160

Liabilities

Savings account : 100

Checking account : 30

Equity : 30

Total Liabilities and Equity: 160

Revenue : 100*5% + 50*10% = 10

Expenses : 100*2.5% = 2.5

Profit : 7.5

ROA = PROFIT/ASSETS = 7.5/160 = 4.69%

ROE = PROFIT/EQUITY = 7.5/30 = 25%

If good loan comes in at the start of the period, and 10 millions also, defaults at the start, then balance sheet will look like below, and therefore profits will also change.

Balance Sheet

Asset

Loan : 80

Security holding : 50

Reserves : 10

Cash : 10

Total Asset: 150

Liabilities

Savings account : 100

Checking account : 30

Equity : 20

Total Liabilities and Equity: 150

Revenue : 80*5% + 50*10% = 9

Expenses : 100*2.5%+10 = 12.5

Profit : -3.5

ROA = PROFIT/ASSETS = -3.5/150 = -2.33%

ROE = PROFIT/EQUITY = -3.5/20 = -17.5%

ROA and ROE got negative, because of NPA (write off of the loan considered as expense in income statement)