Question

Let’s consider two banks with identical balance sheets

                            Bank A

Assets                      Liabilities (unit in million)        

Reserves    $10       Checkable deposits $100

Securities    30           

Loans          80         Bank capital                20

                            Bank B

Assets                      Liabilities (unit in million)        

Reserves    $10       Checkable deposits $85

Securities    30           

Loans          80         Bank capital                35

a) Assume ROA= 1%, the same for both banks. Calculate Equity ratio (ER) for Bank A and B, respectively. How about the return on equity (ROE) for Bank A and B, respectively? (ROE=ROA/ER)

b) Suppose disaster strikes both banks: borrower default on $30 of the loans. When banks write off the bad loans, the balance sheets of the two banks should look like (fill in numbers in the blank)

                            Bank A

Assets                      Liabilities (unit in million)        

Reserves    $10       Checkable deposits $100

Securities    30           

Loans          ____     Bank capital               _____

                            Bank B

Assets                      Liabilities (unit in million)        

Reserves    $10       Checkable deposits $85

Securities    30           

Loans          ____         Bank capital            _______

What is insolvency? Which bank will face with the insolvency cause by loan defaults? Check your answer on part a), it is the bank with higher equity ratio (ER) or one with lower ER?

c. Which kind of trade-off a banker have to face when managing capital?

In a period of economic recession, if you were bank managers, what is your choice (high ER or high ROE) and why?

Answer 1

a)

Equity Ratio = Debt/ Equity

Bank A: ER = 100/20 = 5

Bank B: ER = 85/35 = 2.43

ROE = ROA/ER

Bank A: ROE = 1%/5 = 0.2%

Bank B: ROE = 1%/2.43 = 0.41%

b) Revised balance sheet after write-off loan $30 for both bank's

Bank A

Assets                      Liabilities (unit in million)        

Reserves    $10       Checkable deposits $100

Securities    30

Loans          _$50_   Bank capital $ 20

Allowance for $ 30

doubtful debt

                            Bank B

Assets                      Liabilities (unit in million)        

Reserves    $10       Checkable deposits $85

Securities    30

Loans $ 50__         Bank capital $ 35_

Allowance for $ 30

doubtful debt

Insolvency is a state of financial distress in which an entity is unable to pay their debts or obligations.

The bank A will form face insolvency because the Allowance for bad debt is greater than Bank Capital.

Also for bank A, Equity Ratio is quite high, showing it as more leveraged than bank B.

C. A trade that would be faced to include more debt compenent or equity component.

As a banker, my choice would be high ROE and never ER. High ROE signifies that the return or profitability is higher for the organisation. However high ER ration would show high debt which is not good as it increases the interest and hence obligation.