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Assets Liabilities Reserves 250 Deposits   Required __     Transaction (checking) deposits 1000   Excess __      Savings deposits 3000...

Assets Liabilities
Reserves 250 Deposits
  Required __     Transaction (checking) deposits 1000
  Excess __      Savings deposits 3000
Loans    Money Market deposits 500
    Variable rate loans 750 Time deposits (CDs)
    Short-term loans 1600     Fixed rate 500
   Long-term fixed rate loans    2000     Variable rate 100
Securities Borrowing
   Short-term securities 500     Fed funds borrowed 0
   Long-term securities 600


Refer to the bank balance sheet above. Suppose values are in millions of dollars. Suppose return on assets (ROA) is 1.2%. Suppose bank owners convince bank managers to borrow 1000 million from other banks and make more loans. Assuming no change in ROA, What is the new value for ROE? Answer as a percent and do not enter a % sign.

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Answer #1
Formula
ROA 1.20%
Assets 5700 =250+750+1600+2000+500+600
Net income 68.4 5700*1.2%
Liabilities 5100 =1000+3000+500+500+100
Equity 600 =+assets - liabilities
ROE 11.40% net income / equity
Now
new Liabilities 6100 =5100 + 1000
new Assets 6700 =5700 + 1000
New equity 600 =+assets - liabilities
ROA 1.20%
New net income 80.4 6700*1.2%
New ROE 13.40% net income / equity

So the ROE will increase by taking on more debt. It is obvious since equity remains same but return (i.e. net income) increases on account on higher assets and same ROA.

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