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Macquarie University - AFIN 328 Suppose that a bank has $10 billion of one-year loans and $30 billion of five-year loans
Macquarie University - AFIN 328
Suppose that a bank has $10 billion of one-year loans and $30 billion of five-year loans. These are financed by $35 billion of one-year deposits and $5 billion of five-year deposits. The bank has equity totaling $2 billion and its return on equity is currently 12%. Estimate what change in interest rates next year would lead to the bank's return on equity being reduced to zero. Assume that the bank is subject to a tax rate of 30%.
Expert Solution
Answer:
tax rate = 30%
The bank has equity totaling $2 billion and its return on equity is currently 12%.
The bank's current ROE after tax = 12% of $2 billion = 0.24 billion
The bank currently has $10 billion of one-year loans and $35 billion of one-year deposits and $30 billion of five-year loans and $5 billion of five-year deposits.
since after one year $10 billion of one-year loans would get repaid whilst $35 billion of one-year deposits will be withdrawn, the bank has an asset liability mismatch of $25 billion.
X% change in the interest rate would lead to after tax losses of $25 billion * X% * (100-30)% = 25*0.01X*0.7 = 0.175X
Return on equity(ROE) would become 0 when 0.175X = 0.24
X = 1.37%
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