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Question - Owen bank pays an average interest of 7% for its deposits and the bank receives 10% on average for its loans. Current size of the deposits is $ 1 million, and size of loans is $ 0.9 million. Among the loans, 1% of them will default and end up with 0 values and have a recovery rate of 0%. However, these defaulted loans still pay the interest in full. The bank's fixed cost is 0.5 % of its deposits.
1. Calculate the current profit of the bank.
2. One manager of the bank presents an idea to expand the bank's business. The plan will increase the size of deposits and loans to $ 2 million and $ 1.8 million, respectively. The aggressive marketing attracts "bad borrowers" and default rate becomes 1.5%. The bank's fixed cost is 0.5 % of its deposits.
Different from before, the new plan will recover 50% of the value for a defaulted loan (i.e., the recovery rate=50%). The defaulted loans that cannot be recovered have a value of 0. However, all defaulted loans (no matter whether they can be recovered or not) can still pay the interest in full.
Calculate the new profit of the bank under the new business plan.
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