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First National Bank of Bannerville has posted interest revenues of $63 million and interest costs from all of its borrowings of $42 million. If this bank possesses $700 million in total earning assets, what is First National's net interest margin? Suppose the bank's interest revenues and interest costs double, while its earning assets increase by 50 percent. What will happen to its net interest margin?

Question

First National Bank of Bannerville has posted interest revenues of 63millionandinterestcostsfromallofitsborrowingsof63 million and interest costs from all of its borrowings of 42 million. If this bank possesses $700 million in total earning assets, what is First National's net interest margin? Suppose the bank's interest revenues and interest costs double, while its earning assets increase by 50 percent. What will happen to its net interest margin?

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Solution

To calculate the net interest margin (NIM) for First National Bank of Bannerville, we can use the following formula:

Net Interest Margin (NIM)=Net Interest IncomeTotal Earning Assets \text{Net Interest Margin (NIM)} = \frac{\text{Net Interest Income}}{\text{Total Earning Assets}}

First, we need to determine the net interest income:

Net Interest Income=Interest Revenues−Interest Costs \text{Net Interest Income} = \text{Interest Revenues} - \text{Interest Costs}

Given:

  • Interest Revenues = $63 million
  • Interest Costs = $42 million

So,

Net Interest Income=63−42=21 million dollars \text{Net Interest Income} = 63 - 42 = 21 \text{ million dollars}

Next, we use the total earning assets to find the NIM:

Total Earning Assets=700 million dollars \text{Total Earning Assets} = 700 \text{ million dollars}

Now, we can calculate the NIM:

NIM=21700=0.03 or 3% \text{NIM} = \frac{21}{700} = 0.03 \text{ or } 3\%

Now, let's consider the scenario where the bank's interest revenues and interest costs double, and its earning assets increase by 50 percent.

New Interest Revenues = 2 * 63million=63 million = 126 million

New Interest Costs = 2 * 42million=42 million = 84 million

New Total Earning Assets = 1.5 * 700million=700 million = 1050 million

Calculate the new net interest income:

New Net Interest Income=126−84=42 million dollars \text{New Net Interest Income} = 126 - 84 = 42 \text{ million dollars}

Now, calculate the new NIM:

New NIM=421050=0.04 or 4% \text{New NIM} = \frac{42}{1050} = 0.04 \text{ or } 4\%

So, the net interest margin will increase from 3% to 4% when the bank's interest revenues and interest costs double, and its earning assets increase by 50 percent.

This problem has been solved

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