Suppose a banker tells you that his bank in the year just completed had total interest expenses on all borrowings of $12 million and noninterest expenses of $5 million, while interest income from earning assets totaled $16 million and noninterest revenues totaled $2 million. Suppose further that assets amounted to $480 million, of which earning assets represented 85 percent of that total while total interest-bearing liabilities amounted to 75 percent of total assets. See if you can determine this bank's net interest and noninterest margins and its earnings base and earnings spread for the most recent year.
Question
Suppose a banker tells you that his bank in the year just completed had total interest expenses on all borrowings of 5 million, while interest income from earning assets totaled 2 million. Suppose further that assets amounted to $480 million, of which earning assets represented 85 percent of that total while total interest-bearing liabilities amounted to 75 percent of total assets. See if you can determine this bank's net interest and noninterest margins and its earnings base and earnings spread for the most recent year.
Solution
Step 1: Calculate Net Interest Margin
Net Interest Margin (NIM) is calculated as the difference between the interest income and the interest expense, divided by the average earning assets.
Interest Income = 12 million Earning Assets = 85% of Total Assets = 85% of 408 million
NIM = (Interest Income - Interest Expense) / Earning Assets NIM = (12 million) / 4 million / $408 million = 0.0098 or 0.98%
Step 2: Calculate Noninterest Margin
Noninterest Margin is calculated as the difference between noninterest revenue and noninterest expense, divided by the average total assets.
Noninterest Revenue = 5 million Total Assets = $480 million
Noninterest Margin = (Noninterest Revenue - Noninterest Expense) / Total Assets Noninterest Margin = (5 million) / 3 million / $480 million = -0.00625 or -0.625%
Step 3: Calculate Earnings Base
Earnings Base is the proportion of total assets that are earning assets.
Earnings Base = Earning Assets / Total Assets Earnings Base = 480 million = 0.85 or 85%
Step 4: Calculate Earnings Spread
Earnings Spread is the difference between the return on earning assets (interest income / earning assets) and the cost of carrying liabilities (interest expense / interest-bearing liabilities).
Interest-bearing Liabilities = 75% of Total Assets = 75% of 360 million
Earnings Spread = (Interest Income / Earning Assets) - (Interest Expense / Interest-bearing Liabilities) Earnings Spread = (408 million) - (360 million) Earnings Spread = 0.0392 - 0.0333 = 0.0059 or 0.59%
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