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Suppose First National Bank has [tex]$280 million in assets and $[/tex]28 million in equity capital. If First National has a 4% ROA, what is its ROE? (Enter your answer rounded to two decimal places.)



Answer :

GinnyAnswer
Sure, let's solve this step-by-step together.

1. Understanding the Problem:
- Assets: $280 million
- Equity Capital: $28 million
- Return on Assets (ROA): 4%

2. Calculate the Net Income:
- ROA (Return on Assets) is given by the formula:
[tex]\[ \text{ROA} = \frac{\text{Net Income}}{\text{Total Assets}} \][/tex]
- Rearranging the formula to find Net Income:
[tex]\[ \text{Net Income} = \text{ROA} \times \text{Total Assets} \][/tex]
- Given ROA is 4%, which is 0.04 as a decimal, and Total Assets are $280 million:
[tex]\[ \text{Net Income} = 0.04 \times 280,000,000 = 11,200,000 \][/tex]
- Therefore, the Net Income is $11.2 million.

3. Calculate the Return on Equity (ROE):
- ROE (Return on Equity) is given by the formula:
[tex]\[ \text{ROE} = \frac{\text{Net Income}}{\text{Equity Capital}} \][/tex]
- We have calculated the Net Income to be [tex]$11.2 million and the Equity Capital is $[/tex]28 million:
[tex]\[ \text{ROE} = \frac{11,200,000}{28,000,000} = 0.4 \][/tex]
- ROE as a decimal is 0.4.

4. Convert ROE to a Percentage and Round:
- To convert the decimal ROE to a percentage:
[tex]\[ \text{ROE Percentage} = 0.4 \times 100 = 40.0\% \][/tex]
- The ROE is therefore 40.0%, rounded to two decimal places.

Final Answer:
- Net Income: $11.2 million
- ROE (as a decimal): 0.4
- ROE (as a percentage): 40.0%

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