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%
