Answer :
To calculate the Return on Investment (ROI) based on the given cash flows for each year, let's break down the steps comprehensively:
1. List the Cash Flows per Year:
- Year 2020: [tex]\(-\$2000\)[/tex]
- Year 2021: [tex]\(+\$100\)[/tex]
- Year 2022: [tex]\(+\$300\)[/tex]
- Year 2023: [tex]\(+\$500\)[/tex]
- Year 2024: [tex]\(+\$700\)[/tex]
- Year 2025: [tex]\(+\$900\)[/tex]
2. Calculate Total Cash Flow:
- [tex]\( -2000 + 100 + 300 + 500 + 700 + 900 \)[/tex]
Adding these values together:
- [tex]\( -2000 + 100 = -1900 \)[/tex]
- [tex]\( -1900 + 300 = -1600 \)[/tex]
- [tex]\( -1600 + 500 = -1100 \)[/tex]
- [tex]\( -1100 + 700 = -400 \)[/tex]
- [tex]\( -400 + 900 = 500 \)[/tex]
Therefore, the total cash flow is [tex]\(\$500\)[/tex].
3. Determine the Initial Investment:
- The initial investment is the cash flow in the first year (2020), which is [tex]\(-\$2000\)[/tex].
4. Calculate the Return on Investment (ROI):
The formula for ROI is:
[tex]\[ ROI = \left( \frac{\text{Net Profit}}{\text{Initial Investment}} \right) \times 100 \][/tex]
Where:
- Net Profit = Total Cash Flow - Initial Investment
- Total Cash Flow = \[tex]$500 - Initial Investment = \(-\$[/tex]2000\)
Plugging in the values:
- Net Profit = [tex]\( \$500 - (-\$2000) = \$500 + \$2000 = \$2500 \)[/tex]
Therefore:
[tex]\[ ROI = \left( \frac{\$2500}{|\$2000|} \right) \times 100 = \left( \frac{\$2500}{\$2000} \right) \times 100 = 1.25 \times 100 = 125\% \][/tex]
5. Conclusion:
The Return on Investment (ROI) based on the cash flows for each year is [tex]\(125\%\)[/tex].
Therefore, none of the provided choices [tex]\(25\%, 15\%, 35\%, 45\%\)[/tex] are correct. The correct ROI is [tex]\(125\%\)[/tex].
1. List the Cash Flows per Year:
- Year 2020: [tex]\(-\$2000\)[/tex]
- Year 2021: [tex]\(+\$100\)[/tex]
- Year 2022: [tex]\(+\$300\)[/tex]
- Year 2023: [tex]\(+\$500\)[/tex]
- Year 2024: [tex]\(+\$700\)[/tex]
- Year 2025: [tex]\(+\$900\)[/tex]
2. Calculate Total Cash Flow:
- [tex]\( -2000 + 100 + 300 + 500 + 700 + 900 \)[/tex]
Adding these values together:
- [tex]\( -2000 + 100 = -1900 \)[/tex]
- [tex]\( -1900 + 300 = -1600 \)[/tex]
- [tex]\( -1600 + 500 = -1100 \)[/tex]
- [tex]\( -1100 + 700 = -400 \)[/tex]
- [tex]\( -400 + 900 = 500 \)[/tex]
Therefore, the total cash flow is [tex]\(\$500\)[/tex].
3. Determine the Initial Investment:
- The initial investment is the cash flow in the first year (2020), which is [tex]\(-\$2000\)[/tex].
4. Calculate the Return on Investment (ROI):
The formula for ROI is:
[tex]\[ ROI = \left( \frac{\text{Net Profit}}{\text{Initial Investment}} \right) \times 100 \][/tex]
Where:
- Net Profit = Total Cash Flow - Initial Investment
- Total Cash Flow = \[tex]$500 - Initial Investment = \(-\$[/tex]2000\)
Plugging in the values:
- Net Profit = [tex]\( \$500 - (-\$2000) = \$500 + \$2000 = \$2500 \)[/tex]
Therefore:
[tex]\[ ROI = \left( \frac{\$2500}{|\$2000|} \right) \times 100 = \left( \frac{\$2500}{\$2000} \right) \times 100 = 1.25 \times 100 = 125\% \][/tex]
5. Conclusion:
The Return on Investment (ROI) based on the cash flows for each year is [tex]\(125\%\)[/tex].
Therefore, none of the provided choices [tex]\(25\%, 15\%, 35\%, 45\%\)[/tex] are correct. The correct ROI is [tex]\(125\%\)[/tex].
