Math Problem Statement
Solution
To solve the problem in the image, let's break down the process step by step:
Problem Statement Recap:
-
Project X:
- Initial Investment: Rs. 20,000
- Estimated Life: 6 years
- Scrap Value: Rs. 1,000
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Project Y:
- Initial Investment: Rs. 30,000
- Estimated Life: 6 years
- Scrap Value: Rs. 3,000
Cash Flows:
- Project X Cash Flows (Years 1-6): Rs. 6,000, Rs. 10,000, Rs. 3,000, Rs. 5,000, Rs. 2,000, Rs. 2,000
- Project Y Cash Flows (Years 1-6): Rs. 2,000, Rs. 19,000, Rs. 6,000, Rs. 6,000, Rs. 3,000, Rs. 2,000
Discount Rate:
- 10%
Objective:
Calculate the Net Present Value (NPV) for both projects and determine which project should be selected.
Step-by-Step Calculation:
-
Compute the Present Value (PV) of cash flows for each year using the formula: where is the discount rate (10%), and is the year.
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Sum the PVs for each project.
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Subtract the initial investment from the sum of PVs to get the NPV.
Detailed Calculation:
Let's calculate the NPVs for both projects.
Project X:
- Initial Investment: Rs. 20,000
- Cash Flows for Years 1-6: Rs. 6,000, Rs. 10,000, Rs. 3,000, Rs. 5,000, Rs. 2,000, Rs. 2,000
Project Y:
- Initial Investment: Rs. 30,000
- Cash Flows for Years 1-6: Rs. 2,000, Rs. 19,000, Rs. 6,000, Rs. 6,000, Rs. 3,000, Rs. 2,000
Let me perform these calculations.### NPV Calculation Results:
- NPV of Project X: Rs. 2,323.28
- NPV of Project Y: Rs. 811.76
Conclusion:
Since the NPV of Project X is higher than that of Project Y, Project X should be selected.
Would you like any further details or explanations? Here are some related questions you might find interesting:
- How does changing the discount rate affect the NPV of these projects?
- What are some limitations of using NPV as a decision-making tool?
- How would the inclusion of taxes impact the NPV calculations?
- What if the cash flows were different every year? How would that change the analysis?
- How does the time value of money concept influence the NPV?
Tip: Always consider the sensitivity of your NPV analysis to changes in discount rates and cash flow estimates, as these can significantly alter project rankings.
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Math Problem Analysis
Mathematical Concepts
Net Present Value (NPV)
Discounted Cash Flow (DCF)
Investment Analysis
Formulas
Net Present Value (NPV) = Sum of (Cash Flow / (1 + r)^t) - Initial Investment
Present Value (PV) = Cash Flow / (1 + r)^t
Theorems
Time Value of Money
Suitable Grade Level
Undergraduate Finance/Business Studies
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