Math Problem Statement
Solution
To calculate the Net Present Value (NPV) of the project, we need to calculate the present value of each year's cash flow, including the salvage value and recovery of working capital, and then subtract the initial investment.
Initial Cash Outlay:
- Plant and machinery: ₹2,70,000
- Working capital: ₹40,000
- Total initial investment: ₹3,10,000
Cash Flows and P.V. factor at 15%:
-
Year 1:
- Cash Flow: ₹70,000
- P.V. Factor: 0.8696
- Present Value: ₹70,000 * 0.8696 = ₹60,872
-
Year 2:
- Cash Flow: ₹1,00,000
- P.V. Factor: 0.7561
- Present Value: ₹1,00,000 * 0.7561 = ₹75,610
-
Year 3:
- Cash Flow: ₹1,30,000
- P.V. Factor: 0.6575
- Present Value: ₹1,30,000 * 0.6575 = ₹85,475
-
Year 4:
- Cash Flow: ₹90,000
- P.V. Factor: 0.5718
- Present Value: ₹90,000 * 0.5718 = ₹51,462
-
Year 5:
- Cash Flow: ₹1,55,000 (₹15,000 + ₹40,000 working capital + ₹5,000 scrap value)
- P.V. Factor: 0.4972
- Present Value: ₹1,55,000 * 0.4972 = ₹77,066
Total Present Value of Cash Flows: = ₹60,872 + ₹75,610 + ₹85,475 + ₹51,462 + ₹77,066 = ₹3,50,485
Net Present Value (NPV): = Total Present Value - Initial Investment = ₹3,50,485 - ₹3,10,000 = ₹40,485
Therefore, the NPV of the project is ₹40,485.
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Math Problem Analysis
Mathematical Concepts
Net Present Value (NPV)
Discounting Cash Flows
Present Value
Formulas
NPV = Σ (Cash Flow × PV Factor) - Initial Investment
Present Value = Cash Flow × PV Factor
Theorems
Time Value of Money
Suitable Grade Level
Undergraduate - Finance and Accounting
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