Math Problem Statement

Calculate the Net Present Value (NPV) of the project using the provided cash flows, PV factors, and initial cash outlay.

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%:

  1. Year 1:

    • Cash Flow: ₹70,000
    • P.V. Factor: 0.8696
    • Present Value: ₹70,000 * 0.8696 = ₹60,872
  2. Year 2:

    • Cash Flow: ₹1,00,000
    • P.V. Factor: 0.7561
    • Present Value: ₹1,00,000 * 0.7561 = ₹75,610
  3. Year 3:

    • Cash Flow: ₹1,30,000
    • P.V. Factor: 0.6575
    • Present Value: ₹1,30,000 * 0.6575 = ₹85,475
  4. Year 4:

    • Cash Flow: ₹90,000
    • P.V. Factor: 0.5718
    • Present Value: ₹90,000 * 0.5718 = ₹51,462
  5. 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