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Module 8.2.5: Discounted Cash Flow and Net Present Value (TVOM)

Mar 14, 2025

Net Present Value (NPV) Calculation Using Time Value of Money

Introduction

  • Concept: Discounting cash flows (both inflows and outflows) to present value.
  • Purpose: Facilitate comparability across multiple investment alternatives.

Example: Hogarth's Bottling Machine

  • Initial Investment: $23,000 today.
  • Cash Savings Over Four Years: Utilizes a required rate of return of 16%.
  • Cash Flow Assumptions: All cash flows occur at the end of the year except for the initial investment.

NPV Calculation Method

  • Generic Formula:
    • Dollar amount times the factor.
    • Factor = ( \frac{1}{(1 + \text{rate})^\text{time}} ).

Yearly Cash Flows and Present Value

  • Year 1:
    • Cash Inflow: $10,000.
    • Factor: ( \frac{1}{1 + 0.16} = 0.862 ).
    • Present Value: $10,000 ( \times ) 0.862 = $8,620.
  • Year 2:
    • Cash Inflow: $8,000.
    • Factor: ( \frac{1}{(1 + 0.16)^2} = 0.743 ).
    • Present Value: $8,000 ( \times ) 0.743 = $5,944.
  • Year 3:
    • Cash Inflow: $6,000.
    • Present Value: $6,000 ( \times ) 0.641 = $3,846.
  • Year 4:
    • Cash Inflow: $5,000.
    • Present Value: $5,000 ( \times ) 0.552 = $2,760.

Total Present Value of Inflows

  • Sum of Inflows:
    • $8,620 + $5,944 + $3,846 + $2,760 = $21,170.
  • Comparison:
    • Initial Investment: $23,000.
    • Result: Negative NPV of $1,830, suggesting the investment is not favorable.

Advantages of NPV Method

  • Time Value of Money: Important for long-term projects.
  • Focus on Cash Flows: Useful for assessing project feasibility.
  • Comparability: Allows comparisons across projects with different timings and amounts.

Disadvantages of NPV Method

  • Assumptions: Relies on timing and reinvestment assumptions.
  • Uncertainty: Discount rate can vary, affecting decision-making.

Conclusion

  • NPV is a powerful tool but has limitations.
  • Next Topic: Internal Rate of Return (IRR).