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).