Lecture on Further Aspects of Discounted Cash Flow - Replacement

Overview

• The lecture discusses how often to replace assets, using cars and machines as key examples.
• The focus is on minimizing costs associated with asset replacement.

Key Concepts

Replacement Decision

• Companies need to replace assets periodically, like employee cars or machines.
• Objective: Determine the optimal replacement period to minimize costs.
• Factors to consider:
  • Running Costs: Increase with asset age due to repairs and maintenance.
  • Scrap Value: Decreases with time; older assets fetch lower resale value.
  • Purchase Cost: Frequent replacements mean more frequent spending.

Example

• A machine costs $72,000 with a maximum life of 3 years.
• Running Costs:
  • Year 1: $7,200
  • Year 2: $9,600
  • Year 3: $12,000
• Scrap Values:
  • After 1 year: $24,000
  • After 2 years: $16,600
  • After 3 years: $9,600
• The challenge is finding the cheapest replacement strategy.

Methodology

Cost Calculation

• Calculate the present value of costs for each replacement schedule (1-year, 2-year, 3-year).
• Consider only costs since revenue from the machine remains constant.
• Use discounting to present value future cash flows (15% cost of capital assumed).

Equivalent Annual Cost (EAC)

• Calculate EAC to compare different replacement strategies:
  • Formula: Present Value of First Machine / Annuity Discount Factor for the replacement period.
• This makes costs comparable over uniform time periods.

Analysis

2-Year Replacement Example

• Present value of first machine: $72,972
• Annuity discount factor for 2 years at 15%: 1.626
• EAC: $44,878 per year

3-Year Replacement Example

• Present value of first machine: $87,101
• Annuity discount factor for 3 years at 15%: 2.283
• EAC: $38,152 per year

1-Year Replacement Example

• Present value of first machine: $57,384
• Annuity discount factor for 1 year at 15%: 0.87
• EAC: $65,959 per year

Conclusion

• In this example, replacing every 3 years is the most cost-effective strategy at $38,152 per year.

Considerations and Reservations

• Assumes infinite replacements with constant cash flows.
• Doesn't account for potential improvements in technology (e.g., lower running costs, higher scrap values).
• Market changes and technological advancements can affect future costs and values.
• Real-life scenarios might consider fractional replacement periods (e.g., 2.5 years).

Final Thoughts

• The lecture highlights the importance of considering all costs when planning asset replacement.
• The final lecture in this chapter will discuss lease versus buy decisions.