Lecture Notes: Time Value of Money

Introduction

• Time Value of Money (TVM): Fundamental concept in engineering economy.
  • Determines the value of money today and in the future.
  • Central to investment decisions and returns.

Importance

• Used by banks and firms for investment and return maximization.
• Encourages investing savings for expected returns.
• Investment decisions involve considering TVM.

Key Concepts

• Time Value: If you invest 100 rupees today, what will it be worth in the future?
  • Example: Invest 100 rupees, receive 110 rupees after a year (10% return).

Applications of TVM

1. Investment Option Comparison
   • Compare options using TVM concepts.
2. Best Investment Proposal Selection
   • Select proposals based on TVM.
3. Determining Interest Rate
   • Decide favorable interest rates using TVM.
4. Wages Fixation
   • Determine wages using TVM.

TVM Concepts

• Compounding: Calculating future value given present value.
  • Example: Mr. X invests 1 lakh in 2022; calculate future value after 5 years.
• Discounting: Calculating present value given future value.
  • Example: To get 10 lakh after 3 years, determine today's investment.

Compounding Process

• Example:
  • Mr. X invests 1 lakh at 11% per annum for 5 years.
  • Future Value (FV) = Present Value (PV) x Future Value Interest Factor.
  • Formula: FV = PV x (1 + interest rate)^time.
  • Calculation:
    • PV = 1 lakh
    • Interest = 11% (0.11)
    • Time = 5 years
    • FV = 1 lakh x (1.11)^5 = 1,68,600.

Discounting Process

• Example:
  • Mr. X wants 10 lakh at 8% interest after 5 years.
  • Present Value (PV) = Future Value (FV) x Present Value Interest Factor.
  • Formula: PV = FV x 1 / (1 + interest rate)^time.
  • Calculation:
    • FV = 10 lakh
    • Interest = 8% (0.08)
    • Time = 5 years
    • PV = 10 lakh x 1 / (1.08)^5 = 6,81,000.

Conclusion

• Understanding TVM enhances decision-making capabilities in investments.
• Essential skill for financial planning and investment strategy.