Lecture on Time Value of Money

Introduction

• Starts with a choice between two financial options:
  • $100 today or $100 one year from today.
• Likely preference for $100 today due to immediate availability.

Modifications to the Offer

• Option modified from $100 today to $12 one year from today:
  • Most would still choose $100 today.
• New offer: $100 today or $110 one year from today:
  • Increased future value ($110) makes the future option more attractive.

Concept of Indifference

• Finding the point of indifference between taking money today versus in the future:
  • Example: $100 today vs. $106 in the future.
• This indifference point helps determine the time value of money.
  • Time Value of Money: The rate at which one is indifferent between immediate and future money.
  • Calculated interest rate: 6%

Formula for Future Value

• Future Value (FV) Formula:
  • FV = Present Value (PV) × (1 + r)^n
  • Example: Future value of $106 = Present value of $100 × (1 + 0.06) for 1 year.

Formula for Present Value

• Present Value (PV) Formula:
  • PV = Future Value (FV) / (1 + r)^n
  • Example: PV of $106 = Future value of $106 / (1 + 0.06) for 1 year = $100 today.

Demonstration of Time Value of Money

• A new choice: $100 today or $118 in three years.
• Misconception: $18 interest over three years would equal $118.
  • Reality: Interest compounds over time, not linear.

Financial Calculator Example

• Use of financial calculators (e.g., Texas Instruments BA2 Plus) to solve for future value.
• Inputs:
  • Number of years: 3
  • Interest per year: 6%
  • Present value: $100
  • Payment (coupon on a bond): 0
• Compute future value (FV):
  • $100 at 6% interest should result in $119.10 in three years.

Conclusion

• Would prefer $100 today over $118 in three years due to compounding interest making $119.10 more valuable.
• Key takeaway: Money has a time value which is crucial in financial decision-making.