Module 6: Time Value of Money

Learning Objectives

• Understand cash flows: annuities and perpetuities.
• Calculate loan payments and find interest rates.
• Understand nominal rate, periodic rate, effective rate, and APR.
• Three sections:
  1. Value level cash flows (annuities and perpetuities).
  2. Comparing rates.
  3. Pure discount loans and amortized loans.

Section 1: Value Level Cash Flows

Annuities

• Annuity: A finite series of equal payments at regular intervals.
  • Ordinary Annuity: Payments at the end of the period.
  • Annuity Due: Payments at the beginning of the period.
• Perpetuity: Infinite series of payments.
  • Present value calculated as cash flow divided by rate (C/R).

Calculating Present Value

• Use calculators (end mode for ordinary annuity, beginning mode for annuity due).
• Example: Borrowing for a car with payments of $632 per month at 1% for 48 months results in a present value of approximately $24,000.
• Example: Credit card debt of $1,000 with $20 monthly payments at 1.5% results in a payoff period of approximately 93 months (7.7 years).

Section 2: Comparing Rates

Perpetuities

• Perpetuity: No future value because cash flow is infinite.
• Example: Company stock dividends and calculating expected dividend for a preferred stock.

Nominal Rate vs. Periodic Rate

• Nominal Rate: Annual quoted rate.
• Periodic Rate: Rate per period (e.g., month, day).
• Example: 10% nominal rate compounded semi-annually results in a periodic rate of 5%.

Effective Annual Rate (EAR)

• EAR: Used to compare investments.
• Calculated as ((1 + \text{periodic rate})^M - 1).
• Example: Comparing banks with different compounding frequencies using EAR.

APR (Annual Percentage Rate)

• APR: Disclosed by lenders, calculated as interest rate per period times number of periods per year.
• Example: 1.2% monthly becomes 14.4% APR.

Section 3: Pure Discount Loans & Amortized Loans

• To be covered in the next video.

Conclusion

• Review of key formulas and calculator settings for practical applications.
• Understanding differences and calculations of various rates for informed financial decisions.