Cash Flow Patterns Lecture Notes

Overview

• Focus on understanding cash flow patterns and their applications.
• Key concepts covered:
  • Future Value (FV)
  • Present Value (PV)
  • Lump Sum
  • Annuities
  • Unequal Cash Flows
  • Perpetuities

Key Definitions

Future Value (FV)

• FV is the value of a cash flow at a future date after interest has been applied.
• FV formula for a lump sum:
  FV = Cash Flow × (1 + r)^n Where:
  • Cash Flow = Amount of money to be invested
  • r = interest rate
  • n = number of periods

Present Value (PV)

• PV is the current value of a future amount of money, discounted back at a specific interest rate.
• PV formula for a lump sum:
  PV = Cash Flow / (1 + r)^n

Types of Cash Flows

Lump Sum Cash Flow

• Payment today for a future return (single cash flow).
• Example: For 100 invested at 8% for 5 years:
  PV = 100 / (1.08)^5 FV = 100 × (1.08)^5

Annuities

• Series of equal cash flows received at regular intervals.
• Types:
  1. Ordinary Annuity: Payments made at the end of each period.
     • Example: 5 payments of 100 at the end of each year.
  2. Annuity Due: Payments made at the beginning of each period.
     • Example: 5 payments of 100 starting today.
• Annuity calculation uses the same principles as PV and FV, adjusted for the nature of the cash flow.

Unequal Cash Flows

• Cash flows that are irregular or uneven.
• Examples include:
  1. Payments that are not equal (e.g., 100, 150, 200).
  2. Cash flows that occur at irregular intervals.

Perpetuity

• A cash flow that continues indefinitely.
• Example: Receiving a constant amount every period forever.
  • Simple perpetuity formula:
    PV = Cash Flow / r

Calculator Functions

• TVM Buttons: Allow for the easy computation of PV, FV, and annuities using specific inputs.
  • Input needed:
    1. N (number of periods)
    2. I/Y (interest rate per period)
    3. PV (present value)
    4. PMT (payment)
    5. FV (future value, usually set to 0 for annuity calculations)

Cash Flow Calculation Examples

1. Calculating PV:

   • Example: To find the PV of 100 received in 5 years at 8%:
     PV = 100 / (1.08)^5
   • Use TVM functions on calculator.

2. Using Calculator:

   • Always clear previous entries using 2nd + FV, labeled as "Clear TVM".
   • Follow the order while inputting data to avoid errors.

3. Example Scenario:

   • If a bank offers $100 for 5 years in return for a $600 deposit:
     • Enter -600 for PV, 100 for PMT, and 5 for N to find I/Y (implied interest rate).

Understanding the Flow

• Knowing the structure of calculations helps with memorizing key points and applying them effectively.
• Key takeaways:
  1. PV and FV basics
  2. Different types of cash flows (lump sums, annuities, unequals)
  3. Calculation via financial calculators or Excel formulas.

Conclusion

• Mastering these concepts lays a foundation for understanding financial decisions and investments.
• Practice with various scenarios is encouraged for better comprehension and comfort with calculations.