Unit 6

Lesson 1: Restating Cash Flows to Make Effective Economic Decisions

• Two major techniques for restating cash flows:

  • Compounding:

  • A method where cash flows can be restated to the future.

  • Discounting:

  • A method where cash flows can be restated to the present.

• Time Periods Influence on Future Values:

  • Longer Time Periods:

  • Result in larger future values due to the effect of compound interest over time.

  • Shorter Time Periods:

  • Lead to smaller future values as fewer interest payments are accumulated.

• Interest Rates Influence on Future Values:

  • Higher Interest Rates:

  • Produce larger future values because the interest earned each period compounds, increasing wealth rapidly.

  • Lower Interest Rates:

  • Result in smaller future values due to a lower accumulation of interest.

• Present Values Influence:

  • Present values are affected in an opposite manner to future values by changes in time periods and interest rates.

  • It is crucial to understand these relationships through practical application rather than mere memorization.

Lesson 1: Calculating Single Cash Flows in Multiple Time Periods

• Simple Interest:

  • Defined as interest earned solely on the original principal.

  • Each period, the interest is calculated, but the principal amount remains unchanged.

• Compound Interest:

  • Defined as interest earned that is applied to the principal in each period.

  • Over time, as the principal amount grows, the amount of interest paid each period also increases.

Lesson 2: Evaluating Complex Cash Flows Across Time

• Multiple Time Periods and Cash Flows:

  • Most financial decisions involve cash flows that vary across different time periods.

  • Time Value of Money:

  • Required to evaluate cash flows either to their present value or future value.

• Analyzing cash flows with patterns:

  • Use specialized equations for regular cash flows:

  • Perpetuities:

    • Defined as regular cash flows with an indefinite duration (continue indefinitely).

  • Annuities:

    • Regular cash flows but with a defined life span.

Types of Perpetuities and Annuities

• Cash Flow Types:

  • Both perpetuities and annuities may be:

  • Level:

    • Cash flows are of the same amount across periods.

  • Growing:

    • Cash flows increase at a constant rate over time.

• Factors of Interest in Cash Flows:

  • Decision-makers might seek to determine:

  • Present value or future value of cash flows.

  • Interest rates associated with investments.

  • Individual payments in perpetuities or annuities.

  • Length of the time periods involved.

• Calculating Payments:

  • Payment calculations can be performed easily using financial calculators.

  • Payments may vary in frequency:

  • Monthly Payments:

    • E.g., lease payments.

  • Quarterly Payments:

    • E.g., stock dividends.

  • Semiannual Payments:

    • E.g., bond interest payments.

• Annual Returns Calculation:

  • While most decisions use annual returns, they must account for intra-year compounding periods to compute actual annual rates.

Types of Interest Rates

• Stated Annual Interest Rate:

  • The interest rate expressed on an annual basis.

  • Commonly used in contracts such as loans (e.g., credit cards, auto loans, mortgages).

• Periodic Interest Rate:

  • Interest calculated per period, such as:

  • Semiannual Rate: for bond interest payments.

  • Quarterly Rate: for dividend payments.

• Effective Annual Interest Rate:

  • The annual interest rate reflecting the impact of intra-year compounding.

• Annual Percentage Rate (APR):

  • Calculated as the interest rate charged per period multiplied by the number of periods within a year.