FIN 3000 - Chapter 5a

1. Goals and Governance of the Corporation

  • Overview of governance structures and objectives of corporations.

2. Future Values and Compound Interest

2.1 Future Value Calculation

  • Example Calculation:

    • Initial Investment: $100

    • Interest Rate: 6%

    • Future Value after 1 Year: $100 + ($100 x 0.06) = $106

2.2 Compounding Concept

  • Compound interest results in earning "interest on interest."

  • Formula for future value:Future Value (FV) = Initial Investment x (1 + r)^t

    • Where r is the interest rate and t is the number of years.

  • Example Calculations:

    • After 2 years: $100 x (1.06)^2 = $112.36

    • After 3 years: $100 x (1.06)^3 = $119.10

3. Present Values

3.1 Present Value Basics

  • The concept that a dollar today is worth more than a dollar in the future due to the potential earning capacity.

3.2 Present Value Calculation Formula

  • PV = FV / (1 + r)^t

    • Where:

      • PV = Present Value

      • FV = Future Value

      • r = interest rate

      • t = time in years

3.3 Practical Examples

  • To determine how much needs to be invested today to achieve a future value.

    • Needed: $112.36 in 2 years:PV = $112.36 / (1 + 0.06)^2 = $100

4. Multiple Cash Flows

4.1 Future Value of Cash Flows

  • Example: Investing $1,200 today and $1,400 in 1 year at 8%:

    • FV in 2 years = $1,200(1.08)^2 + $1,400(1.08) = $2,911.68

4.2 Present Value of Cash Flows

  • Present value of multiple future cash flows.

  • PV calculation requires summing individual present values of multiple cash flows.

5. Level Cash Flows: Annuities

5.1 Definition and Formula

  • Annuities provide a series of equal payments over time.

  • Present Value of Annuity:PV = C x [ (1 - (1 + r)^-t) / r ]

    • C = Annual payment, r = interest rate, t = number of years.

5.2 Example of Mortgage Payments

  • Calculate mortgage payment:

    • For a house priced at $150,000 with a mortgage at 6% over 25 years (monthly payments) requires using annuity formulas.

6. Perpetuities and Growing Cash Flows

6.1 Definition of Perpetuities

  • Stream of constant cash flows forever.

  • Present value of a perpetuity:PV = C / r

    • Where C = cash payment, r = interest rate.

6.2 Example of Final Value Calculation

  • For example, funding a perpetual chair at a university requires determining how much must be set aside today.

7. Effective Annual Interest Rates and APR

7.1 Effective Annual Rate

  • Comparison of differently quoted interest rates over varied periods.

7.2 Annual Percentage Rate (APR)

  • Defines the annualized cost of borrowing or earning, excluding compounding effects.

8. Inflation and the Time Value of Money

8.1 Impact of Inflation

  • Inflation erodes purchasing power; therefore, nominal interest rates must be adjusted to real interest rates to measure true growth of investments.

8.2 Calculation of Real Interest Rate

  • Real Interest Rate = Nominal Rate - Inflation Rate

9. Practice and Application Problems

  • Examples to calculate future and present values under various scenarios, encompassing decisions on investments, loans, and retirement savings based on provided interest rates and terms.