Notes on Present Value Calculations and Their Applications

Determining Present Values

• Understanding Present Value

  • Importance of Present Value in financial decision making

  • Present value (PV) reflects the worth of an amount of money to be received in the future in today's terms.

  • The formula used: $ext{Future Value} = ext{Present Value} imes (1 + r)^n$

    • Where:

    • $r$ = the rate of return

    • $n$ = the number of periods

  • To find the present value:

  • Rearrangement of the formula gives:
    $ext{Present Value} = rac{ ext{Future Value}}{(1 + r)^n}$

  • This can also be understood as: $ext{Present Value} = ext{Future Value} imes ext{PVIF}$ (Present Value Interest Factor)

    • Where:

      • $ext{PVIF} = rac{1}{(1 + r)^n}$

• Why Manage Present Values?

  • Financial decisions are made today based on today's valuations.

  • It provides clarity when comparing present costs with future returns.

  • Helps individuals and businesses decide on investments based on current monetary worth.

• Using a Financial Timeline

  • Importance of visualizing cash flows on a timeline.

  • Example scenario:

  • If an investment offers $100 in one year with a required return of 10%, how much is it worth today?

    • The formula for calculation is:
      $ext{Present Value} = rac{100}{(1 + 0.1)^1} = rac{100}{1.1} = 90.91$

  • If successful, this calculation confirms the direct relationship of the invested amount today growing to $100 in the future.

• Calculating Present Values using Excel

  • Utilizing Excel functions for financial calculations:

  • Using the PV function with:

    • Future Value (FV)

    • Rate (r)

    • Number of periods (n)

  • Payments (PMT) are noted but irrelevant when calculating single future values.

  • Important Note: When FV is positive, PV will appear as negative reflecting cash outflow.

  • Engage with hands-on exercises for better comfort in calculating present values using Excel tools.

• Effects of Time and Interest Rates on Present Values

  • Graphical relationships between future values and present values:

  • As interest rates increase or more periods are considered, present values decrease.

  • Concept of diminishing returns on present value calculations:

  • Present values less than future values due to the time value of money.

  • The notion remains under positive interest conditions.

• Application in Cash Flow from Multiple Sources

  • Present Value as a summative calculation across multiple cash flows:

  • Helps in investment opportunities involving diverse cash flows.

  • Example scenario:

  • Cash flow of $100 in one year and $300 in two years at a 10% return:

    • Calculate each cash flow's present value individually.

    • Then sum:
      $PV_{1} = rac{100}{(1 + 0.1)^1} = 90.91$
      $PV_{2} = rac{300}{(1 + 0.1)^2} = 247.93$

    • Combined present value = $90.91 + $247.93 = $338.84

• Understanding Personal and Commercial Finance in Real-World Scenarios

  • Explaining loan structures and repayment systems:

  • Borrowers often repay through installments, impacting perceived costs versus upfront values.

  • Loan structures could include varied installment plans:

  • Example of a car loan offering no interest but structured payments to handle capital and interest through present value calculations:

    • Each future cash flow for loans requires finding its present value for proper assessment with an expected return.

• Summarizing the Time Value of Money Concept

  • Growing wealth over time through compounding opportunities increases future value.

  • Present value allows us to calculate how much investment is necessary today to secure future cash flows:

  • Investors can determine permissible maximum expenditures based on desired rates of return.

  • Financial institutions analyze varied cash flows similarly to estimate profits.