Time Value of Money - Future Value of Uneven Cash Flows









The tutorial is about calculating the future value of uneven cash flows using two methods. Future value can be determined by either manually calculating the future value of each cash flow and then summing them up or by first calculating the net present value (NPV) and then converting it to future value.

In the manual method, the future value of each cash flow is calculated individually using the future value formula: FV = PV * (1 + r)^n, where PV is the present value of the cash flow, r is the interest rate, and n is the number of periods. This method is an example where cash flows are invested at the end of each year and calculates the future value after four years.

In the Excel method, the presenter shows how to calculate the NPV of all cash flows at year zero using the NPV function. Then, the NPV is converted to future value using the FV function, considering the desired number of periods. This method is advantageous for complex scenarios involving multiple cash flows over various time periods.

The presenter emphasizes the importance of understanding both methods and suggests using the Excel method for efficiency, especially in scenarios with numerous cash flows or extended time periods. They encourage viewers to subscribe to their channel for more informative finance videos and invite feedback and comments. Future Value (FV) Formula: The future value formula calculates the value of an investment at a specified future date, based on a given interest rate and the number of periods the investment is held. The formula is: FV = PV * (1 + r)^n

  1. where:

    • FV is the future value of the investment
    • PV is the present value or initial investment
    • r is the interest rate per period (expressed as a decimal)
    • n is the number of periods --------------------------

  2. Net Present Value (NPV) Formula: The net present value formula calculates the present value of a series of cash flows, both inflows and outflows, discounted back to the present date. The formula is: NPV = Σ(CF_t / (1 + r)^t)

    1. where:

      • NPV is the net present value
      • CF_t is the cash flow at time t
      • r is the discount rate (interest rate)
      • t is the time period --------------------------------

    2. Excel NPV Function: The NPV function in Excel calculates the net present value of a series of cash flows at a given discount rate. The syntax for the NPV function is: FV(rate, nper, pmt, [pv, [type]]) where: rate is the interest rate per period nper is the total number of periods pmt is the payment made each period (if any) pv is the present value or initial investment (optional) type is the timing of the payment: 0 for the end of the period (default), 1 for the beginning of the period These formulas and functions are essential tools for calculating the future value and net present value of investments, helping individuals and businesses make informed financial decisions. --------------

    3. Example of Future Value (FV) Formula:

      Let's say you have $1,000 to invest in a savings account that offers an annual interest rate of 5%. You want to calculate the future value of your investment after 5 years.

      Using the Future Value (FV) formula: FV = PV * (1 + r)^n

      where:

      • PV (Present Value) = $1,000
      • r (interest rate per period) = 5% or 0.05 (expressed as a decimal)
      • n (number of periods) = 5 years

      Plug in the values: FV = 1000 * (1 + 0.05)^5 = 1000 * (1.05)^5 ≈ 1000 * 1.27628 ≈ $1,276.28

      So, the future value of your $1,000 investment after 5 years would be approximately $1,276.28. ------------------------------------------------------>

      Example of Net Present Value (NPV) Formula:

      Suppose you are considering an investment opportunity that requires an initial outlay of $5,000 and is expected to generate cash flows of $1,500 at the end of each year for the next 4 years. You want to determine the net present value of this investment assuming a discount rate of 10%.

      Using the Net Present Value (NPV) formula: NPV = Σ(CF_t / (1 + r)^t)

      where:

      • CF_t is the cash flow at time t
      • r is the discount rate (interest rate)
      • t is the time period

      Plug in the values: NPV = (-5000) + (1500 / (1 + 0.10)^1) + (1500 / (1 + 0.10)^2) + (1500 / (1 + 0.10)^3) + (1500 / (1 + 0.10)^4) = -5000 + (1363.64) + (1240.53) + (1127.75) + (1024.32) ≈ $156.24 So, the net present value of the investment opportunity is approximately $156.24. --------------------------------------------->

    4. Example of Excel NPV Function:

      Suppose you are evaluating an investment opportunity with the following cash flows: -$10,000 in year 0, $3,000 in year 1, $4,000 in year 2, and $5,000 in year 3. You want to calculate the net present value of these cash flows at a discount rate of 8%.

      Using the NPV function in Excel: =NPV(0.08, -10000, 3000, 4000, 5000)

      This formula calculates the NPV of the cash flows at a discount rate of 8%. The result will be the present value of all cash flows discounted back to the present date. ------------------------

      Example of Excel FV Function:

      Suppose you are saving for retirement and plan to invest $200 at the end of each month for the next 20 years in an account that earns 6% interest compounded monthly. You want to calculate the future value of your investment.

      Using the FV function in Excel:

      =FV(0.06/12, 20*12, -200)

      This formula calculates the future value of your monthly investments at a monthly interest rate of 0.06/12 (6% annual interest rate divided by 12 months) for a total of 20*12 periods (20 years * 12 months per year). The payment made each month is -$200 (negative because it's an outgoing payment).



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