The Time Value of Money Concepts Future Value Present Value Cash Flow Streams Annuities Other Compounding Periods Equations Tools & Problems TVM Calculator Cash Flow Calculator TVM Exercise Uneven Cash Flow Stream Exercise Time Value of Money Quiz

# Cash Flow Streams

## Present Value

The Present Value of a Cash Flow Stream is equal to the sum of the Present Values of the individual cash flows. To see this, consider an investment which promises to pay \$100 one year from now and \$200 two years from now. If an investor were given a choice of this investment or two alternative investments, one promising to pay \$100 one year from now and the other promising to pay \$200 two years from now, clearly, he would be indifferent between the two choices. (Assuming that the investments were all of equal risk, i.e., the discount rate is the same.) This is because the cash flows that the investor would receive at each point in time in the future are the same under either alternative. Thus, if the discount rate is 10%, the Present Value of the investment can be found as follows:

 Present Value of the Investment PV = \$100/(1 + 0.10) + \$200/(1 + 0.10)2 PV = \$90.91 + \$165.29 = \$256.20

The following equation can be used to find the Present Value of a Cash Flow Stream.

where

• PV = the Present Value of the Cash Flow Stream,
• CFt = the cash flow which occurs at the end of year t,
• r = the discount rate,
• t = the year, which ranges from zero to n, and
• n = the last year in which a cash flow occurs.

 Present Value Example Find the Present Value of the following cash flow stream given that the interest rate is 10%. Solution:

 Example Problems Find the Present Value of the followingcash flow stream. Year Cash Flow 1 \$ 2 \$ 3 \$ 4 \$ Interest Rate: % Present Value: \$

## Future Value

The Future Value of a Cash Flow Stream is equal to the sum of the Future Values of the individual cash flows. For example, consider an investment which promises to pay \$100 one year from now and \$200 two years from now. Given that the discount rate is 10%, the Future Value at the end of year 2 of the investment can be found as follows:

 Future Value of the Investment FV2 = \$100(1 + 0.10) + \$200 FV2 = \$110.00 + \$200.00 = \$310.00

As of year 2, the \$100 received at the end of year 1 would have earned interest for one year while the \$200 received at the end of year 2 would not yet have earned any interest. Thus, the Future Value at the end of year 2, i.e., immediately after the \$200 cash flow was received, is \$310.00.

The following equation can be used to find the Future Value of a Cash Flow Stream at the end of year t.

where

• FVt = the Future Value of the Cash Flow Stream at the end of year t,
• CFt = the cash flow which occurs at the end of year t,
• r = the discount rate,
• t = the year, which ranges from zero to n, and
• n = the last year in which a cash flow occurs.

 Future Value Example Find the Future Value at the end of year 4 of the following cash flow stream given that the interest rate is 10%. Solution:

 Example Problems Find the Future Value of the followingcash flow stream at the end of year 4. Year Cash Flow 1 \$ 2 \$ 3 \$ 4 \$ Interest Rate: % Future Value: \$

© 2002 - 2010 by Mark A. Lane, Ph.D.