In this article, we will look into what a cash flow stream looks like and how to calculate the present value and future value of a cash flow stream, let's first define a cash flow stream and the present value and future value of that cash flow stream.

A cash flow stream is of the form (x

_{1}, x

_{2}, x

_{3}, x

_{4},....,x

_{n}) where x

_{1}, x

_{2}, x

_{3}, x

_{4},....,x

_{n }are the cash flows corresponding to compounding periods 1, 2, 3, 4,....,n.

Typically cash flows occur at the end of each year or at the end of each compounding period.

The present value of the above cash flow stream (x

_{1}, x

_{2}, x

_{3}, x

_{4},....,x

_{n}) at an interest rate 'r' for 'n' periods is given by

The future value of a cash flow stream (x

_{1}, x_{2}, x_{3}, x_{4},....,x_{n}) at an interest rate 'r' for 'n' periods is given byExample:

Lets's keep it simple and try to calculate the present value and future value of a cash flow stream, consider that you invested $100 in a bank for two years at an interest rate 10% compounded annually.

After two years, the growth of the investment would be

FV = 100 * (1 + 10/100) ^ 2 = $121

Here we can define two equivalent cash flows

Cash flow 1: (100, 0, 0) = You invest $100 today for a period of two years ($100 is the initial investment) at an interest rate r = 10%

The present value and future value of this cash flow stream based on the above formula is given by

PV = 100 + 0 / (1.1) + 0 / (1.1) ^ 2 = 100

FV = 100 * (1.1) ^ 2 + 0 * 1.1 + 0 = 121

Cash flow 2: (0, 0, 121) = You get $121 after two periods from the bank (at an interest rate r = 10%), the present value of this cash flow stream based on the above formula is given by

PV = 0 + 0 / (1.1) + 121 / (1.1) ^ 2 = 100

FV = 0 * (1.1) ^ 2 + 0 * 1.1 + 121 = 121

Therefore the cash flows (100, 0, 0) and (0, 0, 121) are equivalent, you invest $100 today in a bank at 10% interest rate and the cash flow at the end of 2 years would be $121and this cash flow can be defined as (100, 0, 0) or (0, 0, 121).

The above cash flow is quite simple, in general different investments produce different cash flow streams at the end of every year (they can be negative, meaning negative returns at the end of a period or a positive value), for any cash flow stream, the above formula can be used to compute the present value and the future value of the stream.

In the next article, we will see an example of a cash flow stream and how the present value value analysis affects an investment decision.

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