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Cash Flow Diagrams

A cash flow diagram is a picture of a financial problem that shows all cash inflows and outflows plotted along a horizontal time line.  It can help you to visualize a financial problem and to determine if it can be solved using TVM methods.

Constructing a CashFlow Diagram

The time line is a horizontal line divided into equal periods such as days, months, or years.  Each cash flow, such as a payment or receipt, is plotted along this line at the beginning or end of the period in which it occurs.  Funds that you pay out such as savings deposits or lease payments are negative cash flows that are represented by arrows which extend downward  from the time line with their bases at the appropriate positions along the line.  Funds that you receive such as proceeds from a mortgage or withdrawals from a saving account are positive cash flows represented by arrows extending upward from the line.

Example: You are 40 years old and have accumulated $50,000 in your savings account.  You can add $100 at the end of each month to your account which pays an annual interest rate of 6% compounded monthly.  Will you be able to retire in 20 years?

The time line is divided into 240 monthly periods (20 years times 12 payments per year) since the payments are made monthly and the interest is also compounded monthly.   The $50,000 that you have now (present value) is a negative cash outflow  since you will treat it as though you were just now depositing it into the account.    It is represented with a downward pointing arrow with its base at the beginning of the first period.  The 240 monthly $100 deposits  are also negative outflows  represented with downward pointing arrows placed at the end of each period.  Finally you will withdraw some unknown amount (the future value) after 20 years.  Represent this positive  inflow with an upward pointing arrow with its base at the very end of the last period.

This diagram was drawn from your point of view.  From the bank's point of view, the present value and the series of deposits are positive cash inflows, and the final withdrawal of the future value will be a negative outflow.

See the Future Value of an Ordinary Annuity page for the solution to this problem.

Identifying TVM Problems

For a financial problem to be solved with time value of money formulas:

  • the periods must be of equal length
  • payments, if present, must all be equal and be all inflows or all outflows
  • payments must all occur either at the beginning or end of a period
  • the interest rate cannot vary along the time line

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