2/20/13 Cash Flow Diagrams

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TVM Component Documentation Concepts Diagrams

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 leasepayments 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 theline.

Example: You are 40 years old and have accumulated $50,000 in yoursavings 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 asthough you were just now depositing it into the account. It is

Concepts

Introduction

Interest

Periods

Payments

Present Value

Single

Annuity

Future Value

Single

Annuity

Amortization

Diagrams

Calculator

2/20/13 Cash Flow Diagrams

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represented with a downward pointing arrow with its base at thebeginning 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 alloutflows

payments must all occur either at the beginning or end of a periodthe interest rate cannot vary along the time line

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