• Table of Contents • Introduction • 1-Time Value • 2-Risk/Return • 3-Accounting • 4-Securities • 5-Business • 6-Regulatory • Case Studies • Student Papers

## 1.1.1 Present value and future value

Time value of money affects our most basic, personal financial decisions. Your bank pays you for the time you keep your money deposited in your savings account. You pay your student loan company for the time you borrow its money to finance your education.

When we face a financial decision we can consider either its present value or its future value. Either technique, correctly applied, will give us the same information. Future values measure what you have at the end of a project; present values measure what you have when you start (time zero). If you must compare a present amount with a future amount, you can either calculate what the present amount would be worth in the future, or what the future amount is worth in the present. Same thing.

Present values and future values can be compared by measuring them at either the end of the investment or at time zero. In our example, we can compute the future value of investing \$10,000 for 5 years and compare it to the future value of investing each of the cash flows for 4, 3, 2 and 1 years. Or we can compute the present value of \$10,000 at time zero (that is, \$10,000) and compare it to the present values of the cash flows.

• To compute future value, use compounding to find the future value of each cash flow at a future time -- and then sum all these future values.
• To compute present value, use discounting to find the present value of each cash flow at time zero -- and then sum all these present values.

Although present value and future value techniques produce the same decisions, financial planners (who live and work at time zero) tend to rely on present value techniques.

A time line depicts cash flows of an investment. Consider an investment of \$10,000 that produces returns over 5 years:

 End of year Amount 0 -10,000 1 +2,000 2 +3,000 3 +4,000 4 +2,000 5 +1,000

Money has time value. In our example, receiving \$2,000 after one year has more value than receiving the same amount after four years. The earlier money may be consumed or reinvested before the later money. We value it more highly.

 1.1 Introduction-Time value of money 1.1.2 Computing present and future values