The Present Value Module

Perhaps you have heard advertisements stating that if you invest $2,000 a year in an Individual Retirement Account (IRA) or other retirement fund beginning at age 30, you will have accumulated over $500,000 by the time you retire at age 65. As the advertisements point out, you will receive substantially more than the $70,000 ($2,000 × 35 years) you have invested because of the interest your investment will earn. This highlights the importance of interest and how quickly it accumulates over a period of time. The focus of this module is on the time value of money and how this concept is used in personal and business financial decisions.

All investment or capital budgeting decisions involve giving up a certain amount of money today in the hope of receiving a greater amount at some future time. In order to determine whether you have made a wise investment, you must consider the time value of money. For example, assume that you are given the following investment opportunity: A real estate developer offers to sell you a vacant lot today for $100,000 and guarantees to repurchase it 10 years from now for a minimum of $175,000. Does that sound like a good investment? Although it is tempting to say yes, because you would be making a profit of $75,000, you must also consider the time value of money. The $175,000 you will receive in 10 years is not really comparable to the $100,000 you have to give up today. Money you will receive in the future will not be as valuable as money you receive today, because money received today can be invested and, as a result, will increase in amount. In the example, if you did not make the investment but instead put the $100,000 in a savings account that earned 8% interest per year, you would have accumulated over $215,800 at the end of 10 years.

The best way to analyze investment opportunities such as this one is to determine the rate of return they offer. In this example, if you invested $100,000 today and received $175,000 in 10 years, you would have earned a rate of return of about 5.76%. You can compare this rate of return with those of other investments of similar risk and logically decide which one presents the best opportunity. In order to make this and similar analyses, you must understand five concepts:

1. Simple versus compound interest

2. Future value of a single amount

3. Present value of a single amount

4. Future value of an annuity

5. Present value of an annuity