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$500 invested at the beginning of year 1

.05 earns interest (assumed) at a rate of 5% for one year,

$525 and we have a compound amount at the end of year 1 amounting to $525,

.05 which earns interest (assumed) at the rate of 5% for another year,

$551 and we have a compound amount at the end of year 2 amounting to $551 (rounded), and so on.

13.3 PRESENT-VALUE ANALYSIS The concept of present-value analysis (http://content.thuzelearning.com/books/Baker.6866.18.1/sections/ch13_sect1_8#ch13_key3) is based on the time value of money (http://content.thuzelearning.com/books/Baker.6866.18.1/sections/ch13_sect1_8#ch13_key4) . Inherent in this concept is the fact that the value of a dollar today is more than the value of a dollar in the future: thus the “present value” terminology. Furthermore, the further in the future the receipt of your dollar occurs, the less it is worth. Think of a dollar bill dwindling in size more and more as its receipt stretches further and further into the future. This is the concept of present-value analysis.

We learned about compound interest in math class. We learned that

Using this concept, it is possible to restate the present values of $1 to be paid out or received at the end of each of these years. It is possible to use equations, but that is not necessary because we have present-value tables (also called “look-up tables,” because one can “look- up” the answer). A present-value table is included at the end of this chapter in Appendix 13- A (http://content.thuzelearning.com/books/Baker.6866.18.1/sections/ch13_app1#ch13_app1) . All of the figures on the present-value table represent the value of a dollar. The interest rate available on this version of the table is on the horizontal columns and ranges from 1% to 20%. The number of years in the period is on the vertical; in this version of the table, the number of years ranges from 1 to 30. To look up a present value, find the column for the proper interest. Then find the line for the proper number of years. Then trace down the

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interest column and across the number-of-years line item. The point where the two lines meet is the number (or factor) that represents the value of $1 according to your assumptions. For example, find the year 10 by reading down the left-hand column labeled “Year.” Then read across that line until you find the column labeled “10%.” The point where the two lines meet is found to be 0.3855. The present value of $1 under these assumptions (10 year/10%) is about 38.5 cents (shown as 0.3855 on the table).

Besides using the look-up table, you can also compute this factor on a business analyst calculator. A reference to business analyst calculators is contained in the Appendix entitled “Web-Based and Software Learning Tools.” This can be found at the end of this text. Besides using either the look-up table or the business calculator, you can use a function on your computer spreadsheet to produce the factor. The important point is this: no matter which method you use, you should get the same answer.

Now that you have the present value of $1, by whichever method, it is simple to find the present value of any other number. You merely multiply the other number by the factor you found on the table—or in the calculator or the computer. Say, for example, you want to find the present value of $8,000 under the assumption used above (10 years/10%). You simply multiply $8,000 by the factor of 0.3855 you found in the table. The present value of $8,000 is $3,084 (or $8,000 times 0.3855).

A compound interest table is also included at the end of this chapter in Appendix 13-B (http://content.thuzelearning.com/books/Baker.6866.18.1/sections/ch13_app2#ch13_app2) , along with a table showing the present value of an annuity of $1.00 in Appendix 13-C (http://content.thuzelearning.com/books/Baker.6866.18.1/sections/ch13_app3#ch13_app3) , so that you have the tools for computation at your disposal.

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