CHAPTER 4 Time Value of Money 151- $10,000 $3,000 $5,000 $4,000 $3,000 $2,000
0123CompoundingDiscounting45Future
ValuePresent
ValueEnd of YearFIGURE 4.2Compounding
and Discounting
Time line showing
compounding to find future
value and discounting to find
present value
at the end of the investment’s 5-year life. Alternatively, the present value tech-
nique uses discountingto find the present valueof each cash flow at time zero
and then sums these values to find the investment’s value today. Application of
this approach is depicted below the time line in Figure 4.2.
The meaning and mechanics of compounding to find future value and of dis-
counting to find present value are covered in this chapter. Although future value
and present value result in the same decisions, financial managers—because they
make decisions at time zero—tend to rely primarily on present value techniques.Computational Tools
Time-consuming calculations are often involved in finding future and present val-
ues. Although you should understand the concepts and mathematics underlying
these calculations, the application of time value techniques can be streamlined.
We focus on the use of financial tables, hand-held financial calculators, and com-
puters and spreadsheets as aids in computation.Financial Tables
Financial tables include various future and present value interest factors that sim-
plify time value calculations. The values shown in these tables are easily devel-
oped from formulas, with various degrees of rounding. The tables are typically
indexed by the interest rate (in columns) and the number of periods (in rows).
Figure 4.3 shows this general layout. The interest factor at a 20 percent interest
rate for 10 years would be found at the intersection of the 20% column and the
10-period row, as shown by the dark blue box. A full set of the four basic finan-
cial tables is included in Appendix A at the end of the book. These tables are
described more fully later in the chapter.