In Chapter 1, we saw that the primary objective of financial management is to maxi-
mize the value of the firm’s stock. We also saw that stock values depend in part on the
timing of the cash flows investors expect to receive from an investment—a dollar ex-
pected soon is worth more than a dollar expected in the distant future. Therefore, it is
essential for financial managers to have a clear understanding of the time value of
money and its impact on stock prices. These concepts are discussed in this chapter,
where we show how the timing of cash flows affects asset values and rates of return.
The principles of time value analysis have many applications, ranging from setting
up schedules for paying off loans to decisions about whether to acquire new equip-
ment. In fact, of all the concepts used in finance, none is more important than the time value
of money,which is also called discounted cash flow (DCF) analysis.Since this con-
cept is used throughout the remainder of the book, it is vital that you understand the
material in this chapter before you move on to other topics.
Time Lines
One of the most important tools in time value analysis is the time line,which is used
by analysts to help visualize what is happening in a particular problem and then to
help set up the problem for solution. To illustrate the time line concept, consider the
following diagram:
Time:012345
Time 0 is today; Time 1 is one period from today, or the end of Period 1; Time 2 is
two periods from today, or the end of Period 2; and so on. Thus, the numbers above
the tick marks represent end-of-period values. Often the periods are years, but other
time intervals such as semiannual periods, quarters, months, or even days can be used.
If each period on the time line represents a year, the interval from the tick mark cor-
responding to 0 to the tick mark corresponding to 1 would be Year 1, the interval from
1 to 2 would be Year 2, and so on. Note that each tick mark corresponds to the end of
one period as well as the beginning of the next period. In other words, the tick mark at
Time 1 represents the endof Year 1, and it also represents the beginningof Year 2 be-
cause Year 1 has just passed.
Cash flows are placed directly below the tick marks, and interest rates are shown
directly above the time line. Unknown cash flows, which you are trying to find in the
analysis, are indicated by question marks. Now consider the following time line:
Time: 0 5% 1 2 3
Cash flows: 100?
Here the interest rate for each of the three periods is 5 percent; a single amount (or
lump sum) cash outflowis made at Time 0; and the Time 3 value is an unknown inflow.
Since the initial $100 is an outflow (an investment), it has a minus sign. Since the Pe-
riod 3 amount is an inflow, it does not have a minus sign, which implies a plus sign.
Note that no cash flows occur at Times 1 and 2. Note also that we generally do not
show dollar signs on time lines to reduce clutter.
Now consider a different situation, where a $100 cash outflow is made today, and
we will receive an unknown amount at the end of Time 2:
56 CHAPTER 2 Time Value of Money
Excellent retirement calcula-
tors are available at http://
http://www.ssa.gov andhttp://
http://www.asec.org.These allow
you to input hypothetical
retirement savings infor-
mation, and the program
shows graphically if current
retirement savings will be
sufficient to meet retirement
needs.
The textbook’s web site
contains an Excelfile that
will guide you through the
chapter’s calculations. The
file for this chapter is Ch 02
Tool Kit.xls,and we encour-
age you to open the file and
follow along as you read the
chapter.
54 Time Value of Money
