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time line
A horizontal line on which time
zero appears at the leftmost end
and future periods are marked
from left to right; can be used to
depict investment cash flows.
FIGURE 4.1
LG1
Time Line
Time line depicting an investment’s
cash flows
The Role of Time Value in Finance
CHAPTER 4 Time Value of Money 131
Because we view the firm as a going concern, we assess the decisions of its
financial managers, and ultimately the value of the firm itself, in light of its
cash flows. The opportunity to earn interest on the firm’s funds makes the timing
of its cash flows important, because a dollar received in the future in not the same
as a dollar received today. Thus, money has a time value, which affects everyone—individuals,
businesses, and government. In this chapter we explore the
concepts related to the time value of money.
Financial managers and investors are always confronted with opportunities to
earn positive rates of return on their funds, whether through investment in
attractive projects or in interest-bearing securities or deposits. Therefore, the timing
of cash outflows and inflows has important economic consequences, which
financial managers explicitly recognize as the time value of money. Time value is
based on the belief that a dollar today is worth more than a dollar that will be
received at some future date. We begin our study of time value in finance by considering
the two views of time value—future value and present value, the computational
tools used to streamline time value calculations, and the basic patterns of
cash flow.
Future Value versus Present Value
Financial values and decisions can be assessed by using either future value or present
value techniques. Although these techniques will result in the same decisions,
they view the decision differently. Future value techniques typically measure cash
flows at the end of a project’s life. Present value techniques measure cash flows at
the start of a project’s life (time zero). Future value is cash you will receive at a
given future date, and present value is just like cash in hand today.
A time line can be used to depict the cash flows associated with a given
investment. It is a horizontal line on which time zero appears at the leftmost end
and future periods are marked from left to right. A line covering five periods (in
this case, years) is given in Figure 4.1. The cash flow occurring at time zero and
that at the end of each year are shown above the line; the negative values represent
cash outflows ($10,000 at time zero) and the positive values represent cash
inflows ($3,000 inflow at the end of year 1, $5,000 inflow at the end of year 2,
and so on).
–$10,000 $3,000 $5,000 $4,000 $3,000 $2,000
0 1 2 3
End of Year
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