150 PART 2 Important Financial Concepts
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.
LG1–$10,000 $3,000 $5,000 $4,000 $3,000 $2,0000123
End of Year45Hint The time value of
money is one of the most
important concepts in finance.
Money that the firm has in its
possession today is more
valuable than future payments
because the money it now has
can be invested and earn
positive returns.
FIGURE 4.1Time Line
Time line depicting an invest-
ment’s cash flows
4.1 The Role of Time Value in Finance
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 tim-
ing of cash outflows and inflows has important economic consequences, which
financial managers explicitly recognize as thetime 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 con-
sidering the two views of time value—future value and present value, the compu-
tational 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 pres-
ent 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 endof a project’s life. Present value techniques measure cash flows at
thestartof a project’s life (time zero).Future valueis cash you will receive at a
given future date, and present value is just like cash in hand today.
A time linecan 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 repre-
sent 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).
Because money has a time value, all of the cash flows associated with an
investment, such as those in Figure 4.1, must be measured at the same point in
time. Typically, that point is either the end or the beginning of the investment’s
life. The future value technique uses compoundingto find the future valueof each
cash flow at the end of the investment’s life and then sums these values to find the
investment’s future value. This approach is depicted above the time line in
Figure 4.2. The figure shows that the future value of each cash flow is measured