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OVERVIEW
A dollar in the hand today is worth more than a
dollar to be received in the future because, if
you had it now, you could invest that dollar and
earn interest.
Of all the techniques used in
finance, none is more important than the
concept of the time value of money
,
or
discounted cash flow (DCF) analysis.
The
principles of time value analysis that are
developed
in
this
chapter
have
many
applications, ranging from setting up schedules
for paying off loans to decisions about whether
to acquire new equipment.
Future value and present value techniques
can be applied to a single cash flow (lump sum),
ordinary annuities, annuities due, and uneven
cash flow streams. Future and present values
can be calculated using a regular calculator or a
calculator with financial functions.
When
compounding occurs more frequently than once
a year, the effective rate of interest is greater
than the quoted rate.
The cash flow time line is one of the most important tools in time value of money analysis.
Cash flow time lines help to visualize what is happening in a particular problem.
Cash flows
are placed directly below the tick marks, and interest rates are shown directly above the
time line; unknown cash flows are indicated by question marks.
Thus, to find the future
value of $100 after 5 years at 5 percent interest, the following cash flow time line can be set
up:
Time:
0
1
2
3
4
5






Cash flows:
100
FV
5
= ?
A
cash outflow
is a payment, or disbursement, of cash for expenses, investments, and so
on.
A
cash inflow
is a receipt of cash from an investment, an employer, or other sources.
Compounding is the process of determining the value of a cash flow or series of cash flows
some time in the future when compound interest is applied.
The future value is the amount
C
HAPTER
3
T
HE
T
IME
V
ALUE OF
M
ONEY
OUTLINE
5%
CHAPTER 3:
THE TIME VALUE OF MONEY
40
to which a cash flow or series of cash flows will grow over a given period of time when
compounded at a given interest rate.
The future value can be calculated as
FV
n
= PV(1 + k)
n
,
where PV = present value, or beginning amount; k = interest rate per period; and n =
number of periods involved in the analysis.
This equation can be solved in one of two ways:
numerically or with a financial calculator.
For calculations, assume the following data that
were presented in the time line above:
present value (PV) = $100, interest rate (k) = 5%, and
number of years (n) = 5.
Compounded interest
is interest earned on interest.
To solve numerically, use a regular calculator to find 1 + k = 1.05 raised to the fifth power,
which equals 1.2763.
Multiply this figure by PV = $100 to get the final answer of FV
5
=
$127.63.
With a financial calculator, the future value can be found by using the time value of money
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