C
HAPTER
2
T
IME
V
ALUE OF
M
ONEY
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
time value of money,
also called
discounted cash flow (DCF) analysis.
Future
value and present value techniques can be ap
plied to a single cash flow (lump sum), ordin
ary annuities, annuities due, and uneven cash
flow streams.
Future and present values can
be calculated using, a regular calculator, a cal
culator with financial functions, or a spread
sheet program. When compounding occurs
more frequently than once a year, the effect
ive rate of interest is greater than the quoted
rate.
OUTLINE
Time lines are used to help visualize what is happening in time value of money problems.
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 a symbol for the particular item
that is missing.
Thus, to find the future value of $100 after 5 years at 5 percent interest, the
following time line can be set up:
Time:
0
5%
1
2
3
4
5






Cash flows:
100
FV
5
= ?
Finding the future value (FV), or compounding, is the process of going from today's values
(or present values) to future amounts (or future values).
It can be calculated as
FV
n
= PV(1 + i)
n
= PV(FVIF
i,n
),
where PV = present value, or beginning amount; i = interest rate per year; and n = number
of periods involved in the analysis.
FVIF
i,n
, the Future Value Interest Factor, is a short
hand way of writing the equation.
This equation can be solved in one of three ways: nu
merically with a regular calculator, with a financial calculator, or with a spreadsheet pro
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2  2
gram.
For calculations, assume the following data that were presented in the time line
above:
present value (PV) = $100, interest rate (i) = 5%, and number of years (n) = 5.
To solve numerically, use a regular calculator to find 1 + i = 1.05 raised to the fifth power,
which equals 1.2763.
Multiply this figure by PV = $100 to get the final answer of
FV = $127.63
5
.
With a financial calculator, the future value can be found by using the time value of money
input keys, where N = number of periods, I = interest rate per period, PV = present value,
PMT = payment, and FV = future value.
By entering N = 5, I = 5, PV = 100, and PMT
= 0, and then pressing the FV key, the answer 127.63 is displayed.
Some financial calculators require that all cash flows be designated as either in
flows or outflows, thus an outflow must be entered as a negative number
(for ex
ample,
PV = 100 instead of PV = 100).
Some calculators require you to press a “Compute” key before pressing the FV
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