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
time value of money,
discounted cash flow (DCF) analysis.
value and present value techniques can be ap-
plied to a single cash flow (lump sum), ordin-
ary annuities, annuities due, and uneven cash
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
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:
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
= PV(1 + i)
where PV = present value, or beginning amount; i = interest rate per year; and n = number
of periods involved in the analysis.
, 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-