Present Value of a Dollar
PRESENT
VALUE ( PV ) OF A DOLLAR
The
present value is the current value of a dollar today that is expected to
be received or paid out at some point in the future. Future dollar values are restated as present values using an
equation that incorporates the Present Value Interest Factor (PVIF). Even if not
stated, the Present Value calculation process implicitly assumes that the a
compound interest (or compound return) process has been used to adjust for the
time value of money.
PRESENT
VALUE OF A SINGLE DOLLAR AMOUNT PROBLEM ( PV $ PROBLEM)
This
is a particular type of present value calculation that assumes a single dollar
amount in the future is brought back to a single dollar amount today.
This is in contrast to the “annuity” type of problem that represents
a stream of equal dollar amounts or a “stream of unequal payments” problem.
The
PV $ amount may either be a cash inflow or a cash outflow.
Present
values are calculated (discounted) using compound rates of return. Even if not
stated, the Presnt Value calculation process implicitly assumes that a
compounding discounting process has been used to arrive at this present dollar
amount.
Unless
stated otherwise, a present value calculation assumes that the future dollar
amount that is being discounted occurs
at the end of the future time period.
The
formula for calculating the present value of a single dollar amount is as
follows:
or
Where:
FV = Future Value
PV = Present Value
i
= annual interest rate or annual rate of return
n
= number of compounding periods
FVIF = Future Value Interest Factor
PVIF = Present Value Interest Factor
If
you are just learning about financial calculations, it is suggested that you
complete the terminology section before continuing on to the examples of PV
calculations.
If
you know about financial calculations and are reviewing the material, you may
want to go directly to the examples of FV $ calculations.
PRESENT
VALUE INTEREST FACTOR (PVIF)
A
PVIF is the interest rate factor that is used to take a dollar value stated at
some point in the future and restate that value as a present value today.
This process is often referred to as discounting future value to present
values. The PVIF reflects both the
applicable interest rate (or rate of return) per period and the number of
periods the compound return is being earned.
The
formula for a PVIF is as follows:
A
small set of present value interest factors is presented in the Present Value
Interest Factor Table below.
The
PVIF Table is sometimes referred to as the Present Value of a Dollar Table.
PRESENT VALUE INTEREST FACTOR (PVIF) TABLE
|
|
i =
1% |
2% |
3% |
4% |
5% |
6% |
7% |
|
# of periods |
|
|
|
|
|
|
|
|
1 |
0.9901 |
0.9804 |
0.9709 |
0.9615 |
0.9524 |
0.9434 |
0.9346 |
|
2 |
0.9803 |
0.9612 |
0.9426 |
0.9246 |
0.9070 |
0.8900 |
0.8734 |
|
3 |
0.9706 |
0.9423 |
0.9151 |
0.8890 |
0.8638 |
0.8396 |
0.8163 |
|
4 |
0.9610 |
0.9238 |
0.8885 |
0.8548 |
0.8227 |
0.7921 |
0.7629 |
|
5 |
0.9515 |
0.9057 |
0.8626 |
0.8219 |
0.7835 |
0.7473 |
0.7130 |
|
6 |
0.9420 |
0.8880 |
0.8375 |
0.7903 |
0.7462 |
0.7050 |
0.6663 |
|
7 |
0.9327 |
0.8706 |
0.8131 |
0.7599 |
0.7107 |
0.6651 |
0.6227 |
|
8 |
0.9235 |
0.8535 |
0.7894 |
0.7307 |
0.6768 |
0.6274 |
0.5820 |
|
9 |
0.9143 |
0.8368 |
0.7664 |
0.7026 |
0.6446 |
0.5919 |
0.5439 |
|
10 |
0.9053 |
0.8203 |
0.7441 |
0.6756 |
0.6139 |
0.5584 |
0.5083 |
|
11 |
0.8963 |
0.8043 |
0.7224 |
0.6496 |
0.5847 |
0.5268 |
0.4751 |
|
12 |
0.8874 |
0.7885 |
0.7014 |
0.6246 |
0.5568 |
0.4970 |
0.4440 |
|
13 |
0.8787 |
0.7730 |
0.6810 |
0.6006 |
0.5303 |
0.4688 |
0.4150 |
|
14 |
0.8700 |
0.7579 |
0.6611 |
0.5775 |
0.5051 |
0.4423 |
0.3878 |
|
15 |
0.8613 |
0.7430 |
0.6419 |
0.5553 |
0.4810 |
0.4173 |
0.3624 |
Example
of use of PVIF table:
You expect to receive $200 at
the end of 6 years. The appropriate
discount rate to use if 7% per year. What
is the present value of the future amount? Using
the table PVIF value; the PVIF value for n
= 6 and i = 7% is .6663.
This value is the same as the .6663422 calculated above and rounded to 4
decimal places. Calculating the Present Value;
Be sure to see the text book assignments for more information on this topic.