| In accounting we are practically never interested in asking
how much something will be worth in the future. Instead we want to know how much
something that will be paid (or received) in the future is worth today. Remember,
what we try to do in accounting: Determine income for the current year (NOW).
Determine the value of assets and liabilities at the end of the current year (NOW).
In other words, we do not case much about future value, instead we want to know Present
Value. Does this mean all the talk about Future Value was wasted? Not at
all. Remember the equation used to answer the question: |
| "If $100 are invested for three years
to earn 10%, how much money will we have at the end of three years?" |
Equation: 100 x FV (10%,3) = X |
| In that example, we solved for Future Value and determined
that X = $ 133.10. Now, let's rephrase this. What if we know how much we will
receive three years from now? A customer promises to pay us $133.10 at the end of
three years. This will is in payment for a purchase made this year. We need to know
how much of the $133.10 is principal (REVENUE) and how much should be considered interest
income which we will earn over the three year period. By the miracles of algebra, we use
the same equation that was used above for Future Value, we just rewrite it a little:
Question: |
| "If three years from now we are to receive
$133.10 and if we want to earn 10% on any investment (compounded annually), what is the
value of the promised payment today?" |
Equation:
- X x FV(10%,3) = $133.10
- X x 1.331 = $133.10
- (X x 1.331)/1.331= $133.10/1.331
- X
= $100
|
TA DA!
Present Value is the reciprocal of Future Value or PV = 1/FV. |
| Therefore: |
PV(10%,3)
= 1/FV(10%,3) |
= 1/(1+.1) |
3 |
= |
0.751 |
|
|
| The question again: What is the value today of $133.10 to be received in
three years, if we want to earn 10% on our investment? |
Equation:
$133.10
x PV(10%, 3) = X |
$133.10
x .751315 = X |
$
100.00 |
|
=
X |
|
| This is the question (and equation) you must know. You
will not use the formula to determine the present value factor. Instead use the
present value tables in your text. Note that different present value tables round to
different decimal places. Some tables, for example would give PV(3, 10%) as .751,
others might go as far as .7513148. Don't worry about that. These are rounding
"errors" and we ignore them. 
Present value tables are to be used for text book problems and exam problems (Yes, you
will receive necessary tables). Some cases (or real life situations) involve
interest rates such as 7.25%, compounded semi-annually (a typical bond - see Chapter 13).
In cases like that you use either the computer spreadsheet program or a calculator
with present value capabilities.
At this time, however, it is important that you learn the concept and not "data
entry" and therefore I will only give you credit if your answer is written in the
equation form shown above. |