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Present Value...
The reason why we don't use future value
techniques in the petroleum industry (and many other industries) for
financial analyses is that future values can be quite cumbersome to
calculate if cash flows are not the same every year. To minimize the
calculations, especially in the days before computers became popular,
financial theorists invented a concept that converted future values
into present values.
To go from future value to present value, we should go through a bunch
of financial theory, but I'm going to skip most of it. I believe your
business intuition will already convince you of the importance of the
present value technique as I introduce it. If you would like to do
some more study, business schools or libraries have financial
textbooks that can explain the theory to you, which may be helpful if
you ever want to study more advanced financial techniques.
You probably have heard these two common business idioms: (1) "Time is
money," and (2) "A dollar earned today is worth more than a dollar
earned tomorrow." These two idioms are actually qualitative present
value techniques, albeit very simplistic versions.
What present value says is that "cash flows in the future are worth
less than cash flows in the present." To quantify how much "less
worth" future cash flows are, the present value technique discounts
future cash by a factor between zero and one. The longer into the
future, the greater the discount.
Present value techniques also state that the discount grows by a
consistent rate. The formula used is:
DF = (1-dr/100)n
where:
● DF is the discount factor (no units)
● dr is the discount rate expressed in % per time step (the time step
is usually in years).
● n is the number of time steps (usually in years).
For example, if the discount rate is 5%, a cash flow one year later
will be discounted by a factor of 0.9500 [(1-5/100)1]
To add to this example, a cash flow two years later will be discounted
by a factor of 0.9025 [(1-5/100)2]. What this says to you
is that $1000 two years from now is worth about $902 in today's
money-if your alternative investment opportunities can indeed provide
you a 5% return.
Let's go back to the example
we did in the future value calculations for our $800 in the first year
vs. $100 a year for ten years. The two present value tables are as
follows:
|
Year |
Discount Factor |
Investment |
Present Value |
|
1 |
1.0000 |
800 |
800 |
|
2 |
0.9500 |
0 |
0 |
|
3 |
0.9025 |
0 |
0 |
|
4 |
0.8574 |
0 |
0 |
|
5 |
0.8145 |
0 |
0 |
|
6 |
0.7738 |
0 |
0 |
|
7 |
0.7351 |
0 |
0 |
|
8 |
0.6983 |
0 |
0 |
|
9 |
0.6634 |
0 |
0 |
|
10 |
0.6302 |
0 |
0 |
|
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Sum: |
800 |
Table 4. Present Value of $800
invested in Year 1 for ten years at 5% discount rate.
|
Year |
Discount Factor |
Investment |
Present Value |
|
1 |
1.0000 |
100 |
100.00 |
|
2 |
0.9500 |
100 |
95.00 |
|
3 |
0.9025 |
100 |
90.25 |
|
4 |
0.8574 |
100 |
85.74 |
|
5 |
0.8145 |
100 |
81.45 |
|
6 |
0.7738 |
100 |
77.38 |
|
7 |
0.7351 |
100 |
73.51 |
|
8 |
0.6983 |
100 |
69.83 |
|
9 |
0.6634 |
100 |
66.34 |
|
10 |
0.6302 |
100 |
63.02 |
|
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Sum: |
802.53 |
Table 5. Present Value of $100 a year
for 10 years at 5% discount rate.
Note that in both tables, the present value for each year is added
to create a total present value.
In Table 4, the $800 invested in the first year investment, shows a
total present value of $800.00. We only had cash flow in the first
year, and there was no discount for the first year.
In Table 5, the present value of the $100 a year for 10 years is $802,
slightly more than the present value of getting $800 in the first
year. These values tell us that the $100 a year for ten years is a
slightly superior investment, which is what the future value
calculation that we did earlier also told us.
Similar to the future value techniques, you can use total present
value calculations to compare two or more investment opportunities.
Download
an EXCEL spreadsheet to calculate PVs in OilFinanicer.
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