Field Roebuck
Roebuck Associates Inc.
Dallas
With only two commonly used constraints, a relatively simple procedure can be used to develop the information most often used for establishing a value for oil or gas properties.
This procedure reduces significantly both the data preparation time and the actual calculations.
The method can even be used with a hand calculator, if that is ever necessary or required. Or it can be adapted easily for use on a microcomputer.
What are the two commonly used constraints?
First, this method can be used only with constant product prices and lease operating costs (and a constant ratio for any second product).
These are common enough assumptions for many evaluations.
Second, the calculation procedure is valid only for a well or property with a producing rate that is expected to exhibit an exponential, constant percentage decline. Again, this is a typical characteristic of many oil wells and is, undoubtedly, the most common assumption used for the projection of future producing rates.
PROPERTY VALUATION
Times and tax regulations being what they are, much of the available oil and gas investment monies are going into the purchase of producing properties, either by direct negotiation or by participation in some type of auction.
Because at least two parties are involved in each transaction, many professionals find themselves spending a great deal of time evaluating producing properties either for purchase or for sale. They all wish for a faster means of accomplishing the task.
One of the most common procedures for arriving at a value for a property consists of first estimating the future annual production with a constant percentage, exponential decline curve. Then a complete cash flow table is constructed to arrive at the future annual cash flows and, ultimately, the discounted present value.
Although most of these calculations can be done with spreadsheets or readily available microcomputer programs, considerable time and effort can still be required, especially if a large number of individual wells or leases are being evaluated.
For property sale or purchase, the total future gross production, the net production, the ultimate net cash flow, and the discounted present value of the total net cash flow are usually sufficient to establish a value for the property.
If this is the case, then why calculate an entire cash flow table? Why not calculate, at least on a preliminary basis, only these final, total numbers? This can be done directly, swiftly, and with a lot less work than is typically needed to construct an entire cash flow table.
For an exponentially declining rate of production, the producing rate after some time, t, can be calculated from the initial rate, qi, and Equation 1 in the equation box. The time required for the producing rate to decline from the initial rate to the later one is given by Equation 2.
In these two well-known equations, D is the exponential decline constant, which can be obtained from the annual percentage decline, P, with the relationship of Equation 3.
Another well-known exponential relationship is that of Equation 4, which yields the total production, N,, as the rate declines from qi to qt.
It should also be noted that, for the case of a constant net product price, these four exponential relationships can be used with rates of revenue as well as with rates of production.
EXAMPLE CALCULATION
To illustrate the use of these relationships and, ultimately, to demonstrate a shortcut method for the swift evaluation of a producing property, consider the following example well:
- Working interest=100%
- Revenue interest=80%
- Producing rate=85 bo/d
- Decline rate=28%/year
- Net oil price=$18.75/bbl (constant)
- Operating cost= $1,200/month (constant)
- Discount rate= 15%/year
First, an evaluation requires the calculation of the economic limit; that is, the ultimate abandonment rate where income equals expenses:
(qt)(0.80)($18.75)
(30.4 days/month) = $1,200
therefore:
qt = $1,200/456 = 2.63 b/d
Second, the exponential decline constant can be obtained from Equation 3:
D = ln[100/(100 - 28)]
0.3285/year
Third, the remaining well life (the time for the rate to decline from 85 bo/d to 2.63 bo/d) and the total future production can be calculated with Equations 2 and 4, respectively:
t = ln(85/2.63)/O.3285
10.58 years
Np = (85 - 2.63)(365)/
0.3285=91,522 bbl
Note that here the daily producing rates have been converted to annual rates because the decline constant, D, is a "per year" constant.
From this point, the standard approach to arriving at a value for this well would be to calculate (by hand or by computer) the entire cash flow table, including the future annual production, income, expenses, and net cash flow. Then each of the future annual net cash flows would be discounted and summed to arrive at a total net present value for the future life of the well, using either point-in-time or uniform-flow discount factors.
With continuous compounding/discounting (that is, "Your money is compounded continuously"), the point-in-time discount factors, DFi, at some nominal annual discount rate, i, are given by Equation 5. The continuous, uniform-flow discount factors are given by Equation 6.
For the shortcut method of evaluation, neither of these discount factor equations are used directly, but two additional relationships are needed. One discounts a value that remains constant over time, such as operating costs; a second discounts a value that is declining exponentially, such as the revenue from production.
The point-in-time discount factor equation, Equation 5, can be integrated over a period of years from today (time zero) to some time, t, in the future. This yields the first needed relationship Equation 7, which can be used to discount any amount that occurs at some uniform, constant rate over a period of time.
For the example well, the total operating costs over the 10.58-year life amount to:
($1,200) (12) (10.58)
$152,352
And, from Equation 7, the discounted present value (at 15%/year) of these future operating costs, is:
PVI 5 = ($1,200) (12) [(l - e (0.15)(10.58))
/0. 1 51 = ($1,200) (12) (5.3031) = $76,365
The second necessary relationship, Equation 8, can be developed by multiplying Equation 1 by Equation 5 and integrating over time from time zero to time t years in the future. Now, if qi is an exponentially declining rate of revenue or income, the discounted present value of the total future revenue over some time, t, can be obtained directly from Equation 8.
For the example well, the beginning rate of net interest revenue is:
Revenue = (0.8)(85)
($18.75) = $1,275/day
And net interest revenue over the 10.58-year life of the well, from Equation 4, is:
Total revenue= [($1,275)
(30.4) - $1,200](12)/
0.3285 - $450,720/0.3285 $1,372,055
Then, using Equation 8 and with D+i-0.3285+ 0.15=0.4785 the present value of this total revenue is:
PV15 = ($1,275)(365)
l(i -e - (10.58)(0.4785))/
(0.4785] - ($1,275)(365)
(2.0766) = $966,398
Because the total revenue and the total operating costs have now been calculated, along with their respective present values, then the final net cash flow and its net present value can be obtained by simple subtraction:
NCF = $1,372,055 $152,352 - $1,219,703
PV15 NCF=$966,398$76,365 = $890,033
This establishes the basis for the property value (see Summary box).
Using these same exponential relationships, additional flexibility can be added. For instance, a period of constant rate production (with a constant rate of net cash flow) prior to the decline period can be inserted, and the discounted present value of the net cash flow for that period can be determined with Equation 7.
Following this, the previously calculated present value of the declining-rate period can be pushed to the appropriate time in the future with an additional discount factor from Equation 5. For instance, consider that this well is expected to produce at the rate of 85 bo/d for 18 months (1.5 years) before beginning its decline. Then the net cash flow during the constant rate period would be:
NCF = [($1,275) (30.4)
$1,200] (18) = [$37,560] (18)
$676,080
And present value of the constant-rate net cash flow, from Equation 7, would be:
PV15 NCF = ($37,560)
(12)[(l - e(0.15)(1.5))/O. 15]
$605,418
Then, the total future net cash flow can be calculated:
Total NCF=NCFconstant+
NCFdecline = $676,080+
$1,219,703 = $1,895,783
The total present value of this net cash flow can be obtained in the same manner, with the present value of the net cash flow during the decline period pushed forward for 18 months with a point-in-time discount factor in Equation 5:
Total PV15 NCF=
PV15 NCFconstant+PV15
NCFdecline = $605,418 +
[($890,033)(e (0.15)(1.5)
$605,418 + $710,706
$1,316,124
These evaluation results, with a beginning constant-rate period, are also summarized in the box.
Of course, this same technique can be applied to the evaluation of a drilling prospect. In either case, the relationships of Equations 7 and 8, with an exponentially declining well and constant prices and costs, can be used to make swift work of an otherwise tedious task of evaluation.
Copyright 1991 Oil & Gas Journal. All Rights Reserved.
