It is commonly said that money has a time value. This is self-evident. Would you prefer to have $1,000 paid to you annually for the next thirty years or to receive $30,000 today? While there may be certain circumstances where the delayed payments are preferable, it is generally obvious that a dollar received today is worth more than a dollar received in the future, assuming that the current and future dollars have the same tax impacts. The concepts of discounting and compounding are closely linked. Most people readily understand the concept of compounding and that if a sum of money (say $100.00) is put into a bank account that pays 5.0% interest that in one year’s time the future value (FV) of the $100.00 would be $105.00. At the end of two years, the FV would be $110.25. There are of course variations on compounding and not all 5.0% interest rates are created equally. The general relationship for compounding is:
FV = PV (1+i)n
The value i is called the compounding rate and is used to compound present values to determine future values. The compounding rate is often referred to as the interest rate. Interest rates are intrinsically associated with lending and discussions of interest rates are often confused with the specific financial instruments, monetary policy, inflation issues, etc. Some of the economic indicators (GRR) we will discuss require compounding and it is more appropriate to use the compounding rate than the term interest rate for such indicators.
Discount rate has a specific meaning in the realm of oil and gas evaluation which is different than other common meanings. Discount rates are those rates used to convert future values to present values. Evaluations often use more than one discount rate and the calculation of PVs as a function of discount rate is common. Most oil companies (or banks, regulators, investors and others who review evaluations and recommendations) have one or two specific interest rates that are considered. There is also a particularly important discount rate used by corporations known as the weighted average cost of capital (WACOC).
The present value of a series of discrete cash flows over n time periods at a given discount rate i, is calculated as:
The time periods can be any convenient ones but should be consistently applied and clearly stated. Annual discounting is common for long lived projects, particularly for those with slowly changing cash flows over time. Monthly discounting may be as (or more) common place than is annual discounting. The following section discusses the specific discount approaches and their relative merits.
Is there a “correct” discounting method? While some may not agree, there is in fact a “best” method and that is a discounting method that most nearly approximates the actual cash flows. If payments are made annually on a given anniversary date (as in a typical lottery payment) then annual discounting (specifically annual end-of-period discounting) exactly models the cash flow and would be the most accurate way to value that cash flow stream.
Because of accounting practices along with production reporting practices, many analysts argue in favor of monthly discounting. In evaluations of properties with rapidly declining (or increasing) cash flows over a short time period near the beginning of the evaluation, monthly discounting will more accurately rank projects than will annual discounting. But if monthly is better than annual, why not weekly, daily, or by the microsecond? Cash flows received from oil and gas operations might well be as infrequent as monthly but in fact are nearly continuous.
In the case of continuous discounting of future cash flows:
Where λ= ln (1+i). Continuous discounting methods applied to discrete cash flows have a simple relationship and the continuous discounting approach is simply a variation on the discount rate used. The technique is most helpful in cases where the cash flows can be described analytically as continuous functions and its use is relatively uncommon in oil and gas evaluations.
Because monthly discounting is so widely used, several characteristics of evaluation approaches should be discussed including:
Some analysts use the actual days per month corresponding with the specific calendar dates of the evaluation including leap year.  Others use equally sized months and account for leap year by using years of length 365.25 days. A month would then have 365.25/12 days or 30.42 days per month. For the purpose of ranking and evaluating oil and gas investment decisions, these methods are generally identical. In the calendar-correct approach, the variations in days per month will result in variations in estimated volumes per month that would look a bit odd if portrayed graphically with equal spacing for months. Graphical displays should reflect elapsed days or account for monthly spacing properly. Similarly, cost estimates based on so many $/month per well or per facility would lead to slightly odd cash flow estimates, particularly as the project reaches the economic limit. These can all be resolved and neither method is radically better than others. The method used must be communicated clearly.
In this blog, some examples (such as the SPEE examples) use 365.25 days per year and equally sized months. Reservoir simulation output such as the tight gas example will tend to use the actual calendar days. In the latter case, an operating expense of X $/month could be treated as (X/30.42)*actual days in each month. Either method is may be sufficiently accurate. Consistency and clearly stated assumptions are important.
 Other meanings deal with the interest rate charged to banks for short-term borrowing directly from the Federal Reserve, fees charged for accepting credit cards, etc.
 A few go so far as to reflect the 23- and 25-hour days corresponding with changes for Daylight Savings Time, a detail that most analysts ignore in property evaluations.