Discounting Methods

Cash flow discounting involves converting future cash flows into their present value. This process, known as discounting the cash flow, utilizes an interest rate referred to as the discount rate.

When engaging in cash flow discounting or compounding, an implicit assumption regarding the timing of the cash flow is made. Typically, it is assumed that the compounding or discounting occurs once per year. Under these circumstances, it is presumed that an initial amount exists today, and interest is either received or paid at the end of one year. The cash flow is expected to take place at the end of that year. For instance, if we start with $100 today and apply an applicable interest rate of 10%, it compounds to $100 x (1 + 10%) = $110.

Thus, if we have $110 at the end of one year, we can determine its present value by discounting it for one full year at 10%, resulting in $100 = $110 / (1 + 10%).

Now, consider a scenario where the interest is compounded biannually at the same annual rate of 10%. In this case, $100 will grow to slightly more than $110. The formula used for this cash flow discounting is $100 x (1 + 10%/2)^2. Here, the compounding period is two instead of one, and the interest rate for each compounding period is 5% (10%/2). The general formula for more frequent compounding is provided below:

When engaging in cash flow discounting, it is essential to ascertain the timing of the cash flow being discounted. Are we discounting the cash flow that occurs at the end of the period or the one that occurs at the beginning of the period? Sometimes, cash flows are presumed to occur in the middle of the year. Below, we present general formulas for some common discounting assumptions and how they relate to the discount rate used in present value calculations.

Upon initial inspection, the formula for cash flow discounting at mid-year may appear unconventional. However, it is straightforward to elucidate. Consider we are in year 2; the cash flow for year 2 occurs in the middle of that year. Therefore, the period for discounting is not 2 years but rather 1.5 years (= 2 - 0.5). The cash flow for the second year takes place at 18 months (1.5 years) from the beginning, not at the 24th month. To perform a present value calculation, illustrating this on a timeline may provide greater clarity in understanding the impact of the discount rate.

There are various assumptions regarding the timing of cash flows, particularly in the context of cash flow discounting. One common assumption is that cash flows occur monthly throughout the year. Alternatively, in a more extreme scenario, continuous compounding may be assumed (and thus continuous discounting), where it is presumed that cash flows occur continuously throughout the year. Below, we provide the formula for the discount factor applicable to this situation, which is essential for accurate present value calculations. Due to the mathematical complexity involved, we will not discuss the derivation of these formulas.

We recommend modifying the model periodicity to monthly and applying a standard discount using the equivalent monthly discount rate for cash flow discounting, rather than employing this complex formula for present value calculation.

In the Oil and Gas upstream sector, cash flow discounting is rarely performed using continuous compounding for present value calculations. This information is provided to familiarize you with these methods. However, the practical application of these discount rates in petroleum economics remains minimal.