Discounting Methods

Discounting involves converting future cash flows into their present value. This process is called discounting the cash flow, and the interest rate used for this purpose is known as the Discount Rate.

When discounting or compounding a cash flow, an implicit assumption about the timing of the cash flow is made. Typically, it is assumed that the compounding or discounting period is once per year. Under such circumstances, it is assumed that an initial amount exists as of today, and interest is received (or paid) on it at the end of one year. The cash flow is presumed to occur at the end of the year. For instance, if we have $100 today, we compound it for one year at an applicable interest rate. If the applicable interest rate is 10%, it compounds to $100 x (1 + 10%) = $110.

Therefore, if we have an amount of $110 at the end of one year, we can bring it to today's value by discounting it for one full year at 10%, which results in $100 = $110 / (1 + 10%).

Now, consider that the interest is compounded biannually at the same annual rate of 10%. In this scenario, $100 will grow to slightly more than $110. The formula used is $100 x (1 + 10%/2)^2. The compounding period is now 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 discounting a cash flow, 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.

Upon initial inspection, the formula for mid-year discounting 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. Illustrating this on a timeline may provide greater clarity.

There are various assumptions regarding the timing of cash flows. One assumption is that cash flows occur monthly throughout the year. Alternatively, in an 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. 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 interest rate or discount rate, rather than employing this complex formula.

In the Oil and Gas upstream sector, continuous compounding is rarely used for discounting purposes. This information is provided to familiarize you with these methods. However, their practical application in petroleum economics is minimal.