Introduction to Oilfield Economics: Discounting – Part II
Posted by D Nathan Meehan February 11, 2011
Category: Oilfield economics   |  Tags: , , , , ,

#### Discounting Monthly Cash Flows

One method of discounting monthly cash flows is to use the number of years (a non-integer) corresponding to those months and use the annual discount factor. Another alternative is to use a monthly discount rate and to use the integer months for the calculation. In this latter example, there are two common methods to convert the annual discount rate to a monthly discount rate. In the first, the “APR” or “Annual Percentage Rate” familiar from home loans and credit cards is used. The other is the “effective monthly interest rate.” This approach results in the compounded monthly interest rate being equal to the annual interest rate.  A simple example of these approaches follows. The annual discount rate used is 10% with 12 monthly cash flows of \$1000 to be discounted using the end-of-period approach. Method A uses the non-integer years approach and the first month’s discounted cash flow would be: In Method B (the APR approach) the monthly interest rate would be 0.1/12 or 0.8333%. In Method C (the effective monthly interest rate approach) the monthly interest rate is calculated from: Or ln (1.1)/12 or 0.7943%. In these last two methods the first month’s cash flow would be calculated as: The APR method is more intuitive, while the effective monthly rate approach is closer to the annual approach, particularly when mid-period discounting is used.

 Annual discount rate 10% Monthly discount rate APR 0.8333% Monthly discount rate effective 0.7943% Month Years Cash flow Method A (monthly, non-integer) Method B (monthly, APR) Method C (monthly, effective) 1 0.083 \$             1,000.00 \$              992.09 \$             991.74 \$          992.12 2 0.167 \$             1,000.00 \$              984.24 \$             983.54 \$          984.30 3 0.250 \$             1,000.00 \$              976.45 \$             975.41 \$          976.55 4 0.333 \$             1,000.00 \$              968.73 \$             967.35 \$          968.85 5 0.417 \$             1,000.00 \$              961.07 \$             959.36 \$          961.22 6 0.500 \$             1,000.00 \$              953.46 \$             951.43 \$          953.64 7 0.583 \$             1,000.00 \$              945.92 \$             943.56 \$          946.13 8 0.667 \$             1,000.00 \$              938.44 \$             935.77 \$          938.67 9 0.750 \$             1,000.00 \$              931.01 \$             928.03 \$          931.28 10 0.833 \$             1,000.00 \$              923.65 \$             920.36 \$          923.94 11 0.917 \$             1,000.00 \$              916.34 \$             912.76 \$          916.66 12 1.000 \$             1,000.00 \$              909.09 \$             905.21 \$          909.43 \$           12,000.00 \$        11,400.49 \$       11,374.51 \$    11,402.78

At higher discount rates, the methods result in greater differences.

#### Period DiscountingAssuming that all cash flows occur at the end of the time period (end-of-period, or EOP) is the most conservative approach for positive cash flows and the most optimistic one for negative cash flows. Annual end-of-period (ANEP) is still widely used; however, mid-period (MP) discounting (assuming that all cash flows occur in the middle of the time period) has become increasingly common. While mathematically possible, beginning-of-period discounting is unusual and not recommended.

In the previous discussion of discounting approaches, the non-integer annual rate method and two monthly rate approaches were used that illustrated monthly EOP approaches. To do the exercise with MP discounting, the years in case A would be lowered by 1/(2*12) or 0.042.  The integer months would be changed from 1, 2, 3…12 to 0.5, 1.5, 2.5…11.5.

 See the SPE recommended practices for more detail.

3 responses | Add Yours

## Responses Rodolfo Galecio says:

The fact that at higher discount rates we get meaningful differences between these approaches leads to the question: what is the right one? or perhaps what could be the selection criteria to be used? Rodolfo Galecio says:

It’s quite interesting that we get higher numbers when we recalculated this exercise using the mid-period approach, what’s the meaning of this result? the time-related value of our cash flow values is less affected in this way? D Nathan Meehan says:

Mid-period discounting essentially approximates the cash flows as you receiving all of the cash at the middle of each tie period…. annual end-of-period assumes that you receive the cash at the end of each year. Thus, for positive inflows mid-period has a higher NPV becasue you get the money sooner. Of course this suggests that the most accurate and relevant discounting isn’t either approximation, but the method that most closely resembles how cash flows are actually received.

The differences in Annual EOP and MP are larger than those for monthly—so the problem becomes less significant than in the illustration.