Key economic parameters for decision making

When the purpose of an economic analysis is to help make a decision, there are several key managerial indicators or economic parameters that are considered. Although there are many parameters that can be considered (see Thompson and Wright, Chap. 3), the most common decision criteria are:

• Net present value
• Internal rate of return
• Profit-to-investment ratio (both discounted and undiscounted)

Net present value

Net present value is the sum of the individual monthly or yearly net cash flows after they have been discounted with Eq.1. In Table 1, the three columns labeled "Discounted Net Cash Flow" show this calculation at annual discount rates of 10, 20, and 34.3%. The net present values (NPV) at these discount rates are $99,368, $51,950, and $0, respectively. In this table, the NPV were calculated on a monthly basis using effective-monthly interest rates converted from annual rates with Eq.2.

After the discounting method has been specified, there is still the question of what discount rate to use. The author recommends the company’s average investment opportunity rate (see Thompson and Wright, pages 3-7 and 3-8 and Newendorp and Schuyler, pages 9 through 12). The average investment opportunity rate is the interest rate that represents, on average, the return of the future investment opportunities available to the company. This is the rate at which the treasury will grow. An alternative interest rate is the weighted average cost of capital (WACC). This is an interest rate that, as the name indicates, is the average of the cost of each source of financing weighted by the fraction of the total financing that source represents. Sources of financing include debt, which has an explicit interest rate associated with it, and equity, which has an implicit cost associated with attracting and retaining investors. The average investment opportunity rate and the weighted average cost of capital are often very similar to each other and often much lower than the typical "hurdle rates" used in the industry.

The use of high discount rates to account for risk is not recommended. Much has been written about the fallacy of using high discount rates (see, for example, Capen). Other pages deal with decisions under uncertainty.

The decision criterion using net present value is very simple. For project screening, all projects with a positive NPV at the company average investment opportunity rate are acceptable. If the projects with a positive NPV perform as projected, they will return more to the treasury than the average company project will return. In the case of mutually exclusive alternatives, where choosing one alternative precludes choosing another, the alternative with the highest NPV should be chosen. An example of mutually exclusive alternatives might be choosing between injecting CO₂ or high- pressure air as a secondary recovery method—only one or the other may be chosen, not both.

....................(1)

....................(2)

Internal rate of return

Internal rate of return (IRR) has been a popular managerial indicator since the 1950s, and it is still widely used today. IRR is defined as that interest rate which, when used in the calculation of NPV, causes the NPV to be zero. In Table 1 that interest rate is 2.488% per month or 34.30% per year. Notice that, once again, we are using the effective monthly interest rate and, therefore, must use Eq.2 to convert to annual interest rate.

IRR can easily be used to screen projects. If the IRR is greater than the average investment opportunity rate, the project passes the screen. However, the unwary might be trapped in a situation where two mutually exclusive projects are being compared. Many evaluators have a tendency to think that the project with the larger IRR is the better project. This is not necessarily so. If IRR is used to compare two mutually exclusive projects, it is necessary to calculate the IRR on the incremental capital used for the project with the larger investment. Although this can lead to the correct decision, the procedure is tedious enough that it is easier to just compare NPVs at the average investment opportunity rate. Choosing the project with the higher NPV, at the average investment opportunity rate, leads to the same decision as calculating incremental IRR.

• 

  Table 1

• 

  Table 1

Multiple rates of return

Under certain circumstances there may be more than one interest rate that will cause the NPV to be zero. This is referred to as multiple rates of return and occurs primarily in the evaluation of acceleration projects. As stated by Phillips, an acceleration project is "one in which money is invested, not necessarily to show a profit but to decrease the time required to obtain the income from a project. In fact, acceleration projects will generally result in a net loss." An example acceleration project might be a decision to downspace from 80 acres to 40 acres in a coalbed methane field. In this hypothetical case, virtually the same amount of gas is expected to be produced over a shorter time period, yet there is a large investment to drill the additional wells. When the infill project is evaluated on an incremental basis, the cash flow stream is negative then positive and then negative again, as shown in Table 2. On an undiscounted basis, the project loses money. The only justification for doing the project (in this hypothetical case) is to "accelerate" the cash flows, so the company can invest them elsewhere.

• 

  Table 2

The number of sign changes in the cash flow stream is the number of potential values for IRR. In Table 2, there are two sign changes (negative to positive in year one and positive to negative in year six), so there are two values of IRR.

Evaluating acceleration projects

The key to evaluating acceleration projects is again to examine the NPV of the project at the company average investment opportunity rate. The rationale for accelerating the cash flows is to invest them elsewhere, so you must know what you are going to do with them (on average). If the NPV of the project is positive at the company average investment opportunity rate, then you can profitably invest the accelerated cash flows elsewhere. If the NPV is negative, you are better off not accelerating the cash flows. Table 2 also illustrates how sensitive some of these projects can be to the company average investment opportunity rate. This project is only profitable at interest rates between 1.2 and 12.9%, as shown in columns E and F. The discounted net cash flow is zero at those interest rates. You would have to be very sure of the numbers to invest $2,500,000 to return $15,374 more than average projects.

Several years ago, a spirited discussion appeared in the literature sparked by E.L. Dougherty’s paper on discounted cash flow rate of return. This discussion presents a good analysis of different points of view.

Discounted profit-to-investment ratio

Discounted profit-to-investment ratio has been touted by R.D. Seba as "the only investment selection criterion you will ever need," in his paper of the same name. This paper and the various discussions of it present a good discussion of the method. Mechanically, profit-to-investment ratio is calculated by dividing the sum of either the net operating income or the net cash flow from a project by the sum of the investments. If undiscounted numbers are used, the result is an undiscounted profit-to-investment ratio; if discounted numbers are used, the result is a discounted profit-to-investment ratio. If net operating income is used in the numerator, a value of 1.0 is a breakeven value where the investment is just recovered. If net cash flow is used in the numerator, a value of 0.0 is a breakeven value. Either definition is appropriate for the numerator, as long as it is clearly stated which definition has been used.

Discounted profit-to-investment ratio at the company average investment opportunity rate is indeed a powerful selection and ranking tool, as stated by Seba. As a selection tool, all projects with a value greater than 1.0 (or 0.0) would be selected. In the presence of limited capital, the projects are ranked in decreasing order of discounted profit-to-investment ratio and selected until the capital available for investment is exhausted. This very simple tool results in the portfolio of projects that causes the treasury to grow at the fastest rate, if the projects perform as expected. Erdogan et al. pointed out that "this approach maximizes expected value but ignores risk. In fact, funding projects with the highest discounted P/I will tend to produce a high-risk portfolio." This is a valid criticism and is addressed at length in portfolio analysis.

The example in Table 1 can be used to demonstrate the calculation of profit to investment ratio.

Example 1

Profit-to-Investment Ratio from Table 1

Total undiscounted net operating income = $585,369. Total undiscounted investment = $425,000. Total undiscounted net cash flow = $160,371. Total investment discounted at 10% = $425,000 (because only one investment was made and that was at time 0). Total net cash flow discounted at 10% = $99,368. Total net operating income discounted at 10% = $99,368 + $425,000 = $524,368.

....................(3)

Alternatively,

....................(4)

Using discounted values,

....................(5)

Again, alternatively,

....................(6)

Nomenclature

F	=	future lump sum of money
i	=	the periodic interest rate
n	=	the number of periods for interest calculations or the hyperbolic exponent for decline curve equations
P	=	present lump sum of money

Noteworthy papers in OnePetro

Lehman, J. 2012. What the Mating Behavior of Birds Can Teach Us About Corporate Decision Making. Society of Petroleum Engineers. http://dx.doi.org/10.2118/162668-PA

External links

Use this section to provide links to relevant material on websites other than PetroWiki and OnePetro

See also

Time value of money

PEH:Petroleum_Economics

Page champions

Russell S J Krasey - P.Eng