Present Value

Posted by D Nathan Meehan March 8, 2011

Present Value (PV) is particularly useful in ranking comparably sized projects with similar investment requirements. *Net* Present Value (NPV) refers to the total of all cash flows to (and from) a given party. It can be a pre-tax or after-tax number. The terms PV and NPV are often used interchangeably with some companies using NPV for after-tax calculations. A specific discount rate is also associated with NPV and that rate (expressed as an annual percentage) is often appended as in NPV10 to mean the net present value at a 10% discount rate.

In the following example, a series of cash flows are compared using the evaluation tools we have discussed so far. Each project has a “time zero” investment *that is not discounted*. A common error among spreadsheet users is to discount all cash flows using (in the case of Microsoft Excel) functions like NPV which will discount the first cash flow by one time period[1]. Time zero cash flows must be added (or subtracted) from the discounted cash flows in a spreadsheet approach. These functions often employ EOP discounting. To use another method the actual discount factors or equations would need to be included.

ANNUAL CASH FLOWS |
|||||

YEAR | Project A | Project B | Project C | Project D | |

0 | -1000 | -1000 | -1000 | -5000 | |

1 | 500 | 100 | 600 | 3000 | |

2 | 500 | 100 | 500 | 2500 | |

3 | 500 | 1400 | 400 | 2000 | |

Undiscounted total | 500 | 600 | 500 | 2500 | |

NPV15 | ANEP | $141.61 | $83.09 | $162.82 | $814.09 |

Payout | (years) | 2 | 2.5 | 1.8 | 1.8 |

NTIR | 1.5 | 2.57 | 1.5 | 1.5 |

In this case NPV15 ranks project A, B and C fairly as does simple payout. NTIR suggests B is the best project but few people would select B over A or C. Project C is superior to A or B at all discount rates above 7 percent. At lower discount rates (*e.g.* 5%) project B is ranked ahead of project C for both NTIR and NPV.

NPV has a number of significant advantages as an economic indicator. These include an indicator of the total wealth being indicated. Unlike DCFROI, it is not a trial and error solution. Even complex cash flows yield unique solutions without the possibility of multiple solutions. It is easy to use with probabilistic analyses and in the course of conventional risk analysis. It can be used to compare alternatives when all cash flows are positive or all cash flows are negative. It fairly evaluates lease *vs.* purchase decisions and forms the basis of evaluation of oil and gas properties.

NPV’s greatest drawback is that it does not indicate the rate of cash generation and investment efficiency. Project D in the prior example looks superior to all other methods at all discount rates based solely on NPV. Project D is, of course, just five times project C. Its greater NPV is due solely to the larger investment. NPV alone cannot rank such projects fairly. Economic parameters that incorporate investment efficiency are required.

In calculating NPV, the appropriate source of the cash flows is net Cash Flow or NCF. It is inappropriate to calculate NPV based on financial book profit (net income), or cash flow from operations. Net income is not the equivalent of NCF and CFOPS does not incorporate the relevant cash outflows for investments in fixed or working capital.

In the SPEE example a series of assumptions were provided that can be used to illustrate the differences between various discounting approaches. The cumulative undiscounted cash flow is $4,914,952. While there is no end point specified in the table, the economic limit can either be calculated in advance or identified based on the monthly calculated cash flows. To calculate it in advance with complexly varying escalations and changing net interests may not be practical. However, in this case, we can calculate it as:

Economic Limit = MONTHLY OPEX/(Oil price*(NRI)*(1-SEV)) or

= 2000*/(25*0.85*(1-0.1) = 104.58 BOPM

For an average month, this results in 3.43 BOPD. The time to abandonment can then be calculated from the hyperbolic decline equation.

Substituting these values results in 37.17 years. While it is *often *possible to perform this calculation in advance, in practice many analysts prefer to make monthly or annual forecasts and simply cut off production when cash flows become negative. Analysts should be cautious about making such determinations and have realistic understandings of the actual nature of operating expenses. It is not obvious from a lease P&L (Profit and Loss) statement which expenses are fixed and which are variable, which of the variable expenses are phase dependent and what the correct forecast is. It is not the historical expenses that are critical in an evaluation, it is the future ones. In many cases a single well having a negative cash flow does not cause operators to immediately shut-in or abandon the well. The monthly operating costs might not decrease by the estimated amounts as (for example) the salary of a pumper watching thirty wells doesn’t decrease if one is shut-in or abandoned. In some cases the operating costs vary by volumes of produced fluids, by groups of shared facilities, offshore platforms, gathering systems, etc.

In the SPEE case we calculate NPV for both monthly and annual forecasts of the production and calculate both NPV and DCFROI. NPV10 is calculated using each of the methodologies discussed. These various approaches make significant impacts on the DCFROI as well as NPV. The SPEE recommended evaluation practice is:

*“The methodology used for discounting should be discussed in either the cover letter or body of the reserve report in such a manner that the user of the report can easily understand the assumptions used. Suggested language for the discussion would be “The cash flows in this report were determined on a monthly basis and discounted using an interest rate of X% per annum compounded annually. Cash flows for a month were assumed to occur at the end of the month in which the hydrocarbon was produced.*

*Cash flows calculated on an annual basis should be discounted using midperiod discounting. The cover letter or body of a reserve report incorporating annual cash flows should discuss the methodology used in a manner that leaves the user of the report with a clear understanding of the issue. Suggested language for the discussion would be: “The cash flows in this report were determined on an annual basis and discounted using an interest rate of X% per annum compounded annually. Cash flows resulting from production for a period were assumed to occur at the middle of the period in which the hydrocarbon was produced.*

*Regardless of whether the cash flows from production are modeled monthly or annually, lump-sum cash flows, such as a lease bonus, property purchase, or major investment which will occur at a given date, should be modeled at the date of anticipated occurrence.”*

*_________________________________________________________________________________________________** *

*It is not the historical expenses that are critical in an evaluation, it is the future ones. In many cases a single well having a negative cash flow does not cause operators to immediately shut-in or abandon the well.*

[1] So if the “time zero” cash flow of negative -1000 appears in A1 and annual positive cash flows of 300 each appear in A2 through A6, the correct EOP discount method is not =NPV(0.1,A1:A6) or $124.76, it is =NPV(0.1,A2:A6)+A1 or $137.24. ANMP results in a higher NPV10 of $192.74. This is because the positive cash flows (of $1500) are discounted one half year less (roughly speaking) using ANMP than ANEP.

4 responses | Add Yours

## Responses

In order to compare different projects how to included in a single parameter, an improved NPV, investment efficiency considerations? What is the difference between NCF and Net income?

I have an entire series planned in this matter. Clearly though, the NPV ratio is the “best” of the investment efficiency parameters if you are going to use only one.

I will also discuss net income and other accounting measures. These are completely different than net cash flow. You can think of NCF as the corporate checkbook….the actual cash being spent and received. Net income is an accounting measure that uses a series of rules to allocate expenses and revenues to certain time periods that are often very different than when actually received or spent. A simple example of this is the purchase of equipment (say a pumping unit)…the net cash flow would record the cost based on when the unit was purchased. For net income purposes, the unit would be depreciated over a certain number of year according to an appropriate scheme (straight-line, declining balance, etc). Thus the costs would be “matched” with the revenues the pump would help generate.

For petroleum economic evaluation purposes it is almost always the case that we should use the actual cash flows for decision making.

Again, I have quite a few remaining blog entries scheduled in this area. Thanks for your interest.

Thanks for answering Mr. Meehan, this is a good opportunity to get first-hand experience on this subject, your blog offers a deeper insight which improves our understanding on this area. Thanks again!

Excellent blog. It’s interesting that certain types of investors (equity or debt) have differing return requirements. Debt (banks) are interested in coverage ratios to meet principal and interest expenses… usually lower discount rate. Equity (private equity, i-banks, etc.) have much higher return requirements. Likewise, some investors are interested in free cash flow and others in earnings (with ultimate goal to flip the assets). Hence, whether or not you use an AFIT or BFIT discount rate is extemely important. An after-tax cash flow model must include not just the step-up in basis, but also the DD&A allowances. The equipment is depreciated using a 7-yr MACRs and the reserves are depleted using a UOP method. It’s not as simple as “1 – tax rate”. I run into this issue frequently when performing valuations.

Once again, terrific blog. I like the way you have simplified the process into the critical issues.

Jim

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