ࡱ> ]_\oq`bjbjqPqP 4:: A 6666666J2228j> <J=j P!P!P!P!P!>!! <<<<<<<$>hTAjC<6)P!P!))C<66P!P!<=H.H.H.)b6P!6P!<H.)<H.H.r9T66[:P!z p2x+9;DR=0=9zA2-A[:[:>A6:@! #vH.0%,\&!!!C<C<-R!!!=))))JJJ$JJJJJJ666666  USING OF EXPONENTIAL FUNCTION IN RISK ASSESSMENT FOR INVESTMENT IN POTENTIAL HYDROCARBON DISCOVERY UPOTREBA EKSPONENCIJALNE FUNKCIJE U PROCJENI INVESTICIJSKOG RIZIKA ULAGANJA U POTENCIJALNO OTKRIE UGLJIKOVODIKA Tomislav MALVI1, Igor RUSAN2, Marko CURI3 1INA-Oil Industry Plc., E&P of Oil and Gas, Reservoir Engineering & Field Development Department, `ubieva 29, 10000 Zagreb, DSc., BSc. in Geology 2INA-Oil Industry Plc., E&P of Oil and Gas, Exploration Department, `ubieva 29, 10000 Zagreb, BSC. in Geology 3Consulted Programmer, Ivana Oraania 8, Zagreb, BSc. in Computers SA}ETAK Svako potencijalno otkrie ugljikovodika prolazi kroz fazu procjene razli itih geoloakih kategorija kojima se odreuje postoje li geoloaki uvjeti za stvaranje i o uvanje le~iata. Takva procjena radi se naj eae kroz pet geoloakih kategorija gdje se procjenjuje vjerojatnost postojanja zamke, rezervoara, mati nih stijena, mogunosti migracije i mogunost o uvanja ugljikovodika. Kona an rezultat je predstavljen kroz vjerojatnost postojanja pretpostavljenog le~iata (izra~enom vrijednoau u intervalu 0-1). Na temelju te vrijednosti mogue je izra unati isplativosti daljnjih ulaganja, uvoenjem dodatnih parametara kojima se opisuje investicijski rizik, a koji ovisi o istra~iva kom bud~etu i troakovima kompanije, geoloakoj vjerojatnosti i o ekivanoj vrijednosti otkria, te naravno o ekivanoj dobiti obzirom na rizik. Ocjena isplativosti istra~ivanja i buaenja izvodi se na temelju neto sadaanje vrijednosti ( net present value ) i o ekivane vrijednosti ( expected value ) potencijalnog otkria. Upotrebom funkcije korisnosti, odnosno funkcije ijim se izra unom definira korisnost otkria obzirom na ulo~ena sredstva i rizik, kompanije mo~e doi do numeri kog podatka koji iskazuje isplativosti toga ulaganja obzirom na njezine financijske mogunosti i obveze. Takvom funkcijom odra~ava se stav prema riziku istra~ivanja, svojstven razli itim pristupima i mogunostima, koji kompanija primjenjuje kroz neko razdoblje. Razli ite oblici te funkcije, posebno eksponencijalni oblici, ve su desetljeima u upotrebi kod razli itih naftnih kompanija i eksperata. Njezina upotreba prikazana je kroz hipotetski slu aj ocjene potencijalnog otkria u hrvatskom dijelu Panonskog bazena. Klju ne rije i: Eksponencijalna funkcija, jedinice korisnosti, ekvivalenti vrijednosti, otkria Predlo~ena kategorija rada: prethodno priopenje ABSTRACT Every potential hydrocarbon discovery could be evaluated through several geological categories that describe existence of geological conditions for reservoir creation and preservation. Such evaluation, the most often, is performed for five geological categories including probability of trap, reservoir and source rocks existence as well as possibilities for migration and hydrocarbon preservation. Final result is expressed as Probability of Success (POS) to discover assumed hydrocarbons (given numerical in interval 0-1). Based on this value, it can be possible to calculate the worth for further investments, adding new parameters for risk describing. Such economic risk depends on exploration budget and company costs, geological probability, expected value and, of course, expected profit vs. risk. Exploration and drilling feasibility studies are based on net present value (NPV) and expected value (EV) for potential discovery. Utility function is tool for evaluation of discover utility, regarding invested money and risk. Numerical result describes possible profit that could be reached regarding company's financial strength and financial obligations. Utility function, in general, represents attitude toward exploration risk, derived from different approaches and possibilities that company applied through some period in the past. Different types of utility function, especially exponential, has been using through decades in different petroleum companies and expert teams. Here is presented hypothetical case for using of such function in purpose of evaluation of potential discovery in Croatian part of Pannonian Basin. Key words: Exponential function, utilities, certain equivalents, discoveries Proposed paper category: Preliminary communication 1. INTRODUCTION Potential discovery is characterised by economic value as base for making decision about further exploration, production or abandoning. Such decision depends on several parameters responsible for discovery worth. Hydrocarbon reserve values mostly resulted from oil and gas prices on global market. This value is not unique in the whole world, and depends on hydrocarbon quality, geographic location of reservoir, transport and refining availabilities and some other factor that could be financially easily included in costs. However, there are more subjective costs that depend on parameters characteristic for particular petroleum company involved in exploration and production activities (E&P). The most important are E&P company's budget, politics to own reserves and attitude of expert teams and entire company toward exploration and investment risks. Generally, risk-attitude is crucial parameter from which can be determined ratio between investment money and profit. Each investment is mostly initiated by expected value (EV) of potential discovery. The term expected value is established in the field of mathematical probability through decades, and transferred in other activities that handle by any type (but especially financial) risk. Expected value (or expected profit) gives to investor pleasure called in economic sciences utility (ref.1). In the field of exploration and production of hydrocarbons the profit (i.e. utility) is connected by geological, market and other risks, and attitude toward risk can be selected as follows: Risk-neutral attitude investments guarantee stable balance or possible profit; Risk-loving attitude investments are encouraged in despite of prognosis indicate on possible loss (>50 %); Risk-averse attitude careful investments including rejection of some prognosis for win (>50 %). Economists use the term marginal utility to explain these attitudes and especial risk-averse approach. Sloman and Sutcliffe1 described marginal utility for win through fact that utility decreased what richness is higher (1 $ of gain from 100 $ is stronger motivator than 1$ from 1000 $). According to this, utility (or satisfaction) to increase capital from 5000 $ to 10.000 $ is higher than increase 10.000 $ to 15.000 $. If it is compared with gambling (taking risk) with 5000 $ (of total amount of 10.000 $) and decrease capital to 5000 $ or increase to 15.000 $, subjective feeling of possibility to gamble and make profit is only 8000 $, lower than starting money. It is short explanation why people mostly preferred risk-averse attitude. Using of utility theory in petroleum industry was proposed by Cozzolino2. He also introduced so called utility function (r) as tools for describing company investment policy in the past. 2. RISK-ADJUSTED VALUE Cozzolino2 proposed to use equitation, derived from utility theory, for calculation so called risk-adjusted value (RAV). This value indicates on optimal and consistent investment level that is based on budget, acceptable risk and expected profit for company. The RAV is calculated using equitation 1:  EMBED Equation.3  (1) Where are: R - gross reward in MM of dollars ; C - cost in MM of dollars ; p - probability of success; r - risk aversion function in MM of dollars. It could be simplified using first approximation of utility function (r) expressed as annual company exploration budget in million dollars (MM$), which could be spent for selected oil and/or gas province. This function can be expressed as equitation 2:  EMBED Equation.3  (2) The connection between budget size and RAV is shown on Figure 1. It is assumed that only one company invests money in prospect, with 100 $ share. The prospect expected value is 1.76 MM$ (example from Rose, 1987). For the company with 200 MM$ annual exploration budget RAV is 95 %. It means that such company is ready to risk 1.67 MM$ for discovery of expected value of 1.76 MM$, if calculated geological risk is approved from the responsible board (or willing to risk 95 of EV). This value of 1.67 is called risk-neutral value or risk-neutral dollars or risk-adjusted value (RAV).  Figure 1. RAV for EV=1.76 MM$ and different annual budget (from Rose, 1987) For budget of 2 MM$ RAV is decreased on 8 % EV, i.e. the amount of risk-neutral dollars is 140.000 $. More to the left RAV is negative, what means any investment for small companies would be unprofitable. However, small companies also can reach profit and bidding for smaller concessions, make their bidding valid only for part of total share. Acquired share in total concession worth can be expresses as ratio RAV/EV, what implicated that RAV of interested is geometrically increased and could be positive. For example the company with budget of 0.5 MM$ can considered as target only 10 % of EV (176.000 $). For this portion the RAV is 37 %, what means that such company need to risk 62.000 $ to reach profit of 176.000 $. 3. HIPOTETICAL CASE Methodology of utility function is applied for hypothetical case of expected new discovery in Croatian part of Pannonian basin. Based on large dataset available for southern part of the Drava depression and the Bjelovar subdepression3,4,5 as well as source6 for Zala, Drava and Sava petroleum provinces it could be assumed that new discovery could reach about 200.000 m3 of recoverable oil (assessment is mostly based on medium values from discovered reserve's histogram). Also, based on independent calculation (in reviewing, Malvi and Rusan, 2006) accompanied geological probability could be 28 %. Moreover, Croatian part of Pannonian Basin encompasses four mature petroleum provinces and risk-averse attitude is the most appropriate. Such attitude could be expressed using exponential utility curve, shown by curve A on figure 2 (e.g. ref.7,8).  Figure 2. Exponential utility curve (from ref.7) 3.1. Calculation of risk-adjusted value for hypothetical case Cozzolino2 proposed a formula 3, based on utility theory, to determine risk-adjusted value (RAV) using the risk-averse function.  EMBED Equation.3  (3) Where are: R = gross reward in MM of dollars ; C = cost in MM$ ; p = probability of success ; r = risk aversion function in MM of dollars. The first approximation of function r is reciprocal values of company exploration budget (in MM$, i.e. 1/annual exploration budget; ref.9). Exponential function also can be expressed through several equations that decreased expected value to some money that is appropriate to invest regarding risk and risk-attitude at all. It starts by calculation of utility function, according with Equation 47,8, transferring NPV value in arbitrarily units called utils and expressed in risk neutral dollars.  EMBED Equation.3  (4) Where are: U - utility units in risk neutral dollars - RN$ ; NPV - net present value in market price of potential discovery and appropriate discount rate ; r - risk tolerance coefficient. In this paper value annual exploration budget, for hypothetical case, was set on 50 MM$, and "r" on 1/5 of annual company budget prepared for selected petroleum province, i.e. r=107. Appropriate NPV value can be calculated using average oil prices and discount level of 10 %, also accompanied by drilling and equipping costs for selected province. (e.g. 2-5 MM$ per well). Expected value (EV) is calculated according equation 5, and costs decreased for risk and risk tolerance coefficient by equation 6:  EMBED Equation.3  (5) Where are: EV expected value ; NPV - net present value ; POS Probability of Success ; COSTS drilling and equipping costs.  EMBED Equation.3  (6) According7,8 the last two calculation of exponential function including expected utility units (EU; equation 7) and certain equivalents (CE; equation 8):  EMBED Equation.3  (7) Where are: EU - expected utility units EU ; U - utilities ; POS geological probability ; NEW_COSTS costs decreased for investment risk.  EMBED Equation.3  (8) Where are: CE - certainty equivalents in RN$ ; EU - expected utility ; r - risk tolerance coefficient. The final result was reached through stand-alone application programmed in JavaTM (ref.10). User interface is shown on Figure 3.  Figure 3. Java application for CE units calculation It is easy, using Java form, to calculate marginal costs and annual exploration budget that could be critical for risk-accepted investment regarding Net Present Value and POS. For small discoveries (NPV between 10-15 MM$) and average POS 25-35 % annual exploration budget of 50 MM$ can not be enough to justify exploration of such discoveries. It means that in mature and/or smaller petroleum provinces (characterised mostly by by-passed oil traps or satellite reservoirs) joint-venture of two or more companies is only acceptable approach in searching for new reserves. 4. DISCUSSION AND CONCLUSIONS Presented methodology could be very interesting for risk evaluation in Croatian part of the Pannonian Basin. This region is mature petroleum province system. It means that risk-averse approach is only valid for risk investment assessment of new potential discoveries. For example, using of exponential function led to the value of 0.72 MM RN$ as money that average company would be willing to invest in discovery by EV*2.06 MM$. It means that 100 % share of discoveries could be characterised by RAV=29 %. But minor modifications, by costs increased at 5 MM$, POS set on 30 % and NPV on 13 MM$, led to negative CE calculation of -0.56 MM$ for EV of 0.4 MM$. In any case, RAV is small (up to 30-35 %), what strongly indicated on joint-venture of two or more companies as the only appropriate approach for further exploration in Croatian petroleum provinces in Pannonian area. 5. 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Sutcliffe, 2004, Economics for Business: Edinburgh, Pearson Education Ltd., 726 p. Cozzolino, J. M., 1977, Management of oil and gas exploration risk: West Berlin, New Jersey, Cozzolino Associates, 420 p. Pletikapi, }., 1964, Naftoplinonosnost Dravske potoline: Nafta, 9, p. 250-254, Zagreb. Pletikapi, }., I. Gjetvaj, M. Jurkovi, H. Urbiha and Lj. Hrn i, 1964, Geologija i naftoplinonosnost Dravske potoline: Geoloaki vjesnik, 17, p. 49-78, Zagreb. Malvi, T., 2003, Oil-Geological Relations and Probability of Discovering New Hydrocarbon Reserves in the Bjelovar Sag: Ph.D. Dissertation, Faculty of Mining, Geology and Petroleum Engineering, Zagreb, 123 p. USGS World Energy Assessment Team, 2000, World Petroleum Assessment 2000 Description and Results: USGS, Zala-Drava-Sava Petroleum System, ref. 404802. Schuyler, J., 1999, Decision Analysis Collection: Decision Precision & OGCI Training Inc., Aurora (Colorado) & Tulsa (Oklahoma) Schuyler, J., 2001, Risk and Decision Analysis in Project (2nd Edition): Project Management Institute Inc., Northern Square (Pennsylvania), 259 p. Rose, P.R., 1987, Dealing with Risk and Uncertainty in Exploration: How Can We Improve?: AAPG Bulletin, 71, 1, p. 1-16, Tulsa. Curi, M. and T. Malvi, 2006, Estimation of Certainty Equivalent units (using utility function) computer program: INA, Zagreb. ACKNOWLEDGEMENT The presented researching is done through activity of Reservoir Engineering & Field Development Department as well as Exploration Department. The both are parts of INA-Oil Industry Plc. We thanks for permission to use some unofficial internal probability calculations. AUTHORS Tomislav Malvi, graduate engineer in geology, PhD in Natural Sciences, INA- Industry of Oil Plc., Exploration and Production of Oil and Gas, Reservoir Engineering & Field Development Department, expert, `ubieva 29, 10000 Zagreb,  HYPERLINK "mailto:tomis.0Ć܆\^ЇԇNOYbdABTVrsԉՉʊΊXZƋ¸¸¸ž¸žh|hc\CJH*mH sH hc\CJmH sH h|hc\CJmH sH h}2h4CJmH sH h}2CJmH sH h|h4CJmH sH #h}2hc\CJ]mH nHsH tHhc\CJmH nHsH tH h|hc\CJmH nHsH tH0B‰UVXhivwZ\68tvxdhgddhgdl6 $dha$gdl6;dh^`;gdl60dh^`0gdl6 & Fdhgdc\36VWXghiԌ ,uw}~"ZΏЏĴvoveXXKIUjhc\hl6CJUhc\hl6CJmH sH hc\hl65CJ h5CJhl6hl65CJhc\hl6CJ hc\CJ h-%YCJhc\hc\CJhhl6aJhl6hl6CJmH sH hl6hl65CJ\mH sH h4CJmH sH hl6CJmH sH h|hc\CJmH sH h|hc\6CJmH sH h}2hc\CJmH sH lav.malvic@ina.hr" tomislav.malvic@ina.hr Igor Rusan, graduate engineer in geology, INA- Industry of Oil Plc., Exploration and Production of Oil and Gas, Exploration Department, head of unit, `ubieva 29, 10000 Zagreb,  HYPERLINK "mailto:igor.rusan@ina.hr" igor.rusan@ina.hr Marko Curi, graduate engineer in computers, consultant, Ivana Oraania 8, Zagreb,  HYPERLINK "mailto:marko.curi@email.t-com.hr" marko.curi@email.t-com.hr APPENDIX Figure list: Figure 1. RAV for EV=1.76 MM$ and differen&(*VXZ\p<Rhl 2468Lܚޚ6:<>prtɹɹɈypɘp`yjZhPEhCJUhhCJhPEh0JCJOJQJjZhPEhCJUjhCJUhc\hCJmH sH hCJmH sH hc\hCJ h5CJ hCJhc\hl60JCJjhc\hl6CJUj7Yhc\hl6CJUhc\hl6CJ"tvx| !,LZ[cdfξh2@jh2@Uhl6CJmH sH hl66CJmH sH hl656CJmH sH Uh|hl66CJmH sH h|hl656CJmH sH hl6hl6CJhl6hl65CJhhl6aJhc\hCJh|hCJmH sH  x|"\ $dha$gdl6dhgdl6t annual budget (from Rose, 1987) Figure 2. Exponential utility curve (from Schuyler, 1999) Figure 3. 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