ࡱ> SUReq`bjbjqPqP 4::< 6666666J8~4J2jRRRRR> {1}1}1}1}1}1}1$V4h6j16$RR$$166RR2&&&$^6R6R{1&${1&&V]/@66/R nY%/ O1,202/T(7%X(7//>(76;0 v&2!,^"11W&R2$$$$JJJJJJJJJ666666  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 Authors: 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 Key words: Exponential function, utilities, certain equivalents, discoveries Klju ne rije i: Eksponencijalna funkcija, jedinice korisnosti, ekvivalenti vrijednosti, otkria 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. 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. ECONOMIC RISK AND UTILITY FUNCTION 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 (Sloman & Sutcliffe, 2004). 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 & Sutcliffe (2004) 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 $, lower than starting money. It is short explanation why people mostly preferred risk-averse attitude. Using of utility theory in petroleum industry was proposed by Cozzolino (1977). He also introduced so called utility function (r) as tools for describing company investment policy in the past. RISK-ADJUSTED VALUE Cozzolino (1977) proposed to use equitation, derived from utility theory, for calculation so called risk-adjusted value (RAV). This value indicates on optimal and consistent investment level that is based on budget, acceptable risk and expected profit for company. The RAV is calculated using equitation 1:  EMBED Equation.3  (1) Where are: R - gross reward in MM of dollars ; C - cost in MM of dollars ; p - probability of success; r - risk aversion function in MM of dollars. It could be simplified using first approximation of utility function (r) expressed as annual company exploration budget in million dollars (MM$), 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 $. HIPOTETICAL CASE Methodology of utility function is applied for hypothetical case of expected new discovery in Croatian part of Pannonian basin. Based on large dataset available for southern part of the Drava depression and the Bjelovar subdepression (Pletikapi, 1964; Pletikapi et al., 1964; Malvi, 2003) as well as USGS report (2000) for Zala, Drava and Sava petroleum provinces it could be assumed that new discovery could reach about 200.000 m3 of recoverable oil (assessment is mostly based on medium values from discovered reserve's histogram). Also, based on independent calculation (in reviewing, Malvi and Rusan, 2006) accompanied geological probability could be 28 %. Moreover, Croatian part of Pannonian Basin encompasses four mature petroleum provinces and risk-averse attitude is the most appropriate. Such attitude could be expressed using exponential utility curve, shown by curve A on figure 2 (e.g. Schuyler, 1999, 2001).  Figure 2. Exponential utility curve (from Schuyler, 1999) Calculation of risk-adjusted value for hypothetical case Cozzolino (1977) proposed a formula 3, based on utility theory, to determine risk-adjusted value (RAV) using the risk-averse function.  EMBED Equation.3  (3) Where are: R = gross reward in MM of dollars ; C = cost in MM$ ; 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$, i.e. 1/annual exploration budget; Rose, 1987). Exponential function also can be expressed through several equations that decreased expected value to some money that is appropriate to invest regarding risk and risk-attitude at all. It starts by calculation of utility function, according with Equation 4 (Schuyler 1999; 2001), transferring NPV value in arbitrarily units called utils and expressed in risk neutral dollars.  EMBED Equation.3  (4) Where are: U - utility units in risk neutral dollars - RN$ ; 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) According Schuyler (1999; 2001) 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. 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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. DISCUSSION 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$. In any case, RAV is small (up to 30-35 %), what strongly indicated on joint-venture of two or more companies as the only appropriate approach for further exploration in Croatian petroleum provinces in Pannonian area. REFERENCES Curi, M. and T. Malvi, 2006, Estimation of Certainty Equivalent units (using utility function)  computer program: INA, Zagreb. Cozzolino, J. M., 1977, Management of oil and gas exploration risk: West Berlin, New Jersey, Cozzolino Associates, 420 p. Malvi, T., 2003, Oil-Geological Relations and Probability of Discovering New Hydrocarbon Reserves in the Bjelovar Sag: Ph.D. Dissertation, Faculty of Mining, Geology and Petroleum Engineering, Zagreb, 123 p. Pletikapi, }., 1964, Naftoplinonosnost Dravske potoline: Nafta, 9xxx2x6xnx~xxxxxxxxxxxxz z$z'z{S{z{{{{{սժʚwwmm`Sh|h|7>CJmH sH hch|7>CJmH sH hCJmH sH hc6CJmH sH h|7>6CJmH sH h|7>56CJmH sH h|h|7>56CJmH sH $jh|7>h|7>5CJUmH sH h|7>h>CJmH sH h|7>5CJmH sH h|7>CJmH sH hc5CJmH sH hcCJmH sH h|7>CJH*mH sH {{{ |||.|<|||}~~~~~01<=FƀʀԀ񢕋~pccch|hHCJmH sH h|hH6CJmH sH h}2hHCJmH sH h}2CJmH sH h|h4CJmH sH h|h5CJmH sH  h|h|OJQJ^JmH sH  h|h8 OJQJ^JmH sH hcOJQJ^JmH sH  h|hlOJQJ^JmH sH h|hh5CJmH sH $=>؁ځ|,n6I;d^`;gdH0d7$8$H$^`0gdH0d^`0gdHƂȂ܂^|LRdj~nHJfgȎɎ˽˩˽˽˽˽˽ܛܩܓh$~jh$~Uh|h4CJH*mH sH U#h}2h4CJ]mH nHsH tHh}2CJmH nHsH tH h|h4CJmH nHsH tHh|h4CJmH sH h}2CJmH sH h}2h4CJmH sH 4, 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. Rose, P.R., 1987, Dealing with Risk and Uncertainty in Exploration: How Can We Improve?: AAPG Bulletin, 71, 1, p. 1-16, Tulsa. 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. Sloman, J. and M. Sutcliffe, 2004, Economics for Business: Edinburgh, Pearson Education Ltd., 726 p. 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