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OGEL Cover v1.3

Oil, Gas & Energy Law Intelligence

Valuation of Undeveloped Oil Reserves with Option Pricing Model by B. Lubiantara

www.gasandoil.com/ogel/ Issue : Vol. 4 - issue 4 November 2006

Valuation of Undeveloped Oil Reserves With Option Pricing Model

Benny Lubiantara

Executive Summary

Modern financial theories such as option theory are increasingly being used to evaluate the economic viability of oil and gas projects. The stimulus for the use of this approach is the limitations of Discounted Cash Flow (DCF) methods such as NPV and IRR. These methods assume that the project is of a “now or never” nature. In fact, this is not the case; as an investor, one has many choices, such as to defer the project if it is not seen as being economically viable. One can also choose to expand or increase production capacity if the price of the commodity rises. The DCF method often condemns a project as being “uneconomical” simply because it does not take into consideration such flexibility. Logically, the existence of such options or flexibility should add to the project’s value. This paper will discuss how the option approach that is usually used in modern financial management theory can be applied to the evaluation of undeveloped reserves. Option is a right, not an obligation. Options have similarities to projects involving mineral reserves. As an Investor, one has the right to develop the reserves; on the other hand, if economic conditions are not conducive, one has the option to postpone the project. This paper will explain how to evaluate the economic viability of an oil reserve that has not been developed (an undeveloped reserve) on the basis of the perspective of Option theory; the method that will be used is one of the better known methods of option pricing theory, the Binomial Tree. Introduction Decision making in Corporate Investment has always been a difficult undertaking for analysts. Traditionally, NPV and Decision Trees have been the fundamental tools for modeling investment opportunities. Recently, there has been a growing interest in financial Option Pricing Models (OPM) in the corporate investment domain. The value of flexibility under uncertainties has been realized long back. Decision trees were the only available tools to quantify this value. However, the complexity of decision trees has hindered their widespread adoption. Real options offer a simpler alternative to assess the value of this flexibility. Options have been studied extensively in financial literature and are well understood in financial domain. An option confers upon the owner the right, but not the obligation, to take an action in the future. Options always have timing restrictions. Every option has an expiration date after which the option can no longer be exercised. European Options can only be exercised on their expiration date unlike American Options that can be exercised on or before their expiration. American options offer interesting opportunities to the owner. The value of the option changes

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over time, as future uncertainties are resolved. The owner can maximize his/her profits by exercising it at the right moment. Options also differ in terms of the right being conferred. In financial market terms, a call option confers upon the owner the right to purchase a security at a fixed price where as a put option offers the right to sell a security at a fixed price. There are six factors affecting the price of the option,

• Current stock prices • Strike price • The time to expiration • The volatility of the stock prices • The risk free interest rate • The dividends expected during the life of the option

There are two most popular methods to calculate the value of the option: first, Black Scholes (BS) method, this method basically using the straightforward formula. Scholes, Merton and Black developed an analytical solution and received the Noble Prize in economics in 1997. The second method is Binomial Tree approach. This paper will discuss only the second method, the first method is beyond the scope of this paper, for those who interest should refer to our previous paper (reference 5). The Binomial Option Pricing Formula The Binomial tree assumes that the stock price follows a multiplicative binomial process over discrete periods. The rate of return on the stock over each period can have two possible values: u – 1 with probability q, or d – 1 with probability 1 – q. If the current stock price is S, the stock price at the end of the period will be either uS or dS. uS with probability q S dS with probability 1 – q To see how to value a call on this stock, start with the simplest situation: the expiration date is one period. Let C the current value of the call, Cu is its value at the end of the period if the stock price goes to uS and Cd is its value at the end of the period if the stock price goes to dS. Since there is now only one period remaining in the life of the call, a rational exercise policy imply that Cu = max[0, uS – K] and Cd = max[0, dS – K]. Therefore, Cu = max[0, uS – K] with probability q C Cd = max[0, dS – K] with probability 1 – q Suppose we form a portfolio containing ∆ shares of stock and the dollar amount B in risk less bonds. This will cost ∆S + B. At the end of the period, the value of this portfolio will be:

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∆uS + rB with probability q ∆S + B ∆dS + rB with probability 1 – q

∆uS + rB = Cu ∆dS + rB = Cd

Solving these equations,

rdudCuC

BSdu

CC uddu

)(,

)( −−

=−−

=∆ …………… (1)

With ∆ and B chosen in this way, this is called as the hedging portfolio.

BSC +∆=rdu

dCuCduCC uddu

)( −−

+−−

= rCduru

Cdudr

du /

−−

+

−−

= ………. (2)

Equation (2) can be simplified by defining

dudr

p−−

≡ and duru

p−−

≡−1

so that: C = [pCu + (1 – p)Cd]/r …………… (3)

Let’s consider the next simplest situation: a call with two periods remaining before its expiration date. In keeping with the binomial process, the stock can take on three possible values after two periods,

u2S uS

S duS dS d2S

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Similarly, for the call, Cuu = max[0, u2S – K] Cu

C Cdu = max[0, duS – K] Cd Cdd = max[0, d2S – K] At the end of the current period there will be one period left in the life of the call, it is identical problem with one period, from previous analysis, we know that when there are two periods left,

Cu = [pCuu + (1 – p)Cud]/r and …….………….. (4)

Cd = [pCdu + (1 – p)Cdd]/r The general formula becomes:

C = [pCi+1, j+1 + (1 – p)Ci+1, j]/r …………………… (5) REAL OPTION IN UPSTREAM APPLICATION The decision of an oil company to develop an oilfield is a good example of Real option; if the company does not develop the field today, it can do so in the future, the return from development depend on the price of oil while the cost of developing the field does not. The flexibility in timing is analogous to a call option to buy the return from the oilfield with the exercise price equaling the cost of development. It is similar to financial option, there is a fixed exercise price and payoff on exercise depends on the price of a traded asset which is the price of oil. Therefore, it is possible to use option pricing techniques to value the real asset and thereby determine the value of acquiring the oilfield as well as determine if and when to exercise the option. A simple DCF analysis would ignore the possibility to defer; it would simply tell a decision maker if it were better to develop today than to abandon development; it would significantly undervalue the oilfield if the option to defer were valuable. The series of options available in upstream business consists of: option to defer, option to expand, option to stop temporarily and option to abandon (figure 1). This paper will only discuss the value of option to defer of undeveloped reserve. The option to defer is one of the most important characteristic of oilfield development; option to defer has value because:

1. When a company has exclusive right to the contract area or concession for specific period, it can defer taking this development until later date.

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2. A traditional investment analysis (DCF) only answers the question of whether the field development is “good” if taken today.

3. The fact that the field development does not pass “standard” investment criteria today (because its NPV is negative or it’s IRR less than its hurdle rate) does not mean that the rights to this undeveloped reserve are not valuable.

PROPOSED METHODOLOGY The methodology proposed is a step further from the traditional Discounted cash Flow (DCF) analysis that commonly used. The first step begin by generating estimated cash inflow and outflow using standard DCF analysis for certain oil price, the second step is to separate the Present Value (PV) of Cash Inflow and PV of Investment Cost. The third step is done by creating the Binomial tree for some periods. The final step is to calculate the value of the undeveloped oil reserve by using binomial tree formula. Case study: Suppose an oil company considers the acquisition opportunity to “BL Block” in Indonesia territory, this area is estimated to have the recoverable reserves of 50 MMBO. Assume, it will take 3 years to prepare the surface facilities, drilling, etc before the wells ready on production. Estimated Capital Expenditure = USD 140 Million, Operating cost = USD 4 per barrel. Expected production profile is shown in figure 2. Contract period on this block is 20 years; the company has the option to defer the field development for maximum 6 years. Cost of Capital = 12 %, Current oil price = USD 15 per barrel. Assumption: since this opportunity located in Indonesia, PSC Indonesia Fiscal Regime will be used (PSC 3rd Generation) with tax 44%. Traditional DCF method will solve this type of problem by providing the investment criteria such as: IRR, NPV. To make it more informative, the sensitivity analysis is done (figure 3). By using traditional DCF method, at the current oil price, the company will REJECT this opportunity because NPV is negative (minus USD 2.28 million). Sensitivity analysis would help the management to make evaluation for different oil prices; unfortunately, it is not assist in providing the most reasonable “single” value. What make the option approach is different from traditional DCF method? The option approach considers the fact that the company has the option NOT TO develop the field NOW, the company can wait for six years (which is not considered by traditional DCF method). How does the proposed method solve this typical problem? Using the proposed methodology, we obtain the Present Value (PV) of Cash inflow and PV of Investment Cost from cash flow stream at current oil price. Binomial tree will be created (figure 4) for some level of oil prices, the PV of cash inflow is calculated, the value of this opportunity is then calculated by binomial formula (figure 5).

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It is shown that the Binomial valuation result is equal to USD 40.15 million. It means that the option indirectly state that even though at current oil prices this opportunity is not interesting, but it has the potential to generate higher NPV by deferring the field development. It is very powerful for managerial decision, if management merely believes on standard DCF method; they will very often reject this type of opportunity which will ruin the long term strategy of company portfolio. In this simplified case, it is assumed that Present Value of Investment Cost (PVIC) or capex is constant, the proposed method can be used for higher capex by changing the PVIC, the capex in reality should link to the oil prices, the company could use their own approach (best estimate) to determine the increasing capex as oil prices increase and incorporate their estimation into the proposed model (PVIC) to improve the result of the calculation. CONCLUSION: This paper shows how the option pricing can be applied to value the undeveloped oil reserve using technique which is derived from modern financial theory, this technique very helpful especially when facing managerial decision such as: farm in/ farm out, oil property acquisition and portfolio optimization. The traditional DCF method that commonly used often condemns a project as being “uneconomical” simply because it does not take into consideration the flexibility. If management only uses the DCF technique, it could disadvantage company strategy because many upstream investment opportunities will be “undervalued”. The sensitivity analysis assists the management to evaluate the investment opportunity by providing the range of value; unfortunately, it is not helpful when the decision makers need single value for bidding strategy or oil property acquisition. It is also important to note that the idea of option pricing approach is not to replace the traditional method (DCF) but as a supplement for decision making, especially for marginal field, when it seems not economics today because of current oil price. It provides you the idea on “how much the price of the asset if I want to sell or to purchase it now”. The option pricing model shows that this is the value of this asset now, given the fact that there are prices uncertainties in the future. REFERENCES:

1. Hull, J.C, “Options, Futures and Other Derivates”, Prentice-Hall Inc, 3rd edition, 1997

2. Cox, Ross, Rubinstein, “Option Pricing – A Simplified Approach”, Journal Of Financial Economics – Sep, 1979

3. Robert Gartner and Andrew Rosenfield, “How Real Option Lead to Better Decision”, Financial Times, October 25, 1999.

4. Benny Lubiantara, “Using Option to Value the Upstream Opportunities”, taken from “Petroleum Economics - Course Material” , Fiqry Jaya Mandiri, 2001.

5. Benny Lubiantara, Bambang HS, Kukuh T “Real Option – An Alternative Approach of Oil and Gas Investment Valuation” Presented on IATMI Symposium, Jakarta, November 2000.

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Figure 1:

l Acquire a lease u Option to Drill a well– Make a Discovery u Option to Develop and Produce the Oil

l Produce Oil u Option to further develop adjacent Oil Fields– Produce More Oil

Yr 0 2 4 6 8 10 12 14 16 18 20 22

Acquire Drill Develop? Start toProduce

OtherProduction

AbandonField

“Upstream” Example:

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Figure 2:

Case Study :- Opportunity for “BL Block”- Recoverable reserve : 5 MMBO- Estimated CAPEX = USD 140 million- OPEX = USD 4 per barrel- Cost of capital 12%- Current oil price = USD 15 per barrel- Contract period 20 years, the

company could postpone the development for maximum 6 years.

- Economic Evaluation is done using PSC Indonesia 3rd Generation. 0

5000

10000

15000

20000

25000

30000

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Year

Pro

du

cti

on

ra

te (

BO

PD

)

Figure 3:Sensitivity Analysis

-20

0

20

40

60

80

100

120

10 15 20 25 30 35

Oil Price (USD per barrel)

NP

V @

12%

(in

mill

ion

US

D)

9

0 1 2 3 4 5 615 18 22 26 31 37 45

12 14 17 21 25 3010 12 14 17 20

8 9 11 136 7 9

5 64

Figure 4:Input for Binomial Model :Current oil price = $15Upward movement = 1.2Downward movement = 0.8Risk free interest rate = 8%

Period = 6 years

Oil Price Movement

Figure 5:

Value of the Undeveloped

reserve :

PV of cash inflow for each oil price (In Million USD)

PV of Investment Cost (In Million USD) = 126,42

Max (PV cash inflow -PV Inv. Cost; 0)

0 1 2 3 4 5 6

124,13 138,05 171,98 198,60 231,88 271,82 325,07

101,94 116,81 138,05 165,32 191,94 225,23

85,08 101,94 116,81 138,05 158,66

61,80 74,86 93,97 109,48

22,62 42,21 74,86

3,04 22,62

-

0 1 2 3 4 5 6

40,15 53,72 71,22 93,52 121,52 156,20 198,65

19,20 27,19 38,19 53,12 73,00 98,81

5,69 8,78 13,54 20,90 32,24

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- - -

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