ECONOMIC EVALUATION OF UNDEVELOPED RESERVES
USING THE BINOMIAL TREE APPROACH.
Presented on Indonesian Society of Petroleum Engineers, October 2002
By : Benny Lubiantara
(aratnaibul@yahoo.com)
ABSTRACT
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
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 :
uS + rB
with probability q
S + B
2
dS + rB
with probability 1 – q
uS + rB = Cu
dS + rB = Cd
Solving these equations,

Cu  C d
uC d  dC u
, B
(u  d ) S
(u  d )r
…………… (1)
With  and B chosen in this way, this is called as the hedging portfolio.
C  S  B 
Cu  Cd uCd  dCu  r  d 
ur  
 

Cu  
Cd  / r ………. (2)
ud
(u  d )r
u d  
 u  d 
Equation (2) can be simplified by defining
p
rd
ur
and 1  p 
ud
ud
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
Similarly, for the call,
Cuu = max[0, u2S – K]
Cu
C
Cdu = max[0, duS – K]
Cd
Cdd = max[0, d2S – K]
3
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 become :
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
depend 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. 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.
2. A traditional investment analysis (DCF) only answer 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 its 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.
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Case study:
Suppose an oil company consider 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 1. 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 3 rd 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 2).
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 consider 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 3) 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 4).
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 price 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
believe on standard DCF method, they will very often reject this type of opportunity
which will ruin the long term strategy of company portfolio.
CONCLUSION :
This paper shows how the option pricing can be applied to value the undeveloped oil
reserves 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
5
management only use 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.
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.
Auhor CV’s :
BSc in Petroleum Engineering, Institut Teknologi Bandung (1989), BA in Economic,
Universitas Indonesia (1997), MBA in Finance and Accounting, Universitas Indonesia
(1997). Currently working for Unocal Indonesia, previous experience : Sr. Petroleum
Egineer of Maxus/YPF.
Email : bennyl@unocal.com or aratnaibul@yahoo.com
Figure 1:
30000
Case Study :
-
-
25000
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.
Production rate (BOPD)
-
20000
15000
10000
5000
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Year
6
Figure 2:
Sensitivity Analysis
NPV @ 12% (in million USD)
120
100
80
60
40
20
0
10
15
20
25
-20
Oil Price (USD per barrel)
7
30
35
Figure 3:
Input for Binomial Model :
Current oil price = $15
Upward movement = 1.2
Downward movement = 0.8
Risk free interest rate = 8%
Period = 6 years
Oil Price Movement
0
15
1
18
12
2
22
14
10
3
26
17
12
8
4
31
21
14
9
6
5
37
25
17
11
7
5
6
45
30
20
13
9
6
4
Figure 4:
PV of cash inflow for each oil price (In Million USD)
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
PV of Investment Cost (In
Million USD) = 126,42
-
0
40,15
1
2
3
4
5
6
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
-
-
-
-
-
-
-
-
-
Value of the
Undeveloped
reserve :
8
Max (PV cash inflow PV Inv. Cost; 0)
9