Energy Economics 45 (2014) 10–18

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Energy Economics

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Dynamicmodeling of uncertainty in the planned values of investments inpetrochemical and refining projects

Juliano Melquiades Vianello a,b,⁎, Leticia Costa a, José Paulo Teixeira a

a Pontifical Catholic University of Rio de Janeiro, Industrial Engineering Department, Rio de Janeiro, RJ, Brazilb Pontifical Catholic University of Rio de Janeiro, Industrial Engineering Department, Rua Marquês de São Vicente 225, Gávea, Rio de Janeiro, RJ, Brazil

⁎ Corresponding author at: Pontifical Catholic UniversEngineering Department, Rua Marquês de São VicenteBrasil - CEP 22453900.

E-mail addresses: jmvianello@yahoo.com.br (J.M. Vianleticiaalmeidacosta@gmail.com (L. Costa), jpt@puc-rio.br

http://dx.doi.org/10.1016/j.eneco.2014.06.0020140-9883/© 2014 Elsevier B.V. All rights reserved.

a b s t r a c t

a r t i c l e i n f o

Article history:Received 19 March 2012Received in revised form 3 June 2014Accepted 6 June 2014Available online 1 July 2014

JEL classification:C15

Keywords:Stochastic processMean reversion movementReal optionsMonte Carlo simulationProject analysis

There is a large gap between the planned value of investment in a project and its financial implementation. Thisfact creates a mismatch between the planned and effectively achieved net present value (NPV) of the project.Considering the project portfolio of a company, this could even threaten your solvency in the future.Therefore, a quantitative-risk analysis that takes into account different possible scenarios for these values ofinvestment is extremely important to measure statistically the real value of a project.The aimof this paper is to present the reasons for thismismatch betweenplanned and executed investments and,from this study, obtain a suitable stochastic process to generate different scenarios for these investments in the oilindustry.Although the results are valid for projects in the petrochemical and refining sector, also called in the oil industryas downstream, the methodology can be applied to the upstream or even other branches of industry.

© 2014 Elsevier B.V. All rights reserved.

1. Introduction

In developing countries, in a time of increasing spending on projects,it is observed that there is a large gap between investment planning andits financial implementation because of the long time it takes betweenthe approval and the spending of the cash settlement added to the eco-nomic and social instability, such as drastic reductions in foreign capital,inflation, and rising costs of the project. This is occurring due to the poorforecasting of investments under uncertainties. That is making compa-nies incur higher expenses than expected, affecting the entire financialsituation of the company.

Regarding the increase in project costs, the main reasons for thesevariations in relation to budgeted costs during the life cycle of theproject are:

a) inadequate specification of requirements. This often leads to the ad-ditive values of the contracts. A survey with a Brazilian companyhighlighted that the scope of the project rarely undergoes revision.An example of this is that, during installation of subsea pipelines, itwas found that these pipelines were buried underwater. Afterreview of scope, it was discovered that a change in the surrounding

ity of Rio de Janeiro, Industrial225, Gávea, Rio de Janeiro, RJ,

ello),(J.P. Teixeira).

concrete made his pipeline not necessary to be buried. Thus, theamount of investment decreased.Also, spare equipment is often considered unnecessary in scope. An-other example is this same company, pointed out that, after review,spare pumps used in the project could be disregarded.

b) introduction of new technologies.c) inadequate or insufficient staff.d) Delay of the project. Often the investment amount is dependent on

the time of investment. In these situations a delay could increasethe value of this project. A survey with a Brazilian company showedthat the main causes of delay in investments are:– Arrival of equipment off-specification.– Rain. Often, a rain cover is used over the entire area to be built in

order to avoid delays, which also increases the costs.– Delays in the executive project.– Delays in receiving items from suppliers and special equipment

(cranes, rigs, etc.).– Delay in signing the contract.– Social and union movements (strike).– Default by the outsourced companieswith its suppliers in order to

retain capital.Often, to compensate these delays, companies could contractemployees to work an extra time, which can lead to a significantincrease in investment.

e) organization does not have a formal and institutionalized process toestimate the costs and manage the risks.

11J.M. Vianello et al. / Energy Economics 45 (2014) 10–18

f) increase in prices of equipment, materials and services associatedwith the project throughout its life.

To model the uncertainty on investment, an important risk factor ininvestment projects, we separate this uncertainty in two components.The reasons a, b, c, d and ewill be grouped as reasons to technical uncer-tainties and this component is modeled in Section 2. The Technicaluncertainty (uncorrelated with macroeconomic movements), forexample, in the case of projects that use new technology where uncer-tainty is present not only in cost, but also in the cost of installation andmaintenance. A key feature of the technical uncertainty is that theimplementation of investments reduces this kind of uncertainty. Thus,the technical uncertainty is endogenous to the investment decision pro-cess anddecreases as theprojectwill be executing and coming to an end(PMBOK, 2004). Tomitigate this technical uncertaintywe use a triangu-lar distribution for the investment in accordance with an AACE costestimate classification system.

The reason f will bemodeled in Section 3 and considered as a compo-nent of increased prices for equipment and services. This uncertainty iscorrelated to movements that are subject to unexpected events such asrecession/heating of the economy, and crop losses for climatic reasons/record harvest. Thus uncertainty is exogenous to the decision process ofa company. This kind of uncertaintywill bemitigatedwith the estimationof future scenarios for component prices that affect the investment. Theinvestment occurs in an uncertainty environment where componentprices (uncertainty factors) follow a stochastic process.

2. Technical component of uncertainty on investment

To simulate the variation of this value, a triangulate stochastic simula-tion is used to generate 10,000 scenarios. According to Silva and Gomes(2004), the triangular distribution is often used when there is no histor-ical data available and is be easy to understand. This type of distribution isdefined by three parameters: minimum, maximum and mode.

As shown in Fig. 1, these parameters (2nd column) aremainly due tothe phase of a project life cycle (1st column), i.e., depend on the level ofproject definition. According to PMBOK (2004), project Managers ororganizations can divide projects into phases to provide bettermanage-ment control over the project. Collectively, these phases are known as

Fig. 1. Cost estimate classification system. Source: AACE (Association for the Advan

the project life cycle. There is no single best way to define an ideal lifecycle of the project. Some companies establish policies that standardizeall projects with a unique life cycle, while others allow the projectmanagement team to choose the most suitable for their own projectlife cycle. The transition from one phase to the next generally involvesthe completion of a set of specific activities or some kind of technicaldelivery or handoff. Generally, the requirements specified withinthe phase must be completed before moving on to the next phase.(See Figs. 2– 13.)

According to PMBOK (2004), a project life cycle defines: what workmust be accomplished; what deliverables must be generated andreviewed; who must be involved and how to control and approveeach phase. The level of uncertainty at the beginning of the project isthe highest and therefore the risk of not achieving the objectives,including the investment value, it's greatest in this stage. As the projectis developed, the uncertainties decrease.

These parameter's values, as shown in Fig. 1, depend on the phase ofthe project within its life cycle, i.e., depend on the level of project defini-tion. Projects with high definition (in more developed stages of the lifecycle) have smaller uncertainties in the values of investments and, con-sequently, lower absolute values to triangle distribution parameters.The opposite is also true, i.e., projects with low definition have higheruncertainties in the investment values and thus higher absolute valuesfor the triangle distribution parameters. The following chart presents acost estimate classification system as a function of maturity of theproject. This classification is given by AACEI (AACE International —Association for the Advancement of Cost Engineering).

3. Component of increased price for equipment, materialsand services

First, we need to define an index that represents the capital cost ofpetrochemical and refinery projects, which are the scope of this study.These projects, in the oil industry, belong to the downstream sector.Downstream includes activities of crude oil refining, natural gas treat-ment, transportation, marketing and distribution of oil.

After analyzing a lot of economic indicators and studying variousstrategic reports related to the topic, it was found that the index DCCI(Downstream Capital Cost Index) is the indicator that best represents

cement of Cost Engineering) International Recommended Practice no 18R-97.

Fig. 2. Historical and market forecast for the nominal price index of steel. Fig. 4. Historical and market forecast for the nominal price index of engineering andproject management.

12 J.M. Vianello et al. / Energy Economics 45 (2014) 10–18

the capital cost of the downstream. The IHS CERA DCCI tracks the costsof equipment, facilities, materials and personnel (both skilled and un-skilled) used in the construction of a geographically diversified portfolioof 40 refining and petrochemical construction projects. It is a proprie-tarymeasure of project cost inflation similar in concept to the consumerprice index (CPI) in that it provides a clear, transparent benchmark toolfor tracking and forecasting a complex and dynamic environment. TheDCCI is a work product of the CERA Capital Costs Analysis Forum forDownstream (CCAF-D).

The process to deriving the DCCI is:

• It is defined as a representative portfolio of projects.• Each project is modeled to the level of definition of equipment.• Each project is priced using a multi-year database of industry costs.• The values of an individual project are aggregated in the indices, withthe components compared and analyzed.

Using this methodology, we can resolve issues involving costs ofinterrelated components, such as:

• With a 10% increase in labor rates, whichwould be the impact on totalcosts of the portfolio?

• Howmuch will reduce the cost of steel to compensate the increase inlabor rates?

Changes in industry fundamentals or geopolitical shocks, lead tochanges in the values of DCCI, and therefore in the project values.

The DCCI components, i.e., the economic factors that make up theindex, and the proportion of each of these factors are presented in thefollowing table:

3.1. Scenarios: why use them?

When we look at the past, we note the presence of changes, disrup-tions and discontinuities in economic structures. This warns against

Fig. 3. Historical and market forecast for the nominal price index of equipment.

simply forecasting the future by extrapolating a short period of pastyears.

The prediction using scenarios is to generate, not only a right predic-tion of the future, but expand the analysis to obtain a more systematicand comprehensive understanding of the various future possibilities ofa more flexible way. It means building blocks of factors that point to afuture that is different from the present. The process of using scenariosis appropriate to model future paths for the energy sector, because ofthe dependence on oil. In this case, many factors are uncertain. Thereare issues related to the subject that have a very wide variety of views.Using scenarios add more views in the discussion about the futurethan a simple line of prediction. They depict a world that can happen,not necessarily a world that should happen.

Four scenarios were used in this study: three scenarios for globalenergy IHS CERA and an own scenario. For each scenario, we obtain de-terministic values for the DCCI components and the index itself over theperiod 2011–2017. These deterministic values form the basis for thegeneration of 10,000 stochastic scenarios for the DCCI.

3.1.1. Energy scenariosThese three scenarios focused on the industry sector represent

distinct visions of the energy future considering different geopolitical,macroeconomic and military contexts. It is based on the Forum men-tioned above.

a) Global Redesign — the planned scenario.This scenario represents a world in transition. Global Security in 2010wasmarked by the power of the United States and allies, but econom-ic growth is increasing in Asia. This imbalance is also presented in thefinancial condition of governments, with Europe, Japan and theUnited States deeper in debt, while many Asian governments are

Fig. 5. Historical and market forecast for the nominal price index of labor.

Fig. 6. Historical and market forecast for the nominal price index of instrumentation andelectrical. Fig. 8. Historical and market forecast for the index DCCI.

13J.M. Vianello et al. / Energy Economics 45 (2014) 10–18

enjoying good financial health. Although there was a reduction in theemission of greenhouse gases, the declining long-term use ofpetroleum products in the global economy continues.b) Meta (morphosis).This scenario is characterized by movement of the economy towardreducing dependence on oil, due to high oil prices, technological in-novations (such as electric cars, biofuels, solar and wind), accidentsin the oil industry, and subsidies in government. The movement ofreducing dependence on oil in this scenario is faster than the previ-ous year.c) Vortex.This scenario is characterized by great volatility in the global eco-nomic growth. Another global economic crisis takes place a fewyears after the so-called Great Recession of 2008–2009. The govern-ments of the United States, Europe and Asia are forced to confronttheir fiscal and trade deficits, resulting in lower global economicgrowth. Climate issues become secondary because of the pressurefor improvement of the domestic economies. However, slower eco-nomic growth coming from government action, promotes less emis-sion of greenhouse gases. The world enters a period of greateconomic volatility greater than that which occurred in the lastthree decades.

3.1.2. Own energy scenariosUsing the software Saiph and from the historical DCCI component to

the period 2000–2011, we simulated with the stochastic process calledMean Reversion Movement (MRM) and Geometric Brownian Motion(GBM), along with the methodology Hybrid Quasi Monte Carlo simula-tion to generate 10,000 correlated scenarios for each of the componentsin the period 2012–2017. The DCCI index of own energy scenario is

Fig. 7. Historical and market forecast for the nominal price index of construction.

given by the weighted average (weights given in Fig. 1) of an averageof 10,000 sets of these DCCI components.

Tables 2 and 3 show the mean values of projected prices for eachcomponent of the index. The investment occurs in an uncertainty envi-ronment where each component of the index (uncertainty factors) fol-lows a stochastic process.

TheGBM is themost popular in financial and real assetsmodeling, inwhat can be explained by its simple application and majorly by its easyunderstanding. It is an appropriate process for variables that increaseexponentially at an α average rate and proportional volatility at thelevel of variable X. In the GBM, the stochastic equation for a variable Xthat varies in time is defined by the following stochastic Eq. (1) (Dixitand Pindyck, 1994):

dX ¼ αXdt þ σXdz ð1Þ

where: X = stochastic variable;

dX instant variation of X;α stochastic variable drift;dt time differential;σ volatility of the stochastic variable;dz Wiener increment = ε

ffiffiffiffiffiffidt;

pε � N 0;1ð Þ;

E dXð Þ ¼ αdt; Var dXð Þ ¼ σ2dt;dz tð Þ ¼ ε tð Þ

ffiffiffiffiffidt

p; ε tð Þ � N 0;1ð Þ; E ε tð Þ; ε sð Þ½ � ¼ 0 t≠s

E dzð Þ ¼ 0; Var dzð Þ ¼ E dz2� �h i

− E dzð Þ½ �2 ¼ E dz2� �h i

¼ dt:

AWiener increment is the increment of aWiener process. Accordingto Dixit and Pindyck (1994), a Wiener process is a continuous-timestochastic process with three important properties: it is a Markovprocess (thismeans that the probability distribution for all future valuesof the process depends only on its current value and is unaffected bypast values of the process); it has independent increments (thismeans that the probability distribution for the change in the processover any time interval is independent of any other time interval); andchanges in the process over any finite interval of time are normallydistributed (with a variance that increases linearly with the timeinterval).

TheWiener increment (dz) is the change (increase) in the infinites-imal motion Brownian, given by the expression: dz (t) = ε tð Þ

ffiffiffiffiffiffidt;

pwhere εt~N(0,1), i.e. a standard normal distribution (zero mean andunit variance). The Wiener increment has normal distribution with avariance proportional to the range time: dz (t) ~ N (0, dt). As the incre-ment depends only on the interval, dt (but not the time, t), the incre-ments are stationary. Moreover, they are independent.

2012 2013 2014 2015 2016 2017 2018

Average 323,3 323,2 321,4 324,4 326,7 326,2 325,8

Maximum 503,6 568,0 725,1 680,6 698,3 707,2 705,4

Minimum 210,6 194,7 162,5 159,0 150,4 143,2 127,5

Standard

deviation 34,3 46,6 54,9 61,4 66,8 70,4 73,4

2012 2013 2014 2015 2016 2017 2018

Average 211,4 211,4 211,5 211,9 212,4 213,0 213,7

Maximum 256,2 272,5 291,5 306,3 329,7 338,1 328,4

Minimum 174,3 165,3 160,1 149,5 144,0 137,8 137,7

Standard

Deviation 10,2 14,3 17,4 19,7 21,9 23,8 25,4

2012 2013 2014 2015 2016 2017 2018

Average 210,7 210,7 211,0 211,5 212,3 213,3 214,6

Maximum 261,8 280,5 289,5 308,4 348,1 336,6 335,4

Minimum 168,3 156,2 148,5 144,0 141,3 132,8 128,7

Standard

Deviation 12,3 16,7 20,0 22,5 24,4 26,1 27,7

2012 2013 2014 2015 2016 2017 2018

Average 216,4 217,0 217,9 219,1 220,6 222,4 224,5

Maximum 242,1 251,8 259,8 265,6 282,6 283,1 285,6

Minimum 194,0 186,3 181,1 176,6 177,5 174,1 171,2

Standard

Deviation 6,2 8,5 10,3 11,9 13,2 14,3 15,3

2012 2013 2014 2015 2016 2017 2018

Average 176,1 175,9 175,8 175,7 175,6 175,5 175,4

Maximum 209,9 225,0 230,8 241,2 249,7 268,9 269,9

Minimum 152,0 133,8 128,3 127,9 119,0 118,0 113,0

Standard

Deviation 7,4 10,4 12,8 14,7 16,4 18,1 19,4

2012 2013 2014 2015 2016 2017 2018

Average 177,8 177,6 177,5 177,4 177,4 177,3 177,3

Maximum 208,4 222,4 233,8 244,5 255,4 276,0 278,4

Minimum 150,3 141,8 137,2 132,5 121,5 117,6 115,6

Standard

Deviation 7,7 10,8 13,2 15,3 17,0 18,6 20,0

A B

C D

E F

Fig. 9. Scenarios and statistic generated for the six components of DCCI in the scenario Global Redesign. (A) Steel and pipe, (B) equipment, (C) engineering and project management, (D)labor, (E) instrumentation and electrical, and (F) construction.

14 J.M. Vianello et al. / Energy Economics 45 (2014) 10–18

150

170

190

210

230

250

270

290

310

2012 2013 2014 2015 2016 2017 2018

2012 2013 2014 2015 2016 2017 2018

Average 223,7 223,8 223,9 224,9 226,0 226,9 227,9

Maximum 272,0 280,7 319,8 323,1 329,5 350,9 334,6

Minimum 190,5 178,5 173,8 169,4 161,7 159,5 159,4

Standard

Deviation 9,8 13,5 16,2 18,2 20,1 21,6 22,8

Fig. 10. Results for the scenario “Global Redesign”.

0

0,2

0,4

0,6

0,8

1

1,2

1,4

1,6

1,8

2012 2013 2014 2015 2016

Fig. 12. Technical uncertainty in the value of the investment depending on thematurity ofthe project (over its life cycle).

15J.M. Vianello et al. / Energy Economics 45 (2014) 10–18

As demonstrated by Dixit and Pindyck (1994), for an Xt variable thatfollows GBM and has a lognormal distribution, the mean and thevariance are given by:

E Xt½ � ¼ X0eαt ð2Þ

Var Xt½ � ¼ X02e2αt eσ

2t−1� �

: ð3Þ

According, Dixit and Pindyck (1994), GBMs tend to wander farfrom their starting points. This is realistic for some economic variables(e.g. asset prices) but not for others. Consider the prices of row com-modities such as steel or oil. Although such prices are often modeledas GBM, one could argue that they should somehow be related tolong-run marginal production costs. In other words, while in the shortrun the price of oil might fluctuate randomly up and down (e.g. inresponse to revolutions in oil-producing countries), in the longer runit ought to be drawn back toward the marginal cost of producing oil.Thus one might argue that the price should be modeled as a MRM.

The arithmetic MRM is the Ornstein–Uhlenbeck process, and it isrepresented by Eq. (4) (Dixit and Pindyck, 1994):

dX ¼ η X−X� �

dt þ σ dz ð4Þ

where:

η mean reversion speed of the stochastic variable;X level of balance or long-term average of the stochastic variable;

8090100110120130140150160170

2012 2013 2014 2015 2016 2017 2018

Fig. 11. Results of the DCCI for the Global Redesign scenario considering a normalizationrelated to the year 2011.

σ volatility of the stochastic variable;dz Wiener increment.

According to Dixit and Pindyck (1994) for an Xt stochastic variablethat follows a MRM the mean and the variance are given by:

E Xt½ � ¼ X þ X0−X� �

e−ηt ð5Þ

Var Xt½ � ¼ 1−e−2ηt� �

σ2=2η: ð6Þ

We simulated with the Hybrid Quasi Monte Carlo simulation. This isthe traditional Monte Carlo simulation but using quasi-randomsequences instead of (pseudo) random numbers. These sequencesare used to generate representative samples from the probability distri-butions that we are simulating in our practical problem. The quasi-random sequences, also called low-discrepancy sequences, in severalcases permit to improve the performance of Monte Carlo simulations,offering shorter computational times and/or higher accuracy (Dias,2005).

Monte Carlo is one of the most versatile and widely used numericalmethods. Its convergence rate is independent of dimension, whichshowsMonte Carlo to be very robust but also slow. Accelerated conver-gence for Monte Carlo quadrature is attained using quasi-randomsequences, which are a deterministic alternative to random sequences.Unlike random sequences, quasi-random sequences do not attemptto imitate the behavior of random sequences. The points in a quasi-random sequence are correlated to provide greater uniformity. Forthis reason, Monte Carlo using quasi-random points converges morerapidly for some constant.

Comparing the results above obtained for DCCI to period 2012–2017,those obtained from theMRM showed a forecasted stable value becauseof the characteristic of MRM. It is noted that the results obtained forDCCI from the GBM present a continuous increase because of the series

0

0,2

0,4

0,6

0,8

1

1,2

1,4

1,6

1,8

2012 2013 2014 2015 2016 2017

Fig. 13. Technical and price uncertainty in the investment value.

Table 1Composition of the DCCI index.

Market category DCCI

Steel and pipe 13.90%Equipment 22.60%Engineering and project management 12.80%Labor 36.20%Instrumentation and electrical 7.90%Construction 6.60%

16 J.M. Vianello et al. / Energy Economics 45 (2014) 10–18

drift. Consider a more appropriate use of the GBM because of thecharacteristics of DCCI.

The estimates using GBM are higher than the estimates using MRMbecause unlike GBM, theMRMprocess does not have a constant expect-ed growing rate. This process is more realistic in the extent that thegrowing rate responds to deviations of prices from their average levels:if price is above the equilibrium level, the component of reversion dropsthe growing rate down, or it even becomes negative. For this reason,mean reverting movements produce a lower level of uncertainty thanthe GBM, allowing price to oscillate around its long-term equilibriumlevel, with higher or lower frequency according to the speed of reversion.

3.2. Historic and forecast to DCCI components

For each of the macroeconomic scenarios presented in the previousitem and from the historical point of DCCI components, we get theannual and nominal forecast to these components.

Regional (North America, Western Europe, Eastern Europe andRussia, Southeast Asia, South America) macroeconomic data were pre-sented in IHS Forum3 and provide a specific situation for each of theseregions.

3.3. DCCI forecast

For each of the scenarios defined in 3.1 and from the projections ofeach of the components defined in 3.2, we calculated annual, globaland nominal projections for the DCCI, as follows:

3.4. Stochastic process for simulation of the DCCI components and DCCI

FromTables 2 and 3, we found that the DCCI has strong participationof commodities. Steel is expressed directly with a share of 13.9%. More-over, its price directly influences other items such as piping, equipmentand construction. The same happens with the price of copper whichdirectly influences the downstream items like equipment and electricalwork. The price of crude oil and oil products influence the price ofdownstream equipment, engineering, project management and labor.

Commodity prices are generally better modeled by a stochastic pro-cess of reversion to a mean (MRM). Soon the DDCI, which is directlyinfluenced by the price of commodities like steel, copper, oil and oilproducts, will have its individual components modeled by a stochasticprocess called modified mean reversion movement (MRMM). The

Table 2Own DCCI scenario using MRM for the nominal price index (2000 = 100).

Component Weights Average

2012 20

Steel and pipe 13.90% 333.0852 34Equipment 22.60% 219.6032 22Engineering and project management 12.80% 216.8489 22Labor 36.20% 203.3756 19Instrumentation and electrical 7.90% 182.621 18Construction 6.60% 186.8088 17DCCI 224.064232 22

reason for using the MRMM instead of MRM is that 10,000 values gen-erated for each component, instead of reverting to a long-term average,revert to a projected curve of each of the above scenarios.

Considering Pt as the price of each component at instant t, it is pos-sible to calculate the logarithms of each price series and build theEq. (7):

ln Ptð Þ ¼ aþ b ln Pt−1ð Þ þ εt ð7Þ

where εt follows a normal standard distribution with zero average andσ2/N variance.

In general, the commodities prices (P) are assumed to have a log-normal distribution. Hence, if X = ln(P), therefore P = eX, what keepsthe commodity price always positive even if the X value could be nega-tive, because there is no sense, for example, in having a price series withnegative values.

To realize the simulation of the stochastic process, it was necessaryto have a discrete equation, in other words, Xt as a function of Xt − 1.The discrete equation of the MRM real simulation for a time interval(Δt) is given, according to Dixit and Pindyck (1994), by Eq. (8) bellow:

Xt ¼ Xt−1e−ηΔt þ X 1−e−ηΔt

� �þ σ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1−e−2ηΔt

2η

sN 0;1ð Þ: ð8Þ

Based on Eq. (7), there is evidence of mean reversionwhen the coef-ficient b is lower than one, that is, if 0 b b b 1. Therefore, the followingregression is made:

ln Ptð Þ− ln Pt−1ð Þ ¼ aþ b−1ð Þ ln Pt−1ð Þ þ εt : ð9Þ

By obtaining the estimated value of the coefficients a and b from theregression (9) and using the volatility calculated through the pricestime series, we can calculate the three MRM parameters (Dixit andPindyck, 1994). Table 4 summaries the formulas for calculating theparameters of the MRM:

In the table that follows, is presented a “back test” which is consid-ered historical data from 2000 to 2009 and simulates 10,000 values forcomponents of the DCCI for the years 2010 and 2011 using theMRMM and the Hybrid Quasi-Monte Carlo simulation (Dias, 2005). Itis observed that the average error between the values generated andthe real value for the years 2010 and 2011 is relatively small, whichdemonstrates the validity of this model to forecast the values for thecomponents of the DCCI.

It is observed that, a greater percentage error in the steel and pipe,could, with the aim of reducing this error, change themodel parameterscalculated based on the history. Thus, for example, in this case the re-gression speed is 0.17 as estimated from the history. Assuming a rateof reversal of 0.5 for example (different from the historical), woulddecrease the error rate to 8% and 14% respectively for the years 2010and 2011.

At the timeof simulation of the behavior ofmembers of theDCCI, it isessential that the interdependence of these components is taken intoaccount to avoid scenarios that are absurd, and unworkable from the

13 2014 2015 2016 2017

2.8571 351.864 360.1659 367.818 374.8717.7969 235.7682 243.5233 251.068 258.40792.8456 228.4599 233.7162 238.6373 243.24451.2204 179.4896 168.1686 157.2429 146.69889.2549 195.855 202.4215 208.9544 215.45417.0138 167.4514 158.1161 149.0025 140.10533.5193 222.9352 222.319 221.6771 221.0154

Table 3Own DCCI scenario using GBM for the nominal price index (2000 = 100).

Component Weights Average

2012 2013 2014 2015 2016 2017

Steel and pipe 13.90% 362.325267 407.0766 457.4465 514.0697 577.5674 649.1215Equipment 22.60% 226.48992 242.8988 260.5356 279.4272 299.6684 321.4494Engineering and project management 12.80% 225.860283 242.3979 260.1954 279.2803 299.7053 321.6976Labor 36.20% 231.789097 248.7682 267.0008 286.557 307.5547 330.0958Instrumentation and electrical 7.90% 185.505935 195.5851 206.2153 217.4183 229.201 241.6644Construction 6.60% 187.504034 197.8909 208.8593 220.4269 232.629 245.5156DCCI 241.397938 261.0718 282.5011 305.812 331.1644 358.843

Table 5

17J.M. Vianello et al. / Energy Economics 45 (2014) 10–18

technical and practical standpoint. Thus, to maintain the historical cor-relations among various components of the DCCI, the generation of sto-chastic scenarios was performed and correlated using the Choleskydecomposition (Kloedn and Platen, 1992) with a total of 10,000 scenar-ios. The use of the Cholesky decomposition implies a recursive identifi-cation scheme which involves restrictions about the relations betweenthe variables. The Cholesky decomposition is useful for efficient numer-ical solutions and Monte Carlo simulations.

In the figure that follows, we show the 10,000 generated values forthe six components of DCCI in the scenario Global Redesign using MRRM and Hybrid Quasi Monte Carlo methodology.

From the values above and using the proportion of each component,we calculated the values for the four scenarios of DCCI. Below, we pres-ent the results for the “Global Redesign” scenario.

4. Stochastic process for investment simulation

Investment is a function of two components: technical uncertaintyand uncertainty regarding the increase of prices of equipment,materialsand services. So it is modeled as the product between these two compo-nents over the years because the characteristics of these uncertainties,the generations by stochastic processes were independent.

For uncertainty technique, we used a triangular distribution (as de-scribed in 2) and for the uncertainty concerning the price increase ofequipment, materials and serviceswe used theMRMM (described in 3).

5. Application to investment projects

There is uncertainty regarding the total investment due to the twocomponents described above. Based on the methodology describedabove, two adaptations took place for investment projects.

As the present study to be considered in value refers to the year 2012(which shows the values of DCCI uncertain because the year has notended) and the values of DCCI presented are referenced to 2000. Thefirst adaptation occurs in the component of uncertainty concerningthe price increase of equipment, materials and services throughoutthe investment period.

These results can be normalizated in relation to the last value avail-able from DCCI history, i.e., one year before the current one in which itcalculates the present value of the project. Thus, we performed anormalization considering the value of DCCI on the year 2011 (197),according to the IHS CERA Forum of August 2011.

The second adjustment occurs in the component of technicaluncertainty. Thus, with the maturity of the project over its life cycle,the parameters (maximum, minimum, and mode) of the triangular

Table 4Formula summary for the MRM parameters estimation.

Estimated parameter Equations

Speed of reversion η = − ln(b)/Δt

Volatility σ ¼ σεffiffiffiffiN

p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2 ln bð Þ= b2−1

� �rLong-run mean P ¼ exp aþ 0;5σ2=N

� �= 1−bð Þ

distribution will be narrower, as defined in Section 2, and the standarddeviation of values of investments smaller.

The graph shows the product of the scenarios generated by thesetwo components of uncertainty on investment.

Thus, in the present day (2012), as an example, a project in phase III(technical uncertainty between −5% and +15%) will have, for each ofthe 10,000 scenarios, an investment in a specific unit planned for onespecific year T given by:

Value of investment in a specific unit planned for the year T=AxB xC x D x E, where:

A total investment estimated at 2012;B percentage of the budget curve to the year T;C percentage of investment of each subunit in relation to total;D technical uncertainty raffled from the 10,000 sets of triangu-

lar distribution with parameters −5%, 0% and +15% (mini-mum, mode and maximum, respectively). As previouslymentioned, these parameters are a function of maturity andcomplexity of each sub-unit of the project. The values forthe technical uncertainty of each subunit are generatedindependently;

E price uncertainty among 10,000 randomly selected scenariosof DCCI for the year T.

6. Conclusion

There is, in some cases, a largemismatch between the planned valueof investment in a project and financial implementation of this. In thissituation, generates a net present value planned different from theeffectively achieved in the future. For a company with a representativeportfolio of projects, this difference can generate a possible insolvencyin the long term.

It is observed that, among the uncertain factors considered whenplanning a project called risk factors, CAPEX is one that most affectsthe net present value.

Therefore, a quantitative risk analysis of projects that consider possi-ble different scenarios for these investment values is extremely importantto measure statistically the real value of this project.

This paper presented the reasons for this mismatch between theplanned and executedvalue of investments and, from this study, obtaineda suitable stochastic process to generate different scenarios for theseinvestments in the oil industry.

Statistical for “back test” used to assess the proposed model.

Component Percentage error2010

Percentage error2011

Steel and pipe 10% 19%Equipment 1% 3%Engineering and project management 0% 0%Labor 5% 11%Instrumentation and electrical 4% 5%Construction 4% 7%

18 J.M. Vianello et al. / Energy Economics 45 (2014) 10–18

The advantages of this type of statistical model for the valuation ofthe investment in relation to other intuitive and casual valuation are:

a) It generates a probability distribution of the value of the investmentand not a deterministic value. Thus, statistical metrics such asmean,standard deviation, 10-percentile, and 90-percentile, among othersare useful for risk management projects.

b) Using this method, we can resolve issues involving costs of interre-lated components.

c) In addition, a modeling using scenarios generates not only one pre-diction and certain future, but expand the analysis to obtain amore systematic and comprehensive understanding of the variousfuture possibilities in a more flexible way.

Although the results are valid for projects in the petrochemical and re-fining sector, also called in the oil industry as downstream, themethodol-ogy can be applied to the upstream or even other branches of industry.

References

Dias, M.A.G., 2005. Opções Reais Híbridas com Aplicações em PetróleoDepartamento deEngenharia Industrial, Pontifícia Universidade Católica do Rio de Janeiro, Rio deJaneiro (Tese de Doutorado).

Dixit, A.K., Pindyck, R.S., 1994. Investment Under Uncertainty. Princeton University Press,New Jersey.

IHS CERA, 2011. IHS CERA Capital Costs Analysis Forum — Downstream: Second Quarter2011 (Market Update).

Kloedn, P.E., Platen, E., 1992. Numerical Solutions of Stochastic Differential Equations.Springer.

PMBOK, 2004. A Guide to the Project Management Body of Knowledge: PMBOK® Guide,Four Campus Boulevard, Newtown Square PA: Project Management Institute 2004,3rd edition.

Silva, B.N., Gomes, L.L., 2004. Análise de risco de projetos de desenvolvimento deprodução Marítima de Petróleo. Anais do Encontro Brasileiro de Finanças, 4, Brasil,Rio de Janeiro, RJ.