Day 3_BO.9.2_ a New Era of Risk and Uncertainty Analysis in Project Evaluation for Improved Decision...

Breakout 9

Mining Asset/Extractive Industries Valuation

A New Era of Risk and Uncertainty Analysis

In Project Valuation

Presented by

Nuzulul Haq

Indonesia

Bali International Convention Center

27 – 30 September 2010

Breakout 9 – Mining Asset/Extractive Industries Valuation 2

A New Era of Risk and Uncertainty Analysis In Project Valuation

Commonly, business practitioners used “one size fits all” single corporate discount rate

method for valuing uncertainty in the project valuation

A new era is coming for the industry. An era where project, business or commercial analyst,

not only ask themselves the question “what if…?” when evaluating their respective project,

but also want to know what is the effect of these “what if...?” uncertainties on their project

evaluation process, as well as the best strategies to follow when facing either an adverse or

a favorable condition.

On this new approach, we can move beyond the static “now or never” decision framework

that is implicit in most current analysis to an explicit modeling and analysis, using Real

Options Analysis (ROA), to examine the effects of the contingent decision sequences that

actually occur in most business situations.

The paper shows that a project that can be produced and abandoned at will has large values

of flexibility. The conventional Net Present Value (NPV) of such a project will underestimate

the true economic value. A further benefit of using the ROA approach discussed here is that

the valuation procedure produces a strategy map showing actions within the project, not just

a number.


I. INTRODUCTION

The era of high uncertain of commodity price requires the economic reassessment of many

mining projects. The primary valuation challenge confronting mining appraiser is to

recognize the uncertainty during the project life and the impact these uncertainties on the

project cash flow uncertainty.

Conventional mining project valuation uses an approach called net present value (NPV)

analysis based on static discounted cash flow (DCF) method.

This method has been used since the late 1800s to value and manage mining projects. This

involves forecasting the cash flows associated with a given mine plan, discounting those

cash flows to the present using a risk-adjusted discount rate (RADR), and then summing the

resultant discounted values.

The mining industry for the most part uses the DCF valuation method to estimate asset

values because it is simple and straight away. However this method is too generalized and

could be misleading especially for valuing mining project.

There are some assumptions behind the DCF valuation method, i.e.:

1. Expected future cash flows from the project are taken as “given”. They are assumed

to be certain to happen

2. Project risk does not change throughout its life

3. The project is a “now or never” opportunity. Once the project is undertaken, it will not

be affected by any future managerial decision.

Since the last two decades, valuation professionals have been actively investigating how to

improve Discounted Cash Flow (DCF) valuation methods by better representing mining

industry complexities in their cash flow models.

They look for the valuation methods that able to:

1. compute and value non linear cash flow pay offs that accrue to project owner

2. asses the impact of the uncertain variables on the project value and risk

3. recognize managerial flexibility to intervene the project in facing either an adverse or

a favorable condition


Real Options (RO) is considered as a modern valuation methods that able to accommodate

the above conditions. This method had been introduced to the mining industry as an

alternative to the DCF valuation methods.

This paper will use two valuation approaches (DCF and RO) to assess the impact of the

uncertainty of the commodity price on the projects value and risk. The difference in their

approach to adjusting project cash flow for risk gives the different results of the project value.

An analysis on one Coal Mine Project illustrates how valuation methods affect the

uncertainty, characteristics, and value of project cash flow streams when both discounted

cash flow (DCF) and real options (RO) methods are used to calculate net present value

(NPV) for project cash flow.

A comparison is made between the DCF and RO risk adjustments applied to each cash flow

stream to show how each method deals with the effects on value of the differences in

uncertainty of project cash flows.

In this paper, we also examine the applicability of Real Options in valuing this coal project

having operating flexibility options.

This paper is organized into the following sections: 1 – Introduction, 2 – The Issues of the

Conventional Valuation on Mining Project, 3 – The Difference between DCF and Real

Options, 4 – Case Study on Mining Project Valuation under Uncertainty, and 5 - Conclusion.

II. THE ISSUES OF THE CONVENTIONAL VALUATION ON MINING PROJECT

Currently, appraisers predominantly use single point forecast Net Present Value (NPV)

resulted from Discounted Cash Flow (DCF) method for their mining project valuation.

The primary limitation of cash flow models relying on single point forecasts is their inability to

compute and value non-linear cash flow pay-offs that accrue to project owner. Non-linear

cash flows have a curved dependence on the uncertain variables (like commodity price) that

are inputs into the cash flow model.


These cash flow models are best estimated using Monte Carlo on the uncertain input

variables. Monte Carlo simulation is one of several methods of random sampling. This type

of approach is preferred because it is best able to account for high dimensional non-linearity

that arises from path dependence inherent in tax loss carry forwards and profitability triggers.

Monte Carlo simulation is used to characterize the exposures of the project owners to the

risky cash flow streams generated from the project

The other issue is related to the assumption behind the conventional NPV that assumes

cash flow uncertainty is growing over the life of the project.

A fundamental principle of valuation theory is that investors are concerned with net cash flow

uncertainty and require compensations for being exposed to risk (i.e. risk adverse). In reality,

net cash flow uncertainty can vary tremendously over the life of the project due to changes in

cost structure, price levels, uncertainty characteristics and operating strategy.

Figure 1. Profile of Net Cash Flow Discount Factor

As shown in figure 1, the conventional NPV analysis would discount project cash flow using

a constant discount rate. This is problematic since it violates the principle of investor risk

aversion where the net cash flow uncertainty is not increasing at a constant rate (Blais et all,

2006). Using this analysis, longer the project would be put on production, higher discounting

factor would be applied to the cash flow generated from the project. This would penalize the

long-lived project like in mining industry.

The other issues in conventional NPV analysis is once of investment is made, the project will

run its course without intervention (“now or never”). It‟s contrary to the real situation that


project owner has a flexibility to intervene that project when there is new information in the

future.

The conventional NPV based DCF looks failed to assess the impact of the uncertainty and

the effect of contingent decision when facing either the adverse or favorable condition in the

future.

III. THE DIFFERENCE BETWEEN DCF AND REAL OPTIONS METHOD

Uncertainty introduces considerable complexity into the mine planning exercise not only

because it makes the problem larger and less tractable, but also because it makes

measuring the value outcomes of the various decision alternatives more difficult.

In the first publishing of Real Options (RO), it is an alternative method for project valuation

that can accommodate managerial flexibility in adapting and revising future decisions in

response to changing circumstances.

Figure 2, Conventional NPV vs. Real Options

As shown in figure 2, this method is mainly based on the flexibility of the project. The more

flexible the project is, the more valuable it is, because it allows the owner to respond to

future events in ways that will increase the value of the firm. Option valuation gives extra

value to the project because of the flexibility.

The NPV resulted from Real Options method is known as Expanded NPV, where the formula

is as follows:

1) Expanded NPV = NPV + Option Value


However, in the recent development of Real Options method, there is a fundamental

difference between DCF and RO methods although there is no flexibility in the project. This

new concept of real options rose up after publishing a series of papers in 1998 discussing

modern asset pricing methods for upstream petroleum project (Laughton, 1998).

Figure 3. DCF vs RO (modified from Samis et all, 2006)

Assuming the main source of the uncertainty of the project is the commodity price, figure 3

shows that in the absence of managerial flexibility, the first step in RO valuation is to apply

risk discount factor to each uncertain cash flow element arising in any one period.

The difference in risk adjustment between the DCF and RO valuation methods appears to be

nuanced but its consequences are potentially large. This process allows senior management

to use financial market information to determine the underlying structure of risk adjustments

for the uncertain variables of interest to the corporation. The detailed project cash flow

dependence on these underlying uncertain variables then determines how these underlying

risk adjustments are transformed implicitly into risk discounts for the project cash flow.

Risk discounting the project cash flows in this way ground the valuation in the financial

markets of relevance to investors. It also tunes the risk discounting in a controllable way to

the types and amounts of risk actually in the project cash flows, as opposed to using some

average discounting that it is not likely to be appropriate for the risk involved.

DCF (net cash flow)

Risk Adjustment Commodity Price

(Source of Uncertainty)

Risk Free Rate

Project Financial Model

Project Net Cash Flow

Project Value

Risk Adjusted Rate

Real Options (at source)


All of this rids the valuation process of some biases that are inherent in the DCF method,

which assumes that all projects and claims against those projects have the same structure of

risk. In the mining industry, these biases include a general bias against investment to reduce

future costs, a bias against mine plan designs with long-term production profiles, and, finally,

a bias against projects that face taxes, that are geared toward taking disproportionately more

revenue in realizations of the future characterized by high output prices.

The difference between DCF and RO methods of adjusting for cash flow risk when

calculating a cash flow NPV can be illustrated using the concept of Net Cash Flow Risk

Discount Factors (NCFRDFs). A NCFRDF calculates the magnitude of risk adjustment that

is applied to each dollar of a cash flow in a particular year. It indicates the amount an

investor will pay for a dollar of cash flow from a particular cash flow stream on a risk adjusted

(but not time adjusted) basis.

A NCFRDF is defined as the present value of a cash flow divided by the expected cash flow

after offsetting the adjustment for the time value of money:

2) )*(

NCFRDFt

tt

t

TDFECF

CFPV

where:

CFPV = the cash flow present value at project time „t‟

ECF = expected cash flow at project time „t‟

TDF = time discount factor at project time „t‟ = 1/(1 + risk free rate)t

RO and DCF have different NCFRDF equations because their respective approaches to risk

discounting differ.

A simple DCF NCFRDF for project owner at time „t‟ can be calculated as follows:

3) DCFt

tttt

tDCFtttRDF

TDFOpCostCmdtypriceMineprod

TDFRDFOpCostCmdtypriceMineprod,

,

OwnerProject DCF, t,*)*(

**)*(NCFRDF

where:

Mineprod = Mine production

Cmdtyprice = expected commodity price

OpCost = expected operating costs

RDFDCF = DCF risk discount factor = 1/(1+risk premium)t


The numerator is the present value of the cash flow as calculated using the DCF method.

The product RDFDCF * TDF is an approximate representation of the conventional discrete

DCF discounting formula that combines the risk and time adjustment into one discount rate.

The TDF in the denominator offsets the effects of time discounting so that we can examine

only the discounting for risk.

Equation 3 shows that project structure does not affect DCF risk discounting since the cash

flow equations in the numerator and denominator cancel each other. However, project

structure is very much part of the RO risk discounting mechanics.

The simple RO NCFRDF for project owner at time „t‟ can be calculated as follows:

4)

)*(

)/)**((

*)*(

)*)**((NCFRDF

,

,

OwnerProject RO, t,

ttt

ttcmdtytt

tttt

ttcmdtytt

OpCostCmdtypriceMineprod

TDFPVOpCostRDFCmdtypriceMineprod

TDFOpCostCmdtypriceMineprod

PVOpCostTDFRDFCmdtypriceMineprod

where:

PVOpCost = PV of expected operating costs

RDFCmdty = a market-based risk adjustment for pure commodity

price uncertainty

In the first line of this derivation the numerator is the present value of the cash flow

calculated using the real option method. The commodity risk adjustments in the RO method

are calculated using formulas that are consistent with the Capital Asset Pricing Model and

are able to recognize commodity price uncertainty. Salahor (1998) provides details of these

risk adjustment formulas.

Equation 4 shows that the cash flow equations cannot be factored out of the value

calculation because RO applies a market-based risk adjustment to the source of uncertainty

and then filters its effect through to the net cash flow stream. The application of a risk-

adjustment to the source of uncertainty results in the effective net cash flow risk adjustment

generated by RO recognizing changes in cash flow uncertainty as operating leverage varies.

Based on the above explanation, basically both DCF and RO has similar mechanism in

modeling future technical and commercial variables within a project, also they can be applied

to model likely managerial reactions to that uncertainty.


However, although real options is also used a discounted cash flow technique, it differs from

DCF method in two important ways i.e.:

1. real options uses market information to discount for the risk in the project cash flow to

recognize the unique risk profile of the projects

2. real options analysis puts particular emphasis on dynamic decision making, the “now

or later” alternative.

In essence, real options values the asset while at the same time anticipating how the asset

will be optimally managed, conditional on the market information and options available to the

manager in each decision period (Davis, 2008).

IV. CASE STUDY ON MINING PROJECT VALUATION UNDER UNCERTAINTY

In this section, a coal mine project is selected to carry out the reality investigations. This coal

project is valued using the following approach:

1. DCF vs. Real Options without early closure options (ignore managerial flexibility)

2. DCF vs. Real Options with early closure options (consider managerial flexibility)

In this case study, we assumed the main source of the uncertainty of the project is the coal

price (S) that will follow a one factor Geometric Brownian Motion (GBM):

5) dz σ dt α S

dS

where: dS = coal price different

= short term price volatility (%, annualized)

α = short term expected price growth (%, annualized)

dz = an increment of standard winner process dt = time different

Based on the above price model, coal price uncertainty will increase over the life of the

project.

The technical and commercial data of the coal project is shown in the table 1.


Parameter Descriptions

Technical Data

Mineable reserve (million ton)

Stripping ratio

Mine life (years)

Average Production plan (ton/year)

Commercial Data

Spot price ($/ton)

Long term price forecast ($/ton)

Operating Cost ($/ton)

Capex ($ millions)

Closure Cost ($/ton) of the coal produced

Royalty

Income Tax

Risk adjusted discount rate

Risk free discount rate

303.7

1:8

7

17.8

60

60

28

179.2

0.1

13.5%

41.75%

15%

5%

Table 1. Technical and Commercial Data of Coal Project

Since mining is a massive industry, the projects in this industry would potentially damage the

environment. Therefore, the company is obliged to conduct mine reclamation after

completed the project. The cost related to this activity is known as closure cost.

Mining appraisers should recognize the impact the closure cost on the cash flow uncertainty

in their project valuation.

In this case, we investigate how DCF and RO method recognize the unique risk profile of

closure cost spending in the end of the project.

4.1 DCF vs. Real Options without options (ignore managerial flexibility)

In this section, we would analyze how DCF and RO methods affect the uncertainty

characteristics and value of project cash flow stream. We assume management would not

intervene the project in the future.


0

50

100

150

200

250

300

0 2 4 6 8 10 12 14 16 18

Project time (years)

Co

al p

rice (

US

$/t

on

)

Coal price Risk-adjusted Coal price Upper confidence bdy

Lower confidence bdy Long Term Equilibrium Price

Figure 4 - Forward Price Model

The uncertainty characteristics of project cash flow over the life of the project were modeled

with Monte Carlo simulation using the coal price models displayed in figure 4.

To quantify the uncertainty, we use a coefficient of variation (CoV) that was recorded

annually for each cash flow. The coefficient of variation is the standard deviation of an

uncertain variable divided by its expected value, providing an indication of cash flow

dispersion (the higher the number the greater the uncertainty). It is used to highlight the level

of uncertainty in project cash flow stream.

0%

50%

100%

150%

200%

250%

0 2 4 6 8 10 12 14 16 18

Project time (year)

Cash

flo

w u

ncert

ain

ty (

% d

evia

tio

n)

Project

High capital

expenditure

Closure Cost

Figure 5 - Coefficients of variation for project owner‟s cash flow stream


Calculating values for the project cash flow streams in a manner consistent with the principle

of investor risk aversion is difficult because the uncertainty characteristics of cash flow

stream vary markedly. This task is further complicated because cash flow uncertainty for

project may vary by year as production rates, costs structures and capital depreciation

balances fluctuate.

Figure 5 presents the various cash flow stream CoVs during production operations. The solid

black line delineates the CoVs for the project cash flows as uncertainty of coal price

increase. The increase of deviation percentage in Year 3 and 4 is caused by high capital

expenditure in that period. The profile of project cash flow CoVs indicates that project cash

flow uncertainty varies in the year 1 to year 5 of the project and going increase after Year 5.

This is caused by the volatility tend to increase and profit margin decrease due to decrease

production.

In the end the project, there is a spike of cash flow uncertainty. This is due to cost spending

for mine closure.

0%

50%

100%

150%

200%

250%

0 2 4 6 8 10 12 14 16 18

Project time (year)

Cash

flo

w d

evia

tio

n (

%)

0.0

0.2

0.4

0.6

0.8

1.0

Net

cash

flo

w d

isco

un

t fa

cto

r

Project CF deviation DCF NCFDF RO NCFDF

Figure 6 - Project owner cash flow DCF and Real Options NCFRDFs

Figures 6 compare the DCF and RO risk adjustments applied to the various project cash

flow streams and links these adjustments to levels of cash flow uncertainty during each year.


In each of these graphs the vertical axis on the left side represents the level of cash flow

uncertainty. These are plotted with a solid black line, taken from Figures 5. The vertical axis

on the right side represents the NCFRDFs. The DCF and RO NCFRDFs are plotted with

grey lines; the dashed line with no data markers delineates the DCF NCFRDF and the lines

with data markers outline the RO NCFRDFs.

The difference between 1.00 and the NCFRDF is the amount of compensation an investor

requires for exposure to uncertainty in project cash flow stream.

The project cash flow uncertainty and risk discounting is provided in Figure 6. Cash flow

uncertainty increases with time as production decline and coal price uncertainty increases.

There is a jump in Year 3 and 4 due to higher capital spending in that period.

The RO NCFRDFs show that the effective project cash flow risk discounting reflects the

cash flow uncertainty. For example, in Year 4 (red circle in figure 6), the risk discount

decreases to $0.45 per dollar of cash flow (i.e. $1 cash flow is worth $0.55 on a risk-adjusted

but not time discounted basis).

Conversely, the DCF NCFRDF reflects a risk adjustment that is increasing over time. This

highlights a DCF assumption that cash flow uncertainty is growing over the life of the project.

The project CoVs show that project cash flow uncertainty in fact rises and falls throughout

the project horizon.

High cash flow risk in the end of the project is described in RO NCFRDFs by applying higher

risk discounting factor than in DCF NCFRDFs.

Cumulative expected net cash flows ($ thousands)

Project Level

Expected time-discounted stakeholder cash flows ($ thousands)

Project Level

Type of Risk discounting DCF RO

Static Monte Carlo Static Monte Carlo

Expected stakeholder cash flow NPV ($ thousands)

Project Level 1,401,328 2,030,366 1,292,735 2,194,521

2,680,505 4,212,416

Static Monte Carlo

4,047,079 6,659,029

Table 2. Cash Flow Summary


The valuation result for the coal project is presented in Table 2. The following cash flows and

Net Present Value (NPV) were calculated for project using both a conventional single-point

forecast cash flow model („Static‟) and a Monte Carlo simulation model:

1. Cumulative expected net cash flow,

2. Time-adjusted cumulative expected net cash flow where discounting is performed at

the risk-free rate of five percent,

3. A DCF NPV calculated using an fifteen per cent discount rate, and

4. A RO NPV calculated with risk-adjusted expected coal price and the risk-free rate of

five percent.

The project in table 2 has an expected cumulative cash flow of US$ 4,047 million using a

spreadsheet model. The Monte Carlo analysis estimates the different value for project

cumulative cash flow of US$ 6,659 million. The difference occurred because as is typical, the

static method underestimates the upside potential value of the project.

US$ 4,047 million cash flow received from project has a present value of US$ 1,401 million

using DCF method with a fifteen per cent discount rate, and the US$ 6,659 million project

cash flow estimated using Monte Carlo analysis has a value of US$ 2,030 million when

discounted at a fifteen per cent discount rate. The difference is true whether Static

spreadsheet or Monte Carlo analysis is used because there are non-linearities in the cash

flows.

None of these values is likely to be correct. However, it is well-recognized that cash flows

that are more sensitive to price variability should be discounted at a higher rate.

Looking back to Figure 5, it is unreasonable to discount the project cash flow in Year 4 at

fifteen per cent, and then discount the project cash flow in Year 5, which has much lower

variability, at the same fifteen per cent. RO valuation methods take this varying cash flow

uncertainty across time and across cash flow type into account.

Under the RO Monte Carlo approach and ignore managerial flexibility, which uses market

information and formal models of risk discounting to estimate appropriate cash flow risk

discounting, the project has a value of US 2,195 million.

Figure 6 also provides an explanation for RO Monte Carlo calculating a higher project NPV

than the DCF Monte Carlo method in Tables 2. On average, the RO method applies a lower


risk adjustment to each dollar of project cash flow than the DCF method because it is picking

up coal price uncertainty and the high correlation between coal price and financial market

uncertainty in its risk adjustments. It is indicated that the DCF discount rate of fifteen per

cent was too high for this project.

4.2 DCF vs. Real Options with early closure options (consider managerial flexibility)

In this section, the applicability DCF and RO method to consider managerial flexibility will be

investigated. Using the previous case study, we extend the case by assuming management

has an ability to close the coal project at any time is incorporated into the project model. An

early closure option is included in DCF and RO methods since managers have the ability to

permanently exit this coal project when coal price turn unfavorable.

There are two options available for management, i.e.:

1. Management can close the coal project early by spending closure cost if coal price is

lower than cash cost

2. Management can keep continue the production if the coal price is still higher than

cash cost.

Type of Risk discounting

No Flexibility Flexibility No Flexibility Flexibility

Equity Level Include Financing 2,030,366 2,079,042 2,194,521 2,552,922

Option Value 48,675 358,400

DCF RO

Table 3. Comparison Result

As shown in table 3, under DCF method, if we consider the managerial flexibility in the

project, the ability to limit downside risk with an early closure option increases project value

by an estimated over $48.7 million, producing a total estimated project value of $2,079

million.

However, under RO method, there is a significant increase of the project value if we consider

early closure option by an estimated over $358.4 million, producing a total estimated project

value of $2,553 million.


Based on this study, the potential value of this coal project would be $2,553 million under

RO valuation method with early closure option.

The results highlight that ignoring managerial flexibility such as early closure option can

generate misleading project value estimates. Managers often have the ability to manage

project risk with operational strategies and this ability can have significantly effect on project

value.

V. CONCLUSIONS

The era of high uncertain of commodity price requires the economic reassessment of many

mining projects. The primary valuation challenge confronting mining appraisers is to

recognize the uncertainty during the project life and the impact these uncertainties on the

project cash flow uncertainty.

This paper investigated the impact of commodity price uncertainty on the cash flows of a

mining project using Monte Carlo simulation. The results show that a conventional cash flow

model using single-point input values may contain important cash flow estimation errors.

The single point forecast can give incorrect result when such non linearity exist in project

cash flow. These errors are corrected in a Monte Carlo analysis.

Monte Carlo simulation corrected these errors by recognizing cash flow non-linearities in the

cash flow stream. Taxes not only introduce complicated non-linearities into the valuation

process, but they also alter the riskiness of the cash flows received by project owner. DCF

method discounts all cash flow streams at the same rate. Real Options method brings this

out, with logically higher discounting of riskier cash flow streams and lower discounting of

less risky cash flow streams.

We have described the concept of Real Options method combined with Monte Carlo

simulation as an alternative method to the DCF method in valuing the mine project.

We have also described how managerial flexibility can be included in both of DCF and RO

method to improve the assessment of project value.


The result shows that improper risk assessment on cash flow uncertainty properly and

ignoring managerial flexibility can generate misleading project value estimates.

The results reported in this paper are preliminary, pending a careful statistical examination of

the robustness of the valuation procedure. However, this paper concludes that the Real

Options can be applied in mining project valuation. The RO method is more likely to reveal a

true picture of the value of the mining projects.

REFERENCES

Abdel Sabour, S.A, Poulin, R (2006), Valuing Real Capital Investments Using Least Squares

Monte CaBoyle, P., M. Broadie, a rlo Method. Eng. Econom 51(2), pp. 141-160

Blais, V, Samis, M., and Poulin, R (2006) "Using Real Options to Incorporate Price Risk Into

the Valuation of A Multi-mineral Mine”, MEMS News, winter 2006, issue no.35, pp. 11-16.

Cortazar, G. (2001) "Simulation and numerical methods in real options valuation." In Real

Options and Investment under Uncertainty: Classical Readings and Recent Contributions,

E.S. Schwartz and L. Trigeorgis, Eds., MIT Press, Cambridge, MA. ch. 27, pp. 601-620.

Davis, G A, and Newman, A M , 2008. Modern Strategic Mine Planning, Proceedings of the

2008 Australian Mining Technology Conference, AusIMM, Carlton, Australia (2008), 129-39

Gamba, A. (2003) "Real options valuation: A Monte Carlo approach." Faculty of

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Meeting of the European Finance Association (EFA), Humboldt University, Berlin, August

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Longstaff, F.A. and E.S. Schwartz. (2001) "Valuing American options by simulation: A simple

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Salahor, G, 1998. Implications of Output Price Risk and Operating Leverage for the

Evaluation of Petroleum Development Projects, Energy Journal, 19(1):13-46.

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flows when there are no options: A real options approach, Resources Policy, 30:285-298.

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