auger 2010

Resources Policy 35 (2010) 292–300

Contents lists available at ScienceDirect

Resources Policy

0301-42

doi:10.1

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John Til

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(J.I. Gu1 W

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journal homepage: www.elsevier.com/locate/resourpol

How rational are investment decisions in the copper industry?$

Felipe Auger, Juan Ignacio Guzman n

College of Engineering and Applied Sciences, Universidad de Los Andes, Av. San Carlos de Apoquindo 2200, Las Condes, Santiago, Chile

a r t i c l e i n f o

Article history:

Received 21 June 2010

Accepted 20 July 2010

JEL classification:

D01

D21

D81

L72

Keywords:

Capacity choice

Investment timing

Rationality

Uncertainty

07/$ - see front matter & 2010 Elsevier Ltd. A

016/j.resourpol.2010.07.002

authors are grateful to Carlos Deck, Andres K

ton for their valuable comments. We also tha

luable suggestions.

esponding author. Tel.: +56 2 412 9879; fax:

ail addresses: [email protected] (F. Auger)

zman).

hile mining investments take place in an envi

pe of this paper is restricted to price. Other

mental, geological, operational, technological

mining, most investment decisions are irrev

sts.

other method is based on Monte Carlo simu

a b s t r a c t

This paper examines ex-post 51 investment decisions made in regard to copper mines coming on

stream from 1957 through 1999. It discusses two critical variables: investment timing and mine

capacity choice. Using a 15% discount rate, results suggest that fewer than half of decisions were made

at the right time – i.e., low price periods – confirming countercyclical investment as the optimal policy.

In terms of capacity choice, the distortion is even higher, as 36 projects should have entered at least 40%

larger or smaller. Realized investment decisions for timing and capacity choice would have caused a

49.1% loss over the NPV potentially achievable under optimal resolutions. Although the difference could

be specifically attributed to copper price uncertainty, this paper discusses how investment evaluation

methodologies could be contributing to firms not being fully rational (in the neoclassical sense) when

investing.

& 2010 Elsevier Ltd. All rights reserved.

Introduction

Uncertainty of commodity prices is often the leading openquestion on which mining project economic evaluation is built1.Yet, the evaluation method currently used in the mining industryconsists of determining the discounted cash flow (DCF), assumingthat uncertainties, especially commodity price, are at expectedvalues. However, this method is known to provide suboptimalresults in uncertain environments, where decisions are irrever-sible (Dixit and Pindyck, 1994)2.

Real options are one method of addressing traditional valuationissues in the mining industry in presence of uncertainty (Dixit andPindyck, 1994; Samis et al., 2006)3. While academia concurs on theneed to use real options in evaluating projects under uncertainty,this technique has been unsuccessful to enter in the miningindustry. As a matter of fact, few companies base their investment

ll rights reserved.

ettlun, Jose Joaquın Jara and

nk an anonymous referee for

+56 2 412 9642.

, [email protected]

ronment full of uncertainties,

uncertainty sources include

, etc.

ersible, since they are mostly

lation of the DCF.

decisions on this technique (Rudenno, 2009)4. Indeed, the authorsare unaware of a single mining firm basing all or part of suchdecisions on the systematic use of real options. Virtually all use (forat least four decades now) DCF techniques for project evaluationwith no explicit consideration of uncertainties (Moyen et al., 1996).

Moyen et al. (1996) note that most mining firms baseeconomic evaluation on long-term prices5 determined by bothin-house analysts and a range of market sources (such as BrookHunt or CRU and the investment banks financing all or part of theproject). They also discuss how the long-term price is normallyadjusted for present conditions. This may well be rooted in thestochastic nature of prices, as these tend to follow random walksat least over short periods of time (Dixit and Pindyck, 1994). Anadditional characteristic of most firms’ forecasts of price vectors isthe absence of cycles. This can be explained since there are noclear parameters of regularity enabling such a forecast (Roberts,2009). Still, price cycles play a key role in mineral markets,especially as they are strongly correlated with business cycles(Pindyck and Rotemberg, 1990).

4 Two factors may account for this. First, the lack of an optimization algorithm

helping determine optimal exploitation under uncertainty. Second, real options

are a relatively new technique dating back to the early seventies, while traditional

DCF analysis (with no explicit consideration of uncertainties) started with Irving

Fisher in the early 20th century, some six decades prior (Fisher, 1907).5 Herrera (2010) poll of nine of South America’s largest copper mining firms

found that eight based mining and investment plans on an expected (determi-

nistic) copper price vector. The remaining firm used price bands, although

restricted to a sensitivity analysis also in a deterministic context.

F. Auger, J.I. Guzman / Resources Policy 35 (2010) 292–300 293

Failure to use real options to assess investments runs against abasic assumption of neoclassical economic theory: under un-certainty, firms ought to maximize their expected profits6. In ourview, two factors may account for investment decisions thatappear non-rational from the neoclassical standpoint: standardinvestment criteria and disregard for commodity price uncer-tainty. As the conceptual line between these factors is thin, theseare discussed separately below.

The DCF criterion is traditionally taught in business and otherschools based on the naıve rule associated with the net presentvalue (NPV) sign, which encompasses both the DCF of profits ineach period and the investments required to generate them. Therule states that if an NPV is positive a project can go ahead, and ifnegative, it should be shelved. In the mining industry, the naıve

NPV rule is used to (i) determine whether to invest, and if so,when and (ii) set investment levels (Cairns, 2001).

While the simple NPV rule7 has been widely criticized(Ingersoll and Ross, 1992; McDonald and Siegel, 1986; Ross,1995), its use (and abuse) remains widespread in the miningindustry and throughout all sectors of the economy. A keycriticism says that a firm using the simple NPV rule will notnecessarily maximize its profits (NPV), even when no uncertaintyis present. As such, it’s very use is to be questioned from thestandpoint of neoclassical economic rationality.

Failure to account for uncertainty in economic evaluation is afactor that holds true for most industries. While strongly relatedto the use of the simple NPV rule (Cyert and March, 1963), anothercritical factor in the mining industries’ failure to account for priceuncertainty is the lack of a robust theory of mine planning underuncertainty and the software necessary to implement it. Toaccount for an uncertainty of price, rather than base decisions onappropriate techniques (such as real options or Monte Carlosimulation), mining firms choose to conduct (albeit not always)sensitivity analysis at various price levels (Cairns, 2001; Moyenet al., 1996).

Basing investment evaluation on an expected price vectorseems at first glance a good initial approach8, notwithstanding theprobability of such a vector is nil9. However, for such a price to beconsistent with maximizing an NPV, it is assumed that the NPV

evaluated for the expected price is equal to the expected NPV

(vis-�a-vis price distribution). However, Jensen’s (1906) inequalityis a good refutation proving that if the NPV is not a linear functionof the price, these two variables are not necessarily equal10.

Using ex-post NPV assessment, this paper attempts to explorethe rationality of investment decisions in 51 copper miningprojects coming on stream in 1957 through 199911. To leverageempirical knowledge of the simple NPV rule, we introduce a weak

6 In a time span of two or more financial periods, profits are replaced by their

respective discounted cash flows.7 From here on out, we will refer to the rule as ‘‘simple,’’ as different from the

expanded NPV rule spanning both the value of real project options and the strategic

project value (Smit and Trigeorgis, 2004).8 However, experience has provided mining firms do not trust price forecasts.

For example, in the case of copper Lay (2009) compares quarterly price forecasts

by various market players for 1996–2008, concluding that forecasts of expected

values are always significantly mistaken when compared with realized prices.9 Assuming a continuous probability distribution for commodity prices, any

specific price used for the evaluation (including the expected price) has a zero

probability of occurrence.10 One of the authors has had first-hand experience with the unfamiliarity of

most mining engineers and executives with the conceptual difference between the

NPV evaluated for the expected price and the expected NPV.11 It is important to note that our assessment is very different to that of

Leveille and Doggett (2006), on both focus and methodology of calculation. Their

goal is to determine the return on investment in copper exploration. However,

their methodology is essentially an in-situ assessment, using an average and

deterministic copper price. Hence, our results are not comparable to Leveille and

Doggett�s.

rationality concept which distinguishes from neoclassical ration-ality (referred to here as strong).

As ex-post NPV assessments are based on realized prices, thisimportant source of uncertainty is removed. Clearly, the ex-postNPV assessment has limited explanatory potential on exploringrationality behind investment decisions, as the real price path isunknown at the time a decision is made. This accounts for somereluctance to using the method, perhaps owing to the hindsight is

20/20 dictum. Another reason for the scant use of ex-postassessment is because decision-makers prefer to ‘‘think positive’’once a decision is made and stick to the belief that their decisionis best; further, restricting available latitude for this type ofexamination12. Still, some mining firms do use ex-post assess-ment to learn from past decisions and apply the insights to futureinvestment (Herrera, 2010).

This paper uses the ex-post NPV assessment method todetermine the optimality of two key issues in mining projects:the timing (i.e., when the decision to invest is made), and mineproduction capacity. While both have been reviewed theoreticallyin the literature13, we have found in actual practice that decisionsare often made without benefit of explicitly accounting for priceuncertainty14.

This paper is organized as follows. ‘‘NPV calculation assump-tions’’ reviews the assumptions used in performing ex-post NPV

assessments of a range of copper mining projects. ‘‘Strong andweak rationality’’ describes the strong and weak rationalityconcepts proposed to – in our view –properly account for thedegree of rationality expected from firms making a decision toinvest. ‘‘The database’’ reviews key figures for the 51 copperindustry projects examined in the ex-post exercise. Section‘‘Investment timing’’ and ‘‘Capacity choice’’ review investmenttiming and mine capacity choice for these projects. ‘‘Testing forrationality in the copper industry’’ discusses copper firm behaviorhypotheses, especially as regards degree of rationality (weak andstrong) at the time of investment. Concluding remarks follow.

NPV calculation assumptions

Ex-post assessments help determine the extent to whichinvestment goals are met. One of their key characteristics isremoval of uncertainties, making it possible to evaluate therealized NPV and compare it to the promised NPV (i.e., the NPV

evaluated at expected values) at the time the decision was made.We had no access to the price vector firms expected when

making a decision to invest in new or expanded mines. As such,rather than comparing the realized NPV to the promised NPV, theformer was expressed as a function of timing and productioncapacity. Thus, assuming that for any one investment, these keyvariables can be expressed by t and K, we have that

NPV ¼NPVðt,KÞ ð1Þ

To build function (1) for a range of investment projects incopper mining, several assumptions were required. Thus, inaddition to the year when the actual decision to invest, tui, wasmade, the i-th investment required defining the installed capacity,K ui, life of mine, T ui, average production cost, cui, total project

12 This is known as the Pollyanna–Nietzsche effect (Carter, 1971).13 For a review of more classical literature on investment timing, see Pindyck

(1991). For specific production capacity in a real options context, see Pindyck

(1988). An empirical model of capacity choice for mining is found in Laserre

(1985).14 In the opinion of McDonald and Siegel (1986), company executives may be

implicitly considering the value of real project options when investing only when

the NPV is high enough (rather than when greater than zero). This is also

sometimes referred to as using NPV multiples.

20 Obviously, firms basing their decisions on a sufficiently positive NPV (i.e.

greater than some arbitrary positive constant) should also be considered rational

in the weak sense advanced here.21 While similar, these are not to ne confused with those defined by O’Donnell

F. Auger, J.I. Guzman / Resources Policy 35 (2010) 292–300294

investment, Iui and annual discount rate, ri15. NPV was assessed

using an annualized discrete model.As to the investment decision year, in general, this is rarely an

observable project variable (particularly in the copper industryand the sample here). As such, the decision to proceed wasassumed to have been made three years before start-up in thecase of open-pit mines and six years prior for undergroundmines16.

This ex-post assessment also assumed production at capacityfor each year in the project lifetime. While this is debatable sincedesign capacity may take one or two years to be reached (or neveris, or even may be exceeded), the fact is that determining averagerump up times is not an easy proposition. That said, we do notbelieve that this factor should skew our results.

Life of mine can be approximated as total reserves divided byproduction capacity. Hence, life of mine is assumed to beinversely proportional to the production capacity. While newreserves are often discovered during development, for thepurposes of this ex-post NPV assessment, the reserves originallyreported in the project were considered as unchanging.

A constant average production cost throughout the life ofmine, required by a lack of annual cost forecast data, is perhapsone of the most restrictive assumptions. Yet, since actual averagecosts were used, this variable is expected to play no major role inchanging our results.

As per Majd and Pindyck (1987), the initial investment17 isconsidered to have been distributed across several years beforeproject start-up. While this predictably varies from one project tothe next, we leveraged the views of experts to build twodistributions: one for open-pit and mixed mines (i.e., combiningopen-pit and underground methods) and another for under-ground mines. For the former, 15% of the total investment isassumed made three years prior to start-up (i.e., immediatelyfollowing the decision). Another 30% and 50% are invested twoand one year prior, respectively, while the final 5% is invested inthe start-up year. Investment distribution for underground minesacross the six-year period from decision to start-up was deemedto stand at 7.5%, 7.5%, 15%, 15%, 25%, 25% and 5%.

As to the discount rate, another non-observable factor, 15%was factored in for all investments. Nevertheless, this exercisewas replicated at rates of 5%, 10% and 20% without significantdifferences;18 15% was chosen since it is identified by Moyen et al.(1996) as commonly used in the mid-nineties (a timeframe withinthe scope of our research)19.

Therefore, if commodity price in year t is given by Pt, the NPV inEq. (1) may be calculated for the i-th investment as follows:

NPViðtui,K uiÞ ¼ �IuiXtuiþoi

t ¼ tui

dit

ð1þriÞt�tuiþ

XT0

iþt0

iþoi

t ¼ t0iþoi

ðPt�cuiÞK ui

ð1þriÞt�tui

ð2Þ

where oi measures construction time for the i-th project (i.e.,oi¼3 or 6 depending on whether open-pit/mixed or under-ground, respectively) and dit is the temporal investment distribu-tion index for the i-th project. As such, for open-pit/mixed,

15 The prime in superscript of each variable denotes that values are as used to

implement the project.16 Averages provided by industry experts. Time lags were shifted by 71 year,

causing no significant changes in the results.17 In the database, we looked for investment estimated at the time the

decision was made (as noted in feasibility studies). As this information was not

always available, in some cases, the realized investment was used instead. We are

cognizant that this is a potential source of an error in our estimation.18 For results at these rates, see Auger (2010).19 This percentage coincides with the median value found in a survey of 200

major corporations in United States (Summers, 1987).

we have

dit ¼

0:15 if t¼ tui0:30 if t¼ tuiþ1

0:50 if t¼ tuiþ2

0:05 if t¼ tuiþ3

8>>>><>>>>:

For underground mines, the temporal distribution index isgiven by

dit ¼

0:075 if t¼ tui0:075 if t¼ tuiþ1

0:15 if t¼ tuiþ2

0:15 if t¼ tuiþ3

0:25 if t¼ tuiþ4

0:25 if t¼ tuiþ5

0:05 if t¼ t0iþ6

8>>>>>>>>>>>><>>>>>>>>>>>>:

Strong and weak rationality

Among other things, Eq. (2) lets us determine whether thetiming and production capacity of industry investments haveeither destroyed or created value (NPViðtui,K uiÞ negative orpositive). Also, an ex-post NPV assessment using Eq. (2) lets usestimate the amount of value created and/or destroyed.

In addition, we can use the ex-post NPV assessment to exploredegrees of rationality in an industry. Although neoclassicalconcepts of economic rationality focus on maximizing the NPV,for consistency with the decision assessment method, we believeit possible to envisage a weak economic rationality based oninvesting if the NPV is positive. It does not seem logical that a firminvesting in a project that creates value (i.e., NPV40), but

not maximize it, should be considered irrational in an economicsense.

To distinguish firms making decisions in order to maximize theNPV from those solely factoring in a positive NPV20, we proposethe concepts of strong and weak rationality21. The former is linkedto an NPV maximization, the latter guarantees a non-negativeNPV22. Hence, in our view, an action is economically irrationalonly if associated with decisions leading to a negative NPV. Assuch, degrees of rationality, rather than a contrivance thought upto explain investment behavior, should hold true for anyeconomic decision and industry23.

It follows then that testing for weak rationality underuncertainty is akin to testing for a positive expected NPV24. Whilecomputing the expected NPV for each investment in an industry isan impossibility given our limited knowledge on analyzedprojects, a simple test can help test for weak rationality acrossthe industry as a whole. Thus, if an NPVi is the realized NPV for the

(1989).22 Under uncertainty, the NPV must be replaced by the expected NPV.23 While we do not intend to explore the theoretical implications of the weak

rationality proposed here, reviewing the scope of a theory based on this

assumption should be an interesting exercise, as presumably most results widely

known in economics are lost. For example, under equilibrium and assuming strong

rationality, prices are equal to the marginal cost in a perfectly competitive market,

yet when weak rationality is assumed, prices become greater than or equal to the

average cost. On the threshold between weak rationality and economic

irrationality (which should be the expected behavior with an infinite number of

players), there can be no profits, a result reached under a strong short-term

rationality assumption only in a contestable market (Baumol et al., 1982).24 This assumes risk neutrality of firms.

30 Construction of a rigorous proof to test for rationality in the strong sense is


i-th investment, and assuming statistical independence across thevarious investments25, based on Kolmogorov’s strong law of largenumbers (Sen and Singer, 1993), if the number of investmentprojects, N, considered is sufficiently large, then we have

E1

N

XN

i ¼ 1

NPVi

" #�

1

N

XN

i ¼ 1

NPVi ð3Þ

where E½d� is the mathematical operator of the expected value.As such, Eq. (3) lets us test whether an average industry

behavior may be considered a weak rational in a context of priceuncertainty. Indeed, if the realized NPV industry average is greaterthan zero, then so will be the average industry investment’sexpected NPV.

Testing for strong rationality as a behavior of firms within anindustry is a harder proposition. While we failed to find amathematical test such as that used for weak rationality, it is stillpossible to determine how far from the potential optimum anindustry is. As such, if t�i and K�i are the timing and productioncapacity maximizing the ex-post NPV of the i-th investment, namely

t�i ,K�i ¼ Arg maxti Ztui ,Ki

NPViðti,KiÞ ð4Þ

Then the maximum potential NPV for the industry will begiven by

NPV� ¼XN

i ¼ 1

NPViðt�i ,K�i Þ ð5Þ

while the realized NPV of the industry will be given by

NPV u¼XN

i ¼ 1

NPViðtui,K uiÞ ð6Þ

Based on Eqs. (5) and (6), it is possible to build a capture index

of the maximum potential NPV, j, given by26

j¼NPV

0

NPV�ð7Þ

As such, j is clearly bounded from above by 127 and j¼ 1occurs when the industry is capable of completely capturing themaximum potential NPV.

Under certainty, computing the j index would help establishan industry’s degree of an economic rationality. Thus, j¼ 1indicates an industry whose firms are strongly rational28, whilejA ½0,1� shows an industry whose firms are weakly rational29.Based on this reasoning, an industry can be considered irrationalonly if jo0.

In an uncertainty scenario, however, jo1 with probability 1.Thus, this index does not allow testing for an industry’s degree ofrationality under uncertainty, as an j index of less than 1 may notnecessarily be due to suboptimal behavior by one or more firms,but to the uncertainty extant at the time decisions were made.That said, it seems reasonable to assume that an j indexsufficiently below 1 may be an indication that the industry doesnot in general behave in a strongly rational manner.

As noted in the introduction, the use of investment evaluationmethods not explicitly accounting for commodity price uncer-tainty suggests a priori that mining industry behavior can hardly

25 This seems a reasonable assumption in mining, since the impact of

commodity prices on a project NPV should be independent of their impact on

another.26 Conceptually, in a perfectly competitive industry, NPV� ¼ 0, so j could not

be well defined. However, in the mining industry, Ricardian rents assure that

NPV�40, even if a perfectly competitive industry is considered.27 However, since NPV

0

can take on any real number value, it will not

necessarily be bounded from below.28 In which case, we have that tui ¼ t�i and K ui ¼ K�i for all i¼ 1,2, . . ., N:29 Note that for industry behavior to be consider rational in the weak sense, it

suffices for one firm to be non-rational in the strong sense.

be considered rational in the strong sense. This should bereflected in an empirical j value well below 130.

The database

As noted, firms in the copper industry were examined forrationality at investment decisions. This industry was selectedbased on the available information and our own empiricalknowledge of industry project evaluation practices.

In order to do the ex-post NPV assessment, a sample of coppermining (and associated processing plants) projects startingproduction in 1950–2000 was considered31. The original list ofprojects was compiled from a range of trade sources (such as theMining Journal and Raw Materials Group Database), and resourcesavailable on the Internet (including company web sites). As aresult, we identified 135 copper mining investment projectsworldwide entering in 1950–2000.

With this original list, we sought for data related to each ofthese projects. Data gathered included investment, productioncapacity, unit operating costs, start-up production year and life ofmine. After reviewing most available resources, the final databaseconsisted of a total of 51 projects involving new mines andexpansion of existing operations, including 34 open-pit, 11 under-ground and 6 mixed (a combination of both) mines (see details inTable 1)32.

Of the 51 mines for which enough information for an ex-postNPV assessment was gathered, 22 were in Chile, 11 in Australia, 3in the United States, 2 in Canada and Zambia, and one each inArgentina, China, Cyprus, Cuba, India, Pakistan, Papua NewGuinea, Peru, Portugal, Turkey and Zimbabwe. While we did notset out to mirror the geographical distribution of copper mineinvestment in the period, to some extent this did occur.

From the standpoint of firm heterogeneity, distributionappears to replicate production standings33. The firm with thelargest number of projects is Codelco, with 6. Next in number ofprojects are BHP Billiton (4), Anglo American (3) and PhelpsDodge (3)34. With two or fewer projects were industry players oflong standing such as Antofagasta Minerals, Grupo Mexico,Noranda, Placer Dome, Rio Tinto and Xstrata35.

For ease of comparison, all dollar amounts were deflated to2008 based on the U.S. CPI. The 51 projects in the sampleaccounted for a combined $25.54 billion (in dollars of 2008).Coupled with project heterogeneity, this shows that while thedatabase is incomplete, it does appear to be representative of thecopper industry in the relevant period.

Ex-post NPV assessment required two additional estimates.First, actual LME price data used was only available through 2008,which required estimating as many years as necessary to matchthe expected mine lifetimes. These estimates were provided by aleading price forecaster and they are available upon request toauthors. However, estimations beyond 2008 have a very minorimpact on the NPV (due to the discount rate used) and only 25 of

open to future research.31 Because we had actual copper prices until 2008, a mine coming on stream

in 2000 could still have been evaluated, based on nine years of realized rather than

forecast prices. While this certainly does not encompass the entire projected

lifetime, it suffices to capture about 2/3 of the realized NPV, given the 15% discount

rate used.32 Projects can be reclassified in 45 greenfields and 6 brownfields.33 Heterogeneity of investments with respect to implementing firms is highly

relevant; otherwise conclusions could not be extrapolated industry-wide.34 Original names were retained. While Phelps Dodge ceased to exist as such

after acquisition by Freeport McMoRan in 2007, the three projects reviewed here

started under its aegis.35 See full list in Auger (2010).

Table 1Investment project database.

Source: Auger (2010).

Name Investment (US$ million) Capacity (kton/year) Cost (US$ 2008/lb) Start-up year Life of mine (years)

Alumbrera 1610 180 0.43 1997 17

Amolanas 74 20 0.73 1993 20

Andacollo 111 20 0.64 1997 11

Andina 222 40 0.72 1970 20

Andina (Exp. I) 177 118 0.64 1986 20

Andina (Exp. II) 827 215 0.56 1999 50

Bwana Mkubwa 42 9.2 0.91 1998 6

Cayeli 272 110 0.65 1994 15

Cerro Colorado 363 50 0.61 1994 23

Collahuasi 2262 400 0.65 1999 50

Dexing Copper 1516 200 0.57 1987 20

El Abra 872 225 0.54 1997 17

El Teniente 1554 280 0.50 1970 50

Eloise 28 45 0.71 1996 20

Escondida 1977 300 0.53 1990 52

Escondida SX 583 125 0.52 1999 14

Flambeau 29 15.6 0.74 1994 6

Girilambone SX 39 14.5 0.64 1993 6

Great Australia 15 5.5 0.75 1996 8

Huckleberry 184 27.3 0.86 1997 18

Konkola 1034 180 0.59 1957 20

La Candelaria 490 90 0.67 1994 34

Lomas Bayas 330 45 0.63 1998 12

Los Bronces 596 120 0.64 1993 21

Los Pelambres 969 260 0.53 1999 30

Louvicourt 308 45 0.71 1994 12

Malanjkhand 216 23 0.73 1983 30

Mantos Blancos 412 120 0.64 1996 18

Mantoverde 244 42 0.78 1996 16

Mantua 65 18 0.58 1998 10

Michilla 119 20 0.78 1992 10

Mt Cuthbert 27 5.5 0.95 1996 5

Mt Gordon 120 44 0.57 1999 15

Mt Lyell 56 30 0.73 1996 10

Neves Corvo 695 65 0.87 1989 15

Nifty 74 16.5 0.55 1993 12

Ok Tedi 284 200 1.33 1987 24

Olympic Dam 955 45 0.87 1989 15

Osborne 162 29 0.89 1995 11

Peak mines 192 2.5 0.75 1992 20

Quebrada Blanca 436 75 0.90 1994 14

Radomiro Tomic 902 150 0.62 1998 25

Robinson 412 66.2 0.67 1996 15

Saindak Mine 489 15.8 0.74 1999 19

Salvador 880 100 0.66 1959 50

Sanyati 18 2.5 0.62 1996 10

Selwyn 13 10 0.69 1987 7

Sierrita 461 80 0.68 1970 20

Skouriotissa 32 8 0.67 1996 8

Toquepala 946 140 0.62 1959 20

Zaldıvar SX-EW 823 125 0.67 1996 17


51 projects use an estimated price for at least one year. Second, asno operating cost data was available for 21 of 51 projects36, atrendline relating costs to production capacity was built on thebasis of the 30 projects for which data was available. For details,see Auger (2010).

Investment timing

Timing may well be the single most important factor forinvestment success in the mining industry. As discussed in thereal options literature (Dixit and Pindyck, 1994), many projects(especially in the mining industry) can choose to postponeinvestment. This is particularly true in copper mining, where

36 Where there was reasonable doubt about costs, this information was

removed and estimated instead.

firms have a right but not an obligation (hence an option) toinvest in a known deposit at any time.

One of the most well known results of real options is preciselythe trigger price to start operating a mine (Brennan and Schwartz,1985; Dixit and Pindyck, 1994). Based on the assumption thatmines have no relevant construction lead times in respect to priceshifts, Brennan and Schwartz (1985) established that a minimumprice must exist to start operating a new mine. In effect, allindustry executives know about real options is the Brennan andSchwartz minimum-price rule to invest. This result also providestheoretical validation for copper mining investment policy, oftenlabelled as cyclical (Roberts and Torries, 1994) in recognition thatin most projects, investment timing often matches high-price (i.e.,economic boom) periods37.

37 Another possible factor that can explain the procyclical investment policy is

a better access to credit during economic boom periods.

Fig. 1. Investment as a function of production capacity. (OLS regression with 51

observations).

40 Since mine and plant infrastructure and equipment depend on design

extraction and processing rates.41 We assumed that operating costs remain unchanged as capacity varies,

which is not necessarily true (O’Hara and Suboleski, 1992). However, we fail to use


Based on the results in Brennan and Schwartz (1985) and mostof the real options literature, a cyclical policy would appear to beoptimal (and consequently rational in the strong sense). However,this overlooks two facts inherent to the copper market. First, adegree of cyclicality in prices (Roberts, 2009). That is, thatexpansion/contraction intervals are not entirely random. Second,construction lead time for mines is significant, taking for someunderground mines and processing facilities up to six years oreven longer (Majd and Pindyck, 1987).

Based on the above, Guzman (2007) acknowledged the studyof investment timing policies in the copper industry as a matter ofinterest. This is, in our knowledge, the first empirical attempt todo that.

Below, we test whether timing was optimal in terms of theNPV computed ex-post. Leaving production capacity, K ui, un-changed, but shifting timing for the i-th project, tui, per theformula

t�i ¼ tuiþpi ð8Þ

where pi is the number of years the i-th project is postponed38,investment timing in Eq. (2) can be shifted to determine theoptimal postponement term p�i (i.e., when the highest NPV isattained). That is, solving the following problem can provide theoptimal deferment term for investment project i-th

p�i ¼ Arg maxpi Z0

NPViðt�i ðpiÞ,K uiÞ ð9Þ

To search for the optimal postponement term, the NPV forvarious periods was compared, using an assessment model basedon formula (2) and allowing terms to shift within the 0–10 yearrange (i.e., pi ¼ 0,1, . . ., 10). Performing this exercise for eachproject yielded that the actual investment timing, t0i, was maximalonly for 24 of 51 projects reviewed. In other words, deferringinvestment increased the NPV in over half of the projects.

While these findings seem disquieting, a look at project size byNPV reveals that the 24 projects investing at the right time standfor 87% of the total realized NPV (i.e., NPV

0

) in the sample. Inaddition to greater average capacity39, these projects that had anoptimal timing, according to an ex-post review, also had loweraverage costs (66 vs. 72 b/lb).

As to the 27 investment decisions made before the optimaltime, on average they should have been postponed by six years.Interestingly, decisions to invest in new or expanded mines priorto the optimal time were made at an average copper price of161 b/lb. This contrasts sharply with the 95 b/lb average price atwhich projects that maximized their NPV made their decisions.Lending added support to a countercyclical policy, the six-yearterm investment decisions should have been deferred by isconsistent with the average copper price cycle (as measured frompeak to trough) noted by Roberts (2009), which stood at 5.5 yearsfor LME prices and 6.1 years for U.S. producer price.

Given both cyclicality of prices and significant mine andprocessing facility construction lead times, this review lendsweight to the countercyclicality hypothesis as an optimal copperindustry investment policy.

In conclusion, suboptimal timing led 27 projects to lose an NPV

of slightly over $2.4 billion (in dollars of 2008) or 9.7% of the totalrealized NPV for the 51 projects reviewed.

38 pi is not considered to be negative, since to flex the start time of projects

backward was not an option when decision was taken.39 Successful projects were entered at 122.9 thousand of tonnes per year

average capacity, while unsuccessful counterparts entered at 60.1 thousand of

tonnes per year—practically half the size.

Capacity choice

Mine capacity (which defines the extraction rate) is another ofthe most important variables for project viability (Sabour, 2002),given that is closely associated with initial investment amounts(O’Hara and Suboleski, 1992)40. To determine whether capacitywas optimally chosen, the above test was applied to the case,where the timing of the i-th realized investment remainsunchanged (i.e., ti ¼ t

0

i), while capacity Ki is allowed to shiftaccording to the formula

K�i ¼ ð1þkiÞK ui ð10Þ

where ki is the percent change in capacity K ui. Numericalevaluation looked at changes ki ¼�50%, �40%, � 30%, �20%,�10%, 0%, 10%, 20%, 30% , 40%, 50%.

When mine extraction capacity K�i is modified, two correctionsare required. First, the life of mine is a function of extractioncapacity, insofar as existing reserves when making the decisionmust be deemed a project constant. Second, investment must beadjusted for the installed mine capacity (and associated proces-sing facilities)41.

Assuming unchanged reserves, the new life of mine, T�i , forinvestment project i-th can be computed as follows:

T�i ¼T ui

1þkið11Þ

With regard to an investment required to increase productioncapacity, the same database was used to estimate a functionrelating total investment to production capacity. Using ordinaryleast squares (OLS), the following regression was estimated:42, 43

Iui ¼ b0þb1K uiþei ð12Þ

As noted in Fig. 1, adjustment of regression (12) seemsadequate enough to use

I�i ðK�i Þ ¼ b0þ b1K�i ð13Þ

available information to estimate changes in operating costs.42 Error ei accounts for non-observable variables having an impact on

investment level for the i-th project, such as degree of vertical integration (i.e.,

whether copper concentrate or cathodes are produced).43 Linear regression was the best fit in a wide set of tested specifications. To

retain consistency of linearity in formula (12), which may be lost for values

straying significantly from realized capacity, variation was kept to 750% of an

original capacity.

Table 2Number of projects that maximize NPV for different levels of capacity variation, ki.

ji (%) Number of projects

�50 6

�40 4

�30 2

�20 5

�10 3

0 (ki ¼ k�i ) 1

+10 1

+20 1

+30 2

+40 3

+50 23

Total 51

Fig. 2. Radomiro Tomic’s NPV surface for various postponements and capacity

variations.


as an estimator of the total investment amount required tomodify the production capacity of the i-th project to K�i , where b0

and b1 are the estimators of the ordinary least squares of b0 andb1, respectively. Estimation of the regression results in anintercept of �$37.9 million (in dollars of 2008)44, while theslope is given by approximately $5.2 million (in dollars of 2008)per additional thousand tonnes of refined copper installedcapacity (with a confidence level above 99.9%).

Eqs. (11) and (13) make it possible to compute the productioncapacity shift that maximizes project NPV, k�i , as follows:

k�i ¼ Arg maxki

NPViðtui,K�i ðkiÞÞ ð14Þ

Table 2 summarizes projects attaining a maximum for eachshift in capacity ki. As shown, only one of 51 projects reviewedachieved NPV maximization at the production capacity level of anoriginal entry (i.e., ki ¼ 0%). Interestingly, for 30 projects (58.9%),installed capacity rates as below optimal (i.e., ki40 %)45. Thisfinding agrees with Aguerrevere (2003), who notes that wheninvestment takes time, firms ought to increase productioncapacity to optimal levels as price uncertainty grows.

In short, suboptimal capacity choice caused firms an NPV lossof some $9.6 billion (in dollars of 2008) or 38% of the realized NPV

for the 51 investment projects reviewed.

Testing for rationality in the copper industry

Of the 51 projects reviewed, 41 appear to have attained apositive realized NPV46. Even without testing for economicrationality, it seems remarkable that only 20% destroyed value47.While failure may have a range of sources48, it seems likely thatthe most common is overestimating copper prices when signingoff on a project49.

Does a relatively low failure rate support a rational behaviorhypothesis in the copper industry, at least in the weak sense? Ifthe sample is sufficiently representative (which given thearguments given is quite probable), the low failure rate can be

44 As expected, the intercept is not significant at confidence levels above 80%.45 Just as interestingly, for 23 projects (45.1%) optimal capacity appears at

least 50% above actual realized capacity (i.e., ki Z50%).46 For discount rates of 5%, 10% and 20%, numbers are 46, 42 and 31,

respectively.47 Unfortunately, we are unaware of similar results in other industries, so is

not possible to make a comparison with other industries.48 As a hypothesis, firms responsible for 10 projects with a negative NPV could

have acted irrationally.49 Although we have no sources confirming this, all projects reviewed should

have been approved, since ex-ante they showed a positive NPV. Surely, the

simplest way to do this is to overestimate the price expected to prevail once the

project enters an operation.

attributed to the fact that even under uncertainty of price, on anaverage the industry does take on a project if the expected NPV ispositive50. In fact, in terms of Eq. (3), and assuming 51 is asufficiently large number for the formula to apply51, the expectedaverage industry NPV ought to stand at some $500.7 million (indollars of 2008)52.

In relative terms, the $25.52 billion (in dollars of 2008) earnedby these 51 projects as implemented (i.e., with tui and K ui forall i¼ 1,2, . . ., 51) and the $25.54 billion (in dollars of 2008)in an investment make for an aggregate profitability index ofpractically 153.

In our view, the low failure rate and high profitability indexmay be a function of high initial investment amounts forcing thecopper industry to conduct thorough financial (and technical)assessments54. Of course, another possible reason is high riskaversion, which coupled with high uncertainty may tend tovalidate only projects with a low risk of loss.

Thus, the ex-post assessment shows that the null hypothesisabout most of the industry behaving rationally in the weak sensediscussed in ‘‘Strong and weak rationality’’, should not berejected. Just as importantly, a vast NPV was created in thecopper industry, at least in the projects reviewed.

However, whether industry investment decisions are designedto maximize the expected NPV is a different story. While ‘‘Strongand weak rationality’’ notes the lack of a test to determinewhether the industry is a maximizer of expected NPV or usesstrong rationality under uncertainty, ex-post NPV assessmenthelps build a capture index for the maximum potential NPV, j,

50 If firms used an NPV rule, then all projects satisfied that NPV at expected

values was non-negative. This is, however, not necessarily equal to request that

expected NPV is non-negative.51 We are unaware of empirical studies on the asymptotic convergence of

Kolmogorov’s strong law, so as to tell under which conditions 51 is a sufficiently

large number.52 This figure may be skewed by a few projects with a very high realized NPV.

However, the median of the NPV (which removes the effect of overly long tails) is

still positive ($113.8 million in dollars of 2008).53 The average profitability index for each project stood at 0.37.54 In this type of project, tens of millions are typically spent on technical and

financial studies.

Fig. 3. Countercyclical investment as optimal investment policy at Radomiro Tomic.

57 In addition to the assumptions used, the objective function of firms may not

be perfectly built as byproducts are not considered. Yet, it seems unlikely that the

j index found should be noticeably affected as most mines in the sample depend


which while not answering the core question, at least hints at ananswer.

Both investment timing and the production capacity shift thatmaximize NPV (t�i and K�i , respectively) can be calculated similarto Eq. (4), but using auxiliary variables pi and ki. The optimalpostponement term and capacity variation for the i-th project arefound as follows:

p�i ,k�i ¼ Arg maxpi Z 0 ,ki

NPViðt�i ðpiÞ,K�i ðkiÞÞ ð15Þ

As an example of simultaneous maximization, Fig. 2 showsNPV from the perspective of postponement and capacity variationfor Radomiro Tomic, one of the mines in the sample. The realizedNPV (i.e., ðpui,kuiÞ ¼ ð0,0%Þ) is estimated at $546.9 million (indollars of 2008). The maximum, however, is attained atðp�i ,k�i Þ ¼ ð6,50%Þ, with an NPV of $950.6 million (in dollars of2008). In other words, deferring the project for six years andincreasing capacity by half over the 150,000 thousand tonnes peryear realized capacity could have earned Radomiro Tomic’s ownerCodelco an additional $403.7 million (in dollars of 2008)—i.e.,73.8% more than the ex-post NPV assessment result for thisproject.

Radomiro Tomic stands as a good example of a mine with acyclical investment timing that, as shown in Fig. 3, should havebeen countercyclical. This figure clearly shows that theinvestment decision was made when copper prices were at apeak. Sure enough, prices through the first six years of operationwere below the peak extant at decision time. Per our calculations,the Radomiro Tomic NPV could have been maximized had thedecision been made in 2001, when the world industry faced oneof the worst price crises in modern history.

Extending the above analysis to all projects55 per Eq. (5) resultsin a maximum NPV, NPV�, of some $38.1 billion (in dollars of2008), 49.1% better than the realized NPV, NPV

056. Hence, themaximum potential NPV capture index is given by j¼0.67.

This is significantly lower than 1, but is it sufficiently a lowvalue to attribute to firms a behavior that is non-rational in thestrong sense? Are there other sources that may account for thismargin, while retaining rational firm behavior in the strongsense?

While we are unable to answer the first question, thedifference between 0.67 and 1 may not all be attributable to apossible lack of strong rationality, as price uncertainty at aninvestment decision time is to be expected to account for part ofthe difference between the realized and maximum potential NPV.

55 Only one project was confirmed to have entered at optimal timing and

capacity.56 Under optimal timing and capacity, 47 projects obtained a positive NPV,

increasing the industry’s potential success rate to 92.2%. That is, fewer than 8% had

no chance of creating value (barring higher copper prices).

Another possible source could even be errors in the estimationperformed in this analysis57.

Conceptually, then, the approximately $12.5 billion margin (indollars of 2008) can be shared among firm irrationality (in thestrong sense), price uncertainty and error in an NPV estimation.While we do not succeed to estimate the role of each, ourconjecture is that assessment methods that fail to explicitlyaccount for price uncertainty may well account for a significantshare of the margin found.

While the role on the margin found of non-rational behavior inthe strong sense for the copper industry can only be hypothesized,simulations conducted by Dimitrakopoulos and Sabour (2007) fora gold mine show the realized NPV rising 11–18% when realoptions are used58. Extrapolating these results to our sample,failure to use real options may have caused losses of $2.8–$4.6billion (in dollars of 2008) or 22–37% of the gap between themaximum potential and realized NPV.

Concluding remarks

Whether firms are rational in the neoclassical sense (i.e.,agents that maximize profits or the NPV) is an assumptiongenerously accepted by most economists59. However, since the50’s, some economists (Cyert and March, 1956; Baumol, 1958)have challenged this view by accounting for administrativefactors and friction between company principals or owners andmanagers. As noted here, an additional source of ‘‘irrationality’’may well be the tools used to make investment decisions,especially when uncertainty exists. Investment evaluation prac-tices that fail to use real options or other tools helping toexplicitly account for copper price uncertainty may possibly be toblame for a significant share of NPV loss in the copper industry.Putting this conjecture to a rigorous test is left open. Undoubt-edly, such research could both help hone our understanding of thecopper industry mindset and contribute to the firm behaviortheory.

To contribute to the study of the economic rationality ofinvestment decisions, this paper advances an expanded scope ofrationality based on a weak rationality regarded as an extensionof neoclassical rationality, referred to here as strong. While the

heavily on copper as a main product.58 This result differs from Cavender (1992), who found no significant

differences by using real options in a hypothetical mining project.59 Friedman (1953) popularized the evolutionist argument positing that firms

not only learn how to do better and do in due course maximize profits, but most

importantly, that otherwise they are bound to perish. As such, it seems reasonable

to expect firms to behave as if they were profit maximizers.


authors have no scientific evidence to show that copper miningfirms are profit or NPV maximizers in uncertain price contexts,results suggest that at least their decisions ought to be consideredrational from a weaker perspective, especially as to the creation ofvalue. Indeed, our estimates lead us to conclude that the projectsin our sample did create considerable NPV.

Furthermore, theoretical examination of the weak rationalityconcept advanced here may well open up a valuable (and fruitfulin our view) line of research capable of improving our under-standing of how the copper and other mining industries work, notto mention markets at large.

Finally, although we did not prove that there is a significantgap in NPV to justify an improvement of investment decisionmaking in mining under price uncertainty, we strongly believethat efforts done for mining companies in the last years toimprove both price forecasts and investment decision making –by including price uncertainty in project evaluations – areworthwhile and they should continue in the future.

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