-=~,,~""--'--, ~-~-~~~~~-~~~----............ _-..... ,

, COST 8RNEFtT ANALYSIS OF A CUSTOM ~llLL

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A COST BENOIT AMLTStS 4lF A CUST(It ~IlLL

FOR SMALL COPPF.R MINES IN NoRTHERN CHIt~E'

\

by

luis N. Henrlquez

A the.18 . ebatitted to the r.culty of ...-"\ Gr.duate Studle. and Re.arch, McGUl

Unlverllty, ln partial fulfl~t of , the rttqulr_nU for tb. des"e. of. Halter of En,iDeeriDa_ .

DepartMnt of Klnlna ancl Hetallurllcal EDaineerina.

~CG111 Unl raity,

Montreal. canada. ,

)

'\ llr.-:b. 1974.

Cl Luis 1 ..... ' ... , 1974 " '~, ~ ~, .. "; ~ ' .. ~ ,.,i.k&~~~~tt...h.. ~,l'.A. d" __ ~ ~" .:1Nl'_irilIiIIliIiIiia_iIiI

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To my parents.

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~"\ 111

ACKNOWLF.OOBMENTS

1 vi.h to expr ., .1ncer~ thanka to .Y r rch dlrector,

t Prof.aaor B: W.,~cken&le, for hia . 18t.nce .nd .dvic~ tbroukhout th. preparation of th la theals.

, Special appreciati~n 1. extended ta Profe or H. A. Loutfi of

~ McCili Univeraity and Profeaear E. Tuleanaz. o~ Univerlidad de Chile

for aUlleationa and k1nd co-operatioa.

Thanu .r. alao due ta Hra. C. Hot.Bren and Mr. K. GUZ1l4n for

provldina .e vith the requlred Infor.ation.

Grateful acknowledae.ent 1 ... de ta Univer.idad Tcnlca deI

Eet.do-Chl1e for th.lr flnanet.l support by ane of .cholaFahlp. vhlch

made tht. work poa.lble.

Special thanka are extended to .y vlfe for her patient, and

underat.ndinl.

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iv

1 The _11 copper alnlnl tleCtor _Ile. an 1IIportant contribution

~ the Chil.an .. cono.y. 1

ln rCent year 'the Govera.ent has actively , i,

, J 'enco\Jraged the developtlent of tbi ... ctot. One font of encouragentent hlt.

~

Q

been the conatructlon and .. nage.ent of custa. .111 facl11tiea to proceas

orea ained fr~ ... 11 copper depo.lts. The provision of cu .. toa mil! "1....-

facUitlea ha .. been a, necesaary condition for the econoal~ vorklng o~ .... ny

of these deposlts. Thua, the Govern.eat cuata. aitls have proven suceessful

in .chievinl s.all .Inlng develo,.eat, aJthoulh the all1 capacitles and

location. choaen haA bepn revealed ta he non-opti __

This study concerna tl~ opt~l%atlon of custoa alll capaclty aod

location. For thle purpoae, an expected value .odel i. developecl t ba.ed

on the evaluation of Indlvldual depoalt cut-off Irade and aine eapacity for

ail knovn depoalta vithln A rellon.

Flnal1y. the expected value nod.l la appllecl for aaalyais of a

particular ca ... tudy the El Salado reslon of northern Chi1e. Bath

fixed location and .obile aJll facllitlee are con.idered a. baaic alternative

The ua. of 125 ton pel' day .obile alll plant. 1. found to be a very attractive

alternative ovar the range of 250-375 tone per day of ore treataent capacity.

Over thie ranle the .,bUe .111 approach ha. a net preaent value whtch 18

hiaher than tlwt of the be.t fised location cu.ta. al11 alternative. Howver'

1t ta iIIportant to DOte tbat aboY. 500 tona per 4ay of ore treataent capscity

(i.e. 4 .obil. -'11.), the capital inw.taeat re.ulred 1. grester tban for

the beat flxed location cuat.oa .111 alternat' ...

'.

J lr ~ :1 [ hm il $,\ t e 1$

v

l..'indu8trle de la petite mine de cuivre contribue d'une faon --.'')

a.ael: importante al' conomir chiltt'nnl',. Le souvern.ment a fortement

encourag le developpelDont de ce secteur durant les dernires quelque.

anne ... Une Jl;lyorm~s d'encouragement a t' la construction et l'ad- mi~lRtrat1on de plu81e\lrl'l UdQ'll df' concentration pour traite'r' le minerai

prove~ant de petits d~p~t. de cuivre. L'implantation de ce systeme .'eat . avr": n~e"u.irt. pour l'exploitation conomique de plusleure de ces petites

mines. L' act ion du gouvernement, chUien a donc favoris le deve10ppement

de ce secteur de l' Indust r le du cuivre, meme si les capacits et le8 sites

cho18iR pour Cf"8 udllcs ne 80 sont pas rvls cOIIIIIe 1' plus ef f icact'8.

Cette r:tude a trait l'optimisation de la capacit et du choix

du aite de moulina de concentration. Pour ce faire, un modlo de valeur

prsente e.t dvelopp, ball sur l'valuation de la teneur de coupure et de

la capacit pour chaqu~ gisement situ dan. une rgion donhe.

I.e modle est i , ,. ' appli9ue ft l'etude d un ca. particulier, la reglon

d'El Salado au nord du Chili. Deux alternative. sont conai~erer quant au

type d'usine de traitement 1 les moulina mobiles faible dbit ct les moulina

emplacement permanent, debit plus lev. L'utilisation de petits moulina

mobile. ayant un dbit de 125 tonnea par jour semble trs intre ant'e. pour

le tratte.en~ d'une quantit de minerat se .it~ant entre 250 et 815 tonnes

par jour Dans cette intervalle, le choix'de moulins mobiles a une valeur ..

prsente auprieure celui du soulin eaplaceaent fixe. Il est cependant

important de noter qu'au del, du traitement de 500 tonne. par jour (qui

nce.aite 4 .ouI in. ~bllea) le capital nce.saire est .u~rieur a celui

requis pour la con.truction d'une usine ~ -.placesent pe~n.nt.

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1

tAlLE or CONTENTS

Chapter

Acknowledgements

Abstract

Resume

Table of Contents

List of Figures

Ust of Tables

Note on Unite Used

Selected Symbols

INTRODUCTION

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1 . SMALL COPPER MINING AND KILLING AtTrvITIES IN CHILE

2

1.1 The Role of Small Minlng in Chile

1.2 ENAHI's R91e in Cu.tom Mil1ing

ECONOMIe EVALUATION OF A CUSTOH MILL

2.1 Literature Survey

2.1.1

2.1.2

2.1.3

Comparative Cost Analysis

Linear Prosramainl Technique.

Other Techniques

2.2 Economie Evaluation Requirementa

2.3 COlt-Benefft Analy.i. Technique \

2.3.1 The Evaluation of Coat. and Ben.Ut. at the T~ When They Occur ~

2.3.2 The Social T~e Preference Kate

~ - <

vi

Pale

Ui

Iv

v

vi

ix ,--

xl

xiii

xlv

1

)

3

6

8

8

8

9 1

11

12

12

13

15

.. ''' ..

I/,

Chapter

3 r

4

5

.. 2.3.3 The Effect of Uncertainty

2.3.4 Redistribution of Inca.e

COST AND REVENUE RELATIONSHIPS FOR EVALUATION OF AN ENAMI CUSTOH MILL

3.1 Revenue

3.2 Capital and Operating Costs

3.2.1 Capital Costa

3.2.2 Operating Costa

3.3 Indirect Benefits and Costa

3.4 Secondary Beneflts and Costs

3.4.1 Direct Employment + 3.4.2 Continuing Effects .

vii

Pase

18

19

23

2S

26

26

31

35

36

38

40

3.5 Total Cost and Revenue Relationships for Econoaic Evaluation 40

3.6 ?rojeet Choiee 41

THE MODEl. - AN EXPECTlID VALUE OPTlMlZATION 43

4.1 Mine Development Decision 43

4.2 Tonnage-Grade Re1ationship 44

4.3 The F~pected Value Mode1 46

4.3.1 Cut-off Grade and Mine Capacity Deteraination for Each Kine 46

4.3.2 Kine Developaent Scheduling 51

4.3.3 CuatOII Kill Capaclty and Location 'Decision 51

A CASE STUDY 55

55

55

61

5.1 Fixed Location_Cu.ta. K111

5.1.1 ~tiaiz.tlon lllauita ,.

5.1.2 Cuatoa Mill Opttaizatlon

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Chapter

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5.1.3 -Eff_ct of v:Jation ln Para,etera

5~2 Mobile Hill Approacb

5.2.1 First Opttmization

5.2.2 Second Opt!mization

5.2.3 Multiple Mobile Milla

SUMMARY ANQ CONCLUSIONS

REFERENCES

BIBLIOGRAPHY

Input

APPENDIX A Assessment of Regional Mineral Potentiel

APPENDIX B

APPENOIX C

Exp1anation of Computer Programme Terma and programm, Listings

. Optlmization'Results

viii

Pale

75

85

85 . ,

" 87

87 '

101

104

lOS

109 .

121

156

... . hl ~,~T..,.

, 1 ,

, ,

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1

2

l

4

5

6

1

8

9

10

11

LIST or PICURES

.,

Revenue and ~peratinl Coat a. Functlona of Hlne Capacity

Flow Chart for Expected Value Model

"_l Flow Chart for Hine Exploitation Schedullnl

El Salado Re81on. Knovn Copper Depo.fta and F .. alble Custa. MIll Locatlona

Iso-Present Value - MIne '14

lao-Present Valu~ .Ratio - Mine 114

lso-Rate of Return - tUne '14

Project Life - Kill Cftpacity Relationship at Location 1 for Different Cu~-oYf Grade and Mine Capaclty Optialzation Criteria

,1

1 Net Preaent Value - Custo. Hill Capaclty Re14tionshlp at Location 1 for Different Cut-off Grade and Mine Capacity Opt1aizatlon Criteria

Effect of Copper Priee and Life Perlod on Cu.to. Hill Present Value for Different Plant Capacities

Effact of Incr.a.lnl Copper Priee on the Optt.um Cut-off Grade - Klne Capacity Coabination for Dlffer.o~ Hloes 1

lx

49-50

52

Sb

62

63

64

69

10

82

8l

IMW' '!, $ ,

,1

12 Iff~t of lnc:r ... ina CuatOll Kill eapad.ty on th Opt~ Cut-off Grade.... - Mine Capcltt COlibination fot Different MIne. .

13' Mob.lle Mill Locationa for the Firat Optla1zatton

14 Mobile Kill Locations for the Second Opt~iz.tlon

x

!!.I!.

83

" 86

91

15 Net Prelent Value - Nu.ber of Mobile Milla WOrking S:laultaneoualy Relationahip / 100

.....

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4

7

J

10

11

l~

11

14

l~

- 1 f

11

18

"

l.tST or TAlLES

Th@ Contribution o( "PequfORA y MMlanA Min@rla" to th@ Chll@An )kon.y, 196o-19f)8

, Inv~"_t~n't An,l'Production for Snurll Copp@r ~fln ...

oln ~AconcA"iu, and Sant iaRo Provinc ...

CUMtom tH 11 lrur" .. tllfOnt (Copp.r FlotAt ton Proc@, ... )

Forflt~n F.xdulI\ll. (;""t01l \M111 tnv@at",.nt .lI. A r"rCl'nt"RC' of Total CU.,t'OII Mtll Inv .... 'tllMlnt

Hill" ot,@utlon Cost - Production RelAtion.hip S"",l 1 ~opp"r Ml,\"R, Provine. of AeoncAllua, 1969

t Hln" tlp('r"t fon COllt Str\tchlr"

Mln(' OpflUt InR COAt R"lRtlon8htr

Product Ivlty VA Inv .... tm .. nt (l'rcwlncf" ~r "conc"auA) Su Il C;oPl'"r r-Um,'a

tllnt"r"l Re.ourc.A of th" R""lon

Nlnt>-Mlll IllNtAnc""

M1l1-Saleltr Hhtances ,

lt,frA .. t ructur@ Inv."ttM'nt

CU.tOM foU 11 Opt t.hat ion At l.ocat fon 1

. Cu.to. Mill Opt t .. hAUon at l.ocat Ion 2

Cuetom tUll OpUahal1on at, t.oc.tion j

\ Cut -Off Grade and Min. Capac il y Opt 1mha tion URina Pr.~ent Value Criteria

~

MIne Elcploitation Sch~ul1nl" U"ing Pr.,ent Value Criteria

~ln@ Ueplet ion S('quen~ Ueina Pr nt Value Criteria

xi

4

28

29

29

)1

12

12

38

57

S8 f

59

6S

66

67

" n

72

13

19 20

21

22

2)

24

25

26

27

28

DetaUs of the &.ploJMllt Generated and Inve.ment Requir_nt, Usina Pr ... nt Value Criteria

Cut~ff Grade and Klne Capacity Optt.izatlon Ueing Preaent Value Ratio Criteria ~

'y

Kine Exploitation Schedul1ng Uaing Present Value Ratio Criteria '

Klne Depletlon Sequence Uatns Present Value Ratio Criteria

-Details of the z.ployaent Cenerated and Investaent Require.entUsing Present Value Ratio Criteria

Effect of Changing Copper Price

Effect of Changing Discount Rate

Mine-Moblle Mill ~stance Sub-Croup A

Hine-Moblle Mill D.stance Sub--Group B

Hine-Hobile Mill Distance Sub-Croup C

xii

14

1ft

77'

78

79

80

81

88

88

89

29 Optl.u. Capaclties for Each Mine - First Optbalzatlon 90

30

)1

32

33

34

35

36

Mill Plant-s.elter Distance. Sub-Group 1

, KinP~ill Plant Distance. Sub-Group 2

Mine-Kill Plant Distance. Sub-Group J

Cut~ff Grade - :Une Capaclty Opt1a1&aUon. Sub-Gtoup 1

1

Cut-off Grade - Hine Capacity Opt1aizatlon. Sub-Group 2

Cut-off Grade - Hine Capaclty Optlaizatlon. Sub-Group )

F.conoaic Evaluation of Several Mobile Mills Working St.ultaneously

92

92

93

94-95

96

97

99 ,

1 -

xiii

NOTE ON UNITS USED

Metric weight and distance unite are uaed throuahout the

study unlesa otherwll1e Indlcated. f;

For comparAtive purpoaea, all economlc eettmatea and values .. usc in the atudy are expressed in constant 1969 United States dollara.

'An excl~nge rate of U.S.$l 9.2 Escudos 18 applied to convert Chllean

monetary values into United States dollars.

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S!LECTED SYMBOLS

A total deposit tonnage

B/CR project cost-benefit ratio

C truck capacity .

c average unit transportation cost

CMFC eus tom mi~l fixed cost

CM! custom mill capital investment

OlOC custom mi11 operating cost

mine capital investment spent in foreign currency

custom ml11 capital Investment spent in foreign currency

th ~ distance from j custoa aill site ta the a.elter

th th distance'from k mine ta j custom mill site

cumulative present value factor

OF dilution factor

ECK number emploYe4 in cuatom mil1 operation !

ECT number employed in concentrate transportation

number employed in mine operation ('

number employed in ore transportation per aine EMTk

EP total direct emp10yaent generat,d by the custOm ai11 Pioject

G cut-off grade

averale ,rade of ore ained

i social discount rate

Iok infrastructure inveataent for kth aine

Il project infra.tructure tave.t.ent

[1

1 La LP a

Melk

M(G)

HOC

HP

HQ

HTC

n

NFEI

OCI

OC2

OC3

PC

PDC

POl

POP

POR

PPV

PROO t

PTe

py

PVR

r

-.ubilCript deootlna .itn: j. 1. a avera,e concentrate ,rade of the .tll

life of the cuatoa ai1l project

nUilber of ai~

aine develo~t investaent ~ ,! ~

. .-.'

cUlMl1ative -.t.l tonnage about cut-off grade G

aine operatina ~o.t

-/

recovered .etaI priee le.a ..alter. refinery and coaaerc1al chargea

aine capec Hy

ore transportation co.t froa the aine to the .111

nuaber of feaalble cuatoa ai11 aites

\

net foreian exchange Incoae aenerated by tbe custoa all1 project

aine ope~atln8 cost spent in fore18n currency

concentrate tran.portation coat apent ln forelan currency

cuatoa al11 operating coat apent in forelgn currency

cuatoa al11 capacity

discounted project coat.

discounted project Inveataent

dllCounted project ,roflt

dtlCounted project revenue

project net pre nt value

productivity of ... 11 copper .tne. for the dlfferent aine capital Inve.c.ent. 1. 1. )

concentrate tranaportatioo coat

net pre.ent value for aiDe.

pr ent value ratio for .tne.

tntemal rate of return for aiDe

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;" . ""."~~.""-,.. .~ - ., .. {> . J' .. "'W"'\.I~f\ . .: ... .,;.:- ~.~~"t::;" ~ -...

1

rp

RF

.. internal rata of return for the ovarall cuatom aill projeet

aill recovery of the copper in the ore

R(G) cu.ulative ore tonnase abave cut-off srade G ,

Rl aal. revenue per aine'obtained in fora1an currency th ,. \

18ar ln which tha k mlne coanene. production

TCYk total coat per year per alne

TIM 'total capital inve.tment per mine

TPYk total proflt per year per aine

TlYk total revenue per y .. r per mlne

VMk I1fe of the klh alne, ranked accordlna to net preaent value

XLK lIine lUe /

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INT1tODUCTION

ln ChUa, a. ln .. ny other countrlea vith trons .lneral

orientation, there la very dlvera1f1ed. extenalve .... U mlning induatfY

.. inly coppel'. The ... 11 coppel' .lninR aector 1 ufficlently import.nt \

ln ChUe that the Gover11llent in recent yeara has allocated ... cI~ effort to

encoura8~ and develop it by provldl08 10ana, technical aaaiatanee. cuatoM

.aelter and concentration planta. Thh aining aector. based on bedded

\ and vetn depoatta. va. the .,at i.port.nt .ource of foreign exchange for

the country ln the second balf' of tbe 1aat century. Today therE' are

sever.I thoueand .-.11 oppratora, .. ny pri .. rily u.ing hand,toole. n\eae ~

ama11 .1ning operationa .. y or .. y not inelude ~om. kind of mll1ing Cac il-

So- U th.ir ore to an ora &uyar or tab It I,to a F r ... "t

aUl, a"" othera baYe tbs! ...... Ullae r.UIH .

Sa rar, governaent cuatom ~il1in~ act~vitiea have been underteken

ln on1y a fev countrie.; ChUe, Peru and Rhodeda for exa.ple. 10

However.

thia fOrll of encoufageaent for the _11 .ln1nl aectol' would .ppear'to have

particular advantalea in teraa of econo.iea of aca1e, the co-ordlnation of

reliona1 .ineral developaent. and financial a.curlty to the lovernaent.

The Eapresa ~c1onal de Minerta (tNAKI) of ChU. l haa obtatned -quit. lood

reaulta vith Ita existlng custoa al11s, altbau,h It h been shown that the J

.ill capacity and location choaen vere not optiau.. The purpoae of thi.

ENAKI la a Chil .. n .ln1na d .. 'lo,..nt a.aney for .adlua and ... 11 ainlo&, .. lo1y copper. It ovna ..".ral cuat .. aUla, 2 coppel' ...ltara and ODe copper ratlnery.

1

"

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1,0 ,

2

.tady ta to d...top .on ....... te ecoaom..c: analy.~ fr....ork for tbe

f .,.el' mt cuau. aUI", opportuait:lea. TIa1.a approach

__ nmt of iadiylclual depoait cut-off gr_e and alne

c paclty optma w.lth1n rea100 _ laaata for .. lectlnS the optt.ua

~-r-pacity and locatioD for a costa. aUi. Chapter 1 providea a J brief

introduction to -.11 copper alnlne .... aUl1Dc acti~itiea 10 Chile and

the role of EBAHI in cuatoa .ulins.

'fte contributions to the liter.ture 10 the aru under inveati-

gation are ex_fned in Chapter 2 and the principl .. of the .ollt appropriate

ecoDOlc ~r-1a teclm.1que for dealina witb the proble cOllt-benefit

analylli~. are outlined~ Coat .... reyeaue re1at:l.onahiplI for evaluation

of an IMMI cuatoa aill .re dey~oped 10 Cbapter 1.. Two .lternative J

approacbea .r..e ex--fned: fUed locat:loll cuatOIl aUl and .,bile all!.

Cbapter 4 deecrlJ)ea the speted value .ethocl developed to "de-

teraine tbe optiaua cut-off gr_e and capacity for each .ine. the acheduling

of aine develo ...... t. and the coat. aill c:apacity and loc:ation deciaiona , Application of the expec:ted value -.ethocl la Uluatrated in

Cbapter 5 b1 a ca. IItud1 of the El Salado reaion ln nordiern ChUe. in-. ,

cludin& a cOllpArt.on of fhed location and .,bUe aU.l approacbea.

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CHAPT~R 1

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From the besinnins of "Empresa Nactona1 de Miner!a"'. (ENAMl'a)

exp,anaion plan for copper production, ~evera1 custom .i11a hav~ been

1 built to provide proceasing faci1itiea for ama1l cOPier mining enter-

priaeal otherwiae it would not have been ec~no.ical1y possible to work

mAny of these small deposits.

1.1 The Role of Small Minina in ChUe ,

The main aource of foreign currency for Chl1e aince the mld-

\\wenties has been the export of a aingle pr~ry commddity - copper.

Copper exporta vere valued at $867 ~illion ln ~970, repreaentlng 17% of

total exporta.

Production (rGa the "pequeiUa y Mediana Mineria"l 1ncreaaed \in

v.lue f~om $31.8 .1l1ion to $148.5 million durina the'perlod 1960-1968,

re~ie.entin8 an Increaae fro. 6.8%' to 16.2% of total exporta (,ee Table 1). ; ,

Thua. the,amall and medium mine.'make an t.portant contribution to the ,

Chilean econoay

'1 , 4,,/""1."_

"pequetUa Kineria" are ... 11 copper ain exploUtMf by privat. ca.panle. or 1ndlvl~ual. and havina a.capltall .. t1oD of $50,000 (75 ba.ic Chil .. n liviDs vap. per Je.r) or 1

"Mediana Mineria" are .adl .... h. copper ain ha"in, a c;apita1.i: izat10n of .lIOre than $50.000 and production of 1 ... than 75,.000 ton. of contained copper .. tal p.r ,.ar.

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.~ .. ,~ .. -,tf.

(

Ya'ar

1960

1961

1962

1963

1964

1965

1966

1967

1968

'Iable 1

'the Contribution ol "Pe!Juda y Hedi.na Mineria"

to the ChU.an Ec:onoar. 1960-1968. 1

"peq.& Med~ Minerl." London Met1 'Iota1 Production (tonl of Exchange Exporta

Contained Metal) Copper Price fra. ChUe (centa/lb) (!ill.$)

55,000 30.8 31.8

70,000 28.7 38.1

86,000 .. 29.3 47.3

99,000 29.3 55.0

95,000 'Ir 44.0 78.7

106,000 58.6 121.5

99,000 69\5 120.1

124,qOO 51.1 130,1

137,000 56.1 148.5

'Ir eatimated valuea.

4

Shar. of Total ChUean Export Value

(1)

6.8

8.0

9.3

10.9

13.8

17 .8

13.9' 14.8

16.2

The amal1 mining .ector accounts, for approx1mtely 3 percent of

Chilean copper production, holding 1 percent of the copper ore reserv "

The medium aector produc about 17 percent of the copper and ho1d. 10

percent of the copper ore reaervea.

"Pequet\a y Hediana Mineria" actlvity la especially concentratad

in the provinces of Atacama and Coqulllbo ("Norte Chico" Zone) a ... i-de.ert

resion where mining il the main source of ~p1oyaent, and in the Province

of Aconcagua (Central Zone) vh!ch ha. Increasad it. copper production in ,

the perlod. of high copper priee. ainee 1964.

1 Thi. Table is taken from publiabed reporta of "Banco Central d. Chile", and "Servlcl0 Minas del Eatado-ChU. tt reproduced in ".u.naque El Mercurio" 1972.

1 .

s

Chile'e copper production 1~ 1970 va. 686,000 tona of .etaI

The contribution of the "pequeiia y Mediana Mlneria" va. 151,000 ton.,

distributed as fol1ova.

Copper Production Sector (taa. of .. tal)1

Mediua private coapaniea (Disputada, Hantos Blancos., POOahuel. Andina and othera) and ... 11 private co.panles whlch hav~ tbelr own proceasina facUiea. 2 97,700

ENAHI sector 3 S3,400

ENAHI plays an i.portant role not on1y a. a generator of foretan

currency, but aIso a. an .-ployer in ainera1-based regions. Nearly 8,000

low income people work ln the ENAHI s.all aininl sector, direct1y sup-

porting 32,000 dependenta.

KNAMI W8S created by the Government durinl the 'fiftiea by aeraer

of various atate institutions whieh had reaponsibilities for ... 11 .1ning.

Since then, EKAMI has played an increa.ingly iaportant ro1e in ... 11 and

mediua aining activity in Chile.

1 o

As copper COllc.~... , 2 So .. of the c nie. have !lad their statu. cbanaed .inee 1971. Puda-

huel and Hantoa Bl. co. bave been natlooalized and the State ha. takeD an equity interest in Diaputada. The .. three aine. are nov adaini.tered by EJWU. Andioa va. nationa1hed in 1971 and incorporated ln the ,''Gran Mineru deI Cobre" (la,.e aining .ector) heina aduntatel'eci by ''Corporaclon deI Cobre"(CODIloCO). Moet of the.e coapanie.' production ie eold a. con-centrate in the international _rut ( .. 1n1y Japan), althoulb eoae quota

- is a~located to ENAMI'. saelter. and reflnery.

3 Althoulh ENAKI operates ~ aines, .ost of ~I's production i. providad by privat. _11 alnina ca.panle. or individua1. who se11 tbeir ore pro-duction to the State enterpr1ae. !NAMI produced 65,100 tone of blieter copper and 91,400 ton. a,f refined copper in 1970 froa'ite proce.et.na facilitie. at 'aipote and Lae Ventaoaa

. .

'.

6

During the 'aixtiea. ~I implemented a plan to increaae the

production of copper fra. the aector under ita control. As a reault,

several cuatom aill. vere built and copper smelting and refining facilitiea

vere oonatructed at Las Ventanaa.

In the 'a.ventiea, ENAMI haa extended ita expanaion plan, IIlUch

effort beins put into the organization of co-operativea for individual

producera, aupported by technical, managerial and'financial aasiatance.

ENAHI baa also attempted to stabilize employment in the amall and mdiua 1

.ining aector throuSh a atable ore and concentrate purch.asins price policy.

1.2 ENAHI'. Role in Cuatom Killing

The organization for a relional cuatom mill can be described as

(ollows;

1) The .ineral producers ae1l their production to the regional

mill and ENAHI must buy ail the available minerai production;

2) ENAHI pays producers the value of the recoverable copper content

in their orea based on the London Hetal Exchange priee, lesa

processing, brokerage and financing charges;

3) ENAKI processes the ore and sella the refined copper in the

international market.

Feasibil1ty studies vere carried out by ENAHI as a basis for in-

vestm.nt in cuatom mill facilitiea. Thea. studies considered currently

prod~cinl ainea aa the basis for mineraI supply to the CUIta. aiii and .. de

hiahly aubjective eatimates of unknown aineral potential. Sensitivity .

analysia vaa uaed to conaider the effecta of critical par ... ters, auch a.

copper priee. aill capacity and discount rate, but no atte.pt va ... de to

opttaize cut-off Irade and aine -capacity for individual aine

7

The follovinl t.o ex.aple. are Slven of ~1'. role ln the

aualy.l. and t.pl ... ntatlon of cu.to. .1ll1ft1 projecta: , 1

1)

2)

El Salado rellonal .111, ln the EL Salado rellon, province of

Atac ... (6). Thl. 1. a .~-de.ert relion, It. e~onomlc ac-

tlvlty dependlng excluaively on the exploitation of .1neral

re.curce

Cate.u reglonal .111, to reactlvate .1nlnl actlvlty ln the Cateau

rellon, province of AconcalUA (7). This rel Ion has been mainly

( alrlcultural, but aevere droulht condition. in recent yeara have ~ cau.ed, a slgnlficant decline in relional econollic actlvity.

The experlence of ENAKI vith lt. producing cuatoll milla haa been

that once rellonal .llia bel ln operatin" they becoae dyfimic centre. for

ainer.,rdevelopaent in the reglon and nev mine. are developed which vere not

consldered ln the fea.lblilty .tudy stage. Thus, aine production has

usually exceeded scheduled ore supply, relulting ln larle ore atockpiles 1

vhlch tle up subetantlal Investaent ln Inventory and place aevere financia1l

pre.sure on ENAHI under the tenu of its cuetom lIi111ng oblllatione. SUCh\,,::)

la-allocatlon of acarce lnv taent funde lllustratea the need for a .ore \'

adequate econoalc anal ys la fr.-ework to be applled at the feaslbl1ity study

/)

, tage. Such an approach would conslder aIl knovn .1neral depo.it. ln the

reslon under .tody and evaluate individuel depolt cut-off grade and cap.-

city opt~; a. a ba.l. for lectlng the optiaua aite and aize for a

The developMnt of thi. type of econoaic analya1s f~&IMIWOrk

~he aubJect of the preaent study.

\

4

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J 0

8

"

CllAPTER 2 ,

ECONOMIe EVAWATION or A .Js-rdK HILL

2.1 Literature Survey 1

The purpoae of thia aection la to.review contributiona to the

literature in the fea under inve.tlgatlon And to comment on applicabil1ty

ta the specifie problem at hand.

2.1.1 Co!parative Coat Analyais

A coaparative coat approach (malnly transportation ~08t) ~s re-

coaDCnded by Isard (16) to determine the location of an industrial plant

given a nUilber of alternate plant aites in a region when both the prlce-.1

coat .tructure and the _Inltude of the market are known. The site whlch

ha. the lovest total cost of produclng and c:Jellvering to !ta market la

aelected.

. ,

Such an approach may be inapproprlate for dealing wlth the prob1em

under .tudy. since the output of the project ls aUocated in the international

urket wh.re a larSe-acale deaand for the product exista. Conaequently, the

cap.city.bf a custo. .i11in8 project is essentially independent of market ....

demande Moreover. 'the location of cuatom .. 111 may be dependent ta .o~ 1

extent upon lts cap.city and, at the .. me time, custom mi11 capaclty depend.

on the capaclty of the mine Under the.e clrcumatance this approach

in!aizes total coat. of the project, but not necessart1y optimise. lta fotal /

profit. For ~let COlt ainta1zatlon could repreaent a hiaher cut-

1

l.

r ~, .

9

off grade and lover aiDe eapacity ca-biDatlon for each aine and hence a o

saaller custoa aill eapacity and a s.al~er profit, and as a resu1t a dif-

ferent custa ~l location than a profit opttaizatlon would require.

2.1.2 Linear Prog!...tna Techniques

The costo. taill opU.aization ia si..tlar to the well-ltnown trans"

portation problea which deals vith the allocation of different kinds of 1

inputs (raw .. terials) coaing fra- va~ioua sources (mines) to several

depots (processing piants and/or markets), opttaizing an objectiv~ function

using linear progra.ai.ng techniques. The objective function say be defined

in teras of transportation cost, the reeovery of a particular eleaent or )

compound. or total profit. So.e applications of this technique in the

aineral industry and related to the topie under study are outlined below.

. i' Paul~er (9) for.ulates a general .odel to solve the problem of SCh4ling ship-.ents of ore froa .. ny sources to a eomplex of reeaction . (

; plants using linear progr...t.ng. The prinCipal purpose of this model is

to reduce fluctuations in the composition of feed products, although at the

~ s&ae time one optiaizes so.e other econoaic ~unetion, which might he the

total transportatlon cost, total value of productlon~ etc. Given the proper

Interpretation, the econoaic funetioD .. y allow manageaent to optimize other

probleaa, such as alning sequence and aine cycling, in addition to mini.aiz1ng

total transportation 'osts.

1 Venkataraai et al. (29) develop a Ilnear progr...tng model to

evaluate the interaction hetveen several crushed atone plants and aarketing

... ctoro 110 ,thet prod"::uoo ocbecluling ...... ,"",BOnal d_nd :001 lOOJdJa the"\ ~ ca.pany's net return. ~'

A stailar probla ls outllned by Willta.s(3~, 31). His etudies

dealvith flodiDa opttau. concentrate ca.binations froa~varioU8 copper aine.

(

. ,

)

10

, to .everal proce_lna pIanu, vith the objectJ.ve. of aax1ll1zina copper

production and .. rainaI contribution to profit.

Vith reference to lons-run production plannina for ore fro.

aultlple depo.lta, Janaaen(l7) appl!es I1near prosr ... lng to production

plannina for dlrect-.hipplna Iron ore fro. a nu.ber of relatively sasll

deposits. He aasumes tbat a conatant nu.ber of cleposits are kept in pro-

ductlon at any given ti~ and no .are than one aine i. depl.ted ln .ny given

year. The latter aaau.ption ia required because the crushina plant of the .. . depleted aine has to be disasseabled and re-eeected at the nev aine, and

personnel availahle can relocate only one plant per year. The constraints

---are product deaand, .dne capacities, lL.itations on ore aixlng, and arade objectives. (8)

Erlancls.on developa an Investaent progr .. for a group of de-

veloplng and produclng Iron aine.. Crude ore froa the aines ls sorted and

proces8ed into .ultiple producta et a nuaber of possible procassinl plant 1

locations. A linear progr...tna .odel is set up to .. asure the change

which would be caused in total profit by different po88ible Investments 1

The objective functlon of the .odel 1. aax~ization of total profit, con-

strained by restrictions in .. terlal balance., bleodins conditions, produc-

tlon capacltie~ and .. rket. The chanse in total profit re8ultinl fr~ the

different invdt.ent alternatives, tOlether vith inveataent and flxed coat,

1. used ln a .erle8 of inve.u.ent analy ... to decide vhich la the bes.t al--

ternative.

A .tudy clo.ely related to our proble. 1. tbat of Hos .. ck(lS).

H18 atudy deal. vith \he selection of a .lte for plant facilitle. under con-

dit10};'8 of aultiple _rlteta. product proca .... and ra ... tedai .0VJc

Hle . pproach ia a coabination of l1near prolr ... iol, Unanc1al .naly,~. and

j~.nnt~ ~ /~ -,-~

"".

11

2.1 .. 3 Other Techniques

Linear proaraaaina introduces severe a1aplif1cationa in deslina

vith o~timal selection of plant aite and plant aize8 for multiple productl

due to the presence of non-l1nearit1ea such 8a economica of acal~ and ..fiJted

costs. Klein and K1impel(18) sUlgest, therefore, application of non-linear

prograDllling, taking into account an integer type of opt1mization. They

assume given forecasts of demand and cast (including trends in technology)

at various geographical cent~ea over a apecified t~e horizon. The authora

suggest that large problema may ~e aolved more re.dily uaing decomposition

programmlng.

, Yu et al. (32) desc~ibe another type of problm of interest. Th.ir

study focuses on solving by simulation the storage problem for various Iron

ores arriving at hard-to-predict intervals ln an extremely ltmited apace at

a steel-making plant site. Storage muet allow blending to meet the steel

plant's overall ore quality requirements.

Most of the above papere aS8uae 1c.novn locationa and capacities for

variou8 sources and/or depota. However, our problem deals with a development

stage where individus1 mine capacity and srade, and custom al1l aite and ca-

pacity are variable. Moreover, the opt1mua coabination of cut-off grade and

mine capacity for each mine depends upon plant location and, aa a reeult. the

custom mil1 capacity depends on the plant site., Beaides, there exista only

one market and mutual1y exclusive alternative. l for the cuatom .i11.

The problem of choosins a cambination of cut-off grade and aine ce-

pacity for each 1II.ne ls not developed in the foregoing papera. Thu." .

diff,erent ,approach 111 required ta deteraine optillwa cu.ta. aill capacity and

location.

1 Frequently, projecte ar. DOt independent of each other. One fora of interdependence. uiete wbea one project can onl)' b. UDdertaken to tlw exclue10n ot another projec:t. The projec:ta are tban Watuall)' exclusive.

'. ..

)

' . " , .. '

12

2.2 Economic Evaluation Requirementa

In a businea. decialon. it ls generally clear whose profita are

to be evaluated. Governaent deciaiona, however. are .ore cOliplex. ' In

chooalng projects. goverument bas to sacertain vhich o&e best satisfies

the intereats and 'objectives of the nation~ The choice of one projeet

rather than another must be viewed ln the context of tbeir relative national

impacts. Impact has to be evaluated in teras of a consistent and appro-

priate set'of objectives. When one project is aelected, the choice has

consequences for employaent, output, consu.ption, saving, foreign exchanae

earning, income distribution and other factors of relevance to national ob-

jectivea. Thus, the purpose of govemaent coat-benefit analyaia is to de-

termine whether these conaequences taken together are desirable in the light

of the national planning objectives.

ln: virtually a11 developing countriea, the national governJlent

plays an important role in formul.ting and evaluating investaent projecta.

although, of course, the aix of private and public-aector inveat.ent variea. ~

The goveroment guides national develop8nt by direct !nvestment in the public

.actor, control of private 1dVeatment, the use of domeatic taxea, tariff,

suhaidiea, and the rat10ning of acarce Inveat .. nt resources. Thua, projects

Should be tormulated and evaluated ln 8uch a vay as to select for t.pl-.en-

tation thoae that will sake tbe best possible contribution to the objectivea

of the country.

2.3 Cost-Bnefit Analy.1. Technique

Coat-benefit analysie is a quantitative evaluation technique for

detena1ninl whic:h of s.veral courass of aet{OIl vill be in 8088 .. nae .o.t

pro fi table. lt providea a rational fra.evork for projeet aelection uaia&

national objective. and valuea. Projecta are judged in ter.."i ~helr I~.I

(1.

'.

13

Ulpact ou the 8COnoay. and thia illpact ia na1_tad by uains paraMtel"a

reflectlna natioaal aoala. l'he r .... e of, a1iernati".~ eu.iaed la deter- . ,

Idnecl by vedoua conatrainta. Mach .. the .ise" of the budaet avaU.ble fOl"" ,

Inve.tllellt. ~he nature, of the pUt",oH to be aened by propoeecl proJect.

and,~echnical fea.lbllity.

The ........ nt ... de ln coat-beoefit analy.ie fa 11 into four

broad catesoriee (19) :

2.3.1

1) The evaluation of co.t end benefit. at the tiMe when the..1

occur;

2) The evaluatlon of costa and benefite at a c()~n point

3)

4)

ln tlae - the problelli of U.e preference aoel t.he opportunity cost of capf.tal;

The evaluation of riak.y outcOMa;

The evaluatio~ of co.ta and benefita a~1ated with peOple having different inc0.8s and reaions having different inca.ea.

The Evaluation of Coat. and lenefite at the TiM When They Occur

Tvo .. in proble118 ariae in- eval_tins net benefita:

1) For .. rk.et it .... _rut pdce ... y he either dtatoJ;'tecl (e.a. by ,

taxes 0'> eonopoly) or reUect a _rket dt.equUibrlu. (e_a- UDeII-

ploy.ent or \balance of pa,.;ent probl_>.

2) For non .... t"lt it_ (includinl public aooda and the external

effect. of .. rat ft_) .. thoda of evaluation nead to he devalopecl

(e.a- for tille." recretional aaenitle., life, etc.).

NalEut I!Perfect:1on Departure. fra. Pareto-opt~ ait_tiona l

\ \ arl88 vhen .ooopoliatic el...ata or other ~rfectiona in aoOda

1 Pareto opU.allty exiata vben DO iDdbidual w1thln the aODdlly cao ba Mde better oU rit.bout 8OII!INne baiDI Mde .,ra. off

..

.. or factor market. ahift relative output avay from the optimum '. which vould prevail under competitive conditiona. In ca.ea of this kind. inveat.ent decisiona baaed on valuations al coat. and

benefit. at market priees may not be appropriate; .11 that i,

posdble i. a partial approach in whieh tl~e adjustmenu IIUlde to

.. rket priees make it more llkely that the right decision il made

than vou Id be the case using ~nadjusted pricea.

Taxes and Controla. lmpertect competition. constitute only one cale

of divergence between market priae and social cast or benefit.

Another la that of taxes on expenditurel. Market priees will,

in practiee, contain elementa of indirect taxation or, .ltetna-,

tively, ~Y, be below the time coat in ao far aa the produet i8 ,

8ubsidiaed. Where a produet 18 highly taxed. the uae of unad-

justed market priees will exalserate the maximum benefits, while

the benefits of a aub.idiaed product wou Id be undervalued. To

correct theae biaaea, aIl output Ihould be valued net of indirect

taxe. and subaidie., e.g. at factor COlt.

tm8!lployment. A divergence of loelal cost from private COlt which 1.

aometim.a of major importance ariaes when there ia unemployment.

When there ia an exeess suppl Y at the current market priee of any , . input, tl~t priee overstates thesocial coat of u.ing that input.

roreign Exchange. The contribution of a projeet to balance of payaent

.. y be an ex\remely important part o~ ita impact. Some projecta

~ll lubatantially improve balance of paymenta wherea. otherl .. y

lead ta a deterioration.

One obviou. r .. .on for,a country ta want a more favourable

balance-of-pay.ents po.ition la that it preaenta certain oppor_ ,

2.3.2

, 15

~unitiea for t.provins ita atandard of living vbieb would not

otherviae he ava1Iable. If tbat ia so. the foreign exchange ia

deairable not for Us ovn sake hut for the sake of other obj ~a ~

to vhich it contributes. e.g. aggregate conau.ption (27)'/ ~

The queation of foreign exchange benefita is expressed in the

deteraination of the approprlate shadov priee for foreign exchange 1

If earning foreign exehange is considered desirable because it per-

aits the country to t.port ecortomic resources from abroad or pe~mits

the country to abatain from exporting certain other goods abroad

that ... y be needed at bo.e. the shadov priee of foreign exchange

vould have to be derived in teras of other objectives. especially

aggregate consu.ption.

Non-Mark:et ItellS. Market prices clearly cannot be used to value benefits

which are not capable of being asrketed. The marginal value which

people place on a good A for instance. for whic~ they do not directly

pay .aney. has therefore to be Inferred from the .oney they would

have to pay for a good B Wbich they sho~ themselves to value qually.

'nle ~SOci.al Ti .. Preference Rate ,

Social Rate of Discount. Chooslog an appropriate rate of interest

la one of the .ost difflcult and .ost ~rtant problems in the evaluation of

public invest .. nt projecta, sinee to a planner interest rates must be viewed

as a .. thod of apportioning benefits and costs to different time periods and

po.sibly betveen different generations. The sacrifice of present consump-

tion for present inves~t vould oot be worth while unless the gains froa

that inVestaent in ter.. of future eonsu.ption are greater. ElIaent taUy.

then. an inveat.ent is worth vb11e if the future gaina in consu.ptlon are

The abadov priee of foreign exchanp is bJ definltion the ccmtrlbution a unit of forelan exchanae l18k.ea to aureaate con.u.ptlon. This obvloualy depends OD hov .. rainaI incre.ents of for.ill' exchan&' are utUlaed.

1

1

1. 1

1

16

reaarded aa bei ... ln aceaa of ~he curren~ uerUice of coaauaption, vieveel

froa the point of .iev of ~he clio ... .octal _Uare fuactlon. Tbeae laiu

viII he dlatrlbuted oYer the llf.t~ of the project and the exiatence of

eocial tt. preference requlres tbat the pr ..... t benefit be wel&hted IIOre

heavUy than the future beoeflt ln calculatlng the eoc:lal value of a project.

Thus, the social rate of discount lnsure. tbat the balance of beneflta and

coata ln one project 1. properly cOliparec:t vith the balance of benefita and

coata ln aIl alternative proJect.(S).

The choiee of the appropriete rate of dlacount la a problea that

i. facecl by aIl project planner lt la, tberefore, a .. tter of national

polley, and it would he Incorrect to expect the aove~nt proJect analyat

to deteraine the rate of discount. "the~ the eoclal discount rate

ahould he dealgnated by the central planninl aaency (27).

The eocial rate of discouat _, differ froa c~rc1al rate. of

intereat for _ny r .. sona 1bere are DO ca.pellins rea801U1 why the .. rltet .. rate of intereat ahould he the approprlate rate at vhlch to dlacoUnt future

benefita. Different approaches have Men aou_tecl for deteralnlna the

aoc1al t'ate of d1acount.

1

1) The aOVrn.ent borrovina rate (reclucecl to aUov fot' expected

lnflatioo and inco.e t~ pay.enta) la a popular and eaal1y

applicable ~aure of coata, bath becauae it la a ftnanclal coat

ln the ca .. of &O"e~t ftnaoced laYeat_nt and becauae lt can

he reaarded .. thl! rl_-free rate of intereat l, abatracUng fl'Oll .

UDCertaint1abou~ the price level.

2) Sc.a coat-beDefi~ .... l,.~a (20) atate that 1t "7 be beat to atart.

IlOt vith a sia.a~e e.t~t. of tlM! social d'iacouot rate, but vith

roI' the ord1Dary 1...... tha adJ..-teci loaa-tena boad ra~e prohabl, 11vea aa Iood .. 1deoce _ OM la lllte1, to .. t OB hl. rlak-fr .. tlM preference.

1 ".

1 \

3)

17

hiah, low and .ediua rate. which could be e.tt.&ted from proJect

that have been accepted in the past, froa inforaation fra. 1n-

duatrial cen.ua.s .and survera} a~d fra. infor.ation about proa-

pective projecta.

Other analyata (27) treat the aocial diacount aa an

unknown of the planning problem and 1ec ~ankina projecta

on the baala of internaI rate of ret~ when aBBreBate conaumption

i. the aole objective. Hovever, the veakneaa of thia criteria

ia ita impliclt aaauaption that' the reinve8t .. n~ rate for the .

future aet of inveatment alternativea, v~ich ia the aame resardle.a

of vhich alternative i. currently accepted, ia equal ta the in-

ternal rate of return of the alternative under consideration and

thua different for each alternative.

Formulae for ProJect Choice. When proJect~ are independent. the , .

&Ost convenient vay to maxiaize the present value of con8uaption 18 ta ~hoo.e

all projecta having poaitive preaent valuea, calc~lated at the relevant

aO,cial discount rate (5, 19, 20, 27). nia; however. requirea ..odification

in the prelence of objective function con.trainta. If an input, luch aa

capital, i8 l1mited in 8upply, it .. y vell he that ail acceptabl~projecta

cannot be undertaken. ln thil in.tance, projects muat be ranked or ordered

ln terms of the objective function. . If there i. capital rationina. for

e~ple, the correct approach ia ta aelect projecta in order of their present \

value par unit of capital required ~til capital reaource8 are exhau.ted.

An industrial cenaua 11ata, for each industry, the value of output and tha valua of tbe .. in inputs, includlna labour, fiaure. for depraciation and for the book value of capital in the tDduatry. After suitable ad-juat .. nt, this data cao be uaed to tt.&te the rate of retum in diffarent industriaa. -,l'

. '

18

Wh"n projecta an mutually "xc1u81ve, th. molt vid.ly aceepted

criteriA l1k. "rate of return" or "colJt-benef lt rat 10" tend to favour

~mal1er proje~t8 (5).

2.3.3 The l\Hect of lIncertintl'

The implicAtionllor uncertAinty for public invel!ltll.nt deddolt1..-tI

ArE' controvpr"lAl And thert> An~ "everAl p08itlon" on th"l l,ulUe (5, 19).,

1) OIlP point of vie., tilt thAt r1Bk should be dh('ottnted in the IItI"M!

WAy for puhlll' illvp"tmpnl "" 1 t lA ror privAte Inv."t ... nt. Hill

8r~\I(td thAl ln lrPAt rililk dtffprently ln the pllblll- "ector wUl

fPAult in oV(1rlnvr.tml ... t in thb I!Ipclor Al th .. exp.n"p of prlvAte

1) A "'econd pOAttion 1. ... tlull th(l Rovprnm .. nt CA" h .. tter cope vith ~

uncertlltnty lhlm rriVllf.e t"vttatont And, tt,en'Core, Rov"rn .. ent In-

ve8tment .. ho\l1d Ilot h" tiVRluAtpd hy the "ame crlt.rlon u.ed ln

ln support of thilt pott1t1on 1t b 8rlu.d that

tht' Movernmt'nt typical1y 'Indttrtakp8 1II8ny projectll and the n.l \

ben"fits (rom (!Ilch project Arp (RPneully .. p .. kt",) ... 11 relllt ive

lo the aJ",reMAtt' conAumpllon of thl' econolllY. Horeover, the,. net

bpllefit .. Arf' Kenerally le .... hi~hly correl .. telt ",ilh the level or

RgaUlatl' conl!lumptlon than lit the contribution of a proJect '.

. f profils to a prlvate firm' .. total profit. Thu., the lovern.ent.

1 ... bl to pool ri.ka to a auch Ireater e.tent then privat. 1n-

veatore. RflJid , it ia aflued that th .or. taxpayara (lnveat.oH)

a aivell risky projact le apread oVer, the ... Uer .. th. individuel

rhk ln pflttice, it .eeaa reaeonabl. to au.. for .oat Inva.~

Th. t.r.a rl.k and une.tt.lnty ar. u " int.rchang.abl, her

19

.. nt project. that the co.t nd benefit ccruina to taxpayera .

Th. lov.~nt ahould th.n .valuste inv t-

.. nt opportuniti accordina to th.lr expected pre nt valu. u.lna "

a rate of dl.count .qual to th .ocial dtBcount rate. Nev.rth.l

it 1. prob.bly correct to .uppose that only under exceptional cir-

cu.atancea la the e~pected present value rule appropriat. in the

eontext of a relional distribution objective. For ... ple, th. ~

railure of a projeet .. y have p.rticul.rly da .. ain, con.equene

for the reglon ln vhich it la loeated. Thus, the 8t.,le expected

pre.ent value rule will not then Bufflee ln evaluaUna net r.lional

benefita and it ~ reasoRable, up to a point, to reward pro-

jecta with a relatively certain outc~ (i._. ~ith .... 11 variane) \

even if they have a lover expected inca.. (hence lover expected

preaent v.lue). One .ulgested .. thod for deallna with Buch c

la to uae the Honte Carlo .iDlUlatlon technique to 1Ii .. I.te .po.dble

variationa of une.rtain input 0 aB to live nu.erlc.l r.pr en-

tatl~n of th. effecta of uneertainty.

J) There ia, in addition, third po.itlon on the IOvern.ent'.

2.3.4

re.pona. lo uneert.inty .nd it rt. th.t ti .. and riek pre-

,f.rence. relev.nt for gov.rnment action .hould be e.tabllahed r

.J<

matter of national poliey by th. appropriate authotit1e8.

Redistribution of Inca ..

A lovernaent hae veral ... n. of redi.tributln, inca.. (i

fiacal policy, taxes and eubald1 , .t~) that c.n be u d vlthout areat

But to a ume that the de.tred redistribution of conauaption 1. to

bo achievod lnd.pendently of project. i. to place undu. r.llanc on fl.c.l ... pol.icy t.xe. and .ubald1 and on the prlelna poliei ueed in the

20

distribution of the outputs of public enterprises Given the concerns

vith inequalities, a govemment should be prepared to sacrifice S0.8 poten-

tial aggregate consumption realizable from public projects in order ta

~prove its diatribution(27).

A government may give expression to its redistribution objectives

by attaching some extra positive weight to the net benefit accruing to the

more deserving groupes) snd/or by attaching some extra negative weight to

the net benefit accruing to the less deserving group(s).

The redistributional benefits to a group are equal to the aggre-

gate-consumption benefita it recelves minus any off-setting payments made

\

. -

/ 21

-vIlere y representa the .. rginal oportion of the direct net redistributional

beneflts. ~, vhich, wf~n respect, reiult in additional net beneflts

to the rgion.

The total net redi.tributional benefit to the region,k~, is:

A ~A~-y- ia the regional-inco.e .ultiplier, and It le applled to the

direct net redistribution benefite ~(t) in a given year t to yield the total

net redistributional benefits Rr(t) to a particular region in that y.ar.

l~ practice, one .. y weIl have to abandon the attempt to measure

the econoay-vide redistributional consequences of a given project and con-\

centrate a~ly on ita aeJor ~act on the local region and local groups.

E!ploJ!!ftt and the Redistribution Objectives. The question of the

social ~rtance of e.plo,-ent creation Is one of the more Intricate aspecte

of project evaluation. ThIR ia partly becauae the proble. ttaelf Is com-

plex, e.ployaent having ~licatlons for a number of disparate planning ob-

ject ives (27)

So.e authora aaeert that eaployment 1. valuable in itaelf, quite

apart froa the contribution It .. kes to output creation. The distrea. of

UIleilployed f_ilies la well known. and probleaa of poverty, undernourialulent,

disease and chaos for f .. iliea vithout work cannot be ignored in project

selection. Horeover, in varioua official and unofficlal etudiee ainlular

e.phasia la placecl on the expansion of ...,loy.ent, and it ta tndeed quit.

ca..on for project selection in practice to consider ...,loyaent a .. jor

objective ln it.elf

On the otber hand, otber autbors cl.ala that ftlPloyaent la d.airabl

DOt for ita OVD .... but rather for vhat ft lenarat , aa.ely, output for the

,-,.Ji

22

productIve ayat_. inca.. for certain people, o,pportunJ.tlea for Je.mina

increased .oderld.u.tion, etc. For exa.ple, one reaaon why eaplo)'Mnt la o

developinl ~

vyUed i~ becauae of ita 'illpact on 1nc0IM diatribution. , ' In

countriea vith a larse volu.. of 8urplus labour a productive 8IIlploywlent,

aven vith 10. output, la preferable to a dol~ ayat ... Under these cir-

cUIIStancea, an expansion of eaploYMnt in spreading the real income very , '

videly .. y contribute efficiently to the red18tributl~n objective. Some-

tt.ea when a whole relion ia knovn to be economieally depressed,income ,

leneratiq in that relion .. y be SiYen a special weisht, and in this vay the

iapact of eaploy.eiit la included, because, ln estimating ,the inc)me lenerated a,

ln that region, note auat be taken of e.ployaent and weges paid out. Thua,

no special effort need be .. de to see that the effects of employment are re-

flected ln the inco.e-distribution objective. Thua, the employment obje-

tive viII be reflected .. lo1y through the aggrelate-consumption objective

and the redIstribution objective.

\

" i.,

1

.;; -;

, ,

';',

\

"; .. 1J

,. r. , .. " ,

\

(

23

\" CHAPTER 3

COST AND REVENuE RELATIONSHIPS

FOR EVALUATION OF AN ENAMI CUSTOM MILL

TIle need to carry out the construction of custoa aliis stems

fra. the general goals established in the 81IUlll and tlediua shed lIining

sectors' expansion plan ("Plan de Expansion de la pequena y Mediana Minerls"),

that EMANI has been 1.ple.entlng since the aid-slxtles. The general ob-

jectivea of th18 expansion plan .re:

1) Regional econo.i~ iaproveaen~ in thoae regions where small and

2)

.edium slzed IIlning actlvity, .specially copper .inlng, ls

essentiaI to developaent.

The 81IUl11 alnes and the custom .ill facility sre c~naidered

an Integrated production sy8te.. According to .stabliahd

criteria, ENAMl, aa the owner of the aill, doea not receive any

profit troa the project. . AlI benefita are trsn.ferr~ to the

... 11 aining ca.panlea throuah EMAKI's purcbase priee for the

ore sURPlied by theae coapaniee. ENAHI'a operations are tax

ex~t but the private .ining c~aniea have to pay 2% lIineral

~ 'salea' taxe Fore1gq exchange earninga to the counery. The .. in econoaic

characterlatic of re.ional aill projecte ls that theY,are net

producers of forelgn currenc1. project output bains exported.

nuas, tlte '-diate t.eneficiarl88 are thos. pereo.... ln the public

l ,

24 - - J

o~ private aector. who U8e thia forsilft ..cha... for .. rainaI . iDC~"'. in bIport If forsip uchanae ia alloc:atecl by ... na

\

of a quota . yat.. iIIporter. _,. bu,. tbeir forsian e~balll. at an officiall,. dete~ned rate aub.tantiall,. le thn his willingne

to pay. in vhlch case the,. directly beneflt. ~ _.

The rest of the t

diTect aiar~~OQ8...,tion benefits retu~. in the fora of

do.estlc cutrency to the ~nlna ca.p&n1e. through ENAHI'a ore

purchaae greeeent.

Ha~g eatabliahed that a .avina of foreign excnanae la ~he

relev.nt net output of the proJect. it i till neee ary to find

a auit.ble .... ure for the value of foreiso exchange. Becauae

the .. rket for forelgn exchange ie not ~oapetltlve and forelgn

exchange ia 80ld at an officially dete~ined rate, .hadov prleea

.u.t be uaed to .alue the do.estie eurrency equivalent of the

foreign exchange. It 1. obvlous. -however. that .badow priee.

for forelgn exe~&e are beat evaluated fS part of central govern-

IICnt planning.

Unfortunately. tl~re 1. ~ recent atudy th~t providea thi.

infor.ation for Chlle. Therefore. the official rate of exchanae

used to value national eurrency (Escudo) in te~ of foreign ex-

change (Us dollars) vill be ellPloyed. , Alao. to eltainate inflation

effecta, 1969 constant dollar valuea are uaed in the proJect

eval .... tion.

'k (

f'k!l ~ "" , "

~

.'.

25

3.1 Revenue

The total revenue pel' 18ar and per aine ~. a funetion of output,

given that the unit priee i8 fbad. Hence. the foUorinl revenue rela-

tionship holds:

where:

TRY 72 x HP x RF ~ DF x x MQ

\

TRY total revenue pel' yesr ($);

HP recovered aetal priee less smelter. refinery abd \:

commercial chargea (cents per pound);

RF - mill recovery of the copper in the ore (expresaed a8

a decimal);

DF - dilution factor (expresaed as a deciaal);

G average grade of ore mined (X);

MQ - mine capacity (ton. of ore mined per day).

Th~s. for RF 0.85. DF 0.90 1 P eopper priee at the London Metal

Exchange~ sr smalter nd refinery charges, and cc co..ercial charges.i~

the follow1ng, relation ls obtalned.

TRY 55.1 (p - sr - cc) x G x MQ 2.1

The sale revenue obt.ined by the country in foreign currency.

RY, la

RY Co x TRY

where Co i. the fraction of TRY obtained by the country,

(6r-avai1able feasibi11ty atudy Co 0.9.

1 Accord1ns to available f ... ibilitr .tudie. (6, 1)

. .

2.1.1 '.

Accordina to an

"

26

3.2 Capital and Oparatina COlta i

~i. typa of project hal' a hiSh taport content for capital Soodl

and some operatina .upplies, involvirta a drain on for.iln exchanse aqulvalent

to the foreian exchange COlt of these inputl. f'

It may happen that the praject doea not draw fro. free foreiln

exchanae for ita imported input by Uling, inatead, an- international loan that

is tied to the project (6, P. If the loan made to thia one project in no way reducea the chances of additional loana to other projects in the country,

the imported inputs result in no Immediate drain on the 8upply of foreian

exehange available to the eeonomy. The relevant costa are deterained fro.

the loan repayment obligations, for it ia only when the.e repayaents are .. de

that forelgn exehange wUl have to be diverted froll other usel.

Once the foreign exehange inputl to a project have been ident1fied,

it on1y remaina to meaaure them according to the principle of willingnels to t

pay. He:re the procedure becomes identieal to the aaeaaurelMnt of foreian

exchange benefits.

3.2.1 Capital Costa

ENAMI is the ovoer of the cuatom mll1 project, providins the inveBt-

ment required for the mill as weil as .olt of the develop.ent fund, required

by the private mining companiel, in the fora of lona-tera loanl. AllO,

ENAMI provides exploration fundl and infrastructure inveataent. ThuI, the

capital eOBts are:

1) Regional Exploration lnveatllent, neceeaary to inaure aineral

aupply for the mill plant. Thia inveat .. nt requir..ent caa

be timaud from the a.ae'alDent of the copper aiaeral poteatial

of the reaion A review of .. thodl for reaional lI10eral apprai .. l

and a ausse.ted method to predict reaional .taaral eDdow.ent for

plannina cu.toa aill facilitlel l, alven iD AppeDdix A.

,.~

2)

3)

'l'ba Infr .. tnstU!'e lnYeatMnt for -tbe projec:t CraU and/or road.)

to provide the required facilitlea cao be eetu.ted by IMans of a

at.ulator vbich tata. dilitized .. p infor.atLDn and ca.putea con-

struction costa of nev acceaa road. for .oving ore fra. the aines ,

to the aill 'plant (14). Consicleration of 8eographic and tech-

noloaical constrainta (existing infrast~cture and supply

facilities) noraally reduce tb practical loeationa for a regional

aiU to a fev possible sites. ~

Kine Develop!!nt Investaent. It 4I8S as.uaed that aine developaent

i~est.ent ~I). as a fonction of aine capacity, la of the

8eneral fon:

MCI - k x KQY 2.2

where k and y are constant.. and 0 < y < l (4. 22, 24)

Uaing relreasion anal,.i.. the folloving curve was fitted

to investaept and production data for ... 11 copper aine. in

Aconcasua and Santiaso province. (see Table 2).

0.67 MCI - 4674.612 x KQ ($) 2.3

4) Custoa Mill Invesaent (flotation proces.). Accordins to the

calculation done in the "El Salado" and"Cateau" feaalbillty

(6 '7) .8tudies the data shawn in Tables 3 and 4 vas avallable.'

, '

Usin8 regreaaion analy.i. ~nd the type of function given,in

equatlon 2.2, the followina curve va. fitted 'to thia d,ta: v '

CHI .' 19017.0 x peO. 73 2.4

vbere:

CHI cu. ta. aill inve.t.ent ($);

PC aill capaeity (tona/day) f

: .' . ,. , , ,\~

1 "

1

1-

,

:; ,-J,

\

\

, . ,

, .

28

Tabl. 2 ,

In"..tMllt rad Produc:t1(!!! Ptt! for S .. l1 Cop2!r Mine. 1 in t e Acon!.ua and S~tia.o Provinc.~l

1

.' \ Mine Location Pto~uet1~n lnvelit_nt Depart_nt tonalxear Eaeuclo. 19692 ,

1. ,. Cats .. 656 37,000

\ 3,000 86,400 Peto~ca Petorca 1,620 551,000 Petorca

. , 10,560 277 ,000 Petorea 18,072 708,000 Pstorea, 6,424 771,000 Illape1- 12,000 629,000 Sa1aaanca 1,420 361,000 Illapel 8,400 280,000 Illap,1 3,000 213,000 San Felipe 2,400 85,000 Pstorea 1 27.480 272,000 Petorea 32,SlO 1,523,000 Putaendo 14 ,100 546,000 p,torea 25,OO 1,201,000 Cate .. 18,500 331,000 Santiago 40,260 1,616,000 Il1.pel 13,560 673.000 ,Il1ape1 21.600 299,000

Source: "Eetudio sobre la. eondicion.. Tcnico-!eonomieas te. 1. 'pe(fuea y Mediana t.ned. Seetor ENAMl" (Survey on the !eonoade and Teehnical Condition. of Medium ,"d S .. 11 Mlnin~ of ENAM! Seetor) )

2, The average offici.1 e.chanas'for 1969 w US $1 E09.2

...

, ,

, ...

, 'fi,. ~~ .. '"\~

\:~ ~~ , .~

'~ .j

, .,

.,

29

Table 3

" __ p ------...,.-~--o:__~____:_, ~,' ~-~~,--rt~

30

5) Cut. Hill r1xed Coat_,: kcoaliDa to IIMlI practice. CU8toa

aill equipMat la depreclated onr a perlod of ta yar. vith a

-,

6)

.. Iv... .,al... of lOI

.... periodl (6. 1).

'lbe bu1J.AllDa ta clepreeiatecl fully in th

Thua, the d.preciatlon coat per year, al.

la:

al

.w .... 1 x (1 + i) 10 an x 0.13 .. - -

, (1 + l)lO - 1

. (dollar lyear)

vber. i eoclal discount rate.

The enaineerlna proJect expendltur. and the t.pGrted equlp.ent

.. 1. charle 18 deprectated over a period of five y .. r..

the depreciatlon char,e per ,..ar. a2. la:

an x 0.08 x 1 x (1 + ilS (I + l)s - 1

,

(dollar/yqr)

The total cuatota .U1 fixecl coat. CMPC. la then:

QOI'C - a. + a2 (dollar/year) 2'.5

Thua,

. ' ~ The For.lan Exehanle capital Coat 1. deteratned usinl foreiln

exchanse lnveat.ent coefficients obtalned fro. available data (6. ?>:

Cl fraction of aine develo.,.ent lov.au.ent in

u.s. dollara - 0.60

,C2 fraction of infraatructure iDvestaent per .1ne in 1

U.S. dollara - 0.20

Cl - fraction of cuatoa alll bveat_nt ln U.S. dollara

- 0.42

Tbu., capital tmre.~t epeat 10 U. S. dollar. per aine, C 11. la:

Cuato. .Ul ... is-at and t. bulldiDa repreaeot re.,eetlftly 621 and 30% of total c:uatoa atl.i. 1DYe.~t.

..

3.2.2

.. . ' 31

Cil - cl x MCl + C2 x 10 ~

($) 2.5.1

whera 10 la lnfr.atructur. inv t .. nt per aine ($), and capltal

inveat .. nt apent in U.S. dollara for the cUltom all1, C12, la:

Cl2 - Cl x CHI ($)

OperaUnl Co.t.

1) Mine Operatina COlt. According to the ~I Planning Depart-.nt'.

SUTVey for the Province of Aconcasua, the data ahoVD in table. 5-1

wa8 jvaUable. (7)

Table 5

Mine Operation Co.t - Production Ralation.hip

Sma11 Copper Mln.l, Province of !cone.lUA, 1969

Tona of copper Tons of ore Operatll\8 COlt recovered 2er lear 1Il1ned Eer leaf ~iltonl .,

25 4.0 18.3

50 8.0 11.9

100 18.0 8.5

200 33.0 , 6.0 400 66.0 4.2t f

v

1000 166.0 " 3.6

The atructure of alnina operation coat va. a. siven in Table 6. 1

Excludina a.ortiaation and tranlportation COlt. and con.id.rina

"other" cona a. flxed, the aine oparatin, co.t va tiuted

aa a1ven ln Tabl. 7.

. ,

. "

' .

l'

, "

32 , ,

Table 6

Mine Qeeratio~ Coat Structure (a. percent of total operatina coat)

Itema Mine Capacity aa388 30:250 tona of >2 tons of copper recovered copper recovered

per year

Salariea and So:ial Charge,. 47.65

Exploaiv~a 4.40

S,teel q.98

Enersy 3~40

Royalty to the Mine Owner 4.20

KainteD4nce and Repaira 7.54

AmorUzatlon 7.05 \

Tranaportation of Mined Orea 18.30

Other ~ 6.48

Table 7

Mine Op.ratina Coat R.elatlooah1p'

Tona of Ore Mined Par Day

4.0

8.0

18.0

33.0

66.0

166.0

. ..

Variable Operatins Coat ($/ton)

12.5

8.1

5.8 4.1

#',

2.6

2.a

=1

per yur

37.70

6.58

2.74

2.56

7.20

6.04

8.04

22.20

6.94

1

/

'ued Operacua Con ($/day)

10.4

10.4

10.4

10.4

10.4

10.4

" '

"

33

Uein, r.are .. ion technique, th,e follovina curve vae fltt'"

to the available data for avera.e op.ratina yariable coat

(MAOVC): .,

MAOVC 22.92 HQ-O.~8

Thu. the ayerase operatina coat la:

Av HOC - 10.4 x HQ-l + 22.92 x MQ-O.48 (dollar/tort/day)

and the total operaUna coat. HOC, la:

HOC 3800.0 + 8360.0 x HQO.~2 (dollara per year) 2.6

. The mine operatins coat apant in foreian currency, CCl. ia:

OCI c .. x HOC 2.6.1

where CI. - fraction of HOC apent in U.S. dollar a 0.18 (6. 7) ~

2) Cr-ca. Hill Operatina Cost. The follovinS data va. avallable(6,7);

Plant Capacity tons

500

1000

OperaUna Coat $/ton

4.3

3.4

A 11near relation vas fltted batween the.e valuea. Thua,

tbe cuato 111 operetlna coat, CHOC, la:

CHOC 5.096 - 1.686 x 10-3 x PC ($/ton) 2.7

The forelau exchanae outlay, OC] . ie:

($) 2;7.1

where C6 fraction of CHOC .pent ln U.S. dollara 0.23 (6,1)

' .. 1 ...

: .

.,..

l,

3) Ore TraneP9rtation Coat froa the 1I1ne ta th .tU, KTC, i.

liftn by:

MTC 360 x MQ x Dkj x c

where

c averale unit transportation cast for ai.ed ore

0.050 ($~ton-km);

Dkj distance in Jana from mine k to cuatom ai11 aite j.

Thua,

HTC 18.0 x MQ x Dkj ($)

4) Coneentrate Tran_port_tion Coat \pTC}

PTe MQ x G x FR x c x Dj x 360

Lm

wherel

G averale Irade mined (X);

2.8

\.

Dj distance in kas from tustom mill site j ta the

Thual

1. smelter;

FR - ~ll recovery factor' 0.85;

La averale concentrate Irade ef the all1 (X)

- 2SX Cu;

c - averale unit tranaportation coat

$0.OS6S/ton-ka (6, 7).

f

PTe 0.692 x MQ x G x Dj ($)

The foretan exchanae outlaYt OCh ia:

OC2 cs x (KTC + P'l'C) ($)

"

LI,

2.9

. .

If'!J J '. -

-'.

S)

3S

vbere:

Cs fraction of (K'rC + Ptt) apent in U.S. dollar.

0.36

(6, 1) ~

SIIel.ter 1 ltef~ery aod ec-ercia1 Chargea. These charges are

discounted froa the unit sale price. Saelter and refinery

charges, based on EHAKI's operat1.on, represent an average-cost

of 10.14 cents .per pound of copper recoverecl; and co.tercial

char.a for EftAMI repr~nt an ave,rage cost of 3.3 cents per

pound of copper rcovered.

3.3 Indirect Benefits and Costs .

The distinction betveen direct and indirect benefits is somewhat

arbttrary. Revertheless, it .ost be adaitted that proje~s often yield a

net gaIn to society that la IlOt wholly captured by those that acquire the , .

'0 1

project output. For exa.ple, if regional econoaic development ia conaidered

as the "in,ecooo.ic objective of project, then the additional benefits /

obtained by those per80~s in the public or private sector who are able ta uae

th~ extra foreign exchange for .. rginal increaQes in ~rts abould be added

to deteraine the overa11 contribution bf the proJect ta the aggregate con-

su.ptlon objective (~7).

Anotbr externality results fr~the building, of tranaportation

systeaa neessary for the project Tb benefit provlded by the roads 1.

DOt l~ited to the servlce of tbe project.

, . They viII also iaprove cowaunl-.. cation. and laver transport co~ts (or t~ vhol~ a~ea, and this ls likely ta

result in lover co.t~ for ~ocal ~try and heoce aet conaumptlon benefit.

for the CCI. ~~y as vltole.

'ntere .. y alllQ'be extenaal co.t., repreael1t1na a l1et 10.. to . .

aoclety. of ~ch pollution ls proainent eznple. 111. fact t~t va.t

.;1'. " ,

, ~

,~

, .

,

\ \,

': , \ \

36

Ar. pre.ent ia the eaviroa.ent doa. not, per . indicata p~llution

Rath.r"pollutlon oceura only vhen wa.t. dlapo .. l practlea., orthe.laek of'

th .. , have adver.e effecta on other partie For exeaple, the affect ol

aine effluenta, aubaidance, and abandonad alne workinS8 on acono.le develop-

.ant de.erves specl.l .. ntion bec.uae they .. y be .l,nifle.nt ln certain

rel ion Certainly, all aininl and aineral procesain, operations have

effecta on the land aurface, and ao.. of the.e affect ... y impo.e damase.

Thua, the v te _nase.nt probl .. lnvolvea detet'lftining:

1) The illpact of waate diac:harsea on quallt:y of the environaent.

vith ~pact .eaaured by the t~. pattern of concentrations

of vaatea;

2) The effecta of ti .. patterns of waate concentrations on uaea

of water and land.

It has to he axpected that .ome data will be missing and .ome

cost. only poorly aeaaured. Sut neUher of theae difficulUe. obvlates

the need for .. kinS deci.iona ih th preaent.

The effect oll land pollution (waste diapo.al) ,i. negl{,lble in

.ast er .. s of Chile, except~lf the proj.~t i. l~at.d in the Central Zone

(IIOre asricultural), in ""ich case tbe coat Incutred fro. t\1e wa.te diapo.al

auat be evaluated.

\~

3.4 Secondar Benefita a Coat.

The aecondary benefit and co~t. are the expan.ionary effect. of a

project'. direct benefits. The differ frpa external co.t. and benefit. ~

in that they are co.pen.eted abift. in eco~ic reaourcea; th.t i., thsy

would occur in any avent, resardl of project t.pl ... nt.~lon. thou~ not &

neceasarlly iD the .... local

..

l '

(

(j

.. , 37

Seconclary national benefita vUl not be Included ln the coat-e

beneflt calculationa, aince aecondary national benefits aaau.e an t.portan~

role only vhen a alsnlfieant portion of aIl natural reeourcea are projected

to be idie over .aat, or aIl, of the project's tiae span, and when the pro-

ject viII e.ploy previously uneaployed reeources. Aa only a fev reaourcea

viII be uneaployed or undere.ployed ln the case under etudy, any reultlng

secondary national benefita viII be quite ... 11 in relation to total project

benefits. Further.are, theae benefita will be offset by other benefits

fra. alternative projects, if the project under conaideration ia not under-

talten. .. ~

Regional benefita, hovever, are aignificant for custom mill c"

project evaluation purpoaea and Any expansion in local eaployaaent and incoM,

as ~ll aa any addltional local invest.ant, occurrlng as a result of the

project, ahould be aaeessed. To do this, tvo typea of effecta ~ust be

diatinguiahed - one-t1ae and contlnuing. One-t~ effecta consiat of an

increase ~n eaploy.e~t and vages in the local area due directly to the project.

Continuing effecte are the indirect reaulta of the project, and conaiat of

aupple.entary econoaic eipansion brought on by the exietence of the prolect,

-ineluding the folloving Iteas:

1) Inerease ln jobs and payrolle (other than tbose occurring

aa a direct reault of the project),

2) Per-capita inca.e,

3) Una.ploy.ent rate;

4) Expapslon 1~ local busineas eatablishments and the creation

of nev eatablisbaenta;

5) I.prove.ent ln,'or expanaion of, local infraatructure, inclod1ng

h1ghvaya, railro-da, doclta and piera, and airporta

, 1

3.4.1 1)

..

"

J 1 1

38

Direc~ I!eloJMlt ,

Total !!eloyeat in K1ni.'Operatlou. ;

The followtlll data ...

av.il.ble -(7): , .

2)

3)

"her.

360 x MQ PIlODj o

j' 1,3'

EH ployaent .enerated per aine.~

39

2.9.1

Employa,nt ln Ore Trln.portltion. It i. a uaed that 10 ton cl

trucka are uaed. tranlportins or. at an avara.e ap.ed of 40 ~/hr., ~

Ther. i. one driver per truck, the real tran.portation t~

per day 1. 5.S hour.(7) and the total available day. per y.ar are

300. Thua,

wlter.

Titus,

!MT

lU x 2 x Dk.J x HQ V x H x C x FF

!MT nuaber employa~. tranaportation per mine;

Ki coefficient t'At tak.e. into Iccount the nuaber

H

of available day. per y.er 1.22;

di.tance aine - custom aUl; ....

averase Ipe.dj

effective U per day;

C truck capacitYi

FF fi1l factor 0.8.

!MT 0.00139 x MQ x Dk.j 2.9.2

Employment ln Concentra~portation. It i sumed (7) tbltz

C 1

10 ton. per trucki

V 50 km/hour;

" 5.5 hours/day; ...

lU 1.22; ..

L 25% Copper (conceotr.te ar.de); m

- fUr 0.85 (recov.ry f.etor).

l,

,-'

:'~ ,. ~~-jJI

-. 40

TllU8, KCT 0.0000381 x PC x G x 0j (number ~loy.d) 2.9.3

wluara ECT e11lploymtl1t in COllctmtrllte transportation;

- average grade mined;

- di8tance cU8tom mill-smelter.

4) ~Rl~YMnt in CUI tom ~il1 Opration.

fitted to the d~ta available (6, 7):

A simple straight line va.

~

ECH - 51 + 0.034 x PC (number employed) 2.9.4

where eCH - employmlnt in CUBtom mill operation.

3.4.2 Continulng Kfffl

The rollowin~ ordera of ma~n1tude appear reallonable for a.s8a.1n8 ., the incume effect of the smitH mining enterprhe in 8 region. Por $1 of

eales revenu .. , $0.90 18 apent ln wagea, capitAl expendltur , materiale and

repaire, servieps, tllX(I!S, 1ntarellt, and d ... bt repayment. or tht. $0.90,

one third ($0.30) 18 Apent 11\ thl' region (6). Thi. expenditure 8~n.rate. an equlvalent amount of $0.30 of secondary income in the region. Thu., the

regional incorne multiplier la $0.30/$0.30 1.0.

3.5 Total Coot and Revenue R14t ion&hip8 for Econ01ftic Evaluation

The total capital inv8Btmant per mine, TIM, 18

TlM MCI + l o (dollara)

The total operating coat for a producing mine per year i. the

aummation of mine operating costa (eq. 2.6), cu.tom mill operatina coet

(eq. 2.7), ore tranllPortatl6\ cost fr01ll the .. ine to the .U1 (eq. 2.8), con-

centrate transportation coat from the .111 to the elter (eq. 2.9), plui

cUltom mill f1xed coat (eq. 2.5).

ThUI, th. total coet for a produclng,.lne per y.ar, TCY, II'

, ., 41

TC1' uoc + QfOC + KTC + PTe + QIFC 2.10'

Accordlna to eq. 2.1, the total revenue pel' 18ar per alne i.: '.

TRY 55.1 x (p - 13.34) x G x KQ (dollars/,ear/alne) 2.11

3.6 proJect Choice

Once a11 benefita and coata at'e calculated, projeet pro,fitablHty

can be assessed. This assessmant concerns the econoalc evaluation of a

nuaber of ~tually exclusive projects vhich dlffer: (1) ln alze of plant,

and, therefore, in the output produced. and (2) in thelr location vithln a

given region.

The (irst taak of the analysls 18 to deter.lne the opt~ mine , 81ze8 and cut-off gra~ea for a given cuata. mill location. The folloving

criteria will be eaployed. As ENAHI does not receive .ny profit from the ,

project, the profit feins tranaferred to the mine producers, it will be as-

su.ed that cach aink producer seeks a cut-off grade and .ine capacity coa-

bination wltich ... d.izes hla profit for .ach of several alternative .Ul

capacUles, regardless of the actions of other 1II1ne producera. Three dif-

ferent optiaizatton criteria are used for comparlsou and criticlsm pre.ent

value, present value ratio and rat~ of return.

The second.atep of the economic analysis la to s~lect the best

custoa aill capacity for each feasible location. At thie point the problem

of scheduling aine deve10pment arises, since the miner.1 aupply may exceed a

siven cu.to. aif1 capacity. Thua, Jor each plant size conaidered and for

the aine optimization criteria, tltere exiata a dUferent solution, assWlllns

an even supp1y to the custom a111 and other constraints, 8uch .a a .1ni~

life for the project, etc. nle aill opttalzatlon problea then becoaee: 1 flnd the plant capaclty that aaxialzee the preaent value of the project dl.-

counted at the social rate of diacount, aubject to conatralnt Since the

42

social discount rate ia to be treated aa an unknown vith!n a 11Ja1ted ranle, ,

values o~8 percent, 10 percent .nd 12 percent hav~ been chosen l

Finally, the best project alternatl!~ among thoae that are the

best for each fea.ible location i. aelected. The present value la employed

J' for ranking the projects. An interelting alternative vith re.pect to mil!',

location ia to consider and ana1yze the use,o! mobile mills. As transporta-

tian costs and lnfrastructure investment have a significant effect on the

economlc resultlS for a fixed cust01l1 ml11, the ule of a mobile plant, th,e

installation of which can be adapted ta any aite lrrespectlve of dlfficulty,

avoiding the foundationa and building requlred for a fixed mill, could prQ-

vide a better solution to the problem at hand than the fixed mill alternatives_

However, due to the complexity of the mobile mill problem and the fact that

there exiata only one coaaaercial mobile 1111112" it 18 nd't possible to gener ...

1Hze.a solution for thla alternative. Rather, cluater analyai8~of exi.ting

ainea and depos1ts need to be carried out, taking into account factors luch

aa existing infrastructure. grade and size of deposita, size of mobile plant,

etc.

2

ENAKt's ~~~g-term borrov1ng rates ai~ 7% and 8% for international loana and natlona~ loanl respectively. A 12% ayerage diacount rate charac-, teriaea the private aector.

GBOKIN Foreign Trade Co. (Ruaanla) ha. developed and manufactured a 125 tpd moblle plant for the 1I.1111na of ba .. .-tal'-or ( Klnlng Hagazine t Jan. 1913. p.9)

( .

) \

CHAPTlR 4

TH! MOOEL .. AN EXPECTED VALUE OnDtlZATlON

lt 1. r .. llatlc ta a.eu.e that. for .ociety aa a whole, there

nor.ally exlet. a larle nuaber of lndependent but broedly .~ilar rl.ky

proJecte ach .. klna a relatlvely ... 11 contribution ta national lncOMe

al)d con ....,t Ion. ln Any Alven year, the net benefit for .0 .. projecta .. y

fa1l aho~t of their expected value while for other. net bencftt .. y exceed

expected value. n~ dl.per.lona fra. expected value for individual project

beneflta will thua tend to cancel out vIlen a11 euch project. Ar. vlewed

toaether Hence, the dl.peuton (roa expccted value of the total Iain ta

.ociety fra. aIl euch proJecta will be auch ... ller t~n the di.pereion for

an lnd1vidual project. lt la thla pooUnS of riak whlch Justifiee ta.. ex-

peeted pr.eent value approach for the social. cholce of a cu.to. .. Ul project.

4.1 Hlne Develop!!nt Declaion

When a .lneral depoeU hae been dl.covered and explored. a decl.1on

.uet be .. de on.whether to d lop lt to production. Furth.~re, if the

depa.lt 1. ta he developed, the aine develo~nt deci.ion auet aleo conetder

hav thla 1. heat achl-.ed by .electing an optt.ua aine developaant alt.rna-

tiv froa .everal f.a.lble alternativ and eo.parln. thl. opt~ vith tho.e

of other inve.tMftt opportunltlee. If the ata. develop_nt alternative 18 \

aufflclently attractive the po.lt la developed to production

j

44

The ~e dnelop.,nt ded.a.loll for the specific case vlth vhich we

are coocernecl ls ba8ed on the optbul balanc1n& of the two ba.le: par_ters

of aille productIon. ..-1y. aine capacity and cut-off arade.

At the tille of tbe"1i1ne clevelopllellt dec:ision. the point in time

cOllaidered' 10 thia .tudy, aine capacity la deterained for a fixed quantlty

of aineral resource in the ground and the regional custOli .i11 capacity Is

deterailled for the knovn set of these deposits vithin the region. At- this

point, there ~ist several alternative .Ine capacities for each depoait and

several alternative ... aill capacities, each of wbich bas Us ovn cast structure.

Since aine capacity ia ~ariable at thia stage, capital and oper.ting coat are

also variable. In thia respect, the optiaizatlon ia achieved on the baais

of long-run conditiona, since aIl the f.ctors are variable, vith the exception ,

of the fied aine raI resource. This is in contrast to when aine capacity

is fixed, since in this c-.e the capital invest.ent required becGmes a sunk

cast, the period beca.es short-run and opttmization is achleved on the basla

of short run operating cost curves for the fixed capaclty.

4.2 TODDage-Grade Relationshlp

Knowledge of the relationship which exista between tonnage and

grade within eacb depoa1t ia required to deteraine available ore and .etal

. tonnage a at dlfferent cut-off grades for a a10eral depoait. Of the two

, (23) relations exaalned, the exponenti.l tonnage-srade distribution was pre-

1

ferred to the log no~l distribution l , aloce it is possible ta show that

Altbough ailleralbation bas DO Inherent need to confor. to exact _the-.. tical lava. there haa been a vldeapread by unprovable bel le f\tha t .,st aiReraI .... y. fit the log DOrMI d1atrlbutlon (26).

Given total tonnase To , vith an .verage grade and requiaite cut-off grade x having a 10sarith.1c variance, 0 2 , the tonnage Above gr.de x will he:

. T(x) - ToC(I/a log (x/. + 0/2 The c...al.ative '_tal toanap at cut-off grade II viII he

( continuacl)

,

pr.-;-""r . ' , . "-' > ~ "

(~

"

'f

~ ...

(

fi:' ..

45

over a luitably ltaited ranaa the axponential tOnn&Ie-arade relation 1. a 't.

good approxt.at~on of the loa"nor.al tonnale-srade ralation. Purthtr.ore,

r ' it 1a eaaier to vork vith because of ita relative at.plicity. Uainl the

expon,ntial relationahip, ore and .etaI tonnage. are calculated'aa functions

of cut-off grade from the followinal 1

R(C) Ae-G/K'" 3.1

M(C) .. KA e-&/K (1 + G/K) 3.2

C(G) .. G + K 3.3

where

A total depo8it tonnale;

K .. the average grade of A;

G the cut-off grade;

R (G) cuaulative ore tonnage above cut-off grade G;

M (G):,. cumulative metai tonnage above cut-off grade G;

G (G) average grade of R(G).

( . contlnued from page 44)

Q(x) .. To G(l/o lOg (x/m - 0/2)

and the average grade of ore reaerves viII be

m(x)

vhere G(lt) is the usuel Gausaian function, whlch ia tabulated aa th~ nor.al diatribution

G(z) .. ~~

, ... ..

-- 'J'l'" ~ fr~ j.

1, '1

'1

..

\

\

"

.'

46

4.3 The Expec,ted Value Hodel

4.3.1 Cut-Dff Gr4d and Mine Capaeitt Deterination for Bach Mine

The folloving aa8U11lptiona have ben made to facilitate the analysle:'

Input values do not change with t1me. Mine and taill capacitiee 1

and cu~-off and average grade8 for each mine are held constant

over time.

~ AlI mtnes are at the development stage, starting operations at 1

full capacity after a pre-production perio~ equal to one year.

A minimum productlon'period of one year ia a8Suaed for eva1uation

/ purposes. J

Revenues and costa are the iame in each time period and are dia-counted at the social diac~unt rate.

From economic theory applied to the min, total profit ia aaxt.lzed

at the point on the average coat curve where unit coat ia a aintaua and rate

of profit per unit time ia maximized at the polnt where .. rgina! coat equala

marginal revenue. Thue, diacounted total profite are maxi.tzed between

these two extremes dcpend1ng on the discount rate uaed (21).

However, the operating and capital coat curves'for the small aines

tl~t are being consldered dUfer from the