Utilising Monte Carlo Simulation for the Valuation of Mining Concessions
Rosli Said and Md Nasir Daud
Cen tre for Stud ieson Urban Real Estate (SURE) Facult y of the BuiltEnv iron ment
University of Malaya
Abs trac t
Valua tio n involves the analyses of various inputdata to produce an estimated value .Since each inp ut isitself often an estimate, there isan elementofuncerta intyin theinput. Thisleads to uncertain ty in the resultant outpu t value. It is argued that a valuati on must also conve y information on the uncert ainty, soas to bemor e mean ingfuland informative to the user. The Mont c Ca rlosimu lation technique can generat etheinformation on uncert aintyand istherefore potentiallyusefu lto valuation. Thispaperreportson the inves tiga tion that hasbeencond ucted to apply Monte Carlo sim ula tion technique in mineral valua tion, mor e sp ecifically, in the valuationofaquarryconcession.
Keyw ords: MOllteCarloSimulation,QuarryValuation,MineralValuation,Risk,LlIlcertaillty,Probability
Introduction
Valua tion is often associated with being anart rather thana science.This isbecau se valuationcanno tclaim to be an altogether objective exercise. In a typical valuation exercise,there is potential forsubjectivity in analysis.Valuation relieson inpu t data to producethe valueestimate;choosingan appropriate valuefor the input is subjective althoughexpe rie nce and knowl ed ge may opera te to guide its determination.The eleme n t of su bjectivity ad ds up as the number of input variables increase s, and as valu ation as signment increases in com p lexi ty, such as ha pp ens when specialist prope rties are involved, where evide nce from the marketplace could be very limited,or evennon-existent,to guide opin ionofvalue.
Valua tio n inva ri ably involves the analysis and syn thes is of various in p ut data to produce a value estimate.Each input
itselfisnotdefinitive bu tratheran estimate tha t a valuer puts to represent what he deemsto be the best in the givensitua tion.
There isthereforethe element of uncertainty in the input. Becaus e of the input uncertainty, the resultant outpu tvalue is equa lly uncertain. Duetothisuncertainty, it is argued that a valua tio n advice mus t increasingly incorpora tea 111CaSU re of the uncertainty soastobemoremeaningfuland informative to the user (Mallinso n et nl, 2000 ). The deter min istic natur e of the analysis in conve n tiona l valuati on unfortunatelydocsnot provide forthattype of information.
Value rs have oftencome under attack fo r the la ck of 'ac cu racy' in the ir recommended value. While there is no doubt that improving valuation accuracy shou ld be a matter of priority for the profe ssional and academics wor king in
iournatafDesigll and theBuil! Enuironment
this discipline (Boyd,2003), the notion of an 'accurate' or'co rrect' valuation is itself deceptive becauseit is inconceivable that a number of competent valuers appraising the same property would, working independently,arrive at the single 'co rrect fig ure ';more likely, they will arrive at a range of values(MallinsoneIal,2000).This is yet another argument why information on risk must be conveyed together with valuation;such informationwill assistthe user in understanding what a valuation involvesand what risks are associatedwith accepting the single value estimate and treatingitas the'co rrec t' figure.
Monte Carlo sim u la ti o n is one technique that a valuer can potentially use to identify and quantify risksin valuation . Although the va lu a tion risks arc pre- determined,the statistical outputsproduced withthis simulation technique may provide useful indicator sto avaluatio n estimateas the rangeof the likelyvalues are given. As such, the valuers can use their own judgment and experience in the market place to support and interpret the given outcomes.
In the United Sta tes, Monte Ca rlo si m u la ti o n gained popularity among analysts in 1990s. In countries such as Malaysia, this technique has not received sufficient attention as to motivate active in ves tig a tio ns into its potential utility, particularly in the context of real estate valuation.The case example will showhow the use of the simulation techniqu e can benefit the valuation of a miningconces sion. Acase will be presented where the valuer could improve the qualityof the valuation adviceby making explicit the treatmentof the likely risks involved, particularly for the uncontrolled input variables. The Monte Carlo simulation technique offers this.This paperaims to demonstrate the benefitsof MonteCarlosim u la tion when itcomes to improvingthe transparencyin reportingthe valuation output.
For mining concession,the valuation is not stra i g h tfo rw a rd and involve s a multitude of input variables whose
estimations arc often a matter of expert judgmentratherthan an objecti veexercis e.
There is nothing so determini stic about their determinations;yet the conventional approach of the valuation techniques operatesonsuch pretense .By using mining conce s s ion as an example valuation situation, the way in which the stochastic treatment of the problem can lead to enhanced information for us er decision- making will be demonstrated .
To provideco ntex t to thedis cussion,it would now be appropriate to give some background to mining co ncession.
Background To The Mining In d u s try
Minerals and their products contribute sign i fic an tl y to the national eco n o my.
Despite a reduced co n tri b u tio n fro m metallic minerals such as tin, gold, iron, copper and bauxite to foreign exchang e earningsand employment in recent times, the total co ntribution from this secto r has not weakened; this has been due to the inc reas ed output of industrial minerals such as clay, kaolin, si li ca, limestone, construction sto ne, sand and gravel to support the ex p an d i ng infrastru cture , construction and manufacturingsectors.In all,the mining ind ustryremainsas a major co n trib u to r to the economic, so ci al and industrial developmentsof the nation (Heng, 2002).
Malaysia 's mining industr y consists ofasmall miningsecto r of coaland ferrous and non-ferrousmetals,and a larg emining and proces singsector of industrialminerals and oil and gas . With the excep tionof oil and gas, mining and mineral-proce ssing businesses were ow n e d and operated by private companies incorporated in Malaysia. Oil and gas explora lion, production,and processin gbusinesse sare owned and operated byPetroleum Nasional Berhad (PETRONAS),whichwasthe sta te- owned oil and gas co mpany, and by joint ven tur es of PETRONAS and foreign comp anies(IMF, 2004). Table 1shows the gross exportofmajor miningcommodities .
Uti/isillg MOllteCarloSimulationfortileVall/atiollof MillillgConcessions
Table1-Gross Export ofmaj orMin ing Commoditi es '
Yea r Tin CrudeOil Natural Gas
'000 Ton nes/RMMil '000tonnes/RM Mil '000 tonnes/M il
2000 20,614 / 435 16,672 / 14,241 15,430 / 11,422
2001 27,269/ 461 15077 / 11,118 15,423 / 11 119
2002 27076 /425 16,192 / 11,600 15,007 / 9888 2003 15,244 / 286 17,913 / 15,659 17,311/ 13,358 2004 29,966/ 946 18,090 / 2,1318 20,729 / 17,079
Source:CentralBankof Malaysia,MonthlyStatisticalBulletin2000·2005
The loans for min ing and quarrying ind ustrieswent throughconsolidationin 2000 bu tcontin ued todrop annuall y at10.5%by 2004, asshow n in Tab le 2.
These major mining and quarrying busines ses consistof gold, iron, tin and cement
Table2: Loans by Sector(M ini ngan dQuarrying)
Year Total(RM Million)
2000 25,992.3
2001 21,064.2
2002 15,760.3
2003 13,018.0
2004 12,315.2
Source :CentralBank of Malaysia, MonthlyStatisticalBu lletin2000-2005
Matters rel at ed to minera ls and mining policies are gov e rne d by the National Mine ral Poli cy. The same policy places geoche m icalsurveysunderthepurview of theDepar tm ent of Minerals and Geoscience Malaysia. Curren tly,theextractionolnon- metallic (industrial) minerals islegislated by theNati on alLan dCod eand theLand Ordina nce. While lan d is a sta te matter, miner al is a fed eral matter. The need to coordinate the tw o differen t tiers 01 governance andaddress issues related to mineral policies, minera l agreements, adm inistrationand managem entled tothe lonna tionoftheNationalMineralCou ncil.
Such a mo ve is aimed at facili tating the healthy growthof themining sector inthis country, in linewith developmenton the
interna tiona l fro nt. Other coun tries that acti vely place high importance on their mining industries are the United States, CanadaandAus tralia.
Ceme n tproductionincreasedby 20.3%
in 2003beca use of increased expor tsand continued grow th in domesti c demand:
cement production wasequivalenttoabout 60% of the ind ustry's installed capacity.
Accord ing to an estima te by Cem en tand ConcreteAssociation01Malaysia,domestic demandfor cemen tgrewby 9%to13Mtand exportsof clinker and cementgrewby39%
to 3.9Mt in 2003. As of 2003, Malaysia's installed capacityofclinkerandcementwas 17.8 Mt/ yr and 28.3 Mt/ yr, resp ect ivel y (Internati on alCementReview ,2003).
/01lm01 ofDesigllandthe Buil!Ellvirolllllelli Min ing prop ert ies fall into tw o categories :static reserveanddynamicreserve.
The forme r is closer to thecommon view with regardtothenatu re amine ral deposit, as onewith afairl y well defined est imate of reserv e quan tity at thebeg inning, and therefore anestima bletime period within which to work on the miner alextraction tothefinish.Examplesincludecoalmining and gravel quarr y reser ves.The latter ,on the other hand ,israther inde terminateand shows a propensity for the mineopera tor to keepfindingand developing morereserve s asneeded torepl acethereser vesextracted;
coppe r and gold de p osits often fit this catego ry (Ell is, 2000). For the formal definition though, only the portions of a mineral depos it that can be extra cted for saleoftheirminera lcont entat a profi tcan be calledreserves(SME, 1999).
It tak es extensive geolog ical stud ies, based onconside rableamou n tof drilling, to ap p raise the deposit with reasonable degreeofconfidence. Preliminarystudies and mine design will have at lea st been conducted todetermine the feasibilit y and costofextracting thereserves (Ellis,2000).
In the caseof a gravelquarry,thisrequires determining the per centage of the stone contained in the mined rock tha tcanbe econom ic ally extracted, as well as determining the costofextrac tion. Due to the prohibitive costs involved,only those withsubstantivehistoricaland geological experience would hav e the capacity to emb a rk on the ap p raisa l (ibid. ). Even so, suc h stud ies are ofte n perfuncto ry, frequently produced merely to meet the req u irements of potential lending instituti on s. Reliance on such inexpert geolo gica l st udi es has the risk of underes timati ng or ov ere s tim ating the reser ve of the quarr y.
Valuing MiningConcession
Mining co nce ss ion valuatio n or quarry business valuation is notso much abou t gett ing the "co rre ct answer " as about select ing the relevantdata,anal ysing this dat a and app lying logi cal reasoning to
arrive at a value concl usion that has the necessarylevelof reliability,sup portability and defensibility for the purp os e and intendeduse ofthevalu ation. Invaluatio n theory,the reare no trul y "correctvalues", butonlyestima tesor opinionsofvalue that are implicitlyassumed to bebased on the interpolati on ofsomeamou n t and quality of facts . The val uer's assu mpt ions and limitin g conditions add to this imper fect information.As aprod uctof the exercise, the value rmus tusuallyarrive ata sing le value that is believed to be the mostprobable estima te of va lue for the purpose and intended use ofthe app rnisal.
The principl es of mineral valua tio n are unlikethe principlesof naturalsciences and mathematics,becau s e they canno tbe derived from or proved by the laws of nature , and the y arc not viewed as fundament al tru ths or axio ms. Mineral valua tionprinciplescanno tbedisco vered;
they are cre ated, develo pe d or decreed.
Mineral s valuation principles are su p po rte d by intuition, au thority and accep tability (Ellis,2000). As a result,the credibility ofmine ra lvaluatio nprincip les rests upon their gene ra l recognition and acceptance, which depend up on suc h criteriaasusefuln ess,rel evance,reliability, aswellasuponcost benefitand materiality considerations.
Shortcomings no rmally res ult from lackof expertiseon the part of thevaluer , the inabilityto viewcertainportionsofthe propert y,theinherentdrawback s of relying on inform ati on sup plied by others and limitationsim posed by thetim e constra ints of this eng ag emen t. There is also the econo micco nstraint in that the budge t is not unlimited forexam ina tion, inspection and acqu is it io n of ad di tio na l data. The value r us es av ailable resources in the collec tion, verification andanalys isstages of this engageme nt in those areas tha the cons ide rs most rel evant to the purpose and intend ed us e; there is a signi fica nt possibilitythatthevaluerdoesnotpossess all theinformation related to theindustry concerned.
UIilisillg Mall te Carlo Sitnulntion for tileVaillaliollof Millillg Concessions
Mine ral valuation requires numerous inputs.Whilesomeofthe inputsarcknown, lllany arc uncertain and requ ire expert judgme n tto ensure a realis ticoutpu t.To improve the outpu taccuracy,itis necessary to iden tif y uncertain inputs that have a substan tia leffect on the resultant outpu t.
The num erous studies that have been carriedou tinthe subjectareasuggest that im p ort antkey variablesinclu dethe volume of stones, th e cost of extract ion, the capitalisa tion rate and the sale price of rocks.
Under the Mal a y si an Val uat io n Standard (MVS) 1997, market value is definedasthe estimated31110un tfo r which an asset should exchange on the date of valuat ion between a willingbuyer and a willing seller in ann's lengt h transac tion afterpropermarketingwhereinthe parties ha ve eachacted knowledgeab ly,pruden tly and withou t compu lsion (MVS, 1997).In the case ofa quarry,an assetrefersto quarry asset. By the abovedefinition, the market valuesho u ld not be affected by specialor creative financi ng or sales concessions gra n tedby any oftheparties involved.
MVS further sta tes that in order to estimateMarket Value(Standard 1), a valuer must first estimatehighest and bestuse or mostprobableuse.Tha t usemay be forthe continua tionofa property'sexisting use or some other alte rnatives where these determinations are based on ma rket evidence. However, Elliseta!(1999) argues tha t comparable market evidence may
.work well forsurface realestate,or even
for precious metal deposits, but notatall for mostindustria l mineralproperties.
At the interna tiona l lev el , a comprehensive frmnework of Generally Accep ted ValuationPrincipleshas existed for some time to caterfor the valua tionof all property or asset typ es, includ ing real property,personalproperty,bus inessesand fin anci al in te re s ts . The In terna tiona l Valua tio nStandards(IVS) have laid down standards for the valuati o n profession inte rnationall y.It is encourag ing to note that the exist ing IVS standards are being
modified to incor p o ra te instructions pertaining tothe extractive industr ies.This willhelpputthe valuationof mineraland petroleumconcessionson an equal fo o ting withother indu st ries.
Traditionally, the valuer has several valuation te c hni qu e s availab le for determining fairmarke tvalue.Threeofthe more popular techniques are asset-based, marke t-based, and in come-ba se d (Ell is eI
at,
2000).As se t- base d techn iqu e (Cost Method) - The basic principleof this techn ique is that thevalueof a businessis the cumulative value ofassets, includingintang ible assets such as goodwill. Quarry assets to be valued using th is approach typicall y include the estimatedvaluesoftheinventoryand any equipment and real estate use d in the bus iness. However, this approach may provide valueunderestimate due to certain valid re a s o n s. For example, quarry bu sines s es are norma lly fa mil y -o w ne d businessesthat have been in operationfor decades . Altho ugh the y arc profitable, thei rowners have elected to retain small eq uipment fleets of older equipment since they prov ide adequate service. Consequently, equ ipmen t values are rela tively low.An obvious exceptioncould be a quarry that has ju st made a la rge inves tm ent in new mobile equipment or processing plant. In thiscase, the reverse couldbe true.
Market-based techn iq ue (Comparable Sales Metho d)-Manyvaluersare familiar with th e us e of th e sales compariso n approach.Thisapproachis commonlyused when selling ho uses, offices, agricultura l pro p e rt y, or other fai rl y liquid re al esta te.The market-based approach for detennin ing the val ue of a quarry is basica lly the same. Th etheory beh indthis me th od is th a t the marke t for privately owned businesses determines whatprice providesanacceptablereturnfor a quarry's earnings stream. Mu ltip les commonly used include sales revenues, earnings, or
[ourualofDesiglland the Buil!Enulronmeni profits. How ever,the approachdoesha ve lim ita tions.For example,abigfutureproject cou ld be un d er estima ted since its impact not yet realised. Similar for quarry business, its ownership position with respect to its mineral reserveand itslifeexpectancy can materi allyimpact value.
Incom e-b ased technique (NPV or OCF Approach) -The income-based techniqu e typicallyprovid esthemostreliable estima te of fairmarket value as inv es tors are actually purch asin gfuture profi ts(morespecifically cash flow). Thisap p roach usesdiscounted cash flow analys is to determi nevalue. It is straigh tforwa rd and widelyused. Itis based ona quarry'slong-te rm planthat takes into accoun tnu m erousvariablessuch as sales andmarket forecast,mineral characteristics, production capacities etc. Ho w ever, the estima tion of future profit may not be accur a teenough due to the fluctu a tion of market variables. The valuer will ne ve r know wheth er his future projection is in linewith the fut ureeCOI1Ol n y situatio n.As such, the uncert ainty factors sho uld be co ns idered in his valua tio n and Mont e CarloSim u la tionwill become an impo rtan t tool in helping the valu er's judgm ent in derivin g avalueconcl us ion.
Alt ho ugh the accu racy of data in traditional approach is seldom ques tionable,they are too deterministic in nature. Wha t needs to be attempted in dealing with this problemis toincorpora te probabilisticaspectsintothetechn iq ues so astomakethemclosertothe realityofthe problem. In thecontext ofmineral valuation, theincorporationof probabilis ticapproach hasbeentried before, in workssuchas by Rosect01(1993)in the valuationof petroleum concession,and hasbeenfound tobeuseful by Gus tavso nct01 (1997). This stud)'also aim s to add to the abov e works by dem on st rating theutility ofaprobabilisti c app roac h, name ly the Mon te Carlo simulation, for the valuation of quarry concession . The application of this simulationtechnique specifica lly to quarry concession hasnot been attemptedbefore.
Monte Ca rl o Si m u la ti o n In Quarry Valuation
Monte Carlo simulation has been an important probabilis tic approach in risk assessmentsincemid -1960s (Hertz,1964).
Each input in the probabilistic mod el is rep resente d b)' a proba bilit y density functi on, ora range of values tha t are possibl e, no t just the sing le most likely value. The lo cat ion and sha p e of distribution determine the chance that a singlevalue willoccur during each iteration ofthe model (Kellihe retal,2000).Themodel is basic all y a series of what- if ana lyses whe realternative estimatesofparameters of the modelare derived from probability distributions attached to the m. If probabilisticinformationisusedin Monte Carlo te ch ni q ue, the re sults will be expressed as a probability distribu tion rath e r than as a single point estima te (Allen,1989) asusedindeterminist ic model.
Thro ug h random selectio n wi th random number generator, the comp uter draw s a series of param eter values from each probability distribution and records result sthat arccalcula ted. Thisprocess is rep e at e d num e rous tim es, each time recording the result (Sirmans el al,1995).
Like any statistically based methods, the successof probabilistic methods depends on the "la w of large nu mbers ", th e requirement fora large numberof valid data points to provide statistical reliability.
The application of sim ula tio n techni que is fair ly well explored in th e realmsof property investmentandproperty de vel o p ment (Maclia r la ne, 1990, 1995;
Mart in ,1978; Vernor, 1989). In the con tex t ofvaluation,how ever,workis very limi ted so far.As"Hurledto earlier,the valuationof mineral depos its involve more than one inputvariable. Each variableneeds to be included in the valuation . Ho w ever, the inputs are not inde p end ent from one ano ther;itisthusnecessaryto consider the int er-relati onshi psor correlationsbetween the variables. The drawback of the convention al method is that, atanyone time, only one variable can be cha nged
lItilisillgMOllte CarloSimulationfor the vntuntionof MillillgConcessions while the others areheld constan t.This is
no ta realistic situa tio n. One ad vant age of Monte Carlo si mu latio n over th e conventional determin istic techniques is that the fonnerallowsthe decisionmaker to incorporate correl ations and othe r inter- dependenciesinthemod el.
Selecting the profile of the probable valuesof key in put variablesisassisted by the rangeof distrib uti on pro files provided insimulationpackages.To implemen tthe simulatio n, anumber ofsoftw are packages are avail ablein themarket,of whichCrys tal Ball and@ Risk a re two.Thesetwosoftware products provide a choice of distribution profileswith in the simulation programme (lJoyd, 2003) altho ugh thei r applicatio ns arcsomehow differen t. An evaluation of the varioussoftwa repackages'performance lies beyond thescop e of this stu dy. Crystal Ball is chosen in thepresentstud y becau se
The first step in the value estima tion would be to assemble the inp u tdata. For stone rese rve, thevalu er would consult a geologica lreportto arriveat an estima teof the to tal ca pa city. For other input data such as the maximum capacit y, expe cted gain/salesrevenue,ope ration cost andyield , estimations arcdone byreferen ce to data from comparable quarry operations. For the examp le,Table3 below sets the basic calcu la tio n for the proj ect ed quany lifespan based onassumedrock extraction rate,asgiven. Basedon thisdata and other input estimat es, a valu er 's usc of the con v entional inco me-base d techn iq ue wouldtyp icall ylead to avaluati onlayout asinTable 4.
Tabl e 3: Bas icData for Qua rry Valuation Maxim umCapacity
ExpectedGain@80%
Therefo re,Annual Production StoneReserv e
Therefore,Projected QuarryLife
this softw a re doc s not have serio us defici en cies, handles analysis as good as other packages,and wasreadilyavailable for the stud y.
In the sub jec t example, a quarry operatorob tai neda freeho ld interest ona pieceoflandfrom the StateGovernmentand was at the same tim e granted a qua rry concessi on on the same land. Under the concession ,the opera tor paysquit rentand royaltyto thestategovern ment. 111e operator has applied for a bankloa n to finance the busines s. The bank requires a valua tion advice onthisinterest inordertodetermine theamountto approveinloan.
40,000tonnes per month 32,000tonnesper month 384,000 tonnesper year 9,600,000 tonnes 25years
Many inpu tvariablesare involved in producin g the sing leoutp u tconclusion to the concess ion value .Howeve r, thenature ofeach inp u t estimat eitself is such thatits accuracyis uncertain.This is because the 'true' valueofthe inputis neverknown;the valuer canonlyaspireto get asclose ashe can to the unknown 'tru e' value throug h cho ice of data or compa riso ns that are perce ived tobe the perfect match for the subjectcase. Cons eq uen tly, the accur acy of the sin g le point outcome estim ate is uncerta in too. To mit igate the ris ks associated with the uncertaint y of the singlevalueestima te,anoption would be
[ournalojDesiglland ilteBuiltEnvironment
Table4: Conve ntiona l Incom e-based Approach
903,840.00 21.000.00 TotalSaleRevenue(RM)
Total Opera tionCost(RM) EstimatedGross Revenue Opera tor'sProfit@30%
QuitRent
EstimatedNetRevenue
Yea rsPurchasefo r25 years@11%
Revertto Land Value 30acrcs@
RM30,000 pel'acre 25 years @ 11%
CAPITALVALUE
to releaseit lo w e r,saferloanamou nt than thevalueproposed by the valuer, From the bank 's poin t ofview,itwouldbehelpfulto knowwhat level of certaintyis attached to releasingthelower amount. Unfortuna tely, the conve n tiona lapproachdocsnotprovide such an ind ic atio n. Fro m the potentia l buyer 'spointofview, itwould beusefulto det ermine the degree of uncert ainty in offering theright value.
Inapplying the simulation techniqu e, a valuer needs to ident ify a probability distribut ion that bes t de scrib es the uncertaint yprofileof avariableandapplies itto that variablein generatingthe simulated samples. In the context of this stud y,six inpu tvariablesareinvol ved,in threetypes of distrib utionas follows:
Norma l Dist ri bu ti o n
Most nat u ral phenomena conform to normaldis tribution.Underthis distribu tion, the mean value is most likel y, the dis tributionissymmetricalabou t the mean and the value is more likely to be closeto the mean rathe r than faraway. The shape, me an and stand a rd deviatio n of the gene rated value will genera llyconform to this definition. Increasing the numbe r of trials will en h a nc e conformity to this distribution.
5,952,000.00 2.939.200.00 3,012,800.00 924.840.00 2,087,960.00
8.42174 17,584,265.99 900,000.00PV
0.07361 66,247.28 17,650,513.27
The no rmal distribu tio n has been adop ted forExpected ExtractionRateand Years Purchase. Assump tion 1 shows a normal distributionfor Expected Extraction Rate with a meanof 80% and a standard deviatio n of2%whileAssump tion2shows the dist ributi on for Years Purchase with meanof11%and standarddeviationof2%.
Theserepresentthe real-lifeassumptionson the twovariables.
Trian gular Dist ri bution
Due to the limit ation of the available data fo r reservedstone and maximumcapacity of th e machine, a valuer cho ose s the tr ian g u lar distr ibutio n because the triang ulardis tributiondescribes asituation where estima tes can be mad e of th e minimum,maximumand mostlikelyvalues to occur .The valuerestimates the reserv ed stone provided in thegeologicalreportat between9 millionand 10.2 million ton nes, with a most likely amoun t of 9.6 million tonnes (Assump tion3). Asin Assump tion 4, the maximum capacity is expe cte d at 35,000 to 45,000 ton nes permon th,witha most likely amount of 40,000 ton nes per month(asused in deterministic approach).
UtilisillgMOilleCo,.lo $i/llllloliOIlfa"theYnhunion of Millillg Concessions Assump tion1: ExpectedExtr act io n Volnme
Norm al distribu tionwithpara me ters : Mean
Std.oev,
80%
2%
c •
tx
Assumpti on 2:YearsPurchase
Normaldistributionwith parameters:
Trian gulardistribution with param eters:
Triang ulardistribu tion withparame ters:
Mean
Std. Dev.
Minimum Likeliest Maxim u m
Minimu m Like liest Maximum
11%
2%
'.. .,.. ,. "" ".. '." ,.. 'I' '"
Assumpti on3: Reser ved Stone s
9,000, 000 9,600 ,000 10,200,000
Assu mptio n 4:Maximum Capaci ty
35,000 40,000 45,000
[ournalo[Desiglland theBuiltEnuironment
Un iform Distribution
Theuniform distribution isusedtodescribe the Total Operatio n Cost and TotalSale Revenue.Thisisbecauseexp erience shows that,withinan identifiedrange of values, these tw o variables ha v e constant probabilities of occurrence . As suc h, its distributionofoccurrence is bestmod eled with a un ifo rm distributio n. For Total Ope rationCos t,thevalue r thinksthat any value between RM2.5million and RM3.5
million has an equalchance ofbeing the actual value(Assump tion5). Further,the uniformdis tribution has tw o parame ters:
Minimum and Maximum, The valuer expec ts that theminimumTotal Opera tion Cost for the quarry operation is RM2.5 million with a maximum value of RM3.5 million. Thevalue r alsoexp ects theTotal Sales Revenue that the operator will get from thisconcession to be RM5.5million witha maximumofap p rox imately RM6.5 million (Assumption6).
Ass umptio n5:TotalOperati on Cost
Uniformdist ributi on withparameters:
Minim um Maximum
2,500,000.00 3,500,000.00
i , _ - - - - - -, I 1 1
I
' iI '-=~-=====-1
,
Assum pti on 6:Total Sale Revenu e
."'...s....II.·....
Uniformdistribu tionwith par am eters:
Minimum Maximum
5,500,000.00 6,547,200.00
,.._,~,,,,,
Ou tc o me Of The Sim u la ti o n Ana lys is
Table5pro vi destheoutcome of thesimulation analysis ofthegiven quarry concession after1,000trials.Thissta tisticwillbeused to elabora te thcresultsusinghist ogramsand cumulative frequency charts.
lltilisil/gMOl/Ie CnrloShnulntionfortileYnluatlon of Mil/il/gCOl/cess iol/s
Table5:Statisticsafter 1,000trials of MonleCarloSimul atio n
STATISTICS CAPITALVALUE
Trials 1,000
Mea n 17,977,845.53
Med ian 17,703,067.61
ModeStandard 17,248,556.78
Devi ation 3,355,833.00
Variance 11,261,615,133,288.70
Skewness 0.43
Minimt im 10,053,050.41
Maximu m 32,491,485.70
Mean Std .Erro r 106,120.76
Chart 1 shows th e total range of mar ket valuespredicted for the quar ryconcessio n.
Each ba r on the chart represents the likelihood, or probability,thatthe true value of the quarry co ncession falls within the give n valuerange.Theclusterof columns near thecentreind ica testhat themostlikely value of the qua rry concession isRM17.2 million.To the valuer, the Mean, Medi an and Mode should beimportan t.
Mean represents the average marke t valuesfor the1,000 ou tp utsobtained from the simu lation analysi s. In this case the mean isRMI7,977,845.53.
Medi anrepresentsthebalance ofpoint for the 1,000 outputs ob tai ned fro m the analysis. The median for the analysis is RMI7,735,441.42.
Mode represe n ts the value with the highest freq ue ncy ofoccurrence forthetotal of 1,000 ou tputs. The mode given forthis simulation is RMI7,248,556.78.
Chart 1:Capita lValueForecast (H istogram) CAPITAL VALUE
£ ::: . L
rz: I
.n
( " om
.1---~~-.0o
0:
0-02o m I
10 ,((( >
I'
12.nOO,orJil,O<) 16,000,1'-'10
c o
20,000,000 00 2-1,000,0(0,00f\1'l1
I
~o
10
' <]
0j
Theoutcomecanalsobe interpreted using theCumulative Frequen cychartas sho w n in Chart2.
JOI/,."olof Desigl/and the BuiltEnuirontnen!
Ch a rt2:Capital Valu e Forecast(Cu m ula tive Frequency Chart) GAP IrALVALUE
l,((l- l -
0.1'0., ~
: :-.-... I
,t:
:~ OGO I
"2
040 -11~-
(L
0,-;-0
0.( 1 >
010,000,000.00 15,000,000 00
,
XI,OOO ,()'l O00
riM
1,(0 0 800
't
(,oo~
r;
"
~rtO :.J
.
'~2~oo
<I
025,000,000.00
- - - -- - - '
Give n the above simulation ou tcomes, two alte rnative situations are pos sible, asfollows:
Sit ua ti o n 1 - Su p pose a bank needs to determine howmuchloantoreleasefo rthis quarry consession.Sho uldthe valuerscrap the value that hasbeen estima ted using a conventional approac horproceed to accept a low er or higher marke t value than the actua lestimatedvaluein helping the bank decisionforloan pur poses?Sho u ldthebank approve add it io na l amo un t of loan as req uestedbythe quarryoperator?
Sit u atio n 2 p Assuming that a potential purcha s er considers buy ing the quarry concession. Sho uld heaccept an amoun t low er or high er tha n the singl e value indicatedbythe conv entiona lapproach ? The au thors argue that in both the above situations, the Monte Carlosim ula tion is useful.
In Char t 3, the dis p lay ran g e includes valuesfro mapp rox ima tely RMlO,lmillion to RM32.5 million ,The char t also shows the Certainty profile to reflec t the probability 01a value level ranging from RM17.6million to positive infinity - the probability of gelling a value, With this information ,the valuer is in a very much bette r position to ma k e de ci sion on whether toacceptthe proposedvalueof a de ter m inistic model of the quarry valua tion. In thisexample,thereisan80.8%
cha nce that the RM17.6 mil li o n is the co rrect value. The valu e r can the refore ca lc ula te a 19.2%cha nce of error in predicting the market value.
Utilisillg MOllteCarloSim ula!;011fortileVa/llaUolI ofMillillg COllcess;olls
Chart3: Certai n ty Profil e (Res u lt forRM17.6milli on ) CAPITAL VALUE
000 0.05
I
'Ii
.Q 001+---
I,.l- /1I
~
003 +:- - _ ....F ,t,~I : I I ' ,
0:
002. ! r .{ if !ii i '
001
i - , I '· I' .
I, J' i '
I ' . I
I j •I I
12.000,000.00 16.000,000.00 20,000,000 00
r uvl
24.000.00000
50
- FA.O~mn~:'tdlslribllJon forecas1willes -
I
' - - . J
Sunun ary:
Certain ty level is80.8%
Cer tain ty ra ngeisfrom 17,650,513.27to Infinity Entire rangeisfrom 10,053,050.41to32,491,485.70 Base case is 17,650,513.27
Afte r 1,000trials,thestd.error of themeanis106,120.76
Cons id er the two sit ua tio ns aga in with certa inty profile at RM15 mi ll iori of marketvalue.
For Situati on 1 above, assuming that the bank considers to approve the maximum amoun tofRM15millionto quarryopera tor. Avaluer canbe 81.9% certain of achiev ing aminimummarketvalueof RM15 milli o n as show n in Chart4. Ifavaluercanshow that amarket value can beat leasttw o-th ird certainofaRM15 million,thebank isready torelease this amount forthisconcession.
In normal ap p lica tio n, the va lu er usu ally
estim a tes the Force d Sale Value of the concession asrequested by the client asa baseforloan determination.
In Situation 2, assum e the result of negotiationbetweena potential purchaser andanownerresultedin aminimummarket valueofRM15 million.Ifthe valueractsfor the purchaser, he should advise that the quarryis worthwhilepurchasing since he can be 81.9%certa inofach iev ing a market valueof RM15 million asshow nin Chart 4.
[ournalof DesiguandttieBuiltEnuironmeni
Charl 4: Certainly Profile (Result For RM15million)
CAPITAL VALUE
0,05 f
, f'i'
004+ ---- ----,
'2
003L /
-g I
Q:
002I
I
o m +---
II I
0,00
12.0r'ol,Ooo,CO 20,000,00000 24,000,000 ,00 fllvl
- FitO~rmr~:ldl~tribl.Alt)O Forecastveues
Summary:
Certain ty levelis 81.9%
Certain ty ran geisfrom 15,000,000.00 toInfini ty En tire rangcisfrom 10,053,050.411032,491,485.70 Base casc is 17,650,513.27
After1,000trials,thc std.erro l'ofthc mea n is106,120.76
Ana lys ing the marketvalue forecastagain for RM21 million, the valuer can see a cer tai n ty lcvcl of 50.4% for ach ie ving a market value ofRM21 million (asgivcn by thc ou tp u t).
AsforSituation1, a valuercouldadvisethe banknot to approveadditionalamountsince the certain ty level of th is amoun t is only 50.4%;thereisa 49.6% chanceofsuffering a los s (100% minus 50.4%) if thc bank approves at RM21million.
Thatmeans ,in Situation 2,the valuer can be only 50.4% certain that RM21million wou ld bethe'correct' marketvalue topay.
On this basis, the valuer can advise the purchaser that the offered amoun t is too high tobc realised in themar ket.
Conclusions
The authors argue that as clien tsbecome mor e disce rn ing and inc re asingly sop his tica te d in their dema n d , it has become increasingly importan t to offer greater transparency in valuation advice.
Transparencymeans,amon g other things, affordi ng to clients an arr a y of analysis ou tp u tsin away that allowshim to choose deci sion in full awareness of the risk s involved.Towardsthis,techniques suchas theMonteCarlosimulationarcusefuland
UtilisillgMOllte CarloSimu lationfortileVaillaliollof MillillgConcessions
Chart 5: Certainty Profile (Result For RM21 million) CAPITALVALUE
10
- <J
0..
24,000.000.00
1 I
so
- - -- 40 :(1
~ ~~W~~~p,---
30-g ,
«..
::>
20
.«
16 ,000,00 0,00
oos
I
~ o.", il
~ 003 - - - - --/1
0:
o 002 .I,
0.01"'"1-- -'
000 LI".,...
Foreca stvalues
Summary:
Certain tylevelis 50.4%
Certain ty rangeisfrom21,000,000.00toInfinity En tire range isfrom 10,053,050.41to 32,491,485.70 Base case is17,650,513.27
After 1,000trials,thestd. error of themeanis106,120.76
sh o u ld increasingl y for m part of the valuation toolkit. The level of comp u ting power cur rentlyavailablesho uldencourage thisdevelopment.The techniqu eitselfdoes not rep lace the conventional valuation methods;it merely serves asan add-on to the ca p ab ility of the conven tio na l method ologies in the way that enha nces thei r transparen cy and acceptabilit y in theeyesof thevalu ati on clients.
The sup e ri ority of Monte Carlo simulation liesinthefact that itallowsthe user to sim ulate a much larger range of possible ou tco mes com pared to other simulationtechniquessuch as scenarioor sensitivity analyses,which producelimited number of valuation outpu ts. With large numb er of ou tcomes, the statistica l reliabilityofconclusionsisimproved.In this way,theMonteCarlosim ulation technique
assists the value r in expressing his value opinionswithgreatercon fidence.
Mont e Carlosim ulation is usefulasa flexible, explicitandtranspar ent"learn ing machine", which allo ws valuers to look carefully at therelationships between the factors affecting the valuation and helps clients lookintothemarketvalueestimates and understand the risks associa ted with them. However, it mea sures on ly uncertainties that are relevant from the point of view of the valuer but does not provi d e any mechanism on how to incorpora te the observed uncertaintyinto the estimationofmark etvalues.
Inthe contextof mineral valuation, thevaluerneedstounderstandthedeposits and mining operationswellin orde r to come tothe'correct' valueasa mining indus try buyer would see it. If the poten tia l for
/ol/mol ofDesigl/and lite BuiltEllvirol/llleni
reserve addi tions throug h exploration is present, this can add sig nifican tly to the value of the dep osit,and should betaken into account. Theestima tionofthepotential reserve is itself a very im portant exercise from the poin tofview of thebasic input data; ad mittedly,MonteCarlosimulation has to wor k within the limitations of the data.
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