APPLICATION OF MONTE CARLO METHODS TO REAP MAXIMUM PROFIT IN COAL OFFTAKING DEALS

By : Antony WaworuntuThis presentation is prepared for the offtaking tender participants

Jakarta, 15 - 16 July 2008

Buying StrategiesBuying Strategies

How would you like to buy coal from us ? Floating price Fixed price Long hedge Comprehensive offtaking deal

Make sure that you utilize the Monte Carlo analysis before you make buying decision !!!

Mining Basic & Geological Facts In Indonesia

IB MATERIAL

OB MATERIAL

Mining Basic & Geological Facts In Indonesia

STRIPPING RATIO (SR)coal

overburden

Understanding Countur LineUnderstanding Countur Line

COUNTUR LINE AT MINING SITECOUNTUR LINE AT MINING SITE

Understanding Coal Reserve Level of Confidence

Coal Reserve Analysis

Deterministic analysis

Stochastic analysis

Deterministic Model

Fixed Drilling Data Set

Fixed Reserve Outcome

Stochastic Model

Variable Drilling Data Set

Variable Reserve Outcome

It takes large amount of drilling data to make a highly accurate model, insufficient amount of data will lead to modeling error

Modeling Risk : Garbage In Garbage Out

DETERMINISTIC ANALYSIS

DETERMINISTIC ANALYSIS

DETERMINISTIC ANALYSIS

DETERMINISTIC ANALYSIS

STRATMODEL SCHEMA

· Model Parameters· Modeling Default· Lithology codes· Elemental Units· Compound Units· Survey· Conformable Sequences· Limits· Faults

DRILL HOLES DATABASE

SAMPLE RESERVE

COAL RESERVE CALCULATION CAN BE DONE BY :

Polygon approach Triangle approach Solid approach Wireframe approach

COMMON FAULT IN GEOLOGICAL MODELLING

Wrong interpretation of geologic anomalies and disturbances

(e.g. treatment of faults)

Wrong correlation

Wrong extrapolation of data point

Inconsistency in thickness used in the reserve and quality data base

Incorrect calculation of coal tonnage and/or waste volumes.

MONTE CARLO METHODFOR THOSE WHO HATE MATH, PLEASE FELL FREE TO SKIP THIS SESSION

Outcome of risk analysis is not a single value, but

a probability of distribution of all possible

outcomes.

Monte carlo method is used to enhanced the normal investment

evaluation method and is not intended to substitute it.

During the computing process, successive scenarios are developed

by using input values for key uncertain variables. Risk variables are determined by utilizing

sensitivity and

uncertainty analysis.

Type Of Probability Distributions

Normal Distribution Example variables such as coal price,

inflation rate Uniform Distribution Example variable such as production

costs Lognormal Example variables such as coal reserve,

stock price, and real estate price

INTEGRATION BY MONTE CARLO FOR THOSE WHO HATE MATH, PLEASE FELL FREE TO SKIP THIS SESSION

Little thing in real world can be described with simple integral.

Thanks to the Monte Carlo methods that can be used for

approximating complex integrals.

Supposing we want to approximate complex integral of f(x) over

some domain D:

F = ∫D f(x)dµ(x)

Where x is a vector of x, indicated that f need not be one

dimensional function.

Let’s assume that we have a probability density function (PDF) p that

is defined over a domain D.

INTEGRATION BY MONTE CARLO FOR THOSE WHO HATE MATH, PLEASE FELL FREE TO SKIP THIS SESSION

The above integral will then is equal to:

F = ∫D [f(x)/d(x)]p(x)dµ(x)

Then by continuous probability, We get the integral is equal to

E [f(x)/p(x)]

Where E[x] is the expected value of random variable X.

This is correct as long as p(x)≠0 and f(x)≠0.

The process of averaging the value of [f(x)/p(x)] for multiple

random sample to approximate the integral is then called

“MONTE CARLO INTEGRATION”.

INTEGRATION BY MONTE CARLO FOR THOSE WHO HATE MATH, PLEASE FELL FREE TO SKIP THIS SESSION

This is a powerful method of approximation. If the number of

sample become infinite, the approximation will converge to the

the value of the complex integral.

Since infinite number of sample can not be done in practical

application, we will measure the accuracy of the Monte Carlo result

by VARIANCE OF RANDOM VARIABLE, which is defined by:

V[X]=E[ (X- E[X])2] = ∫D (x-E[X])2p(x)dx

=E[X2] – E[X]2

MONTE CARLO PRACTICE IN EXCEL

MONTE CARLO PRACTICE IN EXCEL

Xi U(0,1) Xi U(0,100) Xi N(0,1) Xi N(0,100) Xi N(100,20)

0,991241 75,28001 -0,88894 -7,876 65,66239 0,6124370,256264 47,26402 0,098652 46,10899 89,92564 0,9541690,951689 23,0842 -0,86913 -95,6991 94,48337 0,3930580,053438 13,62041 1,733133 -44,5239 90,691320,705039 58,07062 -0,20425 -4,74847 67,294660,816523 16,3213 -0,11173 -173,142 105,72510,972503 97,37846 0,017021 -141,967 86,314110,466323 44,93851 -1,15196 215,9341 80,063830,300211 5,618458 0,511811 -80,463 79,869240,750206 36,86941 2,323686 -77,3816 127,44880,351482 83,07749 0,654148 -157,853 58,469020,775658 35,08713 -1,28133 45,11583 81,900920,074343 25,65996 -1,29271 71,08338 130,75170,198431 8,59096 0,365249 -83,1244 95,586430,064058 62,40425 0,435629 57,18846 118,91840,358348 43,49803 -0,55869 -47,8345 94,072140,487045 71,60863 0,879893 34,50407 121,03760,511216 26,19404 -0,92989 -81,5141 126,98920,373455 36,46046 0,120971 67,63867 83,03992

0,9859 61,2537 0,595285 -53,1004 121,83090,040712 37,03116 0,596565 68,00462 71,656870,23072 58,40327 -0,18538 61,24515 134,4382

Descriptive StatisticsColumn1 Column1 Column1 Column1 Column1

Mean 0,485457 Mean 48,81222 Mean 0,0476 Mean -0,18641 Mean 98,77037Standard Error0,030924 Standard Error2,834972 Standard Error0,106247 Standard Error9,928938 Standard Error2,143868Median 0,46617 Median 47,25944 Median -0,02266 Median -2,22315 Median 96,72062Mode #N/A Mode #N/A Mode #N/A Mode #N/A Mode #N/AStandard Deviation0,309236 Standard Deviation28,34972 Standard Deviation1,062467 Standard Deviation99,28938 Standard Deviation21,43868Sample Variance0,095627 Sample Variance803,7064 Sample Variance1,128835 Sample Variance9858,38 Sample Variance459,6171Kurtosis -1,33092 Kurtosis -0,99496 Kurtosis -0,67826 Kurtosis 0,514209 Kurtosis -0,26043Skewness 0,099757 Skewness 0,051839 Skewness 0,262939 Skewness 0,182492 Skewness 0,158325Range 0,986267 Range 98,45271 Range 4,391077 Range 547,4467 Range 103,5871Minimum 0,004975 Minimum 0,668355 Minimum -2,06739 Minimum -235,803 Minimum 50,74832Maximum 0,991241 Maximum 99,12107 Maximum 2,323686 Maximum 311,6438 Maximum 154,3354Sum 48,5457 Sum 4881,222 Sum 4,759958 Sum -18,6412 Sum 9877,037Count 100 Count 100 Count 100 Count 100 Count 100

NOW, LET’S PUT THOSE WONDERFUL EQUATIONS TO ANALYSE COAL BESR

Production Worksheet - a Block B Seam TBreakeven Strip Ratio

Calendar Year 17,7 6 7 8ROM ProductionROM Production Mtpa 1,26 1,26 1,26 1,26

Waste Removal Mbcm 22,26 7,56 8,82 10,08

Strip Ratio bcm/tonne 17,67 6,00 7,00 8,00

Saleable Production

Bypass Coal % 100% 100% 100% 100%

Mtpa 1,26 1,26 1,26 1,26

Coal Washed % 0% 0% 0% 0%

Mtpa 0,00 0,00 0,00 0,00

Washing Yield % 100% 100% 100% 100%

Product Coal Mtpa 1,26 1,26 1,26 1,26

Overall Product Yield % 100% 100% 100% 100%

Mining CostsOverburden Removal$/bcm 0,00 1,28$ 1,28$ 1,28$ 1,28$

$/t 22,61$ 7,68$ 8,96$ 10,24$

Coal Mining $/t 0,00 $/tonne $/tonne $/tonne $/tonne

Coal Haulage to Mine ROM Stockpile$/t 0,00 4,00$ 4,00$ 4,00$ 4,00$

Miscellaneous$/t 1,28 0,24$ 0,24$ 0,24$ 0,24$

Total Mining Costs to ROM$/tonne 26,85 11,92 13,20 14,48

Total Mining Costs to Product Coal$/tonne 26,85 11,92 13,20 14,48

Other Costs 2 km

Coal Haulage to Port/Barge LoaderRoad 0,24 0,09$ 0,09$ 0,09$ 0,09$

Coal Handling & Crushing ChargeCrushed Coal 0,10 1,25$ 1,25$ 1,25$ 1,25$

Draft Survey - load into shipProduct Coal 0,50 0,10$ 0,10$ 0,10$ 0,10$

Barging Product Coal 0,00 1,30$ 1,30$ 1,30$ 1,30$

Trans ShipmentProduct Coal 0,09 0,25$ 0,25$ 0,25$ 0,25$

Local Government FeeProduct Coal 1,25 US$/tonne US$/tonne US$/tonne US$/tonne

Marketing Costs% of FOB Price 0,10 US$/tonne US$/tonne US$/tonne US$/tonne

Head Office & Technical ServicesBerau Staff 1,30 US$M US$M US$M US$M

Royalty KP Holder 25,0%

Total Other Costs US$/tonne 2,99$ 2,99$ 2,99$ 2,99$

Total Costs - FOBT US$/tonne 29,84$ 14,91$ 16,19$ 17,47$

Total Costs - FOBT US$M 37,60 18,79 20,40 22,01

Revenue & Project MarginCV - kCal/kg (nar)US$/tonne

a Block B Seam T - 0,00 $/t $/t $/t $/t

Total RevenueFree on Vessel US$M

US$/tonne 0,00 0,00 0,00 0,00

Margin

Cash Margin $/t -29,84 -14,91 -16,19 -17,47

Cash Margin US$M -37,60 -18,79 -20,40 -22,01

Monte Carlo Risk Variables: Production Overburden Bypass Coal Coal Washed Geometry model

STRIP

PANEL

BLOK-1

BLOK-2

??

PUSHBACK-6BLOK MODEL

PUSHBACK-5

PUSHBACK-4TOPO AKHIR 2005

PUSHBACK-1PUSHBACK-12233

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THANK YOU FOR ATTENDING THIS PRESENTATION