Dilution influence on value of mining investment projects and selected production figures by a copper mine example

Tom 24 2008 Zeszyt 4/2

ARTUR DYCZKO*, MICHA£ KOPACZ*

Dilution influence on value of mining investment projects and selected production figures by a copper mine example

1. Investment project X description

The calculation was conducted in the way of use literature information about the real copper ore deposit. This information concerned both the existing and projected development plans (required mine’s infrastructure – capital expenditure), necessary for mine operating start-up. This concept also included building additional shaft localized in the centre of copper ore reserves.

Mine excavation was conducted below 850 m in relatively high temperature. Thus, part of the lower-located investigation required intense ventilation or air-conditioning, what has been justified in the planned investment expenditures. Investment project being in the centre of our attention, described by the concept of resources development, projection of the future production, necessary capital expenditure, working capital and its fluctuations, amortization and production costs, contributed for researches in the presented way. Basics production figures describing the investment project X are presented in Table 1.

2. Concept of modelling

To measure influence of dilution on value of the project measured by NPV and selected parameters, the analysis was divided into two parts. In the first step, selection of production systems was done (only those with at least two years of operating). These production systems

* Institute of Mineral Resources and Energy Management of the Polish Academy of Sciences (PAN), Kraków.

had functioned in different geological and ground (mine) conditions. In analysis, each of them were described by a vector of parameters such as:

— estimated reserves to exploit,

— estimated copper ore production (Rws),

— estimated copper ore production (Q),

— potential production of copper refined,

— potential production of silver refined,

— fixed production costs,

— variable production costs.

Upon the data presented above, dilution characteristic for each unit was calculated by a formula:

u Q

= - 1 Rws (1)

To determine the feed rate for processing upon the previously predicted mine output, the following formula was introduced:

Rws Q

u

zekw uekw

zekw uekw

= -

- -

( )

( )

. .

. .

a a

a 1 a

(2)

TABLE 1 Basic production figures describing the X deposit investment project

TABELA 1 Podstawowe wielkoœci produkcyjne opisuj¹ce przedsiêwziêcie inwestycyjne – z³o¿e X

Specification – mine development stage Unit Value

Copper ore production output Mg 21 351 490

Refined copper production Mg 233 625

Refined silver production Mg 531.48

Specification – mine production stage

Copper ore production output Mg 230 353 314

Refined copper production Mg 2 520 489

Refined silver production Mg 5 733.99

Total (both)

Total copper ore production output Mg 251 704 804

Total copper concentrate production Mg 11 034 199

Total refined copper production Mg 2 754 114

Total refined silver production Mg 6 265.47

where:

Rws – mine production including dilution [Mg],

Q – mine production (pure reserves extraction without dilution) [Mg], a

– content of copper (both with silver) [%],

a

– content of copper (both with silver) in rocks [%], u – dilution [%].

Formulas 1 and 2 were included in discounted Cash Flow model to determine the value of the project measured by the NPV. By applying formula (2), we decided that production losses connected with production units would be omitted in the analysis in contrast to calculations of feed rate relate to the predicted mine production, content of copper, content of copper in rocks and dilution indicated (u).

Moreover, it was assumed that percentage share of metals (both cooper and silver) in dilution rocks will make 0.75%. This value derives from historic observation of consistency of basic (Cu) and accompanying (mostly Ag) metals in exploited ore. Determining the volume of metals equivalent (Cu+Ag) was conducted according to formula (3), taken from [1]:

Cu

= % Cu + 0 01 , Ag [g/Mg] (3)

where:

Cu

– metal equivalent (both copper and silver) in the mine output [%],

%Cu – content of copper [%], Ag – content of silver [g/Mg].

In the second step, upon the basis of the constructed Discounted Cash Flow model, simulations of NPV, revenues, production costs, production of copper concentrate, pro- duction of copper and silver were in focus. The simulations was based on an algorithm created in Visual Basic implemented into the calculation sheet, allowing for testing predicted variables due to different levels of dilution and market copper prices. The analytic procedure was aimed at simultaneous estimation of 6 variables at a fixed level of copper price in a given iteration for dilution value changing in a the same step within a range of (0–25)%. For each of copper price from 2500–12 400 USD/Mg (step of Cu price change in simulation – 100 USD/Mg), the algorithm has made 100 estimations. Copper price was selected as the most representative one, of key influence on simulated values in established model.

Assuming 25% as the maximal limit of dilution allowed for calculating effective NPV

values (due to limitations deriving from the applied formulas and the fact that feed to

processing must not change indefinitely) and presenting the variability of the selected

parameters according to the step change of dilution (u) in the following iterations. It is worth

mentioning that the maximal value of (u) based on historic observations was 63.3%, so it

means – allowing the production exceeding 63% of rocks in copper ore. For each iteration,

a vector of simulated values was obtained. Finally, a total variability (sensitivity) of the distinguished parameters was tested in the entire, pre-set range of dilution values.

We also decided that increasing the volume of feed going to processing would only result in increasing production costs connected with processing and refining. The costs were divided into fixed and variable part, dependent on production scale. Upon historical obser- vations, we assumed that the balance between fixed and variable costs would make, appro- ximately, 3:1. Hence, the mining cost of production per 1 Mg was properly defined for:

— development stage – PLN 205.63/Mg in the fixed part and PLN 68.92 /Mg in variable part,

— mine production – PLN 53.03/Mg in the fixed part and PLN 11.77/Mg in variable part.

Along with different feed rate the production costs in the variable part were also changing. It was reflected in total production costs dependent on the exploration rate.

Finally, a diagram of NPV sensitivity was obtained encompassing all production stages process, what was presented in Figures 1 and 7 and in Table 3.

3. Discounted Cash Flow model

Models discounting future cash flows (traditionally referred to a class of discounting models, DCF – Discounting Cash Flow) nowadays are rule of thumb for most of investment decisions taken. It is because of their relative simplicity and popularity [2]. In the hereby paper, this model possesses a fundamental meaning, allowing to estimate the values of future cash flows after including all charges connected with execution of an investment under- taking, discounted (actualised) to present values.

-2 633 474 764 -1 775 106 073 -916 737 382 -58 368 691

25,00% 23,75% 22,50% 21,25% 20,00% 18,75% 17,50% 16,25% 15,00% 13,75% 12,50% 11,25% 10,00% 8,75% 7,50% 6,25% 5,00% 3,75% 2,50% 1,25%

-28,00%

-18,00%

-8,00%

2,00%

12,00%

22,00%

NPV D NPV

NPV [PLN]

Fig. 1. Influence of dilution on project’s value measured by NPV (fixed copper market price

= 4200 USD/Mg)

Rys. 1. Wp³yw zubo¿enia na wartoœæ projektu mierzon¹ wskaŸnikiem NPV przy ustalonej rynkowej cenie miedzi 4200 USD/Mg

In practice, it is assumed that this method can be used for almost all mining projects.

These projects, however, shall be characterized by high precision in defining assumptions in the calculation what is conditioned by data availability and quality [3]. The conducted analyzes was done in Excel spreadsheet including parts of Cash Flow analysis and income

19 000 000 000 21 000 000 000 23 000 000 000 25 000 000 000 27 000 000 000 29 000 000 000 31 000 000 000 33 000 000 000 35 000 000 000 37 000 000 000

25,00% 24,00% 23,00% 22,00% 21,00% 20,00% 19,00% 18,00% 17,00% 16,00% 15,00% 14,00% 13,00% 12,00% 11,00% 10,00% 9,00% 8,00% 7,00% 6,00% 5,00% 4,00% 3,00% 2,00% 1,00%

-30,00%

-25,00%

-20,00%

-15,00%

-10,00%

-5,00%

0,00%

Revenues D revenues Revenues [PLN]

Fig. 2. Influence of dilution on value of revenues generated in the project (fixed copper market price

= 4200 USD/Mg)

Rys. 2. Wp³yw zubo¿enia na wartoœæ przychodów generowanych w projekcie przy ustalonej rynkowej cenie miedzi 4200 USD/Mg

0 5 000 000 000 10 000 000 000 15 000 000 000 20 000 000 000 25 000 000 000 30 000 000 000 35 000 000 000 40 000 000 000 45 000 000 000

25,00% 23,50% 22,00% 20,50% 19,00% 17,50% 16,00% 14,50% 13,00% 11,50% 10,00% 8,50% 7,00% 5,50% 4,00% 2,50% 1,00%

-35,00%

-30,00%

-25,00%

-20,00%

-15,00%

-10,00%

-5,00%

0,00%

Production costs D production costs Production costs [PLN]

Fig. 3. Influence of dilution on value of production costs (fixed copper market price = 4200 USD/Mg) Rys. 3. Wp³yw zubo¿enia na wartoœæ kosztów operacyjnych generowanych w projekcie przy ustalonej

rynkowej cenie miedzi 4200 USD/Mg

statement. Finding the relation between production and economic figures led to determining the NPV what had been done previously by calculating revenues and production costs typical for separate stages of production process.

Moreover, the calculations included:

— capital expenditures for building mine infrastructure, development and assets purchase,

— net working capital and its fluctuations,

— amortization programme,

— calculation of mine’s liquidation fund,

— isk-adjusted discount rate.

0 2 000 000 4 000 000 6 000 000 8 000 000 10 000 000 12 000 000 14 000 000

25,00% 23,75% 22,50% 21,25% 20,00% 18,75% 17,50% 16,25% 15,00% 13,75% 12,50% 11,25% 10,00% 8,75% 7,50% 6,25% 5,00% 3,75% 2,50% 1,25%

-30,00%

-25,00%

-20,00%

-15,00%

-10,00%

-5,00%

0,00%

Concentrate prod.

D con. prod.

Cu concentrate production [Mg]

Fig. 4. Influence of dilution on copper concentrate production (fixed copper market price = 4200 USD/Mg) Rys. 4. Wp³yw zubo¿enia na produkcjê koncentratu miedzi przy ustalonej rynkowej cenie miedzi

4200 USD/Mg

0 500 000 1 000 000 1 500 000 2 000 000 2 500 000 3 000 000

25,00% 24,00% 23,00% 22,00% 21,00% 20,00% 19,00% 18,00% 17,00% 16,00% 15,00% 14,00% 13,00% 12,00% 11,00% 10,00% 9,00% 8,00% 7,00% 6,00% 5,00% 4,00% 3,00% 2,00% 1,00%

-30,00%

-25,00%

-20,00%

-15,00%

-10,00%

-5,00%

0,00%

Cu production D Cu prod.

Cu production [Mg]

Fig. 5. Influence of dilution on copper production (fixed copper market price = 4200 USD/Mg) Rys. 5. Wp³yw zubo¿enia na produkcjê miedzi elektrolitycznej przy ustalonej rynkowej cenie miedzi

4200 USD/Mg

4. Results

Evaluation and measurement of dilution influence on project’s value and change of key financial (economic) and production figures was the core of research visualized in Figures 1–6. In general, the figures show a non-linear relation between dilution and chosen output parameters caused by implementing formulas 1 and 2. For low prices of electrolytic copper (base case – Cu = 4200 USD/Mg), dilution decrease results in increase of project’s value because of lower production costs (fixed value of other variables in the model in the same time). Increase of metal (both copper and silver) amount in feed, reflected by additional sales of copper and silver (as final products of refine processes) is not able to cover high capital expenditures and increase in production cost (variable costs), growing along with growth of production output.

The increase of project’s value caused by decreasing dilution and prices below 6000 USD/Mg of copper derives mostly from applying high discount rate, reducing values of positive future cash flows and, hence, decreasing the potential loss during investment stage.

The dilution influence on project’s value reverts after reaching copper price level guaranteeing economic effectiveness. In the analyzed case, Cu price guaranteeing achieving value of project measured by NPV at least equal to „0” makes ca. 6000 USD/Mg (all other key variables fixed). For Cu prices higher than ‘walkaway’ price, a „positive” NPV relation vs. dilution is revealed increasing both parameters.

Calculations in simulation model, however, were conducted for Cu price level equal to 4200 USD/Mg. Such value was found the most appropriate one to a 30-years-long horizon of

0 1 000 2 000 3 000 4 000 5 000 6 000 7 000

25,00% 23,75% 22,50% 21,25% 20,00% 18,75% 17,50% 16,25% 15,00% 13,75% 12,50% 11,25% 10,00% 8,75% 7,50% 6,25% 5,00% 3,75% 2,50% 1,25%

-30,00%

-25,00%

-20,00%

-15,00%

-10,00%

-5,00%

0,00%

Ag production D Ag production Ag production [Mg]

Fig. 6. Influence of dilution on silver production (fixed copper market price = 4200 USD/Mg) Rys. 6. Wp³yw zubo¿enia na produkcjê srebra metalicznego przy ustalonej rynkowej cenie miedzi

4200 USD/Mg

project’s lifetime. An argument supporting maintaining that idea was the observed, expo- nential character of copper prices’ trend, accompanied by strong, periodical fluctuations.

They usually lead to rapid appreciations of quotations, particularly in periods of demand’s domination over supply. After strong increase, longer and less dynamic corrections usually take place. This is a postulate of magnitude meaning for understanding dynamic regulation of production output (especially with bigger then average dilution coming from the seam roof or floor) including metals. This is also very often a common practice in extracting thin seams.

TABLE 2 Set of assumptions used in estimating value of investment in discounted Cash Flow model

TABELA 2 Zbiór danych wejœciowych wykorzystywanych w szacowaniu wartoœci projektu inwestycyjnego metod¹

zdyskontowanych przep³ywów pieniê¿nych

Unit Assumed

Geological and technical parameters

Dilution (weighed average) [%] 13.85

Copper content (weighed average) [%] 1.67

Silver content (weighed average) [g/Mg] 38.80

Copper content in feed processing (weighed average) [%] 1.25 Silver content in feed processing (weighed average) [g/Mg] 29.1

Copper content in concentrate [%] 26

Economical and financial parameters

Market copper price [USD/Mg] 4 200

Market copper price [PLN/Mg] 10 500

Market silver price [USD/untion] 10.32

Market silver price [PLN/kg] 910

USD rate [PLN] 2.50

Short-term bank deposit rate [%] 4.25

Inflation [%] 1.80

Risk-free rate [%] 4.5

Risk-adjusted discount rate [%] 2007–2016 1017–2034 2035–2037

19.3 10.0 4.5

Technical and technological parameters

Cu output (processing) [%] 91.00

Ag output (processing) [%] 87.00

Cu output (refining) [%] 96.00

Ag output (refining) [%] 94.00

Waste output [%] 95.00

Number of working days per year 292

The attached figures show the parameters sensitivity to dilution (change between 0 to 25%) estimated upon formula 4.

Empiric researches have proofed that for relatively low copper prices, for which the project is very ineffective, as well as for prices guaranteeing high efficiency, sensitivity (variability) of project’s values is relatively low, making ca. 26%. The „minus” sign derives from application of formula (4) and, hence, calculating NPV (and other assumptions) relative sensitivity by negative or decreasing values of project.

The key role in the analysis is played by Cu price level from the range 5700–6500 USD/Mg.

The maximum increase of NPV (ca. 730%) is caused by the price between 5700 and 6500 USD/Mg for dilution values at the ends of the 0 to 25% range, in decreasing sequence.

DX X X

X

u u

u

=

-

max

(4)

where:

DX – percentage change of variable X,

X – simulated variable (NPV, revenues, production costs, Cu concentrate pro- duction, copper production, silver production),

X

– values of simulated variables at the ends of the 0 to 25% dilution range.

TABLE 3 Sensitivity analysis of monitored parameters (fixed range of dilution variability = 0 to 25%, fixed copper

market price = 4200 USD/Mg)

TABELA 3 Ocena zmiennoœci badanych parametrów dla ustalonego przedzia³u zmiennoœci zubo¿enia 0–25%

i zmieniaj¹cej siê w przedziale 2500–12 400 cenie miedzi elektrolitycznej [USD/Mg]

Data simulated/Cu price USD/Mg 2500 2600 … 5700 5800 5900 6000

NPV [PLN] –26.16% –26.13% … –1.45% 12.33% 55.69% –729.36%

Revenues [PLN] –27.02% –27.02% … –27.02% –27.02% –27.02% –27.02%

Production costs [PLN] –29.11% –29.11% … –29.11% –29.11% –29.11% –29.11%

Cu concentrate production [Mg] –27.02% –27.02% … –27.02% –27.02% –27.02% –27.02%

Cu production [Mg] –27.02% –27.02% … –27.02% –27.02% –27.02% –27.02%

Ag production [Mg] –27.02% –27.02% … –27.02% –27.02% –27.02% –27.02%

Data simulated/ Cu price USD/Mg 6100 6200 6300 5700 … 12200 12300 12400 NPV [PLN] –93.97% –62.17% –50.85% –1.45% … –27.87% –27.85% –25.13%

Revenues [PLN] –27.02% –27.02% –27.02% –27.02% … –27.02% –27.02% –27.02%

Production costs [PLN] –29.11% –29.11% –29.11% –29.11% … –29.11% –29.11% –29.11%

Cu concentrate production [Mg] –27.02% –27.02% –27.02% –27.02% … –27.02% –27.02% –27.02%

Cu production [Mg] –27.02% –27.02% –27.02% –27.02% … –27.02% –27.02% –27.02%

Ag production [Mg] –27.02% –27.02% –27.02% –27.02% … –27.02% –27.02% –27.02%

5. Final conclusions and summary of research works

The work was split into 3 parts. In the analytic part, the authors aimed at testing the dilution influence on the project value and selected parameter constructing pricing model to prove or deny such influence. In the second stage, an analysis was conducted in dynamic simulation environment with application of a specially dedicated algorithm made in Visual Basic. This algorithm allowed for measurement and recording vector of values observed by sampling dilution in range (100 steps) from 0 to 25%. For each level of (u), a proper value of production variable costs was estimated as well. The inter- dependence between variable costs and dilution was established using data range (2005–

–2007) typical for a few dozens production unit of one of leading global copper pro- ducers. We made assumption that the increase/decrease of dilution should impact directly and proportionally on the volume of variable production costs. Calculations were con- ducted for copper price from the range 2500–12400 USD/Mg – to be representative in case of searching for the problem solution.

Empiric researches of other authors dealing with the issue have proofed that there are more dilution-sensitive parameters influencing the value of project (for example: US dollar currency rate, total production costs, capital expenditure).

Making also some simplifying assumptions, values and variability (sensitivity) of the most representative parameters subjected to analysis were estimated. The works have proofed that there is a direct dependence between projects’ value, dilution and values of parameters tested. Furthermore, the sensitivity analysis of projects’ value (NPV) due to various levels of dilution a and fixed copper price reviled following conclusion:

NPV sensitivity

-750%

-650%

-550%

-450%

-350%

-250%

-150%

-50%

50%

2500 3000 3500 4000 4500 5000 5500 6000 6500 7000 7500 8000 8500 9000 9500 10000 10500 11000 11500 12000

NPV Cu price [USD/Mg]

D NPV [%]

Fig. 7. Projects’ value sensitivity analysis (different levels of market copper price, fixed range of dilution variability = 0 to 25%)

Rys. 7. Zmiana wartoœci projektów mierzona wskaŸnikiem NPV przy ró¿nych poziomach ceny miedzi elektrolitycznej oraz ustalonym przedziale zmiennoœci zubo¿enia

— dilution significantly influences the key parameters in the model;

— sensitivity of the tested parameters depends on the allowed variability range rather then on its single values;

— value of the project strongly depends on the basic level of parameters (base case scenario), so that determining long-term values of assumptions shall become a subject of an extended analysis;

— in scenario of its negative values, dilution increase causes decrease in project’s value.

Such situation is due to effect of discounting future values of cash flows with high discount rate. When model generates positive cash flows mentioned relation is opposite;

— mined rocks output increased covering fraction of metals results in bigger copper concentrate, fine copper and silver production. In contrary case, a reverted relation takes place independently from the assumed level of copper price;

— the most critical and difficult to evaluate are the projects with assumptions value set making financial effect equal “0”. In such case, the projects’ value change from positive to negative is the most significant. Thus, for projects of NPV close to „0”, alternative pricing (evaluating) methods shall be applied;

— simulation models generate additional value deriving from including the inherent va- riability of parameters taken into consideration for establishing investment value.

Here, their advantage towards deterministic models, very often applied, can be observed. In fact, deterministic models reduce such inherent variability (and of course expected range of values measured) because of mathematic procedures implemen- tation.

REFERENCES

[1] W a n i e l i s t a K. (red.), 1998 – Ekonomiczne kryteria alokacji wydobycia w kopalniach rud. Wyd. IGSMiE PAN, str. 55, Kraków.

[2] C a v e n d e r B.W., 1992 – Determination of the Optimum Lifetime of a Mining Project Using Discounted Cash Flow and Option Pricing Techniques. Society for Mining, Metallurgy, and Exploration, SME Annual Meeting, Phoenix, Arizona, February 1992.

[3] D a v i s G.A., 1995 – Discount Rates and Risk Assessment in Mineral Project Evaluations. by L.D. Smith – Discussion, Transactions, Mining Industry Section, Institution of Mining and Metallurgy.

[4] K i c k i J., D y c z k o A., 2002 – Technologiczne aspekty zubo¿enia w polskich kopalniach rud miedzi. Wyd.

Gospodarka Surowcami Mineralnymi.

[5] Instrukcja w sprawie zasad i sposobu kwalifikowania, obliczania oraz ewidencji strat z³o¿owych ko- palnianych i zubo¿enia rudy metali nie¿elaznych przy eksploatacji górniczej – Ministerstwo Przemys³u Ciê¿kiego, Zjednoczenie Górniczo-Hutnicze Metali Nie¿elaznych, Katowice 1969.

[6] Instrukcja w sprawie zasad i sposobu ustalania przemys³owych zasobów z³ó¿ kopalin, eksploatowanych w resorcie Ministerstwa Hutnictwa – Ministerstwo Hutnictwa, 1976.

[7] D y c z k o A., 2002 – Techniczno-ekonomiczne aspekty zubo¿enia z³ó¿ rud miedzi na przyk³adzie kopalñ KGHM Polska MiedŸ S.A. Wyd. Gospodarka Surowcami Mineralnymi t. 18, z. spec.

[8] D y c z k o A., 2004 – Niektóre aspekty zubo¿enia urobku w kopalniach rud miedzi. Wyd. Gospodarka Surowcami Mineralnymi z. spec.

[9] K i c k i J., K o p a c z M., M u c h a J., S a ³ a c k i J., S a ³ u g a P., W a c ³ a w i k J., W a s i l e w s k a M. 2005 – Wielowariantowa ocena udostêpnienia i eksploatacji z³o¿a G³ogów G³êboki–Przemys³owy, z analiz¹ ryzyka przedsiêwziêcia Etap I. Praca nie publikowana.

[10] B a n a s z a k A., 1994 – Uwagi o stratach eksploatacyjnych Legnicko-G³ogowskiego Okrêgu Miedziowego.

Przeg. Geol. 8, 674–676.

[11] B a n a s z a k A., K u b i a k J., 1994 – WskaŸnik zu¿ycia zasobów jako Ÿród³o informacji o stopniu za- gospodarowania z³o¿a. Mat. IV Konferencji Aktualia i perspektywy surowcami mineralnymi.

[12] B a n a s z a k A., L e s z c z y ñ s k i R., T o m a n i k R., 2006 – Parametry definiuj¹ce gospodarkê z³o¿em rud miedzi LGOM. Górnictwo Odkrywkowe 1–2, 103–107.

[13] K i j e w s k i P., S a l s k i W., 1992 – Analiza operatów ewidencyjnych zasobów przemys³owych, bilansu strat i zubo¿enia oraz prawid³owoœci gospodarki z³o¿em. CBPM Cuprum, (maszynopis), arch. KGHM.

[14] K i j e w s k i P., W a n i e l i s t a K., B u t r a , 1995 – Ujednolicenie metod oceny strat i zubo¿enia rudy. CBPM CUPRUM, Wroc³aw.

[15] S a l s k i W., R y d z e w s k i A., O s z c z e p a l s k i S., 1993 – Analiza strat eksploatacyjnych w kopalniach Legnicko-G³ogowskiego Okrêgu Miedziowego. Przeg. Geol. 9, 620–628.

[16] Œ l i w i ñ s k i P., 2004 – Analiza procesu rozliczenia kosztów wydobycia rudy w kopalniach KGHM PM S.A.

na tle koncepcji rachunku kosztów dzia³añ ABC. Mat. Konf. Szko³y Eksploatacji Podziemnej.

WP£YW ZUBO¯ENIA NA KSZTA£TOWANIE WARTOŒCI GÓRNICZYCH PROJEKTÓW INWESTYCYJNYCH ORAZ WYBRANYCH WIELKOŒCI PRODUKCYJNYCH NA PRZYK£ADZIE Z£O¯A RUD MIEDZI

S ³ o w a k l u c z o w e

Zubo¿enie, analiza wra¿liwoœci, dyskontowy model wyceny, górnicze projekty inwestycyjne

S t r e s z c z e n i e

Dzia³alnoœæ górnicza kopalñ wi¹¿e siê z eksploatacj¹ zasobów o okreœlonych parametrach jakoœciowych. Wie- lokrotnie jednak konieczne staje siê zwiêkszanie wolumenu wybieranej kopaliny o ska³y zuba¿aj¹ce zawieraj¹ce pewn¹ iloœæ pierwiastków o znaczeniu przemys³owym. Okreœlenie i pomiar wp³ywu zubo¿enia na wartoœæ uzyskiwanych wyników kopalñ zarówno na poziomie technicznym jak i ekonomicznym jest problemem istotnym i interesuj¹cym.

Jednym z podstawowych czynników w du¿ym stopniu decyduj¹cych o efektywnoœci pozyskania i wyko- rzystania kopalin jest ich zubo¿enie czêsto zaliczane do strat jakoœciowych. Jest rzecz¹ zrozumia³¹ i nie pod- legaj¹c¹ dyskusj¹, ¿e wydobywana przez przedsiêbiorcê kopalina u¿yteczna ma zazwyczaj gorsze w³aœciwoœci od tych, jakie stwierdzono w trakcie opróbowania z³o¿a. Zjawisko to wystêpujê najwyraŸniej w z³o¿ach metali, a okreœla siê je jako zubo¿enie. Powszechnie wyró¿nia siê trzy kategorie zubo¿enia kopaliny:

— zubo¿enie wynikaj¹ce z przemieszania kopaliny pozabilansowej z kopalin¹ bilansow¹,

— zubo¿enie wynikaj¹ce z przemieszania ska³ p³onnych z kopalin¹ bilansow¹,

— zubo¿enie wynikaj¹ce z utraty bogatych w sk³adnik u¿yteczny, drobnych niewielkich iloœciowo frakcji urobku.

Tak rozumiane zubo¿enie rozpatrywane li tylko na poziomie kopalni uznaæ mo¿na za tradycyjne ujêcie i jako takie zosta³o dok³adnie rozpoznane i opisane. Pytanie jak przekuæ wiedzê na temat rodzaju i wielkoœci zubo¿enia w poszczególnych etapach procesu wydobywczego w informacjê przydatn¹ do oceny prowadzonej dzia³alnoœci tak na etapie analiz technicznych jak i ekonomicznych ca³ego procesu technologicznego? W jaki sposób nadaæ zbieranym informacj¹ now¹ jakoœæ niezbêdn¹ w procesie oceny efektywnoœci funkcjonowania du¿ego koncernu wydobywczego?

Dziœ niemal truizmem jest mówiæ, ¿e dok³adna wiedza o rzeczywistej zawartoœci miedzi i innych metali w strudze materia³u bêd¹cego przedmiotem obróbki jest bardzo istotnym elementem procesu produkcyjnego.

Obecnie wiadomo, ¿e wiedza ta stanowi podstawê oceny wydajnoœci procesów górniczych, a w po³¹czeniu z informacjami o kosztach pozwala oszacowaæ rentownoœæ przedsiêbiorstwa.

W œwietle powy¿szego proces zubo¿enia rozumiany jako straty jakoœciowe eksploatowanego z³o¿a urasta do rangi jednej z bardziej kluczowych cech opisuj¹cych strugê urobku transportowanego w ci¹gu technologicznym z kopalñ do zak³adów wzbogacania i dalej hut.

W literaturze przedmiotu znaleŸæ mo¿na wiele odniesieñ do problemu zubo¿ania eksploatowanych zasobów.

Autorzy podaj¹, oprócz ogólnej charakterystyki zubo¿enia, jego klasyfikacjê oraz prezentuj¹ liczne wzory umo¿- liwiaj¹ce kwantyfikacjê, pomiar i obliczanie tego parametru w ró¿nych warunkach geologiczno-górniczych, technicznych i eksploatacyjnych kopalñ.

Nie ma jednak jednoznacznej odpowiedzi na pytanie, jaki jest wp³yw zubo¿enia tak na efektywnoœæ pro- wadzonej eksploatacji jak i wartoœæ realizowanych w tym sektorze projektów inwestycyjnych, co wynika ze specyfiki poszczególnych z³ó¿ i koncepcji ich zagospodarowywania.

W przedk³adanym artykule oprócz weryfikacji wp³ywu zubo¿enia na wartoœæ ekonomiczn¹ projektu, ocenie poddano zmianê kluczowych parametrów takich jak: przychody z tytu³u prowadzonej dzia³alnoœci górniczej, koszty operacyjne, produkcja koncentratu miedzi, produkcja miedzi elektrolitycznej (Cu), produkcja srebra metalicznego (Ag).

Dysponuj¹c szeregiem danych empirycznych okreœlaj¹cych wyniki produkcyjne jednego z czo³owych œwia- towych producentów miedzi na przestrzeni lat 2005–2007 w³¹cznie postanowiono dokonaæ próby oceny wp³ywu zubo¿enia na zamodelowany projekt inwestycyjny X. Projekt ten ³¹czy³ w sobie koncepcjê zagospodarowania z³o¿a ju¿ istniej¹cego oraz elementy modelowe zaproponowane przez autorów w celu realizacji postulatów badawczych pracy.

Kluczowe z punktu widzenia prowadzonego modelowania za³o¿enie o istnieniu wp³ywu zubo¿enia na osi¹gane w projekcie X wyniki oceny ekonomicznej dla ró¿nych poziomów danych wejœciowych zweryfikowano buduj¹c zmodyfikowany arkusz przep³ywów pieniê¿nych (model dyskontowy), uwzglêdniaj¹cy elementy ra- chunku wyników, wprowadzaj¹c doñ matematyczne zale¿noœci zmiennych. Parametrem, przy pomocy którego weryfikowano wartoœæ ekonomiczn¹ projektu, sta³a siê NPV (wartoœæ zaktualizowana netto, Net Present Value).

DILUTION INFLUENCE ON VALUE OF MINING INVESTMENT PROJECTS AND SELECTED PRODUCTION FIGURES BY A COPPER MINE EXAMPLE

K e y w o r d s

Dilution, sensitivity analysis, Discounted Cash Flow model, mining investment project

A b s t r a c t

Mine production activity is connected with resources exploitation of specified quality parameters. However, it is often necessary to increase the output of production by adding extra rocks, containing some amount of metals having industrial utilization. Determining and measuring the influence of dilution on the mines’ economics results, also on technical level, is an important and interesting issue.

One of the basic factors, deciding in majority on the effectiveness of mining and utilization of mining products is dilution, often considered as quality losses [4]. It is understood and indisputable that crude ore exploited by the company is usually characterized by worse qualities than those indicated by deposit’s ore sample. Such pheno- menon usually takes place in case of metal deposits and is referred to as dilution. Commonly, three kinds of dilution are distinguished:

— dilution deriving from mixing natural ore resources with rocks,

— dilution deriving from mixing gangues with ore resources,

— dilution deriving from loss of rich but little fractions of useful metals.

Dilution regarded in such way, considered only on a mine’s level, can be defined as traditional approach; as such, it has already been precisely recognized and described. The problem here is how to transform the knowledge about amount and type of dilution given at separate stages of exploitation process into information useful for assessment, both at the technical and economical level of the entire technological process? How to provide the

collected information with new quality, necessary in the process of creating and controlling production effecti- veness of a big mining corporation [5, 6]?

Nowadays, it is almost a truism to say that precise knowledge of the actual content of copper and other metals in a vein of processed material is a very important part of the production process. Contemporarily, it is known that such knowledge constitutes a basis for measuring production effectiveness, and combined with cost-related information allows for profit assessment.

In such approach, the dilution referred to quality losses of reserves, rises to one of the most important issue describing the structure of the process in the technological continuum from mines to processing and, further on, to copper concentrate refining.

In the literature, there are many relations to the problem connected with reserves utilization. Besides the general characteristic of dilution, the authors provide classification and present various formulas allowing for its quantification, measurement and calculation in different geological and mining conditions.

On the other hand, there is no clear answer what is the dilution influence on both the mining effectiveness and the value of investment projects classified to the same category because of specific environment condition and development.

In the presented paper, besides verification of dilution influence on investment projects’ value, variability of key parameters were assessed, including: revenues, production costs, production of copper concentrate, production of copper (Cu), production of silver (Ag).

Possessing series of empiric data determining production results from one of the leading global producers of copper in the years 2005–2007, it was decided to quantify the influence of dilution on example of experimental copper project X. The project joined a concept of development of an already existing mine and new elements proposed by the authors to execute research purposes.

The key assumption was verified by constructing a modified Discounted Cash Flow model, including elements of income statement and mathematic modelling. The indicator used for measuring the economic value of the project was NPV (Net Present Value).