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Cut-off grade optimization of open pit mines with multiple processing streams Pettingell, Michael Nash 2017

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CUT-OFF GRADE OPTIMIZATION OF OPEN PIT MINES WITH MULTIPLE PROCESSING STREAMS  by  Michael Nash Pettingell  B.Sc., The University of South Carolina, 2010    A THESIS SUBMITTED IN PARTIAL FULLFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF   MASTER OF APPLIED SCIENCE  in  THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Mining Engineering)   THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)   AUGUST 2017   © Michael Nash Pettingell, 2017  ii ABSTRACT In this study, dynamic cut-off grades and multiple processing streams are used to maximize the value of a mining project based on a finite resource. Optimal cut-off policies are generated using Lane’s method for determining cut-off grade. By maximizing the present value of future profits as a function of cut-off grade, mine project value is increased over the traditional break-even approach. A method for determining multiple cut-off grades at a single deposit was applied to analyze the impact that changes in processing capacity have on NPV. It was found that additional capacity related to a separate mill facility resulted in an economic reclassification of ore and waste. Grade tonnage data used in the case study was simulated to represent the geologic uncertainty associated to low-grade mineral deposits. Results from the hypothetical case study examined in this thesis reveal that a low-grade open pit gold mine will benefit from the use of multiple processing streams when a dynamic cut-off policy is applied. Particularly, when incorporating a “high grade” modular processing stream to maximize the potential revenue of the mineralized material. This means that for a given set of design, production and geological parameters, the classification of ore and waste is what ultimately determines the NPV of a mining project.        iii LAY SUMMARY The purpose of this research was to identify the effects that multiple mineral processing streams have on the overall value of a mining project.  By incorporating more than one processing facility into a mine plan, the classification of ore and waste at a gold deposit was improved. This allowed for each processing facility to process ore best suited for that particular stream, based on the concentration of gold in the ore. Ultimately, by optimizing the grade of ore sent to each facility, mine value was increased over a project with a standalone stream.      iv PREFACE This thesis is original, unpublished, independent work by the author. The Algorithms used are based on dynamic cut-off theory proposed by Lane (1) and work done by Asad and Dimitrakopoulos (2).   v TABLE OF CONTENTS ABSTRACT ...................................................................................................................... ii	LAY SUMMARY ............................................................................................................... iii	PREFACE ....................................................................................................................... iv	TABLE OF CONTENTS ................................................................................................... v	LIST OF TABLES ............................................................................................................ vii	LIST OF FIGURES ......................................................................................................... viii	LIST OF SYMBOLS ........................................................................................................ ix	DEDICATION .................................................................................................................. xii	1	 INTRODUCTION ........................................................................................................ 1	1.1	 THESIS ORGANIZATION ............................................................................................... 3	1.2	 IMPORTANCE TO INDUSTRY ....................................................................................... 4	1.3	 RESEARCH OBJECTIVES ............................................................................................. 5	2	 LIERATURE REVIEW ................................................................................................ 6	2.1	 LANE’S METHOD ........................................................................................................... 6	2.2	 EXTENSIONS/MODIFICATIONS TO LANE’S METHOD ................................................ 8	2.2.1	 INCORPORATING REHABILITATION COSTS ....................................................... 8	2.2.2	 OPTIMIZATION FACTOR ON OPPORTUNITY COSTS .......................................... 8	2.2.3	 NON-LINEAR PROGRAMMING ............................................................................... 9	2.2.4	 VARIABLE CAPACITIES .......................................................................................... 9	2.2.5	 STOCHASTIC PRICES .......................................................................................... 12	2.2.6	 MULTIPLE MILLS ................................................................................................... 12	3	 METHODS ................................................................................................................ 14	3.1	 BREAK-EVEN METHOD ............................................................................................... 14	3.2	 LANE’S METHOD ......................................................................................................... 17	3.2.1	 EXPLOITATION STRATEGY ................................................................................. 17	3.2.2	 LIMITING ECONOMIC CUT-OFF GRADES .......................................................... 20	3.2.3	 BALANCING CUT-OFF GRADES .......................................................................... 23	3.2.4	 EFFECTIVE OPTIMUM CUT-OFF ......................................................................... 24	3.2.5	 CUT-OFF POLICY .................................................................................................. 28	3.2.6	 SHORTCOMINGS OF LANE’S METHOD .............................................................. 30	3.3	 GRADE TONNAGE CURVES ....................................................................................... 30	4	 PROCESSING .......................................................................................................... 33	4.1	 MODULAR PROCESSING ............................................................................................ 33	4.1.1	 CAPITAL AND OPERATING COSTS ..................................................................... 35	4.2	 MULTIPLE STREAMS ................................................................................................... 37	4.2.1	 CUT-OFF GRADE FOR MULTIPLE PROCESSING STREAMS ............................ 40	5	 THE MODEL ............................................................................................................. 44	5.1	 ECONOMIC AND OPERATIONAL INPUTS ................................................................. 45	5.1.1	 GRADE TONNAGE SIMULATION ......................................................................... 45	 vi 5.2	 INITIAL ESTIMATES OF NPV ....................................................................................... 47	5.3	 LIMITING CUT-OFF GRADE ........................................................................................ 48	5.4	 QUANTITY OF ORE, WASTE AND AVERAGE GRADE .............................................. 48	5.5	 QUANTITY MINED, PROCESSED AND REFINED ...................................................... 49	5.6	 ANNUAL CASH FLOW AND NPV ................................................................................. 51	6	 HYPOTHETICAL CASE STUDY .............................................................................. 53	6.1	 MODEL ASSUMPTIONS AND LIMITATIONS .............................................................. 53	6.2	 METHOD ....................................................................................................................... 56	6.2.1	 BASE CASE ........................................................................................................... 57	6.2.2	 MODULAR CASE ................................................................................................... 59	7	 ECONOMIC ANALYSIS ........................................................................................... 63	7.1	 SENSITIVITY ANALYSIS .............................................................................................. 63	8	 CONCLUSIONS ....................................................................................................... 68	9	 RECOMMENDATIONS ............................................................................................ 70	REFERENCES ............................................................................................................... 72	APPENDIX A.  Derivation of Lane’s Equations .............................................................. 74	APPENDIX B.  Simulated Grade Tonnage Data ............................................................ 77	APPENDIX C.  Cut-off Policy Results ............................................................................ 83	APPENDIX D.  Sensitivity Analysis ................................................................................ 89	  vii LIST OF TABLES  Table 1 Estimated unit operating costs for the Gekko Python modular processing plant, from (22). ................................................................................................................ 36	Table 2 Mine design parameters for hypothetical gold mine. ......................................... 55	Table 3 The complete cut-off policy for base case using grade tonnage curve 1 (GT1). ................................................................................................................................ 58	Table 4 Calculated NPVs for both the base and modular scenarios across the set of 15 equally probable simulated grade tonnage curves. ................................................ 58	Table 5 Complete cut-off policy for modular case using GT1. ....................................... 60	Table 6 Base case cut-off policy when HL has capacity of 573,000 t/yr, for GT1. ......... 60	Table 7 Complete break-even cut-off policy for modular case using GT1. .................... 61	Table 8 Comparison of annual gold production across set of simulated grade tonnage curves. .................................................................................................................... 64	Table 9 Cut-off policy for GT13 showing how an increase in HL unit costs by 5% results in an increase in HL COG and a decrease in CIL COG. ......................................... 66	Table 10. Cut-off policy for base case, GT13. ................................................................ 66	Table 11. Cut-off policy for GT13 when HL capacity is increased by +15% of base case values. ..................................................................................................................... 66	  viii LIST OF FIGURES  Figure 3.1 Graphical representation of the break-even relationship between costs and revenue similar to (5). ............................................................................................. 16	Figure 3.2 Graphical representation of balancing cut-off when the mine and the mill are limiting. .................................................................................................................... 24	Figure 3.3 Increment in present value versus cut-off grade with the mine and mill components in balance. .......................................................................................... 26	Figure 3.4 Increment in present value versus cut-off highlighting the maximum value in the feasible region of  ve  when the mine and the mill are in balance. ..................... 27	Figure 3.5 Simulated tonnage histogram of gold deposit. .............................................. 31	Figure 3.6 Sample grade tonnage curve with cut-off grade of 4.0 g/t. ........................... 32	Figure 4.1 Process flow diagram for the Gecko Python Plant, from (22). ...................... 34	Figure 4.2 Cut-off and cutover grade defined by revenue earned per ton of material processed. .............................................................................................................. 41	Figure 6.1 Flow sheet diagram for hypothetical gold mine with capacity constraints (modular case). ....................................................................................................... 54	Figure 6.2 Grade tonnage distribution GT1 for hypothetical gold mine. ......................... 56	  ix LIST OF SYMBOLS 𝑃  [$]  Annual profit. 𝑡  [yr]  Time. 𝑇  [yrs]  Time (life of project). 𝑄𝑚  [t/yr]  Quantity mines. 𝑄𝑐  [t/yr]  Quantity processed. 𝑄𝑟  [oz/yr]  Quantity refined. 𝑀  [t/yr]  Maximum annual mining capacity. 𝐶  [t/yr]  Maximum annual processing capacity. 𝑅  [oz/yr]  Maximum annual marketing/refining capacity. ℎ  [$/t]  Rehabilitation unit cost. 𝑐  [$/t]  Processing unit cost. 𝑦  [%]  Average annual recovery from processing. 𝑔  [g/t]  Average mineral grade.  𝑄  [tons]  Total resource remaining. 𝑞  [t/yr]  Rate of extraction. 𝑉  [$]  Present value. 𝑝  [$/t]  Cash flow from one unit of resource. 𝛿  [%]  Discount rate. 𝐹  [$/-]  Opportunity cost. 𝑆  [$/oz]  Selling price of gold. 𝑟  [$/oz]  Market/refining unit cost. 𝑥  [%]  Ore to mineralized material ratio. 𝑚  [$/t]  Mining unit cost. 𝑓  [$/yr]  Fixed annual cost. 𝑔  [g/t]  Mineral grade. 𝑔!  [g/t]  Mine limiting economic cut-off grade. 𝑔!  [g/t]  Process limiting economic cut-off grade. 𝑔!  [g/t]  Market/refining limiting cut-off grade.  x 𝑔!"  [g/t]  Mine and process balancing cut-off grade. 𝑔!"  [g/t]  Processing and refining balancing cut-off grade. 𝑔!"  [g/t]  Mine and refining balancing cut-off grade.  𝑣  [$/-]  Increment in PV per unit of resource utilized. 𝑣!  [$/-]  Max of the min increment in PV per unit of resource utilized. 𝑊  [$]  Present value one year in the future at t=t+1. 𝑇!   [tons]  Quantity of tons in each grade category ‘n’. 𝑇𝑂   [tons]  Quantity of ore tons above cut-off grade. 𝑇𝑊  [tons]  Quantity of waste tons below cut-off grade. ∆  [-]  Difference between TO/Tn for each process. 𝐺𝑇!   [-]  Grade tonnage data. xi LIST OF ABBREVIATIONS CIC  Carbon in column CIL  Carbon in leach COG  Cut-off grade HL  Heap leach HLF  Heap leach facility LOM  Life of mine NLP  Non-linear programming NPV  Net present value PV  Present value ROM  Run of mine   xii DEDICATION  This thesis is dedicated to Christine A. Pettingell. Thank you for your continuous support.             1 1 INTRODUCTION Current trends in the gold mining industry show that weak commodity prices and an overall decline in metal grades have resulted in less gold being mined (3). There has also been less investment dedicated to exploration in recent years resulting in a smaller inventory of new deposits (4). Although the majority of exploration dollars is spent in remote areas of Latin America and other underdeveloped countries, the lack of infrastructure has made these ore bodies increasingly challenging to mine. The question then becomes how to mine these remote, low-grade deposits economically? Barring any new technological breakthroughs this must be done strategically with capital cost reduction and operational excellence.   One solution is to incorporate a modular processing stream and a dynamic cut-off grade strategy to capture the full value of the resource being mined. By utilizing multiple processing streams the mineralized body can be further classified into zones based on the geology and/or mineral content that is best suited to a particular processing stream. Modular processing provides flexibility to the mine operator to route the mined material to the most economic recovery method no matter how small or remote the zone or mine. A dynamic cut-off strategy refers to what material should be mined based on the current mine design, the local geology and prevailing market conditions. This is fundamental to maximizing the present value of the mining asset.  The simplest definition of cut-off grade (COG) is the amount of metal concentration in  2 the mineralized material that determines what is considered ore versus what is considered waste (1). Mine operators use cut-off grades to optimize mine designs, estimate resources and guide production. As cut-off grades decrease more material is classified as ore and production rates increase. Consequently, the average grade of the ore being processed decreases. The opposite occurs when cut-off grades increase. An optimum dynamic cut-off strategy will change the classification of ore and waste throughout the life of the project to maximize the present value of all future profits. Factors such as, grade distribution, available capacities and variable costs for mining, milling and refining as well as the selling price for the commodity(s) all play a crucial role in determining optimum cut-off grades.   Modular processing technology is ideal for processing material in remote areas, which lack the infrastructure necessary to construct and operate a conventional mill. Modular processing plants are designed to be small and flexible, dividing the components of the mill into separate subsystems that can be added or removed based on the needs of the operator for the material being mined.  The smaller size of the unit over its traditional counterpart allows some modular systems to fit underground in a drive or drift, the idea being that underground processing would lower haulage costs and increase hoisting capacity while reducing energy consumption and in turn the environmental footprint.   There are several manufacturers that offer modular processing solutions ranging from small skid mounted units that can process 10-20 t/hr, to larger units capable of processing over 50tph. There is also a wide range of useful applications for these  3 plants, from gravity concentration to flotation of several different commodities in virtually any location.  To aid in the exploitation of low-grade precious metal deposits multiple mineral recovery process streams can be used. By implementing multiple processing streams the miner has the ability to choose the best processing method for a particular ore type at any given time. This strategy has been used at mining operations where the ore is classified into different categories based on lithology or mineralization. This is common when the deposit is composed of both sulfide and oxide ore.   The benefits of utilizing multiple processing streams combined with modular processing technology include, but are not limited to, reduced blending requirements, additional processing capacity, mitigation of geologic uncertainty and the ability to push revenue forward from higher-grade material. However, the greatest benefits arise from the options available at the time a particular area is mined. With the capability to send material to a low or a high recovery stream over just an ore or waste pile, the miner can have greater influence on the economics of the project through a more refined cut-off strategy.  1.1 THESIS ORGANIZATION The purpose of this research was to identify the effects that multiple processing streams have on cut-off grade policy and how cut-off strategy influences overall project value, particularly when a modular processing plant is introduced to an open pit gold mine with  4 an existing heap leach facility.   The cut-off analysis conducted in this thesis is based on Lane’s (1) method for optimizing cut-off grades by maximizing the present value of future cash flows generated in a specified time period. Section 2 is comprised of a literature and theoretical review outlining past studies on cut-off grade strategy. In section 3, the primary methods for determining cut-off grades are discussed in detail. The concept of modular processing and the use of multiple processing streams are examined in section 4. Section 5 contains the description and steps to the algorithm used to maximize the value of a mine through dynamic cut-off grade optimization. In section 6, the model is applied to a hypothetical small-scale, open-pit gold mine. Section 7 presents a sensitivity analysis on the results obtained in section 5. In the remaining sections, 8 and 9, conclusions and recommendations of this research are presented.   1.2 IMPORTANCE TO INDUSTRY The optimization of cut-off grades in mine planning and design is of practical and theoretical interest. Although it is well known that a dynamic cut-off strategy can improve the net present value (NPV) of a mining project over a break-even cut-off model, many mining companies refrain from incorporating a robust cut-off analysis in their valuations and long-term plans. Hall (5) suggests that junior engineers or geologists are often determining cut-off grades based on past practices. More importantly, the way cut-offs are determined has become indistinguishable from what a cut-off grade is and break-even has become synonymous by default.    5 The model presented here applies Lane’s cut-off theory focusing on modular processing technology as a secondary processing stream, which has the flexibility to be easily expanded or contracted depending on current geologic or market conditions. A strategy of this kind can be applied to low-grade, open pit precious metal deposits where environmental and/or land area constraints prohibit the construction or expansion of conventional process facilities.   1.3 RESEARCH OBJECTIVES The objective of this research was to maximize the value of small-scale, low-grade, open pit homogenous gold deposits using multiple processing streams and optimum dynamic cut-off grade strategy. To accomplish this, two processing streams, a heap leach facility (HLF) and a modular carbon in leach plant (CIL) were incorporated simultaneously to fully exploit a set of simulated grade tonnage curves. An optimum cut-off policy was determined and mineralized material was routed to a waste pile, a high-grade stream or low-grade stream depending on which combination maximized the present value of the resource.   Specific research objectives include: 1. Apply Lane’s methods for determining cut-off grade to maximize the NPV of a gold mine when one processing stream is utilized. 2. Apply Lane’s methods to a gold mine when two processing streams are utilized. 3. Determine if Lane’s methods improve the NPV of a mine over the traditional break-even approach.  6 2 LIERATURE REVIEW Cut-off grade research has been an important topic for mine planners in industry and academia ever since K. Lane published his seminal work in 1964 and subsequent text book in 1988. The following section provides a general review of cut-off theory and highlights the research aimed at improving the optimization of cut-off grades.    2.1 LANE’S METHOD Kenneth Lane was the first to consider cut-off grade as a dynamic value that must be optimized to maximize the value generated from a mine. Instead of maximizing profits, he sought to maximize the present value of the resource as a whole by considering the opportunity cost associated to mining at a particular cut-off. In his book “The Economic Definition of Ore” published in 1988, he explains that due to the time value of money, processing lower grade ore today reduces the potential future value of higher-grade ore if processed at a later date. Therefore, by mining at higher cut-off grades early in the life of the project the opportunity cost is minimized and NPV is increased.  Lane also considers the mining system to be comprised of three main limiting components, the mine, the processing facility and the market. By his theory, at any given time the system will be constrained by one or more of the limiting factors. In order to derive optimal cut-off grades that maximize the NPV of the project, the capacities to the limiting components must be considered and the overall system balanced.     7 Mathematically, the objective function is represented as,     max  NPV =Pt1+ d( )ttT∑   subject to    Qmt ≤M     Qct ≤C     Qrt ≤ R    where  P  is cash flow, d is the discount rate,  t  is time,  Qm  is the quantity of tons mined,  Qc , ore tons processed, and  Qr  is the ounces refined. The variables  M , C  and  R  represent the maximum periodic capacities for the mine, the mill and refinery, respectively.  The initial work done by Lane was based on the assumptions that there was one source of material feeding one treatment plant. He also assumed that the ultimate pit limit had been determined and a mine schedule planned. Furthermore, he used static prices and costs for his economic inputs. These assumptions and limiting parameters often fail to capture the real world complexity related to valuing actual mines in practice. Consequently, many extensions to Lane’s work have been published aimed at improving many of the shortcomings.   8 2.2 EXTENSIONS/MODIFICATIONS TO LANE’S METHOD 2.2.1 INCORPORATING REHABILITATION COSTS  J. Gholamnejad (6) identified that the costs associated with mining and dumping waste represent a portion of the rehabilitation costs, and therefore must be included in the cut-off calculation. This allows the mine planner to strategically account for not only the returns that ore provides but also the costs that are incurred from waste. For rehabilitation costs to be factored into Lane’s original algorithm, Gholamnejad used a rehabilitation cost variable ' h ’ subtracted from the unit processing cost ‘ c ’ in the numerator of the limiting economic cut-off calculation (section 3.2.2).   Incorporating rehabilitation costs can provide a more accurate estimate of the profits obtained through a cut-off grade policy. Results suggest cut off grades determined using a rehabilitation factor will be lower than otherwise in an effort to reduce the total amount of waste rock sent to the waste dump (6). By including these costs into the determination of an optimum cut-off grade Gholamnejad observed an increase in NPV over the traditional method introduced by Lane.   2.2.2 OPTIMIZATION FACTOR ON OPPORTUNITY COSTS Another study conducted by Bascetin and Nieto (7) use an iterative approach based on Lane’s algorithm to determine the optimal cut-off policy for an open pit mine. However, they introduce an “optimization factor” based on the generalized reduced gradient algorithm to maximize the NPV of a project. The optimization factor is included in the limiting cut-off grade calculation and serves as an additional time cost associated with  9 producing one more unit of ore. This is in addition to the opportunity cost introduced by Lane. Their findings suggest that by including a mining cost into the optimal cut-off grade calculation, when the concentrator is the limiting capacity, the overall NPV of a mining project is increased over Lane’s approach.    2.2.3 NON-LINEAR PROGRAMMING Non-linear programming (NLP) can be used to solve an objective function containing non-linear constraints. The solution to optimizing a cut-off grade that maximizes the expected NPV of a mining project is a non-linear objective with several linear and non-linear constraints. The reduced gradient method of solving such a problem is outlined in a paper written by Yasrebi et al (8).  Using a cut-off model based on Lane’s algorithm created with LINGO software, they are able to optimize a single cut-off grade for the entire life of the project. This type of simplified calculation is not optimal because it does not apply dynamic cut-off theory whereby cut-off grades decline as the resource is depleted.   This approach also assumes static prices and costs that will undoubtedly change throughout the life of the project. An attempt to combine a series of NLP equations could provide an updateable policy.  2.2.4 VARIABLE CAPACITIES An algorithm proposed by Abdollahisharif et al (9) examines the idea of variable capacities on the major limiting factors; mine, mill and market. Their method attempts to  10 improve on Lane’s original algorithm, which holds mining, processing and market capacities constant, by calculating them as variable parameters. By substituting the variable for the maximum capacity of a constraint into the equation to find the total quantity utilized for a particular constraint, the maximum efficiency of the investment can be obtained. For example, consider the concentrator to be the limiting capacity for an open pit mine. To find the quantity of material refined ‘ Qr ’ for the life of the project; Lane introduced an equation that provides the relationship between quantity produced and quantity refined    Qr = y * g *Qc    where ‘ y ’ is the percentage of recovered material from processing, ‘ g ’ is the weighted average grade of the mineralized material above cut-off and ‘ Qc ’ is the total amount of material processed over the life of the mine (LOM). By substituting the maximum capacities for both the market and the concentrator for the quantities utilized, the equation can be rewritten as,    C = Ry * g  where ‘ C ’ is the maximum variable capacity for the concentrator and ‘ R ’ is the maximum variable capacity for the refinery. In this case the refinery capacity is assumed to be equal to market demand. In Lane’s algorithm ‘ C ’, ‘ R ’ and ‘ M ’ (maximum mining  11 capacity) are constant and are determined before the calculation of an optimum cut-off grade.  By applying this technique and comparing the results to both Lane’s original algorithm (1) and that offered by Gholamnejad (6), which introduces rehabilitation costs into cut-off grade determination, Abdollahisharif et al (9) find that using variable capacities to calculate cut-off grade provides the greatest NPV. The optimal cut-off grade becomes much lower than the other two methods. This results in more material concentrated, ~29% more than the others, while holding the refining capacity equal to market demand for all three methods. However, the mining throughput rate was reduced by 10% compared to the other proposed methods.  In practice, as cut-off grade changes, so does the amount of material sent to the processing plant and potentially the mining rate, as seen with other studies (1,2,10). In contradiction to Abdollahisharif et al (9), Breed and Heerden (11) state that “to ensure cut-off optimization is done correctly, the capacity constraints must be independent of the cut-off grade”. Therefore using variable capacities to determine the optimal cut-off strategy can only be used to determine potential capacity parameters. The variable capacity algorithm also assumes a single metal, open pit project and does not create a LOM cut-off value policy nor does it capture the opportunity costs associated with mining at different cut-off grades.    12 2.2.5 STOCHASTIC PRICES Lane’s model is based on the assumption that future prices are known.  In reality determining cut-off grades for the life of a project requires some level of price and cost forecasting to accurately estimate the value of the project. Barr suggests in his work on real options (12), that by using a stochastic price model of the entire futures curve and not simply a predetermined price or even stochastic spot price model, optimal cut-off grades are lower than otherwise. This means more mineralized material is classified as ore. Therefore, using deterministic prices and costs lead to higher than optimal cut-off grades, which results in misclassifications of ore and waste (13).   Although applying a stochastic price model and real options valuation to a mine is closer to a real world scenario, the steps taken to forecast price movements are beyond the scope of this research. Readers are directed to (14,15) for a more in depth examination of optimizing COGs under price uncertainty.  2.2.6 MULTIPLE MILLS Asad and Dimitrakopoulos (2) applied a heuristic process to expand on Lane’s algorithm to optimize cut-off grade at a project with multiple processing streams. They also account for geologic uncertainty by simulating several different, but equally probable grade tonnage curves. Using a modified algorithm that is successful at maximizing the NPV for the set of given grade tonnage curves, they are able to determine the optimum cut-off grades for each processing stream. Their approach was applied to a large open pit copper mine where they observed a 13.8% difference between the minimum and  13 maximum NPV generated from the set of simulated grade tonnage curves. They conclude that ignoring geologic uncertainty in the planning stage can have severe economic implications on a mining project (2).   Although Asad and Dimitrakopoulos were successful in applying Lane’s theory to a mine with multiple processing streams, the utilization of those streams was well below capacity. Their results suggest that out of the four processing streams incorporated, for the entire life of the project, not one stream runs at even half of its maximum capacity. This is not practical in a real world situation. A mill design with an annual production capacity of 43.8 million tons of ore would not be justified if its peak production were <10 million tons per year.   The algorithm used in this thesis was based on the work done by Asad and Dimitrakopoulos (2). The difference lies in the incorporation of modular processing as opposed to a permanent mill. This type of technology has the flexibility to increase and decrease capacity in small increments to account for changes in geologic or market conditions. Therefore, when the resource is low the use of an additional mill will be excluded from the model negating the need for a balancing system, as only one processing stream will be limiting.       14 3 METHODS The analysis and optimization of cut-off grades is essential to maximizing the value generated from a mine. The term “cut-off grade” takes on several definitions depending on how it is applied. Taylor defines cut-off grade at an ore deposit as any mineral grade that, for any specific reason, is used to separate two courses of action (16). This could include whether or not to mine a unit of material or which recovery process is best suited for that material. Another definition considers cut-off grade the level of mineral concentration that dictates whether mineralized material is deemed ore or waste (1). In general, cut-off grades are primarily used to classify material at a mine.  Currently, there are two main methods used to determine cut-off grade. The break-even method, which considers only financial factors and Lane’s method which attempts to maximize the NPV of the project subject to mine, mill and market constraints. The following sections introduce these methods with examples.  3.1 BREAK-EVEN METHOD Many mining companies use a break-even analysis to determine cut-off grade. This method considers the prices and costs and average recoveries related to mining and processing. The break-even cut-off grade is where the costs of producing a salable product are equal to the revenue earned from that product (5,17).     Breakeven COG = CostsCommodity Price * Recovery   15 Most commonly this is used to distinguish between ore and waste at the mining level. However, depending on the costs included in the calculation, the break-even cut-off analysis can be applied to many areas of the project.   • Marginal break-even cut-off considers the variable costs of mining and milling  • Mine operating break-even cut-off assumes total mining costs and milling costs  • Site operating break-even cut-off includes total mining, total milling and total site administration costs   Although these calculations are used for different applications they are all based on a break-even principle, by which the revenues earned are equal to the costs of producing.   Consider an example provided by Hall (5) for a simple break-even COG calculation where, • Selling price = $10 /g • Recovery = 90% • Total costs = $60 /t    $60$10 * 90%= 6.67 g / t    Since recovery is 90% and the selling price is $10/g, the revenue earned is $9/g. By applying a total cost break-even COG of 6.67g/t the revenue earned is equal to the costs of producing that revenue. Figure 3.1 below is a graphical representation of the relationship between total cost and revenue.   16   Figure 3.1 Graphical representation of the break-even relationship between costs and revenue similar to (5).  Here, total costs of $60/t are assumed to be independent of grade and are therefore represented as a straight line. The revenue function increases with grade at a rate of $9/g. The point where the total cost and the revenue functions meet is the break-even cut-off grade of 6.67g/t.  This method is widely accepted by the mining industry to ensure the operation remains profitable. However, it fails to maximize the value of the material being mined. Since the break-even model only considers price and costs, other factors such as variability in geology and operational capacities that have an influence on revenue are overlooked. Ignoring such factors can lead to lower than optimum cut-off grades resulting in a lower overall NPV.   0 20 40 60 80 100 0 1 2 3 4 5 6 7 8 9 10 $/ton Grade (g/t) Breakeven Cut-off Grade Total Cost Revenue  17 3.2 LANE’S METHOD The need for optimal cut-off grade calculations based on an available resource and the capacities that limit the extraction and production of that resource is a major challenge in the mining industry. Lane was the first to introduce an algorithm to calculate cut-off grades that maximize the present value of cash flows from a mining project. He derived a set of equations to calculate a cut-off grade specific to which capacity(s) in the mining system are limiting output. Furthermore, he outlined a method for calculating the opportunity cost associated with mining at a particular cut-off to determine a complete cut-off policy for the life of the project.  Until Lane published his initial work on cut-off theory in 1988, cut-off grades were calculated using the costs of mining and processing the ore and the selling price of the commodity. Lane proposed that cut-off grade is a function of not only costs and prices but of capacities that limit mining, processing and refining. Understanding that the primary objective of most mine operators is to maximize the present value of all future profits (1), Lane suggested that to maximize the value of an exhaustible resource an exploitation track that maximizes the present value of the project at all times must be employed.   3.2.1 EXPLOITATION STRATEGY The present value of an operation based on a finite resource is calculated as the total of the future cash flows discounted back to the present.  At a mine, minerals are excavated and processed to recover a salable product. All mineralized material containing sufficient economic value to cover the costs of mining and processing are  18 classified as economic ore, while material with less than enough mineral concentration is considered waste. Ore is sent to the processing facility while waste is sent to a waste pile or left in place. The level of mineral concentration that dictates whether material is classified ore or waste is the cut-off grade (1).  Cut-off grades can be used for several different situations at a mine as a means for classification. Most commonly, it is the lowest grade material that “should” be mined and/or used to calculate total reserves. Most importantly, cut-off grades are used to identify the optimum exploitation strategy for maximizing the present value of an operation (1).   In order to determine the optimum cut-off grades for a deposit two fundamental expressions must be considered. The first determines the optimum exploitation strategy for maximizing the present value of an operation based upon a finite resource. Lane suggested that value is a function of the size of the remaining resource  Q  and the rate of extraction  q  (1). These two variables also define the life of the project  T . Therefore, the present value  V  of the mining operation at any time is a function of the life of mine, the size of the remaining resource and the chosen rate of extraction (18).     V T + t,Q − q( )   [1]  Differentiating  V  with respect to  Q  and  T ,     19   dVdQ= p − tqδV − dVdT⎛⎝⎜⎞⎠⎟  [2]  where,  p  is the cash flow arising from one unit of resource and  t  is the time it takes to process that unit. The tonnage (τ ) is given by  t / q , which represents the time required to process one unit of mineralized material.  The opportunity cost of mining at a particular extraction rate is the term in brackets. Here, the discount rate δ  is multiplied by  V  to reflect the decrease in value of the resource resulting from extraction, which is subtracted by the first derivative of the value ( V ) with respect to time ( T ). The opportunity cost can be rewritten as  F , and the equation that maximizes the present value of a mining operation becomes,      dVdQ= p −τF   [3]  The second necessary expression directly relates cash flows to cut-off grades.  The formula for the cash flow arising from one unit of mineralized material is:     p = S − r( )xyg − xc −m − ft   [4]   20 where  x  is the proportion of mineralized material classified as ore,  g  is the weighted average grade of the ore and  y  is the percentage recovery of mineral from the treatment process. The remaining economic variables are:  S  = unit mineral price  r  = unit market cost (refining cost)  c  = unit processing cost  m  = unit mining cost  f  = fixed costs (annual)   Combining equations [1] and [2] we derive the objective function that must be maximized at all times during the life of mine in order to maximize NPV.      Maxg S − r( )xyg − xc −m − f + F( )t{ }   [5]  In this expression  x  and  g  are directly dependent on the cut-off grade,  g . The time  t  is also dependent on  g  but indirectly, which gives rise to three separate cases for analysis based on which capacity is limiting output.   3.2.2 LIMITING ECONOMIC CUT-OFF GRADES Lane proposed there are three economic capacities in the mining system that limit throughput and the exploitation of the deposit. They are the mine, treatment facility and market (1). The mine represents mining and development rates that govern throughput.  21 The treatment facility consists of the concentrator(s) and ore handling facilities. The market is limited by any restriction imposed by sales contracts or by a refinery or smelter. At any given time during the life of an operation one or more of these capacities will be the limiting factor for the system. Because each of these capacities dictates the supply of salable product they are deemed limiting economic capacities.   Each limiting capacity has its own calculation taking into account the unit costs and the specified capacity for that system. Each calculation also contains the opportunity cost of not mining the remainder of the deposit due to the limiting capacities of the mine, the processing facilities, and the market. Therefore, depending on which area of the total system is limiting, the time ‘ t ’ becomes  Qm / M ,  Qc / C  or  Qr / R  if the mine, the processing plant, or the refinery are limiting, respectively (2), where  Qm  represents the quantity of tons mined,  Qc  is the quantity of tons milled and  Qr  is the quantity of ounces refined in a given period. The maximum annual capacity for the mine, the mill and the market are denoted as  M ,  C  and  R  respectively. The opportunity cost must then be distributed per ton of material mined, per ton of ore processed, or per ounce of metal refined, depending on which component is limiting.      Mine Limiting        gm =cS − r( ) * y   [6]  The equation for a mine limiting economic cut-off grade indicates that the mineralized material should be classified as ore for as long as its implicit value,  S − r( ) * y * g ,  22 exceeds the costs of further processing,  c . It is important to recognize that time costs and mine costs are not relevant. This is because the formula is based on the assumption that the decision to mine beyond the present time has already been made (1). The mine limiting equation also does not make reference to present values due to the fact that there is no trade-off of future losses against present gains to modify the current policy.   Process Limiting        gc =c +f + F( )CS − r( ) * y   [7]  For the process limiting equation, the opportunity cost  F  represents an additional time cost associated with processing the ore. This creates higher cut-offs when  F  is large in the early years of production and lower cut-offs as  F  declines along with the resource. This realization represents dynamic cut-off theory, whereby cut-off grades change throughout the life of a mine to maximize the value of the resource being mined.    Market Limiting        gr =cS − r −f + F( )R⎡⎣⎢⎢⎤⎦⎥⎥* y  [8]  Similar to the process limiting cut-off grade formula, the market limiting equation includes the present value term in the form of an opportunity cost, which along with the fixed costs is distributed according to the limiting capacity. This results in declining cut-off grades as  F  declines due to the resource being depleted.  23 3.2.3 BALANCING CUT-OFF GRADES Often a mine is constrained by more than one of the limiting factors mentioned in the previous section. If this is the case, the optimum cut-off grade is calculated by balancing the limiting cut-off grades and the maximum capacity for each of the limiting factors. As previously mentioned the time ‘ t ’ becomes  Qm / M ,  Qc / C , or  Qr / R  depending if the mine, the processing plant, or the refinery are limiting output, respectively (2). Setting these ratios equal to each other gives rise to three new cut-off grades called balancing cut-off grades.   If both the mine and processing facility are limiting than cut-off grade  gmc  is the grade that satisfies the equation   QmM= QcC  [9]  Similarly, if the processing plant and the refinery are the limiting factors than  gcr  is the grade that satisfies,   QcC= QrR  [10]  And if the mine and the refinery are both limiting than  gmr  must satisfy,   QmM= QrR  [11] Applying these ratios to the cumulative grade distribution curve, a single point is observed where the proportion of; mineralized material, recoverable mineral per unit of  24 mineralized material, and the recoverable mineral per unit of ore above the corresponding grade equals the balancing ratio  C / M ,  R / M , or  R / C  respectively. A graphical representation of  gmc  is shown in Figure 3.2.    Figure 3.2 Graphical representation of balancing cut-off when the mine and the mill are limiting.   Therefore, six possible cut-off grades must be examined to determine the effective optimum cut-off; three break-even cut-off grades based on the limiting capacity and three balancing cut-offs that are dependent on which capacity(s) are limiting the mining system.   3.2.4 EFFECTIVE OPTIMUM CUT-OFF The optimum cut-off grade is selected from the 6 possible cut-offs discussed thus far. Again, this will be dependent on which areas are limiting the output of the mining Proportion of Mineralized Material Grade Cumulative Grade Distribution for a Mine Planning Increment Ratio C/M =Processing cap./Mining cap. Balancing cut-off grade gmc   25 system. Because the cut-off grade  g  corresponds to the present value  V  of the mine, the optimum cut-off grade can be determined by maximizing the rate of change of  V , with respect to resource usage ( dV / dQ ) (1,2,18). Setting equation [5] equal to the variable  v , which represents the increment in present value per unit of resource utilized, we get     v = S − r( )xyg − xc −m − f + F( )t.   [12]  As with the limiting and balancing cut-offs,  v  takes on three forms depending on which area(s) of the mine are limiting.    Mine        vm = S − r( )xyg − xc −m −f + F( )M  [13]   Mill        vc = S − r( )xyg − x c +f + F( )C⎧⎨⎪⎩⎪⎫⎬⎪⎭⎪−m   [14]   Refinery        vr = S − r −f + F( )R⎧⎨⎪⎩⎪⎫⎬⎪⎭⎪xyg − xc −m   [15]  By plotting  v  as a function cut-off grade, it is observed that the graph is concave with a single maximum. This holds true for all forms of  v . The maximum corresponds to the limiting economic grade for the component being analyzed (1).   26   Figure 3.3 Increment in present value versus cut-off grade with the mine and mill components in balance.  When two forms of  v  are plotted on the same graph as in Figure 3.3, the feasible region (shaded in purple) for the optimum form of  v  called  ve  is always the lower of the two curves. The effective optimum cut-off becomes the maximum point along the feasible  ve  curve. In the example above, the maximum value for  ve  occurs at  gmc  when the mine and the mill are in balance. However, in Figure 3.4 the balancing cut-off is above both the mine and mill limiting cut-offs and the maximum point along the feasible  ve  curve must be located.   In Figure 3.4 the effective optimum grade occurs at the process limiting cut-off  gc , or the median value between the limiting and balancing cut-offs. Lane devised a set of conditions that must be applied to determine the effective optimum cut-off grade at a Increment in Present Value (v) Grade  Effective Optimum Cut-Off Grade v mine v mill gm gc 	gmc Process limiting cut-off Mine limiting cut-off 	Maximum ve  27 single point in time.   Figure 3.4 Increment in present value versus cut-off highlighting the maximum value in the feasible region of  ve  when the mine and the mill are in balance.  When the mine and the processing facility are limiting the effective optimum cut-off grade is,   Gmc = gm   if  gmc < gm      = gc   if  gmc > gc      = gmc   otherwise    When the mine and market are limiting,   Gmr = gm   if  gmr < gm      = gr   if  gmr > gr      = gmr   otherwise    Increment in Present Value (v) Grade Effective Optimum Cut-Off Grade v mine v mill Maximum ve gm gc= Gmc gmc  28 When the mill and market are limiting,   Gcr = gr   if  gcr < gr     = gc   if  gcr > gr     = gcr   otherwise    Identifying the feasible region of  ve  is not always as clear as the examples above. Often all three forms of  v  must be analyzed making it difficult to identify the true maximum. Lane admits that the peaks for the various incremental present value curves are easily identified, however, the exact intersections of the feasible region can be difficult to determine graphically and a more robust method such as the golden search method (19) must be applied.  3.2.5 CUT-OFF POLICY A cut-off grade policy is a sequence of optimum cut-off grades over a specified period of time (1). A cut-off policy serves as a long-term strategy for how much material to mine, process and refine as a function of grade that will maximize the value of a mining project. Similar to determining a single effective optimum cut-off grade for a single point in time, a complete cut-off policy will follow an exploitation track that maximizes the present value of the resource being mined at all times, while adhering to the capacity constraints associated to the mine, the mill and the market. It is therefore necessary to have a mine design including all the major operational and economic parameters in order to determine a complete life of mine (LOM) cut-off policy.   29 A cut-off policy calculation begins with identifying a terminal value for  V . Most often the terminal value will be zero if the policy is for the life of the resource. Next, initial values for  V  are estimated to use in the opportunity cost term    F = δV − dVdT⎛⎝⎜⎞⎠⎟  [16]  and a policy is calculated. Finally, the present value at termination is compared to the specified terminal value. Based on the results, the initial estimates for  V  are adjusted and a new policy is calculated. This iterative approach ultimately returns a solution where the present value at termination is within some tolerance of the terminal value.  As stated earlier, the opportunity cost is the rate of change of present value with respect to time. Therefore, an estimate of this term is the difference between the present value at time  t = 0 , ( V ) and the present value at time  t = t +1, ( W ) for the same amount of remaining resource (1). The  F  term then be rewritten as    F = δV +V −W   [17]  The mathematical iterative process proposed by Lane can be quite complex when fluctuations in prices, costs and other variations in economic parameters are introduced. Consequently, robust cut-off policy calculations are most efficiently performed with a computer.   30 3.2.6 SHORTCOMINGS OF LANE’S METHOD Lane’s method for determining optimal cut-off grades is based on maximizing the present value of cash flows generated from a mine. Lane’s model assumes that a single mine producing a single stream of material is processed by one facility and refined at one facility. Therefore mining complexes with multiple sources and multiple processing streams are difficult to model using Lane’s methods. Another major assumption is that the resource has been defined and a mine schedule has already been determined. However, in practice the mine schedule is based on cut-off grades and Lane’s algorithm thus becomes iterative. Also Lane’s methods fail to capture blending requirements related to processing ore. (20)  In an attempt to resolve the shortcomings associated to Lane’s methods many authors have applied extensions or modifications to the original algorithm (2,5,9,19,21).   3.3 GRADE TONNAGE CURVES The use of grade tonnage data is imperative when analyzing cut-off grade strategy. The grade tonnage curve is a frequency distribution of the amount of mineralized material above a calculated cut-off in a particular deposit. The data often comes directly from a geological block model of the mineralized body of rock created from exploration and definition drilling. A block model is a three dimensional array of minable blocks each containing specific attributes such as density, metal grade and lithology. This data is then used to create a histogram of the tonnages belonging to each grade category. An example of a tonnage histogram is shown in Figure 3.5.  31   Figure 3.5 Simulated tonnage histogram of gold deposit.  Next, the cumulative frequency of tons is calculated where,  n  refers to the individual grade categories and  T  represents the tons of material within those grade categories.    Q = Tnn=0∑    The weighted average grade of those tons is then determined by     g =Tngnn=0∑Tnn=0∑   0 200 400 600 800 1000 1200 Tonnage ('000s)  Grade Categories (g/t) Tonnage Histogram  32 where  gn  represents the average grade of tones with in each grade category  n . Plotting the two functions for  Q  and  g  we obtain a grade tonnage curve, as illustrated in Figure 3.6.  Here, the blue line represents the cumulative tonnage of mineralized material and the red line is the average grade of that material plotted on the primary and secondary y-axis, respectively.   Consider a calculated effective optimum cut-off grade of 4.0 g/t. By inspection of the grade tonnage curve it can be seen that there are 1.7 million tons of ore averaging a grade of ~6 g/t.   Figure 3.6 Sample grade tonnage curve with cut-off grade of 4.0 g/t.  Grade tonnage curves serve as a visual aid in evaluating the exploitation potential of a deposit at several different cut-off grade scenarios. The curve displays the average grade and quantity of ore above a specified cut-off. 0.00 2.00 4.00 6.00 8.00 10.00 12.00  -     1   2   3   4   5   6   7  0 1 2 3 4 5 6 7 8 9 10 Avg. Grade Above Cut-off (g/t) Tons Above Cut-off (Millions) Cut-off Grade (g/t) Grade Tonnage Curve Tons Avg. Grade  33 4 PROCESSING At an open pit mine, mineralized material is excavated and sent either to a waste stockpile or a processing facility to recover the minerals of interest. As previously stated, the determination of ore and waste is based on a calculated cut-off grade. A dynamic cut-off strategy based on Lane’s methods must include the capacities for processing in the derivation of the COG. It is therefore imperative to understand how processing and cut-off grades are related. The following chapter is divided in to two categories. The first section defines modular processing and provides a brief overview of the economic and operating parameters. The second section examines how cut off grades are determined when multiple processing streams are utilized.  4.1 MODULAR PROCESSING Modular mineral processing plants are small, often mobile mineral recovery facilities. They concentrate ore through the use of gravity or flotation. The term “modular” refers to the flexible arrangement offered by the design of the milling unit. Traditional processing plants use large, high-energy consuming comminution circuits housed in a permanently constructed building or facility. These facilities require significant amounts of space and depending on the location of the mine and can have very high construction costs. Modular processing plants were originally designed to process ore underground in an effort to reduce the haulage and energy costs associated with traditional milling (22). The smaller size of the mill also reduces the surface footprint when compared to a conventional mill.    34 Modular processing plants are typically designed to process lower tonnages (10-20 tph) than larger fixed facilities (50-125 tph). However, they have the flexibility of being mobile and the option of adding or removing elements of the circuit as necessary. The system itself is designed in such a way that it can be modified based on the type of ore being processed. For example, a newly developed gold mine with considerable amounts of refractory gold at the surface may use flotation to concentrate the ore. Later on, the ore contains coarser gold that benefits from gravity concentration. These units can be added and/or removed at very little capital cost when compared to a fixed infrastructure.  The flow sheet for a modular processing plant is much the same as a conventional facility using the same recovery method except for the size. An example flow sheet diagram for the Gekko Python underground gravity/flotation plant is presented below. The Python uses coarse and fine crushing, wet screening, continuous gravity concentration and flash flotation to concentrate gold (22).    Figure 4.1 Process flow diagram for the Gecko Python Plant, from (22).  35 This type of mill design can benefit any project that is limited in available space but also benefits projects with multiple ore types and/or with varying grades. The modular processing plant can be used in conjunction with a larger conventional plant when it is required that specific ore be processed using a separate recovery method. Consider an open pit deposit containing predominantly low-grade oxide ore with lesser amounts of higher-grade sulfide rich ore. The mine currently blends and processes all the ore using a 3000 t/d heap leach pad with a carbon in column recovery circuit. Lab testing has determined that the HL recovery method is ideal for the oxide ore resulting in a recovery of ~90%. However, test work on the sulfide ore when run as separate batch, has a recovery of ~30%. With exploratory drilling suggesting more high-grade sulfide rich ore, a new processing stream should be incorporated to maximize the recovery of mineral in the sulfide ore. A modular flotation unit is one such solution.   By incorporating a modular flotation plant the need for blending and stockpiling the different ore types is removed. This reduces operating expenses related to transporting and re-handling the previously mined ore.  4.1.1 CAPITAL AND OPERATING COSTS Although the operating and capital expenses of a modular processing plant are far less than a conventional plant, the exact capital and operating costs are difficult to estimate due to the variability in project location and ore type. Each project requires a different set of modules to obtain maximum recovery from the ore being processed resulting in project specific costs. Sepro Systems of Vancouver reports their 30 tph skid mounted  36 gravity/flotation plants cost approximately $1.2-$1.5 million USD (*Personal Communication, Sepro Systems). Table 1 lists the estimated total operating costs for two sizes of the Gekko Python plant, the P200 and P500, installed in an underground South African gold mine. The P200 and the P500 have annual throughput capacities of 146,000 tons and 360,000 tons, respectively. Unit operating costs range from $8.80-$12.50 USD per ton, depending on the throughput rate (22). The variable operating costs for both the Sepro and Gekko modular processing plants are most sensitive to local labor costs followed by consumables and power consumption.    Table 1 Estimated unit operating costs for the Gekko Python modular processing plant, from (22). Estimated	cost	per	ton,	USD	Summary	 P200	 P500	Labor	 $2.80	 $1.20	Management	 $1.60	 $0.60	Consumables	 $3.30	 $3.30	Reagents	 $0.60	 $0.60	Loader	Hire	 $2.00	 $0.80	Dieses/mains	 $1.50	 $1.50		power				Water	 $0.30	 $0.30	Assaying	 $0.20	 $0.20	Equipment	hire	 $0.10	 $0.10	Other	 $0.10	 $0.10						Total	 $12.50	 $8.70	*This	table	assumes	three	operators	per	shift	and	a	power	cost	of	$US	0.1.kWh.	  Along with Sepro and Gekko, several manufacturers offer modular processing solutions. Westpro, also headquartered in BC and Appropriate Process Technology (APT), based in Johannesburg South Africa construct modular processing units tailored to fit the  37 specific needs of their clients. Typical applications include crushing, grinding, flotation, lime slaking, as well as thickening and filtration circuits. Although several companies offer variations of this technology they all aim to reduce start-up costs, plant installation times, energy requirements and environmental impact.  4.2 MULTIPLE STREAMS As mentioned in the example above, a mine can often have multiple minerals of interest associated to multiple ore types that each requires a specific degree of beneficiation. This challenge is overcome by having multiple processing streams each dedicated to processing a specific ore grade or type. In the context of this research, projects that incorporate heap leaching and floatation recovery methods typically require high tonnages of low-grade material with lesser tonnages of high-grade material. The ore also must be amenable to both processes. This is determined by significant amounts of metallurgical testing. The location of the project also has an impact on whether or not HL and milling can be feasibly utilized. Considerations must be given to environmental concerns, remote locations with little to no infrastructure and the climate where the project is located.   Consider the Ruby Hill mine in NV, USA. The project utilized a closed HLF/milling circuit to process gold ore. Low grade, run of mine (ROM) ore was stacked on a leach pad and higher-grade material was sent to a flotation circuit where the gold was extracted. Tailings from the flotation circuit were then pumped to the HL pad and blended with low-grade ore to be leached again.   38  This process increased the value of the ore being mined by processing it under the correct conditions. This approach also reduced the capital and operating costs inherent to a large processing facility and the necessity of a number of tailings management systems.   Alamos Gold’s Mulatos mine located in Sonora Mexico is another example of a mine benefitting from multiple processing streams. The deposit currently contains ~1.5M oz in reserves and another 3M oz in measured and indicated resources (23). The mill design is able to process 18,000 t/d through an HLF and gravity concentrator. The gravity concentrator processes high-grade material from both the Mulatos mine and ore from the nearby San Carlos project while the HLF handles low-grade crushed ore.  The mine was originally designed to crush and convey 10,000 t/d to a heap. A carbon in column (CIC) absorption circuit would then recover the gold. In 2012 Alamos discovered a new high-grade zone that warranted the construction of a $20M 500-t/d gravity mill.  The high-grade milling stream produces gold concentrate through a gravity concentrator followed by intensive leaching. Similar to the closed system used at the Ruby Hill Mine and the underground modular python plant, the tailings from the gravity circuit are dewatered and conveyed to the leach pad for further processing. This removes the need for tailings ponds and reduces the environmental impact of the project.   Finally, consider New Gold’s Mesquite mine in California. The deposit contains  39 approximately 2.2 million oz of gold in reserves, with 32% of the ore being non-oxide ore (24). The remaining ore is classified as either oxide or transitional between oxide and sulfide. Through heap leaching, the non-oxide ore has a historic recovery of ~35% while the oxide ore has 75% recovery (24). To account for the differences in recovery New Gold applies different cut-off grades to each ore type based on the oxide content. The break-even cut-off is 0.003 oz/t for oxide ore and 0.007 oz/t for non-oxide (24). The higher cut-off applied to non-oxide ore ensures that value of gold recovered will offset the low recovery percentage.  This last example highlights the tradeoff between cut-off grade and processing method. If the total reserves contained more non-oxide ore than oxide ore the processing method would likely be different to maximize the value of the ore. By incorporating a cut-off strategy to match a specific ore type New Gold has added flexibility to their mining and processing methods.   Based on the examples mentioned above the use of multiple processing streams and cut-off strategy play a major role in maximizing the value of a particular ore type. All of the above examples are open pit mines utilizing a low cost low recovery method such as a HLF in addition to a higher cost, higher recovery stream. Here, economies of scale greatly affect the cut-off strategy specifically when considering the mining and processing capacities for these low-grade deposits. With a low cost, low recovery-processing method such as heap leaching, the greater the throughput rate the greater the return.  A large HL operation of ~30,000 t/d (typical in Nevada) has a total operating  40 cost half that of a small 3,000 t/d operation (25). This means that a smaller project may not benefit solely from multiple processing streams and optimizing the cut-off strategy becomes paramount.  4.2.1 CUT-OFF GRADE FOR MULTIPLE PROCESSING STREAMS  BREAK-EVEN METHOD  Under the break-even model, if two process streams are utilized, there will be two cut-off grades  gp1  and  gp2 . These two economic grades tell us a few important aspects about the material to be mined and processed. First, the lower of the two cut-offs ( gp1 ) identifies which material will be considered ore vs. waste. This is similar to when only one process stream is utilized. Material below this grade will either be left in the ground or sent to a waste pile. Second, we can determine which process stream any material deemed ore should be sent to. Ore with an average grade above  gp1  and below  gp2  will be processed at the  Cp1  facility. Ore with an average grade above  gp2  will be processed using the  Cp2  facility, unless the  Cp2  stream is at capacity. This second grade tells us at which grade the material to be processed is economic to recover through more expensive methods.   To help illustrate, Figure 4.2 represents the revenue generated per ton of material processed using two processing streams, a heap leach pad and a mill. The break-even cut-off grade ( gHL ) is shown graphically where the green line crosses the x-axis. At a  41 grade just below 0.10 g/t, the revenue per unit of material processed using HL is equal to the cost of processing that unit. Any material above this grade will be considered ore and will be sent to either the leach pad or the mill. Similarly, the break-even grade for the mill is observed to be approximately 0.15 g/t, where the blue line crosses the x-axis. The mill cut-off ( gCIL ) or “cut-over” grade is where the green and blue lines intersect. At this point the revenue earned from sending ore to the mill exceeds that of sending ore to the leach pad. Here, any material with a grade < ~0.35 g/t should be sent to the HLF and any material with a grade > ~0.35 g/t should be processed at the mill.   Figure 4.2 Cut-off and cutover grade defined by revenue earned per ton of material processed.  It is important to note that the example in Figure 4.2 holds processing capacity the same for each method when in practice the capacities could be very different. For example a typical heap leach operation in Nevada will place 20,000+ tons of ore per day on the heap, while a standard conventional mill may only have a throughput capacity of 1,000 tpd (25). This will have a great impact on the availability to process material in the  $(15)  $(10)  $(5)  $-   $5   $10   $15   $20   $25   $30   $35  Revenue per ton Cut-off Grade (g/t) Revenue per ton from HL and CIL CIL HL gHL  gCIL   42 higher-grade stream and the opportunity costs of sending material to one stream instead of the other must be considered (17).  The break-even approach does not optimize the grade or quantity of ore processed for each stream. It is limited by the fact that deposit geology and capacities for both processing and mining are not considered (5). This results in static calculations that do not reflect what happens in many real world situations. For example, when one stream does not have the capacity to process more material two options are presented. One is to process material using the low recovery stream, while the other is to stockpile the excess material until process capacity becomes available. Simply put, the break-even model fails to optimize cut-off grades given changes in capacity and grade uncertainty.   LANE’S METHOD  The goal in analyzing cut-off grade with multiple process streams using Lane’s method remains the same exercise as when analyzing a system with one stream with a few modifications. First, all equations that include the quantity of ore processed,  Qc , must be changed to the summation of quantities produced from each stream,  Qcpp∑ . This also applies to calculations that include unit-processing costs of production and recoveries.   For situations when more than one of the limiting components to the mining system restricts throughput the model must be expanded to account for all of the limiting factors in order to be in balance. Lane’s method considers the three limiting components in the  43 mining system to be the mine, the mill and the market/refinery. Consider an example proposed by Asad (26) where two economic minerals are present at a mine. The ore is mined and concentrated similar to mine with only one ore type. The ore is then delivered to one of two refineries depending on that ore type. The balancing formula must be changed to include the costs and capacity of both refineries. Therefore four components must be balanced: the mine, the mill, refinery 1 and refinery 2. The same theory holds true when there are multiple mills or even multiple mines. The addition of a mill results in an additional limiting component that must be balanced.               44 5 THE MODEL The objective function is to maximize the NPV of future profits subject to mine, mill and market capacity constraints. The dynamic cut-off model proposed by Lane is used in conjunction with heuristic extensions introduced by Assad and Dimitrakopoulos (2). A block diagram overview of the algorithm used is provided in Figure 5.1 below.                      Read Economic data (unit costs, recovery, prices…) Bring in grade tonnage data  Set V=PV (Initial PV=0) Compute limiting cut-off grade for each process  Compute TO, TW and ĝ for each cut-off grade  Compute Qm, Qcp and Qr  Compute annual profit   Calculate PV Compare PVs for convergenceNO Set year to t+1  YES Adjust the grade tonnage curve  Check if total resource QT=0  YES NO Stop Start Figure 5.1 A block flow diagram for the algorithm used.  45 5.1 ECONOMIC AND OPERATIONAL INPUTS The first step is to enter the economic, operational and grade tonnage parameters. The economic data includes the price of gold, fixed and variable costs and the discount rate. The operational inputs include the grade tonnage data, the mining, milling and refining capacities and the average annual recoveries.   5.1.1 GRADE TONNAGE SIMULATION A grade tonnage curve must be created based on the geologic profile of an ore body. This means that a resource has been defined, the mine has been designed and the ultimate pit limit has been determined.  In this thesis, grade tonnage data was simulated to create a set of random but equally probable grade tonnage curves. This allows for the mitigation of geologic uncertainty inherent to a mining project through the use of Monte Carlo simulation.  Monte Carlo simulation is a form of data analysis used to model the results of a process where one or more uncertain variables must be considered (27). A probability distribution is substituted into the random uncertain variable and the probability of a certain outcome can be determined. Examples of uncertain variables in mining include commodity price and metal grade. These variables both have a large impact on the profitability of a mine but more importantly, they both must be estimated when valuing and planning a mining project.   46 Assuming that the metal grades and tonnages follow a lognormal distribution around a low grade mean, with 80% of the resource being less than 1.0g/t and 20% being above 1.0g/t, a frequency distribution can be constructed. Using a mean and variance for Y, of 1.2 and 5.7, respectively, it is possible to calculate the mean and standard deviation for log (Y).   In terms of µ and σ (the mean and standard deviation), the mean of Y is    mean = eµ+σ22⎛⎝⎜⎞⎠⎟  and the variance is    variance = eσ 2( ) −1⎛⎝⎞⎠ e2µ+σ 2( )   By inverting these formulas it is possible to solve for µ  and σ  as functions of  m  and  v . This allows for the lognormal distribution of grade tonnage data using the known parameters for the normal distribution of log (Y).  A total of 15 grade tonnage curves were created using the simulation methods discussed, resulting in 15 different but equally probable realizations of the hypothetical ore body. This exercise served two purposes. First, that simulated controlled data can be applied to the cut-off model. The second is that by simulating several equally probable realizations of the ore body the resulting cut-off policy and its sensitivity to key parameters can be examined in greater statistical detail.   47 5.2 INITIAL ESTIMATES OF NPV The objective is to maximize NPV through optimum cut-off grade strategy. However, since the calculation for the optimum cut-off grades depends on NPV an iterative mathematical approach is necessary. Therefore, initial estimates for the unknown NPV variable must be made. By Lane’s approach, the opportunity cost associated to mining at a particular cut-off affects the overall NPV of the project. This means an opportunity cost must be included in the calculation for cut-off grade. Looking back at Lane’s theory, opportunity cost ( F ) is the rate of change in present value with respect to time, subtracted from the discounted present value.    F = δV − dVdT⎛⎝⎜⎞⎠⎟   As Lane points out, any estimated value for V is valid as long as the resulting terminal value is zero (or a specified value). If not, the initial estimate must be changed and the process repeated.   For projects with existing production, NPV can be calculated and the estimation process is excluded. For LOM cut-off policies of new projects with no production history an initial NPV estimate of zero is valid for the first iteration (7).   48 5.3 LIMITING CUT-OFF GRADE The calculations for determining the limiting economic cut-off grades are the same as was mentioned in section 2.2.2. Because this thesis is focused on projects constrained by the processing stage of the system it is assumed that the mine and the refinery will never be a bottleneck and balancing cut-off grades do not need to be calculated.    Process Limiting        gp =cp +f + F( )CpS − r( ) * yp  [18]  Here, the subscript p refers to the specific process being analyzed. This means that each process  p , will have its own unit costs, capacities and recovery used to determine the limiting cut-off for that process.  5.4 QUANTITY OF ORE, WASTE AND AVERAGE GRADE Once the limiting economic grade 𝑔! for each process is calculated the quantity of ore 𝑇𝑂, the quantity of waste 𝑇𝑊 and the average grade of ore 𝑔 is determined as a function of 𝑔! .    TOgp( ) = Tnn≥n*∑   [19]    TWgp( ) = Tnn<n*∑   [20]   49   ggp( ) =≥ n *Tng n( ) + g(n +1)2⎛⎝⎜⎞⎠⎟n∑TOgp( )  [21]  Here,  n  refers to the individual grade categories that make up the grade tonnage curve,  T  represents the tons of material within those grade categories and  n*  is the grade category selected as cut-off. The sum of all tons in each grade category above cut-off is denoted as  TOgp( ) . Conversely,  TWgp( )  is the sum of all tons within each grade category below cut-off.  The average grade is used to determine the overall concentration of gold in the ore sent to the processing facility. Here,  ggp( )  is the weighted average grade for the tons included in the grade categories above cut-off.  5.5 QUANTITY MINED, PROCESSED AND REFINED Next, the quantity of material mined, Qm , the quantity of ore processed, Qc  (per processing stream,  p ) and the quantity of ounces refined,  Qr , are computed as a function of the cut-off grade. The variables used in these equations are interrelated and therefore specific conditions must be applied in order to determine the values.    Qcp =TOgp( ) − Δ  if  <Cp + ΔCp         otherwise⎧⎨⎪⎩⎪⎫⎬⎪⎭⎪  [22]  50  Here, Δ  represents the difference between the ratios  TOgp( ) /Tn  for each process. By adding Δ  to the given capacity all annual processing quantities are within the maximum bounds. This variable ensures that maximum utilization of capacity is used and no overlapping of resource exists between the two processing streams.     Qm = Qcpp∑⎡⎣ ⎤⎦ * 1+TWmin  gp( )TOgp( )p∑⎡⎣⎢⎢⎤⎦⎥⎥  [23]  The second half of the  Qm  equation refers to the stripping ratio applied to the ore body. It should be noted that not all cut-off calculations require a stripping ratio, only open pit mines. Underground projects use a calculated dilution % to account for the mixing of ore and waste resulting from the mining process.    Qr = Qcp * g gp( ) * ypp∑   [24]  Here, the quantity refined for the entire mine is equal to the sum quantity of ore processed by each process stream multiplied by the product of the average grade of ore sent to each mill and the average mineral recovery from each processing method, expressed as a percentage.   51 5.6 ANNUAL CASH FLOW AND NPV Once the limiting cut-offs have been computed and the quantities for mining, milling and refining determined, the resulting cash flow can be calculated using equation [25] below. The model proposed here uses periods of 1 year for time considerations.     P = S − r( ) *Qr( )− cpp∑ *Qcp −m *Qm − f   [25]  The next step is to calculate the PV of the remaining resource to identify the value and opportunity cost of using the calculated cut-off grades. First, the remaining life of mine (in years) must be determined based on the quantities of ore calculated in Section 5.4 and the quantity of ore processed as calculated in Section 5.5.     lom =TOmin  gp( )Qcpp∑  [26]  Next, the present value  V  for the remaining resource is calculated using the annual profit  P  and the  lom .    V = P *1− 1+δ( )− lomδ⎡⎣⎢⎢⎤⎦⎥⎥  [27]  This is simply the formula for the present value of an annuity discounted by rate, δ . The resulting  V  is then compared to the initial estimate of  V , call it  ′v , for convergence of  52 ±$500,000. If  V  and  ′v  do not converge,  ′v  is set equal to  V  and the process repeated until convergence.  Once converged, the year is set to  t = t +1 and the grade tonnage curve is adjusted in proportionate amounts so that the overall grade distribution remains unchanged (7,26). This is done by removing waste tons,  Qm − Qcpp∑ , below the minimum optimum cut-off and  Qcpp∑  tons above each optimum cut-off. The iterative process continues until the resource is exhausted, the remaining resource is no longer profitable or a predetermined quantity of material remains.             53 6 HYPOTHETICAL CASE STUDY The model outlined in Chapter 5 was applied to a hypothetical gold mine. The case study was separated into two scenarios, a base case and a modular case in order to compare and contrast the results. Holding all design parameters constant for each scenario, the base case only employs the heap leach facility, while the modular case includes a modular carbon-in-leach plant in addition to the heap leach facility.  6.1 MODEL ASSUMPTIONS AND LIMITATIONS Economic assumptions on price, costs and capacities were determined by industry averages, literary examples and personal experience. For simplicity, prices and costs are held constant in this model. However, adjustments can be made to incorporate stochastic price movements or cost escalation (12,28). The model is suited for an open pit gold mine with one source, one or more processing methods, and one refinery. Figure 6.1 is a flow sheet diagram for the mine system in the modular case with the corresponding capacities.   54   Figure 6.1 Flow sheet diagram for hypothetical gold mine with capacity constraints (modular case).  It was assumed that a defined resource and an ultimate pit limit had been determined. Capital costs were excluded from the model but can be considered as cash out flows when calculating the NPV. As mentioned previously, simulated grade tonnage data was used to account for geologic uncertainty and to serve as the primary data set. The economic and operational design parameters are shown in Table 2 and one realization of the simulated grade tonnage data is shown in Figure 6.2.  The parameters in Table 2 highlight the assumed gold price, variable unit costs, annual fixed costs, and the planned capacities for the mine, both mills and the refinery. Average mill recoveries are listed for both the HLF and CIL plant, while the mine and the refinery were assumed to have a 100% recovery.  Mine  (2,000,000 t/yr) Heap Leach  (500,000 t/yr) Market/Refinery (30,000 oz/yr) Modular Mill (73,000 t/yr) Waste (Unlimited)  55 The project was expected to be operational 365 days a year with a mining capacity of 2 million t/yr and a market/refining capacity of 30,000 oz/yr. These values were chosen purposefully so that the mine and refining capacities would never be limiting factors on output. Unit mining costs were $2.65 per ton and assumed to be the same for both ore and waste. The HLF capacity was very small at just 500,000 t/yr with an average annual recovery of 70%. In the modular case, the CIL plant had a capacity of 73,000 tons per year with an average annual recovery of 90%. Unit costs for the HLF and CIL were estimated based on information provided by (22,25). An annual fixed cost of $1.2 million was also assumed.   Table 2 Mine design parameters for hypothetical gold mine. Parameters Value Units Notation Gold price 1500 C$ S Processing cost CIL 16.65 C$/t cCIL Processing cost HL 6.75 C$/t cHL Mining cost ore & waste 2.65 C$/t m Refining cost 5.00 $/oz r Recovery CIL 90% % yCIL Recovery HL 70% % yHL Processing capacity CIL 73,000 t/yr CCIL Processing capacity HL 500,000 t/yr CHL Mining capacity 2,000,000 t/yr M Refining capacity 30,000 oz/yr R Annual fixed 1,200,000 $/yr fa Discount rate 5% % δ    The simulated ore grade distribution was lognormal with a low-grade skew throughout the mineralized body. The grade tonnage data serves as the sole grade tonnage curve for the entire life of the mine. This is a simplification of real world scenarios where multiple mining phases would each have unique grade tonnage curves that make-up the life of mine plans.  56    Figure 6.2 Grade tonnage distribution GT1 for hypothetical gold mine.  It is important to note that a cut-off policy based on dynamic cut-off grades is most valuable in the pre-feasibility stage. Any adjustments to the long-term plan can potentially be very expensive and are therefore most easily implemented in the early planning stages (17).   6.2 METHOD A set of 15 grade tonnage curves and an optimization model following the algorithm discussed in Section 5 was created using Microsoft Excel. The model was then used to analyze the simulated grade tonnage curves with respect to cut-off grade and production, subject to capacity constraints in order to maximize NPV. Then for each grade tonnage simulation, a complete cut-off policy was created. This process was applied to both the base case and modular scenarios.   -     500   1,000   1,500   2,000  Tons (000's) Grade Categories (g/t) Grade Tonnage Distribution  57 6.2.1 BASE CASE Table 3 shows the complete cut-off policy for one of the simulated grade tonnage curves. Included are the cut-off grade, the quantity of material mined, the quantity of ore processed, the quantity of gold ounces refined and the resulting profits for each year of production. LOM quantities and total NPV are also provided.  Each of the 15 simulated grade tonnage curves was exhausted in year 7 for the base case, with little variability in the quantity of ounces produced. The low variability in production suggests that the variance used in the simulated grade tonnage data was not significant enough to severely affect the results.  It can be seen in Table 3 that cut-off grade declines throughout the life of the project as the resource is exhausted. This is expected based on Lane’s theory of dynamic cut-off grades. The higher cut-offs push revenue forward in the early years of production when cash flows are discounted less, increasing the overall NPV. It is also observed that the quantity of material mined decreases with time. This is due to smaller stripping ratios in later years when the cut-off grade is lower.        58  Table 3 The complete cut-off policy for base case using grade tonnage curve 1 (GT1). Base Case (HL) GT1 Year Qchl Qm Qr ghl Profit NPV 1  500,000   1,640,288   13,225  0.45  $10,849,417   $54,758,653  2  500,000   1,535,354   12,682  0.40  $10,315,553   $43,909,236  3  500,000   1,535,354   12,682  0.40  $10,315,553   $34,084,900  4  500,000   1,407,407   11,976  0.35  $9,599,073   $24,728,389  5  500,000   1,407,407   11,976  0.35  $9,599,073   $16,436,349  6  500,000   1,242,507   11,005  0.30  $8,584,343   $8,539,169  7  141,522   351,684   3,115  0.30  $2,429,743   $1,813,111  Total  3,141,521.77   9,120,000.00   76,659.32     $61,692,753.18   $54,758,653     Table 4 shows the calculated NPV for each of the 15 grade tonnage curves used in the analysis. Based on the results the average NPV for the base case was $55,979,753 with an average undiscounted profit of $63,330,324.     Table 4 Calculated NPVs for both the base and modular scenarios across the set of 15 equally probable simulated grade tonnage curves. NPV SIM# Base Case Modular Case GT1 $54,758,653 $60,852,647 GT2 $54,708,668 $61,314,816 GT3 $57,123,583 $63,509,245 GT4 $58,230,506 $64,866,558 GT5 $53,960,510 $60,034,202 GT6 $59,614,937 $66,216,130 GT10 $58,035,176 $64,947,783 GT11 $52,302,068 $58,321,150 GT12 $57,091,653 $63,498,597 GT13 $56,385,943 $62,804,701 GT14 $56,930,227 $63,338,054 GT15 $52,615,118 $58,809,129     59 6.2.2 MODULAR CASE The trend highlighted in Table 5 shows that, similar to the base case policy for GT1, cut-off grades for both processing streams decline as the resource is exhausted. The additional capacity offered by the modular processing plant results in more material being mined in the early years to maximize utilization which in turn results in a shorter LOM over the base case by one year on average.  The total quantity of ounces produced did not vary significantly across the set of simulated grade tonnage curves. The difference between the minimum and maximum was ~9.5% with an average LOM gold production of 82,000 oz. Compared to the average LOM base case production of 78,000 oz, the additional modular capacity resulted in just a 4% increase in gold production.   For GT1, the total quantity of ore processed decreased slightly by 0.03% from the base case. Consequently, NPV increased by $4.2 million. This indicates that in the modular case more of the resource is being classified as ore, maximizing the overall value of the mineralized material. In the final year for the modular case the HL cut-off is 0.25 g/t, which is in fact equal to the HL limiting cut-off. Compared to a cut-off of 0.30 g/t in the final year of the base case.       60  Table 5 Complete cut-off policy for modular case using GT1. Lane Style, Multiple Streams (HL&CIL) GT1 Year QcCIL QcHL  Qm  Qr gCIL gHL  Profit  NPV 1  73,000   500,000   1,818,320   18,961  1.90 0.50 $17,738,312 $60,852,647 2  73,000   500,000   1,703,197   17,313  1.60 0.45 $15,579,715 $43,114,335 3  73,000   500,000   1,606,857   15,678  1.35 0.40 $13,390,269 $28,276,512 4  73,000   500,000   1,538,810   13,929  1.10 0.35 $10,956,044 $16,131,143 5  73,000   500,000   1,472,055   11,664  0.95 0.30 $7,746,641 $6,666,901 6  7,187   268,446   782,479   3,316  0.75 0.25 $374,870 $293,720  Total  372,187   2,768,446   8,921,718   80,863      $65,785,849 $60,852,647  The addition of extra processing capacity has shown to have an impact on the optimum cut-off grade. Therefore, the reclassification of ore and waste when a modular processing plant is introduced is expected. To better analyze the economic outcome of adding a modular processing plant to process “high grade” material, the combined processing capacity must be equal in both scenarios. Consider the situation presented in Table 6, where the HLF capacity in the base case was equal to the combined capacity of the HLF and CIL in the modular case. Here, the LOM  Qr  was still 4.3% less than the LOM  Qr  in the modular case. This suggests the classification of ore and waste that maximizes NPV is when the available processing capacity is divided into separate streams.    Table 6 Base case cut-off policy when HL has capacity of 573,000 t/yr, for GT1. Base Case (HL) with 573K process capacity (GT1) Year Qchl Qm Qr ghl Profit NPV 1  573,000   1,759,515   14,533  0.40 $11,996,823 $56,691,981 2  573,000   1,759,515   14,533  0.40 $11,996,823 $44,695,158 3  573,000   1,612,889   13,724  0.35 $11,175,737 $33,269,612 4  573,000   1,612,889   13,724  0.35 $11,175,737 $23,132,889 5  573,000   1,423,913   12,611  0.30 $10,012,857 $13,478,866 6  382,806   951,279   8,425  0.30 $6,689,329 $5,241,264                Total  3,247,806   9,120,000   77,552    $63,047,307 $56,691,981  61    Another trend observed is the rate at which the cut-off grades decline. In the base case the HLF stream starts with a lower cut-off in year one compared with the modular case, and slowly declines as the resource is removed. In the modular case the HL stream starts at a higher cut-off and declines more rapidly to offset the higher-grade material being diverted to the CIL plant. This is also a function of the additional capacity introduced by the modular processing plant.   The average NPV over the set of 15 grade tonnage curves was $62,376,084 for the modular case compared to $55,979,753 for the base case. The difference of $6,396,331 represents an 11.43% increase in average NPV over the base case.   Table 7 Complete break-even cut-off policy for modular case using GT1. Break-Even, Multiple Streams (HL&CIL) GT1 Year QcCIL QcHL  Qm  Qr gCIL gHL  Profit  NPV 1  73,000   500,000   917,509   12,173  1.05 0.15 $9,976,981 $56,717,896 2  73,000   500,000   929,075   11,995  1.05 0.15 $9,680,284 $46,740,916 3  73,000   500,000   942,432   11,789  1.05 0.15 $9,336,759 $37,521,597 4  73,000   500,000   958,163   11,545  1.05 0.15 $8,930,248 $29,052,882 5  73,000   500,000   977,181   11,247  1.05 0.15 $8,434,810 $21,338,597 6  73,000   500,000   1,001,037   10,868  1.05 0.15 $7,804,992 $14,399,258 7  73,000   500,000   1,032,685   10,353  1.05 0.15 $6,950,265 $8,283,843 8  44,398   500,000   1,025,134   8,107  1.05 0.15 $4,149,097 $3,097,448 9  -   500,000   990,796   4,927  - 0.15 $164,936 $148,762 10  -   174,602   345,990   1,720  - 0.15 $57,596 $37,127 Total   555,398   4,674,602   9,120,000   94,725      $65,485,969 $56,717,896    When comparing the break-even policy from Table 7 to the “Lane style” dynamic COG policy in Table 5, it is clear that using dynamic cut-off grades improves NPV. In the case  62 of GT1, with all other parameters held constant, the Lane style LOM policy has an NPV of $60.85 million representing a 7% increase over the break-even approach. The most important realization is that by mining more material in the early years of production the value of the resource increases. The tradeoff is in the amount of years the project will be operational. The COG policy determined by the break-even approach results in a 10yr LOM while the COG policy based on Lane’s methods have a 6yr LOM.                63 7 ECONOMIC ANALYSIS 7.1 SENSITIVITY ANALYSIS The parameters analyzed in the sensitivity analysis were chosen due to the expectation of a major impact on the outcome of economic evaluation. The parameters focus on economic and production variations. Parameters analyzed: • Gold Price • Unit operating Costs  • Processing Capacity  The sensitivity calculations were performed on the NPV of the project, by applying a range of variations of ±15% to the base case parameter values on GT13. Aside from NPV, the sensitivity analysis was also used to analyze any changes to the cut-off policy as variations of the parameter values were tested. The complete results are presented in Appendix D. The project is most sensitive to changes in gold price, moderately sensitive to operating costs and relatively insensitive to processing capacity.  Overall the NPV is most sensitive to gold price. NPV increased by 28% from the base case, when gold price was increased 15%. This is common with most mining projects, as the selling price of the commodity dictates how much of the material is considered economic. Mineral grade is another parameter that often has significant effect on NPV.    64 In this research, grade uncertainty was accounted for through the set of 15 ore body simulations. The base case scenario had an average LOM  Qr  of 78,758 oz of gold while the modular case had 81,904 oz. Table 8 is a cumulative list of the annual gold production for the min, max and median grade tonnage curves applied to the modular case. It can be seen that the total amount of gold ounces produced varies by ~9.5% from the min to the max. Although this is largely due to the lack of production in year six of GT2, the difference between the max and median case is ~4%. This reiterates the importance of accounting for grade uncertainty when creating a LOM cut-off policy.   Table 8 Comparison of annual gold production across set of simulated grade tonnage curves. Cumulative Annual Qr (oz) (Modular Case)  Year  Min GT2 Median GT8 Max GT6 1  18,346   18,707   19,239  2  35,980   35,971   36,746  3  52,098   51,707   52,679  4  66,385   65,517   66,805  5  78,041   77,115   79,112  6 -  81,195   85,492  Total  78,041   81,195   85,492     NPV was moderately sensitive to unit processing costs, relative to the other parameters tested. NPV increased by 5% when HL unit operating costs were reduced by 15% representing an increase of $3.2 million in pre tax NPV. Changes to CIL unit operating costs were less sensitive, observing only a 1% increase in NPV when CIL unit costs were reduced by 15%. Table 9 shows that an increase in HL unit costs increased HL COG and decreased CIL COG. It is understandable that as unit processing costs for the HL stream increase, the limiting HL break-even cut-off grade will also increase;  65 essentially reclassifying what is considered ore and waste under the current conditions. The interesting realization comes from the reduction in CIL COG as a result of increases to HL unit costs. This occurs because there is less available tonnage in “higher-grade” grade categories requiring the CIL COG to decrease. The opposite is observed as HL unit costs are decreased.  The NPV was least sensitive to changes in processing capacity. It was observed that a 15% increase in HL and CIL capacity resulted in increases of 3% and 1% respectively, in NPV from the base case. Although these changes had minor effects on NPV, changes to capacity had major effects on cut-off policy.   Similar to changes in unit costs, which determine limiting economic cut-offs, as the capacity for a given process is increased the limiting economic cut-off grade is decreased. This redefines what material is classified as ore and waste within the mineralized body. This holds true for both the HL and CIL streams. Tables 10 and 11 highlight this phenomenon, particularly when HL capacity is increased by 15% from the base case. Here it can be observed that LOM was reduced by a year due to more material being classified as ore.      66  Table 9 Cut-off policy for GT13 showing how an increase in HL unit costs by 5% results in an increase in HL COG and a decrease in CIL COG. 	Year Qccil Qchl  Qm  Qr gcil ghl  P  NPV -10% of Base HL Unit Costs 1  73,000   500,000   1,663,436   18,292  1.95 0.45 $17,483,720 $64,981,022 2  73,000   500,000   1,561,050   16,809  1.70 0.40 $15,536,563 $47,497,302 3  73,000   500,000   1,587,420   15,940  1.45 0.40 $14,167,508 $32,700,576 4  73,000   500,000   1,465,846   13,980  1.20 0.35 $11,559,604 $19,850,228 5  73,000   500,000   1,395,591   12,028  1.00 0.30 $8,828,259 $9,864,608 6  22,158   425,986   1,127,222   6,826  0.80 0.25 $3,320,345 $2,601,577 	   387,158   2,925,986   8,800,565   83,874    $70,895,999 $64,981,022 	 	 	 	 	 	 	 	 	 		1  73,000   500,000   1,778,148   18,896  1.90 0.50 $17,916,307 $63,697,797 -5% of Base HL Unit Costs 2  73,000   500,000   1,658,342   17,330  1.65 0.45 $15,893,146 $45,781,490 3  73,000   500,000   1,573,774   15,744  1.40 0.40 $13,745,744 $30,645,160 4  73,000   500,000   1,475,914   13,904  1.15 0.35 $11,255,482 $18,177,365 5  73,000   500,000   1,414,442   11,863  0.95 0.30 $8,366,836 $8,454,456 6  13,118   352,984   984,552   5,259  0.80 0.25 $2,005,089 $1,571,040   378,118   2,852,984   8,885,172   82,996    $69,182,604 $63,697,797             Table 10. Cut-off policy for base case, GT13. Base HL Capacity Year Qccil Qchl  Qm  Qr gcil ghl  P  NPV 1  73,000   500,000   1,778,148   18,896  1.90 0.50 $17,746,307 $62,804,701 2  73,000   500,000   1,658,342   17,330  1.65 0.45 $15,723,146 $45,058,394 3  73,000   500,000   1,573,774   15,744  1.40 0.40 $13,575,744 $30,083,969 4  73,000   500,000   1,475,914   13,904  1.15 0.35 $11,085,482 $17,770,369 5  73,000   500,000   1,414,442   11,863  0.95 0.30 $8,196,836 $8,194,313 6  14,669   301,410   950,588   4,891  0.80 0.30 $1,851,573 $1,450,756 Total  379,669   2,801,410   8,851,209   82,627    $68,179,088 $62,804,701     Table 11. Cut-off policy for GT13 when HL capacity is increased by +15% of base case values. +15% of Base HL Capacity Year Qccil Qchl   Qm   Qr gcil ghl  P  NPV 1  73,000   575,000   1,881,164   20,257  1.95 0.45 $19,002,414 $64,450,611 2  73,000   575,000   1,768,235   18,581  1.65 0.40 $16,795,803 $45,448,197 3  73,000   575,000   1,614,861   16,434  1.35 0.35 $13,992,438 $29,452,194 4  73,000   575,000   1,549,084   14,660  1.15 0.30 $11,514,403 $16,760,641 5  60,949   575,000   1,604,082   12,446  0.90 0.30 $8,282,541 $6,814,067 Total  352,949   2,875,000   8,417,426   82,377    $69,587,598 $64,450,611      67 It is important to note that due to economies of scale, as process capacity is increased the unit costs will decrease. Kappes (25) points out that operating costs are not very sensitive to the size of a HL operation. In an article on heap leach design and practice he reviewed the cash operating costs of 27 HL operations. Including mining costs, a 3000 t/d operation has a unit cost of $10.12 per ton, a 15,000 t/d has a unit cost of $7.70 per ton and a 30,000 t/d (typical of Nevada) has an operating cost of $5.20 per ton.  Similarities are observed when comparing operating costs for modular CIL units as well. Hughes and Gray (22) determine that barring any changes to power, water and reagent consumption, increased capacity means lower unit operating costs.  The Gekko Python P200, with an annual throughput capacity of 146,000 tons, has an estimated operating cost of $12.10 per ton. While the Python P500, with an annual capacity of 360,000 tons has an operating cost of $8.80 per ton.   For both the HL and modular CIL processing streams the unit labor and management costs become the dominating variable. When capacity is low the utilization of man-hour to processed ton is also low. As capacity is increased, and the demand for labor stays the same overall unit costs will decrease. In practice this may not be the case. For example, in a HL operation if the capacity was doubled certain variable costs would indeed increase such as the unit costs for reagents and haulage costs to transport the additional ore. Other areas of the mine will also be affected including waste disposal and tailings management to handle the extra material.  68 8 CONCLUSIONS The objective of this research was to maximize the value of small-scale, low-grade, open pit homogeneous gold deposits through cut-off grade strategy and modular processing. The NPV for the modular case was on average 11.43% higher than that of the base case. This indicates that by adding process capacity and dividing the ore into separate streams, project value will increase.  The hypothetical case in this research does not consider capital costs. However, this study suggests that an additional modular processing plant to process high grade ore should be introduced if the capital cost is less than the difference between the average NPV calculated for both the base and modular case over the set of 15 simulated grade tonnage curves.  It was demonstrated through a sensitivity analysis that gold price has the greatest influence on NPV and therefore ore/waste classification. When gold price was low, cut-off grades are higher and less material is classified as ore. When gold price is high, optimum cut-off grades are low and more material is classified as ore. The methods used in this research based on Lane’s algorithm, determine the optimal ore/waste classification scheme for any point in time during the life of the mine. This confirms the tactic of altering cut-off grade when commodity prices rise or fall.   The results also demonstrate that an optimum cut-off strategy needs to consider the capacities for the limiting components outlined by Lane, and the opportunity costs of  69 mining at a determined cut-off grade level. A comparison of the NPV obtained via the break-even method and dynamic optimization methods presented here, suggest that by overlooking the capacities and opportunity costs, break-even calculations may lead to sub optimal cut-off grades resulting in underutilized resources and revenue loss. This substantiates that cut-off grades determined by the break-even method are inadequate for maximizing the value of a resource.   Results from the hypothetical case study reveal that a low-grade open pit gold mine will benefit from the use of multiple processing streams when a dynamic cut-off policy is used, particularly, when incorporating a “high grade” milling stream to maximize the potential revenue of the mineralized material. Therefore, a mine with increased processing flexibility has more value than a mine that does not. This means that for a given grade tonnage curve and a set of design and production parameters, the classification of ore and waste is what ultimately determines the NPV of a mining project.         70 9 RECOMMENDATIONS The strategy of utilizing multiple processing streams in which ore and waste are more finely classified must be considered when processing low-grade ore in remote locations. The flexibility offered by modular processing streams allows for a wider range of feasible ore grades and commodity prices than that offered by traditional constructed processing plants. Further development of modular processing technology that allows for designs that can be scaled up to throughput rates similar to conventional facilities will require a more robust cut-off analysis.   Work done in this thesis on optimal cut-off policies for mines with multiple processing plants including a modular stream can be further developed with case studies which closer reflect real world situations. For example, projects that do not have the ability to process material using a HLF can be modeled with multiple modular processing streams. A cut-off policy of this kind will benefit a mining complex with multiple ore types and/or multiple phases each containing a separate grade tonnage curve. In theory, the model will provide the best sequence of extraction based on the determined optimum cut-off grades.   Based on the abundance of extensions and modifications to Lane’s methods, it is conceivable that a combination of these extensions could be compiled into one model. This includes: 1. The ability to analyze underground and open-pit mines containing multiple metals of interest. Because most underground mining techniques are selective the  71 functional forms of  Qm  and  Qc  would need to be defined for a specific underground mine. Barr (12) suggests the quantity of material mined and processed could be discrete functions defined by a series of alternative stope designs.   2. The replacement of deterministic prices and costs with stochastic variables. The use of stochastic variables to forecast commodity prices can be included directly in to the limiting cut-off calculation (step 5.3 of algorithm) and the annual profit calculation (step 5.6 of algorithm). This substitution will allow for improved mine design planning when analyzing mines with longer life spans. The longer the mine will be in production the less reliable deterministic prices become  3. The incorporation of rehabilitation costs into the limiting cut-off grade calculation following the methods proposed by Gholamnejad (6).         72 REFERENCES  1.  Lane KF. The Economic Defenition of Ore: Cut-Off Grades in Theory and Practice. 1st ed. London: Mining Journal Books; 1988.  2.  Asad MWA, Dimitrakopoulos R. A heuristic approach to stochastic cutoff grade optimization for open pit mining complexes with multiple processing streams. Resour Policy [Internet]. Elsevier; 2013;38(4):591–7. Available from: http://dx.doi.org/10.1016/j.resourpol.2013.09.008 3.  Schodde R. Recent trends in gold discovery Recent trends in gold discovery. MinEx Consult Pty Ltd. 2011;(November):22–3.  4.  World Exploration Trends. SNL Metals and Mining. 2016.  5.  Hall B. Cut-off Grades and Optimising the Strategic Mine Plan Cut-off Grades and Optimising the Strategic Mine Plan.  6.  Gholamnejad J. Incorporation of rehabilitation cost into the optimum cut-off grade determination. J South African Inst Min Metall. 2009;109(2):89–94.  7.  Bascetin A, Nieto A. Determination of optimal cut-off grade policy to optimize NPV using a new approach with optimization factor. J South African Inst Min Metall. 2007;107(2):87–94.  8.  Yasrebi AB, Wetherelt A, Foster P, Kennedy G, Kaveh Ahangaran D, Afzal P, et al. Determination of optimised cut-off grade utilising non-linear programming. Arab J Geosci. 2015;8(10):8963–7.  9.  Abdollahisharif J, Bakhtavar E, Anemangely M. Optimal cut-off grade determination based on variable capacities in open-pit mining. J South African Inst Min Metall. 2012;  10.  Asad MWA, Topal E. Net present value maximization model for optimum cut-off grade policy of open pit mining operations. J South African Inst Min Metall. 2011;111(11):741–50.  11.  Breed MF, Heerden D Van. Post-pit optimization strategic 2016. 2016;(March 2015):11–2.  12.  Barr D. Stochastic Dynamic Optimization of Cut-off Grade in Open Pit Mines By. 2012;(April):105.  13.  Thompson M, Barr D. Cut-off grade: A real options analysis. Resour Policy. 2014;42:83–92.  14.  Trigeorgis L. Making Use of Real Options Simple: an Overview and Applications in Flexible/Modular Decision Making. Eng Econ. 2005;50(1):25–53.  15.  Samis M, Martinez L, Davis G a, Whtye JB. Using dynamic DCF and real pption methods for cconomic analysis in NI43-101 technical reports. 2012;1–24.  16.  Taylor HK. General background theory of cut-off grades. Inst Min Metall Trans. 1972;81:A160-179.  17.  Rendu J-M. An introduction to cut-off grade estimation [Internet]. Society for Mining, Metallurgy, and Exploration; 2008 [cited 2017 Apr 19]. 106 p. Available from: https://app.knovel.com/web/toc.v/cid:kpICGE0001/viewerType:toc/root_slug:introduction-cut-off/url_slug:breakeven-cut-off-grade?&issue_id=kpICGE0001 18.  Minnitt RCA. Cut-off grade determination for the maximum value of a small wits- 73 type gold mining operation. J South African Inst Min Metall [Internet]. 2004;104(5):277–83. Available from: http://www.scopus.com/inward/record.url?eid=2-s2.0-3142755671&partnerID=tZOtx3y1 19.  Ataei M, Osanloo M. Determination of optimum cutoff grades of multiple metal deposits by using the Golden Section search method. South African Inst Min Metall. 2003;(October):493–500.  20.  Dagdelen K, Kawahata K. Value creation through strategic mine planning and cutoff-grade optimization. Min Eng. 2008;60(1):39.  21.  Asad MWA, Qureshi MA, Jang H. A review of cut-off grade policy models for open pit mining operations. Resour Policy [Internet]. Elsevier; 2016;49:142–52. Available from: http://dx.doi.org/10.1016/j.resourpol.2016.05.005 22.  Hughes TR, Gray AH. The modular Python processing plant – designed for underground preconcentration. Miner Metall Process. 2010;27(2):89–96.  23.  Project M. Mulatos Project Technical Report Update ( 2012 ). 2012.  24.  Reserves G a S, Judgments CA. Management ’ S Discussion and Analysis for the Year Ended December 31 , 2012 Iew of Cen. 2012;  25.  Kappes DW. Precious Metal Heap Leach Design and Practice. 2002;1–25. Available from: http://www.kcareno.com/pdfs/mpd_heap_leach_desn_and_practice_07apr02.pdf 26.  Asad MWA. Cutoff grade optimization algorithm with stockpiling option for open pit mining operations of two economic minerals. Int J Surf Mining, Reclam Environ. 2005;19(3):176–87.  27.  Harrison RL. Introduction to Monte Carlo Simulation. AIP Conf Proc. 2010;1204:17–21.  28.  Asad MWA. Optimum cut-off grade policy for open pit mining operations through net present value algorithm considering metal price and cost escalation. Eng Comput (Swansea, Wales). 2007;24(7):723–36.       74 APPENDIX A.  Derivation of Lane’s Equations  Derivation of the equations used in this thesis for Lane’s method for determining the maximum present value of a mining operation based on a finite resource, from (18).  The value of the mining operation  V , in the first period, is the cash flow ( Pq ) associated with mining  q  units of material and the present value (PV) of any facility is given by:       V T,Q( ) = Pq + 11+δ( )t V T + t,Q − q( )⎡⎣ ⎤⎦            = Pq + V T + t( )⎡⎣ ⎤⎦ / 1+δ( )t  [XXVIII]  Focusing on the second part of the equation,     V T + t,Q − q( )⎡⎣ ⎤⎦1+δ( )t  Using the Binomial Series expansion,    1+ n( )n ≈ 1+ nn( )   if  n ≪1   The equation is rewritten as:    75   V T + t,Q − q( )1+δ( )t=V T + t,Q − q( ) * 1+δ t( )    Next, using the Taylor Series expansion for two variables for this part of the equation,    V T + t( ) =V T( ) + t dVdT +t 22d 2VdT 2+ ...and   [XXIX]   V Q − q( ) =V Q( )− q dVdQ −q22d 2VdQ2+ ...and   [XXX]  Combining equations [II] and [III],    V T + t,Q − q( ) = V T,Q( ) + t dVdT − qdVdQ⎡⎣⎢⎤⎦⎥ * 1+δ t( )   [XXXI]  Multiplying equation [IV] by  −rt t dVdT⎛⎝⎜⎞⎠⎟≈ 0  and because  −rt  is very small, it means  −rt2  and  −rtq  are extremely small, so they can be ignored and equation [IV] becomes:    V T,Q( )− rtV + t dVdT − qdVdQ  [XXXII]  Substituting equation [V] into equation [I],   76   V T,Q( ) = Pq +V T,Q( )− rtV + t dVdT − qdVdQ  [XXXIII]  After differentiation and cancelling of the common terms on both sides of equation [VI], it can be set equal to 0:   Pq − rtV + t dVdT− q dVdQ= 0   [XXXIV]  Next, equation [VII] is solved for the variables of interest,    q dVdQ= Pq − t δV + dVdT⎛⎝⎜⎞⎠⎟  dVdQ= P − tqδV + dVdT⎛⎝⎜⎞⎠⎟   and if,    F = rV + dVdT⎛⎝⎜⎞⎠⎟  and  τ = tq   the maximum PV of a mining operation based on a finite resource  Q  determined by Lane is,    dVdQ= P − Fτ   [XXXV]   77 APPENDIX B.  Simulated Grade Tonnage Data   Grade tonnage data for the set of 15 simulated grade tonnage curves used in this research is presented in Tables B1-B5 below. The data set includes the tons of material, the average grade of the material and the ounces of gold contained in each grade category.   Table B1 Simulated grade tonnage data for GT1-GT3. 	GT1 GT2 GT3 Grade Category (g/t) Tons Avg Grade (g/t) Contained oz Tons Avg Grade (g/t) Contained oz Tons Avg Grade (g/t) Contained oz 0.00-0.05  1,780,000   0.02   1,362   2,030,000   0.02   1,595   1,790,000   0.02   1,411  0.05-0.10  1,300,000   0.08   3,141   1,370,000   0.07   3,267   1,250,000   0.07   2,867  0.10-0.15  810,000   0.12   3,226   820,000   0.12   3,292   730,000   0.13   3,006  0.15-1.20  640,000   0.18   3,656   600,000   0.18   3,377   620,000   0.17   3,447  0.20-0.25  480,000   0.22   3,435   490,000   0.22   3,517   400,000   0.23   2,936  0.25-0.30  440,000   0.27   3,858   310,000   0.28   2,752   470,000   0.28   4,174  0.30-0.35  430,000   0.33   4,531   390,000   0.33   4,079   360,000   0.32   3,728  0.35-0.40  270,000   0.37   3,247   240,000   0.38   2,922   280,000   0.37   3,365  0.40-0.45  190,000   0.42   2,571   220,000   0.42   2,988   310,000   0.42   4,234  0.45-0.50  180,000   0.48   2,749   300,000   0.47   4,559   210,000   0.47   3,206  0.50-0.55  210,000   0.53   3,552   130,000   0.53   2,200   210,000   0.52   3,535  0.55-0.60  120,000   0.57   2,212   170,000   0.57   3,120   180,000   0.58   3,329  0.60-0.65  220,000   0.63   4,439   90,000   0.63   1,810   90,000   0.62   1,803  0.65-0.70  110,000   0.67   2,382   160,000   0.68   3,478   200,000   0.67   4,284  0.70-0.75  120,000   0.72   2,776   160,000   0.72   3,723   180,000   0.72   4,178  0.75-0.80  110,000   0.78   2,752   80,000   0.77   1,990   110,000   0.78   2,749  0.80-0.85  90,000   0.82   2,386   110,000   0.83   2,928   140,000   0.83   3,724  0.85-0.90  100,000   0.87   2,807   110,000   0.87   3,091   80,000   0.87   2,240  0.90-0.95  90,000   0.92   2,670   90,000   0.93   2,690   110,000   0.93   3,293  0.95-1.00  90,000   0.98   2,841   110,000   0.97   3,434   90,000   0.98   2,835  1.00-1.05  100,000   1.03   3,302   40,000   1.03   1,330   80,000   1.02   2,631  1.05-1.10  90,000   1.08   3,124   40,000   1.09   1,398   100,000   1.07   3,451  1.10-1.15  70,000   1.13   2,549   80,000   1.13   2,902   70,000   1.13   2,554  1.15-1.20  60,000   1.17   2,262   60,000   1.17   2,256   50,000   1.17   1,886  1.20-1.25  50,000   1.23   1,977   30,000   1.22   1,181   50,000   1.23   1,972  1.25-1.30  50,000   1.28   2,051   60,000   1.27   2,452   70,000   1.28   2,873  1.30-1.35  20,000   1.33   853   50,000   1.32   2,118   20,000   1.33   854  1.35-1.40  50,000   1.37   2,208   30,000   1.38   1,327   50,000   1.37   2,209  1.40-1.45  60,000   1.44   2,769   40,000   1.43   1,837   80,000   1.43   3,668  1.45-1.50  30,000   1.47   1,416   30,000   1.48   1,428   30,000   1.46   1,410  1.50-1.55  80,000   1.52   3,911    -      -      -     40,000   1.53   1,964  1.55-1.60  60,000   1.58   3,041   50,000   1.57   2,525   50,000   1.58   2,547  1.60-1.65  20,000   1.63   1,046   20,000   1.62   1,040   50,000   1.64   2,632  1.65-1.70  30,000   1.68   1,620   20,000   1.68   1,079   40,000   1.68   2,157  1.70-1.75  60,000   1.73   3,335   60,000   1.73   3,330   10,000   1.70   548  1.75-1.80  60,000   1.78   3,426   20,000   1.79   1,148   30,000   1.76   1,698  1.80-1.85  20,000   1.83   1,176   10,000   1.82   586   40,000   1.81   2,333  1.85-1.90  30,000   1.88   1,809   30,000   1.89   1,821   50,000   1.88   3,015  1.90-1.95   -      -      -     20,000   1.92   1,237   20,000   1.92   1,237   78 1.95-2.00  10,000   1.96   631   30,000   1.98   1,910   30,000   1.98   1,911  2.00-2.05  10,000   2.04   655   40,000   2.03   2,610   80,000   2.02   5,197  2.05-2.10  50,000   2.07   3,332   10,000   2.08   668   20,000   2.08   1,335  2.10-2.15  20,000   2.14   1,379   40,000   2.12   2,731    -      -      -    2.15-2.20  10,000   2.19   704   10,000   2.20   707   50,000   2.17   3,482  2.20-2.25  20,000   2.24   1,439   40,000   2.22   2,854   50,000   2.24   3,593  2.25-2.30  40,000   2.27   2,917   50,000   2.28   3,665   10,000   2.27   731  2.30-2.35  20,000   2.33   1,498   20,000   2.33   1,498   40,000   2.32   2,981  2.35-2.40  10,000   2.35   757   60,000   2.37   4,566   10,000   2.37   762  2.40-2.45  10,000   2.42   779   40,000   2.43   3,123   20,000   2.43   1,565  2.45-2.50  20,000   2.47   1,591   30,000   2.48   2,388   10,000   2.48   798  2.50-2.55  40,000   2.53   3,259   10,000   2.51   806   10,000   2.53   814  2.55-2.60   -      -      -     60,000   2.58   4,968   20,000   2.58   1,659  2.60-2.65  20,000   2.62   1,684   10,000   2.64   848   10,000   2.63   844  2.65-2.70  20,000   2.67   1,719   20,000   2.67   1,714   30,000   2.68   2,587  2.70-2.75  10,000   2.73   877   10,000   2.74   882   10,000   2.70   869  2.75-2.80  30,000   2.78   2,684   10,000   2.75   885    -      -      -    2.80-2.85   -      -      -     20,000   2.83   1,820   10,000   2.81   903  2.85-2.90  10,000   2.87   923    -      -      -     10,000   2.89   928  2.90-2.95  10,000   2.95   948    -      -      -     10,000   2.91   935  2.95-3.00  40,000   2.98   3,829   20,000   2.97   1,908   10,000   2.96   953  Total  9,120,000     134,070   9,200,000     132,354   9,180,000     138,831      Table B2 Simulated grade tonnage data for GT4-GT6.  GT4 GT5 GT6 Grade Category (g/t) Tons Avg Grade (g/t) Contained oz Tons Avg Grade (g/t) Contained oz Tons Avg Grade (g/t) Contained oz 0.00-0.05  1,670,000   0.02   1,248   1,710,000   0.02   1,333   1,760,000   0.03   1,512  0.05-0.10  1,410,000   0.07   3,352   1,190,000   0.07   2,753   1,200,000   0.07   2,763  0.10-0.15  780,000   0.12   3,043   950,000   0.12   3,760   720,000   0.12   2,818  0.15-1.20  620,000   0.17   3,475   690,000   0.17   3,823   700,000   0.17   3,913  0.20-0.25  500,000   0.23   3,627   490,000   0.23   3,578   610,000   0.22   4,411  0.25-0.30  330,000   0.27   2,902   450,000   0.27   3,946   370,000   0.27   3,241  0.30-0.35  360,000   0.33   3,767   420,000   0.33   4,431   310,000   0.32   3,222  0.35-0.40  220,000   0.37   2,642   280,000   0.37   3,348   330,000   0.38   4,003  0.40-0.45  220,000   0.42   2,984   270,000   0.42   3,676   210,000   0.43   2,893  0.45-0.50  210,000   0.47   3,181   250,000   0.48   3,823   260,000   0.47   3,964  0.50-0.55  230,000   0.52   3,866   210,000   0.52   3,544   190,000   0.53   3,221  0.55-0.60  240,000   0.58   4,439   190,000   0.58   3,520   120,000   0.58   2,219  0.60-0.65  150,000   0.63   3,021   210,000   0.62   4,190   110,000   0.62   2,196  0.65-0.70  90,000   0.67   1,942   70,000   0.67   1,517   100,000   0.68   2,176  0.70-0.75  90,000   0.72   2,093   100,000   0.72   2,329   130,000   0.73   3,031  0.75-0.80  90,000   0.77   2,242   50,000   0.77   1,233   190,000   0.77   4,698  0.80-0.85  130,000   0.83   3,454   160,000   0.82   4,216   70,000   0.82   1,843  0.85-0.90  140,000   0.88   3,943   50,000   0.88   1,409   100,000   0.87   2,804  0.90-0.95  100,000   0.92   2,970   130,000   0.93   3,882   100,000   0.91   2,935  0.95-1.00  100,000   0.96   3,097   40,000   0.98   1,261   80,000   0.97   2,507  1.00-1.05  60,000   1.03   1,990   80,000   1.02   2,635   130,000   1.02   4,275  1.05-1.10  70,000   1.07   2,403   50,000   1.08   1,728   20,000   1.07   691  1.10-1.15  90,000   1.12   3,247   80,000   1.12   2,885   90,000   1.13   3,258  1.15-1.20  90,000   1.16   3,365   80,000   1.18   3,038   100,000   1.17   3,757  1.20-1.25  70,000   1.23   2,765   70,000   1.23   2,759   80,000   1.22   3,147  1.25-1.30  50,000   1.27   2,035   80,000   1.28   3,290   50,000   1.27   2,036  1.30-1.35  20,000   1.32   849   50,000   1.34   2,149   90,000   1.31   3,796  1.35-1.40  40,000   1.37   1,766   50,000   1.37   2,198   70,000   1.37   3,092  1.40-1.45  50,000   1.43   2,299   70,000   1.42   3,194   50,000   1.42   2,278  1.45-1.50  50,000   1.48   2,378   40,000   1.47   1,893   30,000   1.48   1,424  1.50-1.55  60,000   1.52   2,933   40,000   1.53   1,964   60,000   1.52   2,934  1.55-1.60  40,000   1.57   2,020   40,000   1.57   2,018   50,000   1.57   2,523  1.60-1.65  90,000   1.63   4,709   40,000   1.63   2,097   50,000   1.63   2,624  1.65-1.70  10,000   1.66   534   20,000   1.67   1,072   20,000   1.67   1,074  1.70-1.75  50,000   1.73   2,785   30,000   1.73   1,668   40,000   1.71   2,197   79 1.75-1.80  30,000   1.77   1,706   30,000   1.76   1,695   70,000   1.78   3,995  1.80-1.85  30,000   1.83   1,768   30,000   1.81   1,743   40,000   1.82   2,345  1.85-1.90  30,000   1.89   1,821   60,000   1.88   3,619   30,000   1.88   1,811  1.90-1.95  30,000   1.93   1,861   10,000   1.92   617   20,000   1.93   1,238  1.95-2.00  40,000   1.97   2,537    -      -      -     20,000   1.95   1,257  2.00-2.05  30,000   2.01   1,943   30,000   2.03   1,954   40,000   2.01   2,589  2.05-2.10  10,000   2.10   674   50,000   2.08   3,338   10,000   2.06   662  2.10-2.15  30,000   2.13   2,058   30,000   2.13   2,053   20,000   2.14   1,379  2.15-2.20  30,000   2.16   2,083   50,000   2.19   3,518   30,000   2.17   2,097  2.20-2.25  10,000   2.24   721    -      -      -     20,000   2.22   1,426  2.25-2.30  10,000   2.27   729   40,000   2.29   2,939   20,000   2.27   1,462  2.30-2.35  10,000   2.32   745   20,000   2.32   1,495   40,000   2.33   2,995  2.35-2.40  20,000   2.39   1,540    -      -      -     10,000   2.37   762  2.40-2.45  50,000   2.43   3,909   20,000   2.42   1,553   10,000   2.44   786  2.45-2.50  10,000   2.46   791   20,000   2.46   1,584   20,000   2.48   1,595  2.50-2.55  40,000   2.52   3,237   20,000   2.51   1,611   20,000   2.52   1,622  2.55-2.60  20,000   2.55   1,643   10,000   2.57   825   10,000   2.57   827  2.60-2.65  40,000   2.62   3,375    -      -      -      -      -      -    2.65-2.70  20,000   2.65   1,706   30,000   2.67   2,574   40,000   2.68   3,444  2.70-2.75   -      -      -     40,000   2.72   3,501   10,000   2.74   882  2.75-2.80   -      -      -     10,000   2.75   885    -      -      -    2.80-2.85  20,000   2.83   1,820    -      -      -     40,000   2.81   3,614  2.85-2.90  20,000   2.87   1,846   10,000   2.89   928    -      -      -    2.90-2.95   -      -      -     10,000   2.95   947   30,000   2.94   2,832  2.95-3.00  20,000   2.96   1,904   20,000   2.99   1,923   20,000   2.98   1,916  Total  9,070,000     137,778   9,270,000     135,460   9,160,000     141,015      Table B3 Simulated grade tonnage data for GT7-GT9.  GT7 GT8 GT9 Grade Category (g/t) Tons Avg Grade (g/t) Contained oz Tons Avg Grade (g/t) Contained oz Tons Avg Grade (g/t) Contained oz 0.00-0.05  1,840,000   0.02   1,399   1,840,000   0.02   1,378   1,790,000   0.03   1,496  0.05-0.10  1,070,000   0.07   2,532   950,000   0.07   2,212   1,230,000   0.07   2,876  0.10-0.15  840,000   0.13   3,393   940,000   0.12   3,677   800,000   0.12   3,122  0.15-1.20  790,000   0.18   4,449   710,000   0.17   3,984   670,000   0.17   3,729  0.20-0.25  440,000   0.22   3,151   570,000   0.22   4,096   520,000   0.22   3,756  0.25-0.30  390,000   0.27   3,405   410,000   0.27   3,605   460,000   0.27   4,054  0.30-0.35  330,000   0.33   3,449   340,000   0.33   3,607   370,000   0.32   3,841  0.35-0.40  270,000   0.37   3,244   330,000   0.37   3,968   340,000   0.37   4,095  0.40-0.45  220,000   0.42   2,972   190,000   0.43   2,596   270,000   0.43   3,707  0.45-0.50  280,000   0.47   4,265   190,000   0.47   2,894   230,000   0.48   3,524  0.50-0.55  100,000   0.53   1,699   200,000   0.53   3,392   240,000   0.52   4,020  0.55-0.60  230,000   0.58   4,265   150,000   0.58   2,779   160,000   0.58   3,000  0.60-0.65  140,000   0.62   2,812   200,000   0.62   4,007   90,000   0.63   1,826  0.65-0.70  140,000   0.68   3,063   130,000   0.67   2,799   140,000   0.67   3,021  0.70-0.75  110,000   0.73   2,575   90,000   0.72   2,093   60,000   0.73   1,414  0.75-0.80  80,000   0.78   1,997   150,000   0.78   3,757   100,000   0.77   2,476  0.80-0.85  110,000   0.83   2,924   110,000   0.82   2,912   100,000   0.83   2,662  0.85-0.90  120,000   0.87   3,355   120,000   0.88   3,387   40,000   0.87   1,119  0.90-0.95  150,000   0.92   4,446   90,000   0.93   2,695   140,000   0.93   4,187  0.95-1.00  110,000   0.97   3,447   130,000   0.97   4,061   90,000   0.98   2,824  1.00-1.05  60,000   1.04   2,000   100,000   1.03   3,306   110,000   1.02   3,617  1.05-1.10  70,000   1.08   2,427   50,000   1.07   1,717   90,000   1.07   3,090  1.10-1.15  110,000   1.12   3,975   60,000   1.13   2,181   70,000   1.13   2,541  1.15-1.20  70,000   1.17   2,642   90,000   1.17   3,397   10,000   1.15   370  1.20-1.25  100,000   1.21   3,899   30,000   1.24   1,194   110,000   1.23   4,337  1.25-1.30  60,000   1.28   2,467   70,000   1.28   2,879   10,000   1.26   406  1.30-1.35  30,000   1.33   1,288   30,000   1.32   1,276   60,000   1.32   2,547  1.35-1.40  30,000   1.36   1,308   40,000   1.38   1,769   70,000   1.37   3,093  1.40-1.45  40,000   1.43   1,843   70,000   1.42   3,202   60,000   1.41   2,727  1.45-1.50  80,000   1.47   3,786   40,000   1.47   1,885   50,000   1.47   2,359  1.50-1.55  50,000   1.53   2,453   20,000   1.52   978   20,000   1.53   982  1.55-1.60  30,000   1.57   1,510   20,000   1.56   1,006   60,000   1.58   3,057  1.60-1.65  50,000   1.63   2,625   20,000   1.64   1,055   30,000   1.62   1,558   80 1.65-1.70  40,000   1.67   2,151   30,000   1.68   1,617   90,000   1.68   4,860  1.70-1.75  10,000   1.74   559   20,000   1.72   1,105   30,000   1.72   1,655  1.75-1.80  50,000   1.78   2,854   50,000   1.77   2,845   30,000   1.78   1,717  1.80-1.85  30,000   1.82   1,752   30,000   1.82   1,756   60,000   1.84   3,550  1.85-1.90  10,000   1.87   601   20,000   1.88   1,211   20,000   1.88   1,207  1.90-1.95  30,000   1.91   1,845   30,000   1.93   1,860    -      -      -    1.95-2.00  10,000   2.00   642   40,000   1.97   2,534    -      -      -    2.00-2.05  50,000   2.03   3,256   20,000   2.01   1,294   20,000   2.02   1,299  2.05-2.10  10,000   2.06   662   30,000   2.07   2,001   10,000   2.05   660  2.10-2.15  20,000   2.11   1,359   20,000   2.13   1,371   20,000   2.12   1,360  2.15-2.20  20,000   2.16   1,387   20,000   2.17   1,392   50,000   2.19   3,517  2.20-2.25   -      -      -     20,000   2.21   1,422   20,000   2.22   1,429  2.25-2.30  20,000   2.26   1,456   40,000   2.29   2,940   20,000   2.28   1,466  2.30-2.35  10,000   2.33   750   30,000   2.31   2,230   30,000   2.34   2,259  2.35-2.40  70,000   2.37   5,340   10,000   2.39   768   20,000   2.38   1,528  2.40-2.45   -      -      -     40,000   2.41   3,104   10,000   2.42   779  2.45-2.50  10,000   2.49   800    -      -      -     20,000   2.47   1,588  2.50-2.55  20,000   2.53   1,624   30,000   2.52   2,432   20,000   2.51   1,617  2.55-2.60  10,000   2.56   823    -      -      -     20,000   2.58   1,656  2.60-2.65  10,000   2.60   836    -      -      -      -      -      -    2.65-2.70  20,000   2.69   1,727   10,000   2.66   857   30,000   2.68   2,584  2.70-2.75  20,000   2.72   1,751   10,000   2.71   873   20,000   2.71   1,743  2.75-2.80  30,000   2.78   2,682   20,000   2.79   1,797   20,000   2.77   1,784  2.80-2.85  20,000   2.81   1,810   30,000   2.82   2,721   10,000   2.84   913  2.85-2.90  40,000   2.88   3,709   10,000   2.88   924    -      -      -    2.90-2.95  30,000   2.91   2,806   20,000   2.94   1,892   10,000   2.90   933  2.95-3.00  10,000   2.99   960   40,000   2.98   3,831   10,000   2.97   954  Total  9,140,000     139,204   9,100,000     134,519   9,180,000     132,492      Table B4 Simulated grade tonnage data for GT10-GT12.  GT10 GT11 GT12 Grade Category (g/t) Tons Avg Grade (g/t) Contained oz Tons Avg Grade (g/t) Contained oz Tons Avg Grade (g/t) Contained oz 0.00-0.05  1,820,000   0.02   1,358   1,860,000   0.03   1,507   1,900,000   0.02   1,447  0.05-0.10  1,150,000   0.07   2,706   1,170,000   0.07   2,725   1,250,000   0.07   2,874  0.10-0.15  810,000   0.12   3,218   1,040,000   0.12   4,039   770,000   0.12   3,093  0.15-1.20  690,000   0.18   3,911   690,000   0.17   3,792   770,000   0.17   4,221  0.20-0.25  460,000   0.22   3,290   500,000   0.23   3,653   490,000   0.22   3,522  0.25-0.30  440,000   0.27   3,852   380,000   0.27   3,340   380,000   0.28   3,380  0.30-0.35  300,000   0.33   3,141   320,000   0.33   3,372   290,000   0.32   3,002  0.35-0.40  370,000   0.38   4,512   210,000   0.37   2,527   240,000   0.37   2,875  0.40-0.45  160,000   0.43   2,187   280,000   0.42   3,816   280,000   0.43   3,859  0.45-0.50  160,000   0.48   2,458   210,000   0.48   3,209   300,000   0.47   4,551  0.50-0.55  250,000   0.52   4,182   130,000   0.52   2,155   190,000   0.53   3,211  0.55-0.60  300,000   0.58   5,562   190,000   0.57   3,502   150,000   0.57   2,753  0.60-0.65  220,000   0.62   4,401   170,000   0.62   3,393   190,000   0.63   3,828  0.65-0.70  150,000   0.68   3,276   120,000   0.67   2,580   140,000   0.67   3,003  0.70-0.75  90,000   0.73   2,110   110,000   0.72   2,548   120,000   0.72   2,787  0.75-0.80  70,000   0.78   1,750   130,000   0.78   3,267   110,000   0.78   2,751  0.80-0.85  150,000   0.83   4,000   150,000   0.82   3,953   70,000   0.83   1,865  0.85-0.90  90,000   0.88   2,545   150,000   0.87   4,202   70,000   0.87   1,967  0.90-0.95  110,000   0.93   3,285   50,000   0.93   1,497   60,000   0.93   1,790  0.95-1.00  50,000   0.96   1,550   80,000   0.97   2,484   90,000   0.98   2,846  1.00-1.05  50,000   1.02   1,641   110,000   1.02   3,619   60,000   1.04   1,997  1.05-1.10  70,000   1.08   2,421   60,000   1.08   2,090   50,000   1.08   1,733  1.10-1.15  50,000   1.12   1,808   70,000   1.12   2,527   50,000   1.11   1,790  1.15-1.20  50,000   1.17   1,875   40,000   1.18   1,512   50,000   1.17   1,888  1.20-1.25  100,000   1.22   3,932   80,000   1.22   3,148   20,000   1.23   791  1.25-1.30  50,000   1.27   2,049   70,000   1.28   2,879   20,000   1.27   817  1.30-1.35  20,000   1.33   855   70,000   1.32   2,967   40,000   1.32   1,696  1.35-1.40  40,000   1.37   1,757   50,000   1.38   2,217   30,000   1.37   1,323  1.40-1.45  80,000   1.43   3,666   60,000   1.42   2,746   30,000   1.43   1,381  1.45-1.50  80,000   1.47   3,790   50,000   1.48   2,381   30,000   1.47   1,416  1.50-1.55  50,000   1.53   2,452   70,000   1.52   3,426   30,000   1.53   1,474   81 1.55-1.60  30,000   1.57   1,519   40,000   1.58   2,031   80,000   1.58   4,062  1.60-1.65  20,000   1.62   1,041   50,000   1.63   2,621   40,000   1.62   2,083  1.65-1.70  70,000   1.68   3,772   60,000   1.67   3,225   40,000   1.67   2,143  1.70-1.75  20,000   1.73   1,112   20,000   1.72   1,104   50,000   1.72   2,771  1.75-1.80  20,000   1.77   1,140   10,000   1.79   576   20,000   1.77   1,138  1.80-1.85  50,000   1.83   2,949   30,000   1.81   1,741   40,000   1.83   2,352  1.85-1.90  20,000   1.87   1,204   10,000   1.88   604   50,000   1.88   3,028  1.90-1.95  20,000   1.92   1,232    -      -      -     50,000   1.93   3,109  1.95-2.00  10,000   1.99   640   20,000   1.99   1,277   20,000   1.98   1,274  2.00-2.05  10,000   2.03   651   40,000   2.03   2,606   50,000   2.03   3,261  2.05-2.10  20,000   2.07   1,332   20,000   2.07   1,331   10,000   2.06   661  2.10-2.15  20,000   2.13   1,370   40,000   2.12   2,731   50,000   2.13   3,424  2.15-2.20  40,000   2.16   2,782   20,000   2.17   1,394   30,000   2.17   2,097  2.20-2.25   -      -      -     30,000   2.22   2,142   30,000   2.23   2,147  2.25-2.30  20,000   2.25   1,449   30,000   2.28   2,201    -      -      -    2.30-2.35  30,000   2.32   2,236   20,000   2.31   1,487   30,000   2.31   2,227  2.35-2.40  10,000   2.36   759   10,000   2.40   771   40,000   2.37   3,043  2.40-2.45  30,000   2.43   2,340    -      -      -     20,000   2.43   1,561  2.45-2.50  50,000   2.47   3,967   30,000   2.48   2,397   30,000   2.49   2,405  2.50-2.55  10,000   2.52   809   10,000   2.51   807   20,000   2.54   1,631  2.55-2.60  10,000   2.59   833   20,000   2.57   1,655   40,000   2.58   3,315  2.60-2.65  40,000   2.63   3,380   20,000   2.62   1,686    -      -      -    2.65-2.70  10,000   2.68   860    -      -      -     20,000   2.69   1,732  2.70-2.75  10,000   2.72   876   10,000   2.72   876    -      -      -    2.75-2.80   -      -      -     10,000   2.76   887   20,000   2.77   1,781  2.80-2.85  10,000   2.84   914   30,000   2.81   2,714   10,000   2.84   912  2.85-2.90  50,000   2.88   4,629    -      -      -     30,000   2.86   2,759  2.90-2.95  30,000   2.92   2,815    -      -      -     10,000   2.94   944  2.95-3.00  30,000   2.98   2,876   20,000   2.96   1,903   40,000   2.96   3,804  Total  9,170,000     139,027   9,270,000     131,838   9,140,000     135,597      Table B5 Simulated grade tonnage data for GT13-GT15.  GT13 GT14 GT15 Grade Category (g/t) Tons Avg Grade (g/t) Contained oz Tons Avg Grade (g/t) Contained oz Tons Avg Grade (g/t) Contained oz 0.00-0.05  1,720,000   0.02   1,310   1,700,000   0.02   1,283   1,730,000   0.02   1,295  0.05-0.10  1,200,000   0.07   2,822   1,320,000   0.07   3,080   1,230,000   0.07   2,937  0.10-0.15  970,000   0.12   3,872   790,000   0.13   3,192   850,000   0.12   3,400  0.15-1.20  750,000   0.17   4,156   840,000   0.17   4,689   670,000   0.17   3,734  0.20-0.25  470,000   0.22   3,365   510,000   0.23   3,738   500,000   0.23   3,619  0.25-0.30  320,000   0.28   2,830   380,000   0.27   3,341   420,000   0.28   3,742  0.30-0.35  330,000   0.33   3,467   350,000   0.33   3,672   470,000   0.33   4,919  0.35-0.40  320,000   0.37   3,831   280,000   0.37   3,360   190,000   0.37   2,268  0.40-0.45  200,000   0.42   2,726   250,000   0.43   3,449   280,000   0.42   3,812  0.45-0.50  240,000   0.47   3,660   210,000   0.48   3,207   210,000   0.48   3,218  0.50-0.55  170,000   0.53   2,879   180,000   0.53   3,046   240,000   0.52   4,050  0.55-0.60  220,000   0.57   4,066   200,000   0.58   3,700   220,000   0.58   4,086  0.60-0.65  150,000   0.62   3,000   150,000   0.63   3,029   130,000   0.62   2,602  0.65-0.70  110,000   0.68   2,395   110,000   0.67   2,372   50,000   0.67   1,076  0.70-0.75  170,000   0.73   3,990   160,000   0.72   3,711   180,000   0.72   4,185  0.75-0.80  110,000   0.78   2,750   100,000   0.78   2,502   90,000   0.77   2,239  0.80-0.85  160,000   0.83   4,255   80,000   0.83   2,127   110,000   0.83   2,925  0.85-0.90  80,000   0.88   2,256   80,000   0.88   2,254   100,000   0.88   2,838  0.90-0.95  40,000   0.92   1,180   80,000   0.92   2,373   110,000   0.93   3,286  0.95-1.00  70,000   0.99   2,220   110,000   0.98   3,457   110,000   0.97   3,440  1.00-1.05  100,000   1.03   3,309   120,000   1.03   3,965   70,000   1.01   2,281  1.05-1.10  100,000   1.07   3,443   30,000   1.07   1,029   90,000   1.08   3,112  1.10-1.15  70,000   1.14   2,555   80,000   1.12   2,880   80,000   1.13   2,908  1.15-1.20  50,000   1.18   1,895   60,000   1.17   2,262   110,000   1.17   4,145  1.20-1.25  70,000   1.23   2,769   70,000   1.23   2,766   30,000   1.22   1,179  1.25-1.30  30,000   1.27   1,222   30,000   1.29   1,247   70,000   1.27   2,864  1.30-1.35  20,000   1.33   854   40,000   1.33   1,712   70,000   1.33   3,001  1.35-1.40  80,000   1.38   3,542   90,000   1.37   3,960   70,000   1.37   3,079  1.40-1.45  90,000   1.43   4,127   20,000   1.43   920   50,000   1.43   2,295  1.45-1.50  30,000   1.49   1,435   50,000   1.48   2,378   40,000   1.48   1,909   82 1.50-1.55  40,000   1.52   1,952   80,000   1.53   3,925   30,000   1.53   1,472  1.55-1.60  40,000   1.56   2,012   50,000   1.57   2,526   20,000   1.59   1,021  1.60-1.65  30,000   1.64   1,577   30,000   1.63   1,574   30,000   1.63   1,573  1.65-1.70  10,000   1.65   532   20,000   1.68   1,079   30,000   1.68   1,623  1.70-1.75  30,000   1.72   1,663   10,000   1.71   549   20,000   1.71   1,100  1.75-1.80  30,000   1.78   1,712   50,000   1.78   2,855   40,000   1.76   2,268  1.80-1.85  40,000   1.83   2,351   10,000   1.84   593   50,000   1.83   2,939  1.85-1.90  60,000   1.88   3,634   40,000   1.87   2,406   10,000   1.88   603  1.90-1.95  40,000   1.93   2,480   40,000   1.92   2,475   80,000   1.93   4,956  1.95-2.00  10,000   1.97   634   10,000   1.97   634   10,000   2.00   641  2.00-2.05  10,000   2.00   643   30,000   2.02   1,944   10,000   2.04   657  2.05-2.10   -      -      -     10,000   2.09   673   10,000   2.06   663  2.10-2.15  20,000   2.14   1,378   40,000   2.12   2,726   10,000   2.15   691  2.15-2.20  10,000   2.15   692   20,000   2.18   1,401   30,000   2.16   2,086  2.20-2.25  10,000   2.23   717   20,000   2.23   1,435   30,000   2.22   2,144  2.25-2.30  30,000   2.26   2,178   10,000   2.25   724   30,000   2.28   2,196  2.30-2.35  20,000   2.31   1,483   60,000   2.33   4,486   10,000   2.34   751  2.35-2.40  60,000   2.36   4,559   20,000   2.35   1,512   20,000   2.39   1,534  2.40-2.45  40,000   2.41   3,104   30,000   2.43   2,346    -      -      -    2.45-2.50  40,000   2.48   3,186   30,000   2.47   2,383    -      -      -    2.50-2.55  30,000   2.52   2,431   10,000   2.54   818   20,000   2.52   1,619  2.55-2.60  30,000   2.57   2,477   30,000   2.58   2,485   20,000   2.57   1,654  2.60-2.65  20,000   2.61   1,680   40,000   2.61   3,353   20,000   2.60   1,673  2.65-2.70  10,000   2.66   856    -      -      -     20,000   2.68   1,721  2.70-2.75  30,000   2.72   2,625    -      -      -     10,000   2.70   868  2.75-2.80   -      -      -     20,000   2.76   1,775    -      -      -    2.80-2.85   -      -      -     10,000   2.84   912   20,000   2.83   1,821  2.85-2.90  10,000   2.86   918   20,000   2.88   1,851   20,000   2.87   1,844  2.90-2.95  10,000   2.91   935   20,000   2.93   1,885   10,000   2.93   943  2.95-3.00  20,000   3.00   1,927   20,000   2.97   1,909   20,000   2.96   1,905  Total  9,170,000     136,521   9,250,000     137,935   9,200,000     133,405                   83 APPENDIX C.  Cut-off Policy Results Calculated complete cut-off policy for each simulated grade tonnage curve including annual  Qm ,  Qr ,  Qc  and cut-off grade (for each process), profit and cumulative NPV. Results for both the modular and base case scenarios are presented in Table C1 and Table C2, respectively.   Table C1 Modular case LOM cut-off policy results for GT1-GT15.   Modular Case Multiple Streams              GT 1 Year Qccil Qchl  Qm  Qr gcil ghl  Profit  NPV   1 73000 500000 1818320 18961 1.9 0.5 17738312 60852647   2 73000 500000 1703197 17313 1.6 0.45 15579715 43114335   3 73000 500000 1606857 15678 1.35 0.4 13390269 28276512   4 73000 500000 1538810 13929 1.1 0.35 10956044 16131143   5 73000 500000 1472055 11664 0.95 0.3 7746641 6666901   6 7187 268446 782479 3316 0.75 0.25 374870 293720                      Total  372187 2768446 8921718 80863     65785849 60852647            GT 2 Year Qccil Qchl  Qm  Qr gcil ghl  Profit  NPV   1 73000 500000 1693033 18346 1.85 0.45 17149684 61314816   2 73000 500000 1684655 17634 1.6 0.45 16108670 44165132   3 73000 500000 1625934 16117 1.35 0.4 13996470 28823542   4 73000 500000 1581052 14288 1.15 0.35 11379597 16128331   5 73000 500000 1501653 11656 0.9 0.3 7655510 6298207                      Total  365000 2500000 8086327 78041     66289931 61314816            GT 3 Year Qccil Qchl  Qm  Qr gcil ghl  Profit  NPV   1 73000 500000 1715441 18368 1.9 0.5 17123770 63509245   2 73000 500000 1616755 17041 1.65 0.45 15401439 46385476   3 73000 500000 1484059 15344 1.4 0.4 13216305 31717439   4 73000 500000 1418586 13881 1.2 0.35 11202691 19729860   5 73000 500000 1341412 11988 1 0.3 8577112 10052555   6 22082 437610 1207639 7564 0.85 0.3 3823923 2996143                       Total 387082 2937611 8783894 84187     69345239 63509245           GT 4 Year Qccil Qchl  Qm  Qr gcil ghl  Profit  NPV   1 73000 500000 1711792 18771 1.95 0.5 17736119 64866558   2 73000 500000 1607207 17305 1.65 0.45 15822129 47130438   3 73000 500000 1500008 15674 1.4 0.4 13666961 32061744   4 73000 500000 1463298 14280 1.2 0.35 11679696 19665407   5 73000 500000 1389223 12230 1 0.3 8812579 9576047   6 28616 332275 989747 6065 0.8 0.3 2968524 2325916                       Total 393616 2832275 8661275 84325     70686008 64866558             84 GT 5 Year Qccil Qchl  Qm  Qr gcil ghl  Profit  NPV   1 73000 500000 1831721 18662 1.85 0.5 17255754 60034202   2 73000 500000 1712326 17119 1.6 0.45 15264050 42778448   3 73000 500000 1590947 15368 1.35 0.4 12968969 28241257   4 73000 500000 1504942 13634 1.15 0.35 10604881 16478020   5 73000 500000 1438372 11607 0.95 0.3 7750468 7317125   6 11985 284430 905386 4241 0.8 0.3 1200721 940796                      Total  376985 2784430 8983694 80632     65044843 60034202            GT 6 Year Qccil Qchl  Qm  Qr gcil ghl  Profit  NPV   1 73000 500000 1768906 19239 1.95 0.5 18284173 66216130   2 73000 500000 1626788 17507 1.7 0.45 16071255 47931957   3 73000 500000 1530596 15933 1.4 0.4 13973632 32626000   4 73000 500000 1423721 14126 1.2 0.35 11555010 19951504   5 73000 500000 1371243 12308 1 0.3 8975477 9969852   6 27608 340044 1023681 6380 0.8 0.3 3300087 2585705                      Total  392608 2840044 8744935 85492     72159634 66216130            GT 7 Year Qccil Qchl  Qm  Qr gcil ghl  Profit  NPV   1 73000 500000 1768906 19272 1.95 0.5 18333720 65375587   2 73000 500000 1640924 17592 1.7 0.45 16161135 47041867   3 73000 500000 1526479 15764 1.4 0.4 13731523 31650310   4 73000 500000 1456878 14118 1.2 0.35 11455950 19195413   5 73000 500000 1395070 12160 1 0.3 8691982 9299333   6 27062 320132 958151 5766 0.8 0.3 2741987 2148418                      Total  392062 2820132 8746409 84672     71116297 65375587           GT 8 Year Qccil Qchl  Qm  Qr gcil ghl  Profit  NPV   1 73000 500000 1768906 18707 1.9 0.5 17488888 60960625   2 73000 500000 1676907 17264 1.6 0.45 15575289 43471737   3 73000 500000 1610211 15736 1.35 0.4 13467876 28638128   4 73000 500000 1512606 13810 1.15 0.35 10846486 16422368   5 73000 500000 1446614 11598 0.95 0.3 7715757 7052765   6 7839 310211 871621 4080 0.8 0.25 899769 704993                      Total  372839 2810211 8886864 81195     65994066 60960625            GT 9 Year Qccil Qchl  Qm  Qr gcil ghl  Profit  NPV   1 73000 500000 1761376 18115 1.85 0.45 16624334 58617803   2 73000 500000 1583138 16177 1.55 0.4 14198514 41993469   3 73000 500000 1603630 15341 1.35 0.4 12895391 28471074   4 73000 500000 1513347 13651 1.15 0.35 10606791 16774574   5 73000 500000 1427052 11530 0.95 0.3 7664773 7612029   6 15107 302776 964002 4804 0.8 0.3 1667081 1306201                      Total  380107 2802776 8852546 79618     63656885 58617803            GT 10 Year Qccil Qchl  Qm  Qr gcil ghl  Profit  NPV   1 73000 500000 1694317 18805 1.95 0.5 17832854 64947783   2 73000 500000 1631560 17508 1.7 0.45 16060445 47114929   3 73000 500000 1533256 15763 1.4 0.4 13712244 31819267   4 73000 500000 1430640 13974 1.2 0.35 11310174 19381857   5 73000 500000 1397631 12236 1 0.3 8798760 9611704   6 23603 373017 1086124 6454 0.8 0.3 3028543 2372943  85                       Total 388603 2873017 8773528 84740     70743020 64947783            GT 11 Year Qccil Qchl  Qm  Qr gcil ghl  Profit  NPV   1 73000 500000 1713694 17674 1.8 0.45 16091029 58321150   2 73000 500000 1727675 16844 1.6 0.45 14812348 42230120   3 73000 500000 1582651 15064 1.35 0.4 12536413 28123122   4 73000 500000 1524972 13610 1.15 0.35 10515861 16752226   5 73000 500000 1472645 11726 0.95 0.3 7837561 7668230   6 16224 272423 911292 4472 0.8 0.3 1557382 1220249                      Total  381224 2772423 8932929 79390     63350594 58321150           GT 12 Year Qccil Qchl  Qm  Qr gcil ghl  Profit  NPV   1 73000 500000 1838533 19591 1.9 0.5 18625395 63498597   2 73000 500000 1669514 17667 1.6 0.45 16196818 44873202   3 73000 500000 1575189 15990 1.35 0.4 13940384 29447661   4 73000 500000 1559029 14436 1.15 0.35 11660687 16803322   5 72060 500000 1548761 12079 0.95 0.3 8180821 6730382                       Total 364060 2500000 8191025 79763     68604105 63498597            GT 13 Year Qccil Qchl  Qm  Qr gcil ghl  Profit  NPV   1 73000 500000 1778148 18896 1.9 0.5 17746307 62804701   2 73000 500000 1658342 17330 1.65 0.45 15723146 45058394   3 73000 500000 1573774 15744 1.4 0.4 13575744 30083969   4 73000 500000 1475914 13904 1.15 0.35 11085482 17770369   5 73000 500000 1414442 11863 0.95 0.3 8196836 8194313   6 14669 301410 950588 4891 0.8 0.3 1851573 1450756                       Total 379669 2801410 8851209 82627     68179088 62804701            GT 14 Year Qccil Qchl  Qm  Qr gcil ghl  Profit  NPV   1 73000 500000 1794540 19075 1.9 0.5 17971269 63338054   2 73000 500000 1706699 17667 1.65 0.45 16098216 45366785   3 73000 500000 1596276 15910 1.4 0.4 13765407 30035151   4 73000 500000 1504683 14047 1.15 0.35 11221971 17549522   5 73000 500000 1444205 11919 0.95 0.3 8201695 7855561   6 11490 272929 911969 4321 0.8 0.3 1414129 1108007                      Total  376490 2772929 8958373 82939     68672686 63338054            GT 15 Year Qccil Qchl  Qm  Qr gcil ghl  Profit  NPV   1 73000 500000 1683954 17651 1.85 0.45 16135286 58809129   2 73000 500000 1685769 16766 1.6 0.45 14807219 42673843   3 73000 500000 1563920 15073 1.35 0.4 12598969 28571730   4 73000 500000 1504309 13559 1.15 0.35 10493694 17144093   5 73000 500000 1382901 11423 0.95 0.3 7622804 8079246   6 19920 340457 1016734 5610 0.8 0.3 2307448 1807946                      Total  384920 2840457 8837587 80081     63965421 58809129      86  Table C2 Base case LOM cut-off policy results for GT1-GT15.  Base Case Single Stream         GT 1 Year Qchl Qm Qr ghl Profit NPV   1 500000 1640288 13225 0.45 10849417 54758653   2 500000 1535354 12682 0.4 10315553 43909236   3 500000 1535354 12682 0.4 10315553 34084900   4 500000 1407407 11976 0.35 9599073 24728389   5 500000 1407407 11976 0.35 9599073 16436349   6 500000 1242507 11005 0.3 8584343 8539169   7 141522 351684 3115 0.3 2429743 1813111                  Total 3141522 9120000 76659   61692753 54758653                 GT 2 Year Qchl Qm Qr ghl Profit NPV   1 500000 1684982 13406 0.45 11001587 54708668   2 500000 1559322 12761 0.4 10369927 43707080   3 500000 1559322 12761 0.4 10369927 33830960   4 500000 1442006 12121 0.35 9724882 24425131   5 500000 1442006 12121 0.35 9724882 16024412   6 500000 1284916 11199 0.3 8763209 8023727   7 88506 227446 1982 0.3 1551193 1157524                   Total 3088506 9200000 76351   61505606 54708668           GT 3 Year Qchl Qm Qr ghl Profit NPV   1 500000 1545455 12923 0.45 10649594 57123583   2 500000 1399390 12154 0.4 9886118 46473989   3 500000 1399390 12154 0.4 9886118 37058639   4 500000 1289326 11528 0.35 9243313 28091639   5 500000 1289326 11528 0.35 9243313 20106918   6 500000 1170918 10803 0.3 8471921 12502421   7 463822 1086195 10021 0.3 7858923 5864449                  Total  3463822 9180000 81111   65239300 57123583           GT 4 Year Qchl Qm Qr ghl Profit NPV   1 500000 1532095 13094 0.45 10940627 58230506   2 500000 1426101 12517 0.4 10358197 47289879   3 500000 1426101 12517 0.4 10358197 37424929   4 500000 1333824 11979 0.35 9798537 28029739   5 500000 1333824 11979 0.35 9798537 19565395   6 500000 1206117 11182 0.3 8946580 11504114   7 336593 811940 7528 0.3 6022705 4494235                  Total  3336593 9070000 80795   66223379 58230506         GT 5 Year Qchl Qm Qr ghl Profit NPV   1 500000 1500000 12288 0.4 9821092 53960510   2 500000 1500000 12288 0.4 9821092 44139418   3 500000 1500000 12288 0.4 9821092 34785997   4 500000 1375371 11615 0.35 9144762 25877977   5 500000 1375371 11615 0.35 9144762 17978387   6 500000 1222955 10737 0.3 8236088 10454969   7 325565 796303 6991 0.3 5362766 4001778                  Total  3325565 9270000 77823   61351654 53960510            87 GT 6 Year Qchl Qm Qr ghl Profit NPV   1 500000 1552542 13316 0.45 11218652 59614937   2 500000 1449367 12752 0.4 10648171 48396285   3 500000 1449367 12752 0.4 10648171 38255170   4 500000 1312321 11948 0.35 9808916 28596965   5 500000 1312321 11948 0.35 9808916 20123654   6 500000 1205263 11270 0.3 9079215 12053834   7 364575 878818 8217 0.3 6620115 4940032                  Total  3364575 9160000 82202   67832157 59614937           GT 7 Year Qchl Qm Qr ghl Profit NPV   1 500000 1549153 13195 0.45 11045689 58634829   2 500000 1441640 12607 0.4 10452209 47589140   3 500000 1441640 12607 0.4 10452209 37634655   4 500000 1328488 11948 0.35 9766218 28154193   5 500000 1328488 11948 0.35 9766218 19717767   6 500000 1212202 11222 0.3 8989560 11683075   7 345812 838388 7761 0.3 6217400 4639520                  Total  3345812 9140000 81287   66689503 58634829           GT 8 Year Qchl Qm Qr ghl Profit NPV   1 500000 1613475 13081 0.45 10705303 54758226   2 500000 1511628 12557 0.4 10192095 44052924   3 500000 1511628 12557 0.4 10192095 34346166   4 500000 1362275 11732 0.35 9354774 25101635   5 500000 1362275 11732 0.35 9354774 17020629   6 500000 1236413 10991 0.3 8580634 9324434   7 203130 502305 4465 0.3 3485968 2601283                  Total  3203130 9100000 77117   61865643 54758226           GT 9 Year Qchl Qm Qr ghl Profit NPV   1 500000 1530000 12311 0.4 9775622 52412378   2 500000 1530000 12311 0.4 9775622 42636757   3 500000 1530000 12311 0.4 9775622 33326641   4 500000 1374251 11487 0.35 8956361 24459864   5 500000 1374251 11487 0.35 8956361 16723023   6 500000 1237197 10704 0.3 8148538 9354602   7 244222 604300 5228 0.3 3980097 2970010                  Total  3244222 9180000 75839   59368222 52412378           GT 10 Year Qchl Qm Qr ghl Profit NPV   1 500000 1543771 13063 0.45 10863728 58035176   2 500000 1464856 12640 0.4 10440094 47171448   3 500000 1464856 12640 0.4 10440094 37228501   4 500000 1310000 11755 0.35 9527278 27759028   5 500000 1310000 11755 0.35 9527278 19529008   6 500000 1206579 11116 0.3 8846390 11690892   7 360498 869938 8015 0.3 6378204 4759514                  Total  3360498 9170000 80985   66023066 58035176           GT 11 Year Qchl Qm Qr ghl Profit NPV   1 500000 1495161 12068 0.4 9503764 52302068  88   2 500000 1495161 12068 0.4 9503764 42798303   3 500000 1495161 12068 0.4 9503764 33747099   4 500000 1400302 11569 0.35 9010000 25126904   5 500000 1400302 11569 0.35 9010000 17343728   6 500000 1276860 10874 0.3 8298540 9931178   7 276872 707052 6022 0.3 4595261 3429055                  Total  3276872 9270000 76237   59425095 52302068           GT 12 Year Qchl Qm Qr ghl Profit NPV   1 500000 1649819 13561 0.45 11326525 57091653   2 500000 1498361 12759 0.4 10528706 45765128   3 500000 1498361 12759 0.4 10528706 35737789   4 500000 1389058 12134 0.35 9884099 26187943   5 500000 1389058 12134 0.35 9884099 17649686   6 500000 1276536 11444 0.3 9151614 9518013   7 171874 438807 3934 0.3 3145853 2347484                  Total  3171874 9140000 78725   64449602 57091653         GT 13 Year Qchl Qm Qr ghl Profit NPV   1 500000 1586505 13097 0.45 10800236 56385943   2 500000 1483819 12558 0.4 10266709 45585707   3 500000 1483819 12558 0.4 10266709 35807889   4 500000 1344575 11773 0.35 9461851 26495681   5 500000 1344575 11773 0.35 9461851 18322178   6 500000 1225936 11058 0.3 8708429 10537890   7 285811 700772 6321 0.3 4977930 3714608                  Total  3285811 9170000 79137   63943716 56385943 GT 14 Year Qchl Qm Qr ghl Profit NPV   1 500000 1634276 13373 0.45 11087056 56930227   2 500000 1501623 12680 0.4 10401793 45843172   3 500000 1501623 12680 0.4 10401793 35936702   4 500000 1376488 11973 0.35 9677024 26501970   5 500000 1376488 11973 0.35 9677024 18142593   6 500000 1246631 11190 0.3 8850349 10181281   7 245811 612871 5501 0.3 4351024 3246801                  Total  3245811 9250000 79370   64446062 56930227           GT 15 Year Qchl Qm Qr ghl Profit NPV   1 500000 1464968 11982 0.4 9455355 52615118   2 500000 1464968 11982 0.4 9455355 43159762   3 500000 1464968 11982 0.4 9455355 34154662   4 500000 1381381 11536 0.35 9011162 25578376   5 500000 1381381 11536 0.35 9011162 17794196   6 500000 1210526 10562 0.3 8008037 10380690   7 343572 831806 7258 0.3 5502679 4106183                  Total  3343572 9200000 76838   59899106 52615118     89 APPENDIX D.  Sensitivity Analysis The sensitivity calculations were performed on the NPV of the project, by applying a range of variations of ±15% to the base case parameter values. Parameters tested were, • Gold price • HL capacity • CIL capacity • HL unit costs • CIL unit costs The results are listed in Table D1 and illustrated graphically in Figure D1 below.    Figure D1 Graphical representation of NPV sensitivity to key project parameters.  $40 $45 $50 $55 $60 $65 $70 $75 $80 $85 -15% -10% -5% Base NPV 5% 10% 15% NPV (Millions) Sensitivity Analysis on NPV Gold Price HL Capacity CIL Capacity CIL Unit Costs HL Unit Costs  90   Table D1 Results of sensitivity analysis on NPV for GT13, modular case. GT13 MULTI -15% -10% -5% Base NPV 5% 10% 15% GOLD PRICE $45,898,931 $51,350,655 $57,090,466 $62,804,701 $68,480,407 $74,616,652 $80,546,998 HL CAP $60,833,463 $61,937,889 $62,391,236 $62,804,701 $63,318,859 $64,003,483 $64,450,611 CIL CAP $62,235,970 $62,437,780 $62,678,428 $62,804,701 $62,983,556 $63,110,742 $63,284,628 CIL UNIT COST $63,651,265 $63,385,699 $63,053,017 $62,804,701 $62,547,919 $62,194,737 $61,952,173 HL UNIT COST $65,983,230 $64,981,022 $63,697,797 $62,804,701 $61,927,599 $60,930,204 $60,111,309        

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