cut-off grade optimization of open pit mines with …
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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.
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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).
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TABLE OF CONTENTS
ABSTRACT ...................................................................................................................... iiLAY SUMMARY ............................................................................................................... iiiPREFACE ....................................................................................................................... ivTABLE OF CONTENTS ................................................................................................... vLIST OF TABLES ............................................................................................................ viiLIST OF FIGURES ......................................................................................................... viiiLIST OF SYMBOLS ........................................................................................................ ixDEDICATION .................................................................................................................. xii1 INTRODUCTION ........................................................................................................ 1
1.1 THESIS ORGANIZATION ............................................................................................... 31.2 IMPORTANCE TO INDUSTRY ....................................................................................... 41.3 RESEARCH OBJECTIVES ............................................................................................. 5
2 LIERATURE REVIEW ................................................................................................ 62.1 LANE’S METHOD ........................................................................................................... 62.2 EXTENSIONS/MODIFICATIONS TO LANE’S METHOD ................................................ 8
2.2.1 INCORPORATING REHABILITATION COSTS ....................................................... 82.2.2 OPTIMIZATION FACTOR ON OPPORTUNITY COSTS .......................................... 82.2.3 NON-LINEAR PROGRAMMING ............................................................................... 92.2.4 VARIABLE CAPACITIES .......................................................................................... 92.2.5 STOCHASTIC PRICES .......................................................................................... 122.2.6 MULTIPLE MILLS ................................................................................................... 12
3 METHODS ................................................................................................................ 143.1 BREAK-EVEN METHOD ............................................................................................... 143.2 LANE’S METHOD ......................................................................................................... 17
3.2.1 EXPLOITATION STRATEGY ................................................................................. 173.2.2 LIMITING ECONOMIC CUT-OFF GRADES .......................................................... 203.2.3 BALANCING CUT-OFF GRADES .......................................................................... 233.2.4 EFFECTIVE OPTIMUM CUT-OFF ......................................................................... 243.2.5 CUT-OFF POLICY .................................................................................................. 283.2.6 SHORTCOMINGS OF LANE’S METHOD .............................................................. 30
3.3 GRADE TONNAGE CURVES ....................................................................................... 304 PROCESSING .......................................................................................................... 33
4.1 MODULAR PROCESSING ............................................................................................ 334.1.1 CAPITAL AND OPERATING COSTS ..................................................................... 35
4.2 MULTIPLE STREAMS ................................................................................................... 374.2.1 CUT-OFF GRADE FOR MULTIPLE PROCESSING STREAMS ............................ 40
5 THE MODEL ............................................................................................................. 445.1 ECONOMIC AND OPERATIONAL INPUTS ................................................................. 45
5.1.1 GRADE TONNAGE SIMULATION ......................................................................... 45
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5.2 INITIAL ESTIMATES OF NPV ....................................................................................... 475.3 LIMITING CUT-OFF GRADE ........................................................................................ 485.4 QUANTITY OF ORE, WASTE AND AVERAGE GRADE .............................................. 485.5 QUANTITY MINED, PROCESSED AND REFINED ...................................................... 495.6 ANNUAL CASH FLOW AND NPV ................................................................................. 51
6 HYPOTHETICAL CASE STUDY .............................................................................. 536.1 MODEL ASSUMPTIONS AND LIMITATIONS .............................................................. 536.2 METHOD ....................................................................................................................... 56
6.2.1 BASE CASE ........................................................................................................... 576.2.2 MODULAR CASE ................................................................................................... 59
7 ECONOMIC ANALYSIS ........................................................................................... 637.1 SENSITIVITY ANALYSIS .............................................................................................. 63
8 CONCLUSIONS ....................................................................................................... 689 RECOMMENDATIONS ............................................................................................ 70REFERENCES ............................................................................................................... 72APPENDIX A. Derivation of Lane’s Equations .............................................................. 74APPENDIX B. Simulated Grade Tonnage Data ............................................................ 77APPENDIX C. Cut-off Policy Results ............................................................................ 83APPENDIX D. Sensitivity Analysis ................................................................................ 89
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LIST OF TABLES
Table 1 Estimated unit operating costs for the Gekko Python modular processing plant,
from (22). ................................................................................................................ 36Table 2 Mine design parameters for hypothetical gold mine. ......................................... 55Table 3 The complete cut-off policy for base case using grade tonnage curve 1 (GT1).
................................................................................................................................ 58Table 4 Calculated NPVs for both the base and modular scenarios across the set of 15
equally probable simulated grade tonnage curves. ................................................ 58Table 5 Complete cut-off policy for modular case using GT1. ....................................... 60Table 6 Base case cut-off policy when HL has capacity of 573,000 t/yr, for GT1. ......... 60Table 7 Complete break-even cut-off policy for modular case using GT1. .................... 61Table 8 Comparison of annual gold production across set of simulated grade tonnage
curves. .................................................................................................................... 64Table 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. ......................................... 66Table 10. Cut-off policy for base case, GT13. ................................................................ 66Table 11. Cut-off policy for GT13 when HL capacity is increased by +15% of base case
values. ..................................................................................................................... 66
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LIST OF FIGURES
Figure 3.1 Graphical representation of the break-even relationship between costs and
revenue similar to (5). ............................................................................................. 16Figure 3.2 Graphical representation of balancing cut-off when the mine and the mill are
limiting. .................................................................................................................... 24Figure 3.3 Increment in present value versus cut-off grade with the mine and mill
components in balance. .......................................................................................... 26Figure 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. ..................... 27Figure 3.5 Simulated tonnage histogram of gold deposit. .............................................. 31Figure 3.6 Sample grade tonnage curve with cut-off grade of 4.0 g/t. ........................... 32Figure 4.1 Process flow diagram for the Gecko Python Plant, from (22). ...................... 34Figure 4.2 Cut-off and cutover grade defined by revenue earned per ton of material
processed. .............................................................................................................. 41Figure 6.1 Flow sheet diagram for hypothetical gold mine with capacity constraints
(modular case). ....................................................................................................... 54Figure 6.2 Grade tonnage distribution GT1 for hypothetical gold mine. ......................... 56
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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.
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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
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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
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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.
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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 =Pt
1+ d( )tt
T
∑
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.
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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 = R
y * 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
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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.
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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.
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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 = Costs
Commodity 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
$/to
n
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 − tq
δV − 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 = c
S − 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 =c
S − 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
Prop
ortio
n of
Min
eral
ized
M
ater
ial
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
Incr
emen
t in
Pres
ent V
alue
(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
Incr
emen
t in
Pres
ent V
alue
(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 − dV
dT⎛⎝⎜
⎞⎠⎟
[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 = Tn
n=0∑
The weighted average grade of those tons is then determined by
g =Tngn
n=0∑
Tnn=0∑
0
200
400
600
800
1000
1200 To
nnag
e ('0
00s)
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.
Gra
de A
bove
Cut
-off
(g/t)
Tons
Abo
ve C
ut-o
ff (M
illio
ns)
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).
Estimatedcostperton,USDSummary P200 P500Labor $2.80 $1.20Management $1.60 $0.60Consumables $3.30 $3.30Reagents $0.60 $0.60LoaderHire $2.00 $0.80Dieses/mains $1.50 $1.50power
Water $0.30 $0.30Assaying $0.20 $0.20Equipmenthire $0.10 $0.10Other $0.10 $0.10
Total $12.50 $8.70*Thistableassumesthreeoperatorspershiftandapowercostof$US0.1.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
Rev
enue
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 convergence
NO 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+σ
2
2⎛
⎝⎜
⎞
⎠⎟
and the variance is
variance = e
σ 2( ) −1⎛⎝
⎞⎠ e
2µ+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 − dV
dT⎛⎝⎜
⎞⎠⎟
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( )Cp
S − 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! .
TO
gp( ) = Tnn≥n*∑ [19]
TW
gp( ) = Tnn<n*∑ [20]
49
ggp( ) =
≥ n *Tn
g 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 TO
gp( ) . Conversely, TW
gp( ) 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, g
gp( ) 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 =TO
gp( ) − Δ if <Cp + Δ
Cp otherwise
⎧⎨⎪
⎩⎪
⎫⎬⎪
⎭⎪ [22]
50
Here, Δ represents the difference between the ratios
TO
gp( ) /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( )TO
gp( )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( )− lom
δ
⎡
⎣
⎢⎢
⎤
⎦
⎥⎥ [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 To
ns (0
00'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 B
ase
HL
Uni
t Cos
ts
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 B
ase
HL
Uni
t C
osts
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.
Bas
e H
L C
apac
ity
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 B
ase
HL
Cap
acity
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 dV
dT+ t 2
2d 2VdT 2 + ...and [XXIX]
V Q − q( ) =V Q( )− q dV
dQ− q2
2d 2VdQ2 + ...and [XXX]
Combining equations [II] and [III],
V T + t,Q − q( ) = V T,Q( ) + t dV
dT− q dV
dQ⎡
⎣⎢
⎤
⎦⎥ * 1+δ t( ) [XXXI]
Multiplying equation [IV] by −rt t dV
dT⎛⎝⎜
⎞⎠⎟≈ 0 and because −rt is very small, it means −rt 2
and −rtq are extremely small, so they can be ignored and equation [IV] becomes:
V T,Q( )− rtV + t dV
dT− q dV
dQ [XXXII]
Substituting equation [V] into equation [I],
76
V T,Q( ) = Pq +V T,Q( )− rtV + t dV
dT− q dV
dQ [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 dV
dT− q dV
dQ= 0 [XXXIV]
Next, equation [VII] is solved for the variables of interest,
q dVdQ
= Pq − t δV + dVdT
⎛⎝⎜
⎞⎠⎟
dVdQ
= P − tq
δV + dVdT
⎛⎝⎜
⎞⎠⎟
and if,
F = rV + dV
dT⎛⎝⎜
⎞⎠⎟
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
(Mill
ions
)
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